Solving the chemical master equation using sliding windows Journal Article

Author(s): Wolf, Verena; Goel, Rushil; Mateescu, Maria; Henzinger, Thomas A
Article Title: Solving the chemical master equation using sliding windows
Affiliation IST Austria
Abstract: Background The chemical master equation (CME) is a system of ordinary differential equations that describes the evolution of a network of chemical reactions as a stochastic process. Its solution yields the probability density vector of the system at each point in time. Solving the CME numerically is in many cases computationally expensive or even infeasible as the number of reachable states can be very large or infinite. We introduce the sliding window method, which computes an approximate solution of the CME by performing a sequence of local analysis steps. In each step, only a manageable subset of states is considered, representing a "window" into the state space. In subsequent steps, the window follows the direction in which the probability mass moves, until the time period of interest has elapsed. We construct the window based on a deterministic approximation of the future behavior of the system by estimating upper and lower bounds on the populations of the chemical species. Results In order to show the effectiveness of our approach, we apply it to several examples previously described in the literature. The experimental results show that the proposed method speeds up the analysis considerably, compared to a global analysis, while still providing high accuracy. Conclusions The sliding window method is a novel approach to address the performance problems of numerical algorithms for the solution of the chemical master equation. The method efficiently approximates the probability distributions at the time points of interest for a variety of chemically reacting systems, including systems for which no upper bound on the population sizes of the chemical species is known a priori.
Journal Title: BMC Systems Biology
Volume: 4
Issue 42
ISSN: 1752-0509
Publisher: BioMed Central  
Date Published: 2010-04-08
Start Page: 1
End Page: 19
Copyright Statement: CC-BY
Sponsor: This research has been partially funded by the Swiss National Science Foundation under grant 205321-111840 and by the Cluster of Excellence on Multimodal Computing and Interaction at Saarland University.
DOI: 10.1186/1752-0509-4-42
Open access: yes (OA journal)
IST Austria Authors
  1. Thomas A. Henzinger
    415 Henzinger
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