On the modelling of biological patterns with mechanochemical models: Insights from analysis and computation

Bulletin of Mathematical Biology
P MoreoM Doblaré

Abstract

The diversity of biological form is generated by a relatively small number of underlying mechanisms. Consequently, mathematical and computational modelling can, and does, provide insight into how cellular level interactions ultimately give rise to higher level structure. Given cells respond to mechanical stimuli, it is therefore important to consider the effects of these responses within biological self-organisation models. Here, we consider the self-organisation properties of a mechanochemical model previously developed by three of the authors in Acta Biomater. 4, 613-621 (2008), which is capable of reproducing the behaviour of a population of cells cultured on an elastic substrate in response to a variety of stimuli. In particular, we examine the conditions under which stable spatial patterns can emerge with this model, focusing on the influence of mechanical stimuli and the interplay of non-local phenomena. To this end, we have performed a linear stability analysis and numerical simulations based on a mixed finite element formulation, which have allowed us to study the dynamical behaviour of the system in terms of the qualitative shape of the dispersion relation. We show that the consideration of mechanotaxis, namely changes...Continue Reading

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Citations

Mar 22, 2012·Journal of Mathematical Biology·Uduak Z GeorgeAnotida Madzvamuse
Nov 11, 2011·Bulletin of Mathematical Biology·Václav KlikaEamonn A Gaffney
Jun 19, 2013·Journal of Theoretical Biology·J Belmonte-BeitiaE A Gaffney
May 27, 2021·Bulletin of Mathematical Biology·Chiara VillaTommaso Lorenzi

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