Models of epileptic discharges and absence seizures
Experimental evidence suggest that some type of epileptic discharges share common mechanisms with other rhythms such as spindle oscillations. In particular, the role of the thalamus was evidenced by a large number of experimental studies. Experiments in thalamic slices showed a transformation between the 10 Hz spindle oscillations to 3 Hz paroxysmal oscillations following block of GABAA receptors. These oscillations depend on the slower GABAB-mediated inhibition. Using a two-cell model of spindles, we investigated the role of the decay of GABAergic currents in determining the frequency of oscillations . We observed a transition from 10 Hz to 3 Hz oscillations in the model when the decay of GABAergic current was changed from fast decay, similar to GABAA inhibition, to slow decay, close to that of GABAB inhibition .
To investigate further the possible role of GABAB receptors in generating 3 Hz thalamic oscillations, the next step was to model precisely the complex properties of these receptors. We designed a model of GABAergic transmission which reproduced in detail the nonlinear activation properties of these receptors. This model was adjusted to dual intracellular recordings in cortical slices  (in collaboration with Alex Thomson, University of London, UK).
This model of GABAB was then used to investigate mechanisms to explain the genesis of 3 Hz oscillations by thalamic circuits. Networks of thalamic TC and RE cells were simulated and synaptic interactions were modeled by AMPA, GABAA and GABAB receptors . This model suggested a mechanism for the transformation between 10 Hz spindle oscillations into paroxysmal discharges at about 3 Hz when GABAA receptors were suppressed. The critical elements involved in the 3 Hz oscillation were the lateral (GABAA-mediated) inhibition between RE cells and the particular properties of GABAB receptors .
The model of GABAB responses also explained a feature observed experimentally, namely that some thalamic TC cells remain quiescent during seizures. This model suggested two possible mechanisms to explain TC quiescence, one of which was based on the particular activation properties of GABAB receptors . According to this mechanism, RE neurons would receive repeated strong excitatory input from cortex, producing TC neuron quiescence due to burst-duration-associated augmentation of the GABAB current.
The properties of GABAB receptors were also at the center of a model of 3 Hz spike-and-wave (SW) oscillations in the thalamocortical system . This model first suggested that the particular stimulus/response relationship of GABAB receptors can explain the genesis of SW waveforms in field potentials. Second, again due to the properties of GABAB responses, the model suggested that corticothalamic feedback can force *intact* thalamic circuits in the 3 Hz mode. Third, in the thalamocortical system, these properties led to the transformation of 10 Hz spindle oscillations into 3 Hz oscillations if cortical excitability was increased beyond a critical level. This model suggested a cellular mechanism for SW in which the properties of GABAB receptors play a essential role . A series of predictions were suggested to test the validity of this mechanism.
The same model also proposed an explanation for the different frequencies of absence seizures in different animal models . The frequency of SW oscillations critically depended on the balance of GABAergic conductances in thalamic relay cells, ranging from 2-4 Hz for strong GABAB conductances to 5-10 Hz when GABAA conductances were dominant. This model therefore suggests that thalamo-cortical circuits can generate two types of spike-and-wave oscillations, which frequency is determined by the receptor type mediating inhibition in thalamic relay cells.
An explicit prediction of the 3 Hz SW model is that the slow frequency is imposed by corticothalamic feedback onto an intact thalamic circuitry  (Fig. 2A-C). We have tested this prediction by stimulating corticothalamic fibers in thalamic slices  (experiments realized in Thierry Bal's group, UNIC). As predicted by the model, corticothalamic feedback can force intact thalamic circuits in the 3 Hz mode (Fig. 2D-F). The same result was also obtained independently in McCormick's lab. This validation of the model prediction is a very important piece of evidence in favor of the proposed mechanism.
Because experimental data also point to an intracortical origin of some types of seizures, we next developed a computational model to investigate possible mechanisms for intracortically-generated SW oscillations  (in collaboration with Diego Contreras and Mircea Steriade). We investigated the possible role of low-threshold spike (LTS) cortical neurons. These neurons are found in slices or in vivo, and they can be modeled based on relatively weak densities of the T-type calcium channel. At the network level, a small minority of LTS pyramidal cells was sufficient to generate paroxysmal oscillations with spike-and-wave field potentials. These oscillations reproduce the properties of intracortical SW paroxysms observed in athalamic cats, such as the slow frequency (1.8-2.5 Hz). This model suggests that calcium-mediated rebound mechanisms intrinsic to cerebral cortex can explain the genesis of intracortical SW activity (see details in ).
Thus, experimental data and models indicate that paroxysmal discharges and oscillations can be generated either intra-thalamically, intra-cortically or by thalamocortical loops. Only the latter mechanism  displays the large-scale synchrony and the 3 Hz spike-and-wave patterns typical of absence seizures. The basis of this mechanism is that oscillations are organized and synchronized through thalamocortical loops with "inhibitory-dominant" corticothalamic feedback . We suggest that absence-type seizures are a direct consequence of a too powerful control of the thalamus by the cortex, which also suggests new ways to suppress such seizures (see details in [10,11,12,13]).
We recently investigated another type of epilepsy, focal seizures in humans , in collaboration with Syd Cash (Harvard University). The main finding was that the excitatory and inhibitory population activities are tightly balanced in normal wake and sleep states, but this balance breaks down during seizures. This suggests that un-balanced activity may be a feature of brain pathological states.
 Destexhe, A., McCormick, D.A. and Sejnowski, T.J. A model for 8-10 Hz spindling in interconnected thalamic relay and reticularis neurons. Biophys. J. 65: 2474-2478, 1993. (see abstract)
 Destexhe, A. and Sejnowski, T.J. G-protein activation kinetics and spill-over of GABA may account for differences between inhibitory responses in the hippocampus and thalamus. Proc. Natl. Acad. Sci. USA 92: 9515-9519, 1995. (see abstract)
 Destexhe, A., Bal, T., McCormick, D.A. and Sejnowski, T.J. Ionic mechanisms underlying synchronized oscillations and propagating waves in a model of ferret thalamic slices. J. Neurophysiol. 76: 2049-2070, 1996. (see abstract)
 Lytton, W.W., Contreras, D., Destexhe, A. and Steriade, M. Dynamic interactions determine partial thalamic quiescence in a computer network model of spike-and-wave seizures. J. Neurophysiol. 77: 1679-1696, 1997. (see abstract)
 Destexhe, A. Spike-and-wave oscillations based on the properties of GABA_B receptors. J. Neurosci. 18: 9099-9111, 1998. (see abstract)
 Thomson, A.M. and Destexhe, A. Dual intracellular recordings and computational models of slow inhibitory postsynaptic potentials in rat neocortical and hippocampal slices. Neuroscience 92: 1193-1215, 1999 (see abstract)
 Destexhe, A. Can GABA_A conductances explain the fast oscillation frequency of absence seizures in rodents ? Eur. J. Neurosci. 11: 2175-2181, 1999 (see abstract)
 Bal, T., Debay, D. and Destexhe, A. Cortical feedback controls the frequency and synchrony of oscillations in the visual thalamus. J. Neurosci. 20: 7478-7488, 2000 ( see abstract)
 Destexhe, A., Contreras, D. and Steriade, M. LTS cells in cerebral cortex and their role in generating spike-and-wave oscillations. Neurocomputing 38: 555-563, 2001 ( see abstract)
 Destexhe, A. and Sejnowski, T.J. Thalamocortical Assemblies, Oxford University Press, 2001 (see abstract)
 Destexhe, A. Cortico-thalamic feedback: a key to explain absence seizures~? In: Computational Neuroscience in Epilepsy, Edited by Soltesz, I. and Staley, K., Elsevier, Amsterdam, pp. 184-214, 2008 (see abstract)
 Destexhe, A. Spike-and-Wave Oscillations, Scholarpedia 2: 1402 (2007).
 Destexhe, A. Network models of absence seizures. In: Neuronal Networks in Brain Function, CNS Disorders and Therapeutics, Edited by Faingold, C.L. and Blumenfeld, H., Elsevier, Amsterdam, pp. 11-35, 2014 (see abstract)
 Dehghani, N., Peyrache, A., Telenczuk, B., Le Van Quyen, M., Halgren, E., Cash, S.S., Hatsopoulos, N.G. and Destexhe, A. Dynamic balance of excitation and inhibition in human and monkey neocortex. Nature Scientific Reports 6: 23176, 2016 (see abstract)
Figure 2: Corticothalamic projections can control the frequency and synchrony of thalamic oscillations. A-C. Prediction formulated by computational models: corticothalamic projections can force the intact thalamus to oscillate at ,3 Hz. A. Connectivity scheme with the different types of synaptic receptors in a circuit composed of thalamocortical (TC) and thalamic reticular (RE) cells. The corticothalamic projection was simulated by glutamatergic synapses (AMPA; left), which are controlled by the action potentials (A.P.) of a TC cell. B. A unique simulation of this pathway (arrow) entrains the circuit in its natural frequency (,10 Hz). C. With strong stimulation intensity, RE cells generate large burst discharges, which evoke strong inhibition (with GABAB receptor activation) in TC cells. In this case, the circuits can be entrained into a slower oscillatory mode, where all cells discharge in synchrony at 3 Hz. D-F. Test of these predictions in visual thalamic slices (LGN-PGN) of ferret. D. Implementation of the stimulation paradigm. Stimulating electrodes are placed in the optic radiation (OR), which contains the corticothalamic axons. The discharge of an intracellularly-recorded TC cell triggers the OR stimulation. E. For weak stimuli (1 shock per AP), the thalamic network oscillates at around 7 Hz (correlograms on the right). F. For stronger stimulation intensity (5 shocks per AP), the entire system switches to a slower oscillation around 3 Hz. This slow oscillation is also more synchronized, as shown by the integrated traces from the extracellular signal (lower curves). Figure modified from Destexhe, J. Neurosci., 1998 and Bal et al., J. Neurosci., 2000.
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