### Abstract

Language | English |
---|---|

Pages | 895-921 |

Journal | Bulletin of Mathematical Biology |

Volume | 76 |

Issue number | 4 |

Early online date | 8 Mar 2013 |

DOIs | |

Status | Published - Apr 2014 |

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### Cite this

*Bulletin of Mathematical Biology*,

*76*(4), 895-921. https://doi.org/10.1007/s11538-013-9827-4

**Stochastic pattern formation and spontaneous polarisation : The linear noise approximation and beyond.** / McKane, Alan J.; Biancalani, Tommaso; Rogers, Tim.

Research output: Contribution to journal › Article

*Bulletin of Mathematical Biology*, vol. 76, no. 4, pp. 895-921. https://doi.org/10.1007/s11538-013-9827-4

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TY - JOUR

T1 - Stochastic pattern formation and spontaneous polarisation

T2 - Bulletin of Mathematical Biology

AU - McKane, Alan J.

AU - Biancalani, Tommaso

AU - Rogers, Tim

PY - 2014/4

Y1 - 2014/4

N2 - We review the mathematical formalism underlying the modelling of stochasticity in biological systems. Beginning with a description of the system in terms of its basic constituents, we derive the mesoscopic equations governing the dynamics which generalise the more familiar macroscopic equations. We apply this formalism to the analysis of two specific noise-induced phenomena observed in biologically inspired models. In the first example, we show how the stochastic amplification of a Turing instability gives rise to spatial and temporal patterns which may be understood within the linear noise approximation. The second example concerns the spontaneous emergence of cell polarity, where we make analytic progress by exploiting a separation of time-scales.

AB - We review the mathematical formalism underlying the modelling of stochasticity in biological systems. Beginning with a description of the system in terms of its basic constituents, we derive the mesoscopic equations governing the dynamics which generalise the more familiar macroscopic equations. We apply this formalism to the analysis of two specific noise-induced phenomena observed in biologically inspired models. In the first example, we show how the stochastic amplification of a Turing instability gives rise to spatial and temporal patterns which may be understood within the linear noise approximation. The second example concerns the spontaneous emergence of cell polarity, where we make analytic progress by exploiting a separation of time-scales.

UR - http://www.scopus.com/inward/record.url?scp=84874641364&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1007/s11538-013-9827-4

UR - http://arxiv.org/abs/1211.0462

U2 - 10.1007/s11538-013-9827-4

DO - 10.1007/s11538-013-9827-4

M3 - Article

VL - 76

SP - 895

EP - 921

JO - Bulletin of Mathematical Biology

JF - Bulletin of Mathematical Biology

SN - 0092-8240

IS - 4

ER -