Journal of Neurophysiology, Vol 72, Issue 3 1395-1401, Copyright © 1994 by APS
A theoretical framework for quantal analysis and its application to long-term potentiation
K. I. Blum and M. A. Idiart
Department of Biology, Brandeis University, Waltham, Massachusetts 02254-3110.
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)
