Models of collective cell behaviour with crowding effects : comparing lattice-based and lattice-free approaches

Plank, Michael & Simpson, Matthew (2012) Models of collective cell behaviour with crowding effects : comparing lattice-based and lattice-free approaches. Journal of the Royal Society Interface.

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Individual-based models describing the migration and proliferation of a population of cells frequently restrict the cells to a predefined lattice. An implicit assumption of this type of lattice based model is that a proliferative population will always eventually fill the lattice. Here we develop a new lattice-free individual-based model that incorporates cell-to-cell crowding effects. We also derive approximate mean-field descriptions for the lattice-free model in two special cases motivated by commonly used experimental setups. Lattice-free simulation results are compared to these mean-field descriptions and to a corresponding lattice-based model. Data from a proliferation experiment is used to estimate the parameters for the new model, including the cell proliferation rate, showing that the model fits the data well. An important aspect of the lattice-free model is that the confluent cell density is not predefined, as with lattice-based models, but an emergent model property. As a consequence of the more realistic, irregular configuration of cells in the lattice-free model, the population growth rate is much slower at high cell densities and the population cannot reach the same confluent density as an equivalent lattice-based model.

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28 citations in Scopus
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28 citations in Web of Science®

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36 since deposited on 14 May 2012
5 in the past twelve months

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ID Code: 50304
Item Type: Journal Article
Refereed: Yes
Additional Information: Published online before print June 13, 2012
Keywords: cell migration, cell proliferation, exclusion process, random walk, lattice based, lattice free
DOI: 10.1098/rsif.2012.0319
ISSN: 1742-5689
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 2012 The Royal Society
Deposited On: 14 May 2012 22:39
Last Modified: 11 Feb 2013 03:19

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