Estimating the synaptic current in a multi-conductance AMPA receptor model

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.