Abstract
BackgroundThe relation between osmotic permeability, Pf, diffusion permeability, Pd, and the number of water molecules, Np, 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.ResultsThis 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 Pf / Pd = Np. 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.ConclusionsThe full pore states and the single vacancy states together with the knock-on and Brownian mechanisms account for the relative values of Pf and Pd 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 Pf / Pd = Np. This resolves a long persisting dichotomy.
Highlights
The relation between osmotic permeability, Pf, diffusion permeability, Pd, and the number of water molecules, Np, in the single-file membrane pore remains an open question
Model The new combinatorial analysis approach developed here assumes: a) There are i slots of diameter equal to the diameter of a water molecule, dw, where i ≥ 1
The vacancy moves more rapidly than in the diffusion case from the exit slot to the entrance slot, where it can fill from the exterior solution. This reduces the lifetime (Tv)osm of the vacancy in the pore so that during osmotic flow the value of this (Tv)osm becomes very much shorter than the lifetime (Tv)diff of any vacancy occurring in the pore during diffusion, which increases osmotic flow through the
Summary
The relation between osmotic permeability, Pf, diffusion permeability, Pd, and the number of water molecules, Np, 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. The relationship between osmotic permeability (Pf) and diffusion permeability (Pd) for water movement across cell membranes in the single-file pore case was intensively studied over the last half of the 20th century [1,2,3]. Recent theoretical analyses using Molecular Dynamics, as well as experimental studies, have employed nanochannels as models with some of the physical properties of biological protein water channels (aquaporins), see reviews [3, 9, 11, 12]. Parisi et al [3] ask, “Which is the molecular mechanism that differentiates diffusion from osmosis in a “single-file” channel?”
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