Synaptic filtering of rate-coded information

In this paper, we analytically examine the influence of synaptic short-term plasticity (STP) on the transfer of rate-coded information through synapses. STP endows each presynaptic input spike with an amplitude that depends on previous input spikes. We develop a method to calculate the spectral statistics of this amplitude modulated spike train (postsynaptic input) for the case of an inhomogeneous Poisson process. We derive in particular analytical approximations for cross-spectra, power spectra, and for the coherence function between the postsynaptic input and the time-dependent rate modulation for a specific model. We give simple expressions for the coherence in the limiting cases of pure facilitation and pure depression. Using our analytical results and extensive numerical simulations, we study the spectral coherence function for postsynaptic input resulting from a single synapse or from a group of synapses. For a single synapse, we find that the synaptic coherence function is largely independent of frequency indicating broadband information transmission. This effect is even more pronounced for a large number of synapses. However, additional noise gives rise to frequency-dependent information filtering.