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De Schutter: Purkinje Cell Model


Figure 1: Activation and inactivation properties of the P-type calcium (CaP, —) ionic conductances in the model. Seady-state activation and inactivation vs. voltage are plotted at the left, the time constants of activation (τm) and inactivation (τh) vs. voltage in the middle (Note: Semilogarithmic scale), and a simulation of representative voltage-clamp currents at the right, obtained from a spherical cell and assuming a complete block of all other channels. They simulate steps from a holding potential of -110 to -70 mV up to 0 mV in 10 mV increments. The voltage-clamp current amplitude has been scaled arbitrarily because we mainly wanted to demonstrate the current kinetics.

P-Type Calcium Current

The P-type Ca2+ channel is a high-threshold, very slowly inactivating channel first described in the Purkinje cell [7]. A complete whole-cell patch clamp study of this channel in freshly dissociated rat Purkinje cells was done by [8]; this provided us with all the data necessary to model the P-type calcium (CaP) current (Fig. 2C). Initial versions of the model were run with equations based on averaged data [8] but, confirming our experience in other systems [2], we found that equations based on data from a single preparation (Figs. 5C and 6C in [8]) made Ca2+ spiking in the model more robust. These data do not support multiple activation states for the CaP channel because there does not seem to be any delay in activation [5] and the steady-state activation curve could be fitted by a Boltzmann-style curve with power 1. Therefore activation of CaP has been modeled with a single gate. This is in contrast to equations for other mammalian Ca2+ currents, which usually show some delay in activation [16].

Recently, [910] also reported CaP channel data on the basis of cell-attached patch clamps of guinea pig Purkinje cells. These results seem to be in accord with the data reported by [8] for activation; the threshold of activation especially is very similar (-41 mV in 2 mM Ca2+ reported by Usowicz et al. [9] vs. -45 to -40 mV in 5 mM Ba2+ [8]. However, Usowicz et al. [10] show little or no inactivation of CaP current, whereas [8] declares that there is a slow inactivation. Other authors claim that there might be several time constants of inactivation for CaP current [4] and to our knowledge a possible Ca2+-dependent inactivation, as found in other high-threshold Ca2+ channels [3] has not been completely excluded. The model used the slow inactivation suggested by [8] (Fig. 2C).


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[10]   MM Usowicz, M Sugimori, B Cherksey, and RR Llinás. P-type calcium channels in the somata and dendrites of adult cerebellar Purkinje cells. Neuron, 9:1185–1199, 1992.