  We introduce a three-dimensional stochastic reaction-diffusion model to
describe MinD/MinE dynamical structures in Escherichia coli. This model
spontaneously generates pole-to-pole oscillations of the membrane-associated
MinD proteins, MinE ring, as well as filaments of the membrane-associated MinD
proteins. Experimental data suggest MinD filaments are two-stranded. In order
to model them we assume that each membrane-associated MinD protein can form up
to three bonds with adjacent membrane associated MinD molecules and that MinE
induced hydrolysis strongly depends on the number of bonds MinD has
established.
