Correlated inhibitory and excitatory inputs to the coincidence detector: analytical solution

We present a solution for the steady-state output rate of an ideal coincidence detector receiving an arbitrary number of excitatory and inhibitory input spike trains. All excitatory spike trains have identical binomial count distributions (which includes Poisson statistics as a special case) and arbitrary pairwise cross correlations between them. The same applies to the inhibitory inputs, and the rates and correlation functions of excitatory and inhibitory populations may be the same or different from each other. Thus, for each population independently, the correlation may range from complete independence to perfect correlation (identical processes). We find that inhibition, if made sufficiently strong, will result in an inverted U-shaped curve for the output rate of a coincidence detector as a function of input rates for the case of identical inhibitory and excitory input rates. This leads to the prediction that higher presynaptic (input) rates may lead to lower postsynaptic (output) rates where the output rate may fall faster than the inverse of the input rate, and shows some qualitative similarities to the case of purely excitatory inputs with synaptic depression. In general, we find that including inhibition invariably and significantly increases the behavioral repertoire of the coincidence detector over the case of pure excitatory input.