1. François Fages New Delhi, Dec.. 2007 Formal Verification and Inference of Biochemical Models François Fages Constraint Programming project-team, INRIA Paris-Rocquencourt, France Main idea: to tackle the complexity of biological systems investigate Programming Theory Concepts Formal Methods of Circuit and Program Verification Automated Reasoning Tools Prototype Implementation in the Biochemical Abstract Machine BIOCHAM modeling environment available at http://contraintes.inria.fr/BIOCHAM

2. François Fages New Delhi, Dec.. 2007 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 behaviors or interactions in large networks of genes and proteins. Systems Biology Markup Language (SBML) : exchange format for reaction models

3. François Fages New Delhi, Dec.. 2007 Issue of Abstraction in Systems Biology Models are built in Systems Biology with two contradictory perspectives :

4. François Fages New Delhi, Dec.. 2007 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

5. François Fages New Delhi, Dec.. 2007 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 !

6. François Fages New Delhi, Dec.. 2007 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 hierarchies 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

7. François Fages New Delhi, Dec.. 2007 Semantics of Living Processes ? Formally, “the” behavior of a system depends on our choice of observables. ? ? Mitosis movie [Lodish et al. 03]

8. François Fages New Delhi, Dec.. 2007 Boolean Semantics Formally, “the” behavior of a system depends on our choice of observables. Presence/absence of molecules over time Boolean transitions 01

9. François Fages New Delhi, Dec.. 2007 Continuous Differential Semantics Formally, “the” behavior of a system depends on our choice of observables. Concentrations of molecules over time Rates of reactions xý

10. François Fages New Delhi, Dec.. 2007 Stochastic Semantics Formally, “the” behavior of a system depends on our choice of observables. Numbers of molecules over time Probabilities of reaction n 

11. François Fages New Delhi, Dec.. 2007 Temporal Logic Semantics Formally, “the” behavior of a system depends on our choice of observables. Presence/absence of molecules over time Temporal logic formulas Fx F x F (x ^ F (  x ^ y)) FG (x v y) …

12. François Fages New Delhi, Dec.. 2007 Constraint Temporal Logic Semantics Formally, “the” behavior of a system depends on our choice of observables. Concentrations of molecules over time Constraint LTL temporal formulas Fx>1x>1 F (x >0.2) F (x >0.2 ^ F (x 0.2)) FG (x>0.2 v y>0.2) …

13. François Fages New Delhi, Dec.. 2007 Language-based Approaches to Cell Systems Biology Qualitative models: from diagrammatic notation to Boolean networks [Kaufman 69, Thomas 73] Petri Nets [Reddy 93, Chaouiya 05] Process algebra 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-Fages 03] [Chabrier-Chiaverini-Danos-Fages-Schachter 04] Quantitative models: from ODEs and stochastic simulations to Hybrid Petri nets [Hofestadt-Thelen 98, Matsuno et al. 00] Hybrid automata [Alur et al. 01, Ghosh-Tomlin 01] HCC [Bockmayr-Courtois 01] Stochastic π–calculus [Priami et al. 03] [Cardelli et al. 06] Reaction rules with continuous time dynamics [Fages-Soliman-Chabrier 04]

14. François Fages New Delhi, Dec.. 2007 Overview of the Talk 1.Rule-based Modeling of Biochemical Systems 1.Syntax of molecules, compartments and reactions 2.Semantics at three abstraction levels: boolean, differential, stochastic 3.Cell cycle control models 2.Temporal Logic Language for Formalizing Biological Properties 1.CTL for the boolean semantics 2.LTL with constraints for the differential semantics 3.Automated Reasoning Tools 1.Inferring kinetic parameter values from Constraint-LTL specification 2.Inferring reaction rules from CTL specification L. Calzone, N. Chabrier, F. Fages, S. Soliman. TCSB VI, LNBI 4220:68-94. 2006. F. Fages, S. Soliman. CMSB’06. F. Fages, A. Rizk CMSB’07.

15. François Fages New Delhi, Dec.. 2007 Syntax of 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 promotion factor

16. François Fages New Delhi, Dec.. 2007 Elementary Reaction Rules Complexation: A + B => A-B Decomplexation A-B => A + B cdk1+cycB => cdk1–cycB

17. François Fages New Delhi, Dec.. 2007 Elementary Reaction Rules 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

18. François Fages New Delhi, Dec.. 2007 Elementary Reaction Rules 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)

19. François Fages New Delhi, Dec.. 2007 Elementary Reaction Rules 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

20. François Fages New Delhi, Dec.. 2007 From Syntax to Semantics R ::= S=>S | S =[O]=> S | S S | S S where A =[C]=> B stands for A+C => B+C A B stands for A=>B and B=>A, etc. | kinetic for R SBML : import/export exchange format, no semantics

21. François Fages New Delhi, Dec.. 2007 From Syntax to Semantics R ::= S=>S | S =[O]=> S | S S | S S where A =[C]=> B stands for A+C => B+C A B stands for A=>B and B=>A, etc. | kinetic for R SBML : import/export exchange format, no semantics BIOCHAM : three abstraction levels 1.Boolean Semantics: presence-absence of molecules 1.Concurrent Transition System (asynchronous, non-deterministic) 2.Differential Semantics: concentration 1.Ordinary Differential Equations or Hybrid system (deterministic) 3.Stochastic Semantics: number of molecules 1.Continuous time Markov chain

22. François Fages New Delhi, Dec.. 2007 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,TCSc’07] Syntactical model

23. François Fages New Delhi, Dec.. 2007 Boolean Semantics Associate to each molecule a Boolean denoting its presence/absence. Compile the rule set into an asynchronous transition system where a reaction like A+B=>C+D is translated into 4 transition rules taking into account the possible complete consumption of reactants: A+B  A+B+C+D A+B   A+B +C+D A+B  A+  B+C+D A+B   A+  B+C+D Necessary for over-approximating the possible behaviors under the stochastic/discrete semantics (abstraction N  {zero, non-zero}) Only the last transition is considered in Pathway logic [Lincoln et al. 02] or Petri nets [Reddy93, Heiner 05, Chaouiya 05]

24. François Fages New Delhi, Dec.. 2007 Type Checking / Inference by Abstract Interpretation Stochastic model Differential model Discrete model abstraction concretization Boolean model Syntactical model [Fages Soliman CMSB ’ 06] Influence graph of proteins Protein functions (kinase, phosphatase, … ) Compartments topology Influence graph of proteins (activation/inhibition)

25. François Fages New Delhi, Dec.. 2007 Hierarchy of Analyses Stochastic model Differential model Discrete model abstraction concretization Boolean model Syntactical model Jacobian circuit analysis Discrete circuit analysis Boolean circuit analysis abstraction Positive circuits are a necessary condition for multistability [Thomas 81] [Soul é 03] [Remy Ruet Thieffry 05] [Kauffman 73]

26. François Fages New Delhi, Dec.. 2007 Example: Cell Cycle Control Model [Tyson 91] MA(k1) for _ => Cyclin. MA(k2) for Cyclin => _. MA(K7) for Cyclin~{p1} => _. MA(k8) for Cdc2 => Cdc2~{p1}. MA(k9) for Cdc2~{p1} =>Cdc2. MA(k3) for Cyclin+Cdc2~{p1} => Cdc2~{p1}-Cyclin~{p1}. MA(k4p) for Cdc2~{p1}-Cyclin~{p1} => Cdc2-Cyclin~{p1}. k4*[Cdc2-Cyclin~{p1}]^2*[Cdc2~{p1}-Cyclin~{p1}] for Cdc2~{p1}-Cyclin~{p1} =[Cdc2-Cyclin~{p1}] => Cdc2-Cyclin~{p1}. MA(k5) for Cdc2-Cyclin~{p1} => Cdc2~{p1}-Cyclin~{p1}. MA(k6) for Cdc2-Cyclin~{p1} => Cdc2+Cyclin~{p1}.

27. François Fages New Delhi, Dec.. 2007 Interaction Graph

28. François Fages New Delhi, Dec.. 2007 Stochastic Simulation

29. François Fages New Delhi, Dec.. 2007 Differential Simulation

30. François Fages New Delhi, Dec.. 2007 Boolean Simulation

31. François Fages New Delhi, Dec.. 2007 Automatic Generation of True CTL Properties Ei(reachable(Cyclin))) Ei(reachable(!(Cyclin)))) Ai(oscil(Cyclin))) Ei(reachable(Cdc2~{p1}))) Ei(reachable(!(Cdc2~{p1})))) Ai(oscil(Cdc2~{p1}))) Ai(AG(!(Cdc2~{p1})->checkpoint(Cdc2,Cdc2~{p1})))) Ei(reachable(Cdc2-Cyclin~{p1,p2}))) Ei(reachable(!(Cdc2-Cyclin~{p1,p2})))) Ai(oscil(Cdc2-Cyclin~{p1,p2}))) Ei(reachable(Cdc2-Cyclin~{p1}))) Ei(reachable(!(Cdc2-Cyclin~{p1})))) Ai(oscil(Cdc2-Cyclin~{p1}))) Ai(AG(!(Cdc2-Cyclin~{p1})->checkpoint(Cdc2-Cyclin~{p1,p2},Cdc2-Cyclin~{p1}))) Ei(reachable(Cdc2))) Ei(reachable(!(Cdc2)))) Ai(oscil(Cdc2))) Ei(reachable(Cyclin~{p1}))) Ei(reachable(!(Cyclin~{p1})))) Ai(oscil(Cyclin~{p1}))) Ai(AG(!(Cyclin~{p1})->checkpoint(Cdc2-Cyclin~{p1},Cyclin~{p1}))))

32. François Fages New Delhi, Dec.. 2007

33. François Fages New Delhi, Dec.. 2007 Mammalian Cell Cycle Control Map [Kohn 99]

34. François Fages New Delhi, Dec.. 2007 Cell Cycle Model-Checking (with BDD NuSMV) biocham: check_reachable(cdk46~{p1,p2}-cycD~{p1}). Ei(EF(cdk46~{p1,p2}-cycD~{p1})) is true biocham: check_checkpoint(cdc25C~{p1,p2}, cdk1~{p1,p3}-cycB). Ai(!(E(!(cdc25C~{p1,p2}) U cdk1~{p1,p3}-cycB))) is true biocham: nusmv(Ai(AG(!(cdk1~{p1,p2,p3}-cycB) -> checkpoint(Wee1, cdk1~{p1,p2,p3}-cycB))))). Ai(AG(!(cdk1~{p1,p2,p3}-cycB)->!(E(!(Wee1) U cdk1~{p1,p2,p3}-cycB)))) is false biocham: why. -- Loop starts here cycB-cdk1~{p1,p2,p3} is present cdk7 is present cycH is present cdk1 is present Myt1 is present cdc25C~{p1} is present rule_114 cycB-cdk1~{p1,p2,p3}=[cdc25C~{p1}]=>cycB-cdk1~{p2,p3}. cycB-cdk1~{p2,p3} is present cycB-cdk1~{p1,p2,p3} is absent rule_74 cycB-cdk1~{p2,p3}=[Myt1]=>cycB-cdk1~{p1,p2,p3}. cycB-cdk1~{p2,p3} is absent cycB-cdk1~{p1,p2,p3} is present

35. François Fages New Delhi, Dec.. 2007 Mammalian Cell Cycle Control Benchmark 165 genes and proteins. 500 variables, 2 500 states. 800 rules. BIOCHAM NuSMV model-checker time in sec. [Chabrier et al. TCS 04] Initial state G2Query:Time: compiling29 s Reachability G1EF CycE2 s Reachability G1EF CycD1.9 s Reachability G1EF PCNA-CycD1.7 s Checkpoint for mitosis complex  EF (  Cdc25~{Nterm} U Cdk1~{Thr161}-CycB) 2.2 s Oscillation EG ( (CycA => EF  CycA) ^ (  CycA => EF CycA)) 31.8 s

36. François Fages New Delhi, Dec.. 2007 Temporal Logic with Constraints over the Reals Constraints over concentrations and derivatives as FOL formulae over the reals: [M] > 0.2 [M]+[P] > [Q] d([M])/dt < 0

37. François Fages New Delhi, Dec.. 2007 Temporal Logic with Constraints over the Reals Constraints over concentrations and derivatives as FOL formulae over the reals: [M] > 0.2 [M]+[P] > [Q] d([M])/dt < 0 Linear Time Logic LTL operators for time X, F, U, G F([M]>0.2) FG([M]>0.2) F ([M]>2 & F (d([M])/dt 0 & F(d([M])/dt<0)))) oscil(M,n) defined as at least n alternances of sign of the derivative Period(A,75)=  t  v F(T = t & [A] = v & d([A])/dt > 0 & X(d([A])/dt < 0) & F(T = t + 75 & [A] = v & d([A])/dt > 0 & X(d([A])/dt < 0)))…

38. François Fages New Delhi, Dec.. 2007 Example: Cell Cycle Control Model [Tyson 91] MA(k1) for _ => Cyclin. MA(k2) for Cyclin => _. MA(K7) for Cyclin~{p1} => _. MA(k8) for Cdc2 => Cdc2~{p1}. MA(k9) for Cdc2~{p1} =>Cdc2. MA(k3) for Cyclin+Cdc2~{p1} => Cdc2~{p1}-Cyclin~{p1}. MA(k4p) for Cdc2~{p1}-Cyclin~{p1} => Cdc2-Cyclin~{p1}. k4*[Cdc2-Cyclin~{p1}]^2*[Cdc2~{p1}-Cyclin~{p1}] for Cdc2~{p1}-Cyclin~{p1} =[Cdc2-Cyclin~{p1}] => Cdc2-Cyclin~{p1}. MA(k5) for Cdc2-Cyclin~{p1} => Cdc2~{p1}-Cyclin~{p1}. MA(k6) for Cdc2-Cyclin~{p1} => Cdc2+Cyclin~{p1}.

39. François Fages New Delhi, Dec.. 2007 3.1 Inferring Parameters from Temporal Properties biocham: learn_parameter([k3,k4],[(0,200),(0,200)],20, oscil(Cdc2-Cyclin~{p1},3),150).

40. François Fages New Delhi, Dec.. 2007 3.1 Inferring Parameters from Temporal Properties biocham: learn_parameter([k3,k4],[(0,200),(0,200)],20, oscil(Cdc2-Cyclin~{p1},3),150). First values found : parameter(k3,10). parameter(k4,70).

41. François Fages New Delhi, Dec.. 2007 3.1 Inferring Parameters from Temporal Properties biocham: learn_parameter([k3,k4],[(0,200),(0,200)],20, oscil(Cdc2-Cyclin~{p1},3) & F([Cdc2-Cyclin~{p1}]>0.15), 150). First values found : parameter(k3,10). parameter(k4,120).

42. François Fages New Delhi, Dec.. 2007 3.1 Inferring Parameters from LTL Specification biocham: learn_parameter([k3,k4],[(0,200),(0,200)],20, period(Cdc2-Cyclin~{p1},35), 150). First values found: parameter(k3,10). parameter(k4,280).

43. François Fages New Delhi, Dec.. 2007 Leloup and Goldbeter (1999) MPF preMPF Wee1 Wee1P Cdc25 Cdc25P APC.. Cell cycle Linking the Cell and Circadian Cycles through Wee1 BMAL1/CLOCK PER/CRY Circadian cycle Wee1 mRNA L [L. Calzone, S. Soliman 2006]

44. François Fages New Delhi, Dec.. 2007 PCN Wee1m Wee1 MPF BN Cdc25

45. François Fages New Delhi, Dec.. 2007 entrainment Condition on Wee1/Cdc25 for Period Synchronization Period synchronization constraint expressed in LTL with the period formula

46. François Fages New Delhi, Dec.. 2007 Inferring Rules from Temporal Properties Given a BIOCHAM model (background knowledge) a set of properties formalized in temporal logic learn revisions of the reaction model, i.e. rules to delete and rules to add such that the revised model satisfies the properties

47. François Fages New Delhi, Dec.. 2007 Model Revision from Temporal Properties Background knowledge T: BIOCHAM model reaction rule language: complexation, phosphorylation, … Examples φ: biological properties formalized in temporal logic language Reachability Checkpoints Stable states Oscillations Bias R: Reaction rule patterns or parameter ranges Kind of rules to add or delete Find a revision T’ of T such that T’ |= φ

48. François Fages New Delhi, Dec.. 2007 Model Revision Algorithm General idea of constraint programming: replace a generate-and-test algorithm by a constrain-and-generate algorithm. Anticipate whether one has to add or remove a rule. Positive ECTL formula: if false, remains false after removing a rule EF(φ) where φ is a boolean formula (pure state description) Oscil(φ) Negative ACTL formula: if false, remains false after adding a rule AG(φ) where φ is a boolean formula, Checkpoint(a,b): ¬E(¬aUb) Remove a rule on the path given by the model checker ( why command) Unclassified CTL formulae

49. François Fages New Delhi, Dec.. 2007 Theory Revision Algorithm Rules Initial state: E transition:  if R |= e E’ transition:  if R |≠ e and  f  {e}  E  U  A, K  {r} |= f

50. François Fages New Delhi, Dec.. 2007 Theory Revision Algorithm Rules Initial state: E transition:  if R |= e E’ transition:  if R |≠ e and  f  {e}  E  U  A, K  {r} |= f U transition:  if R |= u U’ transition:  if R|≠u and  f  {u}  E  U  A, R  {r} |= f U” transition:  if K, si|≠u and  f  {u}  E  U  A, R |= f

51. François Fages New Delhi, Dec.. 2007 Theory Revision Algorithm Rules Initial state: E transition:  if R |= e E’ transition:  if R |≠ e and  f  {e}  E  U  A, K  {r} |= f U transition:  if R |= u U’ transition:  if R|≠u and  f  {u}  E  U  A, R  {r} |= f U” transition:  if K, si|≠u and  f  {u}  E  U  A, R |= f A transition:  if R |= a A’ transition:  if R|≠ a,  f  {u} [ E  U  A, R |= f and Ep  Up is the set of formulae no longer satisfied after the deletion of the rules in Re.

52. François Fages New Delhi, Dec.. 2007 Termination Proposition The model revision algorithm terminates. Proof The termination of the algorithm is proved by considering the lexicographic ordering over the couple where a is the number of unsatisfied ACTL formulae, and n is the number of unsatisfied ECTL and UCTL formulae. Each transition strictly decreases a, or lets a unchanged and strictly decreases n.

53. François Fages New Delhi, Dec.. 2007 Correctness Proposition If the terminal configuration is of the form then the model R satisfies the initial CTL specification. Proof Each transition maintains only true formulae in the satisfied set, and preserves the complete CTL specification in the union of the satisfied set and the untreated set.

54. François Fages New Delhi, Dec.. 2007 Incompleteness Two reasons: 1)The satisfaction of ECTL and UCTL formula is searched by adding only one rule to the model (transition E’ and U’) 2)The Kripke structure associated to a Biocham set of rules adds loops on terminal states. Hence adding or removing a rule may have an opposite deletion or addition of those loops.

55. François Fages New Delhi, Dec.. 2007 Rule Inference in Cell Cycle Control [Tyson et al. 91] model over 6 variables, initial state present(cdc2). _=>Cyclin. Cyclin=>_. Cyclin+Cdc2~{p1}=>Cdc2-Cyclin~{p1,p2}. Cdc2-Cyclin~{p1,p2}=>Cdc2-Cyclin~{p1}. Cdc2-Cyclin~{p1,p2}=[Cdc2-Cyclin~{p1}]=>Cdc2-Cyclin~{p1}. Cdc2-Cyclin~{p1}=>Cdc2-Cyclin~{p1,p2}. Cdc2-Cyclin~{p1}=>Cyclin~{p1}+Cdc2. Cyclin~{p1}=>_. Cdc2=>Cdc2~{p1}. Cdc2~{p1}=>Cdc2.

56. François Fages New Delhi, Dec.. 2007 Automatic Generation of True CTL Properties Ei(reachable(Cyclin))) Ei(reachable(!(Cyclin)))) Ai(oscil(Cyclin))) Ei(reachable(Cdc2~{p1}))) Ei(reachable(!(Cdc2~{p1})))) Ai(oscil(Cdc2~{p1}))) Ai(AG(!(Cdc2~{p1})->checkpoint(Cdc2,Cdc2~{p1})))) Ei(reachable(Cdc2-Cyclin~{p1,p2}))) Ei(reachable(!(Cdc2-Cyclin~{p1,p2})))) Ai(oscil(Cdc2-Cyclin~{p1,p2}))) Ei(reachable(Cdc2-Cyclin~{p1}))) Ei(reachable(!(Cdc2-Cyclin~{p1})))) Ai(oscil(Cdc2-Cyclin~{p1}))) Ai(AG(!(Cdc2-Cyclin~{p1})->checkpoint(Cdc2-Cyclin~{p1,p2},Cdc2-Cyclin~{p1}))) Ei(reachable(Cdc2))) Ei(reachable(!(Cdc2)))) Ai(oscil(Cdc2))) Ei(reachable(Cyclin~{p1}))) Ei(reachable(!(Cyclin~{p1})))) Ai(oscil(Cyclin~{p1}))) Ai(AG(!(Cyclin~{p1})->checkpoint(Cdc2-Cyclin~{p1},Cyclin~{p1}))))

57. François Fages New Delhi, Dec.. 2007 Model Compression biocham: reduce_model. 1: deleting Cyclin=>_ 2: deleting Cdc2-Cyclin~{p1,p2}=[Cdc2-Cyclin~{p1}]=>Cdc2- Cyclin~{p1} 3: deleting Cdc2-Cyclin~{p1}=>Cdc2-Cyclin~{p1,p2} 4: deleting Cdc2~{p1}=>Cdc2 After reduction, 6 rules remain corresponding to the bias ? => ? Deletion(s): Cyclin=>_. Cdc2-Cyclin~{p1,p2}=[Cdc2-Cyclin~{p1}]=>Cdc2-Cyclin~{p1}. Cdc2-Cyclin~{p1}=>Cdc2-Cyclin~{p1,p2}. Cdc2~{p1}=>Cdc2.

58. François Fages New Delhi, Dec.. 2007 Rule Deletion biocham: delete_rules(Cdc2 => Cdc2~{p1}). biocham: check_all. First formula not satisfied Ei(EF(Cdc2-Cyclin~{p1}))

59. François Fages New Delhi, Dec.. 2007 Model Revision from Temporal Properties biocham: revise_model. 1: adding Cdc2-Cdc2~{p1}=>Cdc2+Cdc2~{p1} 2: adding Cdc2=>_ 2: backtracking on previous add -> deleting Cdc2=>_ 2: adding Cdc2=[Cyclin]=>_ 2: backtracking on previous add -> deleting Cdc2=[Cyclin]=>_ 2: adding Cdc2=[Cdc2-Cdc2~{p1}]=>_ 3: adding Cdc2=>Cdc2~{p1} 4: deleting Cdc2=[Cdc2-Cdc2~{p1}]=>_ 5: deleting Cdc2-Cdc2~{p1}=>Cdc2+Cdc2~{p1} Modifications found Deletion(s) Addition(s): Cdc2=>Cdc2~{p1}.

60. François Fages New Delhi, Dec.. 2007 Search for all Solutions biocham: learn_one_addition(elementary_interaction_rules). Time: 5.00 s Rules tested: 112 Solutions found: 3 Cdc2=>Cdc2~{p1} Cdc2=[Cdc2]=>Cdc2~{p1} Cdc2=[Cyclin]=>Cdc2~{p1}

61. François Fages New Delhi, Dec.. 2007 Conclusion Temporal logic with constraints is powerful enough to express both qualitative and quantitative biological properties of systems SBML models are interpreted under three semantics in BIOCHAM : Boolean semantics CTL formulas (rule learning) Differential semantics LTL with constraints over reals (parameter search) Stochastic semantics Probabilistic CTL with integer constraints Parameter search from temporal properties proved useful and complementary to bifurcation theory tools (Xppaut) Rule inference from temporal properties will benefit from types (e.g. protein functions, influences …) to better prune the search.

62. François Fages New Delhi, Dec.. 2007 Collaborations EU STREP APrIL2 : Stephen Muggleton, IC, Luc de Raedt, U. Freiburg,… Learning in a probabilistic logic setting (finished) INRIA ARC MOCA : modularity, compositionality and abstraction EU NoE REWERSE : semantic web, François Bry, Münich, R. Backofen, Connecting Biocham to gene and protein ontologies (types) EU STREP TEMPO : Cancer chronotherapies, INSERM Villejuif, F. Lévi; INRIA J. Clairambault, S. Soliman Coupled models of cell cycle, circadian cycle, cytotoxic drugs. INRA Tours : E. Reiter, D. Heitzler, INRIA F. Clément Model of FSH signaling.