Fig. 9.

Gating schemes and comparison of the voltage dependence of the recovery rates between Na⁺ and T-channels. A, scheme 2 is a more elaborate gating diagram than Scheme 1. Depolarization moves the channel from the fully deactivated state C1 to the activated state O through intermediate closed states C2 to Cn. The binding affinity between the blocking inactivating peptide and its receptor presumably is larger if the channel is more activated (faster binding rate and slower unbinding rate toward state O, represented by the size of thevertical arrows). Channel inactivation is thus coupled to activation. B, The gradually changing recovery rate between −80 and −180 mV in Na⁺ channels (thedashed line and the dashed vertical axison the left) (Kuo and Bean, 1994) is ascribable to rapid redistribution of the inactivated channels among CnB to C1B during the hyperpolarizing recovery pulse. More negative potentials shift the distribution more to the left and thus increase the macroscopic recovery rate, which is saturated at approximately −200 mV when most channels are in the fully deactivated state C1B. The dashed line is a Boltzmann function: recovery rate (msec⁻¹) = 4.5/(1 + exp((V + 140)/16)), where V denotes the membrane potential in millivolts (the horizontal axis) (Kuo and Bean, 1994). In contrast, the recovery rate of inactivated T-channels in thalamic neurons saturates at much less negative potentials (approximately −100 mV; the bold line and the bold vertical axis on the right; also note the 1000-fold difference between the units of the left andright vertical axes). The bold line is a rough estimate (for the rationales underlying the derivation of thebold line, please refer to Discussion) and is a Boltzmann function: recovery rate (sec⁻¹) = 3.5/(1 + exp((V + 85)/6)), where Vdenotes the membrane potential in millivolts. The bold line is redrawn with a different scale (thin line and the thin vertical axis on theright) to demonstrate that the conformational changes represented by the bold line may actually be just one small part of the conformational changes represented by thedashed line. C, scheme 3is modified from scheme 2 and may be a more appropriate gating diagram for T-channels. Note that the unbinding and binding rates (size of the vertical arrows) are unchanged among different closed states because the binding affinity of the inactivating particle toward different closed states C1 to Cn presumably does not change significantly. This scheme may well explain many key observations on T-channels in this study, including early saturation of the exponential recovery phase, apparently steeper slope of the curve describing the voltage dependence of the recovery rate, and OB to CnB transition as the rate-limiting step in the overall deactivation process of the inactivated channel.