Increasing inhibitory input increases neuronal firing rate: why and when? Diffusion process cases

Increasing inhibitory input to single neuronal models, such as the FitzHugh– Nagumo model and the Hodgkin–Huxley model, can sometimes increase their firing rates, a phenomenon which we term inhibition-boosted firing (IBF). Here we consider neuronal models with diffusion approximation inputs, i.e. they share the identical first- and second-order statistics of the corresponding Poisson process inputs. Using the integrate-and-fire model and the IF-FHN model, we explore theoretically how and when IBF can happen. For both models, it is shown that there is a critical input frequency at which the efferent firing rate is identical when the neuron receives purely excitatory inputs or exactly balanced inhibitory and excitatory inputs. When the input frequency is lower than the critical frequency, IBF occurs.