Models of collective cell motion for cell populations with different aspect ratio : diffusion, proliferation and travelling waves

Baker, Ruth & Simpson, Matthew (2012) Models of collective cell motion for cell populations with different aspect ratio : diffusion, proliferation and travelling waves. Physica A : Statistical Mechanics and its Applications, 391(14), pp. 3729-3750.

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Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealizations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data for with varying cell shape.

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11 citations in Scopus
11 citations in Web of Science®
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ID Code: 47935
Item Type: Journal Article
Refereed: Yes
Keywords: cell motility, cell shape, exclusion process, travelling waves, cellular automata
DOI: 10.1016/j.physa.2012.01.009
ISSN: 0378-4371
Divisions: Current > Institutes > Institute of Health and Biomedical Innovation
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2012 Elsevier
Copyright Statement: This is the author’s version of a work that was accepted for publication in Physica A : Statistical Mechanics and its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physica A : Statistical Mechanics and its Applications, Physica A : Statistical Mechanics and its Applications, VOL 391, ISSUE 14, 10.1016/j.physa.2012.01.009.
Deposited On: 04 Jan 2012 23:14
Last Modified: 19 Jul 2017 23:37

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