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Macroscopic model of self-propelled bacteria swarming with regular reversals

Richard Gejji1,2, Pavel M. Lushnikov3, and Mark Alber1

  • 1Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, Indiana 46656, USA
  • 2Mathematical Biosciences Institute, Ohio State University, 1735 Neil Avenue, Columbus, Ohio 43210, USA
  • 3Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131, USA

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Phys. Rev. E 85, 021903 – Published 6 February, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.021903

Abstract

Periodic reversals in the direction of motion in systems of self-propelled rod-shaped bacteria enable them to effectively resolve traffic jams formed during swarming and maximize the swarming rate of the colony. In this paper, a connection is established between a microscopic one-dimensional cell-based stochastic model of reversing nonoverlapping bacteria and a macroscopic nonlinear diffusion equation describing the dynamics of cellular density. Boltzmann-Matano analysis is used to determine the nonlinear diffusion equation corresponding to the specific reversal frequency. Stochastic dynamics averaged over an ensemble is shown to be in very good agreement with the numerical solutions of this nonlinear diffusion equation. Critical density p0 is obtained such that nonlinear diffusion is dominated by the collisions between cells for the densities p>p0. An analytical approximation of the pairwise collision time and semianalytical fit for the total jam time per reversal period are also obtained. It is shown that cell populations with high reversal frequencies are able to spread out effectively at high densities. If the cells rarely reverse, then they are able to spread out at lower densities but are less efficient at spreading out at higher densities.

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Phys. Rev. E 85, 021903– Published 6 February, 2012
  • Received 6 January 2011
Article part of CHORUS

©2012 American Physical Society

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