where gsyn is the synaptic conductance and to is the time of transmitter release. This function peaks at a value of l / e at t = to + T , and decays exponentially with a time constant of T . When multiple events occur in succession at a single synapse, the total conductance at any time is a sum of such waveforms calculated over the individual event times. There are several drawbacks to this method. First, the relationship to actual synaptic conductances is based only on an approximate correspondence of the time-course of the waveform to physiological recordings of the postsynaptic response, rather than plausible biophysical mechanisms. Second, summation of multiple waveforms can be cumbersome, since each event time must be stored in a queue for the duration of the waveform and necessitates calculation of an additional exponential during this period (but see Srinivasan and Chiel 1993). Third, there is no natural provision for saturation of the conductance. An alternative to the use of stereotyped waveforms is to compute synaptic conductances directly using a kinetic model (Perkel eta! . 1981). This approach allows a more realistic biophysical representation and is consistent with the formalism used to describe the conductances of other ion channels. However, solution of the associated differential equations generally requires computationally expensive numerical integration. In this paper we show that reasonable biophysical assumptions about synaptic transmission allow the equations for a simple kinetic synapse model to be solved analytically. This yields a mechanism that preserves the advantages of kinetic models while being as fast to compute as a single tr-function. Moreover, this mechanism accounts implicitly for sat-
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