Stochastic Pattern Formation and Spontaneous Polarisation: The Linear Noise Approximation and Beyond

McKane, Alan J.; Biancalani, Tommaso; Rogers, Tim

doi:10.1007/s11538-013-9827-4

Cited by 81 publications

(157 citation statements)

References 31 publications

Supporting

Mentioning

152

Contrasting

Unclassified

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: 78%

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: 78%

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

“…For further background on how to arrive precisely at the forms given by Eq. (3) the reader is referred to previous discussions in the literature [1,6,43]. If W (1) and W (2) are independent of n, then the selection is known as frequency independent selection.…”

Section: Setting-up the Modelmentioning

confidence: 99%

“…In a previous paper [43], we have reviewed the process of setting-up a description of this class of biological systems in terms of its basic constituents, and from this deriving the mesoscopic equations governing the dynamics which generalise what might be the more familiar macroscopic equations. In particular, in Ref.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Exploiting Fast-Variables to Understand Population Dynamics and Evolution

Constable

McKane

2017

J Stat Phys

Self Cite

View full text Add to dashboard Cite

We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are caused by individual events while the dynamics are described in terms of the time-evolution of a probability density function. In general, the application of the diffusion approximation still leaves a description that is quite complex. However, in many biological applications one or more of the processes happen slowly relative to the system's other processes, and the dynamics can be approximated as occurring within a slow low-dimensional subspace. We review these time-scale separation arguments and analyse the more simple stochastic dynamics that result in a number of cases. We stress that it is important to retain the demographic noise derived in this way, and emphasise this point by showing that it can alter the direction of selection compared to the prediction made from an analysis of the corresponding deterministic model.

show abstract

“…For instance, new effective extrema may be formed through the effects of noise [36], as well as the effective location of extrema being moved. In the present case, the effect is more closely related to the situation found in some kinds of stochastic pattern formation [37,38], where the region of stability of patterns can be increased by the stochastic effects giving a new effective condition for stability which differs from that found through a purely deterministic analysis.…”

Section: Discussionmentioning

confidence: 51%

Modes of competition and the fitness of evolved populations

Rogers

McKane

2015

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

Competition between individuals drives the evolution of whole species. Although the fittest individuals survive the longest and produce the most offspring, in some circumstances the resulting species may not be optimally fit. Here, using theoretical analysis and stochastic simulations of a simple model ecology, we show how the mode of competition can profoundly affect the fitness of evolved species. When individuals compete directly with one another, the adaptive dynamics framework provides accurate predictions for the number and distribution of species, which occupy positions of maximal fitness. By contrast, if competition is mediated by the consumption of a common resource then demographic noise leads to the stabilization of species with near minimal fitness.

show abstract

Stochastic Pattern Formation and Spontaneous Polarisation: The Linear Noise Approximation and Beyond

Cited by 81 publications

References 31 publications

Motif analysis for small-number effects in chemical reaction dynamics

Motif analysis for small-number effects in chemical reaction dynamics

Exploiting Fast-Variables to Understand Population Dynamics and Evolution

Modes of competition and the fitness of evolved populations

Contact Info

Product

Resources

About