A four-compartment model for Ca2+ dynamics: An interpretation of Ca2+ decay after repetitive firing of intact nerve terminals

In the presynaptic nerve terminals of the bullfrog sympathetic ganglia, rep etitive nerve firing evokes [Ca2+] transients that decay monotonically. An algorithm based on an eigenfunction expansion method was used for fitting t hese [Ca2+] decay records. The data were fitted by a linear combination of two to four exponential functions. A mathematical model with three intrater minal membrane-bound compartments was developed to describe the observed Ca 2+ decay. The model predicts that the number of exponential functions, n, c ontained in the decay data corresponds to n - 1 intraterminal Ca2+ stores t hat release Ca2+ during the decay. Moreover, when a store stops releasing o r starts to release Ca2+, the decay data should be fitted by functions that contain one less exponential component for the former and one more for the latter than do the fitting functions for control data. Because of the curr ent lack of a parameter by which quantitative comparisons can be made betwe en two decay processes when at least one of them contained more than one ex ponential components, we defined a parameter, the overall rate (OR) of deca y, as the trace of the coefficient matrix of the differential equation syst ems of our model. We used the mathematical properties of the model and of t he OR to interpret effects of ryanodine and of a mitochondria uncoupler on Ca2+ decay. The results of the analysis were consistent with the ryanodine- sensitive store, mitochondria, and another, yet unidentified store release Ca2+ into the cytosol of the presynaptic nerve terminals during Ca2+ decay. Our model also predicts that mitochondrial Ca2+ buffering accounted for mo re than 86% of all the flux rates across various membranes combined and tha t there are type 3 and type 1 and/or type 2 ryanodine receptors in these te rminals.