Model of gamma frequency burst discharge generated by conditional backpropagation

Pyramidal cells of the electrosensory lateral line lobe (ELL) of the weakly electric fish Apteronotus leptorhynchus have been shown to produce oscilla tory burst discharge in the gamma -frequency range (20-80 Hz) in response t o constant depolarizing stimuli. Previous in vitro studies have shown that these bursts arise through a recurring spike backpropagation from soma to a pical dendrites that is conditional on the frequency of action potential di scharge ("conditional backpropagation"). Spike bursts are characterized by a progressive decrease in inter-spike intervals (ISIs), and an increase of dendritic spike duration and the amplitude of a somatic depolarizing afterp otential (DAP). The bursts are terminated when a high-frequency somatic spi ke doublet exceeds the dendritic spike refractory period, preventing spike backpropagation. We present a detailed multi-compartmental model of an ELL basilar pyramidal cell to simulate somatic and dendritic spike discharge an d test the conditions necessary to produce a burst Output. The model ionic channels are described by modified Hodgkin-Huxley equations and distributed over both soma and dendrites under the constraint of available immunocytoc hemical and electrophysiological data. The currents modeled are somatic and dendritic sodium and potassium involved in action potential generation, so matic and proximal apical dendritic persistent sodium, and K(V)3.3 and fast transient A-like potassium channels distributed over the entire model cell . The core model produces realistic somatic and dendritic spikes, different ial spike refractory periods, and a somatic DAP. However, the core model do es not produce oscillatory spike bursts with constant depolarizing stimuli. We find that a cumulative inactivation of potassium channels underlying de ndritic spike repolarization is a necessary condition for the model to prod uce a sustained gamma -frequency burst pattern matching experimental result s. This cumulative inactivation accounts for a frequency-dependent broadeni ng of dendritic spikes and results in a conditional failure of backpropagat ion when the intraburst ISI exceeds dendritic spike refractory period, term inating the burst. These findings implicate ion channels involved in repola rizing dendritic spikes as being central to the process of conditional back propagation and oscillatory burst discharge in this principal sensory Outpu t neuron of the ELL.