Computational Methods for Systems Biology and Synthetic...

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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 1

Computational Methods for Systems Biology and Synthetic

Biology

François Fages, Constraint Programming Group

INRIA Paris-Rocquencourtmailto:Francois.Fages@inria.frhttp://contraintes.inria.fr/

Overview of the Lectures

1. Introduction

" Transposing concepts from programming to the analysis of living processes

2. Rule-based Modeling in Biocham

" Macromolecules, compartments and elementary processes in the cell

" Boolean, Differential and Stochastic interpretations of reaction rules

" Cell signaling, Gene expression, Retrovirus, Cell cycle

3. Temporal Logic constraints in Biocham

" Qualitative properties in propositional Computation Tree Logic CTL

" Quantitative properties in quantifier-free Linear Time Logic LTL(R)

" Parameter optimization and robustness w.r.t. temporal logic properties

" Conclusion

" Killer lecture: abstract interpretation in Biocham

References

A wonderful textbook:

Molecular Cell Biology. 5th Edition, 1100 pages+CD, Freeman Publ.

Lodish, Berk, Zipursky, Matsudaira, Baltimore, Darnell. Nov. 2003.

Formal Cell Biology in BIOCHAM (tutorial). François Fages and Sylvain Soliman.

8th International School on Computational Systems Biology.

ISpringer-Verlag, LNCS 5016. Mar. 2008.(pdf)

The Biochemical Abstract Machine BIOCHAM. http://contraintes.inria.fr/BIOCHAM

Modeling dynamic phenomena in molecular and cellular biology.

Segel. Cambridge Univ. Press. 1987.

Systems Biology ?

�Systems Biology aims at systems-level understanding [which]

requires a set of principles and methodologies that links the

behaviors of molecules to systems characteristics and functions.�

H. Kitano, ICSB 2000

" Analyze (post-)genomic data produced with high-throughput technologies (stored in databases like GO, KEGG, BioCyc, etc.);

" Integrate heterogeneous data about a specific problem;

" Understand and predict the behaviors of large networks of genes and proteins.

Systems Biology Markup Language (SBML): model exchange format SBML model repositories: e.g. biomodels.net 261 curated models

Issue of Abstraction in Systems Biology

Models are built in Systems Biology with two contradictory perspectives :

1) Models for representing knowledge : the more concrete the better

2) Models for making predictions : the more abstract the better !

These perspectives can be reconciled by organizing formalisms and models into a hierarchy of abstractions.

To understand a system is not to know everything about it but to know

abstraction levels that are sufficient for answering questions about it

Formal Semantics of Living Processes ?

Formally, � the� behavior of a system depends on our choice of observables.

Mitosis movie [Lodish et al. 03]

Boolean Semantics

" Formally, � the� behavior of a system depends on our choice of observables.

" Presence/absence of molecules

" Boolean transitions

Continuous Differential Semantics

" Concentrations of molecules

" Rates of reactions

Stochastic Semantics

" Numbers of molecules

" Probabilities of reaction

Temporal Logic LTL

" Presence/absence of molecules

" Temporal logic formulas

F xF x

F (x ^ F (¬ x ^ y))

FG (x v y)

Temporal Logic LTL(R)

" Concentrations of molecules

" TL with Constraints over R

F x>1F (x >0.2)

F (x >0.2 ^ F (x<0.1 ^ y>0.2))

FG (x>0.2 v y>0.2)

Hierarchy of Semantics

Stochastic model

Differential model

Discrete model

abstraction

concretization

Boolean model

Theory of abstract Interpretation

Abstractions as Galois connections

[Cousot Cousot POPL� 77]

[Fages Soliman CMSB� 06,TCS� 07]

Syntactical

Regulation Graph as Abstraction

Stochastic model

Differential model

Discrete model

abstraction

concretization

Boolean model

Syntactical

model[Fages Soliman CMSB’06]

Syntactic regulation graph

(pos/neg influences w.r.t.

the stoichiometric coef.

in rules)

Thm. Same graphs for

monotonic kinetics

Jacobian regulation graph

(pos/neg influences w.r.t.

the sign of the coefficients)

Regulation Graphs Circuit Analyses

Stochastic model

Differential model

Discrete model

abstraction

concretization

Boolean model

Syntactical

Jacobian circuit analysis

Discrete circuit analysis

Boolean circuit analysisabstraction

abstraction

Thm. Positive circuits are a necessary condition for multistationarity

[Thomas 81] [Soulé 03]

[Remy Ruet Thieffry 05]

[Richard 07]

Reducing and Relating Models

Models of circadian clock in http://www.biomodels.net Reductions as reaction subgraph epimorphisms [Gay Fages Soliman ECCB� 10]

Overview of the Lectures

1. Introduction

" Transposing concepts from programming to the analysis of living processes

2. Rule-based Modeling in Biocham

" Macromolecules, compartments and elementary processes in the cell

" Boolean, Differential and Stochastic interpretations of reaction rules

" Cell signaling, cell cycle models

3. Temporal Logic constraints in Biocham

" Qualitative properties in propositional Computation Tree Logic CTL

" Quantitative properties in quantifier-free Linear Time Logic LTL(R)

" Model inference from temporal logic properties

" Conclusion

" Killer lecture: abstract interpretation in Biocham

Cell Molecules

" Small molecules: covalent bonds 50-200 kcal/mol

� 70% water

� 1% ions

� 6% amino acids (20), nucleotides (5),

� fats, sugars, ATP, ADP, &

" Macromolecules: hydrogen bonds, ionic, hydrophobic, Waals 1-5 kcal/mol

Stability and bindings determined by the number of weak bonds: 3D shape

� 20% proteins (50-104 amino acids)

� DNA (102-106 nucleotides AGCT)

� RNA (102-104 nucleotides AGCU)

DNA Deoxyribonucleic Acid

1) Primary structure: word over 4 nucleotides

Adenine, Guanine, Cytosine, Thymine

DNA Deoxyribonucleic Acid

1) Primary structure: word over 4 nucleotides

Adenine, Guanine, Cytosine, Thymine

2) Secondary structure:

double helix of pairs A--T and C---G

stabilized by hydrogen bonds

Size of DNA = number of pairs

Genes are parts of DNA

Nobel Prizes Watson and Crick (1956)

DNA: Genome Size

140 Gb&

15 Gb&

100 %1 circular5 MbE. Coli (bacteria)

Coding DNAChromosomesGenome sizeSpecies

Artificial life by Craig Venter:fully synthetic bacteria genome (0,39 $/b)implemented in a bacteria without DNA still living and proliferating!

DNA: Genome Size

140 Gb&

15 Gb&

70 %1612 MbS. Cerevisae (yeast)

DNA: Genome Size

140 Gb&

15 Gb&

15 %20, 233 GbMouse, Human

3,200,000,000 pairs of nucleotides

single nucleotide polymorphism 1 / 2kb

Genome Size

140 Gb&

1 %815 GbOnion

100 %14 MbE. Coli (bacteria)

Genome Size

0.7 %140 GbLungfish

1 %815 GbOnion

100 %14 MbE. Coli (bacteria)

DNA Replication

1. Separation of the two helices

2. Production of one complementary strand for each copy

(from one or several starting points of replication)

3. Segregation

4. Mitosis (cell division)

Gene Transcription and Translation

" Activation (Inhibition): Nobel prize Jakob and Monod (1965)

transcription factors bind to the regulatory region of the gene

2. Transcription:

RNA polymerase copies the DNA from start to stop positions

into a single stranded pre-mature messenger pRNA

3. (Alternative) splicing:

non coding regions of pRNA are removed giving mature messenger mRNA

4. Translation:

mRNA moves to cytoplasm and binds to ribosome to assemble a protein

Formal Genes: Syntax

" Part of DNA, unique #E2

" Activation

binding of promotion factor #E2-(E2f13-DP12)

" Repression (inhibition)

binding of another molecule #E2-Rep

Transcription and Translation Rules

Activation

#E2 + E2f13DP12 => #E2E2f13DP12Repression

#E2 + Rep => #E2Rep

Activation

#E2 + Rep => #E2RepTranscription

_ =[#E2E2F13DP12]=> pRNAcycA

Activation

_ =[#E2E2F13DP12]=> pRNAcycA(Alternative) Splicing

pRNAcycA => mRNAcycA (pRNAcycA => mRNAcycA2)

Activation

_ =[#E2E2F13DP12]=> pRNAcycA(Alternative) Splicing

pRNAcycA => mRNAcycA (pRNAcycA => mRNAcycA2) Translation

mRNAcycA => mRNAcycA::cyt mRNAcycA::cyt + ribosome::cyt => cycA::cyt + ribosome::cyt(mRNAcycA2::cyt + ribosome::cyt => cycA2::cyt + ribosome::cyt)

Proteins

1) Primary structure: word of n amino acids residues (20n possibilities)

linked with C-N bonds

Proteins

Example: MPRI

Methionine-Proline-Arginine-Isoleucine

Proteins

Example: MPRI

2) Secondary: word of m α−helix, β−strands, random coils,& (3m-10m)

stabilized by hydrogen bonds H---O

Proteins

Example: MPRI

2) Secondary: word of m α−helix, β−strands, random coils,& (3m-10m)

stabilized by hydrogen bonds H---O

3) Tertiary 3D structure: spatial folding

stabilized by hydrophobic interactions

explains the protein interaction capabilities

Formal Proteins: Syntax" Cyclin dependent kinase 1 Cdk1

(free, inactive)

" Complex Cdk1-Cyclin B Cdk1–CycB(low activity)

(free, inactive)

" Phosphorylated form Cdk1~{thr161}CycBat site threonine 161

(high activity)

Formal Proteins" Cyclin dependent kinase 1 Cdk1

(free, inactive)

" Phosphorylated form Cdk1~{thr161}CycBat site threonine 161

(high activity)

�Mitosis-Promoting Factor�

phosphorylates actin in microtubules nuclear division

Elementary Rule Schemas" Complexation: A + B => A-B. Decomplexation A-B => A + B.

cdk1+cycB => cdk1–cycB

" Phosphorylation: A =[C]=> A~{p}. Dephosphorylation A~{p} =[C]=> A.

Cdk1CycB =[Myt1]=> Cdk1~{thr161}CycBCdk1~{thr14,tyr15}CycB =[Cdc25~{Nterm}]=> Cdk1CycB

" Synthesis: _ =[C]=> A. Degradation: A =[C]=> _.

_=[#E2E2f13Dp12]=>cycA cycE =[@UbiPro]=> _ (not for cycEcdk2 which is stable)

" Transport: A::L1 => A::L2.

Cdk1~{p}CycB::cytoplasm=>Cdk1~{p}CycB::nucleus

Syntax of Objects E == compound | EE | E~{p1,…,pn}

• compound: name of molecule, #gene binding site• : binding operator for protein complexes, gene binding sites, &

Associative and commutative.• ~{…}: modification operator for phosphorylated sites, &

Set of modified sites (Associative, Commutative, Idempotent).

O == E | E::location

• location: symbolic compartment (nucleus, cytoplasm, membrane, & )

Syntax of RulesS ::= _ | O+S

+ : solution operator (Associative, Commutative, Neutral _)

R ::= S => S | kineticexpression for R

Abbreviations

A =[C]=> B stands for A+C => B+CA <=> B stands for A=>B and B=>A,

Compatible with the Systems Biology Markup Language SBML

exchange format for reaction models

Kinetic Rate Constants

" Complexation: probability of reaction upon collision (specificity, affinity)

position of matching surfaces

" Decomplexation: total energy of all bonds

(giving dissociation rates)

" Diffusion speeds (small molecules>substrates>enzymes& )

Average travel in one random walk: 1 μm in 1s, 2μm in 4s, 10μm in 100s

" For one enzyme:

500000 random collisions per second with a substrate concentration of 10-5

50000 random collisions per second with a substrate concentration of 10-6

From Syntax to Semantics" Boolean Semantics: presence-absence of molecules

� Boolean Transition System

(asynchronous, non-deterministic)

" Discrete semantics: levels of molecules

� Discrete Transition System

" Continuous Semantics: concentrations

� Ordinary Differential Equations

� Deterministic hybrid automata

" Stochastic Semantics: numbers of molecules

� Continuous time Markov chain

Cell Signaling" Signals:

� hormones: insulin, adrenaline, steroids, EGF, & ,

� neighboring cell membrane proteins: Delta

� nutriments, light, pressure, &

Cell Signaling" Signals:

� hormones: insulin, adrenaline, steroids, EGF, & ,

� neighboring cell membrane proteins: Delta

� nutriments, light, pressure, &

" Receptors transmembrane proteins:

� Tyrosine kinases,

� G protein-coupled,

� TGFβ,

� Notch,

� Ionic channels

Receptor Tyrosine Kinase RTK

L + R <=> LRLR + LR => LRLRRASGDP =[LRLR]=> RASGTP

MAPK Signaling Pathways " Input:

RAS activated by the receptor activates RAF

RASGTP + RAFP1433 =>RASGDP + RAF + P1433

" Output:

active MAPK moves to the nucleus

phosphorylates a transcription factor which stimulates gene expression

RAF + … => …… => MAPK~{T183,Y185}

Five MAP Kinase Pathways in Budding Yeast

(Saccharomyces Cerevisiae)

Three Levels MAPK Cascade

MAPK Signaling Cascade in BIOCHAMRAF + RAFK <=> RAFRAFK. RAFRAFK => RAFK + RAF~{p1}. RAF~{p1} + RAFPH <=> RAF~{p1}RAFPH. RAF~{p1}RAFPH => RAF + RAFPH. MEK~$P + RAF~{p1} <=> MEK~$PRAF~{p1} where p2 not in $P. MEK~{p1}RAF~{p1} => MEK~{p1,p2} + RAF~{p1}. MEKRAF~{p1} => MEK~{p1} + RAF~{p1}. MEKPH + MEK~{p1}~$P <=> MEK~{p1}~$PMEKPH. MEK~{p1}MEKPH => MEK + MEKPH. MEK~{p1,p2}MEKPH => MEK~{p1} + MEKPH.MAPK~$P + MEK~{p1,p2} <=> MAPK~$PMEK~{p1,p2} where p2 not in $P. MAPKPH + MAPK~{p1}~$P <=> MAPK~{p1}~$PMAPKPH. MAPK~{p1}MAPKPH => MAPK + MAPKPH. MAPK~{p1,p2}MAPKPH => MAPK~{p1} + MAPKPH. MAPKMEK~{p1,p2} => MAPK~{p1} + MEK~{p1,p2}. MAPK~{p1}MEK~{p1,p2} => MAPK~{p1,p2}+MEK~{p1,p2}.

Pattern variables $P for

- Phosphorylation sites

- Molecules

with symbolic constraints

BIOCHAM rules with patterns are expanded in BIOCHAM rules without patterns

Reaction Hypergraph

Bipartite ProteinsReactions Graph

GraphVizhttp://www.research.att.co/sw/tools/graphvi

Influence Graph inferred from the syntactical reaction model of the MAPK � cascade�

Negative feedback loops[Fages Soliman CMSB 06]

Possibility of oscillations[Qiao et al. PLOS 07]

Influence Graph

Reaction Model of the MAPK Cascade [Levchenko et al. PNAS 2000]

(MA(1), MA(0.4)) for RAF + RAFK <=> RAFRAFK.(MA(0.5),MA(0.5)) for RAF~{p1} + RAFPH <=> RAF~{p1}RAFPH.(MA(3.3),MA(0.42)) for MEK~$P + RAF~{p1} <=> MEK~$PRAF~{p1}

where p2 not in $P.(MA(10),MA(0.8)) for MEKPH + MEK~{p1}~$P <=> MEK~{p1}~$PMEKPH.(MA(20),MA(0.7)) for MAPK~$P + MEK~{p1,p2} <=> MAPK~$PMEK~{p1,p2}

where p2 not in $P.(MA(5),MA(0.4)) for MAPKPH + MAPK~{p1}~$P <=> MAPK~{p1}~$PMAPKPH.MA(0.1) for RAFRAFK => RAFK + RAF~{p1}.MA(0.1) for RAF~{p1}RAFPH => RAF + RAFPH.MA(0.1) for MEK~{p1}RAF~{p1} => MEK~{p1,p2} + RAF~{p1}.MA(0.1) for MEKRAF~{p1} => MEK~{p1} + RAF~{p1}.MA(0.1) for MEK~{p1}MEKPH => MEK + MEKPH.MA(0.1) for MEK~{p1,p2}MEKPH => MEK~{p1} + MEKPH.MA(0.1) for MAPKMEK~{p1,p2} => MAPK~{p1} + MEK~{p1,p2}.MA(0.1) for MAPK~{p1}MEK~{p1,p2} => MAPK~{p1,p2} + MEK~{p1,p2}.MA(0.1) for MAPK~{p1}MAPKPH => MAPK + MAPKPH.MA(0.1) for MAPK~{p1,p2}MAPKPH => MAPK~{p1} + MAPKPH.

Differential Simulation

Stochastic Simulation

Boolean Simulation

Rule-based Models" Reaction rule: k*[A]*[B] for A+B => C

" SBML (Systems Biology Markup Lang.): import/export exchange format

" BIOCHAM three abstraction levels

5. Stochastic Semantics: number of molecules

� Continuous time Markov chain

6. Differential Semantics: concentration

� Ordinary Differential Equations

� Hybrid automata

7. Boolean Semantics: presence-absence of molecules

� Asynchronuous Transition System A & B C & A/¬A & B/¬B

Automatic Generation of CTL Propertiesreachable(MAPK~{p1}))

reachable(!(MAPK~{p1})))

oscil(MAPK~{p1}))&

reachable(MAPKPH-MAPK~{p1}))

reachable(!(MAPKPH-MAPK~{p1})))

oscil(MAPKPH-MAPK~{p1}))

AG(!(MAPKPH-MAPK~{p1})->checkpoint(MAPKPH,MAPKPH-MAPK~{p1})))AG(!(MAPKPH-MAPK~{p1})->checkpoint(MAPK~{p1},MAPKPH-MAPK~{p1})))

reachable(MAPK~{p1,p2}))

reachable(!(MAPK~{p1,p2})))oscil(MAPK~{p1,p2}))

Model Reductions Preserving CTL Properties

After reduction, 20 rules remain.

Deletions:

RAF-RAFK=>RAF+RAFK

RAFPH-RAF~{p1}=>RAFPH+RAF~{p1}

MEK-RAF~{p1}=>MEK+RAF~{p1}

MEKPH-MEK~{p1}=>MEKPH+MEK~{p1}

MAPK-MEK~{p1,p2}=>MAPK+MEK~{p1,p2}

MAPKPH-MAPK~{p1}=>MAPKPH+MAPK~{p1}

MEK~{p1}-RAF~{p1}=>MEK~{p1}+RAF~{p1}

MEKPH-MEK~{p1,p2}=>MEKPH+MEK~{p1,p2}

MAPK~{p1}-MEK~{p1,p2}=>MAPK~{p1}+MEK~{p1,p2}

MAPKPH-MAPK~{p1,p2}=>MAPKPH+MAPK~{p1,p2}

Model Reduction as Reaction Graph Morphism

011_levc

MAPK models from SBML model repository http://www.biomodels.net

A graphical method for reducing and relating models [Gay Fages Soliman 2010 ECCB, Bioinformatics]4 graph operations: Delete/Merge Molecules/Reactions subgraph morphisms

Languages for Cell Systems Biology

Qualitative models: from diagrammatic notation to

" Boolean networks [Thomas 73]

" Petri Nets [Reddy 93]

" Milner� s π� calculus [Regev-Silverman-Shapiro 99-01, Nagasali et al. 00]

" Bio-ambients [Regev-Panina-Silverman-Cardelli-Shapiro 03]

" Pathway logic [Eker-Knapp-Laderoute-Lincoln-Meseguer-Sonmez 02]

" Reaction rules [Chabrier-Chiaverini-Danos-Fages-Schachter 04] BIOCHAM-1, Kappa

Quantitative models: from differential equation systems to

" Hybrid Petri nets [Hofestadt-Thelen 98, Matsuno et al. 00]

" Hybrid automata [Alur et al. 01, Ghosh-Tomlin 01]

" Hybrid concurrent constraint languages [Bockmayr-Courtois 01]

" Stochastic π� calculus [Priami 03, Cardelli 04]

" Rules with continuous/stochastic dynamics BIOCHAM-2, BioNetGen,&

A Logical Paradigm for Systems Biology

Biological process model = Concurrent Transition System

Biological property = Temporal Logic Formula

Biological validation = Model-checking

" [Lincoln et al. PSB� 02] [Chabrier Fages CMSB� 03] [Bernot et al. TCS� 04] &

Model: BIOCHAM Biological Properties:

- Boolean - simulation - Temporal logic CTL

- Differential - query evaluation - LTL(R), QFLTL(R) constraints

- Stochastic - rule learning - CSL

(SBML) - parameter search

Abstractions:

- Influence graph, reductions

A Logical Paradigm for Systems Biology

A Programmer View at Cell ComputationsSize of genome

" 5 Mb for bacteria: normal size program (Biocham binary: 15Mb as yeast)

" 3 Gb for human: normal size of a video not for a program

" 140 Gb for lung fish: nature/disk error !

Speed of interactions

" Protein interactions: enzyme-substrate collisions at 0,5 Mhz, quite slow

" Gene expression: hours ! as reinstalling an operating system

Concurrent computation paradigm

" Chemical metaphor for concurrent programming [Banatre, Le Metayer 78]

" CHAM [Berry 85] to express the operational semantics of the Pi-Calculus

" Membranes for modules: just like cell compartments

Concurrent computation paradigm

" Chemical metaphor for concurrent programming [Banatre, Le Metayer 78]

" CHAM [Berry 85] to express the operational semantics of the Pi-Calculus

" Membranes for modules: just like cell compartments

Hybrid continuous+discrete computations (energy + information)

" Trend for future: more physics in informatics, more informatics in physics

Two-stroke Engine with ATP fuel Myosin + ATP => MyosinATP

MyosinATP => Myosin + ADP

http://www.sci.sdsu.edu/movies

http://www-rocq.inria.fr/sosso/icema2

Actin-Myosin microtubule contraction controlled by MPF that phosphorylates myosin

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