A model of the transient, low-threshold voltage-dependent (T-type) Ca2+ current is constructed using recent whole-cell voltage-clamp data from enzymatically isolated rat thalamocortical relay neurons. The T-type Ca2+ current is described according to the Hodgkin-Huxley scheme, using the m3h format, with rate constants determined from the experimental data (22-24°C; extracellular Ca2+ concentration [Ca2+](o) = 3 mM). The T-type Ca2+ current inactivates rapidly during maintained depolarization (time constant, τ(h) ≃ 20 ms at -20 mV), yet recovery from inactivation is slow (time constant, τ(r) ≃ 270 ms at -80 mV). To reconcile these observations, a two-step kinetic scheme is proposed for the inactivation gate. Each of the time constants in this scheme is voltage dependent, with a maximum at about -85 mV (45 ms for one and 275 ms for the other). Numerical simulations of recovery in a two-pulse, voltage-clamp protocol compare favorably with experimental results obtained by Coulter et al. as well as those obtained in an independent series of experiments with guinea pig thalamic neurons ([Ca2+](o) = 10 mM). For current-clamp simulations, a leakage current g(L)(V - V(L)) is included; with V(L) = -65 mV, the calculated resting membrane potential is -63 mV. It is shown that the T-type Ca2+ current together with the leakage current suffices to describe the low-threshold spike (LTS), a slow, triangular-shaped depolarizing event that can be evoked only from relatively hyperpolarized membrane potentials and that underlies the burst firing of Na+-dependent action potentials in thalamic neurons. Outward currents are not required to reproduce the basic shape of the LTS. The LTS can be activated with either a depolarizing current step from a sufficiently hyperpolarized level or on termination of a hyperpolarizing current step. In either case, the amplitude of the LTS is a monotonically increasing, sigmoid-shaped function of the hyperpolarizing current step intensity. Because of the slower kinetic step of the channel's inactivation gate, our model predicts that recovery of the LTS to greater than one-half amplitude would require a prolonged hyperpolarization of >100 ms (at body temperature). This imposes an upper limit (≃10 Hz) on the frequency of repetitive hyperpolarizations that can elicit a train of LTSs and hence on the frequency of any rhythm that requires LTS-mediated bursting of thalamic neurons. This finding is consistent with the views that the T-type Ca2+ current in thalamic neurons is critical to the generation of the 10-Hz spindle oscillations and that it may also play a role in the epileptic discharge during absence seizures.
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