SIMULATION OF THE DYNAMICS OF MYXOBACTERIA SWARMS BASED ON A ONE-DIMENSIONAL INTERACTION MODEL

Myxobacteria have a high level of intercellular coordination. Their swarms show “streets” and “whirls” of parallel gliding cells as well as wave-like moving cell density fields, so called “rippling”. The dependence from two phenomenological parameters, gliding velocity and turning frequency, has turned out to be characteristic for cell behavior at the swarm edge. As cells at the swarm edge are mostly gliding parallel in one dimension, the behavior of single cells can be comprised in a one-dimensional model describing interactions between cells of the same species in a homogenous environment, where turning frequency determines the cell density distribution via a hyperbolic differential integral equation. After specifying the parameter functions appearing in the integral, it is examined how these parameters influence the turning behavior and therefore the edge development of swarms over time.

Numerical simulations of this model are performed both for the stationary and the time dependent case. For the time dependent model a front tracking method is applied using a Lagrange interpolation at the swarm edge. The simulations show that perception of different gliding directions is significant for the dynamics of swarm expansion and retraction.