Synchronization properties of spindle oscillations in a thalamic reticular nucleus model

1. We address the hypothesis of Steriade and colleagues that the thalamic reticular nucleus (RE) is a pacemaker for thalamo-cortical spindle oscillations by developing and analyzing a model of a large population of all-to-all coupled inhibitory RE neurons. 2. Each RE neuron has three ionic currents: a low-threshold T-type Ca²⁺ current (I(Ca-T)), a calcium- activated potassium current (I(AHP)) and a leakage current (I(L)). I(Ca-T) underlies a cell's postinhibitory rebound properties, whereas I(AHP) hyperpolarizes the neuron after a burst. Each neuron, which is a conditional oscillator, is coupled to all other RE neurons via fast γ-aminobutyric acid- A (GABA(A)) and slow GABA(B) synapses. 3. For generating network oscillations I(AHP) may not be necessary. Synaptic inhibition can provide the hyperpolarization for deinactivating I(Ca-T) that causes bursting if the reversal potentials for GABA(A) and GABA(B) synapses are sufficiently negative. 4. If model neurons display sufficiently powerful rebound excitability, an isolated RE network of such neurons oscillates with partial but typically not full synchrony. The neurons spontaneously segregate themselves into several macroscopic clusters. The neurons within a cluster follow the same time course, but the clusters oscillate differently from one another. In addition to activity patterns in which clusters burst sequentially (e.g., 2 or 3 clusters bursting alternately), a two-cluster state may occur with one cluster active and one quiescent. Because the neurons are all-to-all coupled, the cluster states do not have any spatial structure. 5. We have explored the sensitivity of such partially synchronized patterns to heterogeneity in cells' intrinsic properties and to simulated neuroelectric noise. Although either precludes precise clustering, modest levels of heterogeneity or noise lead to approximate clustering of active cells. The population-averaged voltage may oscillate almost regularly but individual cells burst at nearly every second cycle or less frequently. The active-quiescent state is not robust at all to heterogeneity or noise. Total asynchrony is observed when heterogeneity or noise is too large, e.g., even at 25% heterogeneity for our reference set of parameter values. 6. The fast GABA(A) inhibition (with a reversal potential more negative than, say, -65 mV) favors the cluster states and prevents full synchrony. Our simulation results suggest two mechanisms that can fully synchronize the isolated RE network model. With GABA(A) removed or almost totally blocked, GABA(B) inhibition (because it is slow) can lead to full synchrony, which is partially robust to heterogeneity and noise. A second possibility, also robust to heterogeneity and noise, is realized if the GABA(A) synapses have a less negative reversal potential and provide shunting rather than hyperpolarizing inhibition. 7. We examined the effects of fast excitation from thalamocortical (TC) cells. The TC output is generated by a synchronous TC pool that receives GABA(A) and GABA(B) inhibition from the RE network and sends back amino-3-hydroxy-5-methyl-4-isoxazole-propionic acid (AMPA)- mediated excitation. The TC pool has three ionic currents: I(Ca-T), I(L), and a hyperpolarization-activated cation ('sag') current, I(sag). 8. Modest excitation from the TC pool can eliminate cluster oscillations and synchronize fully the RE network, with robustness to heterogeneity and noise. Furthermore, strong AMPA excitation can create synchronized oscillations in cases where without it the RE system is at rest. 9. The oscillation frequency of the RE-TC network depends mainly on the GABA inhibition from the RE cells to the TC pool. Blocking GABA(A) decreases the frequency because of an indirect enhancement of the sag current in the TC pool, whereas blocking GABA(B) increases it.