The Mathematical Institute, University of Oxford, Eprints Archive

Power spectra methods for a stochastic description of diffusion on deterministically growing domains

Woolley, T. E. and Baker, R. E. and Gaffney, E. A. and Maini, P. K. (2011) Power spectra methods for a stochastic description of diffusion on deterministically growing domains. Physical Review E, 84 (2). 021915-1-021915-15. ISSN 1063-651X

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Abstract

A central challenge in developmental biology is understanding the creation of robust spatiotemporal heterogeneity. Generally, the mathematical treatments of biological systems have used continuum, mean-field hypotheses for their constituent parts, which ignores any sources of intrinsic stochastic effects. In this paper we consider a stochastic space-jump process as a description of diffusion, i.e., particles are able to undergo a random walk on a discretized domain. By developing analytical Fourier methods we are able to probe this probabilistic framework, which gives us insight into the patterning potential of diffusive systems. Further, an alternative description of domain growth is introduced, with which we are able to rigorously link the mean-field and stochastic descriptions. Finally, through combining these ideas, it is shown that such stochastic descriptions of diffusion on a deterministically growing domain are able to support the nucleation of states that are far removed from the deterministic mean-field steady state.

Item Type:Article
Subjects:A - C > Biology and other natural sciences
ID Code:1380
Deposited By:Philip Maini
Deposited On:13 Aug 2011 09:55
Last Modified:13 Aug 2011 09:55

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