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A model for mesoscale patterns in motile populations

Author

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  • Simpson, Matthew J.
  • Landman, Kerry A.
  • Hughes, Barry D.
  • Fernando, Anthony E.

Abstract

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.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:7:p:1412-1424
    DOI: 10.1016/j.physa.2009.12.010
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    Cited by:

    1. 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.
    2. Rotem Aharon & Peter W Janes & Anthony W Burgess & Kais Hamza & Fima Klebaner & Martin Lackmann, 2014. "A Mathematical Model for Eph/Ephrin-Directed Segregation of Intermingled Cells," PLOS ONE, Public Library of Science, vol. 9(12), pages 1-19, December.

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