New Computational Methods for Systems Biology

Transcription

1 New Computational Methods for Systems Biology François Fages, Sylvain Soliman The French National Institute for Research in Computer Science and Control INRIA Paris-Rocquencourt Constraint Programming Group 1

2 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& Systems Biology Markup Language (SBML): model exchange format SBML model repositories: e.g. biomodels.net 241 curated models 2

3 Issue of Abstraction in Systems Biology Models are built in Systems Biology with two contradictory perspectives : 3

4 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 4

5 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! 5

6 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 6

7 Formal Semantics of Living Processes? Formally, the behavior of a system depends on our choice of observables.?? Mitosis movie [Lodish et al. 03] 7

8 Boolean Semantics " Formally, the behavior of a system depends on our choice of observables. " Presence/absence of molecules " Boolean transitions 0 1 Mitosis movie [Lodish et al. 03] 8

9 Continuous Differential Semantics " Formally, the behavior of a system depends on our choice of observables. " Concentrations of molecules " Rates of reactions x ý Mitosis movie [Lodish et al. 03] 9

10 Stochastic Semantics " Formally, the behavior of a system depends on our choice of observables. " Numbers of molecules " Probabilities of reaction n τ Mitosis movie [Lodish et al. 03] 10

11 Temporal Logic LTL " Formally, the behavior of a system depends on our choice of observables. " Presence/absence of molecules " Temporal logic formulas F x F x F (x ^ F ( x ^ y)) FG (x v y) & Mitosis movie [Lodish et al. 03] 11

12 Temporal Logic LTL(R) " Formally, the behavior of a system depends on our choice of observables. " 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) & Mitosis movie [Lodish et al. 03] 12

13 Hierarchy of Semantics abstraction Boolean model Discrete model Theory of abstract Interpretation Abstractions as Galois connections [Cousot Cousot POPL 77] [Fages Soliman CMSB 06,TCS 07] Stochastic model Differential model concretization 13 Syntactical model

14 refinement Hierarchy of Model Reductions 011_levc reduction MAPK models from the SBML model repository 4 graphical operations delete/merge molecules/reactions subgraph morphisms A graphical method for reducing and relating models [Gay Fages Soliman 2010 ECCB, Bioinformatics] 14

15 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) " Parameter search in high dimension w.r.t. LTL(R) specifications " Robustness and sensitivity analyses w.r.t. LTL(R) specifications 4. Conclusion 15

16 Cell Molecules " Small molecules: covalent bonds 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 ( amino acids) RNA ( nucleotides AGCU) DNA ( nucleotides AGCT) 16

17 Formal Genes: Syntax " Part of DNA #E2 " Activation binding of promotion factor #E2-(E2f13-DP12) " Repression (inhibition) Genes and signals [Ptashne Gann 01] binding of another molecule #E2-Rep 17

18 Transcription and Translation Rules Activation #E2 + E2f13 DP12 => #E2 E2f13 DP12 Repression #E2 + Rep => #E2 Rep Genes and signals [Ptashne Gann 01] 18

19 Transcription and Translation Rules Activation #E2 + E2f13 DP12 => #E2 E2f13 DP12 Repression #E2 + Rep => #E2 Rep Transcription _ =[#E2 E2F13 DP12]=> prnacyca 19

20 Transcription and Translation Rules Activation #E2 + E2f13 DP12 => #E2 E2f13 DP12 Repression #E2 + Rep => #E2 Rep Transcription _ =[#E2 E2F13 DP12]=> prnacyca (Alternative) Splicing prnacyca => mrnacyca (prnacyca => mrnacyca2) 20

21 Transcription and Translation Rules Activation #E2 + E2f13 DP12 => #E2 E2f13 DP12 Repression #E2 + Rep => #E2 Rep Transcription _ =[#E2 E2F13 DP12]=> prnacyca (Alternative) Splicing prnacyca => mrnacyca Translation mrnacyca => mrnacyca::cyt (prnacyca => mrnacyca2) mrnacyca::cyt + ribosome::cyt => cyca::cyt + ribosome::cyt (mrnacyca2::cyt + ribosome::cyt => cyca2::cyt + ribosome::cyt) 21

22 Formal Proteins: Syntax " Cyclin dependent kinase 1 Cdk1 (free, inactive) 22

23 Formal Proteins: Syntax " Cyclin dependent kinase 1 Cdk1 (free, inactive) " Complex Cdk1-Cyclin B Cdk1 CycB (low activity) 23

24 Formal Proteins: Syntax " Cyclin dependent kinase 1 Cdk1 (free, inactive) " Complex Cdk1-Cyclin B Cdk1 CycB (low activity) " Phosphorylated form Cdk1~{thr161} CycB at site threonine 161 (high activity) 24

25 Formal Proteins " Cyclin dependent kinase 1 Cdk1 (free, inactive) " Complex Cdk1-Cyclin B Cdk1 CycB (low activity) " Phosphorylated form Cdk1~{thr161} CycB at site threonine 161 (high activity) Mitosis-Promoting Factor phosphorylates actin in microtubules nuclear division 25

26 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. Cdk1 CycB =[Myt1]=> Cdk1~{thr161} CycB Cdk1~{thr14,tyr15} CycB =[Cdc25~{Nterm}]=> Cdk1 CycB " Synthesis: _ =[C]=> A. Degradation: A =[C]=> _. _=[#E2 E2f13 Dp12]=>cycA cyce =[@UbiPro]=> _ (not for cyce cdk2 which is stable) " Transport: A::L1 => A::L2. Cdk1~{p} CycB::cytoplasm=>Cdk1~{p} CycB::nucleus 26

27 Biocham Syntax of Objects Entities E == name E E 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 location: symbolic compartment (nucleus, cytoplasm, membrane, & ) dynamic volume 27

28 Biocham Syntax of Rules Solutions S ::= _ O + S i*o + S + : solution operator (Associative, Commutative, Neutral element _) Rules R ::= S => S kinetic expression 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 Import/export exchange format for reaction models Biomodels.net: repository of 241 curated SBML models of cell processes 28

29 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) 29

30 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) " Stochastic Semantics: numbers of molecules Continuous time Markov chain A, B p A--, B--, C++ 30

31 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) " Stochastic Semantics: numbers of molecules Continuous time Markov chain A, B p A--, B--, C++ " Boolean Semantics: presence-absence of molecules Asynchronous Transition System A, B C, A/ A, B/ B 31