Generalized Langevin Methods for Calculating Transmembrane Diffusivity.

Area of Science:

• Computational chemistry
• Physical chemistry
• Biophysics

Background:

• Estimating membrane permeability requires the solute's transmembrane diffusivity profile (D(z)).
• The generalized Langevin equation enables calculating position-dependent diffusivity via molecular dynamics simulations.
• Diffusivity is derived from solute friction, using correlation functions.

Purpose of the Study:

• To validate and compare two methods for calculating solute diffusivity: velocity autocorrelation function (VACF) and position autocorrelation function (PACF).
• To assess these methods for determining transmembrane diffusivity profiles, particularly in lipid bilayers.

Main Methods:

• Molecular dynamics simulations with harmonic restraints along the transmembrane axis (z).
• Calculation of solute diffusivity using VACF and PACF methods, based on Roux and Hummer's derivations.
• Validation of methods using H2O and O2 in homogeneous liquids before application to lipid bilayers.

Main Results:

• The VACF method showed incrementally lower errors and less sensitivity to thermostat forces compared to PACF.
• PACF method yielded spuriously low diffusivity in lipid bilayers due to long-lived correlations from membrane inhomogeneities.
• VACF method avoids this artifact and predicts higher diffusion rates within the bilayer.

Conclusions:

• The VACF method is more reliable for calculating transmembrane diffusivity profiles in complex systems like lipid bilayers.
• VACF-based calculations provide more accurate predictions of solute diffusion rates across membranes.
• This work offers improved computational strategies for membrane transport studies.