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Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
1
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
2
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance AnalysisOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
bull Through the use of genome-scale metabolic network reconstructions Flux Balance Analysis (FBA) can be used to calculate the flow of metabolites through a metabolic network This capability makes it possible to predict the growth rate of an organism andor the rate of production of a given metabolite
bull FBA has limitations It does not use kinetic parameters thus it cannot predict metabolite concentrations It is also only capable of determining fluxes at steady state Typically FBA does not account for regulatory effects such as activation of enzymes by protein kinases or regulation of gene expression Therefore its predictions may not always be accurate
4
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
5
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
6
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Identifying Metabolic Reactions and Metabolites
(Gene-Protein-Reactions)
Objective
Create A biochemically genetically and genomically (BiGG) structured knowledge base
Reconstruction and Use of Microbial Metabolic Networks the Core Escherichia coli Metabolic Model as an Educational Guide by Orth Fleming and Palsson (2010)
7
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Desired Reaction Information1 Reaction Name2 Reaction Description3 Reaction Formula4 Gene-reaction Association5 Genes (Gene Locus) 6 Proteins
7 Cellular Subsystem (eg Glycolysis)
8 Reaction Direction9 Flux Lower Bound10 Flux Upper Bound11 Confidence Score (1-5)12 EC Number13 Notes14 References
Reconstruction and Use of Microbial Metabolic Networks the Core Escherichia coli Metabolic Model as an Educational Guide by Orth Fleming and Palsson (2010) Required
8
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Reconstruction Reactions9
ecoli_textbookxls
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Desired Metabolite Information
1 Metabolite Name2 Metabolite Description3 Metabolite Neutral Formula4 Metabolite Charged Formula5 Metabolite Charge6 Metabolite Compartment 7 Metabolite KEGGID 8 Metabolite PubChemID9 Metabolite CheBI ID10Metabolite Inchi String11 Metabolite Smile
RequiredThiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
10
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Reconstruction Metabolites11
ecoli_textbookxls
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Becker S A et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
Reactions(mmolgDWhr)
Metabolites(mmol)
hexokinase
glucose-6-phosphate isomerase
Phosphofructokinasefructose-bisphosphatase
fructose-bisphosphate aldolase
triose-phosphate isomerase
D-Glucose
D-Glucose 6-phosphate
D-Fructose 6-phosphate
D-Fructose 16-bisphosphate
Dihydroxyacetone phosphate Glyceraldehyde 3-phosphate
Exchange Reaction (mmolgDWhr)
MetabolicPathway
12
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
System BoundariesExchange amp Transport Reactions
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
Cytoplasm [c]
Periplasm [p]
Extracellular [e] Exchange Reactions
Transport Reactions
13
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstructions
bull Overview
bull Draft Reconstruction
bull Refinement of Reconstruction
bull Conversion of Reconstruction into Computable Format
bull Network Evaluation
bull Data Assembly and Dissemination
Draft Reconstruction
Network Evaluation
Conversion of Reconstruction
Refinement of Reconstruction
Data Assemblyand
Dissemination
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
14
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reconstruction Process 96 Step ProtocolThiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
15
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EcoliCore Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
Glycolysis
Glycoxylate Cycle Gluconeogenesis and
Anapleurotic Reactions
Tricarbonoxylic Acid Cycle (TCA)
Oxidative Phosphorylation and Transfer of Reducing
Equivalents
Ana TCA
OxP
PPP
Glyc
Ferm
NNitrogen
Metabolism
Fermentation
Pentose Phosphate Pathway
16
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
17
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Creating A Stoichiometric Matrix
Becker S A A M Feist et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
The stoichiometric matrix S is the centerpiece of a mathematical representation of genome-scale metabolic networks This matrix represents each reaction as a column and each metabolite as a row where each numerical element is the corresponding stoichiometric coefficient
18
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstruction
Reed J L I Famili et al (2006) Towards multidimensional genome annotation Nature reviews Genetics 7(2) 130-141
BIGGDatabase
Stoichiometric Matrix
MetabolicPathway
Gene-Protein-Reaction(GPR) Associations
19
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
20
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
How can we use the Stoichiometric Matrixbull The stoichiometric matrix S is a linear transformation of the flux
vector v to a vector of time derivatives of the concentration vector x Reactions
Met
abol
ites
ddt
= sdotx S v
bull The concentration vector x represents the concentration of each of the metabolites
bull If we assume that a cell will be in a particular phenotype for a time much larger than the changing time of metabolites then we can also assume that the concentration pools for the metabolites will be non-changing thus setting dxdt = 0 This is the steady state assumption of flux balance analysis
0ddt
= = sdotx S v
bull Since there are normally many more reactions (columns) than metabolites (rows) more unknown variables than equations then there is no unique solutions (could be a large number of solutions)
bull Need to find a way to constrain the solution space
21
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Dynamic Mass BalanceA simple network
A B
C
e1 e2
e3
v1
v4
v3v2
Linear Differential Equations
Linear Transformation
1 2 3 1
1 4 2
2 3 4 3
dA v v v edtdB v v edtdA v v v edt
= minus minus + +
= + minus
= minus minus minus
ddt
= sdotx S v
1
2
3
4
1
2
3
1 1 1 0 1 0 01 0 0 1 0 1 00 1 1 1 0 0 1
vdA vdt vdB vdt
edCedte
minus minus = minus minus minus minus
0 = sdotS v
Dynamic Mass Balance (Steady State) 1
2
3
4
1
2
3
0 1 1 1 0 1 0 00 1 0 0 1 0 1 00 0 1 1 1 0 0 1
vvvveee
minus minus = minus minus minus minus
Stoichiometric Matrix
Note More unknown variables than equationsthus no unique solutions Need constraints
22
ν1 ν2 ν3 ν4 e1 e2 e3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Conceptual Basis of Constraint-based Modeling
With no constraints the flux distribution of a biological network may lie at any point in a solution space When mass balance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (label 2) are applied to a network it defines an allowable solution space The network may acquire any flux distribution within this space but points outside this space are denied by the constraints Through optimization of an objective function using linear programming FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
23
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
2
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance AnalysisOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
bull Through the use of genome-scale metabolic network reconstructions Flux Balance Analysis (FBA) can be used to calculate the flow of metabolites through a metabolic network This capability makes it possible to predict the growth rate of an organism andor the rate of production of a given metabolite
bull FBA has limitations It does not use kinetic parameters thus it cannot predict metabolite concentrations It is also only capable of determining fluxes at steady state Typically FBA does not account for regulatory effects such as activation of enzymes by protein kinases or regulation of gene expression Therefore its predictions may not always be accurate
4
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
5
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
6
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Identifying Metabolic Reactions and Metabolites
(Gene-Protein-Reactions)
Objective
Create A biochemically genetically and genomically (BiGG) structured knowledge base
Reconstruction and Use of Microbial Metabolic Networks the Core Escherichia coli Metabolic Model as an Educational Guide by Orth Fleming and Palsson (2010)
7
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Desired Reaction Information1 Reaction Name2 Reaction Description3 Reaction Formula4 Gene-reaction Association5 Genes (Gene Locus) 6 Proteins
7 Cellular Subsystem (eg Glycolysis)
8 Reaction Direction9 Flux Lower Bound10 Flux Upper Bound11 Confidence Score (1-5)12 EC Number13 Notes14 References
Reconstruction and Use of Microbial Metabolic Networks the Core Escherichia coli Metabolic Model as an Educational Guide by Orth Fleming and Palsson (2010) Required
8
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Reconstruction Reactions9
ecoli_textbookxls
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Desired Metabolite Information
1 Metabolite Name2 Metabolite Description3 Metabolite Neutral Formula4 Metabolite Charged Formula5 Metabolite Charge6 Metabolite Compartment 7 Metabolite KEGGID 8 Metabolite PubChemID9 Metabolite CheBI ID10Metabolite Inchi String11 Metabolite Smile
RequiredThiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
10
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Reconstruction Metabolites11
ecoli_textbookxls
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Becker S A et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
Reactions(mmolgDWhr)
Metabolites(mmol)
hexokinase
glucose-6-phosphate isomerase
Phosphofructokinasefructose-bisphosphatase
fructose-bisphosphate aldolase
triose-phosphate isomerase
D-Glucose
D-Glucose 6-phosphate
D-Fructose 6-phosphate
D-Fructose 16-bisphosphate
Dihydroxyacetone phosphate Glyceraldehyde 3-phosphate
Exchange Reaction (mmolgDWhr)
MetabolicPathway
12
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
System BoundariesExchange amp Transport Reactions
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
Cytoplasm [c]
Periplasm [p]
Extracellular [e] Exchange Reactions
Transport Reactions
13
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstructions
bull Overview
bull Draft Reconstruction
bull Refinement of Reconstruction
bull Conversion of Reconstruction into Computable Format
bull Network Evaluation
bull Data Assembly and Dissemination
Draft Reconstruction
Network Evaluation
Conversion of Reconstruction
Refinement of Reconstruction
Data Assemblyand
Dissemination
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
14
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reconstruction Process 96 Step ProtocolThiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
15
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EcoliCore Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
Glycolysis
Glycoxylate Cycle Gluconeogenesis and
Anapleurotic Reactions
Tricarbonoxylic Acid Cycle (TCA)
Oxidative Phosphorylation and Transfer of Reducing
Equivalents
Ana TCA
OxP
PPP
Glyc
Ferm
NNitrogen
Metabolism
Fermentation
Pentose Phosphate Pathway
16
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
17
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Creating A Stoichiometric Matrix
Becker S A A M Feist et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
The stoichiometric matrix S is the centerpiece of a mathematical representation of genome-scale metabolic networks This matrix represents each reaction as a column and each metabolite as a row where each numerical element is the corresponding stoichiometric coefficient
18
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstruction
Reed J L I Famili et al (2006) Towards multidimensional genome annotation Nature reviews Genetics 7(2) 130-141
BIGGDatabase
Stoichiometric Matrix
MetabolicPathway
Gene-Protein-Reaction(GPR) Associations
19
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
20
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
How can we use the Stoichiometric Matrixbull The stoichiometric matrix S is a linear transformation of the flux
vector v to a vector of time derivatives of the concentration vector x Reactions
Met
abol
ites
ddt
= sdotx S v
bull The concentration vector x represents the concentration of each of the metabolites
bull If we assume that a cell will be in a particular phenotype for a time much larger than the changing time of metabolites then we can also assume that the concentration pools for the metabolites will be non-changing thus setting dxdt = 0 This is the steady state assumption of flux balance analysis
0ddt
= = sdotx S v
bull Since there are normally many more reactions (columns) than metabolites (rows) more unknown variables than equations then there is no unique solutions (could be a large number of solutions)
bull Need to find a way to constrain the solution space
21
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Dynamic Mass BalanceA simple network
A B
C
e1 e2
e3
v1
v4
v3v2
Linear Differential Equations
Linear Transformation
1 2 3 1
1 4 2
2 3 4 3
dA v v v edtdB v v edtdA v v v edt
= minus minus + +
= + minus
= minus minus minus
ddt
= sdotx S v
1
2
3
4
1
2
3
1 1 1 0 1 0 01 0 0 1 0 1 00 1 1 1 0 0 1
vdA vdt vdB vdt
edCedte
minus minus = minus minus minus minus
0 = sdotS v
Dynamic Mass Balance (Steady State) 1
2
3
4
1
2
3
0 1 1 1 0 1 0 00 1 0 0 1 0 1 00 0 1 1 1 0 0 1
vvvveee
minus minus = minus minus minus minus
Stoichiometric Matrix
Note More unknown variables than equationsthus no unique solutions Need constraints
22
ν1 ν2 ν3 ν4 e1 e2 e3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Conceptual Basis of Constraint-based Modeling
With no constraints the flux distribution of a biological network may lie at any point in a solution space When mass balance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (label 2) are applied to a network it defines an allowable solution space The network may acquire any flux distribution within this space but points outside this space are denied by the constraints Through optimization of an objective function using linear programming FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
23
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance AnalysisOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
bull Through the use of genome-scale metabolic network reconstructions Flux Balance Analysis (FBA) can be used to calculate the flow of metabolites through a metabolic network This capability makes it possible to predict the growth rate of an organism andor the rate of production of a given metabolite
bull FBA has limitations It does not use kinetic parameters thus it cannot predict metabolite concentrations It is also only capable of determining fluxes at steady state Typically FBA does not account for regulatory effects such as activation of enzymes by protein kinases or regulation of gene expression Therefore its predictions may not always be accurate
4
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
5
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
6
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Identifying Metabolic Reactions and Metabolites
(Gene-Protein-Reactions)
Objective
Create A biochemically genetically and genomically (BiGG) structured knowledge base
Reconstruction and Use of Microbial Metabolic Networks the Core Escherichia coli Metabolic Model as an Educational Guide by Orth Fleming and Palsson (2010)
7
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Desired Reaction Information1 Reaction Name2 Reaction Description3 Reaction Formula4 Gene-reaction Association5 Genes (Gene Locus) 6 Proteins
7 Cellular Subsystem (eg Glycolysis)
8 Reaction Direction9 Flux Lower Bound10 Flux Upper Bound11 Confidence Score (1-5)12 EC Number13 Notes14 References
Reconstruction and Use of Microbial Metabolic Networks the Core Escherichia coli Metabolic Model as an Educational Guide by Orth Fleming and Palsson (2010) Required
8
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Reconstruction Reactions9
ecoli_textbookxls
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Desired Metabolite Information
1 Metabolite Name2 Metabolite Description3 Metabolite Neutral Formula4 Metabolite Charged Formula5 Metabolite Charge6 Metabolite Compartment 7 Metabolite KEGGID 8 Metabolite PubChemID9 Metabolite CheBI ID10Metabolite Inchi String11 Metabolite Smile
RequiredThiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
10
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Reconstruction Metabolites11
ecoli_textbookxls
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Becker S A et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
Reactions(mmolgDWhr)
Metabolites(mmol)
hexokinase
glucose-6-phosphate isomerase
Phosphofructokinasefructose-bisphosphatase
fructose-bisphosphate aldolase
triose-phosphate isomerase
D-Glucose
D-Glucose 6-phosphate
D-Fructose 6-phosphate
D-Fructose 16-bisphosphate
Dihydroxyacetone phosphate Glyceraldehyde 3-phosphate
Exchange Reaction (mmolgDWhr)
MetabolicPathway
12
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
System BoundariesExchange amp Transport Reactions
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
Cytoplasm [c]
Periplasm [p]
Extracellular [e] Exchange Reactions
Transport Reactions
13
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstructions
bull Overview
bull Draft Reconstruction
bull Refinement of Reconstruction
bull Conversion of Reconstruction into Computable Format
bull Network Evaluation
bull Data Assembly and Dissemination
Draft Reconstruction
Network Evaluation
Conversion of Reconstruction
Refinement of Reconstruction
Data Assemblyand
Dissemination
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
14
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reconstruction Process 96 Step ProtocolThiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
15
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EcoliCore Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
Glycolysis
Glycoxylate Cycle Gluconeogenesis and
Anapleurotic Reactions
Tricarbonoxylic Acid Cycle (TCA)
Oxidative Phosphorylation and Transfer of Reducing
Equivalents
Ana TCA
OxP
PPP
Glyc
Ferm
NNitrogen
Metabolism
Fermentation
Pentose Phosphate Pathway
16
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
17
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Creating A Stoichiometric Matrix
Becker S A A M Feist et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
The stoichiometric matrix S is the centerpiece of a mathematical representation of genome-scale metabolic networks This matrix represents each reaction as a column and each metabolite as a row where each numerical element is the corresponding stoichiometric coefficient
18
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstruction
Reed J L I Famili et al (2006) Towards multidimensional genome annotation Nature reviews Genetics 7(2) 130-141
BIGGDatabase
Stoichiometric Matrix
MetabolicPathway
Gene-Protein-Reaction(GPR) Associations
19
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
20
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
How can we use the Stoichiometric Matrixbull The stoichiometric matrix S is a linear transformation of the flux
vector v to a vector of time derivatives of the concentration vector x Reactions
Met
abol
ites
ddt
= sdotx S v
bull The concentration vector x represents the concentration of each of the metabolites
bull If we assume that a cell will be in a particular phenotype for a time much larger than the changing time of metabolites then we can also assume that the concentration pools for the metabolites will be non-changing thus setting dxdt = 0 This is the steady state assumption of flux balance analysis
0ddt
= = sdotx S v
bull Since there are normally many more reactions (columns) than metabolites (rows) more unknown variables than equations then there is no unique solutions (could be a large number of solutions)
bull Need to find a way to constrain the solution space
21
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Dynamic Mass BalanceA simple network
A B
C
e1 e2
e3
v1
v4
v3v2
Linear Differential Equations
Linear Transformation
1 2 3 1
1 4 2
2 3 4 3
dA v v v edtdB v v edtdA v v v edt
= minus minus + +
= + minus
= minus minus minus
ddt
= sdotx S v
1
2
3
4
1
2
3
1 1 1 0 1 0 01 0 0 1 0 1 00 1 1 1 0 0 1
vdA vdt vdB vdt
edCedte
minus minus = minus minus minus minus
0 = sdotS v
Dynamic Mass Balance (Steady State) 1
2
3
4
1
2
3
0 1 1 1 0 1 0 00 1 0 0 1 0 1 00 0 1 1 1 0 0 1
vvvveee
minus minus = minus minus minus minus
Stoichiometric Matrix
Note More unknown variables than equationsthus no unique solutions Need constraints
22
ν1 ν2 ν3 ν4 e1 e2 e3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Conceptual Basis of Constraint-based Modeling
With no constraints the flux distribution of a biological network may lie at any point in a solution space When mass balance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (label 2) are applied to a network it defines an allowable solution space The network may acquire any flux distribution within this space but points outside this space are denied by the constraints Through optimization of an objective function using linear programming FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
23
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance AnalysisOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
bull Through the use of genome-scale metabolic network reconstructions Flux Balance Analysis (FBA) can be used to calculate the flow of metabolites through a metabolic network This capability makes it possible to predict the growth rate of an organism andor the rate of production of a given metabolite
bull FBA has limitations It does not use kinetic parameters thus it cannot predict metabolite concentrations It is also only capable of determining fluxes at steady state Typically FBA does not account for regulatory effects such as activation of enzymes by protein kinases or regulation of gene expression Therefore its predictions may not always be accurate
4
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
5
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
6
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Identifying Metabolic Reactions and Metabolites
(Gene-Protein-Reactions)
Objective
Create A biochemically genetically and genomically (BiGG) structured knowledge base
Reconstruction and Use of Microbial Metabolic Networks the Core Escherichia coli Metabolic Model as an Educational Guide by Orth Fleming and Palsson (2010)
7
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Desired Reaction Information1 Reaction Name2 Reaction Description3 Reaction Formula4 Gene-reaction Association5 Genes (Gene Locus) 6 Proteins
7 Cellular Subsystem (eg Glycolysis)
8 Reaction Direction9 Flux Lower Bound10 Flux Upper Bound11 Confidence Score (1-5)12 EC Number13 Notes14 References
Reconstruction and Use of Microbial Metabolic Networks the Core Escherichia coli Metabolic Model as an Educational Guide by Orth Fleming and Palsson (2010) Required
8
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Reconstruction Reactions9
ecoli_textbookxls
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Desired Metabolite Information
1 Metabolite Name2 Metabolite Description3 Metabolite Neutral Formula4 Metabolite Charged Formula5 Metabolite Charge6 Metabolite Compartment 7 Metabolite KEGGID 8 Metabolite PubChemID9 Metabolite CheBI ID10Metabolite Inchi String11 Metabolite Smile
RequiredThiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
10
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Reconstruction Metabolites11
ecoli_textbookxls
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Becker S A et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
Reactions(mmolgDWhr)
Metabolites(mmol)
hexokinase
glucose-6-phosphate isomerase
Phosphofructokinasefructose-bisphosphatase
fructose-bisphosphate aldolase
triose-phosphate isomerase
D-Glucose
D-Glucose 6-phosphate
D-Fructose 6-phosphate
D-Fructose 16-bisphosphate
Dihydroxyacetone phosphate Glyceraldehyde 3-phosphate
Exchange Reaction (mmolgDWhr)
MetabolicPathway
12
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
System BoundariesExchange amp Transport Reactions
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
Cytoplasm [c]
Periplasm [p]
Extracellular [e] Exchange Reactions
Transport Reactions
13
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstructions
bull Overview
bull Draft Reconstruction
bull Refinement of Reconstruction
bull Conversion of Reconstruction into Computable Format
bull Network Evaluation
bull Data Assembly and Dissemination
Draft Reconstruction
Network Evaluation
Conversion of Reconstruction
Refinement of Reconstruction
Data Assemblyand
Dissemination
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
14
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reconstruction Process 96 Step ProtocolThiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
15
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EcoliCore Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
Glycolysis
Glycoxylate Cycle Gluconeogenesis and
Anapleurotic Reactions
Tricarbonoxylic Acid Cycle (TCA)
Oxidative Phosphorylation and Transfer of Reducing
Equivalents
Ana TCA
OxP
PPP
Glyc
Ferm
NNitrogen
Metabolism
Fermentation
Pentose Phosphate Pathway
16
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
17
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Creating A Stoichiometric Matrix
Becker S A A M Feist et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
The stoichiometric matrix S is the centerpiece of a mathematical representation of genome-scale metabolic networks This matrix represents each reaction as a column and each metabolite as a row where each numerical element is the corresponding stoichiometric coefficient
18
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstruction
Reed J L I Famili et al (2006) Towards multidimensional genome annotation Nature reviews Genetics 7(2) 130-141
BIGGDatabase
Stoichiometric Matrix
MetabolicPathway
Gene-Protein-Reaction(GPR) Associations
19
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
20
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
How can we use the Stoichiometric Matrixbull The stoichiometric matrix S is a linear transformation of the flux
vector v to a vector of time derivatives of the concentration vector x Reactions
Met
abol
ites
ddt
= sdotx S v
bull The concentration vector x represents the concentration of each of the metabolites
bull If we assume that a cell will be in a particular phenotype for a time much larger than the changing time of metabolites then we can also assume that the concentration pools for the metabolites will be non-changing thus setting dxdt = 0 This is the steady state assumption of flux balance analysis
0ddt
= = sdotx S v
bull Since there are normally many more reactions (columns) than metabolites (rows) more unknown variables than equations then there is no unique solutions (could be a large number of solutions)
bull Need to find a way to constrain the solution space
21
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Dynamic Mass BalanceA simple network
A B
C
e1 e2
e3
v1
v4
v3v2
Linear Differential Equations
Linear Transformation
1 2 3 1
1 4 2
2 3 4 3
dA v v v edtdB v v edtdA v v v edt
= minus minus + +
= + minus
= minus minus minus
ddt
= sdotx S v
1
2
3
4
1
2
3
1 1 1 0 1 0 01 0 0 1 0 1 00 1 1 1 0 0 1
vdA vdt vdB vdt
edCedte
minus minus = minus minus minus minus
0 = sdotS v
Dynamic Mass Balance (Steady State) 1
2
3
4
1
2
3
0 1 1 1 0 1 0 00 1 0 0 1 0 1 00 0 1 1 1 0 0 1
vvvveee
minus minus = minus minus minus minus
Stoichiometric Matrix
Note More unknown variables than equationsthus no unique solutions Need constraints
22
ν1 ν2 ν3 ν4 e1 e2 e3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Conceptual Basis of Constraint-based Modeling
With no constraints the flux distribution of a biological network may lie at any point in a solution space When mass balance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (label 2) are applied to a network it defines an allowable solution space The network may acquire any flux distribution within this space but points outside this space are denied by the constraints Through optimization of an objective function using linear programming FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
23
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
5
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
6
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Identifying Metabolic Reactions and Metabolites
(Gene-Protein-Reactions)
Objective
Create A biochemically genetically and genomically (BiGG) structured knowledge base
Reconstruction and Use of Microbial Metabolic Networks the Core Escherichia coli Metabolic Model as an Educational Guide by Orth Fleming and Palsson (2010)
7
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Desired Reaction Information1 Reaction Name2 Reaction Description3 Reaction Formula4 Gene-reaction Association5 Genes (Gene Locus) 6 Proteins
7 Cellular Subsystem (eg Glycolysis)
8 Reaction Direction9 Flux Lower Bound10 Flux Upper Bound11 Confidence Score (1-5)12 EC Number13 Notes14 References
Reconstruction and Use of Microbial Metabolic Networks the Core Escherichia coli Metabolic Model as an Educational Guide by Orth Fleming and Palsson (2010) Required
8
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Reconstruction Reactions9
ecoli_textbookxls
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Desired Metabolite Information
1 Metabolite Name2 Metabolite Description3 Metabolite Neutral Formula4 Metabolite Charged Formula5 Metabolite Charge6 Metabolite Compartment 7 Metabolite KEGGID 8 Metabolite PubChemID9 Metabolite CheBI ID10Metabolite Inchi String11 Metabolite Smile
RequiredThiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
10
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Reconstruction Metabolites11
ecoli_textbookxls
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Becker S A et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
Reactions(mmolgDWhr)
Metabolites(mmol)
hexokinase
glucose-6-phosphate isomerase
Phosphofructokinasefructose-bisphosphatase
fructose-bisphosphate aldolase
triose-phosphate isomerase
D-Glucose
D-Glucose 6-phosphate
D-Fructose 6-phosphate
D-Fructose 16-bisphosphate
Dihydroxyacetone phosphate Glyceraldehyde 3-phosphate
Exchange Reaction (mmolgDWhr)
MetabolicPathway
12
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
System BoundariesExchange amp Transport Reactions
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
Cytoplasm [c]
Periplasm [p]
Extracellular [e] Exchange Reactions
Transport Reactions
13
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstructions
bull Overview
bull Draft Reconstruction
bull Refinement of Reconstruction
bull Conversion of Reconstruction into Computable Format
bull Network Evaluation
bull Data Assembly and Dissemination
Draft Reconstruction
Network Evaluation
Conversion of Reconstruction
Refinement of Reconstruction
Data Assemblyand
Dissemination
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
14
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reconstruction Process 96 Step ProtocolThiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
15
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EcoliCore Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
Glycolysis
Glycoxylate Cycle Gluconeogenesis and
Anapleurotic Reactions
Tricarbonoxylic Acid Cycle (TCA)
Oxidative Phosphorylation and Transfer of Reducing
Equivalents
Ana TCA
OxP
PPP
Glyc
Ferm
NNitrogen
Metabolism
Fermentation
Pentose Phosphate Pathway
16
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
17
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Creating A Stoichiometric Matrix
Becker S A A M Feist et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
The stoichiometric matrix S is the centerpiece of a mathematical representation of genome-scale metabolic networks This matrix represents each reaction as a column and each metabolite as a row where each numerical element is the corresponding stoichiometric coefficient
18
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstruction
Reed J L I Famili et al (2006) Towards multidimensional genome annotation Nature reviews Genetics 7(2) 130-141
BIGGDatabase
Stoichiometric Matrix
MetabolicPathway
Gene-Protein-Reaction(GPR) Associations
19
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
20
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
How can we use the Stoichiometric Matrixbull The stoichiometric matrix S is a linear transformation of the flux
vector v to a vector of time derivatives of the concentration vector x Reactions
Met
abol
ites
ddt
= sdotx S v
bull The concentration vector x represents the concentration of each of the metabolites
bull If we assume that a cell will be in a particular phenotype for a time much larger than the changing time of metabolites then we can also assume that the concentration pools for the metabolites will be non-changing thus setting dxdt = 0 This is the steady state assumption of flux balance analysis
0ddt
= = sdotx S v
bull Since there are normally many more reactions (columns) than metabolites (rows) more unknown variables than equations then there is no unique solutions (could be a large number of solutions)
bull Need to find a way to constrain the solution space
21
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Dynamic Mass BalanceA simple network
A B
C
e1 e2
e3
v1
v4
v3v2
Linear Differential Equations
Linear Transformation
1 2 3 1
1 4 2
2 3 4 3
dA v v v edtdB v v edtdA v v v edt
= minus minus + +
= + minus
= minus minus minus
ddt
= sdotx S v
1
2
3
4
1
2
3
1 1 1 0 1 0 01 0 0 1 0 1 00 1 1 1 0 0 1
vdA vdt vdB vdt
edCedte
minus minus = minus minus minus minus
0 = sdotS v
Dynamic Mass Balance (Steady State) 1
2
3
4
1
2
3
0 1 1 1 0 1 0 00 1 0 0 1 0 1 00 0 1 1 1 0 0 1
vvvveee
minus minus = minus minus minus minus
Stoichiometric Matrix
Note More unknown variables than equationsthus no unique solutions Need constraints
22
ν1 ν2 ν3 ν4 e1 e2 e3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Conceptual Basis of Constraint-based Modeling
With no constraints the flux distribution of a biological network may lie at any point in a solution space When mass balance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (label 2) are applied to a network it defines an allowable solution space The network may acquire any flux distribution within this space but points outside this space are denied by the constraints Through optimization of an objective function using linear programming FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
23
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
6
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Identifying Metabolic Reactions and Metabolites
(Gene-Protein-Reactions)
Objective
Create A biochemically genetically and genomically (BiGG) structured knowledge base
Reconstruction and Use of Microbial Metabolic Networks the Core Escherichia coli Metabolic Model as an Educational Guide by Orth Fleming and Palsson (2010)
7
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Desired Reaction Information1 Reaction Name2 Reaction Description3 Reaction Formula4 Gene-reaction Association5 Genes (Gene Locus) 6 Proteins
7 Cellular Subsystem (eg Glycolysis)
8 Reaction Direction9 Flux Lower Bound10 Flux Upper Bound11 Confidence Score (1-5)12 EC Number13 Notes14 References
Reconstruction and Use of Microbial Metabolic Networks the Core Escherichia coli Metabolic Model as an Educational Guide by Orth Fleming and Palsson (2010) Required
8
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Reconstruction Reactions9
ecoli_textbookxls
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Desired Metabolite Information
1 Metabolite Name2 Metabolite Description3 Metabolite Neutral Formula4 Metabolite Charged Formula5 Metabolite Charge6 Metabolite Compartment 7 Metabolite KEGGID 8 Metabolite PubChemID9 Metabolite CheBI ID10Metabolite Inchi String11 Metabolite Smile
RequiredThiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
10
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Reconstruction Metabolites11
ecoli_textbookxls
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Becker S A et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
Reactions(mmolgDWhr)
Metabolites(mmol)
hexokinase
glucose-6-phosphate isomerase
Phosphofructokinasefructose-bisphosphatase
fructose-bisphosphate aldolase
triose-phosphate isomerase
D-Glucose
D-Glucose 6-phosphate
D-Fructose 6-phosphate
D-Fructose 16-bisphosphate
Dihydroxyacetone phosphate Glyceraldehyde 3-phosphate
Exchange Reaction (mmolgDWhr)
MetabolicPathway
12
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
System BoundariesExchange amp Transport Reactions
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
Cytoplasm [c]
Periplasm [p]
Extracellular [e] Exchange Reactions
Transport Reactions
13
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstructions
bull Overview
bull Draft Reconstruction
bull Refinement of Reconstruction
bull Conversion of Reconstruction into Computable Format
bull Network Evaluation
bull Data Assembly and Dissemination
Draft Reconstruction
Network Evaluation
Conversion of Reconstruction
Refinement of Reconstruction
Data Assemblyand
Dissemination
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
14
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reconstruction Process 96 Step ProtocolThiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
15
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EcoliCore Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
Glycolysis
Glycoxylate Cycle Gluconeogenesis and
Anapleurotic Reactions
Tricarbonoxylic Acid Cycle (TCA)
Oxidative Phosphorylation and Transfer of Reducing
Equivalents
Ana TCA
OxP
PPP
Glyc
Ferm
NNitrogen
Metabolism
Fermentation
Pentose Phosphate Pathway
16
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
17
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Creating A Stoichiometric Matrix
Becker S A A M Feist et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
The stoichiometric matrix S is the centerpiece of a mathematical representation of genome-scale metabolic networks This matrix represents each reaction as a column and each metabolite as a row where each numerical element is the corresponding stoichiometric coefficient
18
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstruction
Reed J L I Famili et al (2006) Towards multidimensional genome annotation Nature reviews Genetics 7(2) 130-141
BIGGDatabase
Stoichiometric Matrix
MetabolicPathway
Gene-Protein-Reaction(GPR) Associations
19
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
20
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
How can we use the Stoichiometric Matrixbull The stoichiometric matrix S is a linear transformation of the flux
vector v to a vector of time derivatives of the concentration vector x Reactions
Met
abol
ites
ddt
= sdotx S v
bull The concentration vector x represents the concentration of each of the metabolites
bull If we assume that a cell will be in a particular phenotype for a time much larger than the changing time of metabolites then we can also assume that the concentration pools for the metabolites will be non-changing thus setting dxdt = 0 This is the steady state assumption of flux balance analysis
0ddt
= = sdotx S v
bull Since there are normally many more reactions (columns) than metabolites (rows) more unknown variables than equations then there is no unique solutions (could be a large number of solutions)
bull Need to find a way to constrain the solution space
21
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Dynamic Mass BalanceA simple network
A B
C
e1 e2
e3
v1
v4
v3v2
Linear Differential Equations
Linear Transformation
1 2 3 1
1 4 2
2 3 4 3
dA v v v edtdB v v edtdA v v v edt
= minus minus + +
= + minus
= minus minus minus
ddt
= sdotx S v
1
2
3
4
1
2
3
1 1 1 0 1 0 01 0 0 1 0 1 00 1 1 1 0 0 1
vdA vdt vdB vdt
edCedte
minus minus = minus minus minus minus
0 = sdotS v
Dynamic Mass Balance (Steady State) 1
2
3
4
1
2
3
0 1 1 1 0 1 0 00 1 0 0 1 0 1 00 0 1 1 1 0 0 1
vvvveee
minus minus = minus minus minus minus
Stoichiometric Matrix
Note More unknown variables than equationsthus no unique solutions Need constraints
22
ν1 ν2 ν3 ν4 e1 e2 e3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Conceptual Basis of Constraint-based Modeling
With no constraints the flux distribution of a biological network may lie at any point in a solution space When mass balance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (label 2) are applied to a network it defines an allowable solution space The network may acquire any flux distribution within this space but points outside this space are denied by the constraints Through optimization of an objective function using linear programming FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
23
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Identifying Metabolic Reactions and Metabolites
(Gene-Protein-Reactions)
Objective
Create A biochemically genetically and genomically (BiGG) structured knowledge base
Reconstruction and Use of Microbial Metabolic Networks the Core Escherichia coli Metabolic Model as an Educational Guide by Orth Fleming and Palsson (2010)
7
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Desired Reaction Information1 Reaction Name2 Reaction Description3 Reaction Formula4 Gene-reaction Association5 Genes (Gene Locus) 6 Proteins
7 Cellular Subsystem (eg Glycolysis)
8 Reaction Direction9 Flux Lower Bound10 Flux Upper Bound11 Confidence Score (1-5)12 EC Number13 Notes14 References
Reconstruction and Use of Microbial Metabolic Networks the Core Escherichia coli Metabolic Model as an Educational Guide by Orth Fleming and Palsson (2010) Required
8
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Reconstruction Reactions9
ecoli_textbookxls
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Desired Metabolite Information
1 Metabolite Name2 Metabolite Description3 Metabolite Neutral Formula4 Metabolite Charged Formula5 Metabolite Charge6 Metabolite Compartment 7 Metabolite KEGGID 8 Metabolite PubChemID9 Metabolite CheBI ID10Metabolite Inchi String11 Metabolite Smile
RequiredThiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
10
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Reconstruction Metabolites11
ecoli_textbookxls
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Becker S A et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
Reactions(mmolgDWhr)
Metabolites(mmol)
hexokinase
glucose-6-phosphate isomerase
Phosphofructokinasefructose-bisphosphatase
fructose-bisphosphate aldolase
triose-phosphate isomerase
D-Glucose
D-Glucose 6-phosphate
D-Fructose 6-phosphate
D-Fructose 16-bisphosphate
Dihydroxyacetone phosphate Glyceraldehyde 3-phosphate
Exchange Reaction (mmolgDWhr)
MetabolicPathway
12
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
System BoundariesExchange amp Transport Reactions
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
Cytoplasm [c]
Periplasm [p]
Extracellular [e] Exchange Reactions
Transport Reactions
13
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstructions
bull Overview
bull Draft Reconstruction
bull Refinement of Reconstruction
bull Conversion of Reconstruction into Computable Format
bull Network Evaluation
bull Data Assembly and Dissemination
Draft Reconstruction
Network Evaluation
Conversion of Reconstruction
Refinement of Reconstruction
Data Assemblyand
Dissemination
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
14
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reconstruction Process 96 Step ProtocolThiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
15
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EcoliCore Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
Glycolysis
Glycoxylate Cycle Gluconeogenesis and
Anapleurotic Reactions
Tricarbonoxylic Acid Cycle (TCA)
Oxidative Phosphorylation and Transfer of Reducing
Equivalents
Ana TCA
OxP
PPP
Glyc
Ferm
NNitrogen
Metabolism
Fermentation
Pentose Phosphate Pathway
16
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
17
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Creating A Stoichiometric Matrix
Becker S A A M Feist et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
The stoichiometric matrix S is the centerpiece of a mathematical representation of genome-scale metabolic networks This matrix represents each reaction as a column and each metabolite as a row where each numerical element is the corresponding stoichiometric coefficient
18
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstruction
Reed J L I Famili et al (2006) Towards multidimensional genome annotation Nature reviews Genetics 7(2) 130-141
BIGGDatabase
Stoichiometric Matrix
MetabolicPathway
Gene-Protein-Reaction(GPR) Associations
19
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
20
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
How can we use the Stoichiometric Matrixbull The stoichiometric matrix S is a linear transformation of the flux
vector v to a vector of time derivatives of the concentration vector x Reactions
Met
abol
ites
ddt
= sdotx S v
bull The concentration vector x represents the concentration of each of the metabolites
bull If we assume that a cell will be in a particular phenotype for a time much larger than the changing time of metabolites then we can also assume that the concentration pools for the metabolites will be non-changing thus setting dxdt = 0 This is the steady state assumption of flux balance analysis
0ddt
= = sdotx S v
bull Since there are normally many more reactions (columns) than metabolites (rows) more unknown variables than equations then there is no unique solutions (could be a large number of solutions)
bull Need to find a way to constrain the solution space
21
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Dynamic Mass BalanceA simple network
A B
C
e1 e2
e3
v1
v4
v3v2
Linear Differential Equations
Linear Transformation
1 2 3 1
1 4 2
2 3 4 3
dA v v v edtdB v v edtdA v v v edt
= minus minus + +
= + minus
= minus minus minus
ddt
= sdotx S v
1
2
3
4
1
2
3
1 1 1 0 1 0 01 0 0 1 0 1 00 1 1 1 0 0 1
vdA vdt vdB vdt
edCedte
minus minus = minus minus minus minus
0 = sdotS v
Dynamic Mass Balance (Steady State) 1
2
3
4
1
2
3
0 1 1 1 0 1 0 00 1 0 0 1 0 1 00 0 1 1 1 0 0 1
vvvveee
minus minus = minus minus minus minus
Stoichiometric Matrix
Note More unknown variables than equationsthus no unique solutions Need constraints
22
ν1 ν2 ν3 ν4 e1 e2 e3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Conceptual Basis of Constraint-based Modeling
With no constraints the flux distribution of a biological network may lie at any point in a solution space When mass balance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (label 2) are applied to a network it defines an allowable solution space The network may acquire any flux distribution within this space but points outside this space are denied by the constraints Through optimization of an objective function using linear programming FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
23
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Desired Reaction Information1 Reaction Name2 Reaction Description3 Reaction Formula4 Gene-reaction Association5 Genes (Gene Locus) 6 Proteins
7 Cellular Subsystem (eg Glycolysis)
8 Reaction Direction9 Flux Lower Bound10 Flux Upper Bound11 Confidence Score (1-5)12 EC Number13 Notes14 References
Reconstruction and Use of Microbial Metabolic Networks the Core Escherichia coli Metabolic Model as an Educational Guide by Orth Fleming and Palsson (2010) Required
8
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Reconstruction Reactions9
ecoli_textbookxls
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Desired Metabolite Information
1 Metabolite Name2 Metabolite Description3 Metabolite Neutral Formula4 Metabolite Charged Formula5 Metabolite Charge6 Metabolite Compartment 7 Metabolite KEGGID 8 Metabolite PubChemID9 Metabolite CheBI ID10Metabolite Inchi String11 Metabolite Smile
RequiredThiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
10
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Reconstruction Metabolites11
ecoli_textbookxls
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Becker S A et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
Reactions(mmolgDWhr)
Metabolites(mmol)
hexokinase
glucose-6-phosphate isomerase
Phosphofructokinasefructose-bisphosphatase
fructose-bisphosphate aldolase
triose-phosphate isomerase
D-Glucose
D-Glucose 6-phosphate
D-Fructose 6-phosphate
D-Fructose 16-bisphosphate
Dihydroxyacetone phosphate Glyceraldehyde 3-phosphate
Exchange Reaction (mmolgDWhr)
MetabolicPathway
12
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
System BoundariesExchange amp Transport Reactions
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
Cytoplasm [c]
Periplasm [p]
Extracellular [e] Exchange Reactions
Transport Reactions
13
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstructions
bull Overview
bull Draft Reconstruction
bull Refinement of Reconstruction
bull Conversion of Reconstruction into Computable Format
bull Network Evaluation
bull Data Assembly and Dissemination
Draft Reconstruction
Network Evaluation
Conversion of Reconstruction
Refinement of Reconstruction
Data Assemblyand
Dissemination
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
14
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reconstruction Process 96 Step ProtocolThiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
15
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EcoliCore Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
Glycolysis
Glycoxylate Cycle Gluconeogenesis and
Anapleurotic Reactions
Tricarbonoxylic Acid Cycle (TCA)
Oxidative Phosphorylation and Transfer of Reducing
Equivalents
Ana TCA
OxP
PPP
Glyc
Ferm
NNitrogen
Metabolism
Fermentation
Pentose Phosphate Pathway
16
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
17
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Creating A Stoichiometric Matrix
Becker S A A M Feist et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
The stoichiometric matrix S is the centerpiece of a mathematical representation of genome-scale metabolic networks This matrix represents each reaction as a column and each metabolite as a row where each numerical element is the corresponding stoichiometric coefficient
18
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstruction
Reed J L I Famili et al (2006) Towards multidimensional genome annotation Nature reviews Genetics 7(2) 130-141
BIGGDatabase
Stoichiometric Matrix
MetabolicPathway
Gene-Protein-Reaction(GPR) Associations
19
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
20
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
How can we use the Stoichiometric Matrixbull The stoichiometric matrix S is a linear transformation of the flux
vector v to a vector of time derivatives of the concentration vector x Reactions
Met
abol
ites
ddt
= sdotx S v
bull The concentration vector x represents the concentration of each of the metabolites
bull If we assume that a cell will be in a particular phenotype for a time much larger than the changing time of metabolites then we can also assume that the concentration pools for the metabolites will be non-changing thus setting dxdt = 0 This is the steady state assumption of flux balance analysis
0ddt
= = sdotx S v
bull Since there are normally many more reactions (columns) than metabolites (rows) more unknown variables than equations then there is no unique solutions (could be a large number of solutions)
bull Need to find a way to constrain the solution space
21
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Dynamic Mass BalanceA simple network
A B
C
e1 e2
e3
v1
v4
v3v2
Linear Differential Equations
Linear Transformation
1 2 3 1
1 4 2
2 3 4 3
dA v v v edtdB v v edtdA v v v edt
= minus minus + +
= + minus
= minus minus minus
ddt
= sdotx S v
1
2
3
4
1
2
3
1 1 1 0 1 0 01 0 0 1 0 1 00 1 1 1 0 0 1
vdA vdt vdB vdt
edCedte
minus minus = minus minus minus minus
0 = sdotS v
Dynamic Mass Balance (Steady State) 1
2
3
4
1
2
3
0 1 1 1 0 1 0 00 1 0 0 1 0 1 00 0 1 1 1 0 0 1
vvvveee
minus minus = minus minus minus minus
Stoichiometric Matrix
Note More unknown variables than equationsthus no unique solutions Need constraints
22
ν1 ν2 ν3 ν4 e1 e2 e3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Conceptual Basis of Constraint-based Modeling
With no constraints the flux distribution of a biological network may lie at any point in a solution space When mass balance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (label 2) are applied to a network it defines an allowable solution space The network may acquire any flux distribution within this space but points outside this space are denied by the constraints Through optimization of an objective function using linear programming FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
23
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Reconstruction Reactions9
ecoli_textbookxls
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Desired Metabolite Information
1 Metabolite Name2 Metabolite Description3 Metabolite Neutral Formula4 Metabolite Charged Formula5 Metabolite Charge6 Metabolite Compartment 7 Metabolite KEGGID 8 Metabolite PubChemID9 Metabolite CheBI ID10Metabolite Inchi String11 Metabolite Smile
RequiredThiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
10
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Reconstruction Metabolites11
ecoli_textbookxls
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Becker S A et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
Reactions(mmolgDWhr)
Metabolites(mmol)
hexokinase
glucose-6-phosphate isomerase
Phosphofructokinasefructose-bisphosphatase
fructose-bisphosphate aldolase
triose-phosphate isomerase
D-Glucose
D-Glucose 6-phosphate
D-Fructose 6-phosphate
D-Fructose 16-bisphosphate
Dihydroxyacetone phosphate Glyceraldehyde 3-phosphate
Exchange Reaction (mmolgDWhr)
MetabolicPathway
12
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
System BoundariesExchange amp Transport Reactions
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
Cytoplasm [c]
Periplasm [p]
Extracellular [e] Exchange Reactions
Transport Reactions
13
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstructions
bull Overview
bull Draft Reconstruction
bull Refinement of Reconstruction
bull Conversion of Reconstruction into Computable Format
bull Network Evaluation
bull Data Assembly and Dissemination
Draft Reconstruction
Network Evaluation
Conversion of Reconstruction
Refinement of Reconstruction
Data Assemblyand
Dissemination
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
14
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reconstruction Process 96 Step ProtocolThiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
15
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EcoliCore Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
Glycolysis
Glycoxylate Cycle Gluconeogenesis and
Anapleurotic Reactions
Tricarbonoxylic Acid Cycle (TCA)
Oxidative Phosphorylation and Transfer of Reducing
Equivalents
Ana TCA
OxP
PPP
Glyc
Ferm
NNitrogen
Metabolism
Fermentation
Pentose Phosphate Pathway
16
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
17
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Creating A Stoichiometric Matrix
Becker S A A M Feist et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
The stoichiometric matrix S is the centerpiece of a mathematical representation of genome-scale metabolic networks This matrix represents each reaction as a column and each metabolite as a row where each numerical element is the corresponding stoichiometric coefficient
18
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstruction
Reed J L I Famili et al (2006) Towards multidimensional genome annotation Nature reviews Genetics 7(2) 130-141
BIGGDatabase
Stoichiometric Matrix
MetabolicPathway
Gene-Protein-Reaction(GPR) Associations
19
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
20
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
How can we use the Stoichiometric Matrixbull The stoichiometric matrix S is a linear transformation of the flux
vector v to a vector of time derivatives of the concentration vector x Reactions
Met
abol
ites
ddt
= sdotx S v
bull The concentration vector x represents the concentration of each of the metabolites
bull If we assume that a cell will be in a particular phenotype for a time much larger than the changing time of metabolites then we can also assume that the concentration pools for the metabolites will be non-changing thus setting dxdt = 0 This is the steady state assumption of flux balance analysis
0ddt
= = sdotx S v
bull Since there are normally many more reactions (columns) than metabolites (rows) more unknown variables than equations then there is no unique solutions (could be a large number of solutions)
bull Need to find a way to constrain the solution space
21
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Dynamic Mass BalanceA simple network
A B
C
e1 e2
e3
v1
v4
v3v2
Linear Differential Equations
Linear Transformation
1 2 3 1
1 4 2
2 3 4 3
dA v v v edtdB v v edtdA v v v edt
= minus minus + +
= + minus
= minus minus minus
ddt
= sdotx S v
1
2
3
4
1
2
3
1 1 1 0 1 0 01 0 0 1 0 1 00 1 1 1 0 0 1
vdA vdt vdB vdt
edCedte
minus minus = minus minus minus minus
0 = sdotS v
Dynamic Mass Balance (Steady State) 1
2
3
4
1
2
3
0 1 1 1 0 1 0 00 1 0 0 1 0 1 00 0 1 1 1 0 0 1
vvvveee
minus minus = minus minus minus minus
Stoichiometric Matrix
Note More unknown variables than equationsthus no unique solutions Need constraints
22
ν1 ν2 ν3 ν4 e1 e2 e3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Conceptual Basis of Constraint-based Modeling
With no constraints the flux distribution of a biological network may lie at any point in a solution space When mass balance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (label 2) are applied to a network it defines an allowable solution space The network may acquire any flux distribution within this space but points outside this space are denied by the constraints Through optimization of an objective function using linear programming FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
23
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Desired Metabolite Information
1 Metabolite Name2 Metabolite Description3 Metabolite Neutral Formula4 Metabolite Charged Formula5 Metabolite Charge6 Metabolite Compartment 7 Metabolite KEGGID 8 Metabolite PubChemID9 Metabolite CheBI ID10Metabolite Inchi String11 Metabolite Smile
RequiredThiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
10
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Reconstruction Metabolites11
ecoli_textbookxls
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Becker S A et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
Reactions(mmolgDWhr)
Metabolites(mmol)
hexokinase
glucose-6-phosphate isomerase
Phosphofructokinasefructose-bisphosphatase
fructose-bisphosphate aldolase
triose-phosphate isomerase
D-Glucose
D-Glucose 6-phosphate
D-Fructose 6-phosphate
D-Fructose 16-bisphosphate
Dihydroxyacetone phosphate Glyceraldehyde 3-phosphate
Exchange Reaction (mmolgDWhr)
MetabolicPathway
12
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
System BoundariesExchange amp Transport Reactions
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
Cytoplasm [c]
Periplasm [p]
Extracellular [e] Exchange Reactions
Transport Reactions
13
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstructions
bull Overview
bull Draft Reconstruction
bull Refinement of Reconstruction
bull Conversion of Reconstruction into Computable Format
bull Network Evaluation
bull Data Assembly and Dissemination
Draft Reconstruction
Network Evaluation
Conversion of Reconstruction
Refinement of Reconstruction
Data Assemblyand
Dissemination
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
14
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reconstruction Process 96 Step ProtocolThiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
15
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EcoliCore Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
Glycolysis
Glycoxylate Cycle Gluconeogenesis and
Anapleurotic Reactions
Tricarbonoxylic Acid Cycle (TCA)
Oxidative Phosphorylation and Transfer of Reducing
Equivalents
Ana TCA
OxP
PPP
Glyc
Ferm
NNitrogen
Metabolism
Fermentation
Pentose Phosphate Pathway
16
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
17
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Creating A Stoichiometric Matrix
Becker S A A M Feist et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
The stoichiometric matrix S is the centerpiece of a mathematical representation of genome-scale metabolic networks This matrix represents each reaction as a column and each metabolite as a row where each numerical element is the corresponding stoichiometric coefficient
18
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstruction
Reed J L I Famili et al (2006) Towards multidimensional genome annotation Nature reviews Genetics 7(2) 130-141
BIGGDatabase
Stoichiometric Matrix
MetabolicPathway
Gene-Protein-Reaction(GPR) Associations
19
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
20
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
How can we use the Stoichiometric Matrixbull The stoichiometric matrix S is a linear transformation of the flux
vector v to a vector of time derivatives of the concentration vector x Reactions
Met
abol
ites
ddt
= sdotx S v
bull The concentration vector x represents the concentration of each of the metabolites
bull If we assume that a cell will be in a particular phenotype for a time much larger than the changing time of metabolites then we can also assume that the concentration pools for the metabolites will be non-changing thus setting dxdt = 0 This is the steady state assumption of flux balance analysis
0ddt
= = sdotx S v
bull Since there are normally many more reactions (columns) than metabolites (rows) more unknown variables than equations then there is no unique solutions (could be a large number of solutions)
bull Need to find a way to constrain the solution space
21
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Dynamic Mass BalanceA simple network
A B
C
e1 e2
e3
v1
v4
v3v2
Linear Differential Equations
Linear Transformation
1 2 3 1
1 4 2
2 3 4 3
dA v v v edtdB v v edtdA v v v edt
= minus minus + +
= + minus
= minus minus minus
ddt
= sdotx S v
1
2
3
4
1
2
3
1 1 1 0 1 0 01 0 0 1 0 1 00 1 1 1 0 0 1
vdA vdt vdB vdt
edCedte
minus minus = minus minus minus minus
0 = sdotS v
Dynamic Mass Balance (Steady State) 1
2
3
4
1
2
3
0 1 1 1 0 1 0 00 1 0 0 1 0 1 00 0 1 1 1 0 0 1
vvvveee
minus minus = minus minus minus minus
Stoichiometric Matrix
Note More unknown variables than equationsthus no unique solutions Need constraints
22
ν1 ν2 ν3 ν4 e1 e2 e3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Conceptual Basis of Constraint-based Modeling
With no constraints the flux distribution of a biological network may lie at any point in a solution space When mass balance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (label 2) are applied to a network it defines an allowable solution space The network may acquire any flux distribution within this space but points outside this space are denied by the constraints Through optimization of an objective function using linear programming FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
23
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Reconstruction Metabolites11
ecoli_textbookxls
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Becker S A et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
Reactions(mmolgDWhr)
Metabolites(mmol)
hexokinase
glucose-6-phosphate isomerase
Phosphofructokinasefructose-bisphosphatase
fructose-bisphosphate aldolase
triose-phosphate isomerase
D-Glucose
D-Glucose 6-phosphate
D-Fructose 6-phosphate
D-Fructose 16-bisphosphate
Dihydroxyacetone phosphate Glyceraldehyde 3-phosphate
Exchange Reaction (mmolgDWhr)
MetabolicPathway
12
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
System BoundariesExchange amp Transport Reactions
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
Cytoplasm [c]
Periplasm [p]
Extracellular [e] Exchange Reactions
Transport Reactions
13
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstructions
bull Overview
bull Draft Reconstruction
bull Refinement of Reconstruction
bull Conversion of Reconstruction into Computable Format
bull Network Evaluation
bull Data Assembly and Dissemination
Draft Reconstruction
Network Evaluation
Conversion of Reconstruction
Refinement of Reconstruction
Data Assemblyand
Dissemination
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
14
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reconstruction Process 96 Step ProtocolThiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
15
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EcoliCore Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
Glycolysis
Glycoxylate Cycle Gluconeogenesis and
Anapleurotic Reactions
Tricarbonoxylic Acid Cycle (TCA)
Oxidative Phosphorylation and Transfer of Reducing
Equivalents
Ana TCA
OxP
PPP
Glyc
Ferm
NNitrogen
Metabolism
Fermentation
Pentose Phosphate Pathway
16
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
17
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Creating A Stoichiometric Matrix
Becker S A A M Feist et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
The stoichiometric matrix S is the centerpiece of a mathematical representation of genome-scale metabolic networks This matrix represents each reaction as a column and each metabolite as a row where each numerical element is the corresponding stoichiometric coefficient
18
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstruction
Reed J L I Famili et al (2006) Towards multidimensional genome annotation Nature reviews Genetics 7(2) 130-141
BIGGDatabase
Stoichiometric Matrix
MetabolicPathway
Gene-Protein-Reaction(GPR) Associations
19
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
20
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
How can we use the Stoichiometric Matrixbull The stoichiometric matrix S is a linear transformation of the flux
vector v to a vector of time derivatives of the concentration vector x Reactions
Met
abol
ites
ddt
= sdotx S v
bull The concentration vector x represents the concentration of each of the metabolites
bull If we assume that a cell will be in a particular phenotype for a time much larger than the changing time of metabolites then we can also assume that the concentration pools for the metabolites will be non-changing thus setting dxdt = 0 This is the steady state assumption of flux balance analysis
0ddt
= = sdotx S v
bull Since there are normally many more reactions (columns) than metabolites (rows) more unknown variables than equations then there is no unique solutions (could be a large number of solutions)
bull Need to find a way to constrain the solution space
21
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Dynamic Mass BalanceA simple network
A B
C
e1 e2
e3
v1
v4
v3v2
Linear Differential Equations
Linear Transformation
1 2 3 1
1 4 2
2 3 4 3
dA v v v edtdB v v edtdA v v v edt
= minus minus + +
= + minus
= minus minus minus
ddt
= sdotx S v
1
2
3
4
1
2
3
1 1 1 0 1 0 01 0 0 1 0 1 00 1 1 1 0 0 1
vdA vdt vdB vdt
edCedte
minus minus = minus minus minus minus
0 = sdotS v
Dynamic Mass Balance (Steady State) 1
2
3
4
1
2
3
0 1 1 1 0 1 0 00 1 0 0 1 0 1 00 0 1 1 1 0 0 1
vvvveee
minus minus = minus minus minus minus
Stoichiometric Matrix
Note More unknown variables than equationsthus no unique solutions Need constraints
22
ν1 ν2 ν3 ν4 e1 e2 e3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Conceptual Basis of Constraint-based Modeling
With no constraints the flux distribution of a biological network may lie at any point in a solution space When mass balance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (label 2) are applied to a network it defines an allowable solution space The network may acquire any flux distribution within this space but points outside this space are denied by the constraints Through optimization of an objective function using linear programming FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
23
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Becker S A et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
Reactions(mmolgDWhr)
Metabolites(mmol)
hexokinase
glucose-6-phosphate isomerase
Phosphofructokinasefructose-bisphosphatase
fructose-bisphosphate aldolase
triose-phosphate isomerase
D-Glucose
D-Glucose 6-phosphate
D-Fructose 6-phosphate
D-Fructose 16-bisphosphate
Dihydroxyacetone phosphate Glyceraldehyde 3-phosphate
Exchange Reaction (mmolgDWhr)
MetabolicPathway
12
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
System BoundariesExchange amp Transport Reactions
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
Cytoplasm [c]
Periplasm [p]
Extracellular [e] Exchange Reactions
Transport Reactions
13
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstructions
bull Overview
bull Draft Reconstruction
bull Refinement of Reconstruction
bull Conversion of Reconstruction into Computable Format
bull Network Evaluation
bull Data Assembly and Dissemination
Draft Reconstruction
Network Evaluation
Conversion of Reconstruction
Refinement of Reconstruction
Data Assemblyand
Dissemination
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
14
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reconstruction Process 96 Step ProtocolThiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
15
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EcoliCore Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
Glycolysis
Glycoxylate Cycle Gluconeogenesis and
Anapleurotic Reactions
Tricarbonoxylic Acid Cycle (TCA)
Oxidative Phosphorylation and Transfer of Reducing
Equivalents
Ana TCA
OxP
PPP
Glyc
Ferm
NNitrogen
Metabolism
Fermentation
Pentose Phosphate Pathway
16
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
17
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Creating A Stoichiometric Matrix
Becker S A A M Feist et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
The stoichiometric matrix S is the centerpiece of a mathematical representation of genome-scale metabolic networks This matrix represents each reaction as a column and each metabolite as a row where each numerical element is the corresponding stoichiometric coefficient
18
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstruction
Reed J L I Famili et al (2006) Towards multidimensional genome annotation Nature reviews Genetics 7(2) 130-141
BIGGDatabase
Stoichiometric Matrix
MetabolicPathway
Gene-Protein-Reaction(GPR) Associations
19
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
20
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
How can we use the Stoichiometric Matrixbull The stoichiometric matrix S is a linear transformation of the flux
vector v to a vector of time derivatives of the concentration vector x Reactions
Met
abol
ites
ddt
= sdotx S v
bull The concentration vector x represents the concentration of each of the metabolites
bull If we assume that a cell will be in a particular phenotype for a time much larger than the changing time of metabolites then we can also assume that the concentration pools for the metabolites will be non-changing thus setting dxdt = 0 This is the steady state assumption of flux balance analysis
0ddt
= = sdotx S v
bull Since there are normally many more reactions (columns) than metabolites (rows) more unknown variables than equations then there is no unique solutions (could be a large number of solutions)
bull Need to find a way to constrain the solution space
21
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Dynamic Mass BalanceA simple network
A B
C
e1 e2
e3
v1
v4
v3v2
Linear Differential Equations
Linear Transformation
1 2 3 1
1 4 2
2 3 4 3
dA v v v edtdB v v edtdA v v v edt
= minus minus + +
= + minus
= minus minus minus
ddt
= sdotx S v
1
2
3
4
1
2
3
1 1 1 0 1 0 01 0 0 1 0 1 00 1 1 1 0 0 1
vdA vdt vdB vdt
edCedte
minus minus = minus minus minus minus
0 = sdotS v
Dynamic Mass Balance (Steady State) 1
2
3
4
1
2
3
0 1 1 1 0 1 0 00 1 0 0 1 0 1 00 0 1 1 1 0 0 1
vvvveee
minus minus = minus minus minus minus
Stoichiometric Matrix
Note More unknown variables than equationsthus no unique solutions Need constraints
22
ν1 ν2 ν3 ν4 e1 e2 e3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Conceptual Basis of Constraint-based Modeling
With no constraints the flux distribution of a biological network may lie at any point in a solution space When mass balance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (label 2) are applied to a network it defines an allowable solution space The network may acquire any flux distribution within this space but points outside this space are denied by the constraints Through optimization of an objective function using linear programming FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
23
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
System BoundariesExchange amp Transport Reactions
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
Cytoplasm [c]
Periplasm [p]
Extracellular [e] Exchange Reactions
Transport Reactions
13
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstructions
bull Overview
bull Draft Reconstruction
bull Refinement of Reconstruction
bull Conversion of Reconstruction into Computable Format
bull Network Evaluation
bull Data Assembly and Dissemination
Draft Reconstruction
Network Evaluation
Conversion of Reconstruction
Refinement of Reconstruction
Data Assemblyand
Dissemination
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
14
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reconstruction Process 96 Step ProtocolThiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
15
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EcoliCore Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
Glycolysis
Glycoxylate Cycle Gluconeogenesis and
Anapleurotic Reactions
Tricarbonoxylic Acid Cycle (TCA)
Oxidative Phosphorylation and Transfer of Reducing
Equivalents
Ana TCA
OxP
PPP
Glyc
Ferm
NNitrogen
Metabolism
Fermentation
Pentose Phosphate Pathway
16
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
17
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Creating A Stoichiometric Matrix
Becker S A A M Feist et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
The stoichiometric matrix S is the centerpiece of a mathematical representation of genome-scale metabolic networks This matrix represents each reaction as a column and each metabolite as a row where each numerical element is the corresponding stoichiometric coefficient
18
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstruction
Reed J L I Famili et al (2006) Towards multidimensional genome annotation Nature reviews Genetics 7(2) 130-141
BIGGDatabase
Stoichiometric Matrix
MetabolicPathway
Gene-Protein-Reaction(GPR) Associations
19
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
20
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
How can we use the Stoichiometric Matrixbull The stoichiometric matrix S is a linear transformation of the flux
vector v to a vector of time derivatives of the concentration vector x Reactions
Met
abol
ites
ddt
= sdotx S v
bull The concentration vector x represents the concentration of each of the metabolites
bull If we assume that a cell will be in a particular phenotype for a time much larger than the changing time of metabolites then we can also assume that the concentration pools for the metabolites will be non-changing thus setting dxdt = 0 This is the steady state assumption of flux balance analysis
0ddt
= = sdotx S v
bull Since there are normally many more reactions (columns) than metabolites (rows) more unknown variables than equations then there is no unique solutions (could be a large number of solutions)
bull Need to find a way to constrain the solution space
21
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Dynamic Mass BalanceA simple network
A B
C
e1 e2
e3
v1
v4
v3v2
Linear Differential Equations
Linear Transformation
1 2 3 1
1 4 2
2 3 4 3
dA v v v edtdB v v edtdA v v v edt
= minus minus + +
= + minus
= minus minus minus
ddt
= sdotx S v
1
2
3
4
1
2
3
1 1 1 0 1 0 01 0 0 1 0 1 00 1 1 1 0 0 1
vdA vdt vdB vdt
edCedte
minus minus = minus minus minus minus
0 = sdotS v
Dynamic Mass Balance (Steady State) 1
2
3
4
1
2
3
0 1 1 1 0 1 0 00 1 0 0 1 0 1 00 0 1 1 1 0 0 1
vvvveee
minus minus = minus minus minus minus
Stoichiometric Matrix
Note More unknown variables than equationsthus no unique solutions Need constraints
22
ν1 ν2 ν3 ν4 e1 e2 e3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Conceptual Basis of Constraint-based Modeling
With no constraints the flux distribution of a biological network may lie at any point in a solution space When mass balance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (label 2) are applied to a network it defines an allowable solution space The network may acquire any flux distribution within this space but points outside this space are denied by the constraints Through optimization of an objective function using linear programming FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
23
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstructions
bull Overview
bull Draft Reconstruction
bull Refinement of Reconstruction
bull Conversion of Reconstruction into Computable Format
bull Network Evaluation
bull Data Assembly and Dissemination
Draft Reconstruction
Network Evaluation
Conversion of Reconstruction
Refinement of Reconstruction
Data Assemblyand
Dissemination
Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
14
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reconstruction Process 96 Step ProtocolThiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
15
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EcoliCore Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
Glycolysis
Glycoxylate Cycle Gluconeogenesis and
Anapleurotic Reactions
Tricarbonoxylic Acid Cycle (TCA)
Oxidative Phosphorylation and Transfer of Reducing
Equivalents
Ana TCA
OxP
PPP
Glyc
Ferm
NNitrogen
Metabolism
Fermentation
Pentose Phosphate Pathway
16
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
17
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Creating A Stoichiometric Matrix
Becker S A A M Feist et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
The stoichiometric matrix S is the centerpiece of a mathematical representation of genome-scale metabolic networks This matrix represents each reaction as a column and each metabolite as a row where each numerical element is the corresponding stoichiometric coefficient
18
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstruction
Reed J L I Famili et al (2006) Towards multidimensional genome annotation Nature reviews Genetics 7(2) 130-141
BIGGDatabase
Stoichiometric Matrix
MetabolicPathway
Gene-Protein-Reaction(GPR) Associations
19
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
20
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
How can we use the Stoichiometric Matrixbull The stoichiometric matrix S is a linear transformation of the flux
vector v to a vector of time derivatives of the concentration vector x Reactions
Met
abol
ites
ddt
= sdotx S v
bull The concentration vector x represents the concentration of each of the metabolites
bull If we assume that a cell will be in a particular phenotype for a time much larger than the changing time of metabolites then we can also assume that the concentration pools for the metabolites will be non-changing thus setting dxdt = 0 This is the steady state assumption of flux balance analysis
0ddt
= = sdotx S v
bull Since there are normally many more reactions (columns) than metabolites (rows) more unknown variables than equations then there is no unique solutions (could be a large number of solutions)
bull Need to find a way to constrain the solution space
21
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Dynamic Mass BalanceA simple network
A B
C
e1 e2
e3
v1
v4
v3v2
Linear Differential Equations
Linear Transformation
1 2 3 1
1 4 2
2 3 4 3
dA v v v edtdB v v edtdA v v v edt
= minus minus + +
= + minus
= minus minus minus
ddt
= sdotx S v
1
2
3
4
1
2
3
1 1 1 0 1 0 01 0 0 1 0 1 00 1 1 1 0 0 1
vdA vdt vdB vdt
edCedte
minus minus = minus minus minus minus
0 = sdotS v
Dynamic Mass Balance (Steady State) 1
2
3
4
1
2
3
0 1 1 1 0 1 0 00 1 0 0 1 0 1 00 0 1 1 1 0 0 1
vvvveee
minus minus = minus minus minus minus
Stoichiometric Matrix
Note More unknown variables than equationsthus no unique solutions Need constraints
22
ν1 ν2 ν3 ν4 e1 e2 e3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Conceptual Basis of Constraint-based Modeling
With no constraints the flux distribution of a biological network may lie at any point in a solution space When mass balance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (label 2) are applied to a network it defines an allowable solution space The network may acquire any flux distribution within this space but points outside this space are denied by the constraints Through optimization of an objective function using linear programming FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
23
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reconstruction Process 96 Step ProtocolThiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
15
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EcoliCore Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
Glycolysis
Glycoxylate Cycle Gluconeogenesis and
Anapleurotic Reactions
Tricarbonoxylic Acid Cycle (TCA)
Oxidative Phosphorylation and Transfer of Reducing
Equivalents
Ana TCA
OxP
PPP
Glyc
Ferm
NNitrogen
Metabolism
Fermentation
Pentose Phosphate Pathway
16
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
17
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Creating A Stoichiometric Matrix
Becker S A A M Feist et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
The stoichiometric matrix S is the centerpiece of a mathematical representation of genome-scale metabolic networks This matrix represents each reaction as a column and each metabolite as a row where each numerical element is the corresponding stoichiometric coefficient
18
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstruction
Reed J L I Famili et al (2006) Towards multidimensional genome annotation Nature reviews Genetics 7(2) 130-141
BIGGDatabase
Stoichiometric Matrix
MetabolicPathway
Gene-Protein-Reaction(GPR) Associations
19
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
20
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
How can we use the Stoichiometric Matrixbull The stoichiometric matrix S is a linear transformation of the flux
vector v to a vector of time derivatives of the concentration vector x Reactions
Met
abol
ites
ddt
= sdotx S v
bull The concentration vector x represents the concentration of each of the metabolites
bull If we assume that a cell will be in a particular phenotype for a time much larger than the changing time of metabolites then we can also assume that the concentration pools for the metabolites will be non-changing thus setting dxdt = 0 This is the steady state assumption of flux balance analysis
0ddt
= = sdotx S v
bull Since there are normally many more reactions (columns) than metabolites (rows) more unknown variables than equations then there is no unique solutions (could be a large number of solutions)
bull Need to find a way to constrain the solution space
21
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Dynamic Mass BalanceA simple network
A B
C
e1 e2
e3
v1
v4
v3v2
Linear Differential Equations
Linear Transformation
1 2 3 1
1 4 2
2 3 4 3
dA v v v edtdB v v edtdA v v v edt
= minus minus + +
= + minus
= minus minus minus
ddt
= sdotx S v
1
2
3
4
1
2
3
1 1 1 0 1 0 01 0 0 1 0 1 00 1 1 1 0 0 1
vdA vdt vdB vdt
edCedte
minus minus = minus minus minus minus
0 = sdotS v
Dynamic Mass Balance (Steady State) 1
2
3
4
1
2
3
0 1 1 1 0 1 0 00 1 0 0 1 0 1 00 0 1 1 1 0 0 1
vvvveee
minus minus = minus minus minus minus
Stoichiometric Matrix
Note More unknown variables than equationsthus no unique solutions Need constraints
22
ν1 ν2 ν3 ν4 e1 e2 e3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Conceptual Basis of Constraint-based Modeling
With no constraints the flux distribution of a biological network may lie at any point in a solution space When mass balance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (label 2) are applied to a network it defines an allowable solution space The network may acquire any flux distribution within this space but points outside this space are denied by the constraints Through optimization of an objective function using linear programming FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
23
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EcoliCore Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
Glycolysis
Glycoxylate Cycle Gluconeogenesis and
Anapleurotic Reactions
Tricarbonoxylic Acid Cycle (TCA)
Oxidative Phosphorylation and Transfer of Reducing
Equivalents
Ana TCA
OxP
PPP
Glyc
Ferm
NNitrogen
Metabolism
Fermentation
Pentose Phosphate Pathway
16
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
17
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Creating A Stoichiometric Matrix
Becker S A A M Feist et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
The stoichiometric matrix S is the centerpiece of a mathematical representation of genome-scale metabolic networks This matrix represents each reaction as a column and each metabolite as a row where each numerical element is the corresponding stoichiometric coefficient
18
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstruction
Reed J L I Famili et al (2006) Towards multidimensional genome annotation Nature reviews Genetics 7(2) 130-141
BIGGDatabase
Stoichiometric Matrix
MetabolicPathway
Gene-Protein-Reaction(GPR) Associations
19
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
20
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
How can we use the Stoichiometric Matrixbull The stoichiometric matrix S is a linear transformation of the flux
vector v to a vector of time derivatives of the concentration vector x Reactions
Met
abol
ites
ddt
= sdotx S v
bull The concentration vector x represents the concentration of each of the metabolites
bull If we assume that a cell will be in a particular phenotype for a time much larger than the changing time of metabolites then we can also assume that the concentration pools for the metabolites will be non-changing thus setting dxdt = 0 This is the steady state assumption of flux balance analysis
0ddt
= = sdotx S v
bull Since there are normally many more reactions (columns) than metabolites (rows) more unknown variables than equations then there is no unique solutions (could be a large number of solutions)
bull Need to find a way to constrain the solution space
21
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Dynamic Mass BalanceA simple network
A B
C
e1 e2
e3
v1
v4
v3v2
Linear Differential Equations
Linear Transformation
1 2 3 1
1 4 2
2 3 4 3
dA v v v edtdB v v edtdA v v v edt
= minus minus + +
= + minus
= minus minus minus
ddt
= sdotx S v
1
2
3
4
1
2
3
1 1 1 0 1 0 01 0 0 1 0 1 00 1 1 1 0 0 1
vdA vdt vdB vdt
edCedte
minus minus = minus minus minus minus
0 = sdotS v
Dynamic Mass Balance (Steady State) 1
2
3
4
1
2
3
0 1 1 1 0 1 0 00 1 0 0 1 0 1 00 0 1 1 1 0 0 1
vvvveee
minus minus = minus minus minus minus
Stoichiometric Matrix
Note More unknown variables than equationsthus no unique solutions Need constraints
22
ν1 ν2 ν3 ν4 e1 e2 e3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Conceptual Basis of Constraint-based Modeling
With no constraints the flux distribution of a biological network may lie at any point in a solution space When mass balance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (label 2) are applied to a network it defines an allowable solution space The network may acquire any flux distribution within this space but points outside this space are denied by the constraints Through optimization of an objective function using linear programming FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
23
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
17
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Creating A Stoichiometric Matrix
Becker S A A M Feist et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
The stoichiometric matrix S is the centerpiece of a mathematical representation of genome-scale metabolic networks This matrix represents each reaction as a column and each metabolite as a row where each numerical element is the corresponding stoichiometric coefficient
18
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstruction
Reed J L I Famili et al (2006) Towards multidimensional genome annotation Nature reviews Genetics 7(2) 130-141
BIGGDatabase
Stoichiometric Matrix
MetabolicPathway
Gene-Protein-Reaction(GPR) Associations
19
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
20
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
How can we use the Stoichiometric Matrixbull The stoichiometric matrix S is a linear transformation of the flux
vector v to a vector of time derivatives of the concentration vector x Reactions
Met
abol
ites
ddt
= sdotx S v
bull The concentration vector x represents the concentration of each of the metabolites
bull If we assume that a cell will be in a particular phenotype for a time much larger than the changing time of metabolites then we can also assume that the concentration pools for the metabolites will be non-changing thus setting dxdt = 0 This is the steady state assumption of flux balance analysis
0ddt
= = sdotx S v
bull Since there are normally many more reactions (columns) than metabolites (rows) more unknown variables than equations then there is no unique solutions (could be a large number of solutions)
bull Need to find a way to constrain the solution space
21
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Dynamic Mass BalanceA simple network
A B
C
e1 e2
e3
v1
v4
v3v2
Linear Differential Equations
Linear Transformation
1 2 3 1
1 4 2
2 3 4 3
dA v v v edtdB v v edtdA v v v edt
= minus minus + +
= + minus
= minus minus minus
ddt
= sdotx S v
1
2
3
4
1
2
3
1 1 1 0 1 0 01 0 0 1 0 1 00 1 1 1 0 0 1
vdA vdt vdB vdt
edCedte
minus minus = minus minus minus minus
0 = sdotS v
Dynamic Mass Balance (Steady State) 1
2
3
4
1
2
3
0 1 1 1 0 1 0 00 1 0 0 1 0 1 00 0 1 1 1 0 0 1
vvvveee
minus minus = minus minus minus minus
Stoichiometric Matrix
Note More unknown variables than equationsthus no unique solutions Need constraints
22
ν1 ν2 ν3 ν4 e1 e2 e3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Conceptual Basis of Constraint-based Modeling
With no constraints the flux distribution of a biological network may lie at any point in a solution space When mass balance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (label 2) are applied to a network it defines an allowable solution space The network may acquire any flux distribution within this space but points outside this space are denied by the constraints Through optimization of an objective function using linear programming FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
23
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Creating A Stoichiometric Matrix
Becker S A A M Feist et al (2007) Quantitative prediction of cellular metabolism with constraint-based models the COBRA Toolbox Nature protocols 2(3) 727-738
The stoichiometric matrix S is the centerpiece of a mathematical representation of genome-scale metabolic networks This matrix represents each reaction as a column and each metabolite as a row where each numerical element is the corresponding stoichiometric coefficient
18
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstruction
Reed J L I Famili et al (2006) Towards multidimensional genome annotation Nature reviews Genetics 7(2) 130-141
BIGGDatabase
Stoichiometric Matrix
MetabolicPathway
Gene-Protein-Reaction(GPR) Associations
19
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
20
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
How can we use the Stoichiometric Matrixbull The stoichiometric matrix S is a linear transformation of the flux
vector v to a vector of time derivatives of the concentration vector x Reactions
Met
abol
ites
ddt
= sdotx S v
bull The concentration vector x represents the concentration of each of the metabolites
bull If we assume that a cell will be in a particular phenotype for a time much larger than the changing time of metabolites then we can also assume that the concentration pools for the metabolites will be non-changing thus setting dxdt = 0 This is the steady state assumption of flux balance analysis
0ddt
= = sdotx S v
bull Since there are normally many more reactions (columns) than metabolites (rows) more unknown variables than equations then there is no unique solutions (could be a large number of solutions)
bull Need to find a way to constrain the solution space
21
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Dynamic Mass BalanceA simple network
A B
C
e1 e2
e3
v1
v4
v3v2
Linear Differential Equations
Linear Transformation
1 2 3 1
1 4 2
2 3 4 3
dA v v v edtdB v v edtdA v v v edt
= minus minus + +
= + minus
= minus minus minus
ddt
= sdotx S v
1
2
3
4
1
2
3
1 1 1 0 1 0 01 0 0 1 0 1 00 1 1 1 0 0 1
vdA vdt vdB vdt
edCedte
minus minus = minus minus minus minus
0 = sdotS v
Dynamic Mass Balance (Steady State) 1
2
3
4
1
2
3
0 1 1 1 0 1 0 00 1 0 0 1 0 1 00 0 1 1 1 0 0 1
vvvveee
minus minus = minus minus minus minus
Stoichiometric Matrix
Note More unknown variables than equationsthus no unique solutions Need constraints
22
ν1 ν2 ν3 ν4 e1 e2 e3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Conceptual Basis of Constraint-based Modeling
With no constraints the flux distribution of a biological network may lie at any point in a solution space When mass balance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (label 2) are applied to a network it defines an allowable solution space The network may acquire any flux distribution within this space but points outside this space are denied by the constraints Through optimization of an objective function using linear programming FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
23
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Genome-scale Metabolic Reconstruction
Reed J L I Famili et al (2006) Towards multidimensional genome annotation Nature reviews Genetics 7(2) 130-141
BIGGDatabase
Stoichiometric Matrix
MetabolicPathway
Gene-Protein-Reaction(GPR) Associations
19
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
20
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
How can we use the Stoichiometric Matrixbull The stoichiometric matrix S is a linear transformation of the flux
vector v to a vector of time derivatives of the concentration vector x Reactions
Met
abol
ites
ddt
= sdotx S v
bull The concentration vector x represents the concentration of each of the metabolites
bull If we assume that a cell will be in a particular phenotype for a time much larger than the changing time of metabolites then we can also assume that the concentration pools for the metabolites will be non-changing thus setting dxdt = 0 This is the steady state assumption of flux balance analysis
0ddt
= = sdotx S v
bull Since there are normally many more reactions (columns) than metabolites (rows) more unknown variables than equations then there is no unique solutions (could be a large number of solutions)
bull Need to find a way to constrain the solution space
21
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Dynamic Mass BalanceA simple network
A B
C
e1 e2
e3
v1
v4
v3v2
Linear Differential Equations
Linear Transformation
1 2 3 1
1 4 2
2 3 4 3
dA v v v edtdB v v edtdA v v v edt
= minus minus + +
= + minus
= minus minus minus
ddt
= sdotx S v
1
2
3
4
1
2
3
1 1 1 0 1 0 01 0 0 1 0 1 00 1 1 1 0 0 1
vdA vdt vdB vdt
edCedte
minus minus = minus minus minus minus
0 = sdotS v
Dynamic Mass Balance (Steady State) 1
2
3
4
1
2
3
0 1 1 1 0 1 0 00 1 0 0 1 0 1 00 0 1 1 1 0 0 1
vvvveee
minus minus = minus minus minus minus
Stoichiometric Matrix
Note More unknown variables than equationsthus no unique solutions Need constraints
22
ν1 ν2 ν3 ν4 e1 e2 e3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Conceptual Basis of Constraint-based Modeling
With no constraints the flux distribution of a biological network may lie at any point in a solution space When mass balance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (label 2) are applied to a network it defines an allowable solution space The network may acquire any flux distribution within this space but points outside this space are denied by the constraints Through optimization of an objective function using linear programming FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
23
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
20
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
How can we use the Stoichiometric Matrixbull The stoichiometric matrix S is a linear transformation of the flux
vector v to a vector of time derivatives of the concentration vector x Reactions
Met
abol
ites
ddt
= sdotx S v
bull The concentration vector x represents the concentration of each of the metabolites
bull If we assume that a cell will be in a particular phenotype for a time much larger than the changing time of metabolites then we can also assume that the concentration pools for the metabolites will be non-changing thus setting dxdt = 0 This is the steady state assumption of flux balance analysis
0ddt
= = sdotx S v
bull Since there are normally many more reactions (columns) than metabolites (rows) more unknown variables than equations then there is no unique solutions (could be a large number of solutions)
bull Need to find a way to constrain the solution space
21
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Dynamic Mass BalanceA simple network
A B
C
e1 e2
e3
v1
v4
v3v2
Linear Differential Equations
Linear Transformation
1 2 3 1
1 4 2
2 3 4 3
dA v v v edtdB v v edtdA v v v edt
= minus minus + +
= + minus
= minus minus minus
ddt
= sdotx S v
1
2
3
4
1
2
3
1 1 1 0 1 0 01 0 0 1 0 1 00 1 1 1 0 0 1
vdA vdt vdB vdt
edCedte
minus minus = minus minus minus minus
0 = sdotS v
Dynamic Mass Balance (Steady State) 1
2
3
4
1
2
3
0 1 1 1 0 1 0 00 1 0 0 1 0 1 00 0 1 1 1 0 0 1
vvvveee
minus minus = minus minus minus minus
Stoichiometric Matrix
Note More unknown variables than equationsthus no unique solutions Need constraints
22
ν1 ν2 ν3 ν4 e1 e2 e3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Conceptual Basis of Constraint-based Modeling
With no constraints the flux distribution of a biological network may lie at any point in a solution space When mass balance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (label 2) are applied to a network it defines an allowable solution space The network may acquire any flux distribution within this space but points outside this space are denied by the constraints Through optimization of an objective function using linear programming FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
23
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
How can we use the Stoichiometric Matrixbull The stoichiometric matrix S is a linear transformation of the flux
vector v to a vector of time derivatives of the concentration vector x Reactions
Met
abol
ites
ddt
= sdotx S v
bull The concentration vector x represents the concentration of each of the metabolites
bull If we assume that a cell will be in a particular phenotype for a time much larger than the changing time of metabolites then we can also assume that the concentration pools for the metabolites will be non-changing thus setting dxdt = 0 This is the steady state assumption of flux balance analysis
0ddt
= = sdotx S v
bull Since there are normally many more reactions (columns) than metabolites (rows) more unknown variables than equations then there is no unique solutions (could be a large number of solutions)
bull Need to find a way to constrain the solution space
21
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Dynamic Mass BalanceA simple network
A B
C
e1 e2
e3
v1
v4
v3v2
Linear Differential Equations
Linear Transformation
1 2 3 1
1 4 2
2 3 4 3
dA v v v edtdB v v edtdA v v v edt
= minus minus + +
= + minus
= minus minus minus
ddt
= sdotx S v
1
2
3
4
1
2
3
1 1 1 0 1 0 01 0 0 1 0 1 00 1 1 1 0 0 1
vdA vdt vdB vdt
edCedte
minus minus = minus minus minus minus
0 = sdotS v
Dynamic Mass Balance (Steady State) 1
2
3
4
1
2
3
0 1 1 1 0 1 0 00 1 0 0 1 0 1 00 0 1 1 1 0 0 1
vvvveee
minus minus = minus minus minus minus
Stoichiometric Matrix
Note More unknown variables than equationsthus no unique solutions Need constraints
22
ν1 ν2 ν3 ν4 e1 e2 e3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Conceptual Basis of Constraint-based Modeling
With no constraints the flux distribution of a biological network may lie at any point in a solution space When mass balance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (label 2) are applied to a network it defines an allowable solution space The network may acquire any flux distribution within this space but points outside this space are denied by the constraints Through optimization of an objective function using linear programming FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
23
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Dynamic Mass BalanceA simple network
A B
C
e1 e2
e3
v1
v4
v3v2
Linear Differential Equations
Linear Transformation
1 2 3 1
1 4 2
2 3 4 3
dA v v v edtdB v v edtdA v v v edt
= minus minus + +
= + minus
= minus minus minus
ddt
= sdotx S v
1
2
3
4
1
2
3
1 1 1 0 1 0 01 0 0 1 0 1 00 1 1 1 0 0 1
vdA vdt vdB vdt
edCedte
minus minus = minus minus minus minus
0 = sdotS v
Dynamic Mass Balance (Steady State) 1
2
3
4
1
2
3
0 1 1 1 0 1 0 00 1 0 0 1 0 1 00 0 1 1 1 0 0 1
vvvveee
minus minus = minus minus minus minus
Stoichiometric Matrix
Note More unknown variables than equationsthus no unique solutions Need constraints
22
ν1 ν2 ν3 ν4 e1 e2 e3
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Conceptual Basis of Constraint-based Modeling
With no constraints the flux distribution of a biological network may lie at any point in a solution space When mass balance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (label 2) are applied to a network it defines an allowable solution space The network may acquire any flux distribution within this space but points outside this space are denied by the constraints Through optimization of an objective function using linear programming FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
23
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Conceptual Basis of Constraint-based Modeling
With no constraints the flux distribution of a biological network may lie at any point in a solution space When mass balance constraints imposed by the stoichiometric matrix S (label 1) and capacity constraints imposed by the lower and upper bounds (ai and bi) (label 2) are applied to a network it defines an allowable solution space The network may acquire any flux distribution within this space but points outside this space are denied by the constraints Through optimization of an objective function using linear programming FBA can identify a single optimal flux distribution that lies on the edge of the allowable solution space
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
23
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
REI601M Introduction to Systems Biology Dr Innes Thiele2012 httpssystemsbiologyhiiswikiREI601M
Role of Constraints
24
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Optimization(Linear Programming or Linear Optimization Problem)
i ii
Z c v= = sdotsum c v
j j j
ddt
vα β
= sdot =
le le
x S v 0
Maximize the objective function
with the following constraints
wherex = concentration vectorv = flux vectorc = objective function weightsS = Stoichiometric matrixαj = Lower bound of fluxβj = upper bound of flux
The goal is to create and objective function that is biologically meaningful These could include
1 Cellular growth (maximization)
2 Particular metabolite engineering (maximization)
3 Energy consumption (minimization)
For the case of cellular growth as the objective function (Biomass Function)
1 ldquoIt has been shown that under rich growth conditions (ie no lack of phosphate and nitrogen) E coli grows in a stoichiometrically optimal mannerrdquo (Schilling 2001 Edwards 1994)
2 ldquoIt is reasonable to hypothesize that unicellular organisms have evolved toward maximal growth performancerdquo (Segre 2002)
25
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
26
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass Precursorsbull The biomass reaction accounts for
all the fractional contributions from biosynthetic precursors and key cofactors to create 1g of biomass
bull These factional contributions need to be determined experimentally for cells growing in log phase
bull It may not be possible to obtain a detailed biomass composition for the target organism In this case one can estimate the relative fraction of each precursor from existing databases Thiele I and B O Palsson (2010) A protocol for generating a high-quality
genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
27
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Precursor Metabolites
Heptose in LPS
2-Keto-3-deoxyoctanate
Pyruvate familyAlanineValineLeucineIsoleucineIsoprenoids
Fatty AcidsMureinLeucine
Glutamate familyGlutamate -gt HemesGlutamineArginine -gt PolyaminesProline
Heme
Aspartate familyAsparagineThreonineMethionine -gt SpermidineAspartate -gt Nicotinamide coenzymes
-gt Pyrimidine nucleotidesLysine
Serine FamilySerine -gt Tryptophan
-gt Ethanolamine-gt 1-C units
Glycine -gt Purine nucleotidesCysteine
Amino sugarsNicotinamide coenzymesGlycerol-3-phosphate -gt Phospholipids
Sugar nucleotidesVitamins and cofactorsFolatesRiboflavinCoenzyme AAdenosylcobalamineNicotinamide
Purine nucleotides
Pyrimidine nucleotides
Phosphoribosylpyrophosphate
HistidineTryptophan
Aromatic FamilyTyrosineTryptophanPhenylalanine
Chorismate
Vitamins and cofactorsUbiquinoneMenaquinoneFolates
28
M Schaechter et al Microbe ASM Press 2006 p 116
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Maintenance Energy Requirementsbull To simulate growth the energy required to maintain the cell growth must
be accounted for
bull Two forms of energy are required growth associated maintenance (GAM) energy and non-growth associated maintenance (NGAM) energy (eg turgor pressure)
bull GAM reaction accounts for the energy (ATP) necessary to replicate a cell It is represented in the model by
x ATP +x H20 -gt x ADP +x Pi + x H+
Where x is the number of required phosphate bonds (5981 in core model) This will be included in the biomass reaction
bull The NGAM reaction (ATPM) is given by
1 ATP + 1H2O -gt 1 ADP + 1 Pi + 1 H+
where the flux through this reaction is constrained by experimental data to 839 mmol gDW
-1h-1 Thiele I and B O Palsson (2010) A protocol for generating a high-quality genome-scale metabolic reconstruction Nature protocols 5(1) 93-121
29
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass ReactionFor Ecoli Core Model
(1496) 3pg + (37478) accoa + (598100) atp + (03610) e4p + (00709) f6p + (01290) g3p + (02050) g6p + (02557) gln-L + (49414) glu-L + (598100) h2o + (35470) nad + (130279) nadph + (17867) oaa + (05191) pep + (28328) pyr + (08977) r5p --gt (598100) adp + (41182) akg + (37478) coa + (598100) h + (35470) nadh + (130279) nadp + (598100) pi
ecoli_core_modelsxls Key Cofactors
30
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
iaf1260 Biomass Objective Function(Ec_biomass_iAF1260_core_59p81M)
Z = 0000223 10fthf[c] + 0000223 2ohph[c] + 05137 ala-L[c] + 0000223 amet[c] + 02958 arg-L[c] + 02411 asn-L[c] + 02411 asp-L[c] +
59984 atp[c] + 0004737 ca2[c] + 0004737 cl[c] + 0000576 coa[c] + 0003158 cobalt2[c] + 01335 ctp[c] + 0003158 cu2[c] + 009158
cys-L[c] + 002617 datp[c] + 002702 dctp[c] + 002702 dgtp[c] + 002617 dttp[c] + 0000223 fad[c] + 0007106 fe2[c] + 0007106 fe3[c]
+ 02632 gln-L[c] + 02632 glu-L[c] + 06126 gly[c] + 02151 gtp[c] + 54462 h2o[c] + 009474 his-L[c] + 02905 ile-L[c] + 01776 k[c] +
001945 kdo2lipid4[e] + 04505 leu-L[c] + 03432 lys-L[c] + 01537 met-L[c] + 0007895 mg2[c] + 0000223 mlthf[c] + 0003158 mn2[c] +
0003158 mobd[c] + 001389 murein5px4p[p] + 0001831 nad[c] + 0000447 nadp[c] + 0011843 nh4[c] + 002233 pe160[c] + 004148
pe160[p] + 002632 pe161[c] + 004889 pe161[p] + 01759 phe-L[c] + 0000223 pheme[c] + 02211 pro-L[c] + 0000223 pydx5p[c] +
0000223 ribflv[c] + 02158 ser-L[c] + 0000223 sheme[c] + 0003948 so4[c] + 0000223 thf[c] + 0000223 thmpp[c] + 02537 thr-L[c] +
005684 trp-L[c] + 01379 tyr-L[c] + 55e-005 udcpdp[c] + 01441 utp[c] + 04232 val-L[c] + 0003158 zn2[c] -gt 5981 adp[c] + 5981 h[c]
+ 59806 pi[c] + 07739 ppi[c]
31
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Formulation of Flux Balance Analysis
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
32
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Core Model
Orth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
httpsystemsbiologyucsdeduDownloadsE_coli_Core
Ana TCA
OxP
PPP
Glyc
Ferm
33
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli model ldquoecoli_iaf1260xmlrdquo
Ecoli K-12 MG1655Genome-Scale Reconstructions
BIGG Models httpbiggucsdedu
iAF1260 ndash 6Feist A M C S Henry et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Molecular Systems Biology 3 121
iJO1366 - Orth J D and B O Palsson (2012) Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions BMC systems biology 6(1) 30
34
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
The Iterative Reconstruction and History of the E Coli Metabolic Network
Feist A M and B O Palsson (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli Nature biotechnology 26(6) 659-667
35
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Ecoli Genome-scale Reconstructionsbull Escherichia coli 042
bull Escherichia coli 536
bull Escherichia coli 55989
bull Escherichia coli ABU 83972
bull Escherichia coli APEC O1
bull Escherichia coli ATCC 8739
bull Escherichia coli B str REL606
bull Escherichia coli BL21(DE3) AM946981
bull Escherichia coli BL21(DE3) BL21-Gold(DE3)pLysS AG
bull Escherichia coli BL21(DE3) CP001509
bull Escherichia coli BW2952
bull Escherichia coli CFT073
bull Escherichia coli DH1
bull Escherichia coli DH1 ME8569
bull Escherichia coli E24377A
bull Escherichia coli ED1a
bull Escherichia coli ETEC H10407
bull Escherichia coli HS
bull Escherichia coli IAI1
bull Escherichia coli IAI39
bull Escherichia coli IHE3034
bull Escherichia coli KO11FL
bull Escherichia coli LF82
bull Escherichia coli NA114
bull Escherichia coli O103H2 str 12009
bull Escherichia coli O111H- str 11128
bull Escherichia coli O127H6 str E234869
bull Escherichia coli O157H7 EDL933
bull Escherichia coli O157H7 str EC4115
bull Escherichia coli O157H7 str Sakai
bull Escherichia coli O157H7 str TW14359
bull Escherichia coli O26H11 str 11368
bull Escherichia coli O55H7 str CB9615
bull Escherichia coli O83H1 str NRG 857C
bull Escherichia coli S88
bull Escherichia coli SE11
bull Escherichia coli SE15
bull Escherichia coli SMS-3-5
bull Escherichia coli str K-12 substr DH10B
bull Escherichia coli str K-12 substr MG1655
bull Escherichia coli str K-12 substr W3110
bull Escherichia coli UM146
bull Escherichia coli UMN026
bull Escherichia coli UMNK88
bull Escherichia coli UTI89
bull Escherichia coli W
bull Escherichia coli W CP002185
bull Escherichia coli K-12 MG1655
Monk J M P Charusanti et al (2013) Proceedings of the National Academy of Sciences of the United States of America 110(50) 20338-20343
36
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Phylogenetic Coverage of Genome-scale Network
Reconstructions
Monk J J Nogales et al (2014) Optimizing genome-scale network reconstructions Nature biotechnology 32(5) 447-452
37
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
38
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Cobra ToolboxMatlab Cobra Toolbox
bull Flux Optimizationbull Flux Variability Analysisbull Robustness Analysisbull Phenotype Phase Plane Analysisbull Parsimonious FBAbull Visualization Toolsbull Gene Additions amp Knockoutsbull Production Envelopes
Load ModelsSBML Excel
Graphical Output
Output Maps
Numerical Output
Save Models
Matlab CodeM-Files
Links for installing COBRA toolbox for MATLAB
ndash httpwwwnaturecomprotocolexchangeprotocols2097introduction
ndash httpbenheavnercomsystemsbioindexphptitle=Installing_COBRA_toolbox_for_MATLAB
ndash httpopencobrasourceforgenetopenCOBRAInstallhtml
39
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Matlab Interface40
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Drawing Flux Values on a Map
41
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Print Flux Values
ACONTa 600725ACONTb 600725AKGDH 506438ATPM 839ATPS4r 45514Biomass_0873922CO2t -228098CS 600725CYTBD 43599ENO 147161EX_co2(e) 228098EX_glc(e) -10EX_h2o(e) 291758EX_h(e) 175309EX_nh4(e) -476532EX_o2(e) -217995EX_pi(e) -32149
PGK -160235PGL 495998PGM -147161PIt2r 32149PPC 250431PYK 175818RPE 267848RPI -22815SUCDi 506438SUCOAS -506438TALA 149698TKT1 149698TKT2 11815TPI 747738
FBA 747738FUM 506438G6PDH2r 495998GAPD 160235GLCpts 10GLNS 0223462GLUDy -454186GND 495998H2Ot -291758ICDHyr 600725MDH 506438NADH16 385346NH4t 476532O2t 217995PDH 928253PFK 747738PGI 486086
GrowthRate
Inputs amp Outputs(Exchange Reactions)
42
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
EX_co2(e) 406527
EX_glc(e) -185
EX_h2o(e) 526943
EX_h(e) 331606
EX_nh4(e) -901387
EX_o2(e) -387416
EX_pi(e) -608116
Exchange Reactions
EX_glc(e)
EX_nh4(e)
EX_o2(e)
EX_pi(e) EX_co2(e)EX_h2o(e)
EX_h(e)
Aerobic Growth on Glucose
43
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Close-up of TCA Cycle
44
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Biomass 0470565
EX_ac(e) 151732
EX_co2(e) -0840759
EX_etoh(e) 146749
EX_for(e) 321194
EX_glc(e) -185
EX_h2o(e) -120879
EX_h(e) 567321
EX_nh4(e) -25659
EX_pi(e) -173107
Exchange Reactions
Anaerobic Growth on Glucose
45
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Aerobic Growth Anaerobic Growth
Aerobic vs Anaerobic GrowthOrth J D I Thiele et al (2010) What is flux balance analysis Nature biotechnology 28(3) 245-248
a b
46
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Substrate Maximum Growth RateSubstrate Aerobic (hr-1) Anaerobic (hr-1)acetate 03893 0
acetaldehyde 06073 0
2-oxoglutarate 10982 0
ethanol 06996 0
D-fructose 17906 05163
fumarate 07865 0
D-glucose 17906 05163
L-glutamine 11636 0
L-glutamate 12425 0
D-lactate 07403 0
L-malate 07865 0
pyruvate 06221 00655
succinate 08401 0(What is flux balance analysis - Supplementary tutorialldquo)
The core E coli model contains exchange reactions for 13 different organic compounds each of which can be used as the sole carbon source under aerobic or anaerobic conditions
47
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
48
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Methods in Constraint-based Reconstruction and
Analysis
49
Lewis N E H Nagarajan et al (2012) Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods Nature reviews Microbiology 10(4) 291-305
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Flux Balance Analysis Overview
bull Flux Balance Analysis Overview
bull Reactions Metabolites amp Pathways
bull Mathematical Representation of Reactions amp Constraints
bull Mass Balanced Linear Equations
bull Biomass Reaction
bull Calculating Fluxes
bull Flux Balance Analysis Toolbox
50
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Learning Objectives
Each student should be able to
bull Explain flux balance analysis (FBA)
bull Explain reactions metabolites amp pathways
bull Explain mass balanced linear equations
bull Explain the biomass reaction
bull Explain how to create a stoichiometric matrix from reactions and metabolites
bull Explain gene-protein-reaction associations
bull Explain the constraint-based modeling
51
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
Constraint-based Metabolic Reconstructions amp Analysis
Lesson Flux Balance Analysis OverviewBIE 55006500Utah State University
H Scott Hinton 2017
Reflective Questions1 What is flux balance analysis2 What does steady state mean in flux balance analysis (FBA)3 What is the difference between a reaction a metaboite and a
pathway4 What is a gene-protein-reaction (GPR)5 What is a gene locus6 What is the difference between a single enzyme an isozymes
and a protein complex7 What is a reaction formula8 What is the difference betwen a metabolite neutral formula
and a metabolite charged formula9 What is a metabolite compartment10 What is an exchange reaction11 What are the units of flux12 What is the mathematical sign for uptake and secretion13 What is the difference between extracellular envionrment and
intracellular space14 What are transport reactions
15 Are the rows of a stoichhiometric matrix metaobites or reactions
16 Why is the product of the stoichiometric matrix and the flux set to zero
17 What is the purpose of linear programming18 What is the purpose on an objective function19 What are biomass precursors20 What is the purpose of growth associated maintenance (GAM)21 What is the purpose of non-growth associated maintenance energy
(NGAM)22 What is the purpose of the biomass reaction23 What are genome-scale metabolic network reconstruction24 What phase of growth does FBA assume (lag exponential
stationary death)25 What are the limits of FBA26 What role does the stoichiometric matrix play in FBA27 Why are visualization tools needed
52
![Multiscale Metabolic Modeling: Dynamic Flux Balance Analysis on a Whole-Plant Scale1[W]](https://img.pdfslide.net/doc/110x75/61fca1ec9d50e757a521e22e/multiscale-metabolic-modeling-dynamic-flux-balance-analysis-on-a-whole-plant-scale1w.jpg)
