A minimum mechanism for Na+-Ca++ exchange: net and unidirectional Ca++ fluxes as functions of ion composition and membrane potential.

Both simultaneous and consecutive mechanisms for Na+-Ca++ exchange are formulated and the associated systems of steady-state equations are solved numerically, and the net and unidirectional Ca++ fluxes computed for a variety of ionic and electrical boundary conditions. A simultaneous mechanism is shown to be consistent with a broad range of experimental data from the squid giant axon, cardiac muscle and isolated sarcolemmal vesicles. In this mechanism, random binding of three Na+ ions and one Ca++ on apposing sides of a membrane are required before a conformational change can occur, translocating the binding sites to the opposite sides of the membranes. A similar (return) translocation step is also permitted if all the sites are empty. None of the other states of binding can undergo such translocating conformational changes. The resulting reaction scheme has 22 reaction steps involving 16 ion-binding intermediates. The voltage dependence of the equilibrium constant for the overall reaction, required by the 3:1 Na+: Ca++ stoichiometry was obtained by multiplying and dividing, respectively, the forward and reverse rate constants of one of the translocational steps by exp(-FV/2RT). With reasonable values for the membrane density of the enzyme (approximately 120 sites micron 2) and an upper limit for the rate constants of both translocational steps of 10(5) . sec-1, satisfactory behavior was obtainable with identical binding constants for Ca++ on the two sides of the membrane (10(6) M-1), similar symmetry also being assumed for the Na+ binding constant (12 to 60 M-1). Introduction of order into the ion-binding process eliminates behavior that is consistent with experimental findings.