A two-variable model of somatic-dendritic interactions in a bursting neuron.

Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, ON, Canada, K1N 6N5.
Bulletin of Mathematical Biology (Impact Factor: 1.29). 10/2002; 64(5):829-60. DOI: 10.1006/bulm.2002.0303
Source: PubMed

ABSTRACT We present a two-variable delay-differential-equation model of a pyramidal cell from the electrosensory lateral line lobe of a weakly electric fish that is capable of burst discharge. It is a simplification of a six-dimensional ordinary differential equation model for such a cell whose bifurcation structure has been analyzed (Doiron et al., J. Comput. Neurosci., 12, 2002). We have modeled the effects of back-propagating action potentials by a delay, and use an integrate-and-fire mechanism for action potential generation. The simplicity of the model presented here allows one to explicitly derive a two-dimensional map for successive interspike intervals, and to analytically investigate the effects of time-dependent forcing on such a model neuron. Some of the effects discussed include 'burst excitability', the creation of resonance tongues under periodic forcing, and stochastic resonance. We also investigate the effects of changing the parameters of the model.

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    ABSTRACT: We give an overview of the analysis of a new type of bursting (ìghostburstingî) seen in pyramidal cells of weakly electric sh. We start with the experimental observations and characterization of the bursting, describe a compartmental model of a pyramidal cell that undergoes ghostbursting and the development of a simplied yet realistic conductanceñbased model of this cell. This model then motivates a minimal leaky integrateñandñr e model that also has the qualitative features of ghostbursting.
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    ABSTRACT: Prediction and cancelation of redundant information is an important feature that many neural systems must display in order to efficiently code external signals. We develop an analytic framework for such cancelation in sensory neurons produced by a cerebellar-like structure in wave-type electric fish. Our biologically plausible mechanism is motivated by experimental evidence of cancelation of periodic input arising from the proximity of conspecifics as well as tail motion. This mechanism involves elements present in a wide range of systems: (1) stimulus-driven feedback to the neurons acting as detectors, (2) a large variety of temporal delays in the pathways transmitting such feedback, responsible for producing frequency channels, and (3) burst-induced long-term plasticity. The bursting arises from back-propagating action potentials. Bursting events drive the input frequency-dependent learning rule, which in turn affects the feedback input and thus the burst rate. We show how the mean firing rate and the rate of production of 2- and 4-spike bursts (the main learning events) can be estimated analytically for a leaky integrate-and-fire model driven by (slow) sinusoidal, back-propagating and feedback inputs as well as rectified filtered noise. The effect of bursts on the average synaptic strength is also derived. Our results shed light on why bursts rather than single spikes can drive learning in such networks "online", i.e. in the absence of a correlative discharge. Phase locked spiking in frequency specific channels together with a frequency-dependent STDP window size regulate burst probability and duration self-consistently to implement cancelation.
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