Statistical Mechanical Theories of Membrane Permeability

Area of Science:

• Computational chemistry
• Physical chemistry
• Biophysics

Background:

• The inhomogeneous solubility-diffusion (ISD) model is a popular theoretical framework for calculating molecular permeability across membranes.
• The ISD model relies on the potential of mean force and position-dependent diffusivity, often derived from molecular dynamics (MD) simulations.
• Limitations of the ISD model include approximations in diffusivity calculations and the neglect of memory effects.

Purpose of the Study:

• To develop alternative theoretical formulations for determining the permeability coefficient that address the limitations of the ISD model.
• To derive expressions for permeability that account for memory effects and nonequilibrium flux.
• To validate new theoretical strategies using computational simulations.

Main Methods:

• Application of Green-Kubo linear response theory to derive a constitutive relation for membrane flux.
• Derivation of a nonequilibrium flux expression using time-correlation functions.
• Utilizing transition path theory to develop alternative permeability coefficient expressions.
• Stochastic simulations based on the generalized Langevin equation.
• Unbiased molecular dynamics simulations of water permeation through a lipid bilayer.

Main Results:

• Established a Green-Kubo based expression for nonequilibrium flux across a membrane.
• Derived alternative permeability coefficient expressions using transition path theory.
• Demonstrated the utility of the new theoretical approaches through simulations.
• Showcased improved accuracy in permeability calculations compared to the ISD model.

Conclusions:

• The developed theoretical frameworks offer more comprehensive methods for calculating molecular permeability.
• Accounting for memory effects and nonequilibrium dynamics leads to more accurate permeability predictions.
• The study provides valuable tools for understanding molecular transport across biological and artificial membranes.