@PhDThesis{ itlic:2008-003,
author = {Andreas Hellander},
title = {Numerical Simulation of Well Stirred Biochemical Reaction
Networks Governed by the Master Equation},
school = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2008},
number = {2008-003},
type = {Licentiate thesis},
month = oct,
day = {15},
pages = {34},
note = {Included papers available at
\url{http://dx.doi.org/10.1016/j.jcp.2007.07.020},
\url{http://dx.doi.org/10.1007/s10543-008-0174-z}, and
\url{http://dx.doi.org/10.1063/1.2897976}},
abstract = {Numerical simulation of stochastic biochemical reaction
networks has received much attention in the growing field
of computational systems biology. Systems are frequently
modeled as a continuous-time discrete space Markov chain,
and the governing equation for the probability density of
the system is the (chemical) master equation. The direct
numerical solution of this equation suffers from an
exponential growth in computational time and memory with
the number of reacting species in the model. As a
consequence, Monte Carlo simulation methods play an
important role in the study of stochastic chemical
networks. The stochastic simulation algorithm (SSA) due to
Gillespie has been available for more than three decades,
but due to the multi-scale property of the chemical systems
and the slow convergence of Monte Carlo methods, much work
is currently being done in order to devise more efficient
approximate schemes.
In this thesis we review recent work for the solution of
the chemical master equation by direct methods, by exact
Monte Carlo methods and by approximate and hybrid methods.
We also describe two conceptually different numerical
methods to reduce the computational time when studying
models using the SSA. A hybrid method is proposed, which is
based on the separation of species into two subsets based
on the variance of the copy numbers. This method yields a
significant speed-up when the system permits such a
splitting of the state space. A different approach is taken
in an algorithm that makes use of low-discrepancy sequences
and the method of uniformization to reduce variance in the
computed density function.}
}