Figure 1.

Schematic of the two different models for proton migration along the membrane surface. The non-equilibrium model (a) envisions proton diffusion within the confinement of the membrane hydration layers without the involvement of titratable residues on the surface. Proton surface-to-bulk release is thought to be irreversible (equation (1)). The quasi-equilibrium model (b) treats proton surface diffusion as a succession of jumps between titratable residues. The proton uptake and release reactions are in equilibrium. In the absence of real proton acceptors and donors, fictional moieties are assumed to take their place. Accordingly, their pK _a value is obtained as a fitting parameter of the model (equations (3–6)).