Diffusive Models of Membrane Permeation with Explicit Orientational Freedom

Accurate calculation of permeabilities from first-principles has been a long-standing challenge for computer simulations, notably in the context of drug discovery, as a route to predict the propensity of small, organic molecules to spontaneously translocate biological membranes. Of equal importance is the understanding of the permeation process and the pathway followed by the permeant from the aqueous medium to the interior of the lipid bilayer, and back out again. A convenient framework for the computation of permeabilities is provided by the solubility-diffusion model, which requires knowledge of the underlying free-energy and diffusivity landscapes. Here, we develop a formalism that includes an explicit description of the orientational motion of the solute as it diffuses across the membrane. Toward this end, we have generalized a recently proposed method that reconciles thermodynamics and kinetics in importance-sampling simulations by means of a Bayesian-inference scheme to reverse-solve the underlying Smoluchowski equation. Performance of the proposed formalism is examined in the model cases of a water and an ethanol molecule crossing a fully hydrated lipid bilayer. Our analysis reveals a conspicuous dependence of the free-energy and rotational diffusivity on the orientation of ethanol when it lies within the headgroup region of the bilayer. Specifically, orientations for which the hydroxyl group lies among the polar lipid head groups, while the ethyl group recedes toward the hydrophobic interior are associated with free-energy minima ∼2kBT deep, as well as significantly slower orientational kinetics compared to the bulk solution or the core of the bilayer. The conspicuous orientational anisotropy of ethanol at the aqueous interface is suggestive of a complete rotation of the permeant as it crosses the hydrophobic interior of the membrane.