A model for anomalous rectification: Electrochemical-potential-dependent gating of membrane channels

A model is presented for “anomalous rectification” based upon electrical measurements on the egg cell membrane of the starfish. The objective is to postulate a plausible molecular mechanism which yields an expression for the conductance similar to that deduced empirically by Hagiwara and Takahashi (1974), i.e., $$G_K = \frac{{Bc_K^{1/2} }}{{1 + \exp \left( {\frac{{\Delta V - \Delta V_h }}{v}} \right)}},$$ whereB, ΔV _h andv are constant,c_K is the external K⁺ concentration, and ΔV(=V−V₀) is the displacement of the membrane potential from its resting value. It is shown that a similar dependence of the conductance on ΔV is expected for a particular class of models in which the K⁺ ions are also implicated in “gating”. To give a specific example, we consider the case in which the formation of ion-permeable pores requires a voltage-induced orientation of membrane-bound, electrically-charged groups and subsequent complexation of these groups with the external cations. Furthermore, the proportionality betweenG_K andc ₁ ^2/K , when the internal K⁺ concentration is constant, is accounted for by conventional descriptions of the ionic fluxes using Eyring's rate reaction theory. In terms of the present model,B and ΔV _h are explicit functions of the internal K⁺ concentrations and are thus constant only as long as this is unvaried. The particular value ofv required to fit the data (v≃8.4 mV) is rationalized by the assumption that each of the orientable groups carries three negative elementary charges. In addition, the predictions of the present model are compared with those deduced from an alternative viewpoint, which is related to Armstrong's “blocking particle hypothesis”, in that the probability for opening and closing of the pore is assumed to depend on whether the pore is occupied or empty. Differences and similarities between the two models, as well as ways to discriminate between them, are discussed.