How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations?

Grima, Ramon; Thomas, Philipp; Straube, Arthur V.

doi:10.1063/1.3625958

Cited by 110 publications

(168 citation statements)

References 41 publications

Supporting

Mentioning

161

Contrasting

Order By: Relevance

“…26 As is discussed in Introduction, recent numerical studies support the validity of chemical Fokker-Planck equation up to smaller value of Ω than the range adopted for LNA. 7,31,32 In fact, we also demonstrated that the direct numerical simulations agree quite well with the predictions of chemical Fokker-Planck equation for all motifs marked by "+" or "++" in Fig. 1, where small-number effects are well reproduced by the chemical Fokker-Planck equation, rather than by the LNA.…”

Section: Discussionsupporting

confidence: 63%

Motif analysis for small-number effects in chemical reaction dynamics

Saito

Sughiyama

Kaneko

2016

The Journal of Chemical Physics

View full text Add to dashboard Cite

The number of molecules involved in a cell or subcellular structure is sometimes rather small. In this situation, ordinary macroscopic-level fluctuations can be overwhelmed by non-negligible large fluctuations, which results in drastic changes in chemical-reaction dynamics and statistics compared to those observed under a macroscopic system (i.e., with a large number of molecules). In order to understand how salient changes emerge from fluctuations in molecular number, we here quantitatively define small-number effect by focusing on a 'mesoscopic' level, in which the concentration distribution is distinguishable both from micro-and macroscopic ones, and propose a criterion for determining whether or not such an effect can emerge in a given chemical reaction network. Using the proposed criterion, we systematically derive a list of motifs of chemical reaction networks that can show small-number effects, which includes motifs showing emergence of the power law and the bimodal distribution observable in a mesoscopic regime with respect to molecule number. The list of motifs provided herein is helpful in the search for candidates of biochemical reactions with a small-number effect for possible biological functions, as well as for designing a reaction system whose behavior can change drastically depending on molecule number, rather than concentration.

show abstract

Section: Discussionsupporting

confidence: 63%

Motif analysis for small-number effects in chemical reaction dynamics

Saito

Sughiyama

Kaneko

2016

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…The various different approximations are all closely related, see, e.g., Ref. 11 for further details.…”

Section: Introductionmentioning

confidence: 99%

Gaussian approximations for stochastic systems with delay: Chemical Langevin equation and application to a Brusselator system

Brett

Galla

2014

The Journal of Chemical Physics

View full text Add to dashboard Cite

“…In this case, the system description with uncorrelated white noise in the Ito interpretation does not predict correctly the system behavior. This is not surprising because it has been known that for second-order reactions, the FPE with independent white noise is not accurate (Grima et al, 2011;Thomas et al, 2013). Different approaches have been introduced to resolve the discrepancy, exemplified by the colored noise approximations (Shahrezaei et al, 2008).…”

Section: Discussionmentioning

confidence: 99%

An open-loop approach to calculate noise-induced transitions

Maleki

Becskei

2017

Journal of Theoretical Biology

View full text Add to dashboard Cite

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

show abstract

How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations?

Cited by 110 publications

References 41 publications

Motif analysis for small-number effects in chemical reaction dynamics

Motif analysis for small-number effects in chemical reaction dynamics

Gaussian approximations for stochastic systems with delay: Chemical Langevin equation and application to a Brusselator system

An open-loop approach to calculate noise-induced transitions

Contact Info

Product

Resources

About