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
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formal systems / synthetic biology modelling re-engineered Jonathan Blakes 1 st year PhD student 2008-06-20
Sedwards S. Cyto-Sim Example Models: Oscillators. 2006
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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
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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
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why is stochasticity important? Gilmore S. A Beginner's Guide to Stochastic Simulation . Uni. Edinburgh, Systems Biology Club talk, 16/11/2005
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
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)
``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
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
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