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Multi-species simple exclusion processes

Author

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

Abstract

A motility mechanism based on a simple exclusion process, where the movement of discrete agents on a lattice is either unbiased (symmetric) or biased (asymmetric) is considered. Estimates of diffusivities from tracking data do not describe the population-level response of the system. This mismatch between the individual-level and population-level behaviour can be resolved by averaging the individual-level mechanism in terms of an expected site occupancy. New insight into simple exclusion processes is obtained by representing the system as a series of interacting subpopulations. This formalism leads to a system of nonlinear advection–diffusion equations which can be interpreted in terms of the agent fluxes. These interactions have consequences for both agent-based modelling and continuum modelling in cell biology, such as tracking subpopulations of cells within a total cell population.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:4:p:399-406
    DOI: 10.1016/j.physa.2008.10.038
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    Citations

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    Cited by:

    1. Irons, Carolyn & Plank, Michael J. & Simpson, Matthew J., 2016. "Lattice-free models of directed cell motility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 110-121.
    2. Cirillo, Emilio N.M. & Krehel, Oleh & Muntean, Adrian & van Santen, Rutger & Sengar, Aditya, 2016. "Residence time estimates for asymmetric simple exclusion dynamics on strips," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 436-457.
    3. 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.
    4. Clements, Alastair J. & Fadai, Nabil T., 2022. "Agent-based modelling of sports riots," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    5. Matthew J Simpson & Parvathi Haridas & D L Sean McElwain, 2014. "Do Pioneer Cells Exist?," PLOS ONE, Public Library of Science, vol. 9(1), pages 1-11, January.

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