A model for mesoscale patterns in motile populations
Simpson, Matthew, Landman, Kerry A. , Hughes, Barry , & Fernando, Anthony (2010) A model for mesoscale patterns in motile populations. Physica A: Statistical Mechanics and its Applications, 389(7), pp. 1412-1424.
Experimental observations of cell migration often describe the presence of mesoscale patterns within motile cell populations. These patterns can take the form of cells moving as aggregates or in chain-like formation. Here we present a discrete model capable of producing mesoscale patterns. These patterns are formed by biasing movements to favor a particular configuration of agent–agent attachments using a binding function f(K), where K is the scaled local coordination number. This discrete model is related to a nonlinear diffusion equation, where we relate the nonlinear diffusivity D(C) to the binding function f. The nonlinear diffusion equation supports a range of solutions which can be either smooth or discontinuous. Aggregation patterns can be produced with the discrete model, and we show that there is a transition between the presence and absence of aggregation depending on the sign of D(C). A combination of simulation and analysis shows that both the existence of mesoscale patterns and the validity of the continuum model depend on the form of f. Our results suggest that there may be no formal continuum description of a motile system with strong mesoscale patterns.
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|Item Type:||Journal Article|
|Keywords:||Cell motility, Chain migration, Aggregation, Exclusion process, Nonlinear diffusion|
|Subjects:||Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Biological Mathematics (010202)|
|Divisions:||Past > QUT Faculties & Divisions > Faculty of Science and Technology|
Past > Schools > Mathematical Sciences
|Copyright Owner:||Copyright 2009 Elsevier|
|Deposited On:||01 Dec 2010 08:19|
|Last Modified:||01 Mar 2012 00:28|
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