Comparing methods for modelling spreading cell fronts

Markham, Deborah C., Simpson, Matthew, Maini, Philip K., Gaffney, Eamonn, & Baker, Ruth (2014) Comparing methods for modelling spreading cell fronts. Journal of Theoretical Biology, 353, pp. 95-103.

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Abstract

Spreading cell fronts play an essential role in many physiological processes. Classically, models of this process are based on the Fisher-Kolmogorov equation; however, such continuum representations are not always suitable as they do not explicitly represent behaviour at the level of individual cells. Additionally, many models examine only the large time asymptotic behaviour, where a travelling wave front with a constant speed has been established. Many experiments, such as a scratch assay, never display this asymptotic behaviour, and in these cases the transient behaviour must be taken into account. We examine the transient and asymptotic behaviour of moving cell fronts using techniques that go beyond the continuum approximation via a volume-excluding birth-migration process on a regular one-dimensional lattice. We approximate the averaged discrete results using three methods:

(i) mean-field, (ii) pair-wise, and (iii) one-hole approximations.

We discuss the performace of these methods, in comparison to the averaged discrete results, for a range of parameter space, examining both the transient and asymptotic behaviours. The one-hole approximation, based on techniques from statistical physics, is not capable of predicting transient behaviour but provides excellent agreement with the asymptotic behaviour of the averaged discrete results, provided that cells are proliferating fast enough relative to their rate of migration. The mean-field and pair-wise approximations give indistinguishable asymptotic results, which agree with the averaged discrete results when cells are migrating much more rapidly than they are proliferating. The pair-wise approximation performs better in the transient region than does the mean-field, despite having the same asymptotic behaviour. Our results show that each approximation only works in specific situations, thus we must be careful to use a suitable approximation for a given system, otherwise inaccurate predictions could be made.

Impact and interest:

4 citations in Scopus
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4 citations in Web of Science®

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10 since deposited on 19 Feb 2014
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ID Code: 67531
Item Type: Journal Article
Refereed: Yes
Additional URLs:
Keywords: travelling front, cell migration, cell proliferation, cancer, wound healing
DOI: 10.1016/j.jtbi.2014.02.023
ISSN: 0022-5193
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Biological Mathematics (010202)
Divisions: Current > Institutes > Institute of Health and Biomedical Innovation
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2014 Elsevier Ltd.
Copyright Statement: NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Theoretical Biology. 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 Journal of Theoretical Biology, [Volume 353, (21 July 2014)] DOI: 10.1016/j.jtbi.2014.02.023
Deposited On: 19 Feb 2014 22:47
Last Modified: 22 Jul 2015 09:13

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