IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v389y2010i7p1412-1424.html
   My bibliography  Save this article

A model for mesoscale patterns in motile populations

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437109010061
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2009.12.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:389:y:2010:i:7:p:1412-1424. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.