Pattern formation within Escherichia coli: diffusion, membrane   attachment, and self-interaction of MinD molecules
  In E. coli, accurate cell division depends upon the oscillation of Min proteins from pole to pole. We provide a model for the polar localization of MinD based only on diffusion, a delay for nucleotide exchange, and different rates of attachment to the bare membrane and the occupied membrane. We derive analytically the probability density, and correspondingly the length scale, for MinD attachment zones. Our simple analytical model illustrates the processes giving rise to the observed localization of cellular MinD zones. 
Rahul V. Kulkarni, Kerwyn Casey Huang, Morten Kloster, and Ned S.   Wingreen