TITLE:
Simplifying Stochastic Mathematical Models of Biochemical Systems
AUTHORS:
Silvana Ilie, Samaneh Gholami
KEYWORDS:
Stochastic Modeling; Sensitivity Analysis; Model Reduction Techniques; Chemical Langevin Equation
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.1A,
January
30,
2013
ABSTRACT: Stochastic modeling of biochemical reactions taking place at the cellular level has become the subject of intense research in recent years. Molecular interactions in a single cell exhibit random fluctuations. These fluctuations may be significant when small populations of some reacting species are present and then a stochastic description of the cellular dynamics is required. Often, the biochemically reacting systems encountered in applications consist of many species interacting through many reaction channels. Also, the dynamics of such systems is typically non-linear and presents multiple time-scales. Consequently, the stochastic mathematical models of biochemical systems can be quite complex and their analysis challenging. In this paper, we present a method to reduce a stochastic continuous model of well-stirred biochemical systems, the Chemical Langevin Equation, while preserving the overall behavior of the system. Several tests of our method on models of practical interest gave excellent results.