Molecular transport through membranes: Accurate permeability coefficients from multidimensional potentials of mean force and local diffusion constants

Abstract

Estimating the permeability coefficient of small molecules through lipid bilayer membranes plays an important role in the development of effective drug candidates. simulations can produce acceptable relative permeability coefficients for a series of small molecules; however, the absolute permeability coefficients from simulations are usually off by orders of magnitude. In addition to differences between the lipid bilayers used and , the poor convergence of permeation free energy profiles and over-simplified diffusion models have contributed to these discrepancies. In this paper, we present a multidimensional inhomogeneous solubility-diffusion model to study the permeability of a small molecule drug (trimethoprim) passing through a POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) lipid bilayer. Our approach improves the permeation model in three ways: First, the free energy profile (potential of mean force, PMF) is two-dimensional in two key coordinates rather than simply one-dimensional along the direction normal to the bilayer. Second, the 2-D PMF calculation has improved convergence due to application of the recently developed transition-tempered metadynamics with randomly initialized replicas, while third, the local diffusivity coefficient was calculated along the direction of the minimum free energy path on the two-dimensional PMF. The permeability is then calculated as a line integral along the minimum free energy path of the PMF. With this approach, we report a considerably more accurate permeability coefficient (only 2-5 times larger than the experimental value). We also compare our approach with the common practice of computing permeability coefficients based only on the translation of the center of mass of the drug molecule. Our paper concludes with a discussion of approaches for minimizing the computational cost for the purpose of more rapidly screening a large number of drug candidate molecules.

Water-ion permselectivity of narrow-diameter carbon nanotubes

“…A 1D PMF was then obtained by calculating the minimum free energy path on the 2D PMF. In all simulations, two CVs were used to facilitate PMF convergence ( 50 , 51 ), including the center of mass distance between the oxygen atom of the water molecule and CNT along the direction of the tube axis, and the radial position of the water molecule with respect to the center of CNT. Hydrogen bond analysis was based on a simple geometrical criterion adapted from ( 52 ).…”

Does Size Really Matter? Probing the Efficacy of Structural Reduction in the Optimization of Bioderived Compounds – A Computational “Proof-of-Concept”

“…Although both compounds adhered to the defined PSA threshold of ≤140Å 2 , a relatively low value of 26.3 Å 2 was estimated for SB640 while Ang-D had a higher TPSA value of 63.6 Å 2 . These imply that SB640 possessed better physiological transport attributes than the parent compound, Ang-D. Hydrogen bonds also influence the solubility of therapeutic compounds since they must be broken to allow their permeation across the lipid bilayer membrane [ [112] , [113] , [114] ]. In other words, a high hydrogen bond number affects permeation by passive diffusion due to a reduction in partitioning from the aqueous phase into the lipid bilayer membrane.…”

Molecular dynamics trajectories for 630 coarse-grained drug-membrane permeations

“…Equation 1 depends exponentially on G(z), but only linearly on D(z), making the latter quantity less critical-it was also found to depend rather weakly on the chemistry of the drug 10 . A large number of enhanced-sampling studies have demonstrated the capability to not only converge the PMF, but also to provide permeability coefficients that exhibit high correlation with experimental measurements [10][11][12][13][14][15][16] . An illustrative example of the PMF is shown in Fig.…”