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SUMMARY:Hybrid modelling of stochastic chemical kinetics - Andrew Duncan (
 University of Sussex\; The Alan Turing Institute)
DTSTART:20160407T084500Z
DTEND:20160407T093000Z
UID:TALK65367@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span> <span>Co-authors: Radek Erban (University of Oxford)\, 
  Kostantinos Zygalakis (University of Edinburgh)<br></span></span><span><b
 r>It is well known that stochasticity can play a fundamental role in vario
 us  biochemical processes\, such as cell regulatory networks and enzyme ca
 scades.  Isothermal\, well-mixed systems can be adequately modelled by Mar
 kov processes  and\, for such systems\, methods such as Gillespie&#39\;s a
 lgorithm are typically  employed. While such schemes are easy to implement
  and are exact\, the  computational cost of simulating such systems can be
 come prohibitive as the  frequency of the reaction events increases. This 
 has motivated numerous coarse  grained schemes\, where the "fast" reaction
 s are approximated either using  Langevin dynamics or deterministically. W
 hile such approaches provide a good  approximation for systems where all r
 eactants are present in large  concentrations\, the approximation breaks d
 own when the fast chemical species  exist in small concentrations\, giving
  rise to significant errors in the  simulation. This is particularly probl
 ematic when using such methods to compute  statistics of extinction times 
 for chemical species\, as well as computing  observables of cell cycle mod
 els. In this talk\, we present a hybrid scheme for  simulating well-mixed 
 stochastic kinetics\, using Gillepsie-type dynamics to  simulate the netwo
 rk in regions of low reactant concentration\, and chemical  Langevin dynam
 ics when the concentrations of all species is large. These two  regimes ar
 e coupled via an intermediate region in which a "blended"&#39\;  jump-diff
 usion model is introduced. Examples of gene regulatory networks  involving
  reactions occurring at multiple scales\, as well as a cell-cycle model  a
 re simulated\, using the exact and hybrid scheme\, and compared\, both in 
 terms  weak error\, as well as computational cost.</span>
LOCATION:Seminar Room 1\, Newton Institute
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