A unifying theory to describe transmembrane transport derived from thermodynamic principles

Cells communicate with their environments using transmembrane molecular transport that is, in turn, mediated by proteins that facilitate diffusion (channels), or alternatively, translocate ions against the electrochemical gradient (pumps). Transmembrane transport has been modelled in many studies using many functional forms that were not always derived from the same assumptions. A generic formulation that describes transmembrane fluxes regard- less of whether they are mediated by pumps or open channels is presented here. The functional form of the flux was obtained from thermodynamic first principles. Further, taking a slightly different approach, the same generic formulation mentioned above can be obtained from the Nernst-Planck equation for the case of channel-mediated electrodiffusion. The generic formula can be regarded as the product of an amplitude term and a driving force term. 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.