The DOI matches its Crossref record.
The chemical Langevin equation
Abstract
The stochastic dynamical behavior of a well-stirred mixture of N molecular species that chemically interact through M reaction channels is accurately described by the chemical master equation. It is shown here that, whenever two explicit dynamical conditions are satisfied, the microphysical premise from which the chemical master equation is derived leads directly to an approximate time-evolution equation of the Langevin type. This chemical Langevin equation is the same as one studied earlier by Kurtz, in contradistinction to some other earlier proposed forms that assume a deterministic macroscopic evolution law. The novel aspect of the present analysis is that it shows that the accuracy of the equation depends on the satisfaction of certain specific conditions that can change from moment to moment, rather than on a static system size parameter. The derivation affords a new perspective on the origin and magnitude of noise in a chemically reacting system. It also clarifies the connection between the stochastically correct chemical master equation, and the deterministic but often satisfactory reaction rate equation.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
No references could be resolved yet.
Research works printed but not linked: 15
- 1967, J. Appl. Probab., 4, 413, 10.2307/3212214 · doi:10.2307/3212214 · Paper page
- 1976, J. Comput. Phys., 22, 403, 10.1016/0021-9991(76)90041-3 · DOI · Paper page
- 1969, J. Chem. Phys., 50, 460, 10.1063/1.1670820 · DOI
- 1992, Physica A, 188, 404, 10.1016/0378-4371(92)90283-V · DOI · Paper page
- 1996, J. Chem. Phys., 105, 8257, 10.1063/1.472679 · DOI
- 1973, J. Stat. Phys., 9, 51, 10.1007/BF01016797 · DOI · Paper page
- 1996, Am. J. Phys., 64, 1246, 10.1119/1.18387 · DOI
- 1905, Ann. Phys. (Leipzig), 19, 549
- 1961, Can. J. Phys., 39, 551, 10.1139/p61-056 · DOI
- 1980, J. Chem. Phys., 72, 5363, 10.1063/1.439029 · doi:10.1063/1.439029
- 1976, Math. Progr. Stud., 5, 67, 10.1007/BFb0120765 · DOI
- 1978, Stoch. Proc. Appl., 6, 223, 10.1016/0304-4149(78)90020-0 · DOI · Paper page
- 1976, J. Chem. Phys., 65, 2007, 10.1063/1.433300 · doi:10.1063/1.433300
- 1981, Ann. Phys. (N.Y.), 131, 283, 10.1016/0003-4916(81)90033-6 · doi:10.1016/0003-4916(81)90033-6
- 1997, Proc. Natl. Acad. Sci. USA, 94, 814, 10.1073/pnas.94.3.814 · DOI · Paper page
Cited by
Modelling and analysis of gene regulatory networks
Karlebach, G., & Shamir, R. (2008) · Nature Reviews Molecular Cell Biology · doi:10.1038/nrm2503 · Cited by 1,296
Reverse engineering of biological complexity
Csete, M. E., & Doyle, J. C. (2002) · Science · doi:10.1126/science.1069981 · Cited by 1,215
Control, exploitation and tolerance of intracellular noise
Rao, C. V., Wolf, D. M., & Arkin, A. P. (2002) · Nature · doi:10.1038/nature01258 · Cited by 1,006
Golightly, A., & Wilkinson, D. J. (2011) · Interface Focus · doi:10.1098/rsfs.2011.0047 · Cited by 282
Bayesian methods in bioinformatics and computational systems biology
Wilkinson, D. J. (2006) · Briefings in Bioinformatics · doi:10.1093/bib/bbm007 · Cited by 230
Metadata
- Authors
- Gillespie, D. T.
- Venue
- The Journal of Chemical Physics
- Publisher
- AIP Publishing
- Published
- 2000-07-01
- Volume
- 113
- Issue
- 1
- Pages
- 297-306
- ISSN
- 0021-9606 (ISSN-L)
- 1089-7690
- OpenAlex
- W2046451925
- Cited by
- 1,475
- References
- 0
- FWCI
- 4.60
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: The chemical Langevin equation. https://app.cochat.ai/papers/10.1063/1.481811
- The paper
- Gillespie, D. T. (2000). The chemical Langevin equation. The Journal of Chemical Physics. https://doi.org/10.1063/1.481811
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
