Osmotic and diffusive flows in single-file pores: new approach to modeling pore occupancy states

BACKGROUND: The relation between osmotic permeability, P(f), diffusion permeability, P(d), and the number of water molecules, N(p), in the single-file membrane pore remains an open question. Theoretical analyses, empirical studies on aquaporins and nanotubes, and molecular dynamics simulations have yet to provide a consensus view. RESULTS: This paper presents a new combinatorial analysis of the different pore states formed from water molecules and the presence of a vacancy that differs from the several previous combinatorial approaches to analyzing pore states. It is the first such analysis to show that P(f) / P(d) = N(p). It is rooted in the concept of different classes of pore occupancy states, tracer states and tracer exit states, present in the pore. This includes pores with and without a single vacancy. The concepts of knock-on collisions and concerted Brownian fluctuations provide the mechanisms underlying the behaviors of the tracer and vacancy as each moves through the pore during osmotic or diffusive flow. It develops the important role of the knock-on collision mechanism for osmotic flow. An essential feature of the model is the presence, or absence, of a single vacancy in the pore. The vacancy slows down tracer translocation through the pore. Its absence facilitates osmotic flow. CONCLUSIONS: The full pore states and the single vacancy states together with the knock-on and Brownian mechanisms account for the relative values of P(f) and P(d) during osmotic and diffusive flow through the single-file pore. The new approach to combinatorial analysis differs from previous approaches and is the first to show a simple intuitive basis for the relation P(f) / P(d) = N(p). This resolves a long persisting dichotomy.