Proton transport via coupled surface and bulk diffusion

Abstract

Translocation of protons across biological membranes is carried out by special membrane proteins, proton pumps. Surprisingly, the turnover rate of some proton pumps, such as cytochrome c oxidase (CcO), is higher than the bulk diffusion limit (i.e., the rate at which protons can be supplied to the entrance of the proton conducting channel via free bulk diffusion). It has been suggested that the diffusion of protons along the membrane surface that surrounds the entrance of the proton conducting channel can increase the supply of the protons and therefore explain the puzzling high turnover rates. Here we consider a phenomenological model of proton transport to a proton collecting channel. The model takes into account both the diffusion in the bulk and the coupled diffusion of protons along the membrane surface. In our model a homogeneous membrane surface, which mediates proton diffusion toward the channel entrance, is populated with protolytic groups that can exchange protons with a bulk solution. Equations which describe the coupled surface-bulk proton diffusion are derived and solved. The maximum (diffusion limited) rate at which protons can be delivered to the pump is examined. It is found that there are two regimes of surface-mediated proton transport, depending on the rate of proton exchange between the bulk and the surface. In both regimes proton transport is dominated by the contribution of surface diffusion. Due to two-dimensional character of the surface diffusion, the transport rate depends on the size of the channel entrance in a weak, logarithmic fashion. The theory also provides a simple expression for the maximum distance that a proton can migrate on the surface before it is fully equilibrated with the bulk. This result allows one to examine whether the chemiosmotic coupling between a proton source on a membrane surface, such as CcO, and a sink, such as ATP synthase, occurs via diffusion along the membrane, or involves equilibration with the bulk.