Theoretical study of the voltage and concentration dependence of the anomalous mole fraction effect in single calcium channels. New insights into the characterization of multi-ion channels.

Several recent independent studies on macroscopic Ca currents have demonstrated the anomalous mole fraction effect in mixtures of Ca and Ba at concentrations of 10 mM or less. Recently, Hess and Tsien (1984; Nature 309) proposed a dual binding site model, based upon Eyring rate theory, to account for this effect in L-type cardiac Ca channels. This model predicts that the anomalous mole fraction effect can be accounted for solely in terms of open single channel permeation properties; it was able to adequately reproduce the effect for macroscopic Ca currents recorded in 10 mM solutions. However, the electrochemical gradients under which single Ca channel current recordings are routinely made with the patch clamp technique vary dramatically from those used for macroscopic Ca currents. To properly assess the general validity of the Hess and Tsien model at the single Ca channel level, the effects of both large electrical potentials and elevated divalent concentrations must be understood. Computer simulations were therefore carried out using the original parameters used by Hess and Tsien under conditions designed to mimic those used in patch clamp studies. The permeation behavior generated by this model is quite complex. In particular, hyperpolarization and increased divalent concentration combine to reduce and ultimately abolish the anomalous mole fraction effect. It may therefore be very difficult to observe the anomalous mole fraction effect at the single Ca channel level; the dual-site model displays a relationship between current and mole fraction generally associated with a single-site model under the conditions frequently employed to resolve single Ca channel activity. Nonetheless, analysis of such monotonic mole fraction behavior can still be used as a test for the general validity of the dual-site model. Apparent Kms for Ca and Ba can be extracted from such monotonic behavior, and may not only be functions of membrane potential but may also depend upon the total divalent cation concentration. This is a unique prediction which is incompatible with the simple single-site model. Our analysis provides (a) a possible resolution for the apparent discrepancies presently existing in the experimental literature regarding the existence of the anomalous mole fraction effect at the single Ca channel level, (b) a mechanistic description of previously unexplained observations on the voltage-dependence of the anomalous mole fraction effect, and (c) a useful theoretical framework for future experimentation designed to test the general validity of the dual binding site model of the Ca channel.