Statistical Mechanical and Transition Path Theory Approaches to Membrane Permeation

A rigorous theory for the treatment of biological membrane permeation by small molecules is developed. The inhomogeneous solubility-diffusion model that is commonly used to compute membrane permeability from molecular dynamics simulations is lacking because it neglects the effects of memory on the rate of barrier crossing. Memory effects are accounted for through the extension of transition path theory to membrane permeability through time-correlation functions of the committor probability. Special attention is paid to the permeation of water because theoretical predictions can be validated based on highly accurate brute force simulations. Using a deep learning framework, the position-dependent memory function of water was extracted from umbrella sampling molecular dynamics simulations. The inhomogeneous solubility-diffusion model, Grote-Hynes theory, and direct simulation of the generalized Langevin equation with position-dependent memory are invoked to demonstrate that memory effects are most likely negligible for water permeation. An additional consideration is the permeation of nicotine, which is a small ionizable molecule. The pH-partition hypothesis is confirmed for nicotine based on a transition path theory treatment of the permeation pathway that incorporates the experimental rates of protonation. In sum, several permeation processes are subjected to rigorous theories of statistical mechanics and transition path theory in order to confirm the validity of classic assumptions.