2015
DOI: 10.1103/physreve.92.042124
|View full text |Cite
|
Sign up to set email alerts
|

Linear-noise approximation and the chemical master equation agree up to second-order moments for a class of chemical systems

Abstract: It is well known that the linear-noise approximation (LNA) agrees with the chemical master equation, up to second-order moments, for chemical systems composed of zero and first-order reactions. Here we show that this is also a property of the LNA for a subset of chemical systems with second-order reactions. This agreement is independent of the number of interacting molecules.

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1

Citation Types

3
47
0

Year Published

2016
2016
2021
2021

Publication Types

Select...
5
2
1

Relationship

1
7

Authors

Journals

citations
Cited by 51 publications
(51 citation statements)
references
References 23 publications
(42 reference statements)
3
47
0
Order By: Relevance
“…Our framework relies on three main approximations: the linear-noise approximation, the separation between timescales of the intrinsic and extrinsic fluctuations, and the small extrinsic noise expansion. First, the LNA will give an accurate approximation of the CME when the molecular species populations are sufficiently large, when the nonlinearity in the reaction rates is sufficiently weak or else for special classes of biochemical systems ( [32]; see discussion later). Second, our theory requires the extrinsic fluctuations to be slow with respect to the system's intrinsic dynamics.…”
Section: Discussionmentioning
confidence: 99%
See 1 more Smart Citation
“…Our framework relies on three main approximations: the linear-noise approximation, the separation between timescales of the intrinsic and extrinsic fluctuations, and the small extrinsic noise expansion. First, the LNA will give an accurate approximation of the CME when the molecular species populations are sufficiently large, when the nonlinearity in the reaction rates is sufficiently weak or else for special classes of biochemical systems ( [32]; see discussion later). Second, our theory requires the extrinsic fluctuations to be slow with respect to the system's intrinsic dynamics.…”
Section: Discussionmentioning
confidence: 99%
“…However, as the current system is linear (i.e. it contains no bimolecular reactions), the LNA will give the exact expressions for the mean and variance independent of the value of Ω [32]. For this reason, we have chosen Ω = 1 here.…”
Section: A Nonlinear Effects Of Extrinsic Fluctuations On a Linear Mmentioning
confidence: 99%
“…Indeed, the huge complexity of biological systems, their dependence on a large number of variables and the system-to-system variability make the unraveling of these issues, whether using experimental or computational approaches, a highly non-trivial task.More specifically, while the noise control is relatively well understood for small and simple networks, it is still far from clear how the fluctuations propagate through more general and complicated networks and what is the link of the network topology and complexity with the noise buffering or amplification. Different investigations addressed these issues from various perspectives, for example by characterizing the stochastic properties of the chemical reaction networks (CRNs) and studying the propagation of the fluctuations [21,23,24,25]. From a physics-oriented perspective, other studies analyzed the connection between the non-equilibrium thermodynamic properties of the network and the noise level [26,27,28].…”
mentioning
confidence: 99%
“…The fluctuations associated with at least one of the species participating in each of the second-order reaction are Poissonian and uncorrelated with the fluctuations of other species. Also, LNA remains valid for faster activation and deactivation (or synthesis and degradation) rates of the corresponding components compared to the coarse-grained (steady state) time scale [30][31][32][33][34][35][36][37][38][39][40].…”
Section: Introductionmentioning
confidence: 99%
“…II and Appendix). Recent theoretical development [32] shows that LNA is not only limited to high copy number but also exact up to second moments of any chemical species involved in a second-order reaction. The fluctuations associated with at least one of the species participating in each of the second-order reaction are Poissonian and uncorrelated with the fluctuations of other species.…”
Section: Introductionmentioning
confidence: 99%