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.
Highlights
Mathematical modeling of biochemical reactions within a cell is crucial for understanding cellular dynamics [1]
We present below a brief introduction to the stochastic modeling of chemical kinetics for well-stirred systems, in the regime of large molecular populations
We developed a method to reduce biochemical systems modeled with the Chemical Langevin Equation
Summary
Mathematical modeling of biochemical reactions within a cell is crucial for understanding cellular dynamics [1]. The existing model reduction schemes for deterministic models of chemical reaction systems may be grouped into sensitivity analysis methods [7], lumping methods [8,9] and time-scale analysis methods [10,11]. Our contribution in this paper is to provide a novel method for reducing a stochastic continuous model of biochemical systems, the Chemical Langevin Equation. Sensitivity analysis is widely used in quantifying the characteristics of the system [20], such as robustness with respect to perturbations in its parameters These parameters include the reaction rate constants or the initial supplies of species. Sensitivity analysis studies the variation in molecular populations with respect to small changes in parameters It enables the identification of the kinetic parameters with a negligible impact on the species of interest.
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