On the application of rate theory to complex multibarrier flow co-ordinates: Membrane permeability

Abstract

Zwolinski, Eyring & Reese (1949), considering a cellular membrane as a succession of equal energy barriers, used absolute rate theory to derive a general expression for the steady-state flux. This theory is further generalized and adapted to complex flow co-ordinates more typical of actual solution membrane systems. The reciprocal of the permeability constant for very general flow co-ordinates is simply and intuitively expressed as a sum of linear terms, each term proportional to the product of a unique rate constant and an equilibrium constant. These are related to distribution and diffusion constants in the usual way and the influence of the various components of inhomogeneous membranes on the steady-state permeability (at zero volume flow) may be easily estimated. Applied to the simple lipid membrane the standard expression for the permeability constant is reclaimed. A similar treatment of the protein-lipid bilayer results in a clear illustration of the relative importance of various sublayers on permeability as a function of the water: lipid distribution ratio. The linear form of the equations makes them adaptable to the approximate solution of more general diffusion problems. A semi-imperical calculation of the average self diffusion constant for water within a pore in which the activation energy is a function of pore radius is described.