A unifying theory for physiological transmembrane transport derived from thermodynamic principles

Cellular homeostasis involves transmembrane molecular transport mediated by membrane-spanning proteins. Such proteins either carry the molecules across the membrane, or facilitate their diffusion. A generic formulation that describes transmembrane fluxes, derived from basic thermodynamic principles, and describing fluxes mediated by carrier proteins or by open channels using the same functional form is presented here. An alternative derivation from the Nernst-Planck equation that yields the same generic formulation can be obtained for the case of channel- mediated electrodiffusion. In general terms, the generic formulation is a product of an amplitude and a driving force. The amplitude models properties of the protein mediating the transport including basal rates of transport. The driving force term that depends non-linearly on the transmembrane concentrations of the molecules being transported, and possibly the transmembrane potential. The model applied for channel mediated currents is capable of displaying rectification. Further, an extension for channel gating derived en passage allows fitting of currents recorded in voltage-clamp without using powers for the gating variables. The generic formulation explicitly shows that the basal rate at which ions cross the membrane is the main macroscopic difference between currents mediated by carrier proteins and channels. Many functional forms that were not always derived from the same assumptions can be found in modelling studies of transmembrane transport, especially those studies focusing on the membrane potential of excitable cells. The derivations presented here unify the theory of biological transmembrane transport. Of particular interest, electrogenic transmembrane fluxes described with the general formulation can be converted to currents for the construction of models of membrane excitability; all based on the same assumptions and having the same functional form. The applicability of the generic derivations presented here is illustrated with models of excitability for neurones and pacemaker cardiocytes.