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Analysis of wave phenomena in a morphogenetic mechanochemical model and an application to post-fertilization waves on eggs

Lane, David C. and Murray, James Dickson and Manoranjan, V. S. (1987) Analysis of wave phenomena in a morphogenetic mechanochemical model and an application to post-fertilization waves on eggs. IMA Journal of Mathematics Applied in Medicine and Biology, 4. pp. 309-331. ISSN 1477-8602

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Identification Number: 10.1093/imammb/4.4.309

Abstract

Wave solutions to a mechanochemical model for cytoskeletal activity are studied and the results applied to the waves of chemical and mechanical activity that sweep over an egg shortly after fertilization. The model takes into account the calcium-controlled presence of actively contractile units in the cytoplasm, and consists of a viscoelastic force equilibrium equation and a conservation equation for calcium. Using piecewise linear caricatures, we obtain analytic solutions for travelling waves on a strip and demonstrate uiat the full nonlinear system behaves as predicted by the analytic solutions. The equations are solved on a sphere and the numerical results are similar to the analytic solutions. We indicate how the speed of the waves can be used as a diagnostic tool with which the chemical reactivity of the egg surface can be measured.

Item Type: Article
Official URL: http://www.oup.co.uk/
Additional Information: © 1987 Oxford University Press
Subjects: Q Science > Q Science (General)
Sets: Research centres and groups > Managerial Economics and Strategy Group
Research centres and groups > Management Science Group
Date Deposited: 07 Aug 2008 16:06
Last Modified: 14 Jun 2012 13:50
URI: http://eprints.lse.ac.uk/id/eprint/20565

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