Cells are capable of overcoming the randomizing effect of lateral diffusion in order to regionally differentiate their surfaces. Such local structural specializations are of major significance to cellular function. In some cases, they may be explained by diffusion rates that are insufficient to completely randomize surface gradients over biologically relevant times scales. However, in other cases, absolute and permanent regionalizations are also observed. Mechanistically, the problem is analogous to equilibrium across a dialysis bag: either an absolute barrier exists or the (...) chemical potential between two adjacent regions must be equal. The interactive nature of the system, where localizations of one component lead to localization of others, are also considered here. (shrink)