A model for passive and active transmembrane transport derived from thermodynamical principles

All transmembrane ionic fluxes, whether electrodiffusive or driven by active transport, can be thought of in terms of the energy required to move ions across the membrane. A generic formulation for the transmembrane flux of ions is derived from thermodynamical principles combining a kinetic scheme with the Butler-Volmer equation. The formulation describes active (i.e. mediated by pumps) and passive transmembrane transport (e.g. channel-mediated) mechanisms with the same functional form. The flux described by the formulation is a product of a basal rate and a difference of exponential functions that depends on the transmembrane concentrations of the ions undergoing transport, a term that controls the symmetry of the transport, and the direction in which each of the molecules is transported. Electrogenic fluxes described by the generic formulation also depend on the transmembrane potential, and can be readily converted into currents. The linear approximation around the reversal potential for the generic current turns out to be the widely used conductance-based formulation. The derivations presented here show that models of transmembrane potential can be formulated in terms of currents with a common functional form and provide theoretical explanations for the quantitative differences and the qualitative similarities between pump- and channel mediated ionic fluxes. The applicability of the generic formulations is illustrated with models of transmembrane potential that reproduce the dynamics of pacemaking in cardiocytes. The generic formulations presented here provide a common ground for the study of physiological phenomena that depend on transmembrane transport.