(318d) A Methodology of Quantifying Membrane Permeability Based on Returning Probability Theory and Molecular Dynamics Simulation

Permeation of substrates (permeants) through cell membranes is a fundamental process for biological systems. Most permeants, including drug molecules, enter a cell with passive permeation driven by the concentration gradient of permeants between the donor and acceptor phases. Hence, the permeability coefficient that characterizes the efficiency of passive permeation is a valuable indicator for drug discovery.

Molecular dynamics (MD) simulation is the most popular method to elucidate the detailed mechanisms of the permeation process from a theoretical point of view. The inhomogeneous solubility-diffusion (ISD) model incorporating MD simulations has played a central role in analyzing the permeation processes. This model is based on the Smoluchowski equation, realizing the simple treatment of permeation processes. However, the difficulty arises when the permeant shows the subdiffusive motion inside the membrane in the long-time limit. In such a case, employing the Smoluchowski equation is inappropriate. In the present study, we develop an alternative MD-based methodology for quantifying the permeability coefficient for membrane systems starting from the rigorous equation of motion for the system of interests with the reaction sink term that describes the reaction (permeation) probability on the reactive phase existing inside the membranes. We first derive the exact relationship between the permeability coefficient and the permeant distribution function at unsteady state. Then, by employing the perturbative expansion technique utilized in returning probability (RP) theory, a rigorous bimolecular theory, the tractable expression of the permeability coefficient at steady state is derived. In this expression, the coefficient is represented in terms of the thermodynamic and kinetic properties of the permeants inside the membrane. Thus, by computing these properties with MD simulations, the estimation of the permeability coefficients is realized.

We apply the present MD-based method to the permeation processes of ethanol and methylamine through the lipid bilayer composed of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholin (POPC). The dilute and 1 mol% permeant systems are examined. Regarding the 1 mol% systems, we also perform the brute-force MD simulations to compute the permeability coefficients without resorting to any theoretical models.

For the 1 mol% systems, the present method predicts a larger permeability coefficent for ethanol (0.12 ± 0.01 cm/s) than for methylamine (0.069 ± 0.006 cm/s) for the 1 mol% systems, consistent with the brute-force MD. Furthermore, the values of permeability coefficients are satisctorily close to those obtained from the brute-force MD [0.18±0.03 cm/s and 0.052 ± 0.005 cm/s for ethanol and methylamine, respectively]. An increase in the coefficient is observed for the ethanol systems as ethanol concentration increases, while such a change is hardly discernible for the methylamine systems. This trend is consistent with the experimental observation that ethanol enhances the membrane permeability of drug compounds.

The analysis of the thermodynamic and kinetic contributions to the coefficient according to the theoretical expression of permeability coefficient provided by the RP theory reveals that the thermodynamic contribution is responsible for the enhancement of ethanol permeability with increasing ethanol concentration.