Generalized Langevin Methods for Calculating Transmembrane Diffusivity

Abstract

The membrane permeability coefficient of a solute can be estimated using the solubility-diffusion model. This model requires the diffusivity profile (D(z)) of the solute as it moves along the transmembrane axis, z. The generalized Langevin equation provides one strategy for calculating position-dependent diffusivity from straightforward molecular dynamics simulations where the solute is restrained to a series of positions on the z-coordinate by a harmonic potential. The diffusivity of the solute is calculated from its correlation functions, which are related to the friction experienced by the solute. Roux and Hummer have derived expressions for the diffusion coefficient from the velocity autocorrelation function (VACF) and position autocorrelation function (PACF), respectively. In this work, these methods are validated by calculating the diffusivity of HO and O in homogeneous liquids. These methods are then used to calculate transmembrane diffusivity profiles. The VACF method is less sensitive to thermostat forces and has incrementally lower errors but is more sensitive to the spring constant of the harmonic restraint. For the permeation of a solute through a lipid bilayer, the diffusion coefficients calculated using these methods provided significantly different results. Long-lived correlations of the restrained solute due to inhomogeneities in the bilayer can result in spuriously low diffusivity when using the PACF method. The method based on the VACF does not have this issue and predicts higher rates of diffusion inside the bilayer.

C-terminal kink formation is required for lateral gating in BamA

“…S8. Diffusivities needed for the MFPT calculation were determined using ACFCalculator from Gaalswyk et al (72) (see SI Appendix).…”

Effects of lipid composition on membrane permeation

“…Regarding the diffusion coefficient (D(z) in equation 1), it should be noted that, in general, computing reliable local diffusion coefficients from restrained simulations remains a very active research field [84][85][86][87] . One of the most popular methods is the one introduced by Hummer 88 (in turn based on the previous works of Woolf and Roux 89 and Berne et al 90 ).…”

Shedding light on the puzzle of drug-membrane interactions: Experimental techniques and molecular dynamics simulations

“…Hence, with this approach, the local diffusivities can be calculated in US simulations. The different methods for calculating local diffusion coefficients were compared in several publications (e.g., [226]). When using MD simulations to calculate the parameters of the inhomogeneous solubility-diffusion model, the major limitation is the low accuracy in dynamic properties (e.g., diffusion) [227].…”