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.
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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|Item Type:||Journal Article|
|Additional Information:||Published online before print June 13, 2012|
|Keywords:||cell migration, cell proliferation, exclusion process, random walk, lattice based, lattice free|
|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:||15 May 2012 08:39|
|Last Modified:||11 Feb 2013 13:19|
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