1. We study the propagation and dynamics of spindle waves in thalamic slices by developing and analyzing a model of reciprocally coupled populations of excitatory thalamocortical (TC) neurons and inhibitory thalamic reticular (RE) neurons. 2. Each TC neuron has three intrinsic ionic currents: a low-threshold T type Ca+2 current (I(Ca-T)), a hyperpolarization-activated cation ('sag') current (I(h)), and a leak current. Each RE cell also has three currents: I(Ca-T), a leak current, and a calcium-activated potassium current (I(AHP)). Isolated TC cells are at rest, can burst when released or depolarized from a hyperpolarized level, and burst rhythmically under moderate constant hyperpolarizing current. Isolated RE cells are at a hyperpolarized resting membrane potential and can burst when depolarized. 3. TC cells excite RE cells with fast α-amino-3-hydroxy-5- methyl-4-isoxazolepropionic acid (AMPA) synapses, and RE cells inhibit TC cells with fast γ-aminobutyric acid-A (GABA(A)) and slow GABA(B) synapses and inhibit each other with GABA(A) synapses only. GABA(B) postsynaptic conductances operate far from saturation, and the slow inhibitory postsynaptic potentials (IPSPs) increase with the width of the presynaptic burst. The model network is a one-dimensional cellular array with localized coupling. The synaptic coupling strength decays with the distance between the pre- and postsynaptic cells, either exponentially or as a step function. 4. The 'intact' network can oscillate with partial synchrony and a population frequency of ~10 Hz. RE cells emit bursts almost at every oscillation cycle, whereas TC cells do so almost at every other cycle. Block of GABA(B) receptors hardly changes the network behavior. Block of GABA(A) receptors leads the network to a slowed oscillatory state, where the population frequency is ~4 Hz and both RE and TC cells fire unusually long bursts at every cycle and in full synchrony. These results are consistent with the experimental observations of von Krosigk, Bal, and McCormick. We obtain such consistency only when the above assumptions regarding the synaptic dynamics, particularly nonsaturating GABA(B) synapses, are fulfilled. 5. The slice model has a stable rest state with no neural activity. By initially depolarizing a few neurons at one end of the slice while all the other cells are at rest, a recruitment process may be initiated, and a wavefront of oscillatory activity propagates across the slice. Ahead of the wavefront, neurons are quiescent; neurons behind it oscillate. We find that the wave progresses forward in a lurching manner. TC cells that have just become inhibited must be hyperpolarized for a long enough time before they can fire rebound bursts and recruit RE cells. This step limits the wavefront velocity and may involve a substantial part of the cycle when no cells at the front are depolarized. 6. The wavefront velocity increases linearly with the characteristic spatial length of the connectivity (the footprint length). It increases only gradually with the synaptic strength, logarithmically in the case of an exponential connection function and only slightly for a step connection function. It also decreases gradually with a potassium leak conductance that hyperpolarizes RE cells. 7. To reproduce the experimentally measured wavefront velocity of ~1 mm/s, together with other in vitro observations, both the RE-to-TC and the TC-to-RE projections in the model should be spatially localized. The sum of the RE-to-TC and the TC-to-RE synaptic footprint lengths should be on the order of 100 μm. 8. Neurons at different positions along the slice model oscillate with different phases. In the case of GABA(A) blockade, the phase shifts increase linearly with the distance between neurons and decay only slowly with time. Depending on parameter values, the phase shift can be positive or negative, because in a given bursting cycle a neuron lites before or after those on its right side, respectively. With GABA(A) intact, the phase shift's dependence on interneuronal distance can fluctuate and be more complex. 9. In addition to a propagating wavefront, the network can display various other types of spatiotemporal behaviors as parameter values and initial conditions are varied. Even a few endogenously oscillating cells, as expected in a heterogeneous population, can lead to several initiation points for waves propagating in both directions. The isolated RE network can oscillate with partial synchrony if the RE cells are less hyperpolarized, similar to in vivo results on the isolated RE nucleus by Steriade and colleagues.
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