A stochastic cellular automaton modeling gliding and aggregation of myxobacteria

The myxobacteria are ubiquitous soil bacteria which aggregate under starvation conditions and build fruiting bodies to survive. Until recently the mechanisms of their social gliding, aggregation, and fruiting body formation have not been well understood. In this paper a stochastic cellular automaton model is presented to describe and provide an understanding of how the bacteria manage to build higher organized structures. In the automaton myxobacteria move on a square grid with periodic boundary conditions. They respond to the four nearest neighbors of their frontal cell poles, mainly through two factors: slime and a diffusing chemoattractant; both are produced by the bacteria themselves. Simulations show the interdependence of the different mechanisms which finally cause aggregation. A simplified version of this model is formally approximated by a system of partial differential equations, a chemotaxis system. A related publication [SIAM J. Appl. Math., 61 (2000), pp. 183-212] deals with the first rigorous derivation of this type of equations from an interacting stochastic many particle system.