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

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    Type
    Article
    Authors
    Moreo, P.
    Gaffney, E. A.
    García-Aznar, J. M.
    Doblaré, M.
    KAUST Grant Number
    KUK-C1-013-04
    Date
    2009-11-14
    Online Publication Date
    2009-11-14
    Print Publication Date
    2010-02
    Permanent link to this record
    http://hdl.handle.net/10754/599063
    
    Metadata
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    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.
    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).
    Publisher
    Springer Nature
    Journal
    Bulletin of Mathematical Biology
    DOI
    10.1007/s11538-009-9452-4
    PubMed ID
    19915925
    ae974a485f413a2113503eed53cd6c53
    10.1007/s11538-009-9452-4
    Scopus Count
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