Modeling and Analysis Techniques in Systems Biology. CS 6221 Lecture 1 P.S. Thiagarajan

Modeling and Analysis Techniques in Systems Biology.

CS 6221 Lecture 1

P.S. Thiagarajan

Basic Info

• P.S. Thiagarajan• COM2 #03 – 55 ; Tel Ext. 67998• [email protected]• www.comp.nus.edu.sg/~thiagu• Course web page:

– www.comp.nus.edu.sg/~cs6221– We will be using the IVLE system extensively.

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Office Hours

• Send mail first and fix an appointment.

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Course Material

• Selected Parts of the text book :– Systems Biology in Practice: E. Klipp, R. Herwig, A.

Kowald, C. Wierling, H. Lehrach (Wiley)

• Selected Survey papers, book chapters. • Lecture slides.• Research Articles.

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Assignments

• Lab Assignments– 3– tool based (Cell Illustrator, COPASI, SimBio)– Individual

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Term Papers

• Read a paper or –more likely- a bunch of papers on a topic.

• Summarize in the form of a term paper.• First assignment: Common• Second assignment:

– More substantial– Can be aligned to your interests

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Talk

• Give talk based on the second term paper.– 25 + 5 minutes.

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Grading (Tentative)

• Lab assignments 45% (15 + 15 + 15) • Term papers 40% (15 + 25)• Talk: 15%

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What is the Course About?

• Computational systems biology– Computational aspects of systems biology.

• Systems biology:– Not just focus on individual components.

• genes, mRNAs, proteins, membranes, ligands ….

– But study a system of such components and their interactions.

• Many different views of systems biology.

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Why Systems Biology?

• Biology has traditionally –and extremely successfully!- focused on what individual parts of a cell do .

• Bio-chemistry of large and small molecules– The structure of DNA and RNA– Proteins, ligands,…

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• But functionality of a system is determined crucially by the interactions of the parts.

• Many fundamental biological processes are dynamic.– cell growith/division/differentiation– Metabolism,….

• Many diseases are marked by malfunctioning of these processes.

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• Advances in experimental technology are producing vast amounts of data concerning biological processes.– Which genes get expressed “when” in controlled

conditions.

• One would like to understand this data in a systemic way.

• Enter: computational systems biology!

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The CSB Approach

• View selected biological processes as dynamical systems.– Model– Simulate– Analyze– Predict

• Many research communities study dynamical systems …

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What do we need ?

• Biology for computer scientists.– basic biological sub-systems/processes– experimental techniques.

• Modeling, analysis and simulation techniques.

• Biologists as collaborators!

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Current Status

• Modeling techniques.– Mathematical

• differential equations, Linear algebra, probability theory, statistics, Boolean networks, Markov chains, Bayesian networks,….

– CS-specific:• Automata, Petri nets, Hybrid functional Petri nets,

hybrid automata, Bayesian networks/inferencing/learning, Markov chains, Model checking….

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Current Status

• Metabolism– Kinetics “laws” (models).

– Enzyme kinetics, law of mass action, Michelis-Menten kinetics

– Metabolic network models and flux analysis.

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Current Status

• Signal Transduction• Receptor-ligand interactions• Protein actors• signaling dynamics

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Current Status

• Other biological processes• biological oscillations• protein folding kinetics• cell cycle• Gene expression, regulation

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Current Status

• Modeling tools• Cell Illustrator, COPASI, SimBio, …..

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What shall we do?

• Selected basic topics.– To illustrate the current state of the field.– To critically examine what is missing.– To discuss promising lines of research.

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What can CS offer?

• We “know” how to deal with complex systems.– Hierarchy

• silicon realization of circuits, digital design, micro-architectures, assemble language, programming languages, GUIs, …

– separation of concerns.– concepts (models), techniques, tools at each layer

and for connecting the layers.

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What can CS offer?

• Deal with other disciplines.– Multi-media– Control– Manufacturing– Communications– Business!

• Using computing power via algorithms and data structures!

• Computational thinking?!

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What can CS offer?

• Find the right level abstractions.– approximations

• Handle distributed dynamics• Deal with hybrid behaviors• Build tools.

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What the Course is NOT about.

• We will not deal with:– Traditional “Bio-Informatics” topics

• data mining, sequence analysis, …

– Computational aspects of structural biology• Proteins structure, folding…

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Contents

• Bio-chemical networks– The basics of chemical kinetics

• Three types of bio-chemical networks– Gene networks– Metabolic networks– Signaling pathways

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Bio-pathways

• Many studies of biological sub-systems boil down to studying:– bio-pathways

• A network of bio-chemical reactions.

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The hierarchy of bio-chemical networks

Interacting networks of Bio-Chemical reactions

Bio-Chemical reactions

A network of Bio-Chemical reactions

Cell functions

Metabolic pathways

Signaling pathways

Gene regulatory networks

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Biopathways

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Gene Regulatory networks

• Boolean models• Differential equations• Bayesian networks.

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Metabolic pathways

• Petri nets• Linear algebra• Flux analysis

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Signaling Pathways

• Differential equations.• Hybrid functional Petri nets• Hybrid automata• Stochastic models.

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Our Research

• ODEs based modeling.– Parameter estimation techniques

• Stochastic approximations of ODEs dynamics.– Parameter estimation, sensitivity analysis

• GPU implementations• Probabilistic (statistical ) model checking

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Our Research

• Collaboration with biologists:– Signaling pathways:

• AKT/MAPK pathway• Complement pathway • TLR3-TLR7 signaling pathways• DNA damage/repair pathways

• www.comp.nus.edu.sg/~rpsysbio

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Expected Outcomes

• Have a sound grasp of:– current modeling and simulation techniques

(Signaling pathways)– Reaction kinetics– stochastic models and simulations– Analysis techniques:

• Parameter estimation, sensitivity analysis

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Expected Outcomes

• Be aware of the limitations of current techniques and state of knowledge

• Be ready to undertake modeling and simulation work.

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Let us get started.

Basic Biology: Sources

• Chapter 2 (Biology in a Nutshell) of the book “Systems Biology in Practice” by E. Klipp et.al.

• Chapter 1 (Molecular Biology for Computer Scientists) of the book “Artificial Intelligence and Molecular Biology” by Lawrence Hunter.

• The internet!

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A major goal of biology

• Understand the molecular biology of eukaryotic cells.

• Cell: the basic building block.– Two major families: Prokaryotes and Eukaryotes.– Eukaryotes

• More complex; genetic material is contained in the nucleus;

• Most multi-cellular organisms are made up of eukroyotes.; WE are made up of these types of cells.

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Cells

• In multi-cellular organisms;– Cells are differentiated.– Different types of cells have different functions

(and composition).– Groups of cells for specific functionalities

• tissues.• we have 14 different types of tissues.

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Source ?

Major Classes of Bio-Molecules

• Carbohydrates• Lipids• Proteins• Nucleic acids

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Proteins

• Many functions!• Build up the cytoskeletal structure of the cell (the

scaffolding)• Responsible for cell movements (motility)• Serve as catalytic enzymes for bio-chemical

reactions.• Induce signal transductions.• Control transcriptions and translation of genes• Control degradation of proteins.

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Proteins

• Proteins consist of polypeptides.– Polypeptide - a LONG chain of amino acids bonded

together by peptide bonds between adjacent amino acid residues.

• The order of amino acids constituting a peptide is fundamental.– Primary structure– coded by genetic information

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Proteins

• 20 (23?) different amino acids• A protein can have 50 – 4000 amino acids

sequence. (50 – 1000 is the typical range)• 201000 possible proteins!• Actually, only a tiny fraction is found in

nature.

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Nucleic Acids

• DNA (Deoxyribonucleic acid) molecules store genetic information.– Present in all living organisms

• RNA (Ribonucleic acid) takes part in a large number of processes.– Transferring hereditary information in the DNA to

synthesize proteins.

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The Central Dogma

• First enunciated by Francis Crick in 1958[1]– re-stated in a Nature paper published in 1970:[2]

• Three major classes of information-carrying biopolymers:– DNA, RNA, proteins– Information encoded as sequences of molecules.

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The Central Dogma

• In principle there can be 9 types of transfers:

DNA RNA Proteins

DNA RNA Proteins

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The Central Dogma

• The “simple” form of central dogma states:

RNA

DNA

Proteins

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The Central Dogma

• Information cannot be transferred back from protein to either protein or nucleic acid.

• 'once information gets into protein, it can't flow back to nucleic acid.'

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Current Known Information Flows

Special flows occur in retro viruses !

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Information Flows

DNA DNA (Replication)

DNA mRNA

(Transcription)

mRNA Proteins (Translation)

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Mechanism of Cellular Functions

– Replication (of DNA)– Transcription of RNA and Processing –by splicing-

to yield mRNA which migrates to the cytoplasm.– Translation (by ribosomes) of the code carried by

mRNA into proteins.

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Legend:

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Post-translational Modifications

• Proteins undergo many modifications to implement cellular functions– Phosphorylation (Activation of proteins)– Dephosphorylation (Deactivation of proteins)– Methylation and acetylation (Gene silencing. Plays

a role in cell differentiation)– Cleavage (Cutting of genes and proteins. For

degradation and apoptosis)– Ubiquitination (Marking of proteins for further

degradation)

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Interaction roles of proteins

• Proteins have specific roles in the form of chemical interactions.– Kinase (Catalyzes phosphorylation, thereby

activating other proteins)– Phosphatase (Catalyzes dephosphorylation)– Transcriptional Co-factors

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Role of Bio-pathways

• Apoptosis– programmed cell death

• Differentiation– Cells getting specialized for specific functions

• Cell-cycle– Growth and replication of cells

• Many others!

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Example: Wnt Signaling Pathway• Most studies on each of the two types of pathways (Signaling

and GRN) done in isolation

• Wnt canonical pathway, starts with the binding of the Wnt ligand to Frz receptor

• Chain of chemical reactions occur, which results in the transcription factor β-Catenin being translocated to the nucleus

• Cofactor with TCF/LEF to up-regulate the transcription of several genes

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Wnt Signaling Pathway (Canonical)Wnt

Dsh GSK-3B

Axin

APC

Lef Tcf

p

p

B-Catenin B-CateninpB-Catenin

pDsh

p

Degradation Complex form when GSK-3B binds and phosphorylates APC and Axin

Cytoplasmic B-catenin will be phosphorylated by the complex and gets ‘marked’ for degradation

When Wnt ligand binds to Frz, Dsh is recruited to the plasma membrane and gets activated

It will inhibit the formation of the degradation complex

Cytoplasmic B-catenin can then translocate to nucleus where it binds to co-factors Tcf and Lef

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Reaction Kinetics

Sources

• Chapter 5 (Metabolism) of the book “Systems Biology in Practice” by E. Klipp et.al.

• Other related material to be uploaded.

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Bio-Chemical Reactions

• Bio-Chemical reaction:– A basic unit of biological processes.– Convert molecules of one type into another

• Can be modeled at different levels of abstraction (time scales).– Microscopic: single molecules and their

interactions– Macroscopic: Concentrations and rates (changes

of concentration per time unit).

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Reactions

• Bio-chemical reaction:– Involves bio-molecules.

• Proteins, carbohydrates, lipids,…

– Creation and transformation of bio-molecules.– Control the flow of energy , materials and

information through the cell.

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Kinetic Models of Reactions

• Reaction: – A chemical process resulting in inter-conversion of

the reactants.• motion of electrons cause chemical bonds to break

and form.

• Reaction types– Isomerization

• structural rearrangement (transform one isomer to another)

• no change in net atomic composition

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Reaction Types

• Direct combination or synthesis:– two or more chemical elements or compounds

unite to form a more complex product. • 2H2 + O2 → 2H2O

• Chemical decomposition – a compound is decomposed into smaller

compounds: • 2H2O → 2H2 + O2

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Reaction Types

• Single displacement or substitution– an element being displaced out of a compound by

a more reactive element: • 2Na + 2HCl → 2NaCl + H2

• Double displacement – two compounds in aqueous solution exchange

elements or ions to form different compounds. • NaCl + AgNO3 → NaNO3 + AgCl

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Reaction Kinetics

• Kinetics:– Determine reaction rates

• Fix reaction law and • determine reaction rate constant • Solve the equation capturing the dynamics.

• The reaction rate for a product or reactant in a particular reaction:– the amount (in moles or mass units) per unit time

per unit volume that is formed or removed.

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Reaction Rates

• Influenced by:– Temperature– Concentration– Pressure– Light– Order (zero, first, second)– catalyst

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Rate Laws

• Rate law:– An equation that relates the concentrations of the

reactants to the rate.

• Differential equations are often used to describe these laws.

• Assumption: The reactants participating in the reactions are abundant.

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Rate Laws

• Mass action law:– The reaction rate is proportional to the probability

of collision of the reactants– Proportional to the concentration of the reactants

to the power of their molecularities.

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Mass action law

S1 + S2 PV

V = k. [S1] [S2] [S1] is the concentration (Moles/ litre) of S1

[S2] is the concentration (Moles/ litre) of S

k is the rate constant

V, the rate of the reaction

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Mass action law

S1 + S2 2PV1

V2

V = (V1) - (V2) = k1. [S1] [S2] – k2 [P]2

[S1] ([S2]) is the concentration (Moles/litre) of S1 (S2)

k1 and k2 are the rate constants

V1, the rate of the forward reaction

V2, the rate of the backward reaction

V, the net rate

Molecularity is 1 for each substrate (reactant) of the forward reaction and 2 for the backward reaction

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Mass-action Kinetics

E + S ES E + P

k1

k 2

k3

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To be continued……..

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• Assuming mass law kinetics we can write down a system of ordinary differential equations for the 6 species.

• But we don’t know how to solve systems of ordinary (non-linear) differential equations even for dimension 4!

• We must resort to numerical integration.

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Given:

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Initial values chosen “randomly”

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Michaelis-Menton Kinetics

• Describes the rate of enzyme-mediated reactions in an amalgamated fashion:– Based on mass action law.– Subject to some assumptions

• Enzymes– Protein (bio-)catalysts

• Catalyst:– A substance that accelerates the rate of a reaction

without being used up.– The speed up can be enormous!

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Enzymes

• Substrate binds temporarily to the enzyme.– Lowers the activation energy needed for the reaction.

• The rate at which an enzyme works is influenced by:– concentration of the substrate– Temperature

• beyond a certain point, the protein can get denatured– Its 3 dimensional structure gets disrupted

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Enzymes

• The rate at which an enzyme works is influenced by:– The presence of inhibitors

• molecules that bind to the same site as the substrate (competitive)

– prevents the substrate from binding

• molecules that bind to some other site of the enzyme but reduces its catalytic power (non-competitive)

– pH (the concentration of hydrogen ions in a solution)• affects the 3 dimensional shape

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i) A reversible formation of the Enzyme-Substrate complex ES

ii) Irreversible release of the product P from the enzyme.

This is for a single substrate; no backward reaction; at least negligible if we focus on the initial phase of the reaction.

E + S ES E + P

k1

k 2

k3

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Michaelis-Menten Kinetics

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Use mass action law to model each reaction.

E + S ES E + P

k1

k 2

k3

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(1)

Assumption1:

[ES] concentration changes much more slowly than those of [S] and [P] (quasi-steady-state)

We can then write:

This is the rate at which P is being produced.

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(2)

This simplifies to:

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(1)

(2)

Define (Michaelis constant)

(3)

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Assumption1:

[ES] concentration changes much more slowly than those of [S] and [P] (quasi-steady-state)

Assumption2: The total enzyme concentration does not change with time.

[E0] = [E] + [ES]

[E0] - initial concentration

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][][][ 0 ESEE

][])[]]([[ 0 ESKESES M

]][[][]][[ 0 SESESKES M

][][

]][[ 0 ESKS

ES

M

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(1)

][][

]][[ 0 ESKS

ES

M

][3 ESkv

MKS

ESkv

][

]][[ 03

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Michaelis-Menton KineticsVmax is achieved when all of the enzyme (E0) is substrate-bound.

(assumption: [S] >> [E0])

at maximum rate,

Thus,

][][ 0EES

][][ 033max EkESkv

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][3 ESkv


This is the Michaelis-Menten equation!

MKS

ESkv

][

]][[ 03

][ 03max Ekv

MKS

Svv

][

][max

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This is the Michaelis-Menten equation!

MKS

ESkv

][

]][[ 03

][ 03max Ekv

MKS

Svv

][

][max

So what?

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Consider the case:

The KM of an enzyme is therefore the substrate concentration at which the reaction occurs at half of the maximum rate.

MKS

Svv

][

][max

MKS

Svv

][

][

2maxmax

][2][ SKS M ][SKM

2maxv

v

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• KM is an indicator of the affinity that an enzyme has for a given substrate, and hence the stability of the enzyme-substrate complex.

• At low [S], it is the availability of substrate that is the limiting factor.

• As more substrate is added there is a rapid increase in the initial rate of the reaction.

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Modeling Bio-Chemical networks

• Enzyme catalyzed reaction

ES PS.E+ E +k1

k2

k3

S.E

t1 : k1[S][E]

E

S P

t2 : k2[S.E]

t3 : k3[S.E]

(a)

(b)E

S P

t4 : Vmax[S] / (KM + [S])

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Modeling and Analysis Techniques in Systems Biology. CS 6221 Lecture 1 P.S. Thiagarajan