Stochastic pattern formation and spontaneous polarisation: The linear noise approximation and beyond

Alan J. McKane, Tommaso Biancalani, Tim Rogers

Research output: Contribution to journalArticle

47 Citations (Scopus)
138 Downloads (Pure)

Abstract

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.
Original languageEnglish
Pages (from-to)895-921
JournalBulletin of Mathematical Biology
Volume76
Issue number4
Early online date8 Mar 2013
DOIs
Publication statusPublished - Apr 2014

Fingerprint Dive into the research topics of 'Stochastic pattern formation and spontaneous polarisation: The linear noise approximation and beyond'. Together they form a unique fingerprint.

  • Cite this