Kinetics of proton diffusion in the regimes of fast and slow exchange between the membrane surface and the bulk solution.

The phenomenological model developed in our recent publications [9,10] is used to investigate the kinetics of proton diffusion from a source to a detector on the membrane surface. In most cases the observed kinetics shows a single diffusional maximum with the exponential ascending front and the power-law descending tail. The kinetics depends on the distance between the source and the detector. If the detector is located inside the proton collecting antenna, the kinetics corresponds to the surface diffusion at the times near the maximum and shortly thereafter, and it turns into the bulk diffusion kinetics at longer times, after the equilibrium is established between the membrane surface and the bulk solution. If the detector is located outside the antenna, the kinetics corresponds to the bulk diffusion at all times where the signal is nonvanishing. What is seen at locations near the antenna radius depends on the exchange regime. In the regime of fast exchange between the surface and the bulk as compared to the bulk diffusion, the kinetics shows a single peak whose location is intermediate between the peaks for the surface and bulk diffusion. In the regime of slow exchange there are two maxima corresponding to the surface and bulk diffusion. In buffered solutions the antenna radius decreases with increasing buffer concentration, which changes the kinetics from the surface to bulk diffusion. The theory is applied to interprete recent experiments on a phospholipid membrane [25]. It is found that (i) the fast exchange regime is operating since only a single maximum is observed; (ii) the shift of the maximum toward longer times with increasing buffer concentration is a manifestation of the transition from the surface to bulk diffusion kinetics.