Transient responses of activity-dependent synapses to modulated pulse trains

Synapses exhibit complex filtering properties on short time scales with respect to their presynaptic pulse trains. In particular, the quantal model of neurotransmitter release has been shown to be highly selective for particular presynaptic pulse patterns. However, due to the iterative, pulse-based nature of the original equations describing the quantal model, such analysis has been relegated to heuristics and simulations. In contrast, we derive an explicit expression for the quantal model and apply it to analyzing the transmission of modulated pulse trains across a synapse. We show that for biologically realistic parameters, the quantal model favors periodically modulated pulse trains (such as bursting, chattering or stuttering) over non-modulated (i.e. regular) ones.