(243f) Stochastic Operator Splitting Method for Biological Systems

^aDepartment
of Mechanical and Aerospace Engineering

^b Department
of Bioengineering

^cGraduate
Program in Bioinformatics

^dDepartment
of Chemistry & Biochemistry

University of California, San
Diego, 9500 Gilman Dr La Jolla, CA 92093

E-mail addresses:
TaiJung
Choi: tjchoi@ucsd.edu

Mano
Ram Maurya: mano@sdsc.edu

Daniel
M. Tartakovsky: dmt@ucsd.edu
Shankar
Subramaniam: Shankar@ucsd.edu

Deterministic models
of biological and biochemical processes at the sub-cellular level
might become improper when a series of chemical reactions is executed
by a few molecules. Inherent randomness of such phenomena calls for
the use of stochastic simulations. Moreover, in case of inhomogeneous
environment, such as receptor induced signaling in membrane and
chemotaxis due to existence of chemoattractants , spatial effect also
should be considered. Therefore, diffusion phenomenon induced by
chemical gradient becomes another important factor in biological
analysis. However, being computationally intensive, such simulations
become infeasible for large and complex reaction networks. To improve
their computational efficiency in handling these networks, we present
an operator splitting approach(1), in which reactions are handled
through exact stochastic simulation like Gillespie algorithm(2) and
diffusions are treated through Brownian dynamics. The proposed
operator splitting algorithm is used to model the simplified DNA/RNA
synthesis and reactions/diffusions of CheY molecules through the
cytoplasm of Escherichia coli(3). At relatively high concentrations,
the response characteristics obtained with the stochastic and
deterministic simulations coincide, which validates both approaches.
At low doses, the response characteristics of some key chemical
species, such as levels of CheY, predicted with stochastic
simulations differ quantitatively from their deterministic
counterparts.

References:

1. RodrÃguez
Vidal J, et al. Spatial stochastic modelling of the
phosphoenolpyruvate-dependent phosphotransferase (PTS) pathway in
Escherichia coli. Bioinformatics 2006;22:1895-1901.

2. Gillespie,
D. T. 1976. General method for numerically simulating stochastic time
evolution of coupled chemical-reactions. Journal of Computational
Physics. 22:403-434.

3. Lipkow
K, et al.
Simulated diffusion of phosphorylated CheY through the cytoplasm of
Escherichia coli. J. Bacteriol. 2005;187:45-53.