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dc.contributor.authorMacfarlane, Fiona Ruth
dc.contributor.authorChaplain, Mark Andrew Joseph
dc.contributor.authorLorenzi, Tommaso
dc.identifier.citationMacfarlane , F R , Chaplain , M A J & Lorenzi , T 2020 , ' A hybrid discrete-continuum approach to model Turing pattern formation ' , Mathematical Biosciences and Engineering , vol. 17 , no. 6 , pp. 7442-7479 .
dc.identifier.otherORCID: /0000-0001-5727-2160/work/83481900
dc.identifier.otherORCID: /0000-0003-2242-7745/work/83482035
dc.descriptionFunding: MAJC gratefully acknowledges support of EPSRC Grant No. EP/N014642/1 (EPSRC Centre for Multiscale Soft Tissue Mechanics–With Application to Heart & Cancer)en
dc.description.abstractSince its introduction in 1952, with a further refinement in 1972 by Gierer and Meinhardt, Turing’s (pre-)pattern theory (the chemical basis of morphogenesis) has been widely applied to a number of areas in developmental biology, where evolving cell and tissue structures are naturally observed. The related pattern formation models normally comprise a system of reaction-diffusion equations for interacting chemical species (morphogens), whose heterogeneous distribution in some spatial domain acts as a template for cells to form some kind of pattern or structure through, for example, differentiation or proliferation induced by the chemical pre-pattern. Here we develop a hybrid discrete-continuum modelling framework for the formation of cellular patterns via the Turing mechanism. In this framework, a stochastic individual-based model of cell movement and proliferation is combined with a reaction-diffusion system for the concentrations of some morphogens. As an illustrative example, we focus on a model in which the dynamics of the morphogens are governed by an activator-inhibitor system that gives rise to Turing pre-patterns. The cells then interact with the morphogens in their local area through either of two forms of chemically-dependent cell action: Chemotaxis and chemically-controlled proliferation. We begin by considering such a hybrid model posed on static spatial domains, and then turn to the case of growing domains. In both cases, we formally derive the corresponding deterministic continuum limit and show that that there is an excellent quantitative match between the spatial patterns produced by the stochastic individual-based model and its deterministic continuum counterpart, when sufficiently large numbers of cells are considered. This paper is intended to present a proof of concept for the ideas underlying the modelling framework, with the aim to then apply the related methods to the study of specific patterning and morphogenetic processes in the future.
dc.relation.ispartofMathematical Biosciences and Engineeringen
dc.subjectCell pattern formationen
dc.subjectTuring patternsen
dc.subjectHybrid modelsen
dc.subjectIndividual-based modelsen
dc.subjectReaction-diffusion systemsen
dc.subjectQA Mathematicsen
dc.subjectQH301 Biologyen
dc.titleA hybrid discrete-continuum approach to model Turing pattern formationen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. School of Mathematics and Statisticsen
dc.contributor.institutionUniversity of St Andrews. Applied Mathematicsen
dc.description.statusPeer revieweden

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