Cells as Machines: towards deciphering biochemical programs in the - PowerPoint PPT Presentation

Cells as Machines: towards deciphering biochemical programs in the cell François Fages Inria Paris-Rocquencourt France http://lifeware.inria.fr/ To tackle the complexity of biochemical reaction systems, investigate: • Programming theory concepts • Formal methods of circuit and program verification • Temporal logic constraints and model synthesis tools Implementation in BIOCHAM v3.5 (Biochemical Abstract Machine) ICDCIT 2014 Bhubaneswar François Fages

Systems Biology Challenge Gain system-level understanding of multi-scale biological processes in terms of their elementary interactions at the molecular level. Mitosis movie [Lodish et al. 03] ICDCIT 2014 Bhubaneswar François Fages

Systems Biology Challenge Gain system-level understanding of multi-scale biological processes in terms of their elementary interactions at the molecular level. Mitosis movie [Lodish et al. 03] Reverse engineering perspective � Post-genomic data (protein- protein interactions, RNAs,…) � Systems Biology Markup Language (SBML): model exchange format � Model repositories: e.g. biomodels.net 1000 models of cell processes � Modeling environments (Cell designer, Cytoscape, Copasi, Biocham ,…) � Simulation of a whole-cell mycoplasma genitalium [Karr et al 12] ICDCIT 2014 Bhubaneswar François Fages

Models in Systems Biology Models are built in Systems Biology with two contradictory perspectives : 1) Models for representing knowledge : the more detailed the better 2) Models for answering questions : the more abstract the better [Kohn 1999] [Tyson 1991] � Organize models and formalisms in hierarchies of abstractions ICDCIT 2014 Bhubaneswar François Fages

Formal Biochemical Reaction Rules Binding, complexation, polymerisation: ������������������� � �� � �� • ���� � ����� � ��������� Unbinding, decomplexation: �� � ��� � � • Transformation, phosphorylation, transport: �� � �� • ��������� � ���������� � ��������� �� � ���������� �� ������� Synthesis, transcription, traduction: ����������������������������� � �� � ��� • ��������� � ���������� � ������� Degradation: �� ����� • ICDCIT 2014 Bhubaneswar François Fages

Formal Biochemical Reaction Rules ����� �� Binding, complexation, polymerisation: ������������������� � �� • ���� � ����� � ��������� ��� � � � � Unbinding, decomplexation: �� • ��������� � ��������� �� Transformation, phosphorylation, transport: �� • ��������� � ���������� � ��������� �� � ���������� �� ������� ��� � ����� � � �� � ��� � � ����� � � Synthesis, transcription, traduction: ����������������������������� • ��������� � ���������� � ������� ��� ���� Degradation: �� • ICDCIT 2014 Bhubaneswar François Fages

Semantics of Reaction Programs ����� �� � � �� • Stochastic Semantics: numbers of molecules Continuous Time Markov Chain (CTMC) ICDCIT 2014 Bhubaneswar François Fages

Semantics of Reaction Programs ����� �� � � �� • Stochastic Semantics: numbers of molecules Continuous Time Markov Chain (CTMC) • Differential Semantics: concentrations Ordinary Differential Equation (ODE) ICDCIT 2014 Bhubaneswar François Fages

Semantics of Reaction Programs ����� �� � � �� • Stochastic Semantics: numbers of molecules Continuous Time Markov Chain (CTMC) • Differential Semantics: concentrations Ordinary Differential Equation (ODE) � � �� � �� • Petri Net Semantics: numbers of molecules Multiset rewriting A , B � C++ A- - B- - CHAM [Berry Boudol 90] [Banatre Le Metayer 86] ICDCIT 2014 Bhubaneswar François Fages

Semantics of Reaction Programs ����� �� � � �� • Stochastic Semantics: numbers of molecules Continuous Time Markov Chain (CTMC) • Differential Semantics: concentrations Ordinary Differential Equation (ODE) � � �� � �� • Petri Net Semantics: numbers of molecules Multiset rewriting A , B � C++ A- - B- - CHAM [Berry Boudol 90] [Banatre Le Metayer 86] • Boolean Semantics: presence-absence of molecules Asynchronous Transition System A � B � C � A/ � A � B/ � B ICDCIT 2014 Bhubaneswar François Fages

Hierarchy of Semantics abstraction Theory of abstract Interpretation Abstractions as Galois connections [Cousot Cousot POPL’77] Boolean traces Thm. Galois connections between the Discrete traces syntactical, stochastic, discrete and Boolean semantics ODE traces [Fages Soliman CMSB’06,TCS’08] Stochastic traces Cor. If a behavior is not possible in the Boolean semantics it is not possible in the stochastic semantics for any reaction rates Reaction rules concretization ICDCIT 2014 Bhubaneswar François Fages

Hierarchy of Semantics abstraction Theory of abstract Interpretation Abstractions as Galois connections [Cousot Cousot POPL’77] Boolean traces Thm. Galois connections between the Discrete traces syntactical, stochastic, discrete and Boolean semantics ODE traces [Fages Soliman CMSB’06,TCS’08] Stochastic traces Thm. Under appropriate conditions the Reaction rules ODE semantics approximates the mean stochastic behavior concretization [Gillespie 71] ICDCIT 2014 Bhubaneswar François Fages

Influence Graph Abstraction abstraction Influence graph � � �� � �� , �� � ��� � � �� � �� � �� � �� � � � � �� � ��� �� � �� Reaction hypergraph � ����� �� � � �� concretization ICDCIT 2014 Bhubaneswar François Fages

Influence Graph Abstraction abstraction Thm. Positive (resp. negative) circuits in the influence graph are a necessary condition for multistationarity (resp. oscillations) [Thomas 81] [Snoussi 93] [Soulé 03] [Remy Ruet Thieffry 05] [Richard 07] [Soliman13] Jacobian matrix Thm. Both graphs are Stoichiometric = Influence Graph equal if monotonic kinetics Influence Graph and in absence of double positive-negative pairs [Fages Soliman FMSB 08] ODE Reactions concretization ICDCIT 2014 Bhubaneswar François Fages

Cell Cycle Control ICDCIT 2014 Bhubaneswar François Fages

Mammalian Cell Cycle Control Map [Kohn 99] ICDCIT 2014 Bhubaneswar François Fages

Influence Graph of Kohn’s Map of Cell Cycle • No double positive-negative influence pair • Stoichiometric influence graph = Differential influence graph for any monotonic reaction rates • Positive circuit analysis: – Necessary condiiton for multi-stationnarity (cell differentiation) • Negative circuit analysis: – Necessary condition for oscillations (homeostasis) ICDCIT 2014 Bhubaneswar François Fages

Boolean Semantics Queries Computation Tree Logic CTL [Emerson Clarke 80] Non-det. E A Non-determinism E, A Time exists always EX ( � ) AX ( � ) X AG next time EF ( � ) AF ( � ) F � AG ( � � ) finally liveness EG ( � ) AG ( � ) G � AF ( � � ) globally safety EF F,G,U E ( � 1 U � 2) A ( � 1 U � 2) U Time until ICDCIT 2014 Bhubaneswar François Fages

Kohn’s Map Boolean Model -Checking 800 reactions, 165 proteins and genes, 500 variables, 2 500 states. Biocham NuSMV symbolic model-checker time in seconds [Chabrier et al. TCS 04] Initial state G2 Query: Time in sec. compiling 29 Reachability G1 EF CycE 2 Reachability G1 EF CycD 1.9 Reachability G1 EF PCNA-CycD 1.7 � EF ( � Cdc25~{Nterm} Checkpoint 2.2 for mitosis complex U Cdk1~{Thr161}-CycB ) EG ( (EF � CycA ) & (EF CycA )) Oscillations CycA 31.8 EG ( (EF � CycB ) & (EF CycB )) false ! Oscillations CycB 6 ICDCIT 2014 Bhubaneswar François Fages

Quantitative Model of Cell Cycle Control [Tyson 91] k1 for _ => Cyclin. k3*[Cyclin]*[Cdc2~{p1}] for Cyclin + Cdc2~{p1} => Cdc2~{p1}-Cyclin~{p1}. k6*[Cdc2-Cyclin~{p1}] for Cdc2-Cyclin~{p1} => Cdc2 + Cyclin~{p1}. k7*[Cyclin~{p1}] for Cyclin~{p1} => _. k8*[Cdc2] for Cdc2 => Cdc2~{p1}. k9*[Cdc2~{p1}] for Cdc2~{p1} => Cdc2. k4p*[Cdc2~{p1}-Cyclin~{p1}] 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}. ICDCIT 2014 Bhubaneswar François Fages

Linear Time Logic LTL(R lin ) ICDCIT 2014 Bhubaneswar François Fages

Parameter Search from LTL(R) Properties biocham: search_parameter([k3,k4],[(0,200),(0,200)],20, oscil(Cdc2-Cyclin~{p1},3),150). ICDCIT 2014 Bhubaneswar François Fages