  A pre-synaptic neuron releases diffusing neurotransmitters such as glutamate
that activate post-synaptic receptors. The amplitude of the post-synaptic
current, mostly mediated by glutamatergic (AMPARs) receptors, is a fundamental
signal that may generate an action potential. However, although various
simulation results \cite{kullman,Barbour,Raghavachari} have addressed how
synapses control the post-synaptic current, it is still unclear how this
current depends analytically on factors such as the synaptic cleft geometry,
the distribution, the number and the multi-conductance state of receptors, the
geometry of post-synaptic density (PSD) and the neurotransmitter release
location. To estimate the synaptic current maximal amplitude, we present a
semi-analytical model of glutamate diffusing in the synaptic cleft. We modeled
receptors as multi-conductance channels and we find that PSD morphological
changes can significantly modulate the synaptic current, which is maximally
reliable (the coefficient of variation is minimal) for an optimal size of the
PSD, that depends on the vesicular release active zone. The existence of an
optimal PSD size is related to nonlinear phenomena such as the multi-binding
cooperativity of the neurotransmitter to the receptors. We conclude that
changes in the PSD geometry can sustain a form of synaptic plasticity,
independent of a change in the number of receptors.
