A channel model with fluctuating barrier structures.

Following the theory 'Fluctuations of barrier structure in ionic channels' (Läuger, P., Stephan, W. and Frehland, E. (1980) Biochim. Biophys. Acta 602, 167-180), we constructed a model of a channels with several conformational states. The origin of these conformational states and the source for the transitions from one to the other are given explicitly for the presented model. In this work the effect of multiple conformational states on the ion transport process is analyzed. We considered a channel protein with two main barriers and one binding site. The site is surrounded by dipolar groups. The dipole moment of these groups can be reoriented by thermal activity and also by electrical interaction with the transported ions. Differently polarized states generate different activation energy barriers for the ions. The set of conformational states of the channel is constituted by all the possible polarized states of the binding site. Using the rate-theory analysis of ion transport (Glässtone, S., Laider, K.J. and Eyring, H. (1941) The theory of rate processes, McGraw-Hill, New York), the possible coupling between ion flux and the channel conformational transitions has been incorporated into the model by considering the dependence of the rate constants on the heights of the energy barriers. The resulting multistate kinetic equations have been solved numerically. It was shown that the simple saturation characteristic of the flux-concentration curve was obtained. For certain values of the model parameters, the channel shows a strongly different conductance for anions compared to cations. In fact, the model contains an interesting mechanism that exhibits selectivity with respect to the charge of the ions.

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.