Model of the hyperpolarization-activated current Ih and its regulation by calcium
With Agnessa Babloyantz (University of Brussels, Belgium), we introduced a biophysical model of the hyperpolarization-activated current Ih to account for the unusual kinetic features of this current . This model allowed us to account for several features of the oscillatory behavior of thalamocortical neurons. The model included a dual gating process of the channel, with a fast and a slow gate. This combination of fast and slow gates allowed the model to reproduce the unusual features of Ih in voltage-clamp experiments .
In a subsequent study with Terrence Sejnowski (Salk Institute, USA), we introduced a regulation of Ih by intracellular calcium , inspired from results in cardiac electrophysiology. The model consisted of a selective binding of calcium ions to the open state of the Ih channel, leading to prolongation of its opening time, and a shift of its steady-state activation characteristics in the presence of calcium . Coupled with the T-type calcium current, this model of Ih allowed us to reproduce a variety of oscillatory states in thalamic neurons, such as waxing-and-waning oscillations . A more elaborate model was introduced later , based on the indirect regulation of Ih channels by calcium, through a second messenger (for example cAMP). This model reproduced realistically the oscillatory behavior of thalamic neurons and networks . A similar model also reproduced a form of persistent activity activated by hyperpolarization (HAGPA)  (see Section 2.3).
 Destexhe, A. and Babloyantz, A. A model of the inward current Ih and its possible role in thalamocortical oscillations. NeuroReport 4: 223-226, 1993 (see abstract)
 Destexhe, A., Babloyantz, A. and Sejnowski, T.J. Ionic mechanisms for intrinsic slow oscillations in thalamic relay neurons. Biophys. J. 65: 1538-1552, 1993 (see abstract)
 Destexhe, A., Bal, T., McCormick, D.A. and Sejnowski, T.J. Ionic mechanisms underlying synchronized oscillations and propagating waves in a model of ferret thalamic slices. J. Neurophysiol. 76: 2049-2070, 1996 (see abstract)
 Winograd, M., Destexhe, A. and Sanchez-Vives, M.V. Hyperpolarization-activated graded persistent activity in the prefrontal cortex. Proc. Natl. Acad. Sci. USA 105: 7298-7303, 2008 (see abstract)
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