Can a combination of constrained-based and kinetic modeling bridge time scales in progressive diseases?

Lorentz workshop Multiscale Systems Biology of Cancer

Leiden, NL, Nov. 16, 2012

Natal van Riel Dept. of Biomedical Engineering, [email protected]

• Parameter Transition Analysis (PTA)

• Progressive adaptations in metabolism associated with diseases (or therapeutic intervention)

• Linking phenotypes • Integrate metabolome, proteome, transcriptome

• Indentifying and exploiting the structure of the parameter space

unidentifiability ↔ constraints paradox (?) • Quantifying and analyzing uncertainty in model and data

/ biomedical engineering PAGE 2 19-8-2013

Systems biology and metabolic diseases

• Changes in metabolism associated with multi-factorial, progressive diseases


Kinetic modeling

• ATP metabolism in mitochondria


Chance, Comput Biomed Res.1967;1:251-64.

Schmitz et al. PLoS ONE 2012, 7(3): e34118.

Kinetic modeling


Chalhoub et al, 2007 AJP Endocrinol 93(6): E1676-

liver

skeletal muscle

Schmitz,et al. Am J Physiol Cell Physiol 2012 Oct 31

Constrained-based modeling


• Genome-Scale Metabolic Modeling (GSMM) • Liver specific GSMM’s:

− Jerby, Shlomi and Ruppin 2010 Mol Sys Biol 6: 401 − Gille,…, Holzhutter 2010 Mol Syst Biol 6: 411

Constraints: • Physical-chemical: network topology,

conservation of mass, thermodynamics • Flux Balance Analysis (FBA)

• Data: • Shlomi,…, Ruppin 2008 Nat Biotech 26: 1003

• Inverse problems

• Numerical optimization

• Variability / Uncertainty analysis


2

1

( )( )N

i id

i i

y dXσ=

−

∑ pp

( )ˆ arg min ( )dX=p

p p

( ) ( ( ), , )d t t tdt

=s Nv s p

=Nv 0subject to

i i ia v b< <

( )ˆ arg max ( )X=v

v v

Metabolic Syndrome (MetS)

• The characteristics of plasma lipoprotein profiles codetermine metabolic and cardiovascular disease risks

• Underlying molecular mechanisms are not fully understood • Multi-factorial and progressive


• Preclinical research

• Cohort studies: cross-sectional e.g. BMI matched

• Patient-specific (VPH, ITFoM)



• Different diets • Genetic manipulation

• Pharmacological compounds

…

experiments phenotype A

experiments phenotype B

Identify adaptations

Modulate lipoprotein metabolism

• Activate Liver X Receptor (nuclear receptor) plays a central role in the control of cellular lipid and sterol metabolism

• Metabolic profiling


0 10 200

100

200Hepatic TG

Time [days]

[um

ol/g

]

0 10 200

1

2

3Hepatic CE

Time [days]

[um

ol/g

]

0 10 200

2

4

6Hepatic FC

Time [days]

[um

ol/g

]

0 10 200

50

100Hepatic TG

Time [days]

[um

ol]

0 10 200

0.5

1

1.5Hepatic CE

Time [days]

[um

ol]

0 10 200

2

4Hepatic FC

Time [days]

[um

ol]

0 10 200

1000

2000

3000Plasma CE

Time [days]

[um

ol/L

]

0 10 200

1000

2000

3000HDL-CE

Time [days]

[um

ol/L

]

0 10 200

500

1000

1500Plasma TG

Time [days]

[um

ol/L

]

0 10 206

8

10

12VLDL clearance

Time [days]

[-]

0 10 20100

200

300

400ratio TG/CE

Time [days]

[-]

0 10 200

5

10

15VLDL diameter

Time [days]

[nm

]

0 10 200

1

2

3VLDL-TG production

Time [days]

[um

ol/h

]

0 10 201

2

3Hepatic mass

Time [days]

[gra

m]

0 10 200

0.2

0.4DNL

Time [days]

[-]

• Computational model

Grefhorst et al. Atherosclerosis, 2012, 222: 382– 389 Tiemann et al. BMC Systems Biology, 2011, 5:174

Control, 1, 2, 4, 7, 14, 21 days

Phenotype snapshots

• Observed:

• Unobserved:

• Metabolic network topology is invariant

• Adaptations in metabolism: - metabolic control - interaction with proteome and transcriptome

Metabolic parameters (e.g. Vmax) can change


Metabolome

Proteome

Transcriptome

Parameter Trajectory Analysis (PTA)

• Algorithm: nesting of simulation and parameter estimation


Progressive disease / Treatment intervention

Phenotype data at different stages

Monte Carlo sampling of data interpolants

Estimation of parameter and flux trajectories

Analysis

A priori information

Metabolic network topology & Reaction kinetics

Differential Equation model with time-dependent parameters

( ) ( ( ), , )d t t tdt

=s Nv s p

( ) ( ( ) ,( ), )d t t tdt

t=s Nv s p

2

1

( )( )N

i id

i i

y dXσ=

−

∑ pp

( )( )

ˆ ( ) arg min ( ( )dt

t X t=p

p p

Parameterization

• Sampling parameter space

• Single phenotype snapshot


100

101

10210

2

103

104

TG formation (ER)

CE

form

atio

n (E

R)

LXR activation

reference

• Connecting phenotypes

• Numerical results • ensemble

• Visualization • 2D historgram


Monte Carlo approach to assess different dynamic behavior

• To account for uncertainty in the data



…

Input

Output

From adaptations in metabolome…

• … to predict changes in proteome / transcriptome

/ biomedical engineering PAGE 18 8/19/2013

T0901317

LXR

model development

predict changes

Metabolome

Proteome

Transcriptome

enzyme parameter gene/protein HDL-CE synthesis ABCA1 HDL-CE uptake SR-B1 FC production ABCG5 … …

Fas, Abcg5, Abcg8, Cyp7a1, Lpl, Pltp, Cd36

Effects of LXR activation

• Increased cholesterol efflux from periphery to HDL particles • Accumulation of hepatic TG (hepatic steatosis) • Metabolic adaptation: decreased

hepatic capacity to clear cholesterol • Predicts a decrease in SR-B1


• Experimental validation

Tiemann et al, submitted

The hepatic HDL-C uptake capacity is reduced upon LXR activation


• The hepatic HDL-C uptake flux is increased (steatosis): • increase in plasma HDL-C (metabolic control) • transcriptional control (SR-B1) counteracts hepatic overloading

• Increase in plasma HDL-C is due to only a small imbalance in uptake vs efflux in the beginning of the intervention

VLDL synthesis flux to plasma decreases

• VLDL-TG production is increased • TG and CE content per VLDL particle increases 10 fold


Activation of LXR by pharmaceutical compound T0901317

• Beneficial effect: • increased excretion of cholesterol

from the body • large, anti-atherogenic HDL

• Side effects: • hepatic steatosis • triglyceride-rich VLDL

• Model analysis predicts how side effects could be prevented


Liver section of mice treated 4 days with LXR agonist T0901317

Oil-Red-O staining for neutral fat

hepatic steatosis

VLDL

HDL

T0901317

Is this possible with less data?

• A subset of the data (cross-sectional data) • Only day 0 and day 4


…

Flux trajectories for acceptable parameter sets


[mM]

[mM/h]

4 days after LXR activation

reference

Analysis of under-constrained trajectories

• Some show a clear pattern (positive correlation between HDL-CE synthesis and HDL-CE uptake by the liver), others just ‘clouds’ of solutions

• Can the ‘structure’ in one cross-section of the parameter space be used to interpret other flux adaptations?


Predictions about changes in gene/ protein expression

• Clustering of scenarios - testable hypotheses

• Also here SR-B1 is predicted to be decreased • Measuring ABCG5, but especially ABCA1 is predicted to be

discriminative


fluxes parameters

Trajectories can be used for many analyses

• Analysis of the cascade of induced adaptations • Sensitivity and control analyses • Optimal experiment design

which additional measurement (which metabolite, when) is most effective in reducing the uncertainty in a prediction of interest and tradeoff with the ‘cost’

• …


A theoretical study

• Insight in the approach • Test and optimize computational methods • Identify possibilities for further improvements


R1

u2

u1 1 S1

S3S2S4

3

4 5

2

7

6

1 2 3 4 5 0

0.5

1

1.5

2 S 1

1 2 3 4 5 0 0.1 0.2 0.3 0.4 0.5

S 2

1 2 3 4 5 0 0.2 0.4 0.6 0.8

1 S3

1 2 3 4 5 0

0.2

0.4

0.6

0.8 S 4

u2

u1 1 S1

S3S2S4

3

4 5

2

Van Riel et al, submitted

Outlook: including other omics

• Transcriptomics

• Proteomics

• Trajectories correlating with gene expression data are more likely than parameter changes that do not correlate

‘A transparent black box’ / biomedical engineering PAGE 29 19-8-2013

Metabolome

Proteome

Transcriptome2 2

1 1

( )( )N M

i i id

i ii i

y d d dtdRNA dt

θ θχ θ λσ= =

−+

∑ ∑

Acknowledgement

Collaborators • Computational Biology (TU/e)

• Ceylan Çölmekçi Öncü • Christian Tiemann • Joep Schmitz • Joep Vanlier • Huili Yuan • Peter Hilbers • Marijke Dermois • Gijs Hendriks • Fianne Sips • Sandra van Tienhoven • Robbin van den Eijnde • Bram Wijnen • Sjanneke Zwaan

Funding • Netherlands Genomics Initiative

Netherlands Consortium for Systems Biology

• AstraZeneca

• Univ. Medical Centre Groningen (NL) • Aldo Grefhorst • Maaike Oosterveer • Jan Albert Kuivenhoven • Barbara Bakker • Bert Groen

• Biomedical NMR (TU/e)

• Klaas Nicolay • Jeanine Prompers

• Ko Willems-van Dijk, Leiden University Medical Center, Netherlands

• FP7-HEALTH.2012.2.1.2-2: Systems medicine: Applying systems biology approaches for understanding multifactorial human diseases and their co-morbidities, starting in 2013

Technology

Can a combination of constrained-based and kinetic modeling bridge time scales in progressive diseases?