Presented by:
Konstantinos Zygalakis University of Edinburgh
Date:
Wednesday 3rd February 2016 - 15:00 to 16:00
Venue:
INI Seminar Room 1
Abstract:
It is well known that stochasticity can play a
fundamental role in various biochemical processes, such as cell regulatory
networks and enzyme cascades. Isothermal, well-mixed systems can be adequately
modelled by Markov processes and, for such systems, methods such as Gillespie's
algorithm are typically employed. While such schemes are easy to implement and
are exact, the computational cost of simulating such systems can become
prohibitive as the frequency of the reaction events increases. This has motivated
numerous coarse grained schemes, where the ``fast''
reactions are approximated either using Langevin dynamics
or deterministically. While such approaches provide a good approximation for
systems where all reactants are present in large concentrations, the
approximation breaks down when the fast chemical species exist in small
concentrations, giving rise to significant errors in the simulation. This is
particularly problematic when using such methods to compute statistics of
extinction times for chemical species, as well as computing observables of cell
cycle models. In this talk, we present a hybrid scheme for simulating
well-mixed stochastic kinetics, using Gillepsie--type dynamics to simulate the
network in regions of low reactant concentration, and chemical langevin
dynamics when the concentrations of all species is large. These two regimes are
coupled via an intermediate region in which a ``blended'' jump-diffusion model
is introduced. Examples of gene regulatory networks involving reactions
occurring at multiple scales, as well as a cell-cycle model are simulated,
using the exact and hybrid scheme, and compared, both in terms weak error, as
well as computational cost.
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