Proton decay kinetics for vesicles containing buffers—an analytical solution

Abstract

The problem of predicting the kinetics of proton efflux and the decay of the internal proton concentration for vesicles containing one or more buffers for which the internal proton concentration is initially higher than that of the surrounding medium is examined. An analytical solution is derived that describes the time course of the proton efflux from vesicles and the decay of the internal proton concentration under conditions of zero transmembrane electric potential. The effect of the internal buffers is to increase the time required for the proton concentration gradient to equilibrate across the membrane. To simplify the analysis we assume that the equilibration of the internal and external proton activity is due primarily to proton diffusion through the membrane, and not to hydroxyl ion flux. For a vesicle containing a single buffer the solution requires six independent physical parameters: the initial internal proton concentration, the external proton concentration, the ratio of the vesicle surface area to the internal volume, the permeability coefficient of the membrane for protons, the total concentration of the internal buffer, and the equilibrium constant for the dissociation of the internal buffer. Determination of these physical values is sufficient to predict the time dependence of the internal proton concentration and of the proton efflux. Over a pH range that is below or near the pK of the internal buffer the solution is complex. However, if the initial pH is one unit or more higher than the pK of the internal buffer the kinetics of the internal proton concentration and proton efflux can be described by a pseudo first order reaction. In this case the apparent rate constant depends linearly on the permeability coefficient and is dominated by the total internal buffer concentration and its pK. For example, increasing the internal buffer concentration inside a vesicle by 10-fold results in an approximately 10-fold increase in the half-time of the proton efflux kinetics. The theoretical analysis is applied to thylakiod vesicles using experimentally determined values for the physical parameters. The predictions of the analysis are compared to experimentally observed kinetics.