Some comments on steady state transport of ions across a charged biological membrane

Abstract

The results of our statistical mechanical considerations of diffusion of ions inside a charged membrane are further analyzed. It is demonstrated on a rigorous basis that the relative magnitude of concentrations of localized charges as compared to local concentrations of diffusing ions inside a plane region of charged membrane play a decisive role in determining the direction of fluxes of mobile diffusing ions. This effect is of immense interest and it is shown that the mutual direction of two kinds of mobile ions may undergo even a change in sign depending on certain inequalities. Identical physically meaningful conditions are suggested both by steady state and non-equilibrium considerations. Inequalities determining the mutual direction of fluxes of two kinds of mobile ions are derived as 4πθ ∑ δ c δZ 2 δ(1−ƞ) ≶ k 2(A 1 + A 2ƞ) A 1 ≶ k 2(A 1 + A 2ƞ) A 2 where k 2 = 4πθ ∑ γ c γZ 2 γ, ƞ = ( D ° 1u 2 D ° 1u 1 and θ = e 2 ε kT A α = Z 2 αc α k is related to ion atmosphere parameter of theory of electrolytes, e is the magnitude of electron charge, k the Boltzmann constant and T the temperature. Z α and c α denote the valence charge and local concentration of ions of type a. D α o is the self diffusion coefficient in infinite dilution of ion of kind α and ( u α / kT) is its mobility inside the charged medium. ϵ is the local dielectric constant. Plausible explanations of specificity and the ion-pump mechanism are suggested. Important considerations of ion transport in biological systems are presented.