  At chemical synapses, an arriving electric signal induces the fusion of
vesicles with the presynaptic membrane, thereby releasing neurotransmitters
into the synaptic cleft. After a fusion event, both the release site and the
vesicle undergo a recovery process before becoming available for reuse again.
Of central interest is the question which of the two restoration steps acts as
the limiting factor during neurotransmission under high-frequency sustained
stimulation. In order to investigate this question, we introduce a novel
non-linear reaction network which involves explicit recovery steps for both the
vesicles and the release sites, and includes the induced time-dependent output
current. The associated reaction dynamics are formulated by means of ordinary
differential equations (ODEs), as well as via the associated stochastic jump
process. While the stochastic jump model describes a single release site, the
average over many release sites is close to the ODE solution and shares its
periodic structure. The reason for this can be traced back to the insight that
recovery dynamics of vesicles and release sites are statistically almost
independent. A sensitivity analysis on the recovery rates based on the ODE
formulation reveals that neither the vesicle nor the release site recovery step
can be identified as the essential rate-limiting step but that the
rate-limiting feature changes over the course of stimulation. Under sustained
stimulation the dynamics given by the ODEs exhibit transient changes leading
from an initial depression of the postsynaptic response to an asymptotic
periodic orbit, while the individual trajectories of the stochastic jump model
lack the oscillatory behavior and asymptotic periodicity of the ODE-solution.
