Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 895-921 |
| Journal | Bulletin of Mathematical Biology |
| Volume | 76 |
| Issue number | 4 |
| Early online date | 8 Mar 2013 |
| DOIs | |
| Publication status | Published - Apr 2014 |
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Stochastic pattern formation and spontaneous polarisation : The linear noise approximation and beyond. / McKane, Alan J.; Biancalani, Tommaso; Rogers, Tim.
In: Bulletin of Mathematical Biology, Vol. 76, No. 4, 04.2014, p. 895-921.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Stochastic pattern formation and spontaneous polarisation
T2 - The linear noise approximation and beyond
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 -