Electrostatic coupling of ion pumps

In this paper the electrostatic interactions between membrane-embedded ion-pumps and their consequences for the kinetics of pump-mediated transport processes have been examined. We show that the time course of an intrinsically monomolecular transport reaction can become distinctly nonexponential, if the reaction is associated with charge translocation and takes place in an aggregate of pump molecules. First we consider the electrostatic coupling of a single dimer of ion-pumps embedded in the membrane. Then we apply the treatment to the kinetic analysis of light-driven proton transport by bacteriorhodopsin which forms two-dimensional hexagonal lattices. Finally, for the case of nonordered molecules, we also consider a model in which the pumps are randomly distributed over the nodes of a lattice. Here the average distance is equal to that deduced experimentally and the elemental size of the lattice is the effective diameter of one single pump. This latter model is applied to an aggregate of membrane-embedded Na, K- and Ca-pumps. In all these cases the electrostatic potential considered is the exact solution calculated from the method of electrical images for a plane membrane of finite thickness immersed in an infinite aqueous solution environment. The distributions of charges (ions or charged binding sites) are considered homogeneous or discrete in the membrane and/or in the external solution. In the case of discrete distributions we compare the results from a mean field approximation and a stochastic simulation