article
Solving the chemical master equation using sliding windows
published
yes
Verena
Wolf
author
Rushil
Goel
author
Maria
Mateescu
author 3B43276C-F248-11E8-B48F-1D18A9856A87
Thomas A
Henzinger
author 40876CD8-F248-11E8-B48F-1D18A9856A870000−0002−2985−7724
ToHe
department
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.
https://research-explorer.app.ist.ac.at/download/3834/5217/IST-2012-72-v1+1_Solving_the_chemical_master_equation_using_sliding_windows.pdf
application/pdfno
'https://creativecommons.org/licenses/by/4.0/'
BioMed Central2010
eng
BMC Systems Biology10.1186/1752-0509-4-42
4421 - 19
Wolf V, Goel R, Mateescu M, Henzinger TA. 2010. Solving the chemical master equation using sliding windows. BMC Systems Biology. 4(42), 1–19.
V. Wolf, R. Goel, M. Mateescu, T.A. Henzinger, BMC Systems Biology 4 (2010) 1–19.
V. Wolf, R. Goel, M. Mateescu, and T. A. Henzinger, “Solving the chemical master equation using sliding windows,” <i>BMC Systems Biology</i>, vol. 4, no. 42, pp. 1–19, 2010.
Wolf, Verena, et al. “Solving the Chemical Master Equation Using Sliding Windows.” <i>BMC Systems Biology</i>, vol. 4, no. 42, BioMed Central, 2010, pp. 1–19, doi:<a href="https://doi.org/10.1186/1752-0509-4-42">10.1186/1752-0509-4-42</a>.
Wolf, Verena, Rushil Goel, Maria Mateescu, and Thomas A Henzinger. “Solving the Chemical Master Equation Using Sliding Windows.” <i>BMC Systems Biology</i> 4, no. 42 (2010): 1–19. <a href="https://doi.org/10.1186/1752-0509-4-42">https://doi.org/10.1186/1752-0509-4-42</a>.
Wolf V, Goel R, Mateescu M, Henzinger TA. Solving the chemical master equation using sliding windows. <i>BMC Systems Biology</i>. 2010;4(42):1-19. doi:<a href="https://doi.org/10.1186/1752-0509-4-42">10.1186/1752-0509-4-42</a>
Wolf, V., Goel, R., Mateescu, M., & Henzinger, T. A. (2010). Solving the chemical master equation using sliding windows. <i>BMC Systems Biology</i>, <i>4</i>(42), 1–19. <a href="https://doi.org/10.1186/1752-0509-4-42">https://doi.org/10.1186/1752-0509-4-42</a>
38342018-12-11T12:05:25Z2019-08-02T12:38:17Z