Spike shape and synaptic-amplitude distribution interact to set the high-frequency firing-rate response of neuronal populations

The dynamics of an ensemble of particles driven out of a potential well, with replacement, by the Poissonian arrival of amplitude-distributed shot noise is examined. A general formula for the high-frequency limit of the escape-rate susceptibility is derived. For certain choices of potential well and amplitude distribution the decay of the high-frequency susceptibility exhibits a nonuniversal exponent. This is a qualitatively different response to that predicted by the diffusion approximation. To provide an example the general framework is applied to a problem of current interest in the biophysics of neuronal voltage dynamics. It is shown that the firing-rate response of neurons to rapidly varying stimuli can be significantly enhanced depending on the ratio between the scale of excitatory postsynaptic potentials and the voltage range over which an action potential initiates. The result is robust to various choices of threshold definition and also to synaptic filtering at physiologically reasonable time scales.