Dynamical Systems in Neuroscience:

316 Simple Modelsthrough an appropriate thalamic nucleus. Anatomically, the thalamic system consistsof three major types of neurons: thalamocortical (TC) neurons, which relay signals intothe neocortex, reticular thalamic nucleus (RTN) neurons, and thalamic interneurons,which provide local reciprocal inhibition (Shepherd 2004). The three types have distinctelectrophysiological properties and firing patterns.There are undoubtedly subtypes with each type of thalamic neurons, however, theclassification is not as elaborate as the one in neocortex. This, and the differencebetween species, age and various thalamic nuclei, explains the contradictory reportsof different firing patterns in presumably the same types of thalamic neurons. Belowwe use the simple model (8.5, 8.6) to simulate a “typical” TC, TRN, and interneuron.The reader should realize, though, that our attempt is as incomplete as the attemptto simulate a “typical” neocortical neuron ignoring the fact that there are RS, IB, CH,FS, etc., cells.8.3.1 Thalamo-cortical (TC) relay neuronsThalamocortical (TC) relay neurons, the type of thalamic neurons that project sensoryinput to the cortex, have two prominent models of firing, illustrated in Fig. 8.31: tonicand burst mode. Both modes are ubiquitous in vitro and in vivo, including awake andbehaving animals, and both represent different patterns of relay of sensory informationinto the cortex (Sherman 2001). The transition between the firing modes depend onthe degree of inactivation of low-threshold Ca 2+ T-current (Jahnsen and Llinas 1984,McCormick and Huguenard 1992), which in turn depends on the holding membranepotential of the TC neuron.In tonic mode, the resting membrane potential of a TC neuron is around −60 mV,which is above the inactivation threshold of the T-current. The slow Ca 2+ current isinactivated and is not available to contribute to spiking behavior. The neuron fires Na + -K + tonic spikes with a relatively constant frequency that depends on the amplitude ofthe injected current and could be as low as a few Hertz (Zhan et al. 1999). Such acell, illustrated in Fig. 8.31, is a typical Class 1 excitable system near a saddle-node oninvariant circle bifurcation. It exhibits regular spiking behavior similar to that of RSneocortical neurons. It relays transient inputs into outputs, and for this reason, manyrefer to the tonic mode as relay mode of firing.To switch a TC neuron into the burst mode, an injected dc-current or inhibitorysynaptic input must hyperpolarize the membrane potential to around −80 mV for atleast 50-100 ms. While hyperpolarized, the Ca 2+ T-current deinactivates and becomesavailable. As soon as the membrane potential is returned to the resting or depolarizedstate, there is an excess of the inward current that drives the neuron over thresholdand results in a rebound burst of high-frequency spikes, as in Fig. 8.31, called a lowthreshold(LT) spike or a Ca 2+ spike.In Fig. 8.31, right, we simulate TC neuron using simple model (8.5, 8.6), treating uas the low-threshold Ca 2+ current. Since the current is inactivated in the tonic mode,i.e., u ≈ 0, we take b = 0. The resting and threshold voltages of the neuron in the