A Residence-Time Approach for Determining Position-Dependent Diffusivities from Biased Molecular Simulations

Abstract

We introduce a residence-time approach (RTA) for determining position-dependent diffusivities from biased molecular dynamics simulations. The method is formulated for trajectory segments in which the effective drift along the transport coordinate is negligible, as realized here using adaptive biasing force simulations. In this regime, local diffusivities are obtained directly from mean first-exit times out of finite spatial intervals. Unlike conventional fluctuation-based approaches, the RTA does not require dedicated harmonically restrained simulations or numerical integration of noisy time-correlation functions. We assess the method for oxygen diffusion across a hexadecane slab, water permeation across a lipid bilayer, and permeation of water and selected volatile organic compounds through a model skin-barrier membrane. In the slab system, the RTA reproduces independently determined bulk diffusivities within statistical uncertainty. In the membrane systems, the inferred diffusivity profiles are supported by propagator-level validation. These results establish the RTA as a practical approach for extracting position-dependent diffusivities from biased molecular simulations.

Figures (8)

• Figure 1: Convergence of PMF profiles from ABF simulations of oxygen diffusion across the hexadecane/water slab.
• Figure 2: Diffusivity profiles for oxygen permeation across the hexadecane/water slab. Symbols denote computed diffusivities; lines are guides to the eye. The plotted diffusivities were obtained by averaging over 10 individually tracked oxygen molecules. Details of the bulk diffusivity calculations and individual profile data are provided in Sections S1.3 and S1.6.
• Figure 3: Convergence of PMF profiles from ABF simulations of water permeation across a POPC bilayer.
• Figure 4: Diffusivity profiles across the POPC lipid bilayer obtained from the VACF, PACF, and residence-time approaches (RTA). Symbols denote computed diffusivities; lines are guides to the eye.
• Figure 5: Comparison of MD-derived propagators with model predictions obtained using diffusivity profiles from the VACF, PACF, and residence-time approaches (RTA) for water permeation across the POPC bilayer. Propagators originate from $z_0=0$, corresponding to the membrane center. Results are shown for lag times of (a) 75ps and (b) 200ps.