---
_id: '3834'
abstract:
- lang: eng
  text: "Background\r\n\r\nThe 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.\r\nResults\r\n\r\nIn 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.\r\n\r\n\r\nConclusions\r\n\r\nThe
    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."
acknowledgement: 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.
article_processing_charge: No
author:
- first_name: Verena
  full_name: Wolf, Verena
  last_name: Wolf
- first_name: Rushil
  full_name: Goel, Rushil
  last_name: Goel
- first_name: Maria
  full_name: Mateescu, Maria
  id: 3B43276C-F248-11E8-B48F-1D18A9856A87
  last_name: Mateescu
- first_name: Thomas A
  full_name: Henzinger, Thomas A
  id: 40876CD8-F248-11E8-B48F-1D18A9856A87
  last_name: Henzinger
  orcid: 0000−0002−2985−7724
citation:
  ama: 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>
  apa: Wolf, V., Goel, R., Mateescu, M., &#38; Henzinger, T. A. (2010). Solving the
    chemical master equation using sliding windows. <i>BMC Systems Biology</i>. BioMed
    Central. <a href="https://doi.org/10.1186/1752-0509-4-42">https://doi.org/10.1186/1752-0509-4-42</a>
  chicago: Wolf, Verena, Rushil Goel, Maria Mateescu, and Thomas A Henzinger. “Solving
    the Chemical Master Equation Using Sliding Windows.” <i>BMC Systems Biology</i>.
    BioMed Central, 2010. <a href="https://doi.org/10.1186/1752-0509-4-42">https://doi.org/10.1186/1752-0509-4-42</a>.
  ieee: 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. BioMed Central, pp. 1–19, 2010.
  ista: Wolf V, Goel R, Mateescu M, Henzinger TA. 2010. Solving the chemical master
    equation using sliding windows. BMC Systems Biology. 4(42), 1–19.
  mla: 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>.
  short: V. Wolf, R. Goel, M. Mateescu, T.A. Henzinger, BMC Systems Biology 4 (2010)
    1–19.
corr_author: '1'
date_created: 2018-12-11T12:05:25Z
date_published: 2010-04-08T00:00:00Z
date_updated: 2025-09-30T09:37:27Z
day: '08'
ddc:
- '005'
department:
- _id: ToHe
doi: 10.1186/1752-0509-4-42
external_id:
  isi:
  - '000277612700001'
file:
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  creator: system
  date_created: 2018-12-12T10:16:29Z
  date_updated: 2020-07-14T12:46:16Z
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  file_name: IST-2012-72-v1+1_Solving_the_chemical_master_equation_using_sliding_windows.pdf
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file_date_updated: 2020-07-14T12:46:16Z
has_accepted_license: '1'
intvolume: '         4'
isi: 1
issue: '42'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '04'
oa: 1
oa_version: Published Version
page: 1 - 19
publication: BMC Systems Biology
publication_status: published
publisher: BioMed Central
publist_id: '2374'
pubrep_id: '72'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Solving the chemical master equation using sliding windows
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 4
year: '2010'
...