Transport properties of single-file pores with two conformational states

Complex facilitative membrane transporters of specific ligands may operate via inner channels subject to conformational transitions. To describe some properties of these systems, we introduce here a kinetic model of coupled transport of two species, L and w, through a two-conformational pore. The basic assumptions of the model are: a) single-file of, at most, n molecules inside the channel; b) each pore state is open to one of the compartments only; c) there is at most only one vacancy per pore; d) inside the channel, a molecule of L occupies the same positions as a molecule of w; and e) there is at most only one molecule of L per pore. We develop a general representation of the kinetic diagram of the model that is formally similar to the one used to describe one-vacancy transport through a one-conformational single-file pore. In many cases of biological importance, L could be a hydrophilic (ionic or nonionic) ligand and w could be water. The model also finds application to describe solute (w) transport under saturation conditions. In this latter case, L would be another solute, or a tracer of w. We derive steady-state expressions for the fluxes of L and w, and for the permeability coefficients. The main results obtained from the analysis of the model are the following. 1) Under the condition of equilibrium of w, the expression derived for the flux of L is formally indistinguishable from the one obtainable from a standard four-state model of ligand transport mediated by a two-conformational transporter. 2) When L is a tracer of w, we can derive an expression for the ratio between the main isotope and tracer permeability coefficients (Pw/Pd). We find that the near-equilibrium permeability ratio satisfies (n - 1) < or = (Pw/Pd)eq < or = n, a result previously derived for the one-conformational, single-file pore for the case that n > or = 2. 3) The kinetic model studied here represents a generalization of the carrier concept. In fact, for the case that n = 1 (corresponding to the classical single-occupancy carrier), the near-equilibrium permeability ratio satisfies 0 < or = (Pw/Pd)eq < or = 1, which is characteristic of a carrier performing exchange-diffusion.