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

Yan Yi Peng, Kwang Shang Wang

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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.

Original languageEnglish (US)
Pages (from-to)275-298
Number of pages24
JournalJournal of Computational Neuroscience
Issue number3
StatePublished - 2000

All Science Journal Classification (ASJC) codes

  • Sensory Systems
  • Cognitive Neuroscience
  • Cellular and Molecular Neuroscience


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