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Analysis of bursting in a thalamic neuron model

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Abstract

We extend a quantitative model for low-voltage, slow-wave excitability based on the T-type calcium current (Wang et al. 1991) by juxtaposing it with a Hodgn-Huxley-like model for fast sodium spiking in the high voltage regime to account for the distinct firing modes of thalamic neurons. We employ bifurcation analysis to illustrate the stimulus-response behavior of the full model under both voltage regimes. The model neuron shows continuous sodium spiking when depolarized sufficiently from rest. Depending on the parameters of calcium current inactivation, there are two types of low-voltage responses to a hyperpolarizing current step: a single rebound low threshold spike (LTS) upon release of the step and periodic LTSs. Bursting is seen as sodium spikes ride the LTS crest. In both cases, we analyze the LTS burst response by projecting its trajectory into a fast/slow phase plane. We also use phase plane methods to show that a potassium A-current shifts the threshold for sodium spikes, reducing the number of fast sodium spikes in an LTS burst. It can also annihilate periodic bursting. We extend the previous work of Rose and Hindmarsh (1989a–c) for a thalamic neuron and propose a simpler model for thalamic activity. We consider burst modulation by using a neuromodulator-dependent potassium leakage conductance as a control parameter. These results correspond with experiments showing that the application of certain neurotransmitters can switch firing modes.

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Authors and Affiliations

  1. Mathematical Research Branch, NIDDK, National Institutes of Health, 20892, Bethesda, MD, USA

    Maureen E. Rush & John Rinzel

  2. Department of Applied Mathematics, University of Maryland, 20742, College Park, MD, USA

    Maureen E. Rush

Authors
  1. Maureen E. Rush
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  2. John Rinzel
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Rush, M.E., Rinzel, J. Analysis of bursting in a thalamic neuron model. Biol. Cybern. 71, 281–291 (1994). https://doi.org/10.1007/BF00239616

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  • DOI: https://doi.org/10.1007/BF00239616

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