ANALYSIS OF BURSTING IN A THALAMIC NEURON MODEL

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 Hodgkin-Huxley-like model for fast sodium spiking in the hi gh voltage regime to account for the distinct firing modes of thalamic neurons. We employ bifurcation analysis to illustrate the stimulus-re sponse behavior of the full model under both voltage regimes. The mode l neuron shows continuous sodium spiking when depolarized sufficiently from rest. Depending on the parameters of calcium current inactivatio n, there are two types of low-voltage responses to a hyperpolarizing c urrent step: a single rebound low threshold spike (LTS) upon release o f the step and periodic LTSs. Bursting is seen as sodium spikes ride t he LTS crest. In both cases, we analyze the LTS burst response by proj ecting 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 previo us work of Rose and Hindmarsh (1989a-c) for a thalamic neuron and prop ose a simpler model for thalamic activity. We consider burst modulatio n by using a neuromodulator-dependent potassium leakage conductance as a control parameter. These results correspond with experiments showin g that the application of certain neurotransmitters can switch firing modes.