A binding site model of membrane transport: binary and cooperative flows.

The flows of solute molecules in a membrane under the influence of concentration gradients are considered within the framework of classical physical theories. A lattice model is constructed in which the binding sites represent potential minima and the flows are regarded as a result of molecules' making discrete transitions between the binding sites. Expressions for two-component currents are derived from certain descriptions for the transition mechanism. Where the molecular movement is given the crudest description, permeability coefficients are identical for both components and there is no current coupling. Where the molecular movement is given some finer detail, the permeability coefficients differ and positive coupling of flows appears. Our result applies to a combination of flows of tracer and abundant species as well as, more generally, to any combination of flows of two components which are distinguishable yet kinetically similar. Also considered are binary currents whose transport mechanism is further controlled by allosteric cooperativity. Whether the cooperative control is short or long ranged, permeability coefficients and fluxes differ appreciably from those without cooperative control. Thus, unlike in the case of channel flow, current coupling here may be either positive or negative, depending on the strength and nature of cooperative coupling. Numerical evidence suggests that the permeability and coupling may have discontinuous behavior, possibly indicating the existence of phase transitions. Our lattice model, from which the formulations for the flows are obtained, is compatible with current concepts of membrane structure.