Active transport: conditions for linearity and symmetry far from equilibrium.

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Abstract
The impressive linearity of force-flow relationships in epithelial active-transport systems suggests the utility of a linear, nonequilibrium-thermodynamic analysis. We here present a plausibility argument for the appropriateness of such a treatment. Conventional phenomenological equations of nonequilibrium thermodynamics constitute an incomplete description of the processes under study, because a given thermodynamic force may be induced in an infinite number of ways. In general, therefore, flows are nonlinear functions of the forces, and the Onsager reciprocal relations are obeyed only very near equilibrium. If, however, the forces of two coupled processes can be constrained to "proper" pathways, each flow is a linear function of each force, and the phenomenological cross-coefficients are equal far from equilibrium. The nature of such proper pathways is investigated in terms of a simple model of a sodium-active transport system. Where the treatment is appropriate (i.e., for sufficiently small perturbations about a steady state far from equilibrium) it permits a complete thermodynamic characterization of a system, even when only one of the two forces can be controlled experimentally while the other remains constant.