Title: A unifying theory to describe transmembrane transport derived from thermodynamic principles
Abstract: A unifying theory of physiological transmembrane transport. Cellular homeostasis involves transmembrane molecular transport along, or against the (electro) chemical gradient of the molecules being transported. Such transport is typically mediated by membrane-spanning proteins that either carry the molecules across the membrane, or facilitate their (electro)diffusion. Transmembrane transport has been modelled in many studies using many functional forms that were not always derived from the same assump- tions. A generic formulation that describes transmembrane fluxes, mediated either by carrier proteins or by open channels, is presented here. The functional form of the flux was obtained from basic thermodynamic principles. The same generic formulation mentioned above can also be obtained from the Nernst-Planck equation for the case of channel-mediated electrodiffusion. The generic formulation can be regarded as the product of an amplitude term and a driving force term, both nonlinear functions of the transmembrane concentrations of the molecules being transported, and possibly the transmembrane potential. The former captures the characteristics of the membrane- spanning protein mediating the transport and the latter is a non-linear function of the transmembrane concentrations of the ions. The generic formulation explicitly shows that the basal rate at which ions cross the membrane is the main difference between currents mediated by pumps and channels. Electrogenic transmembrane fluxes can be converted to currents to construct models of membrane excitability in which all the transmembrane currents have the same functional form. The applicability of the generic derivations presented here is illustrated with models of excitability for neurones and pacemaker cardiocytes.