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 oscillatory burst discharge in the gamma-frequency range (20-80 Hz) in response to constant depolarizing stimuli. Previous in vitro studies have shown that these bursts arise through a recurring spike backpropagation from soma to apical dendrites that is conditional on the frequency of action potential discharge ("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 afterpotential (DAP). The bursts are terminated when a high-frequency somatic spike 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 and 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 immunocytochemical and electrophysiological data. The currents modeled are somatic and dendritic sodium and potassium involved in action potential generation, somatic 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, differential spike refractory periods, and a somatic DAP. However, the core model does not produce oscillatory spike bursts with constant depolarizing stimuli. We find that a cumulative inactivation of potassium channels underlying dendritic spike repolarization is a necessary condition for the model to produce a sustained gamma-frequency burst pattern matching experimental results. This cumulative inactivation accounts for a frequency-dependent broadening of dendritic spikes and results in a conditional failure of backpropagation when the intraburst ISI exceeds dendritic spike refractory period, terminating the burst. These findings implicate ion channels involved in repolarizing dendritic spikes as being central to the process of conditional backpropagation and oscillatory burst discharge in this principal sensory output neuron of the ELL.