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

Lane, D. C. ORCID: https://orcid.org/0000-0001-6658-7041, Murray, J. D. 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 (4). pp. 309-331. ISSN 1477-8602

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Abstract/Summary

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
Refereed:Yes
Divisions:No Reading authors. Back catalogue items
Henley Business School > Business Informatics, Systems and Accounting
ID Code:38191
Publisher:Oxford University Press

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