A theoretical framework for quantal analysis and its application to long-term potentiation.

1. We present a new mathematical description of the complete distribution of electrical responses to stochastic synaptic activity (quantal analysis) that is intended as a model of experiments on central neuronal synapses. Unlike previous treatments, this distribution is calculated for each instant after the release of transmitter into the cleft. 2. We follow the traditional description of probabilistic presynaptic vesicle release. On the postsynaptic side, however, we assume that channel fluctuations are important and we take them into account. The probability of finding a given channel open after a certain amount of transmitter is released is calculated from detailed receptor/channel and neurotransmitter clearance kinetics. This approach allows us to naturally include the nonlinear dependence of open probability on the amount of transmitter released, with saturation for large transmitter doses. The distribution of open channels is calculated from this probability. 3. We also allow the possibility that multiple synaptic inputs to a target neuron may be active in a typical experiment. We have not treated cable effects. We explore the implications of multiple synapses for the nonlinearities of the system. The most important of these is that vesicles in different synapses have independent responses, and therefore their effects add linearly. 4. The resulting distributions depend heavily on what region of the nonlinear dose-response curve the synapses are in. Far from saturation, peaks in the distribution are due to vesicles, and close to saturation they are due to active synapses. Peak widths are due to channel fluctuations and instrumental noise, which we introduce to make closer contact with experiments.(ABSTRACT TRUNCATED AT 250 WORDS)