20080620 Formal systems/synthetic biology modelling re-engineered

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

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