The oscillatory properties of single thalamocortical neurons were investigated by using a Hodgkin-Huxley-like model that included Ca2+ diffusion, the low-threshold Ca2+ current (lT) and the hyperpolarization-activated inward current (lh). lh was modeled by double activation kinetics regulated by intracellular Ca2+. The model exhibited waxing and waning oscillations consisting of 1–25-s bursts of slow oscillations (3.5–4 Hz) separated by long silent periods (4–20 s). During the oscillatory phase, the entry of Ca2+ progressively shifted the activation function of lh, terminating the oscillations. A similar type of waxing and waning oscillation was also observed, in the absence of Ca2+ regulation of lh, from the combination of lT, lh, and a slow K+ current. Singular approximation showed that for both models, the activation variables of lh controlled the dynamics of thalamocortical cells. Dynamical analysis of the system in a phase plane diagram showed that waxing and waning oscillations arose when lh entrained the system alternately between stationary and oscillating branches. © 1993, The Biophysical Society. All rights reserved.
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