The movement of H⁺ is one of the most important and ubiquitous reactions to take place in biological systems. The gramicidin A (gA) dimer, which forms a water-filled channel selective to small monovalent cations in biological membranes, is used as a model system to study the molecular determinants of biological proton transport with computer simulations. The single-file chain of water molecules, or water wire, embedded in the channel interior mediates the translocation of H⁺ via a hop-and-turn Grotthuss relay mechanism. Earlier work showing how the mobility of the excess proton in gA is essentially determined by the fine structure and the dynamic fluctuations (structural diffusion) of the hydrogen-bonded network is summarized. The structure and fluctuations of a methanol-containing water chain in the channel lumen suggest a molecular mechanism for the experimentally-measured attenuation of proton conductance by methanol.