Calculation of the permeability coefficients of small molecules through lipid bilayers by free-energy reaction network analysis following the explicit treatment of the internal conformation of the solute.

Biomembrane permeation represents a major barrier to pharmacokinetics. During preclinical drug discovery, the coefficients of the permeation of molecules through lipid bilayers account for a valuable property of such molecules. Therefore, the control of the permeation of molecules through lipid bilayers is an essential factor in drug design, and the estimation of the permeation phenomena is a crucial study in pharmacy. Thus, there are many published studies on the theoretical estimations of permeation coefficients. Here, we propose a molecular dynamics (MD) simulation method for estimating the permeation of small molecules through lipid bilayers based on the free-energy reaction network (FERN) analysis. In this method, the collective variables (CVs) of the free energy calculations explicitly include the conformational changes in the rotational bonds of the solute molecules. The advantages of the present method over the other method are that it is possible to estimate reaction pathways and their reaction rates, i.e., permeation coefficients or passage times, in multidimensional space spanned by CVs though conventional methods such as the umbrella sampling method and target MDs often dealt with a few degrees of freedom. To demonstrate the efficacy of our method, we calculate the coefficients of the permeation of three small aromatic peptides, namely N-acetylphenylalanineamide (Ac-Phe-NH2 or NAFA), N-acetyltyrosineamide (Ac-Tyr-NH2 or NAYA), and N-acetyltryptophanamide (Ac-Trp-NH2 or NATA), through a 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) lipid bilayer. In these cases we adopted one CV for the permeation direction and four CVs for the internal rotational coordinates. The results reveal that the permeation coefficients of NAFA, NAYA, and NATA are 1.7 × 10-2, 0.51 × 10-4, and 5.7 × 10-4 cm s-1, respectively. Compared with the experimental data, our simulation results followed the same trend, i.e., NAFA > NATA > NAYA. By analyzing the structures of metastable points of the solute molecules, our simulation result reveals that the aforementioned trend is caused by the differences in stability among their rotamers. Furthermore, we evaluate the statistical fluctuation of the rotamers, and the time scale of flipping the side chain reveals that the structures rigidify as the ligand moves deeper into the membrane.