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

Handle URI:
http://hdl.handle.net/10754/599063
Title:
On the Modelling of Biological Patterns with Mechanochemical Models: Insights from Analysis and Computation
Authors:
Moreo, P.; Gaffney, E. A.; García-Aznar, J. M.; Doblaré, M.
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.
Citation:
Moreo P, Gaffney EA, García-Aznar JM, Doblaré M (2009) On the Modelling of Biological Patterns with Mechanochemical Models: Insights from Analysis and Computation. Bull Math Biol 72: 400–431. Available: http://dx.doi.org/10.1007/s11538-009-9452-4.
Publisher:
Springer Nature
Journal:
Bulletin of Mathematical Biology
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
14-Nov-2009
DOI:
10.1007/s11538-009-9452-4
PubMed ID:
19915925
Type:
Article
ISSN:
0092-8240; 1522-9602
Sponsors:
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).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorMoreo, P.en
dc.contributor.authorGaffney, E. A.en
dc.contributor.authorGarcía-Aznar, J. M.en
dc.contributor.authorDoblaré, M.en
dc.date.accessioned2016-02-25T13:52:09Zen
dc.date.available2016-02-25T13:52:09Zen
dc.date.issued2009-11-14en
dc.identifier.citationMoreo P, Gaffney EA, García-Aznar JM, Doblaré M (2009) On the Modelling of Biological Patterns with Mechanochemical Models: Insights from Analysis and Computation. Bull Math Biol 72: 400–431. Available: http://dx.doi.org/10.1007/s11538-009-9452-4.en
dc.identifier.issn0092-8240en
dc.identifier.issn1522-9602en
dc.identifier.pmid19915925en
dc.identifier.doi10.1007/s11538-009-9452-4en
dc.identifier.urihttp://hdl.handle.net/10754/599063en
dc.description.abstractThe 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.en
dc.description.sponsorshipThe 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).en
dc.publisherSpringer Natureen
dc.subjectFinite element simulationen
dc.subjectPattern formationen
dc.titleOn the Modelling of Biological Patterns with Mechanochemical Models: Insights from Analysis and Computationen
dc.typeArticleen
dc.identifier.journalBulletin of Mathematical Biologyen
dc.contributor.institutionUniversidad de Zaragoza, Zaragoza, Spainen
dc.contributor.institutionCIBER Bioingenieria, Biomateriales y Nanomedicina, Zaragoza, Spainen
dc.contributor.institutionEBERS Medical Technology S.L., Zaragoza, Spainen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en

Related articles on PubMed

All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.