On the Modelling of Biological Patterns with Mechanochemical Models: Insights from Analysis and Computation

P. Moreo, E. A. Gaffney, J. M. García-Aznar, M. Doblaré

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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 in migration speeds and directions in response to mechanical stimuli alters the conditions for pattern formation in a singular manner. Furthermore without non-local effects, responses to mechanical stimuli are observed to result in dispersion relations with positive growth rates at arbitrarily large wavenumbers, in turn yielding heterogeneity at the cellular level in model predictions. This highlights the sensitivity and necessity of non-local effects in mechanically influenced biological pattern formation models and the ultimate failure of the continuum approximation in their absence. © 2009 Society for Mathematical Biology.
Original languageEnglish (US)
Pages (from-to)400-431
Number of pages32
JournalBulletin of Mathematical Biology
Volume72
Issue number2
DOIs
StatePublished - Nov 14 2009
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: The authors gratefully acknowledge the research support of the Spanish Ministry of Sci-ence and Technology through Research Projects DPI2006-14669 and DPI2006-09692 andthe FPU graduate research fellowship program. This publication is based on work sup-ported in part by Award No. KUK-C1-013-04, made by King Abdullah University ofScience and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

Fingerprint Dive into the research topics of 'On the Modelling of Biological Patterns with Mechanochemical Models: Insights from Analysis and Computation'. Together they form a unique fingerprint.

Cite this