Abstract
We describe a mathematical model of synaptic transmitter release that is based on the finding that transmitter release sites and Ca 2+ ion channels are colocalized in the presynaptic terminal. Because Ca 2+ channels open and close stochastically, the release model is inherently stochastic. We develop a simple method for representing the collective effect of a population of sites and channels by constructing a system of ordinary differential equations for the mean release. A multiple scale analysis of this system reveals several features of transmitter release and fast facilitation, where release is enhanced if preceded by a conditioning impulse. These include an inverse relation between facilitation and Ca 2+ cooperativity, a step-like frequency dependence of facilitation, and a release time course that is invariant to changes in the magnitude of release that occurs as the model synapse facilitates or when the external Ca 2+ concentration is changed. The model is sufficiently simple to be used in conjunct...
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