A Four-Compartment Model for Ca²⁺ Dynamics: An Interpretation of Ca²⁺ Decay after Repetitive Firing of Intact Nerve Terminals

Abstract

In the presynaptic nerve terminals of the bullfrog sympathetic ganglia, repetitive nerve firing evokes [Ca²⁺] transients that decay monotonically. An algorithm based on an eigenfunction expansion method was used for fitting these [Ca²⁺] decay records. The data were fitted by a linear combination of two to four exponential functions. A mathematical model with three intraterminal membrane-bound compartments was developed to describe the observed Ca²⁺ decay. The model predicts that the number of exponential functions, n, contained in the decay data corresponds to n − 1 intraterminal Ca²⁺ stores that release Ca²⁺ during the decay. Moreover, when a store stops releasing or 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 current lack of a parameter by which quantitative comparisons can be made between two decay processes when at least one of them contained more than one exponential components, we defined a parameter, the overall rate (OR) of decay, as the trace of the coefficient matrix of the differential equation systems of our model. We used the mathematical properties of the model and of the 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 more than 86% of all the flux rates across various membranes combined and that there are type 3 and type 1 and/or type 2 ryanodine receptors in these terminals.