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Models of collective cell motion for cell populations with different aspect ratio: Diffusion, proliferation and travelling waves

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  • Baker, Ruth E.
  • Simpson, Matthew J.

Abstract

Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealisations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population-level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two-dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data with varying cell shape.

Suggested Citation

  • Baker, Ruth E. & Simpson, Matthew J., 2012. "Models of collective cell motion for cell populations with different aspect ratio: Diffusion, proliferation and travelling waves," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(14), pages 3729-3750.
  • Handle: RePEc:eee:phsmap:v:391:y:2012:i:14:p:3729-3750
    DOI: 10.1016/j.physa.2012.01.009
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    References listed on IDEAS

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    1. Simpson, Matthew J. & Landman, Kerry A. & Clement, T.Prabhakar, 2005. "Assessment of a non-traditional operator split algorithm for simulation of reactive transport," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(1), pages 44-60.
    2. Simpson, Matthew J. & Landman, Kerry A. & Hughes, Barry D. & Fernando, Anthony E., 2010. "A model for mesoscale patterns in motile populations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(7), pages 1412-1424.
    3. Simpson, Matthew J. & Landman, Kerry A. & Hughes, Barry D., 2010. "Cell invasion with proliferation mechanisms motivated by time-lapse data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3779-3790.
    4. Simpson, Matthew J. & Landman, Kerry A. & Hughes, Barry D., 2009. "Multi-species simple exclusion processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 399-406.
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    Cited by:

    1. Rashmi Priya & Guillermo A Gomez & Srikanth Budnar & Bipul R Acharya & Andras Czirok & Alpha S Yap & Zoltan Neufeld, 2017. "Bistable front dynamics in a contractile medium: Travelling wave fronts and cortical advection define stable zones of RhoA signaling at epithelial adherens junctions," PLOS Computational Biology, Public Library of Science, vol. 13(3), pages 1-19, March.

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