Mathematical models of cochlear nucleus onset neurons: II. model with dynamic spike-blocking state.

Onset (On) neurons in the cochlear nucleus (CN), characterized by their prominent response to the onset followed by little or no response to the steady-state of sustained stimuli, have a remarkable ability to entrain (firing 1 spike per cycle of a periodic stimulus) to low-frequency tones up to 1000 Hz. In this article, we present a point-neuron model with independent, excitatory auditory-nerve (AN) inputs that accounts for the ability of On neurons to both produce onset responses for high-frequency tone bursts and entrain to a wide range of low-frequency tones. With a fixed-duration spike-blocking state after a spike (an absolute refractory period), the model produces entrainment to a broad range of low-frequency tones and an On response with short interspike intervals (chopping) for high-frequency tone bursts. To produce On response patterns with no chopping, we introduce a novel, more complex, active membrane model in which the spike-blocking state is maintained until the instantaneous membrane voltage falls below a transition voltage. During the sustained depolarization for a high-frequency tone burst, the new model does not chop because it enters a spike-blocking state after the first spike and fails to leave this state until the membrane voltage returns toward rest at the end of the stimulus. The model entrains to low-frequency tones because the membrane voltage falls below the transition voltage on every cycle when the AN inputs are phase-locked. With the complex membrane model, On response patterns having moderate steady-state activity for high-frequency tone bursts (On-L) are distinguished from those having no steady-state activity (On-I) by requiring fewer AN inputs. Voltage-gated ion channels found in On-responding neurons of the CN may underlie the hypothesized dynamic spike-blocking state. These results provide a mechanistic rationale for distinguishing between the different physiological classes of CN On neurons.