Facilitated diffusion and membrane permeation of fatty acid in albumin solutions

Facilitated transport is characteristic of most living systems, and usually involves a series of consecutive adjacent transfer regions, each having different transport properties. As a first step in the analysis of the multiregional problem, we consider in a single unstirred layer the facilitated diffusion of fatty acid (F) in albumin (A) solution under conditions of slow versus rapid association-dissociation, accounting for differing diffusivities of the albumin-fatty acid complex (AF). Diffusion gradients become established in an unstirred layer between a source of constant concentration of A, AF, and F in equilibrium, and a membrane permeable to F. The posited system does not reduce to a thin- or thick-layer approximation. The transient state is prolonged by slower on/off binding rates and by increasing the thickness of the unstirred layer. Solutions to transient and steady state depend upon the choice of boundary conditions, especially for thin regions. When there are two regions (each with its specific binding protein) separated by a permeable membrane, the steady-state fluxes and concentration profiles depend on the rates of association and dissociation reactions, on the diffusion coefficients, local consumption rates, and on the membrane permeability. Sensitivity analysis reveals the relative importance of these mechanisms.