Sodium-calcium exchange: Derivation of a state diagram and rate constants from experimental data

A mechanism is developed for Na +-Ca 2+ exchange using a new approach made possible by the availability of computer software that allows the systematic search of a large parameter space for optimum sets of parameters to fit multiple sets of experimental data. The approach was to make the experimental data dictate the form of the mechanism: the qualitative features of the data dictating the number and nature of the states of the exchanger and their interrelationship, and the quantitative aspects of the data dictating the values of the rate constants that govern the amount of each state relative to the total amount of exchanger. A single set of experimental data served this initial purpose, namely, observations of equilibrium Ca 2+-Ca 2+ exchange in cardiac sarcolemmal vesicles (Slaughter et al., 1983, J. biol. Chem. 258, 3183–3190). From this data a minimum mechanism was induced having 56 states (SYM56), which gave satisfactory quantitative fits to the experimental data. With this set of parameters additional experimental data were fitted, from the same preparation, the single cardiac cell and the squid giant axon, with some changes in parameters, but none dramatic. In spite of the symmetric nature of the mechanism, i.e. binding constants for Na + and Ca 2+ do not depend on the orientation of the binding sites, the mechanism exhibits marked asymmetric behavior similar to that observed experimentally. Finally, in accounting for Ca 2+-Ca 2+ exchange in the absence of monovalent cations, Ca 2+ influx becomes dependent on intracellular Ca 2+—an unexpected outcome—exactly in keeping with the “essential activator” role of intracellular Ca 2+ observed by DiPolo & Beaugé (1987, J. gen. Physiol. 90, 505–525). Observations of Na +-Ca 2+ exchange in the retinal rod outer segment are well fitted with a simplified version of SYM56 comprising 25 states (namely, SYM25), supporting the notion that the exchanger in the retinal rod outer segment differs from that in cardiac sarcolemma and squid axon. Maximum turnover rate of 840 sec −1 for SYM56 and 20 sec −1 for SYM25 are comparable to those reported for the exchanger in cardiac muscle and retinal rod outer segment, respectively.