New Computational Methods for Systems Biology

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New Computational Methods for Systems Biology

François Fages, Sylvain Soliman

The French National Institute for Research in Computer Science and Control

INRIA Paris-Rocquencourt

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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 behavior of large networks of genes and proteins;

" Multi-scale models of cell processes, tissues, organisms, ecosystems&

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Issue of Abstraction in Systems Biology

Models are built in Systems Biology with two contradictory perspectives :

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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

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Issue of Abstraction in Systems Biology

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

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Issue of Abstraction in Systems Biology

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

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Formal Semantics of Living Processes ?

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

? ?

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Boolean Semantics

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

" Presence/absence of molecules

" Boolean transitions

0 1

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Continuous Differential Semantics

" Concentrations of molecules

" Rates of reactions

x ý

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Stochastic Semantics

" Numbers of molecules

" Probabilities of reaction

n τ

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Temporal Logic LTL

" Presence/absence of molecules

" Temporal logic formulas

F x

F (x ^ F ( ¬ x ^ y)) FG (x v y)

&

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Temporal Logic LTL(R)

" Concentrations of molecules

" TL with Constraints over R

F x

>1

F (x >0.2)

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

&

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Hierarchy of Semantics

Stochastic model Differential model Discrete model

abstraction

Boolean model

Theory of abstract Interpretation

Abstractions as Galois connections

[Cousot Cousot POPL 77]

[Fages Soliman CMSB 06,TCS 07]

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Hierarchy of Model Reductions

011_levc

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

reduction

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Overview of the Tutorial

1. Introduction

" Transposing programming concepts to the analysis of living processes 2. Rule-based modeling of biochemical systems

" Syntax: molecules, reactions, regulations, SBML/SBGN Biocham notations

" Semantics: Boolean, Differential and Stochastic interpretations of reactions

" Static analyses: consistency, influence graph circuits, protein functions,&

" Examples in cell signaling, gene expression, virus infection, cell cycle 3. Temporal Logic based formalization of biological properties

" Qualitative model-checking in propositional Computation Tree Logic CTL

" Quantitative model-checking in Linear Time Logic LTL(R)

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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) RNA (10²-10⁴ nucleotides AGCU)

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Formal Genes: Syntax

" Part of DNA #E2

" Activation

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

" Repression (inhibition) Genes and signals [Ptashne Gann 01]

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Transcription and Translation Rules

Activation

#E2 + E2f13DP12 => #E2E2f13DP12 Repression

#E2 + Rep => #E2Rep

Genes and signals [Ptashne Gann 01]

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Transcription and Translation Rules

Activation

#E2 + Rep => #E2Rep Transcription

_ =[#E2E2F13DP12]=> pRNAcycA

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Transcription and Translation Rules

Activation

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

pRNAcycA => mRNAcycA (pRNAcycA => mRNAcycA2)

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Transcription and Translation Rules

Activation

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

pRNAcycA => mRNAcycA (pRNAcycA => mRNAcycA2)

Translation

mRNAcycA => mRNAcycA::cyt

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Formal Proteins: Syntax

" Cyclin dependent kinase 1 Cdk1 (free, inactive)

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Formal Proteins: Syntax

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

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Formal Proteins: Syntax

" Phosphorylated form Cdk1~{thr161}CycB at site threonine 161

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Formal Proteins

" Phosphorylated form Cdk1~{thr161}CycB at site threonine 161

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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}CycB

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

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

_=[#E2E2f13Dp12]=>cycA cycE =[@UbiPro]=> _

(not for cycEcdk2 which is stable)

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Biocham Syntax of Objects

Entities E == name | EE | E~{p1,…,pn}

name of molecular compound or #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).

Objects O == E | E::location

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Biocham Syntax of Rules

Solutions S ::= _ | O + S | i*O + S + : solution operator (Associative, Commutative, Neutral element _)

Rules R ::= S => S | kineticexpression for R Abbreviations for catalytic reactions: A =[C]=> B stands for A+C => B+C reversible reactions: A <=> B stands for A=>B and B=>A,

Syntax compatible with the Systems Biology Markup Language SBML

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Semantics of Rule-based Models

Reaction rule k*[A]*[B] for A+B => C

" Differential Semantics: concentrations

Ordinary Differential Equations dA/dt = -k*[A]*[B]

dB/dt = -k*[A]*[B]

dC/dt = k*[A]*[B]

Hybrid automata (for kinetics with conditional expressions)

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Semantics of Rule-based Models

dB/dt = -k*[A]*[B]

dC/dt = k*[A]*[B]

" Stochastic Semantics: numbers of molecules

Continuous time Markov chain A, B p A--, B--, C++

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Semantics of Rule-based Models

dB/dt = -k*[A]*[B]

dC/dt = k*[A]*[B]

" Stochastic Semantics: numbers of molecules

Continuous time Markov chain A, B p A--, B--, C++