A THEORETICAL FRAMEWORK FOR QUANTAL ANALYSIS AND ITS APPLICATION TO LONG-TERM POTENTIATION

1. We present a new mathematical description of the complete distribut ion of electrical responses to stochastic synaptic activity (quantal a nalysis) that is intended as a model of experiments on central neurona l synapses. Unlike previous treatments, this distribution is calculate d for each instant after the release of transmitter into the cleft. 2. We follow the traditional description of probabilistic presynaptic ve sicle release. On the postsynaptic side, however, we assume that chann el fluctuations are important and we take them into account. The proba bility of finding a given channel open after a certain amount of trans mitter is released is calculated from detailed receptor/channel and ne urotransmitter clearance kinetics. This approach allows us to naturall y include the nonlinear dependence of open probability on the amount o f transmitter released, with saturation for large transmitter doses. T he distribution of open channels is calculated from this probability. 3. We also allow the possibility that multiple synaptic inputs to a ta rget neuron may be active in a typical experiment. We have not treated cable effects. We explore the implications of multiple synapses for t he nonlinearities of the system. The most important of these is that v esicles in different synapses have independent responses, and therefor e their effects add linearly. 4. The resulting distributions depend he avily on what region of the nonlinear dose-response curve the synapses are in. Far from saturation, peaks in the distribution are due to ves icles, and close to saturation they are due to active synapses. Peak w idths are due to channel fluctuations and instrumental noise, which we introduce to make closer contact with experiments. 5. Application of our approach to the alpha-amino-3-hydroxy-5 methyl-4-isoxazolepropiona te receptor/channel system allows us to examine in detail the effects of both presynaptic and postsynaptic changes on response distributions . Using ranges of parameter values within currently available experime ntal limits, we explore which combinations of parameter values generat e clear or ambiguous distinctions in response distributions. We consid er changes in release probability, kinetic rate constants, number of c hannels, and number of synapses, both close to saturation and away fro m saturation. We find that it is possible to differentiate between man y presynaptic and postsynaptic mechanisms of long-term potentiation ex pression.