Solute flux through a fluctuating membrane channel

Abstract

Protein channels of biological membranes are dynamic structures that are subject to equilibrium thermal fluctuations. The most well-known empirical manifestation of such fluctuations is channel gating, i.e., the channel's ability to spontaneously switch between states of different conductance. However, channel gating, which provides functional regulation of channel-facilitated transport in response to voltage, ligands, stress, and other factors, does not exhaust the variety of possible structural fluctuations and their consequences. In this study, we investigate the impact of a fluctuating side chain on the transport properties of the channel. We limit ourselves to the case of a two-state three-dimensional cylindrical channel that, due to fluctuations in the chain conformation, undergoes random transitions between fully open and partially (or completely) blocked states. When transitions are slow, the average flux through the channel is just a weighted sum of the fluxes through the fully open and blocked channel states. Here, we demonstrate that this simple relationship breaks down when the characteristic time of conformational fluctuations becomes comparable to that of solute dynamics in the channel. Using the framework of a continuum diffusion model, we show that the blocking effect of the side chain decreases as the fluctuation rate increases. Importantly, this surprising asymptotic behavior persists independent of the blockage degree and the probability of finding the channel in the blocked state, thus suggesting that the “closed state,” obtained in crystallography or other structural methods, may in fact be open for solute transport.