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Abstraction in Systems Biology

Biologie du système de signalisation cellulaire induit par la FSH ASC 2006, projet AgroBi INRIA Rocquencourt Thème “Systèmes symboliques” Projet “Programmation par contraintes” François Fages http://contraintes.inria.fr/. Abstraction in Systems Biology.

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Abstraction in Systems Biology

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  1. Biologie du système de signalisation cellulaire induit par la FSH ASC 2006, projet AgroBiINRIA RocquencourtThème “Systèmes symboliques”Projet “Programmation par contraintes” François Fageshttp://contraintes.inria.fr/

  2. Abstraction in Systems Biology • Models are built in Systems Biology with two contradictory perspectives :

  3. Abstraction in Systems Biology • Models are built in Systems Biology with two contradictory perspectives : • Models for representing knowledge : the more concrete the better

  4. Abstraction in Systems Biology • Models are built in Systems Biology with two contradictory perspectives : • Models for representing knowledge : the more concrete the better • Models for making predictions : the more abstract the better

  5. Abstraction in Systems Biology • Models are built in Systems Biology with two contradictory perspectives : • Models for representing knowledge : the more concrete the better • Models for making predictions : the more abstract the better • These perspectives can be reconciled by organizing models into hierarchies of abstraction. • To understand a system is not to know everything about it but to know abstraction levels that are sufficient to answering questions about it.

  6. A Logical Paradigm for Systems Biology • Biochemical model = Transition system • Biological property = Temporal Logic formula • Biological validation = Model-checking

  7. A Logical Paradigm for Systems Biology • Biochemical model = Transition system • Biological property = Temporal Logic formula • Biological validation = Model-checking • Several abstraction levels : • Boolean : presence/absence of molecules (non-deterministic TS); • Discrete : levels of concentrations (non-deterministic TS); • Differential : concentrations, reaction and transport kinetics (ODE’s) ; • Stochastic : number of molecules (continuous time Markov’s chain).

  8. A Logical Paradigm for Systems Biology • Biochemical model = Transition system • Biological property = Temporal Logic formula • Biological validation = Model-checking • Several abstraction levels : • Boolean : presence/absence of molecules (non-deterministic TS); • Discrete : levels of concentrations (non-deterministic TS); • Differential : concentrations, reaction and transport kinetics (ODE’s) ; • Stochastic : number of molecules (continuous time Markov’s chain). • Biochemical Abstract Machine BIOCHAM : modelling environment • for making in silico experiments http://contraintes.inria.fr/BIOCHAM

  9. Mammalian Cell Cycle Control Map [Kohn 99]

  10. Transcription of Kohn’s Map in BIOCHAM • _ =[ E2F13-DP12-gE2 ]=> cycA. • ... • cycB =[ APC~{p1} ]=>_. • cdk1~{p1,p2,p3} + cycA => cdk1~{p1,p2,p3}-cycA. • cdk1~{p1,p2,p3} + cycB => cdk1~{p1,p2,p3}-cycB. • ... • cdk1~{p1,p3}-cycA =[ Wee1 ]=> cdk1~{p1,p2,p3}-cycA. • cdk1~{p1,p3}-cycB =[ Wee1 ]=> cdk1~{p1,p2,p3}-cycB. • cdk1~{p2,p3}-cycA =[ Myt1 ]=> cdk1~{p1,p2,p3}-cycA. • cdk1~{p2,p3}-cycB =[ Myt1 ]=> cdk1~{p1,p2,p3}-cycB. • ... • cdk1~{p1,p2,p3} =[ cdc25C~{p1,p2} ]=> cdk1~{p1,p3}. • cdk1~{p1,p2,p3}-cycA =[ cdc25C~{p1,p2} ]=> cdk1~{p1,p3}-cycA. • cdk1~{p1,p2,p3}-cycB =[ cdc25C~{p1,p2} ]=> cdk1~{p1,p3}-cycB. 165 proteins and genes, 500 variables, 800 rules [Chabrier et al. 04]

  11. Biological Properties Formalized in Temporal Logic • Properties of wild-life or mutated organisms • reachable(Cdc2~{p1}) • reachable(Cyclin) • reachable(Cyclin~{p1}) • reachable(Cdc2-Cyclin~{p1}) • reachable(Cdc2~{p1}-Cyclin~{p1}) • oscil(Cdc2) • oscil(Cdc2~{p1}) • oscil(Cdc2~{p1}-Cyclin~{p1}) • oscil(Cyclin) • checkpoint(Cdc2~{p1}-Cyclin~{p1},Cdc2-Cyclin~{p1})) • … • Automatically checked / generated by model-checking techniques

  12. Cell Cycle Model-Checking • biocham: check_reachable(cdk46~{p1,p2}-cycD~{p1}). • true • biocham: check_checkpoint(cdc25C~{p1,p2}, cdk1~{p1,p3}-cycB). • true • biocham: check_checkpoint(Wee1, cdk1~{p1,p2,p3}-cycB))))). • false • biocham: why. • 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

  13. Searching Parameters from Temporal Properties • biocham: learn_parameter([k3,k4],[(0,200),(0,200)],20, • oscil(Cdc2-Cyclin~{p1},3),150).

  14. Searching 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).

  15. Searching 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).

  16. Searching Parameters from Temporal Properties • 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).

  17. Modelling Methodology in BIOCHAM • Biochemical model = Transition system • Biological property = Temporal Logic formula • Biological validation = Model-checking • Semi-qualitative semi-quantitative temporal properties • Automatic parameter search and rule inference from temporal properties • Model: BIOCHAM Biological Properties: • - Boolean - simulation - Temporal Logic • - Differential - query evaluation - TL with constraints • - Stochastic - reaction rule inference • (SBML) - parameter search

  18. Other Collaborations • EU STREP Tempo INSERM Villejuif, F. Lévi, CNRS Roscoff L. Meyer, CNRS Nice F. Delaunay, CINBO Italy, Physiomics, Helios, … • Models of cell and circadian cycles and cancer chronotherapeutics • ARC MOCA, INRIA SYMBIOSE, CNRS Paris 7, Marseille, D. Thieffry • Modularity, compositionality and abstraction in regulatory networks • EU NoE REWERSE: Reasoning on the web with rules and semantics • F. Bry, Münich, R. Backofen Freiburg, M. Schroeder Dresden, … • Connecting BIOCHAM to gene and protein ontologies • EU STREP APRIL 2: Applications of probabilistic inductive logic, L. de Raedt, Freiburg, M. Sternberg, S. Muggleton, Imperial College London • Learning in a probabilistic logic setting

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