Depressing synapse as a detector of frequency change

In this article we discuss the short-term synaptic depression using a mathematical model. We derive the model of synaptic depression caused by the depletion of synaptic vesicles for the case of infinitely short stimulation time and show that the analytical formulas for the postsynaptic potential (PSP) and kinetic functions take simple closed form. A solution in this form allows an analysis of the characteristics of depression as a function of the models parameters and the derivation of analytic formulas for measures of short time synaptic depression commonly used in experimental studies. Those formulas are used to validate the model by fitting it to two types of synapses described in the literature. Given the fitted parameters we discuss the behavior of the synapse in situations involving frequency change. We also indicate a possible role of depressing synapses in information processing as not only a filter of high frequency input but as a detector of the return from high frequency stimulation to the stimulation within frequency band specific for a given synapse.