Subcellular protein localization in {\it E. coli}: diffusion and membrane attachment of MinD molecules

In {\it E. coli}, accurate cell division depends upon the oscillation of Min proteins. We provide a model for polar localization of MinD based only on diffusion, a delay for nucleotide exchange, and different rates of attchment to the bare membrane and 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.