Nathalie Leresche
email: nathalie.leresche@upmc.fr

Régis C Lambert

GABA receptors and T-type Ca 2+ channels crosstalk in thalamic networks

Keywords: Cav3, long-term potentiation, long-term depression, synapse, nucleus reticularis thalami, thalamocortical

published or not. The documents may come

GABA receptors and T-type Ca2+ channels crosstalk in thalamic networks

Compared to other CNS regions, such as the cortex, hippocampus or cerebellum, the thalamic GABAergic network may appear at first glance very modest. While for example the morphological, molecular and physiological features of cortical interneurons are so diverse that researchers had to join force to propose a classification of these complex neuronal populations [START_REF] Defelipe | New insights into the classification and nomenclature of cortical GABAergic interneurons[END_REF], the intrathalamic GABAergic neurons come down to two types, the neurons located in the nucleus reticularis thalami and the local interneurons that are present in different thalamic nuclei. However, except in the dorsal lateral geniculate nucleus very few interneurons (less than 5% of the total neuronal population) are present in thalamic nuclei of rodents [START_REF] Cavdar | Comparison of numbers of interneurons in three thalamic nuclei of normal and epileptic rats[END_REF][START_REF] Jones | The thalamus[END_REF]. Therefore, most of the available data on GABAergic inhibition in rodent primary thalamic nuclei deals with inhibitory mechanisms originating from the NRT (Fig. 1A). Despite this paucity of GABAergic cell types, the thalamic network is one of the most interesting systems where GABA impact on neuronal excitability can be studied. Indeed, both glutamatergic thalamocortical (TC) and GABAergic nucleus reticularis thalami (NRT) neurons present a high expression of T-type voltagedependent Ca 2+ channels whose activation, which generates the so-called rebound lowthreshold spike (LTS) and is the bases of the thalamic bursting mode of firing, critically depends upon a preceding hyperpolarisation (Fig. 1B) [START_REF] Deschenes | Electrophysiology of neurons of lateral thalamic nuclei in cat: resting properties and burst discharges[END_REF][START_REF] Jahnsen | Electrophysiological properties of guinea-pig thalamic neurones: an in vitro study[END_REF]. T-type voltage-dependent Ca 2+ currents activate around -60 mV, are fully inactivated after a few tens of milliseconds and their steady-state inactivation is nearly complete at membrane potentials more depolarized than -60 mV [START_REF] Perez-Reyes | Molecular physiology of low-voltage-activated t-type calcium channels[END_REF].

Therefore, hyperpolarization allowing some channels to recover from inactivation is required to evoke a substantial T-current (Fig. 1C) creating a strict dependence of the LTS upon a preceding hyperpolarization such as those mediated by the GABA A and GABA B receptors.

In this review we will highlight how the functional impact of GABA receptors activation in thalamic neurons far exceeds the traditional "shunting" effect and shapes the whole thalamic network excitability. We will show how GABA released during either tonic or burst firing of GABAergic thalamic neurons targets diverse GABA A and GABA B receptors. We will discuss how the complex functional relationship between GABA release and T-channel-dependent excitability is finely tuned by the T-channel activation itself and how an impaired balance between T-channels and GABA receptors can lead to pathological activities.

T-channels and GABA A receptors

The archetypal and best-studied physiological activity pattern that exemplifies the crosstalk between GABA inhibitory post-synaptic potentials (IPSPs) and the T-current is the 7-14 Hz spindle oscillation wave that occurs during non-REM sleep [START_REF] Deschenes | Electrophysiology of neurons of lateral thalamic nuclei in cat: resting properties and burst discharges[END_REF][START_REF] Steriade | Thalamocortical oscillations in the sleeping and aroused brain[END_REF]. During these waves, NRT neuron activity is characterized by the occurrence of high frequency bursts of action potentials generated by LTSs at spindle frequency. These bursts of action potentials elicit fast rising multicomponent GABA A IPSPs in TC neurons that, if strong enough, generate an LTS as rebound activity [START_REF] Deschenes | Electrophysiology of neurons of lateral thalamic nuclei in cat: resting properties and burst discharges[END_REF] (Fig. 2A). At the population level, the thalamocortical output is therefore characterized by the occurrence of high-frequency bursts at each oscillation cycle. The output firing associated to the LTSs provides excitatory synaptic drive back to NRT neurons as well as to cortical neurons. It is still unclear whether the repetitive LTS occurrence in NRT neurons at spindle frequency intrinsically originates in the NRT nucleus, as suggested by some in vivo studies [START_REF] Steriade | The deafferented reticular thalamic nucleus generates spindle rhythmicity[END_REF] or requires the interplay between NRT and TC neurons as shown in vitro [START_REF] Bal | Mechanisms of oscillatory activity in guinea-pig nucleus reticularis thalami in vitro: a mammalian pacemaker[END_REF][START_REF] Bal | Role of the ferret perigeniculate nucleus in the generation of synchronized oscillations in vitro[END_REF][START_REF] Von Krosigk | Cellular mechanisms of a synchronized oscillation in the thalamus[END_REF]. Notwithstanding this issue, the capability of spindle waves to drive cortical networks and generate the non-REM EEG spindle rhythm critically depends on the ability of the summating GABA A IPSPs to remove Tchannel inactivation and thus allow the generation of LTSs in TC neurons [START_REF] David | Essential thalamic contribution to slow waves of natural sleep[END_REF].

Synaptic and extrasynaptic GABA A receptors

Interestingly, it was recently shown that such efficient GABA inputs do not only involve synaptic but also extrasynaptic GABA A receptors. Indeed, TC neurons express two types of GABA A receptors that differ by their localization, subunit composition and functional properties, predominantly 1 2 2 for synaptic and 4 2 for extrasynaptic receptors [START_REF] Jia | An extrasynaptic GABAA receptor mediates tonic inhibition in thalamic VB neurons[END_REF][START_REF] Kralic | Compensatory alteration of inhibitory synaptic circuits in cerebellum and thalamus of gammaaminobutyric acid type A receptor alpha1 subunit knockout mice[END_REF][START_REF] Peden | Developmental maturation of synaptic and extrasynaptic GABAA receptors in mouse thalamic ventrobasal neurones[END_REF][START_REF] Pirker | GABA(A) receptors: immunocytochemical distribution of 13 subunits in the adult rat brain[END_REF]. Classically, the synaptic GABA A receptors, that are characterized by a fast kinetic, a low sensitivity to GABA and a rapid desensitization, are responsible for the phasic IPSPs while the extrasynaptic receptors, that show a high sensitivity to GABA and a much slower desensitization, account for the tonic current activated by the ambient GABA [START_REF] Semyanov | Tonically active GABA A receptors: modulating gain and maintaining the tone[END_REF]. However, recent in vitro studies demonstrated that the extrasynaptic GABA A receptors also contribute to NRT burst-mediated phasic IPSPs [START_REF] Herd | Extrasynaptic GABA(A) receptors couple presynaptic activity to postsynaptic inhibition in the somatosensory thalamus[END_REF][START_REF] Rovo | Phasic, Nonsynaptic GABA-A Receptor-Mediated Inhibition Entrains Thalamocortical Oscillations[END_REF]. Firstly, in 1 -/- mice TC neurons that are devoid of synaptic GABA A receptors, stimulation of NRT neurons that potentially triggered NRT burst firing still evoked inhibitory postsynaptic currents (IPSCs) (Fig. 2B). Although delayed and reduced in amplitude, these residual IPSCs demonstrated that TC neuron extrasynaptic GABA A receptors were recruited by synaptic activity during NRT burst firing. Indeed, upon deletion of the extrasynaptically located 4 subunit the amplitude of the multiple peak IPSCs was not modified but the tail of the burst-mediated

IPSCs was much reduced in pairs of monosynaptically connected NRT and TC neurons.

Finally, even during NRT tonic firing, the decay rate of the evoked IPSCs in TC neurons was significantly faster in 4 -/-or -/-mice suggesting that extrasynaptic GABA A receptors participate to single IPSC in wild type animals [START_REF] Herd | Extrasynaptic GABA(A) receptors couple presynaptic activity to postsynaptic inhibition in the somatosensory thalamus[END_REF]. Overall, these data demonstrate that recruitment of extrasynaptic GABA A receptors critically prolonged phasic inhibition, which should increase T-channel deinactivation and in turn facilitate rebound LTS generation.

Indeed, a later study confirmed these findings and enlarged them by showing the role of GABA A receptors in the generation of rebound LTSs during spontaneous oscillatory thalamic activities. In somatosensory TC neurons of the ventrobasal thalamic nucleus, Rovo et al. [START_REF] Rovo | Phasic, Nonsynaptic GABA-A Receptor-Mediated Inhibition Entrains Thalamocortical Oscillations[END_REF] reported in addition to the spontaneous "classical" fast GABA A IPSCs the occasional presence of slower events. Following the focal removal of 2 subunits using local virus injections that suppressed synaptically localized GABA A receptors, the fast IPSCs were abolished when NRT neurons fired tonically but large and slow phasic GABA A IPSCs were still present when NRT neurons fired bursts, indicating a burst-specific recruitment of non-synaptic GABA A receptors (Fig. 2C1). Indeed bursting activities of TC neurons resulting from GABA evoked rebound LTSs were little affected by 2 subunit deletion (Fig. 2C2).

Moreover during ketamine-xylazine induced slow oscillations, suppression of synaptic GABA A receptors had no effect on the burst properties in TC neurons of the posterior thalamic nucleus and only decreased the number of bursts and the intra-burst frequencies of action potentials without affecting the intra-burst action potential number in ventrobasal somatosensory TC neurons. Importantly, detailed analysis of sleep spindle waves in urethane anesthetized animals showed a similar rate of occurrence, number of cycles and lengths of spindle waves after removal of the fast synaptic inhibition (Fig. 2D). Finally, EEG analysis showed that bilateral focal thalamic deletion of the 2 subunits had no effect on the spindle oscillatory activities present during natural non-REM sleep, in contrast to the disruption of the slow oscillations observed when all types of thalamic GABA A receptors were blocked by local application of the GABA A antagonist gabazine [START_REF] Rovo | Phasic, Nonsynaptic GABA-A Receptor-Mediated Inhibition Entrains Thalamocortical Oscillations[END_REF].

Therefore, when NRT neurons are firing in bursts not only conventional synaptic GABA A receptors but also extrasynaptic GABA A receptors are recruited by GABA spillover. This extrasynaptic receptor recruitment appears especially important during thalamocortical oscillations since it provides by itself large enough phasic hyperpolarization to allow the recruitment of T-channels and the generation of rebound LTSs in TC neurons to sustain physiological activities.

Tonic GABA A current and T-channels

The various results reviewed above clearly demonstrate that activation of peri/extrasynaptic receptors, containing 4 2 subunits, by GABA spillover contributes to phasic GABAergic inhibition. However because of their high sensitivity, these receptors can also be activated by the ambient GABA creating a tonic inhibitory current (Fig. 3A) and a number of studies described the properties of this tonic current in TC neurons [START_REF] Belelli | Extrasynaptic GABAA receptors of thalamocortical neurons: a molecular target for hypnotics[END_REF][START_REF] Bright | Synaptic release generates a tonic GABA(A) receptor-mediated conductance that modulates burst precision in thalamic relay neurons[END_REF][START_REF] Chandra | GABAA receptor alpha 4 subunits mediate extrasynaptic inhibition in thalamus and dentate gyrus and the action of gaboxadol[END_REF][START_REF] Cope | GABAA receptor-mediated tonic inhibition in thalamic neurons[END_REF][START_REF] Jia | An extrasynaptic GABAA receptor mediates tonic inhibition in thalamic VB neurons[END_REF]. In this context, additional functional links can be established between activation of extrasynaptic GABA A receptors and T-channels recruitment. Thus, extracellular recordings of TC neurons in ventrobasal thalamic slices showed that the block of this tonic current by gabazine or its enhancement by the GABA A agonist THIP stops or promotes LTS burst firing [START_REF] Cope | GABAA receptor-mediated tonic inhibition in thalamic neurons[END_REF] and modulate rebound LTS latency [START_REF] Bright | Synaptic release generates a tonic GABA(A) receptor-mediated conductance that modulates burst precision in thalamic relay neurons[END_REF] (Fig. 3B). These results clearly suggest that tonic activation of the GABA A receptors brings TC neurons into a membrane potential range where a significant proportion of T-channels is available [START_REF] Dreyfus | Selective T-type calcium channel block in thalamic neurons reveals channel redundancy and physiological impact of I(T)window[END_REF][START_REF] Perez-Reyes | Molecular physiology of low-voltage-activated t-type calcium channels[END_REF].

These channels could then be activated by any incoming input resulting once again in the generation of an LTS. Along this line, it is interesting to mention that THIP, a potent hypnotic selective for extrasynaptic GABA A receptors, in both humans and rats promotes slow-wave sleep activities characterized by the rhythmic occurrence of LTSs in TC neurons [START_REF] Faulhaber | The GABAA agonist THIP produces slow wave sleep and reduces spindling activity in NREM sleep in humans[END_REF].

T-channel and GABA crosstalk during attentive behaviours

The impact of the T-channel and GABA A receptor crosstalk on TC neuron excitability, however, is not limited to LTS generation during sleep [START_REF] Lambert | The many faces of T-type calcium channels[END_REF] but is also crucial in TC neuron functions during the awake state. First, GABA A IPSPs -LTS sequences can be observed during sensory processing in awake animals. Thus, during natural viewing, when the receptive field is covered by a stimulus of the non-preferred sign, the inhibition associated to the "push-pull" sequence allows T-channels to deinactivate and upon reversion of the stimulus contrast, the retinal input can trigger an LTS burst [START_REF] Wang | Feedforward excitation and inhibition evoke dual modes of firing in the cat's visual thalamus during naturalistic viewing[END_REF]. In this case, the GABAergic inhibition likely arises from local interneurons in the dorsal lateral geniculate nucleus although a role of the feedback inhibition through NRT cannot be ruled out. The synaptic or extrasynaptic nature of the GABA A receptors involved was not investigated but emphasis was made on the functional role of such GABA A IPSPs -LTS sequence in sensory processing. Indeed convincing evidence indicate that bursts play a role in vision [START_REF] Alitto | Dynamic properties of thalamic neurons for vision[END_REF][START_REF] Niell | Modulation of visual responses by behavioral state in mouse visual cortex[END_REF][START_REF] Sherman | Tonic and burst firing: dual modes of thalamocortical relay[END_REF] and that compared to tonic trains of spikes, they evoke postsynaptic action potentials with maximal efficacy, likely enhancing sensory information propagation [START_REF] Swadlow | The impact of 'bursting' thalamic impulses at a neocortical synapse[END_REF][START_REF] Usrey | Paired-spike interactions and synaptic efficacy of retinal inputs to the thalamus[END_REF]. In addition, while for years T-channel functions beyond burst generation were difficult to unravel due to the lack of specific pharmacology (see [START_REF] Lambert | The many faces of T-type calcium channels[END_REF] for review) the recent synthesis of the first potent and selective T-type channel antagonists, mainly based on a piperidine chemical structure [START_REF] Dreyfus | Selective T-type calcium channel block in thalamic neurons reveals channel redundancy and physiological impact of I(T)window[END_REF][START_REF] Shipe | Design, synthesis, and evaluation of a novel 4-aminomethyl-4-fluoropiperidine as a T-type Ca2+ channel antagonist[END_REF] has led to the discovery of new critical roles for T-currents during wakefulness. Indeed, using TTA-P2, it has recently been demonstrated that in the range of resting membrane potentials observed in TC neurons of awake animals [START_REF] Urbain | Whisking-Related Changes in Neuronal Firing and Membrane Potential Dynamics in the Somatosensory Thalamus of Awake Mice[END_REF], T-channels can be recruited by incoming excitatory inputs, amplifying the excitatory post-synaptic potentials (EPSPs), and therefore controlling tonic firing [START_REF] Deleuze | T-type calcium channels consolidate tonic action potential output of thalamic neurons to neocortex[END_REF]. Since the fraction of deinactivated Tchannels increases upon hyperpolarisation, this T-mediated amplification is intrinsically voltage-dependent (Fig. 3C1) and helps to stabilize the firing probability against membrane hyperpolarization (Fig. 3C2). As a consequence, one can propose a novel functional link between extra-synaptic GABA receptors and T-channels since at least part of the decrease in tonic firing that should result from a GABA tonic current-induced hyperpolarization will be counteracted by a stronger recruitment of T-channels amplifying the incoming EPSPs.

T-channels and GABA B receptors

Activation of the metabotropic GABA B receptors also elicit a hyperpolarization that can deinactivate T-channels and lead to the generation of a rebound LTS [START_REF] Crunelli | A role for GABAB receptors in excitation and inhibition of thalamocortical cells[END_REF]. The thalamus is one of the brain areas showing the highest GABA B receptor level [START_REF] Bowery | GABAA and GABAB receptor site distribution in the rat central nervous system[END_REF][START_REF] Princivalle | Distribution of GABA(B) receptor protein in somatosensory cortex and thalamus of adult rats and during postnatal development[END_REF][START_REF] Princivalle | Distribution of GABA(B(1a)), GABA(B(1b)) and GABA(B2) receptor protein in cerebral cortex and thalamus of adult rats[END_REF]. These receptors are composed of two subunit isoforms, GABA B1a and GABA B1b , that combine with a GABA B2 subunit to form heteromeric GABA B(1a,2) and GABA B(1b,2) receptors [START_REF] Bettler | Molecular structure and physiological functions of GABA(B) receptors[END_REF][START_REF] Kaupmann | GABA(B)-receptor subtypes assemble into functional heteromeric complexes[END_REF]. A subcellular localization study showed a similar localization of the different GABA B receptors, mostly on the dendrites of TC neurons. These receptors are predominantly extrasynaptic with a higher density around GABAergic than glutamatergic synapses on TC neuron dendrites [START_REF] Kulik | Distinct localization of GABA(B) receptors relative to synaptic sites in the rat cerebellum and ventrobasal thalamus[END_REF]. In addition, GABA B receptors are also present presynaptically on GABAergic and glutamatergic (both sensory and corticothalamic) afferents where they control the release of GABA and glutamate, respectively [START_REF] Emri | Tonic activation of presynaptic GABA(B) receptors on thalamic sensory afferents[END_REF][START_REF] Le Feuvre | GABAA receptor-mediated IPSCs in rat thalamic sensory nuclei: patterns of discharge and tonic modulation by GABAB autoreceptors[END_REF][START_REF] Luo | Activation of presynaptic GABAB receptors modulates GABAergic and glutamatergic inputs to the medial geniculate body[END_REF][START_REF] Ulrich | GABAB receptor-mediated responses in GABAergic projection neurones of rat nucleus reticularis thalami in vitro[END_REF]. Already in the '80s it was shown that, in TC neurons of the dorsal lateral geniculate nucleus, GABA B IPSPs evoked by inhibitory interneurons activation following sensory afferent stimulation can elicit a rebound LTS [START_REF] Crunelli | Cl--and K+dependent inhibitory postsynaptic potentials evoked by interneurones of the rat lateral geniculate nucleus[END_REF][START_REF] Crunelli | A role for GABAB receptors in excitation and inhibition of thalamocortical cells[END_REF]. Since these initial findings linking GABA B receptor and LTS generation, a number of studies focusing on the excitability of the thalamic network investigated how the occurrence of GABA B IPSPs contributes to oscillatory activities in the thalamocortical system. As described above, sleep spindle waves depend on the presence of bursts of action potentials in NRT neurons that activate GABA A receptor-mediated IPSPs in TC neurons with occasional rebound LTSs, setting the network oscillation at a frequency of 7-14 Hz [START_REF] Deschenes | Electrophysiology of neurons of lateral thalamic nuclei in cat: resting properties and burst discharges[END_REF]. Interestingly, if the NRT bursts are markedly increased by, for example, strong cortical inputs, these fast IPSPs are converted into large amplitude, long duration (around 300ms) IPSPs followed by a potent rebound LTS. These slower IPSPs are due to the activation of both GABA A and GABA B receptors [START_REF] Blumenfeld | Corticothalamic inputs control the pattern of activity generated in thalamocortical networks[END_REF]. This data were interpreted by assuming that in condition of strong NRT burst firing the large amount of released neurotransmitter allowed a spillover of GABA to the extrasynaptically localized GABA B receptors. Hence, in conditions of strong NRT burst firing, the slow GABA A -GABA B IPSP followed by the rebound LTS resulted in a slowing down of the thalamic oscillations from the 7-14Hz spindle frequency to about 3-4 Hz [START_REF] Bal | Cortical feedback controls the frequency and synchrony of oscillations in the visual thalamus[END_REF][START_REF] Blumenfeld | Corticothalamic inputs control the pattern of activity generated in thalamocortical networks[END_REF]. This result illustrates how the dynamic interaction between GABA A -GABA B IPSPs and T-channel activation fundamentally sets the global intrathalamic network activity and explains how abnormalities in the GABAergic NRT to TC neuron synapse could result in pathological excitability.

Pathological consequences of disruption in the GABA / T current equilibrium

This issue has been particularly investigated in the context of absence seizures. These seizures are non-convulsive epileptic attacks present in many generalized genetic epilepsies that are characterized by a sudden and relatively brief impairment of consciousness, invariably accompanied by generalized and synchronous 2.5 -4Hz spike-and-waves discharges in human EEG [START_REF] Crunelli | Childhood absence epilepsy: genes, channels, neurons and networks[END_REF]. On the basis of the in vitro experiments performed in ferret thalamic slices, McCormick and his colleagues proposed that the recruitment of GABA B IPSPs due to a pathologically strong corticothalamic input, and their associated potent rebound LTSs, underlies absence seizure generation [START_REF] Blumenfeld | Corticothalamic inputs control the pattern of activity generated in thalamocortical networks[END_REF] (see also [START_REF] Bal | Cortical feedback controls the frequency and synchrony of oscillations in the visual thalamus[END_REF]). While in vivo recordings in cat and rat models of absence epilepsy have so far failed to report the presence of GABA B IPSPs followed by rebound LTS in TC neurons during seizures, they nevertheless show rhythmic sequences of composite GABA A IPSPs which occur in synchrony with each spike and wave complex [START_REF] Pinault | Intracellular recordings in thalamic neurones during spontaneous spike and wave discharges in rats with absence epilepsy[END_REF][START_REF] Steriade | Relations between cortical and thalamic cellular events during transition from sleep patterns to paroxysmal activity[END_REF]. This suggests that the rhythmic occurrence of GABA IPSPs that frame the thalamic output is a fundamental component of the mechanism that lead to the generation of this pathological rhythm. In addition, tonic GABA A inhibition is increased in almost all rodent models of absence epilepsy [START_REF] Cope | Enhanced tonic GABAA inhibition in typical absence epilepsy[END_REF] and, in the best established pharmacological model of absence epilepsy, the GHB model, the pathological rhythmic activity relies on the activation of GABA B receptors [START_REF] Venzi | A critical evaluation of the gammahydroxybutyrate (GHB) model of absence seizures[END_REF]. Whatever the receptor type involved, the high level of GABA inhibition present in TC neurons during spike-and-waves discharges is sustained by robust LTSs in NRT neurons at each spike and wave complex, as observed in fentanyl-anesthetized rat model of absence epilepsy [START_REF] Slaght | Activity of thalamic reticular neurons during spontaneous genetically determined spike and wave discharges[END_REF]. In agreement with the importance of LTSs in NRT neurons, an increased T-current was observed in these neurons in absence epilepsy-prone compared to non-epileptic rats [START_REF] Tsakiridou | Selective increase in T-type calcium conductance of reticular thalamic neurons in a rat model of absence epilepsy[END_REF]. In summary, although the precise cellular mechanisms are still debated, numerous evidences point to the importance of both GABA inhibitory tonus and T-current activation in the pathogenesis of absence epilepsy.

Interestingly, the pathogenicity of an impaired balance between thalamic T-channels and GABA receptors is now considered in a larger context than absence epilepsy. Indeed, an increasing number of clinical studies have reported the presence of slower theta thalamocortical oscillations in awake patients who present a wide variety of neurological and psychiatric conditions, including neurogenic pain, tinnitus and Parkinson's disease [START_REF] Jeanmonod | Low-threshold calcium spike bursts in the human thalamus. Common physiopathology for sensory, motor and limbic positive symptoms[END_REF][START_REF] Llinas | Thalamocortical dysrhythmia: A neurological and neuropsychiatric syndrome characterized by magnetoencephalography[END_REF][START_REF] Steriade | Thalamocortical oscillations in the sleeping and aroused brain[END_REF]. While the mechanisms of such dysrhythmia are still to be explored, a common principle has been proposed implying an increase inhibitory tonus that removes thalamic T-channel inactivation [START_REF] Llinas | Bursting of thalamic neurons and states of vigilance[END_REF].

T-channel activity controls GABA synapses

While the functional links between GABA IPSPs and LTS generation in the thalamic network have been studied for many years [START_REF] Deschenes | Electrophysiology of neurons of lateral thalamic nuclei in cat: resting properties and burst discharges[END_REF][START_REF] Steriade | Thalamocortical oscillations in the sleeping and aroused brain[END_REF], the reverse relationship has only recently started to be investigated [START_REF] Pigeat | Sleep slow wave-related homo and heterosynaptic LTD of intrathalamic GABAAergic synapses: involvement of T-type Ca2+ channels and metabotropic glutamate receptors[END_REF][START_REF] Sieber | Non-Hebbian long-term potentiation of inhibitory synapses in the thalamus[END_REF]. Calcium imaging studies in NRT neurons showed that LTSs are associated with a widespread dendritic calcium influx via T-channels [START_REF] Chausson | Dynamics of Intrinsic Dendritic Calcium Signaling during Tonic Firing of Thalamic Reticular Neurons[END_REF][START_REF] Crandall | Low-threshold Ca2+ current amplifies distal dendritic signaling in thalamic reticular neurons[END_REF] and combining somatodendritic recordings, calcium imaging and computational modelling Connelly et al. [START_REF] Connelly | The Global Spike: Conserved Dendritic Properties Enable Unique Ca2+ Spike Generation in Low-Threshold Spiking Neurons[END_REF] further demonstrated that LTSs are global events that occur synchronously throughout the dendritic tree. In view of the existence of dendrodendritic synapses between NRT neurons, at least in certain species [START_REF] Deschenes | Dendrodendritic synapses in the cat reticularis thalami nucleus: a structural basis for thalamic spindle synchronization[END_REF][START_REF] Pinault | Dendrodendritic and axoaxonic synapses in the thalamic reticular nucleus of the adult rat[END_REF][START_REF] Yen | The morphology of physiologically identified GABAergic neurons in the somatic sensory part of the thalamic reticular nucleus in the cat[END_REF], one may speculate that distal dendrite Tcurrents could contribute to dendritic GABA release and activation of these intra-NRT GABAergic synapses. In addition, a recent study demonstrated the existence of T-channel and syntaxin1A complexes in rat brains and showed a clear colocalization of these proteins in NRT neurons [START_REF] Weiss | A Ca(v)3.2/syntaxin-1A signaling complex controls T-type channel activity and low-threshold exocytosis[END_REF], suggesting the potential involvement of T-channels in the synaptic mechanism of GABA release.

The importance of T-currents in the control of thalamic GABA synaptic function is also demonstrated by the presence of T-channel-dependent long-term synaptic plasticity, either potentiation (LTP) or depression (LTD). Indeed, in the associative posterior thalamic medial nucleus, an LTP of the GABAergic synapses is triggered by postsynaptic repetitive LTSassociated bursting activities in TC neurons (Sieber et al., 2013) (Fig 4A). LTSs provided a depolarizing drive throughout the dendritic arbor [START_REF] Connelly | The Global Spike: Conserved Dendritic Properties Enable Unique Ca2+ Spike Generation in Low-Threshold Spiking Neurons[END_REF] that activated highvoltage L-type calcium currents. The subsequent rise in intracellular calcium induced the production of nitric oxide, retrogradely activating presynaptic guanylyl cyclase and increasing GABA release probability [START_REF] Sieber | Non-Hebbian long-term potentiation of inhibitory synapses in the thalamus[END_REF]. In contrast, at the inhibitory synapses between NRT and primary sensory TC neurons, Pigeat et al. described an LTD [START_REF] Pigeat | Sleep slow wave-related homo and heterosynaptic LTD of intrathalamic GABAAergic synapses: involvement of T-type Ca2+ channels and metabotropic glutamate receptors[END_REF] (Fig. 4B) that is triggered by pairing the stimulation of the reticulothalamic input to rhythmic activation of post-synaptic T-currents, mimicking the pattern of LTSs occurrence during sleep delta waves. Importantly, this LTD mechanism required a specific funnelling of calcium though the T-channels and could not be triggered by Ca 2+ entry through other members of the voltage-dependent Ca 2+ channel family. The large influx of calcium through T-channels leads to the activation of the calcium-sensitive phosphatase calcineurin that dephosphorylates the GABA A receptors inducing their long-term desensitization. Therefore, the strict requirement of T-channel activation to trigger LTD of the GABAergic synapses suggests the existence of preferential links between these channels and other partners of the synaptic plasticity, such as GABA A receptors and/or calcineurin. Such interactions including direct protein-protein interactions have already been described between T-channels and other ionic channels [START_REF] Anderson | The Cav3-Kv4 complex acts as a calcium sensor to maintain inhibitory charge transfer during extracellular calcium fluctuations[END_REF][START_REF] Anderson | Regulation of neuronal activity by Cav3-Kv4 channel signaling complexes[END_REF][START_REF] Engbers | Intermediate conductance calciumactivated potassium channels modulate summation of parallel fiber input in cerebellar Purkinje cells[END_REF], but data demonstrating colocalization of GABA A receptors or calcineurin with T-channels are still lacking. In contrast to the LTP described in the posterior thalamic medial nucleus [START_REF] Sieber | Non-Hebbian long-term potentiation of inhibitory synapses in the thalamus[END_REF], the LTD in primary sensory nuclei did not affect all GABAergic synapses but only a subset of NRT synapses [START_REF] Pigeat | Sleep slow wave-related homo and heterosynaptic LTD of intrathalamic GABAAergic synapses: involvement of T-type Ca2+ channels and metabotropic glutamate receptors[END_REF]. Indeed, transient application of GABA A receptors antagonist during the induction protocol demonstrated that the LTD was only triggered at activated GABA A synapses. Finally, it should be noted that this LTD is both homosynaptic and heterosynaptic as it is also closely gated by glutamate released from the corticothalamic afferents that activates metabotropic receptors on the post-synaptic TC neurons. Therefore, the crucial relationship between the intrathalamic GABA drive and the Tchannel activity, as a main actor of both sensory information transfer and oscillatory susceptibility of the thalamocortical network, is finely tuned by the cortical feedback itself [START_REF] Pigeat | Sleep slow wave-related homo and heterosynaptic LTD of intrathalamic GABAAergic synapses: involvement of T-type Ca2+ channels and metabotropic glutamate receptors[END_REF]. In conclusion, although different in term of signs and mechanisms, these two studies clearly highlight that GABAergic synaptic responses are dynamically modulated by T-channel activation. Overall, from the analysis of the results summarized so far, a clear picture emerges of a bidirectional relationship between GABA receptors and Tchannels that shapes the excitability of the thalamocortical system.

Perspective

This review mainly focuses on the inhibitory synapses between NRT afferents and TC neurons located in primary sensory nuclei. However, thalamic neurons localized in the other thalamic nuclei (higher order sensory nuclei, motor nuclei, midline and intralaminar nuclei) received, in addition to NRT afferents, inhibitory inputs originating from extra-thalamic sources, mainly basal ganglia, zona incerta, anterior pretectum and pontine reticular formation that can also evoked rebound LTS in TC neurons [START_REF] Halassa | Thalamic Inhibition: Diverse Sources, Diverse Scales[END_REF][START_REF] Wanaverbecq | Contrasting the functional properties of GABAergic axon terminals with single and multiple synapses in the thalamus[END_REF]. In contrast to the NRT GABAergic synapses, single axon terminals from the extra-thalamic GABAergic sources contact the postsynaptic TC neuron via several active zones wrapped in a glial cover that probably restrict GABA spillover.

Moreover, while NRT to TC neuron synapses show a marked paired-pulse depression [START_REF] Bessaih | Nucleus-specific abnormalities of GABAergic synaptic transmission in a genetic model of absence seizures[END_REF], these GABAergic synapses of extrathalamic origin display little shortterm plasticity [START_REF] Giber | A subcortical inhibitory signal for behavioral arrest in the thalamus[END_REF][START_REF] Wanaverbecq | Contrasting the functional properties of GABAergic axon terminals with single and multiple synapses in the thalamus[END_REF] supporting a more faithful transmission. Whether the complex bidirectional relationships described here between activation of GABA receptors and T-currents also contribute to the regulation of the excitability of these non-NRT inhibitory synapses remains to be investigated. B1: modified with permission from [START_REF] Jahnsen | Electrophysiological properties of guinea-pig thalamic neurones: an in vitro study[END_REF]. B. Superimposed traces of GABA currents evoked by NRT neuron stimulation in TC neurons of wild-type (WT) mice and mice devoid of either the synaptic α 1 (α 1 -/-) or the extrasynaptic α 4 (α 4 -/-) or δ (δ -/-) GABA A receptor subunits. Note that the decay of the evoked multiple IPSC waveforms was accelerated in mice lacking the extrasynaptic subunits (α 4 and δ) but that significant, although reduced, GABA currents were still observed when the synaptic α 1 subunits were deleted (holding potential: -50 mV ;

GABA Erev: -85 mV).

C.

In TC neurons where the expression of the γ 2 subunit that anchors synaptic GABA Hz). Wavelet analysis (bottom) of one raw multiunit channel shows the presence of thalamic oscillations at spindle frequency in these mice devoid of synaptic γ 2 subunits.

Modified with permission from: A: [START_REF] Steriade | Cellular thalamic mechanisms[END_REF]; B: [START_REF] Herd | Extrasynaptic GABA(A) receptors couple presynaptic activity to postsynaptic inhibition in the somatosensory thalamus[END_REF]; C & D: [START_REF] Rovo | Phasic, Nonsynaptic GABA-A Receptor-Mediated Inhibition Entrains Thalamocortical Oscillations[END_REF]. Representative averaged IPSPs during baseline (black) and after LTD induction (grey). LTD induction is blocked by application of the metabotropic glutamate receptor antagonist, LY367395 (2.). GABA A receptor activation is required for LTD induction.

IPSCs were evoked in TC neurons in response to the stimulation of two independent inhibitory pathways. One NRT pathway (black) was not stimulated during the induction protocol. Note that the depression of the IPSCs was only observed for the pathway that underwent the induction protocol including the synaptic stimulation (3).

In all graphs gray area represents the induction period.

Modified with permission from: A: [START_REF] Sieber | Non-Hebbian long-term potentiation of inhibitory synapses in the thalamus[END_REF]; B: [START_REF] Pigeat | Sleep slow wave-related homo and heterosynaptic LTD of intrathalamic GABAAergic synapses: involvement of T-type Ca2+ channels and metabotropic glutamate receptors[END_REF].

Funding:

  Our work in this field was supported by CNRS LIA528, Agence Nationale de la Recherche 06-Neuro, Agence Nationale de la Recherche MNMP 2009.

Figure 1 :

 1 Figure 1: GABA mediated hyperpolarization recruits thalamic T-currents A. Schematic drawing of the thalamic network. The GABAergic neurons from the NRT innervate the glutamatergic TC neurons that project back to the NRT neurons and relay the information arising from extra-thalamic afferents (aff.) to the cortex. B. Hyperpolarization of TC neurons resulting from either step current injection (1., low trace) or NRT afferent activation (2., plain triangle) deinactivates T-channels that open upon membrane repolarization generating a rebound LTS and associated highfrequency burst firing. C. Superimposed traces of typical T-currents evoked in TC neurons by successive step depolarization at increasing membrane potentials (1., holding potential: -100 mV, first step: -70 mV, step: 2.5 mV). Typical voltage-dependency relationships of the steadystate inactivation and activation for T currents recorded in TC neurons (2.).

Figure 2 :

 2 Figure 2: Recruitment of extrasynaptic GABA receptors during NRT neuron burst firing A. Intracellular recordings of NRT neuron (top trace) and TC neuron (bottom trace) activities during spindle oscillations. The rhythmic occurrence of LTSs, and associated high-frequency firing, in NRT neurons induce GABA IPSPs at spindle frequency in TC neurons that occasionally generate rebound LTSs.

  receptors was locally suppressed (AAV-Cre), NRT neuron burst firing still generated a large GABA current (1., holding potential: -30 mV). Such current could evoke a rebound LTS in TC neurons clamped at -70 mV (2.) D. Cortical local field potential (LFP) recording (top) and thalamic multiunit activities (MUA) in adjacent channels (middle) during spindle oscillations observed under urethane anesthesia (black: raw traces; red: same traces pass-band filtered at 7-15

Figure 3 :

 3 Figure 3: Tonic GABA A current and thalamic T-current activation A. Recording from a ventrobasal TC neuron under control conditions. Focal application of the GABA A receptor antagonist gabazine (GBZ 50 µM; white bar) blocks inward IPSCs and reveals an outward shift in baseline current indicative of the presence of a tonic GABA A current. B. In a dorsal lateral geniculate TC neuron, application of low concentration (50 nM) of GBZ that preferentially block tonic GABA A current, caused a 3mV depolarization blocking the LTS repetitive burst firing. (1.). Extracellular single-unit recording of another neuron under control conditions showing repetitive LTS burst firing (top trace and inset) that is blocked by bath application of 50 nM GBZ (bottom trace) (2.). C. Contribution of the T-current to the EPSPs in TC neurons. 1., EPSPs evoked in a ventrobasal TC neuron using the dynamic clamp technique to mimic sensory AMPA inputs. The neuron was maintained at three different membrane potentials in control condition (TTX) and in the presence of the T-channel blocker TTA-P2 (TTX+TTA-P2). T-current largely contributed to the responses evoked at -70 and -65 mV, and slightly prolonged the EPSP recorded at more depolarized membrane potential. 2., T-current stabilizes the firing probability of TC neurons across a large range of membrane potentials. Voltage traces recorded in a TC neuron maintained at average membrane potentials of -60, -65, and -70 mV while being submitted to AMPA conductances (gAMPA) of fixed amplitude. In control condition the firing of the neuron remained almost invariant across the entire voltage range (CTR) while it was strongly decreased upon hyperpolarization when T-currents were antagonized (TTA-P2). Dotted lines indicate -60mV.Modified with permission from: A:[START_REF] Errington | Aberrant GABA(A) receptormediated inhibition in cortico-thalamic networks of succinic semialdehyde dehydrogenase deficient mice[END_REF]; B:[START_REF] Cope | GABAA receptor-mediated tonic inhibition in thalamic neurons[END_REF]; C1:[START_REF] Deleuze | T-type calcium channels consolidate tonic action potential output of thalamic neurons to neocortex[END_REF]; C2:[START_REF] Behuret | Corticothalamic Synaptic Noise as a Mechanism for Selective Attention in Thalamic Neurons[END_REF].

Figure 4 .

 4 Figure 4. T-currents control long-term synaptic plasticity of GABAergic intrathalamic synapses.

Figure 5 .

 5 Figure 5. Schematic illustration of the interactions between thalamic GABA receptors and T-currents.Top enlargement: Release of GABA induced by tonic (grey shaded region) or Tchannel mediated burst firing (grey + red shaded region) of NRT neurons at the NRT to TC synapse. During tonic action potential firing, GABA release preferentially targets the synaptic (α1β2γ) GABA A receptors although some extrasynaptic (α4β2δ) receptors can also be recruited. Bursting of NRT neurons increases GABA release producing a spillover of GABA in peri/extrasynaptic domains recruiting both extrasynaptic GABA A and GABA B receptors. Activation of the three types of receptors generates a hyperpolarization that can elicit an LTS as rebound activity. Repetitive LTS activation produces a large influx of calcium through T-channels (i) and membrane depolarization that can activate other voltage-dependent channels (ii). i)The increase in calcium concentration leads to the activation of the calcium-sensitive phosphatase calcineurin. Calcineurin will then dephosphorylate the activated GABA A receptors inducing their long-term desensitization and an LTD of the synapse. ii)

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Bénar Cg

Grova

Jirsa Vk

Lina Jm

Differences in MEG and EEG power-law scaling explained by a coupling between spatial coherence and frequency: a simulation study

Keywords: power-law spectrum, EEG, MEG, biophysical model, scale-free dynamics

Electrophysiological signals (electroencephalography, EEG, and magnetoencephalography , MEG), as many natural processes, exhibit scale-invariance properties resulting in a powerlaw (1/f) spectrum. Interestingly, EEG and MEG differ in their slopes, which could be explained by several mechanisms, including non-resistive properties of tissues. Our goal in the present study is to estimate the impact of space/frequency structure of source signals as a putative mechanism to explain spectral scaling properties of neuroimaging signals.

We performed simulations based on the summed contribution of cortical patches with different sizes (ranging from 0.4 to 104.2 cm 2 ). Small patches were attributed signals of high frequencies, whereas large patches were associated with signals of low frequencies, on a logarithmic scale. The tested parameters included i) the space/frequency structure (range of patch sizes and frequencies) and ii) the amplitude factor c parametrizing the spatial scale ratios. We found that the space/frequency structure may cause differences between EEG and MEG scale-free spectra that are compatible with real data findings reported in previous studies. We also found that below a certain spatial scale, there were no more differences between EEG and MEG, suggesting a limit for the resolution of both methods.

Our work provides an explanation of experimental findings. This does not rule out other mechanisms for differences between EEG and MEG, but suggests an important role of spatio-temporal structure of neural dynamics. This can help the analysis and interpretation of power-law measures in EEG and MEG, and we believe our results can also impact computational modeling of brain dynamics, where different local connectivity structures could be used at different frequencies.

Introduction

Electrophysiological signals, as many other natural processes, exhibit scale-free characteristics expressed as a spectrum [START_REF] Freeman | A field-theoretic approach to understanding scale-free neocortical dynamics[END_REF]. In practice, this implies that a spectrum is piece-wise linear in a log-log representation, the slope of which (parameter ϒ) could be an important marker of brain state [START_REF] He | Scale-free brain activity: past, present, and future[END_REF]). In the case of local field potentials, several mechanisms have been proposed in order to explain these scale-free properties, as reviewed in (G. [START_REF] Buzsaki | The origin of extracellular fields and currents--EEG, ECoG, LFP and spikes[END_REF]) and [START_REF] Pesaran | Investigating largescale brain dynamics using field potential recordings: analysis and interpretation[END_REF]): low-pass frequency properties of dendrites, capacitive properties of tissues, network properties including relationships between phase coherence and distance, noise from evenly distributed ion channels across dendrites. Other putative mechanisms are more generic, taken from the domain of spatiotemporal pattern formation on the cortex [START_REF] Jirsa | Neural field dynamics with local and global connectivity and time delay[END_REF]).

An interesting observation is that EEG and MEG have different 1/f profiles, with EEG having a steeper slope in a log-log representation. This was shown clearly in the work of Dehghani and colleagues, which interpreted these findings as resulting from non-resistive tissue properties [START_REF] Dehghani | Comparative power spectral analysis of simultaneous elecroencephalographic and magnetoencephalographic recordings in humans suggests non-resistive extracellular media[END_REF]. In this study, a theoretical investigation was conducted that predicts similar frequency dependence for MEG and EEG within a purely resistive1 medium, thus suggesting an impact of non-resistive aspects of the volume conductor on the difference between slopes. The authors develop there a mathematical framework that describes the electric and magnetic field in a linear but not purely resistive framework, where the measures at sensor level depend on the frequency. This can explain why EEG and MEG are differently filtering brain activity.

An alternative -and not exclusive -hypothesis would be a dependence between the size of coherent cortical active regions and the frequency of oscillatory activity, as proposed in early works [START_REF] Pfurtscheller | Frequency dependence of the transmission of the EEG from cortex to scalp[END_REF]. Indeed, the fact that EEG and MEG have different levels of spatial smearing (due to the little influence of skull on magnetic signals [START_REF] Hämäläinen | Magnetoencephalography-theory, instrumentation, and applications to noninvasive studies of the working human brain[END_REF])) could result in different levels of spatial signal cancellation at different frequencies (such cancellation effects are illustrated very schematically in Figure 1). Different scenarios (resistive, non-resistive, with or without dependence of extent of active tissue on frequency) are shown in a schematic manner on Figure 2.

In order to test this latter hypothesis, within a resistive medium, we conducted a series of simulations where the "granularity" of signals at the cortical level (i.e. the size of coherent cortical activity) was varied across frequencies, with higher level of spatial coherence for low frequencies. Our objective was to show that such spatio-temporal coupling -resulting from pure geometrical considerations within a resistive medium -may result in differences in EEG and MEG spectra that are consistent with observations done on real signals.

Materials and methods

Cortex parcellation and EEG/MEG forward modeling

We used the geometry for cortex, MEG sensor placement and EEG electrode localization from a patient recorded for source localization of epileptic discharges [START_REF] Gavaret | MEG and EEG sensitivity in a case of medial occipital epilepsy[END_REF]). The MEG system was a CTF system with 151 z-gradiometers and EEG was recorded using a 64 channel MEG-compatible system. The cortical surface (grey/white matter interface) was segmented with the Brainvisa software [START_REF] Cointepas | The BrainVISA project: a shared software development infrastructure for biomedical imaging research[END_REF]. Sensor location and cortical surface were imported into the BrainStorm toolbox [START_REF] Tadel | Brainstorm: a user-friendly application for MEG/EEG analysis[END_REF] within Matlab (Mathworks, Naticks, MA), and the cortical surface was then downsampled to 15004 vertices. The resolution of the EEG/MEG forward model provided the gain matrix linking the amplitude of each cortical dipole, located at each vertex and normal to the surface, to the EEG/MEG sensors. Forward model was estimated using the Boundary Element Model method implemented within the OpenMEEG [START_REF] Gramfort | OpenMEEG: opensource software for quasistatic bioelectromagnetics[END_REF]) plugin of Brainstorm.

The forward model implemented in OpenMEEG is based on equations that only depend on resistivity of the medium, considering that the quasistatic assumption holds at low frequencies. Details are in [START_REF] Gramfort | OpenMEEG: opensource software for quasistatic bioelectromagnetics[END_REF], a summary follows. For the electric field and potential, this results in the law of electrostatics:

(1) where σ is the conductivity of the medium, V is the electric potential, and J p dipolar source distribution within the domain. The boundary condition at the interface between piecewise linear conductive regions (between brain and skull, skull and scalp, scalp and air) is:

(2) With j the normal current and n the vector normal to the surface. The magnetic field has a dependence on both the electric potential and on the current source distribution, as described by the Biot and Savart law:

(3) This formalism assumes that there is no dependence on frequency for the propagation of electric and magnetic fields. This allows computing two gain matrices G MEG and G EEG that link the amplitude of a dipole on the brain surface to the MEG and EEG measures respectively, which then do not depend on the frequency.

A more generic formulation was proposed by Deghani and colleagues (2010), in which the medium is considered to be linear but not purely resistive. This is expressed by equations ( 10) and ( 12) in [START_REF] Dehghani | Comparative power spectral analysis of simultaneous elecroencephalographic and magnetoencephalographic recordings in humans suggests non-resistive extracellular media[END_REF]):

(4) (5) With a complex valued conductivity , which depends on pulsation ω=2πf and permittivity ε f , and 'inv' denoting the inverse. This formulation that prevents from using a single gain matrix for all frequencies, and would require more detailed modelling of the biophysics of the problem at hand, was not considered in our study.

We considered three layers, scalp, outer skull and inner skull, with skull conductivity set as 1/40 of scalp and brain conductivities. This resulted in two gain matrices: G MEG of size 151 channels x 15004 dipoles and G EEG of size 64 channels x 15004 dipolar sources.

Our goal was to generate realistic simulated datasets exhibiting an interaction between spatial scale and temporal frequencies, with high frequencies recruiting small brain areas, and low frequencies recruiting spatially large areas. The dependence between frequency and extent of active cortex has been observed in animal studies [START_REF] Destexhe | Spatiotemporal analysis of local field potentials and unit discharges in cat cerebral cortex during natural wake and sleep states[END_REF]. Our working hypothesis was that such spatio-temporal structure alone would exhibit spectral densities differing between EEG and MEG signals due to different spatial 'blurring' properties. To do so, we used the random parcellation function of Brainstorm, with a fixed number of regions n s (i.e., number of brain patches at scale s), varying the spatial scale s of the parcellation by successive factors of two: s=15, 30, ... 7680.

In a given configuration, we chose the specifics scales to be included in the simulation, as well as the frequency ranges to be attributed to each scale. Three scales of parcellation are illustrated in Figure 3 for two configurations (detailed configurations are listed in Table 1). The contribution of a given region to the MEG sensors was obtained by summing the unit contribution of the dipoles within the region (given by the corresponding columns of the gain matrix). We thus obtained at each scale s coarse gain matrices G s MEG of size 151 channels x n s and G s EEG of size 64 channels x n s , with n s being the number of regions at scale s.

Dimensionality of gain matrix

In order to quantify the variations of dimensionality of the gain matrix across scales, we computed for each scale a singular value decomposition of the EEG and MEG gain matrices. Importantly, each row was standardized (removal of mean and division by standard deviation) in order to compensate for impact of the depth of the source on channel-level amplitudes. We estimated the subspace dimension by finding the first dimension explaining more than 90%, 95% or 99% of the total variance (computed as the cumulative sum of the singular values normalized by the sum of all singular values).

Generation of signals

At each parcellation level, a single random time course was applied to each region, and the time course at sensor level was obtained by multiplying the summed contribution of the dipoles in a given region (obtained from simplified gain matrices G s MEG and G s

EEG

) with its corresponding time course.

We chose heuristically the range of spatial scales to be considered, either s = 15 to 480 or s= 30 to 3840. The number of regions at scale s is given by ( 6)

with n 1 number of regions at scale 1.

The time course of each region was generated as a white noise (function rand of Matlab) considered to be sampled at a frequency F s of 1250 Hz, with a length of 30s. Importantly, we standardized each signal (removal of mean and normalized by standard deviation) in order to remove the influence of the filter bandwidth on signal amplitude.

The total band of interest was subdivided logarithmically between two bounds that may vary across configurations (details in table 1). Configurations were designed in order to span a range of possibilities -Configuration 1: mostly low frequencies (1-100Hz) and larges patches (which mimics non-REM sleep-like behavior with large synchronies and dominant low frequencies) -Configuration 2: higher frequencies and smaller patches, which simulates the awake state -Configuration 3: spans a large range of sizes and frequencies -Configuration 4: only one scale, in order to verify that there is no difference on the spectra between EEG and MEG in that case.

Finally, a random offset of +-20% was applied to the limits of each frequency band across regions at a given scale, in order to avoid systematic effects in the spectrum (e.g., notches at frequency boundaries). Large patches were attributed a signal with low frequency contents, while small patches were matched with a signal with high frequency content (see left column of Figure 3 for illustration). The band limited noise E s i for each patch i and each scale s was obtained by filtering white noise in the frequency band FB s (with offset) adapted to the scale s. We used the function fftfilt of the EEGlab toolbox [START_REF] Delorme | EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis[END_REF], which is based on Fourier filtering. For each patch i, we compute the corresponding contribution on EEG and MEG by projecting the random activity to the sensors though the corresponding gain matrix:

(7)

with i the index of the patch, E s i a white noise filtered in band FB s , j a channel index and t time. The simulated MEG or EEG data M(j,t) was obtained by summing over the scales the contributions from all regions i at a given scale. In this summation, the data from each scale s was scaled by a multiplicative coefficient equal to the s th power of a scaling parameter ranging from 1 to 1.9:

(8)

The signal M is at the sensor level. The parameter c allows a fine tuning of the slope of the resulting 1/f spectrum. It can be seen as representing the 'local' level of synchrony on each patch [START_REF] Cosandier-Rimélé | Modeling and interpretation of scalp-EEG and depth-EEG signals during interictal activity[END_REF]) as a function of frequency. The range of c was chosen in order to result in a realistic range of spectrum slopes.

Computation of power spectra

We computed the spectrum S(f) of each channel of the simulated MEG and EEG data using the Welch estimator (spectrogram function of Matlab). Thus, the FFT was computed with a window size of 1s (resulting in a frequency resolution of 1Hz), a Hanning tapering, and an overlap of 50% between consecutive windows. The mean spectra across channels were then computed separately for EEG and MEG, and normalized with respect to the higher frequency value, as suggested in [START_REF] Dehghani | Comparative power spectral analysis of simultaneous elecroencephalographic and magnetoencephalographic recordings in humans suggests non-resistive extracellular media[END_REF]. This normalization was necessary in order to compare the shape of the spectra independently of the actual values (differing between EEG and MEG).

If we assume that in a given frequency range the spectrum has a 1/f α shape, then a simple linear regression in a log-log representation will provide an estimation of α:

(9)

The slopes α of the spectra were estimated with linear regression and compared to one another with a t-test.

Results

Figure 4a and 4b present the spectra obtained in configuration 1 (low frequencies configuration) and 2 (high frequencies configuration) respectively. In both cases, the slope between EEG and MEG differ, with MEG presenting less attenuation with increasing frequencies that EEG as hypothesized (i.e., a smaller α in ( 9)). For configuration 1, EEG slope was -1.55 and MEG slope -1.27, and in configuration 2,EEG slope was -1.73 and MEG slope -1.47.

Figure 4c, corresponds to configuration 3, where we tested a large range of scales, which permits to see that above a particular scale, corresponding to 480 regions, the difference between EEG and MEG spectra seem to disappear.

In Figure 4d, we show the results of configuration 4, with only one scale. As expected, in this minimal space/frequency structure, there is no difference between EG and MEG spectra.

In Figure 5, we illustrate the impact of the scaling parameter c on the slope of the spectra, varying the values around the 'absence of scaling factor' (c=1, i.e. same amplitude at each scale). For a small c (0.6), we obtain large slopes (around -3) and a smaller difference between the EEG and MEG spectra than with c=1. Conversely, with a high value of c (1.4), we obtain smaller slopes and large differences between EEG and MEG

We show in Figure 6 the dimensionality of the gain matrix, as a function of the spatial scale (i.e; number of regions). For a percentage of explained variance of 90%, i.e. at a coarse level of description, EEG and MEG exhibited very similar profiles of dimensionality as a function of number of regions involved in the simulations. For higher levels, i.e. when considering a 'finer' explanation of data at sensor level, the dimensionality of the EEG and MEG behave differently. In particular, we found that EEG dimensionality "saturates" for a number of regions above 480. For 90% of explained variance, there was no notable difference between EEG and MEG. For higher levels, and in particular when accounting for 99% of explained variance, the dimensionality of MEG was higher than EEG, suggesting that it can capture finer spatial details than EEG.

Discussion

Several mechanisms have been proposed for explaining the 1/f spectrum in MEG-EEG data. Some arise from the structure of the spatio-temporal dynamics. For instance, Jirsa demonstrated that spatially continuous dynamic systems with homogeneous (gray matter) connectivity always generate characteristics in the power spectrum. [START_REF] Jirsa | Neural field dynamics with local and global connectivity and time delay[END_REF]. Other are related to the non-resistive aspect of the tissues, which lead to filtering effects [START_REF] Dehghani | Comparative power spectral analysis of simultaneous elecroencephalographic and magnetoencephalographic recordings in humans suggests non-resistive extracellular media[END_REF]; see review in [START_REF] Pesaran | Investigating largescale brain dynamics using field potential recordings: analysis and interpretation[END_REF]).

In the present study, we implemented a model with scale-free properties both in the time domain (tuned with a scaling factor c) and in the spatial domain (patch size that differ by a factor of two across different scales). This model has both phenomenological aspects, as we used filtered noise, in contrast to computational models, and mechanistic aspects, by relying on a specific space/frequency structure. Importantly, we explicitly introduced a dependence between the size of the patch (spatial scale) and the frequency range and bandwidth it is endowed with: the smaller the patch, the higher the frequency. The model shows that such dependence resulted in differences between EEG and MEG scale-free spectra, in agreement with previous findings obtained both theoretically and in real data [START_REF] Dehghani | Comparative power spectral analysis of simultaneous elecroencephalographic and magnetoencephalographic recordings in humans suggests non-resistive extracellular media[END_REF]. This shows that a specific space/frequency structure of brain activity could generate selfsimilarity and can can explain differences between spectra, resulting in different slope of the 1/f processes when comparing EEG and MEG. Such a behavior is not exclusive of other mechanisms that are more likely also play a role on real data [START_REF] Dehghani | Comparative power spectral analysis of simultaneous elecroencephalographic and magnetoencephalographic recordings in humans suggests non-resistive extracellular media[END_REF][START_REF] Buzsaki | The origin of extracellular fields and currents--EEG, ECoG, LFP and spikes[END_REF]), but it is to be noted that this mechanism alone seems sufficient to explain the observed differences between the spectra. The full magnitude of the proposed mechanisms requires a systematic quantification of the various contributions, which has so far not been performed, but remains a future task to be performed.

A key assumption of our model is that the spatial extent of temporally coherent sources decreases and scales with frequency, i.e. that high frequencies tend to be more spatially local, whereas low frequencies tend to involve larger spatial cortical regions. This assumption is physiologically plausible, and was specifically stated in the influential Buszaki book "rhythms of the brain" (G Buzsaki 2006): "Long term observations consistently show that coherence of neuronal activity rapidly decreases as a function of distance at high frequency but deceases less for low frequencies.". An intuitive explanation is that it is easier to synchronize oscillators at a low frequency compared to high frequencies, as a small time delay will have a much stronger influence on phase shift at high frequencies compared to low frequencies. Again, from Buszaki book (p. 122) "when the rhythm is fast, only small groups can follow the beat perfectly because of the limitation of axon conductance and synaptic delays. Slower oscillations spanning numerous axon conduction delay periods, on the other hand, allow the recruitment of very large number of neurons. Thus, the slower the oscillation, the more neurons can participate; hence, the integrated mean field is larger." Differences in local and global processing, and effect of distance on spatial coherence was discussed in (P. L. [START_REF] Nunez | Toward a quantitative description of large-scale neocortical dynamic function and EEG[END_REF].

Still, we have to acknowledge that there are only a few observations on real data that support this phenomenon.

Bullock an McClune have reported data from rodent's brain surface recording (electrocorticography, ECoG), that coherence (on temporal signals) decreased more rapidly with frequency when increasing electrode distance [START_REF] Bullock | Lateral coherence of the electrocorticogram: a new measure of brain synchrony[END_REF]. A study performed in humans by the same group, confirmed these findings [START_REF] Bullock | EEG coherence has structure in the millimeter domain: subdural and hippocampal recordings from epileptic patients[END_REF]. Destexhe and colleagues have measured the spatial decay of coherence for two different states (slow wave sleep and wake) that involve different frequency content, on the cortex of cat [START_REF] Destexhe | Spatiotemporal analysis of local field potentials and unit discharges in cat cerebral cortex during natural wake and sleep states[END_REF]. They found that on, the correlation between LFP signals decreased from 1 to 0.25 over 7mm, whereas the decrease was only from 1 to approximately 0.7 in slow wave sleep (<1Hz)

In [START_REF] Von Stein | Different frequencies for different scales of cortical integration: from local gamma to long range alpha/theta synchronization[END_REF], a relationship was suggested from surface EEG between the extent of functional integration and the synchronization frequency.

However, one has to note that observations in human data are challenging. Firstly, it is necessary to have a sufficient spatial coverage (e.g., high density sampling of ECoG electrodes). Secondly, one needs to deal with the convoluted folding of the cortex, which does not allow recording within sulci and could produce abrupt changes when going from one gyrus to another. Volume conduction issues may take place, which make it difficult to assess where the signal actually come from.

The current progress in multi-electrode arrays, and in particular highly conformable ECoG arrays based on polymer thin sheets [START_REF] Khodagholy | Highly conformable conducting polymer electrodes for in vivo recordings[END_REF], should allow recording across large surfaces and may assess accurately the space/frequency structure of coherent activity, resulting in estimates of extent of coherent cortex and signal attenuation across scales. Interestingly, recent work based on structural MRI has proposed to describe the anatomical connectivity by the eigenvectors of the Laplacian performed on diffucsion tensor imaging graphs. This results in basic spatial patterns (an equivalent of the Fourier basis set, but in the spatial domain), with harmonics representing different spatial extent. These spatial harmonics could be the physical substrate for oscillators at different frequencies, and would fit nicely into our proposed framework. More work is needed based on electrophysiology data, in order to link structure to function within a scale-free framework [START_REF] Ciuciu | Interplay between functional connectivity and scale-free dynamics in intrinsic fMRI networks[END_REF].

It was noted from early work, using simultaneous subdural and scalp EEG recordings, that different frequency contents when comparing direct recordings on the brain surface and scalp recordings could originate from the spatial filtering properties of EEG [START_REF] Pfurtscheller | Frequency dependence of the transmission of the EEG from cortex to scalp[END_REF]. The authors ruled out impedance effects of the skull, which are similar across the frequency range of interest. They proposed instead that the blurring effect of the skull produces summation of activities at different phases, which is particularly visible at high frequencies where a small temporal jitter between different oscillators causes high phase dispersion and thus high signal cancellation (see schematic illustration in Figure 1). Previous modeling studies, investigating signal space/frequency scales reported that " EEG amplitude in each frequency band can be related to the synchrony of the underlying current sources" [START_REF] Srinivasan | EEG and MEG coherence: measures of functional connectivity at distinct spatial scales of neocortical dynamics[END_REF], this topic being presented in details in (P. [START_REF] Nunez | Electric Fields of the Brain: The Neurophysics of EEG[END_REF]. The influence of the geometry on cancellation effects is investigated in [START_REF] Ahlfors | Cancellation of EEG and MEG signals generated by extended and distributed sources[END_REF]. It is interesting to note that summation do not occur over an infinite number of oscillators (which would result in perfect cancellation), which means that high frequencies still have a chance to 'express' themselves at the surface, as suggested in [START_REF] Von Ellenrieder | Sparse asynchronous cortical generators can produce measurable scalp EEG signals[END_REF].

In this context, it is plausible that different spatial filtering properties of MEG and EEG (with EEG being more 'blurred' than MEG because of higher impact of skull conductivity (and more selective impact of dipolar sources orientations on MEG data) can produce different temporal filtering properties. This is indeed what we observed in our simulated data, resulting in a steeper profile for EEG when compared to MEG. Interestingly, a better sensitivity to (relatively high frequency) gamma-band activity in MEG when compared to EEG has been observed during visual stimulation [START_REF] Muthukumaraswamy | Visual gamma oscillations: the effects of stimulus type, visual field coverage and stimulus motion on MEG and EEG recordings[END_REF]. These results are compatible with differential profiles in the two modalities.

In our simulation study, the differential effects are lost after a certain level of granularity, i.e. when considering synchronicity over only small patches. This finding is also consistent with our study on dimensionality of gain matrix, which demonstrated that the dimension saturates for small patches sizes, although not as fast in MEG when compared to EEG). Interestingly, this saturation of the effect results in a change of slope on the MEG spectra which could be potential explanations for previous observations of abrupt changes of slopes in the spectrum [START_REF] Miller | Power-law scaling in the brain surface electric potential[END_REF].

We have simulated a uniform spatio-temporal structure by using an unique scaling parameter c across the whole brain. However, it has been observed regional differences in alpha. In [START_REF] Dehghani | Comparative power spectral analysis of simultaneous elecroencephalographic and magnetoencephalographic recordings in humans suggests non-resistive extracellular media[END_REF], three main regions are highlighted, parieto-temporal, vertex and frontal areas. These differences could be reproduced by local variations in frequency to scale mapping, or simply with different c parameter across different brain regions.

Finally, it is worth to note that the real-life MEG spectra are usually contaminated by ambient noise, which we do not model in the present study. The study by Deghani and colleagues [START_REF] Dehghani | Comparative power spectral analysis of simultaneous elecroencephalographic and magnetoencephalographic recordings in humans suggests non-resistive extracellular media[END_REF] , based on empty room recordings, gives an indication of the correction factor that can be applied to the slopes of spectra in order to take into account the contribution of the ambient noise. In this later study, it is shown that the correction will lower the alpha band and thus would amplify the differences between EEG and MEG described in the present work.

Conclusion

In conclusion, we demonstrated that the combination of the spatio-temporal structure of brain activity and biophysical effects is a putative mechanism to explain differences in spectra between EEG and MEG. Thus, our simulations provide a phenomenological explanation to previous experimental findings. This is relevant for signal processing, where properties of EEG or MEG signals need to be properly accounted for [START_REF] Roehri | Time-frequency strategies for increasing high frequency oscillation detectability in intracerebral EEG[END_REF]), as well as for recording, as different electrode sizes (resulting in different impedances) integrate brain activity over different volumes [START_REF] Nelson | Physical model of coherent potentials measured with different electrode recording site sizes[END_REF]. The scale-free properties of signals attract increasing interest as new biomarkers of brain state. This goes beyond the classical analysis of frequency peaks in the spectrum, by quantifying the nonoscillatory ("arrhythmic") part of the signals [START_REF] He | Scale-free brain activity: past, present, and future[END_REF], which is reflected in the overall slope of the spectrum, independently of the presence of local peaks. Our findings highlight a putative mechanism that could be important to take into account in the interpretation of results in MEG and EEG. In particular, they would need to be corrected for if one wants to integrate EEG and MEG into a common view of scale-free properties of brain signals. Our findings may also potentially have a strong impact on computational modeling of brain signals [START_REF] Sanz Leon | The Virtual Brain: a simulator of primate brain network dynamics[END_REF][START_REF] Sanz-Leon | Mathematical framework for large-scale brain network modeling in The Virtual Brain[END_REF]. Indeed, our results suggest that it could be interesting to model the space/frequency properties of neuronal activity, with different local connectivity matrices at different frequencies, which could for example be based on decomposition of tractography-based connectivity matrices [START_REF] Atasoy | Human brain networks function in connectome-specific harmonic waves[END_REF].

The processes that we describe here are not exclusive of other possible mechanisms. More investigation should be conducted in evaluation the range of activated cortex as a function of frequency, in varying brain states (in particular awake versus sleep). Future work could address the different contributions of these mechanisms to the observed signals, as well as improvement in biophysical modelling [START_REF] Bangera | Experimental validation of the influence of white matter anisotropy on the intracranial EEG forward solution[END_REF]). The study of the relationships between structure and function, which is currently attracting much interest, would be particularly relevant in this context [START_REF] Atasoy | Human brain networks function in connectome-specific harmonic waves[END_REF][START_REF] Wirsich | Whole-brain analytic measures of network communication reveal increased structure-function correlation in right temporal lobe epilepsy[END_REF].

Figure 1: Schematic illustration of differential effect of spatial smoothing at different frequencies. The top row shows realizations of a sine wave with random jitter (taken uniformly in 0-100ms). These signals can be seen as representing neighboring neuronal oscillators from a small brain region. The bottom row is the average across realizations. The cancellation resulting from averaging is smaller for the low frequency (left column, 3 Hz oscillations) than for high frequency (right column, 15 Hz oscillations). This effect was discussed in [START_REF] Pfurtscheller | Frequency dependence of the transmission of the EEG from cortex to scalp[END_REF].

Figure 2: Schematic view of different biophysical scenarios for explaining differences between EEG and MEG spectra. a) the conductive medium is purely resistive (i.e., the electric potential follows Ohm's law U= σ I with U potential, σ resistance and I intensity), and propagation of electric and magnetic does not depend on frequency. Two schematic patches of cortex are represented, with synchronous activity involving equal surfaces, one for the low frequencies (LF) and one for high frequencies. The arrows represent equivalent current dipoles corresponding to the activity of pyramidal cells. Here, the spectra for EEG and MEG are the same. b) The patches of active cortex remain of equal size for high and low frequencies, but the medium is not purely resistive, i.e. propagation of electromagnetic fields depend on frequency (as proposed by Deghani et al 2010). Here, EEG and MEG spectra differ due to the properties of the conductive medium. c) Low frequencies involve large patches of cortex, while high frequencies involve synchrony over smaller regions. Here, the spectra also differ, but this time because of the different smoothing properties of EEG and MEG, as EEG integrates activity over larger volumes. This is the hypothesis proposed in the current study. At each level, a single time course is applied to all the dipoles within a given region. The bandwidth of the random noise that is applied to each region varies with the patch size, low frequencies for large regions and high frequencies for small regions (see Table a 1), for different parameters of the amplitude scaling coefficient c. The absolute value of the slope increases with smaller c, as expected, with alpha ranging between 3.08 and 0.35. Differences between EEG and MEG are higher for higher c. 99%). For 90% of explained variance, there was no notable difference between EEG and MEG. For higher levels, and in particular when accounting for 99% of explained variance, the dimensionality of MEG was higher than EEG, suggesting that it can capture finer spatial details than EEG.

Figure 3 :

 3 Figure 3: Illustration of the simulation framework. a) Examples of levels of brain parcellation.At each level, a single time course is applied to all the dipoles within a given region. The bandwidth of the random noise that is applied to each region varies with the patch size, low frequencies for large regions and high frequencies for small regions (see Tablea) b) Signals corresponding to configuration 1 (low frequencies, only three scales are shown here) c) Signals corresponding to Configuration 2 (high frequencies, only three scales are shown here) The resulting data for each configuration is the sum of the simulated MEG signals generated across levels.

  Figure 3: Illustration of the simulation framework. a) Examples of levels of brain parcellation.At each level, a single time course is applied to all the dipoles within a given region. The bandwidth of the random noise that is applied to each region varies with the patch size, low frequencies for large regions and high frequencies for small regions (see Tablea) b) Signals corresponding to configuration 1 (low frequencies, only three scales are shown here) c) Signals corresponding to Configuration 2 (high frequencies, only three scales are shown here) The resulting data for each configuration is the sum of the simulated MEG signals generated across levels.

Figure 4 :

 4 Figure 4: EEG and MEG spectra obtained for the different configuration, with a scale parameter c=1 (only 1/3 of channels are shown). a) Configuration 1 (low frequencies) b) Configuration 2 (high frequencies) c) Configuration 3 (large range of scales) d) Configuration 4 (only one scale).All the configuration presenting a space/frequency structure (1-3), there is a difference between EEG and MEG spectra, at least below a certain scale (corresponding to 480 regions).

Figure 5 :

 5 Figure 5: Comparison of the slopes of EEG and MEG average spectra across sensors, in Configuration 1 (see Table1), for different parameters of the amplitude scaling coefficient c. The absolute value of the slope increases with smaller c, as expected, with alpha ranging between 3.08 and 0.35. Differences between EEG and MEG are higher for higher c.

Figure 6 :

 6 Figure6: Dimensionality analysis of the EEG and MEG gain matrices as a function of the spatial scale (number of regions), for different values of explained variance (90%, 95%, 99%). For 90% of explained variance, there was no notable difference between EEG and MEG. For higher levels, and in particular when accounting for 99% of explained variance, the dimensionality of MEG was higher than EEG, suggesting that it can capture finer spatial details than EEG.

In a purely resistive medium, the propagation of electromagnetic fields only depends on the electrical resistance of the different components (here, brain, skull, CSF, scalp…). Importantly, in this case, there is no dependency of the observed fields on frequency. In other words, there is no filtering effect of the tissues, in contrast with non-resistive tissues where signals may be attenuated at high frequencies.

Acknowledgments

CGB thanks Jean Gotman for useful discussions on spatial coherence. Research supported by grants ANR-16-CONV-0002 (ILCB), ANR-11-LABX-0036 (BLRI) and ANR-11-IDEX-0001-02 (A*MIDEX)". This work has been carried out within the FHU EPINEXT with the support of the A*MIDEX project (ANR-11-IDEX-0001-02) funded by the "Investissements d'Avenir" French Governement program managed by the French National Research Agency (ANR).Part of this work was funded by a joint Agence Nationale de la Recherche (ANR) and Direction Génerale de l'Offre de Santé (DGOS) under grant "VIBRATIONS" ANR-13-PRTS-0011-01. This work was performed within a platform member of France Life Imaging network (grant ANR-11-INBS-0006)