Analytical description of the activation of multi-state receptors by continuous neurotransmitter signals at brain synapses

Chemical synaptic transmission is a fundamental component of interneuronal communications in the central nervous system (CNS). Discharge of a presynaptic vesicle containing a few thousand molecules (a quantum) of neurotransmitter into the synaptic cleft generates a transmitter concentration signal that drives postsynaptic ion-channel receptors. These receptors exhibit multiple states, with state transition kinetics dependent on neurotransmitter concentration. Here, a novel and simple analytical approach for describing gating of multi-state receptors by signals with complex continuous time courses is used to describe the generation of glutamate-mediated quantal postsynaptic responses at brain synapses. The neurotransmitter signal, experienced by multi-state N-methyl-D-aspartate (NMDA)- and L-alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionate (AMPA)-type glutamate receptors at specific points in a synaptic cleft, is approximated by a series of step functions of different intensity and duration and used to drive a Markovian, multi-state kinetic scheme that describes receptor gating. Occupancy vectors at any point in time can be computed interatively from the occupancy vectors at the times of steps in transmitter concentration. Multi-state kinetic schemes for both the low-affinity AMPA subtype of glutamate receptor and for the high-affinity NMDA subtype are considered, and expected NMDA and AMPA components of synaptic currents are calculated. The amplitude of quantal responses mediated by postsynaptic receptor clusters having specific spatial distributions relative to foci of quantal neurotransmitter release is then calculated and related to the displacement between the center of the postsynaptic receptor cluster and the focus of synaptic vesicle discharge. Using this approach we show that the spatial relation between the focus of release and the center of the postsynaptic receptor cluster affects synaptic efficacy. We also show how variation in this relation contributes to variation in synaptic current amplitudes