Two-dimensional protonic percolation on lightly hydrated purple membrane

The capacitance and dielectric loss factor were measured for a sample of purple membrane of Halobacterium halobium as a function of hydration level (0.017 to >0.2 g of water/g of membrane) and frequency (10 kHz to 10 MHz). The capacitance and the derived conductivity show explosive growth above a threshold hydration level, h(c) approximately 0.0456. The conductivity shows a deuterium isotope effect, H/(2)H = 1.38, in close agreement with expectation for a protonic process. The level h(c) is frequency independent and shows no deuterium isotope effect. These properties are analogous to those found for lysozyme in a related study. Protonic conduction for the purple membrane can be considered, as for lysozyme, within the framework of a percolation model. The critical exponent, t, which describes the conductivity of a percolative system near the threshold, has the value 1.23. This number is in close agreement with expectation from theory for a two-dimensional percolative process. The dielectric properties of the purple membrane are more complex than those of lysozyme, seen in the value of h(c) and in the frequency and hydration dependence of the loss factor. There appear to be preferred regions of proton conduction. The percolation model is based upon stochastic behavior of a system partially populated with conducting elements. This model suggests that ion transport in membranes and its control can be based on pathways formed of randomly connected conducting elements and that a fixed geometry (a proton wire) is not the only possible basis for a mechanism of conduction.