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

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

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Cells as Machines: towards deciphering biochemical programs in the cell Franois Fages Inria Paris-Rocquencourt France http://lifeware.inria.fr/ To tackle the complexity of biochemical reaction systems, investigate: Programming theory

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François Fages ICDCIT 2014 Bhubaneswar

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)

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François Fages ICDCIT 2014 Bhubaneswar

Systems Biology Challenge

Gain system-level understanding of multi-scale biological processes in terms

  • f their elementary interactions at the molecular level.

Mitosis movie [Lodish et al. 03]

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François Fages ICDCIT 2014 Bhubaneswar

Systems Biology Challenge

Gain system-level understanding of multi-scale biological processes in terms

  • f 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]

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François Fages ICDCIT 2014 Bhubaneswar

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

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François Fages ICDCIT 2014 Bhubaneswar

Formal Biochemical Reaction Rules

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

Formal Biochemical Reaction Rules

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

  • Stochastic Semantics: numbers of molecules

Continuous Time Markov Chain (CTMC)

Semantics of Reaction Programs

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  • Stochastic Semantics: numbers of molecules

Continuous Time Markov Chain (CTMC)

  • Differential Semantics: concentrations

Ordinary Differential Equation (ODE)

Semantics of Reaction Programs

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François Fages ICDCIT 2014 Bhubaneswar

  • 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]

Semantics of Reaction Programs

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François Fages ICDCIT 2014 Bhubaneswar

  • 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

Semantics of Reaction Programs

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Hierarchy of Semantics

Stochastic traces Discrete traces

abstraction concretization

Boolean traces

Theory of abstract Interpretation Abstractions as Galois connections

[Cousot Cousot POPL’77]

  • Thm. Galois connections between the

syntactical, stochastic, discrete and Boolean semantics

[Fages Soliman CMSB’06,TCS’08]

  • 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 ODE traces

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Hierarchy of Semantics

Stochastic traces ODE traces Discrete traces

abstraction concretization

Boolean traces

  • Thm. Under appropriate conditions the

ODE semantics approximates the mean stochastic behavior

[Gillespie 71]

Reaction rules

Theory of abstract Interpretation Abstractions as Galois connections

[Cousot Cousot POPL’77]

  • Thm. Galois connections between the

syntactical, stochastic, discrete and Boolean semantics

[Fages Soliman CMSB’06,TCS’08]

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Influence Graph Abstraction

abstraction concretization

Reaction hypergraph Influence graph

  • ,
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Influence Graph Abstraction

ODE

abstraction concretization

Reactions

  • Thm. Both graphs are

equal if monotonic kinetics and in absence of double positive-negative pairs

[Fages Soliman FMSB 08]

=

Stoichiometric Influence Graph Jacobian matrix Influence Graph

  • 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]

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Cell Cycle Control

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Mammalian Cell Cycle Control Map [Kohn 99]

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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)

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Boolean Semantics Queries

Computation Tree Logic CTL [Emerson Clarke 80]

Time Non-determinism E, A

F,G,U EF AG

Non-det. Time E exists A always X next time EX() AX() F finally EF() AG( ) AF() liveness G globally EG() AF( ) AG() safety U until E (1 U 2) A (1 U 2)

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Kohn’s Map Boolean Model-Checking

800 reactions, 165 proteins and genes, 500 variables, 2500 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 Checkpoint for mitosis complex EF ( Cdc25~{Nterm} U Cdk1~{Thr161}-CycB) 2.2 Oscillations CycA EG ( (EF CycA) & (EF CycA)) 31.8 Oscillations CycB EG ( (EF CycB) & (EF CycB)) false ! 6

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François Fages ICDCIT 2014 Bhubaneswar

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}.

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Linear Time Logic LTL(Rlin)

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biocham: search_parameter([k3,k4],[(0,200),(0,200)],20,

  • scil(Cdc2-Cyclin~{p1},3),150).

Parameter Search from LTL(R) Properties

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Parameter Search from LTL(R) Properties

biocham: search_parameter([k3,k4],[(0,200),(0,200)],20,

  • scil(Cdc2-Cyclin~{p1},3),150).

First values found : parameter(k3,10). parameter(k4,70).

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Parameter Search from LTL(R) Properties

biocham: search_parameter([k3,k4],[(0,200),(0,200)],20,

  • scil(Cdc2-Cyclin~{p1},3) & F([Cdc2-Cyclin~{p1}]>0.15), 150).

First values found : parameter(k3,10). parameter(k4,120).

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biocham: search_parameter([k3,k4],[(0,200),(0,200)],20, period(Cdc2-Cyclin~{p1},35), 150). First values found: parameter(k3,10). parameter(k4,280).

Parameter Search from LTL(R) Properties

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biocham: search_parameter([k3,k4],[(0,200),(0,200)],20, period(Cdc2-Cyclin~{p1},35), 150). First values found: parameter(k3,10). parameter(k4,280).

Parameter Search from LTL(R) Properties

p ( , )

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LTL(R) Satisfaction Degree

Bifurcation diagram on k4, k6 Continuous satisfaction degree in [0,1]

[Tyson 91] of the LTL(R) formula for oscillation

with amplitude constraint

[Rizk Batt Fages Soliman CMSB 08]

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[Rizk Batt Fages Soliman ISMB’09 Bioinformatics]

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Conclusion

  • Biochemical programs are

– Stochastic, continuous time, distributed, poorly isolated in compartments, – Natural programs acquired by (yet surviving to) evolution

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Conclusion

  • Biochemical programs are

– Stochastic, continuous time, distributed, poorly isolated in compartments, – Natural programs acquired by (yet surviving to) evolution

  • New focus in Programming: numerical methods, time matters

– Beyond discrete machines: stochastic, continuous, hybrid dynamics – Quantitative transition systems, hybrid systems – Continuous satisfaction degree of Temporal Logic specifications – From program verification to program optimization

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Conclusion

  • Biochemical programs are

– Stochastic, continuous time, distributed, poorly isolated in compartments, – Natural programs acquired by (yet surviving to) evolution

  • New focus in Programming: numerical methods, time matters

– Beyond discrete machines: stochastic, continuous, hybrid dynamics – Quantitative transition systems, hybrid systems – Continuous satisfaction degree of Temporal Logic specifications – From program verification to program optimization

  • New focus in Computational Systems Biology: formal methods

– Beyond diagrammatic notations: formal semantics, abstract interpretation – Beyond simulation: symbolic execution, model-checking – Beyond curve fitting: high-level specifications in temporal logic – Parameter optimization. Model reduction.

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Acknowledgments

  • Lifeware team at Inria Paris-Rocquencourt : Grégory Batt, Sylvain Soliman, …
  • Inria/INRA project coord. F. Clément (Inria); E. Reiter (INRA); R. Lefkowitz (Duke)

– Complex dynamics of GPCR signaling networks

  • EraNet SysBio C5Sys on cancer chronotherapies, coord. Francis Lévi (INSERM)

– Coupled models of the cell cycle and circadian clock, cytotoxic drugs.

  • OSEO Biointelligence, coord. Dassault-Systèmes

– Modeling platform PLM for pharma industry

  • ANR Iceberg, coord. Grégory Batt, with P. Hersen (CNRS MSC), O Gandrillon

– Model-based control of gene expression in microfluidic

  • ANR Syne2arti, coord. Grégory Batt, with D. Drasdo (Inria), R. Weiss (MIT)

– Model-based control of tissue growth in synthetic biology