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20080620 Formal systems/synthetic biology modelling re-engineered

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2008 RAD

2008 RAD

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  • bipartite digraph, place and transition nodes
  • stochastic methods associate an experimental determined rate with each reaction
  • Circadian clock actually a consequence of continuous quantities
  • A critical reaction is a reaction with positive propensity function such that a small number of firings is currently left before exhausting one of its reactants. All the other reactions are named, instead, noncritical reactions.
  • if our approach implements tau-leaping it really can’t work any differently than in DPP, therefore the two approaches are united
  • shortage of rate constants
  • relative or absolute heat measures
  • T-invariants can be used to analyse can average heat over simulation intervals to see which reactions were most likely in interval comparing averages for different intervals could highlight unknown switches in behaviour theoretically infinite number of strings
  • Transcript

    • 1. formal systems / synthetic biology modelling re-engineered Jonathan Blakes 1 st year PhD student 2008-06-20
    • 2. systems biology modelling
      • systems biology operates at molecular, cellular, tissue/colony, organism/population levels
      • model molecular reactions
      • model cellular organisation
        • compartments (dynamic)
      • model cellular interactions
          • development (growth/division/differentiation)
      • observe emergent behaviour
      • generate/test hypotheses in silico
    • 3. synthetic biology modelling
      • synthetic biology operates at molecular level
      • (re)programming cellular chassis with new genes
      • model molecular reactions
        • gene expression/regulation
        • protein interactions
        • metabolite turnover (I/O)
      • modular assembly (orthogonality)
      • prototype organism design
      medical / commercial potential
    • 4. executable biology
      • choose an appropriate formalism
      • simulate / execute model
    • 5. formalisms bacteria environment bacteria Petri nets P systems π -calculus reactions interactions lasI S 100 [ lasI ] -> [ lasI + LasI ] [ LasI + S ] -> [ LasI + 3OC12 ] [ 3OC12 ] -> 3OC12 [ ] LasR rhlR 3OC12 [ ] -> [ 3OC12 ] [ LasR+3OC12 ] -> [ LasR.3OC12 ] [ LasR.3OC12 + LasR.3OC12 ] -> [ LasR.3OC12 2 ] [ LasR.3OC12 2 + rlhR ] -> [ LasR.3OC122 + rlhR ] 3OC12 50
    • 6. reaction-based formalism equivalence
      • P system rules can be flattened to a Petri net:
      • Sedwards S. Cyto-Sim Example Models: Oscillators. 2006
    • 7. biological mapping Petri nets P systems π -calculus molecular species place symbol symbol molecule token object process population of molecules marking of net multiset processes reactions transitions rewriting rules communication
    • 8. properties Petri nets P systems π -calculus discrete (mechanistic) concurrent non-deterministic ( uniform time steps ) stochastic variants ( realistic time steps ) SPN MCG, DPP S π compartments distinct places: X nucleus X cytoplasm membranes S π @ BioAmbients Brane calculi
    • 9. why is stochasticity important? Gilmore S. A Beginner's Guide to Stochastic Simulation . Uni. Edinburgh, Systems Biology Club talk, 16/11/2005
    • 10. Gillespie algorithm
      • generates a statistically correct trajectory (simulation) of a stochastic system
      • ensembles of simulations average to ODE
      • limited to 2 reactants (higher order reactions modelled as sequence of binary reactions)
      • assumes
        • constant temperature and pressure
        • no electrostatic, H-bonding, Van der Waals forces
        • well-mixed volume
      1 10 100
    • 11. Gillespie algorithm
      • Direct Method:
      • for each reaction calculate propensity:
      • propensity (a i ) = k ∙ hazard function
      • hazard = # distinct combinations of reactants
      • generate uniform random number r = 0 ≤ 1
      • selected reaction = r ∙ Σ propensities
      • sample τ (time to wait) from negative exponential distribution with parameter
      • Σ propensities (a 0 )
      a + b -> c k
    • 12. 2 stochastic P system approaches
      • Multi-Compartmental Gillespie (MCG) algorithm
        • ‘ exact’ SSA algorithm running in each membrane
        • rule with lowest τ (smallest time step) in all membranes executed - inherently linear
      • Dynamical Probabilistic P systems (DPP)
        • rules selected à la Gillespie, objects assigned to selected rule, repeated until all objects assigned
        • all rules in all membranes applied simultaneously
        • maximal parallelism, bounded by mute rules: a -> a
        • uniform time steps – qualitative
        • parallel implementation using MPI C library
    • 13. three ideas based on observations from literature review
      • to increase performance
        • τ -leaping simulation algorithm facilitates parallelisation of multi-compartment models
      • to increase realism
        • molecular volumes can enable correct simulation of cell growth and division dynamics
      • to increase knowledge
        • combining static information (reaction topology) with stochastic execution in a visualisation can aid reasoning about system
    • 14. three ideas based on observations from literature review
      • to increase performance
        • τ -leaping simulation algorithm facilitates parallelisation of multi-compartment models
      • to increase realism
        • molecule volumes can efficiently enable correct simulation of cell growth and division dynamics
      • to increase knowledge
        • combining static information (reaction topology) with stochastic execution in a visualisation can aid reasoning about system
    • 15. parallelising stochastic P systems
      • P systems with exact SSA inside each membrane are parallel at the level of membranes but sequential at the level of rules
      • one rule selected in each membrane, different waiting time for each
      • different time lines - difficult to synchronise
      • can we synchronise waiting times and speed up algorithm?
    • 16. tau-leaping
      • exact stochastic simulation can be very slow as it tracks every reaction event in system
      • tau-leaping tracks groups of reactions instead
      • approximate which events occur in a period:
        • leap condition ε provides propensities do not change dramatically
        • safe τ computed
        • reactions drawn using Poisson distribution of τ
        • one/none critical reactions fired, many non-critical reactions fired also
    • 17. a faithful approximation Gilmore S. “ Beginner’s Guide to Stochastic Simulation” University of Edinburgh Systems Biology Club talk 16/11/05
    • 18. tau-leaping in parallel DPP
      • tau leaping is a form of bounded parallelism because it restricts the number of reactions
      • in tau-DPP each membrane computes a safe τ
      • smallest safe τ used to select reactions in each
      • reactions applied in all membranes in parallel and system advances in leaps of time τ
      • whereas DPP simulations would normally proceed in qualitative steps, now proceed in actual time so quantitative
      • tau-MCG would unify our approaches
      Cazzaniga P, Pescini D, Besozzi D, Mauri, G. “Tau Leaping Stochastic Simulation Method in P Systems” WMC 7 2006 298-313
    • 19. three ideas based on observations from literature review
      • to increase performance
        • τ -leaping simulation algorithm facilitates parallelisation of multi-compartment models
      • to increase realism
        • molecule volumes can efficiently enable correct simulation of cell growth and division dynamics
      • to increase knowledge
        • combining static information (reaction topology) with stochastic execution in a visualisation can aid reasoning about system
    • 20. rates and volumes
      • consider a compartment (volume v)
      • with a sub-compartment (volume v’)
      • calculating reaction propensity requires rate k
      • [ A + B ] -> [ C ] propensity = k ∙ A ∙ B
      • k implicitly contains the volume
      • same reaction in v and v’ k v ≠ k v’
      • probability of a binary collision is inversely proportional to volume
        • measure/calculate k in reference volume
        • make volume explicit propensity = (k /v) ∙ A ∙ B
      v v’ Smaldon J, Blakes J, Lancet D, Krasnogor N. "A Multi-scaled Approach to Artificial Life Simulation With P Systems and Dissipative Particle Dynamics" paper accepted for GECCO 2008 Atlanta, USA. k
    • 21. affect of membrane structure v = v – v’ v v’
    • 22. dynamic volumes v 2v cells grow
    • 23. dynamic volumes v cells divide
    • 24. dynamic volumes cells divide v/2 v/2
    • 25. but how to calculate volume?
      • extend stochastic π -calculus syntax with compartments (S π @) SPiM compatible
      • S π @: compartments or molecules have volume
      • compartment volume =
      • ∑ (species i quantity x species i volume )
      • species volume ≈ molecular weight
      • need to model water -> calculate pH
      Versari C and Busi N. “ Efficient Stochastic Simulation of Biological Systems with Multiple Variable Volumes.” Electronic Notes in Theoretical Computer Science 2007 94(3) 165-180. Proceedings of the First Workshop "From Biology To Concurrency and back” (FBTC 2007)
    • 26.  
    • 27. three ideas based on observations from literature review
      • to increase performance
        • τ -leaping simulation algorithm facilitates parallelisation of multi-compartment models
      • to increase realism
        • molecule volumes can efficiently enable correct simulation of cell growth and division dynamics
      • to increase knowledge
        • combining static information (reaction topology) with stochastic execution in a visualisation can aid reasoning about system
    • 28. visualise propensity information
      • The Next Reaction Method (and Optimized Direct Method) use a dependency graph to recalculate only the propensities of the affected reactions
    • 29.
      • use dependency graph to visualise state of system during simulation of stochastic P system
      • propensity of each reaction colours nodes hot or cold
      visualise propensity information
    • 30. example
      • first reaction fires
    • 31. example
      • molecules are consumed and produced,
      • two propensities changed
    • 32. example
      • second, unlikely, reaction fires
    • 33. example
      • three propensities changed,
      • dramatic effect on next reaction
    • 34. example
      • visualisation of discarded information
      • can reveal more than simply tracking quantities
    • 35. example
      • visualisation of discarded information
      • can reveal more than simply tracking quantities
      ``The specific value of visual modeling lies in tapping the potential of high bandwidth spatial intelligence, as opposed to lexical intelligence used with textual information.” Samek, M. “Practical Statecharts in C/C++: Quantum Programming for Embedded Systems” CMP Books, 2002
    • 36. observations
      • novel visualisation method for pathways
      • topology same as Petri net minus places
      • identify cliques – define modules
      • visualisation of modules only, zooming out
      • can use as heuristic for simulation algorithm selection: automatically determine when to use slow-scale SSA (respond to stiffness)
      • not-suitable for string rewriting rules
    • 37. references
      • Wilkinson D J. Stochastic Modelling for Systems Biology . “Chapter 8: Beyond the Gillespie algorithm” Chapman & Hall / CRC 2006
      • Cazzaniga P, Pescini D, Besozzi D, Mauri, G. “Tau Leaping Stochastic Simulation Method in P Systems” WMC 7 2006 298-313
      • Gilmore S. “Beginner’s Guide to Stochastic Simulation” University of Edinburgh Systems Biology Club talk 16/11/05
      • Versari C and Busi N. “Efficient Stochastic Simulation of Biological Systems with Multiple Variable Volumes” Electronic Notes in Theoretical Computer Science 2007 94(3) 165-180. Proceedings of the First Workshop "From Biology To Concurrency and back” (FBTC 2007)
      • Smaldon J, Blakes J, Lancet D, Krasnogor N. "A Multi-scaled Approach to Artificial Life Simulation With P Systems and Dissipative Particle Dynamics" paper accepted for GECCO 2008 Atlanta, USA. Cazzaniga P, Pescini D, Besozzi D, Mauri, G. “Tau Leaping Stochastic Simulation Method in P Systems” WMC 7 2006 298-313
      • Gibson M A, Bruck J. “Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels” J. Phys. Chem. A 2000 1876-1889
    • 38. acknowledgements
      • Supervisor Dr. Natalio Krasnogor
      • Dr. Francisco J. Romero-Campero
      • Dr. Jamie Twycross
      • Questions?

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