Multioccupancy models for single filing ionic channels: Theoretical behavior of a four-site channel with three barriers separating the sites

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Abstract
A procedure is developed for dealing with multioccupancy in single-filing channels having any number of sites internal to the barriers at the channel ends but having the outermost sites in equilibrium with the bathing solutions. Using this procedure, a general theory is developed for a single-filing channel having three barriers and four sites, the outermost of which are in equilibrium with the bathing solutions. By introducing a vectorial representation, it is shown that the four-site model can be reduced to an equivalent two-site model with respect to the number of possible transitions, thereby simplifying the algebraic steps required to solve transport equations for the system. The transport coefficients are derived and expressed in terms of the energy levels of the peaks and the wells for the different occupancy configurations. An explicit solution to the transport equations is given in a comprised form for a single permeable species. The solution allows some important properties for the system to be deduced, specifically with regard, to the conductance at zero current, the correlation factor between electrical conductance and tracer flux, and the current-voltage relationship. Examples are given for the use of the present results in a physical interpretation of the data from the gramicidin A channel.