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Macroscopic limits of individual-based models for motile cell populations with volume exclusion

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Dyson, Louise, Maini, Philip K. and Baker, Ruth E. (2012) Macroscopic limits of individual-based models for motile cell populations with volume exclusion. Physical Review E, 86 (3). 031903 . doi:10.1103/PhysRevE.86.031903

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Official URL: http://dx.doi.org/10.1103/PhysRevE.86.031903

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Abstract

Partial differential equation models are ubiquitous in studies of motile cell populations, giving a phenomenological description of events which can be analyzed and simulated using a wide range of existing tools. However, these models are seldom derived from individual cell behaviors and so it is difficult to accurately include biological hypotheses on this spatial scale. Moreover, studies which do attempt to link individual- and population-level behavior generally employ lattice-based frameworks in which the artifacts of lattice choice at the population level are unclear. In this work we derive limiting population-level descriptions of a motile cell population from an off-lattice, individual-based model (IBM) and investigate the effects of volume exclusion on the population-level dynamics. While motility with excluded volume in on-lattice IBMs can be accurately described by Fickian diffusion, we demonstrate that this is not the case off lattice. We show that the balance between two key parameters in the IBM (the distance moved in one step and the radius of an individual) determines whether volume exclusion results in enhanced or slowed diffusion. The magnitude of this effect is shown to increase with the number of cells and the rate of their movement. The method we describe is extendable to higher-dimensional and more complex systems and thereby provides a framework for deriving biologically realistic, continuum descriptions of motile populations.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Q Science > QH Natural history
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Differential equations, Partial, Cell populations, Stochastic models
Journal or Publication Title: Physical Review E
Publisher: American Physical Society
ISSN: 1539-3755
Official Date: 5 September 2012
Dates:
DateEvent
5 September 2012Published
Volume: 86
Number: 3
Article Number: 031903
DOI: 10.1103/PhysRevE.86.031903
Status: Peer Reviewed
Publication Status: Published
Publisher Statement: © 2012 American Physical Society
Access rights to Published version: Restricted or Subscription Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
Oxford SystemsBiology Doctoral Training Centre[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266

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