Diffusive
Models of Membrane Permeation with Explicit
Orientational Freedom
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Abstract
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 ∼2<i>k</i><sub>B</sub><i>T</i> 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