This paper describes a framework model for proton conduction through gramicidin; a model designed to incorporate information from molecular dynamics and use this to predict conductance properties. The state diagram describes both motion of an excess proton within the pore as well as the reorientation of waters within the pore in the absence of an excess proton. The model is constructed as the diffusion limit of a random walk, allowing control over the boundary behavior of trajectories. Simple assumptions about the boundary behavior are made, which allow an analytical solution for the proton current and conductance. This is compared with corresponding expressions from statistical mechanics. The random walk construction allows diffusing trajectories underlying the model to be simulated in a simple way. Details of the numerical algorithm are described.
Schumaker, M. F., Pomès, R., & Roux, B. (2001). Framework model for single proton conduction through gramicidin. Biophysical Journal, 80(1), 12–30. https://doi.org/10.1016/S0006-3495(01)75992-9