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SUMMARY:Hybrid modelling of stochastic chemical kinetics - Konstantinos Zy
 galakis (University of Edinburgh)
DTSTART:20160203T150000Z
DTEND:20160203T160000Z
UID:TALK64687@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:It is well known that stochasticity can play a fundamental rol
 e in various biochemical processes\, such as cell regulatory networks and 
 enzyme cascades. Isothermal\, well-mixed systems can be adequately modelle
 d by Markov processes and\, for such systems\, methods such as Gillespie&#
 39\;s algorithm are typically employed. While such schemes are easy to imp
 lement and are exact\, the computational cost of simulating such systems c
 an become prohibitive as the frequency of the reaction events increases. T
 his has motivated numerous coarse grained schemes\, where the ``fast&#39\;
 &#39\;   reactions are approximated either using Langevin dynamics or dete
 rministically. While such approaches provide a good approximation for syst
 ems where all reactants are present in large concentrations\, the approxim
 ation breaks down when the fast chemical species exist in small concentrat
 ions\, giving rise to significant errors in the simulation. This is partic
 ularly problematic when using such methods to compute statistics of extinc
 tion times for chemical species\, as well as computing observables of cell
  cycle models. In this talk\, we present a hybrid scheme for simulating we
 ll-mixed stochastic kinetics\, using Gillepsie--type dynamics to simulate 
 the network in regions of low reactant concentration\, and chemical langev
 in dynamics when the concentrations of all species is large. These two reg
 imes are coupled via an intermediate region in which a ``blended&#39\;&#39
 \; jump-diffusion model is introduced. Examples of gene regulatory network
 s involving reactions occurring at multiple scales\, as well as a cell-cyc
 le model are simulated\, using the exact and hybrid scheme\, and compared\
 , both in terms weak error\, as well as computational cost.  &nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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