Macroscopic model of selfpropelled bacteria swarming with regular reversals
Abstract
Periodic reversals in the direction of motion in systems of selfpropelled rodshaped 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 onedimensional cellbased stochastic model of reversing nonoverlapping bacteria and a macroscopic nonlinear diffusion equation describing the dynamics of cellular density. BoltzmannMatano 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 p_{0} is obtained such that nonlinear diffusion is dominated by the collisions between cells for the densities p>p_{0}. 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.
 Publication:

Physical Review E
 Pub Date:
 February 2012
 DOI:
 10.1103/PhysRevE.85.021903
 arXiv:
 arXiv:1101.1287
 Bibcode:
 2012PhRvE..85b1903G
 Keywords:

 87.18.Ed;
 05.40.a;
 05.65.+b;
 87.18.Hf;
 Aggregation and other collective behavior of motile cells;
 Fluctuation phenomena random processes noise and Brownian motion;
 Selforganized systems;
 Spatiotemporal pattern formation in cellular populations;
 Physics  Biological Physics;
 Nonlinear Sciences  Chaotic Dynamics;
 Quantitative Biology  Cell Behavior
 EPrint:
 21 pages, 30 figures