Model of gamma frequency burst discharge generated by condit

Model of Gamma Frequency Burst Discharge Generated by Conditional Backpropagation

BRENT DOIRON,1ANDRE′LONGTIN,1RAY W.TURNER,2AND LEONARD MALER3

1Physics Department,University of Ottawa,Ottawa,Ontario K1N6N5;2Department of Cell Biology and Anatomy, Neuroscience Research Group,University of Calgary,Calgary,Alberta T2N4N1;and3Department of Cellular and Molecular Medicine,University of Ottawa,Ottawa,Ontario K1H8M5,Canada

Received18January2001;accepted in?nal form10May2001

Doiron,Brent,Andre′Longtin,Ray W.Turner,and Leonard

Maler.Model of gamma frequency burst discharge generated by

conditional backpropagation.J Neurophysiol86:1523–1545,2001.

Pyramidal cells of the electrosensory lateral line lobe(ELL)of the

weakly electric?sh Apteronotus leptorhynchus have been shown to

produce oscillatory burst discharge in the?-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 backpropa-

gation”).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 back-

propagation.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 modi?ed 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 prox-

imal apical dendritic persistent sodium,and K

V 3.3and fast transient

A-like potassium channels distributed over the entire model cell.The core model produces realistic somatic and dendritic spikes,differen-tial spike refractory periods,and a somatic DAP.However,the core model does not produce oscillatory spike bursts with constant depo-larizing stimuli.We?nd that a cumulative inactivation of potassium channels underlying dendritic spike repolarization is a necessary con-dition for the model to produce a sustained?-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 ?ndings 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.

rent(Magee and Carruth1999;Williams and Stuart1999). Alternatively,the amplitude of the DAP can be in?uenced by dendritic morphology because the dendrite-to-soma current ?ow increases with the relative dendritic to somatic surface area and decreases with axial resistance(Mainen and Sej-nowski1996;Quadroni and Knofnel1994).Lemon and Turner (2000)recently described a novel mechanism of“conditional spike backpropagation”that modulates DAP amplitude and produces a?-frequency oscillatory burst discharge in pyrami-dal neurons of the electrosensory system.

Electrosensory lateral line lobe(ELL)pyramidal cells are principal output cells in the medulla that respond to AM of electric?elds detected by peripheral electroreceptors(Bastian 1981;Shumway1989).Several studies have described the properties of burst discharge in ELL pyramidal cells(Bastian and Nguyenkim2001;Gabbiani and Metzner1999;Gabbiani et al.1996;Lemon and Turner2000;Metzner et al.1998; Rashid et al.2001;Turner and Maler1999;Turner et al.1994, 1996).Signal detection analysis has shown that ELL pyramidal cells generate burst discharge in relation to speci?c signal features,such as up or down strokes in the external electric ?eld(Gabbiani and Metzner1999;Gabbiani et al.1996; Metzner et al.1998).Further,signi?cant progress has been made in identifying how conditional backpropagation gener-ates an oscillatory pattern of spike bursts in ELL pyramidal cells in vitro.Pyramidal cell spike bursts are initiated when a Na?spike backpropagating over the initial200?m of apical dendrites generates a somatic DAP(Turner et al.1994).A frequency-dependent broadening of dendritic spikes potenti-ates the DAP until a high-frequency spike doublet is triggered at the soma(Lemon and Turner2000).The short inter-spike interval(ISI)of the doublet falls within the dendritic refractory period and blocks spike backpropagation,removing the den-dritic depolarization that drives the burst.Repetition of this conditional process of backpropagation groups repetitive spike discharges into bursts in the?-frequency range.A key issue that remains in understanding the mechanism of ELL burst discharge is the identity of factor(s)underlying the frequency-dependent broadening of dendritic spikes that drives burst discharge.

Our present knowledge of spike discharge in ELL pyramidal cells and the simple mechanism underlying conditional back-propagation provides an excellent opportunity to model a form of?-frequency burst discharge and test hypotheses about burst generation.This study presents a detailed compartmental

model of an ELL pyramidal cell that is based on extensive

electrophysiological and morphological data.We establish the

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