The Mathematical Institute, University of Oxford, Eprints Archive

A modified Oster-Murray-Harris mechanical model of morphogenesis

Vaughan, JR., B. and Baker, R. E. and Kay, D. and Maini, P. K. (2013) A modified Oster-Murray-Harris mechanical model of morphogenesis. Siam Journal of Applied Mathematics, 73 (6). pp. 2124-2142.

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Abstract

There are two main modeling paradigms for biological pattern formation in developmental biology: chemical prepattern models and cell aggregation models. This paper focuses on an example of a cell aggregation model, the mechanical model developed by Oster, Murray, and Harris [Development, 78 (1983), pp. 83--125]. We revisit the Oster--Murray--Harris model and find that, due to the infinitesimal displacement assumption made in the original version of this model, there is a restriction on the types of boundary conditions that can be prescribed. We derive a modified form of the model which relaxes the infinitesimal displacement assumption. We analyze the dynamics of this model using linear and multiscale nonlinear analysis and show that it has the same linear behavior as the original Oster--Murray--Harris model. Nonlinear analysis, however, predicts that the modified model will allow for a wider range of parameters where the solution evolves to a bounded steady state. The results from both analyses are verified through numerical simulations of the full nonlinear model in one and two dimensions. The increased range of boundary conditions that are well-posed, as well as a wider range of parameters that yield bounded steady states, renders the modified model more applicable to, and more robust for, comparisons with experiments.

Item Type:Article
Uncontrolled Keywords:pattern formation, mechanochemical models, morphogenesis, multiscale analysis
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:1763
Deposited By: Philip Maini
Deposited On:08 Jan 2014 08:49
Last Modified:29 May 2015 19:27

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