An analytical expression for Na+-Ca2+ exchange currents in cardiac cells has been obtained for an eight-state model. The equation obtained has been used to derive theoretical expressions for current-voltage relationships, maximum Na+-Ca2+ exchange currents, and half-saturating concentrations for Na+ and Ca2+. These equations were analyzed over a wide range of cytoplasmic and extracellular Na+ and Ca2+ concentrations, under forward and reverse 'zero-trans' conditions. Correspondence of theoretical results with those obtained from giant excised patch experiments are presented. Rate constants from published reports were used to evaluate turnover rates for Na+-Ca2+ exchange in the forward and reverse directions. A factor, ε, is introduced that permits prediction of the extent to which the Na+-Ca2+ exchange cycle is under voltage or diffusion control. This factor can be conveniently used for data interpretation and comparison. The derived equations also provide a foundation for continuing experimental evaluation of the fidelity of this model.
Omelchenko, A., & Hryshko, L. V. (1996). Current-voltage relations and steady-state characteristics of Na+- Ca2+ exchange: Characterization of the eight-state consecutive transport model. Biophysical Journal, 71(4), 1751–1763. https://doi.org/10.1016/S0006-3495(96)79376-1