Simulation-Based Approaches for Determining Membrane Permeability of Small Compounds

Abstract

Predicting the rate of nonfacilitated permeation of solutes across lipid bilayers is important to drug design, toxicology, and signaling. These rates can be estimated using molecular dynamics simulations combined with the inhomogeneous solubility-diffusion model, which requires calculation of the potential of mean force and position-dependent diffusivity of the solute along the transmembrane axis. In this paper, we assess the efficiency and accuracy of several methods for the calculation of the permeability of a model DMPC bilayer to urea, benzoic acid, and codeine. We compare umbrella sampling, replica exchange umbrella sampling, adaptive biasing forces, and multiple-walker adaptive biasing forces for the calculation of the transmembrane PMF. No definitive advantage for any of these methods in their ability to predict the permeability coefficient Pm was found, provided that a sufficiently long equilibration is performed. For diffusivities, a Bayesian inference method was compared to a Generalized Langevin method, both being sensitive to chosen parameters and the slow relaxation of membrane defects. Agreement within 1.5 log units of the computed Pm with experiment is found for all permeants and methods. Remaining discrepancies can likely be attributed to limitations of the force field as well as slowly relaxing collective movements within the lipid environment. Numerical calculations based on model profiles show that Pm can be reliably estimated from only a few data points, leading to recommendations for calculating Pm from simulations.

The CHARMM36 Force Field for Lipids Can Be Used With More Accurate Water Models

“…42 Several theoretical models have been developed to predict the rates of permeation from molecular simulations, although the solubility-diffusion model has been particularly popular. 7,[43][44][45][46] This model predicts the rate of permeation from the potential of mean force and the diffusivity of the permeating solute as a function of its position, z, along the trans- These results are in line with previous simulations. 46,47 The TIP3P-FB and TIP4P-FB water models have viscosity/self-diffusion coefficients that are much closer to the experimental values and the diffusivity of the permeating water molecule is lower accordingly.…”

“…These issues are sources of error in quantitative calculations of some membrane processes, particularly for transport properties like membrane permeation and partitioning. [6][7][8] The CHARMM36 model for lipids was developed for use with the TIP3P water model.…”

Subdiffusion in Membrane Permeation of Small Molecules

“…For instance, errors as small as 1.4 kcal/mol are sufficient to bias the permeability by a factor of ten. In the context of solute permeation through lipid bilayers, several different approaches for rigorously computing free-energy profiles from molecular simulations have been used with comparable results, including constrained molecular dynamics62223, umbrella sampling2425, metadynamics21, bias-exchange metadynamics26, the oscillating forward-reverse method27, the adaptive biasing force (ABF) algorithm2829 and multiple-walker ABF25. Two comprehensive reviews on the calculation of free energies for lipid bilayer permeation were recently provided by Neale and Pomès30 and Shinoda31.…”

In silico screening of drug-membrane thermodynamics reveals linear relations between bulk partitioning and the potential of mean force

“…While the computational investment of atomistic simulations prevents the estimation of the potential of mean force for many compounds, 7,42 we show that coarsegrained simulations can provide an efficient proxy. Indeed, as a first test of the accuracy of a coarse-grained potential of mean force in reproducing the permeability of a compound, we computed the log P value of mannitol in a DOPC membrane at T = 323K, and compared it to reference atomistic results.…”