Stochastic Operator Splitting Method for Biological Systems

Stochastic Operator Splitting Method for Biological Systems TaiJung Choi^a, Mano Ram Maurya^b, Daniel M. Tartakovsky^a, and Shankar Subramaniam^b,c,d,1

^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. RodrĂguez 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.

1 Corresponding author: E-mail: shankar@sdsc.edu, Phone: (858) 822 0986, Fax: (858) 822 3752.