Power spectra methods for a stochastic description of diffusion on deterministically growing domains
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 ef...
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| Format: | Journal article |
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American Physical Society
2011
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| _version_ | 1826285876663025664 |
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| author | Woolley, T Baker, R Gaffney, E Maini, P |
| author_facet | Woolley, T Baker, R Gaffney, E Maini, P |
| author_sort | Woolley, T |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T01:35:24Z |
| format | Journal article |
| id | oxford-uuid:95001718-b0a9-4c71-baff-e4ac4f99869a |
| institution | University of Oxford |
| last_indexed | 2024-03-07T01:35:24Z |
| publishDate | 2011 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:95001718-b0a9-4c71-baff-e4ac4f99869a2022-03-26T23:43:13ZPower spectra methods for a stochastic description of diffusion on deterministically growing domainsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:95001718-b0a9-4c71-baff-e4ac4f99869aMathematical Institute - ePrintsAmerican Physical Society2011Woolley, TBaker, RGaffney, EMaini, PA 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. |
| spellingShingle | Woolley, T Baker, R Gaffney, E Maini, P Power spectra methods for a stochastic description of diffusion on deterministically growing domains |
| title | Power spectra methods for a stochastic description of diffusion on deterministically growing domains |
| title_full | Power spectra methods for a stochastic description of diffusion on deterministically growing domains |
| title_fullStr | Power spectra methods for a stochastic description of diffusion on deterministically growing domains |
| title_full_unstemmed | Power spectra methods for a stochastic description of diffusion on deterministically growing domains |
| title_short | Power spectra methods for a stochastic description of diffusion on deterministically growing domains |
| title_sort | power spectra methods for a stochastic description of diffusion on deterministically growing domains |
| work_keys_str_mv | AT woolleyt powerspectramethodsforastochasticdescriptionofdiffusionondeterministicallygrowingdomains AT bakerr powerspectramethodsforastochasticdescriptionofdiffusionondeterministicallygrowingdomains AT gaffneye powerspectramethodsforastochasticdescriptionofdiffusionondeterministicallygrowingdomains AT mainip powerspectramethodsforastochasticdescriptionofdiffusionondeterministicallygrowingdomains |