Yehezkel Romain Nardou

Ilgam Khalilov

Bumetanide, an NKCC1 Antagonist, Does Not Prevent Formation of Epileptogenic Focus but Blocks Epileptic Focus Seizures in Immature Rat Hippocampus

Excitatory GABA action induced by high [Cl -] i is thought to contribute to seizure generation in neonatal neurons although the mechanism of this effect remains unclear. We report that bumetanide, a NKCC1 antagonist, reduces driving force of GABAmediated currents (DF GABA ) in neonatal hippocampal neurons and blocks the giant depolarizing potentials (GDPs), a spontaneous pattern of network activity. In the preparation composed of two intact interconnected hippocampi, bumetanide did not prevent generation of kainate-induced seizures, their propagation to the contralateral hippocampus, and formation of an epileptogenic mirror focus. However, in the isolated mirror focus, bumetanide effectively blocked spontaneous epileptiform activity transforming it to the GDP-like activity pattern. Bumetanide partially reduced DF GABA and therefore the excitatory action of GABA in epileptic neurons. Therefore bumetanide is a potent anticonvulsive agent although it cannot prevent formation of the epileptogenic mirror focus. We suggest that an additional mechanism other than NKCC1-mediated contributes to the persistent increase of DF GABA in epileptic neurons.

INTRODUCTION

GABA-the principal inhibitory neurotransmitter in adultsexcites immature neurons because of a higher [Cl -] i in different animal species and brain structures [START_REF] Ben-Ari | Excitatory actions of GABA during development: the nature of the nurture[END_REF].

This difference is thought to play an important role in higher incidence of seizures early in life in humans [START_REF] Hauser | Epidemiology of epilepsy in children[END_REF][START_REF] Moshe | Increased seizures susceptibility of the immature brain[END_REF], lower seizure threshold in experimental animals, and higher neuronal excitability [START_REF] Holmes | Seizures in the developing brain: perhaps not so begin after all[END_REF][START_REF] Khazipov | Developmental changes in GABAergic actions and seizure susceptibility in the rat hippocampus[END_REF]).

This early elevated [Cl -] i is due to a sequential development of two chloride co-transporters: NKCC1, which imports chloride, and KCC2, which extrudes it (Kahle and Staley 2008a,b;[START_REF] Mikawa | Developmental changes in KCC1, KCC2 and NKCC1 mRNAs in the rat cerebellum[END_REF][START_REF] Shimizu-Okabe | Layer-specific expression of Cl-transporters and differential [Cl-]i in newborn rat cortex[END_REF][START_REF] Wang | Developmental changes in KCC1, KCC2, and NKCC1 mRNA expressions in the rat brain[END_REF]. Several observations suggest a link between the excitatory action of GABA and seizure generation at an early developmental stage [START_REF] Dzhala | Excitatory actions of endogenously released GABA contribute to initiation of ictal epileptiform activity in the developing hippocampus[END_REF][START_REF] Khazipov | Developmental changes in GABAergic actions and seizure susceptibility in the rat hippocampus[END_REF]). Other observations suggest that bumetanide, a NKCC1 antagonist, Address for reprint requests and other correspondence: Y Ben-Ari, INMED U901 INSERM, 163, route de Luminy, 13273 Marseille Cedex 09, France (Email ben-ari@inmed.univ-mrs.fr ) attenuates epileptiform activity in the immature rodent hippocampus by reducing [Cl -] i . The effects of bumetanide were observed neither in NKCC1 knock-out mice nor when GABA receptors were blocked, confirming the importance of [Cl -] i accumulation [START_REF] Dzhala | NKCC1 transporter facilitates seizures in the developing brain[END_REF]. However, bumetanide was efficient against seizures acutely induced in vitro by some convulsants but not by others [START_REF] Kilb | Model-specific effects of bumetanide on epileptiform activity in the in-vitro intact hippocampus of the newborn mouse[END_REF], indicating that in the latter case a NKCC1-independent mechanism was involved in seizure generation. Epilepsy is, however, a chronic disorder associated with permanent changes of several signaling cascades. Acute seizures models only partly reflect multiple events that occur in the epileptic network and are less relevant to the clinical situation.

Excitatory actions of GABA have been reported in adult human epileptic temporal lobe neurons [START_REF] Cohen | On the origin of interictal activity in human temporal lobe epilepsy in vitro[END_REF][START_REF] Huberfeld | Perturbed chloride homeostasis and GABAergic signaling in human temporal lobe epilepsy 1[END_REF]) and in chronic epileptic foci in animal models [START_REF] Khalilov | In vitro formation of a secondary epileptogenic mirror focus by interhippocampal propagation of seizures[END_REF][START_REF] Khalilov | Epileptogenic actions of GABA and fast oscillations in the developing hippocampus[END_REF]. Presumably, a gradual accumulation of intracellular chloride during recurrent seizures caused these GABA effects. It is therefore important to define a link between seizures, alterations in [Cl -] i , and epileptogenesis.

We studied these issues in the intact interconnected hippocampal formation (IIHF). Using this preparation in a three-compartment chamber [START_REF] Khalilov | Maturation of kainate-induced epileptiform activities in interconnected intact neonatal limbic structures in vitro[END_REF], we were able to initiate seizures in one hippocampus and then to investigate the effects of drugs on both the seizure propagation to other hippocampus and seizure-induced epileptogenic mirror focus formation [START_REF] Khalilov | In vitro formation of a secondary epileptogenic mirror focus by interhippocampal propagation of seizures[END_REF][START_REF] Khalilov | Epileptogenic actions of GABA and fast oscillations in the developing hippocampus[END_REF] in that hippocampus.

Our first aim was to investigate whether bumetanide acts as an antiepileptogenic agent and therefore prevents formation of the epileptogenic mirror focus by seizures. If this is not the case, bumetanide can still block seizures in the mirror focus and thus to cause an anticonvulsive effect.

The second aim was to investigate the role of NKCC1 in an increased neuronal [Cl -] i in epileptogenic mirror foci.

Because it recently has been shown that the invasive recordings provide inadequate measures of the resting membrane potential (E m ) [START_REF] Tyzio | Membrane potential of CA3 hippocampal pyramidal cells during postnatal development[END_REF] and the perforated-patch technique may cause systematic errors in measurements of the reversal potential of GABA-induced currents (E GABA ) [START_REF] Brumback | Thermodynamic regulation of NKCC1-mediated Cl-cotransport underlies plasticity of GABA(A) signaling in neonatal neurons[END_REF], we used noninvasive single N-methyl-D-aspartate (NMDA) and GABA channel recordings to determine, respectively, E m and E GABA .

METHODS

Experiments were performed on neonatal Wistar rats (postnatal days P7-P8). All experiments have been carried out in accordance with the European Communities Council Directive of 24 November 1986 (86/609/EEC).

Hippocampal preparation

The interconnected intact hippocampal formations were prepared as described previously [START_REF] Khalilov | A novel in vitro preparation: the intact hippocampal formation[END_REF]. In brief, neonatal Wistar rats were decapitated after hypothermic anesthesia, and the brain rapidly removed to oxygenated (95% O 2 -5% CO 2 ) ice-cold artificial cerebrospinal fluid (ACSF). Complexes including two interconnected hippocampi were isolated and transferred into a beaker with oxygenated ACSF containing (in mM) 126 NaCl, 3.5 KCl, 2.0 CaCl 2 , 1.3 MgCl 2 , 25 NaHCO 3 , 1.2 NaH 2 PO 4 , and 11 glucose (pH 7.4) and incubated 1 h before use. The intact hippocampal formations were placed into the conventional fully submerged three-compartment chamber (Fig. 3, see diagram) and superfused with oxygenated ACSF (30-32°C, 10-15 ml/min). The hippocampi were fixed by entomological needles to the silicone elastomer (Sylgard)-covered bottom.

Slice preparation

Slices were prepared as described previously [START_REF] Ben-Ari | Giant synaptic potentials in immature rat CA3 hippocampal neurones[END_REF]. In brief, after decapitation, the brain was rapidly removed and placed in oxygenated, ice-cooled ACSF; hippocampal transverse slices (500 µm) were cut with a McIIwain tissue chopper and kept in oxygenated ACSF at room temperature for 1 h before use. Individual slices were then transferred to the recording chamber where they were fully submerged and superfused with oxygenated ACSF (30-32°C, 2-3 ml/min).

Electrophysiological recordings

All recordings were made from CA3 pyramidal layer. Whole cell patch-clamp recordings in voltage-or current-clamp configuration were collected using an Axopatch 200B amplifier (Axon Instruments). Patch pipette solution were: 1) for recordings of single GABA(A) channels containing (in mM) 120 NaCl, 20 TEA-Cl, 5 KCl, 5 4-aminopyridine, 0.1 CaCl 2 , 10 MgCl 2 , 10 glucose, 10 HEPES-NaOH buffered to pH 7.2-7.3 and 1 µM GABA; 2) for recordings of single NMDA channels: nominally Mg 2+ -free ACSF with 10 µM NMDA and 1 µM glycine; 3) for whole cell recordings (in mM): 140 CsCl, 1 CaCl 2 , 10 EGTA, 10 HEPES, 2 MgATP, and 0.4 GTP, pH 7.25, osmolarity 280, patch pipettes had a resistance of 8-10 M; 4) for gramicidin perforated-patch recording (in mM): 150 KCl and 10 HEPES, buffered to pH 7.2 with Tris-OH. Gramicidin was first dissolved in DMSO to prepare a stock solution of 40 mg/ml and then diluted to a final concentration of 80 µg/ml in the pipette solution. The gramicidin-containing solution was prepared 30 min before the experiment. Patch pipettes were filled with a gramicidincontaining solution, and then the tip was dipped into and filled with a gramicidin-free solution by applying a negative pressure for 30-40 s to facilitate cell-attached formation (4-10 G). Twenty to 30 min after cell-attached formation, series resistance decreased and stabilized. At the end of each recording, negative pressure applied to break the membrane and establish whole cell configuration. This was associated with a shift of the reversal potential of the GABA A mediated responses to near 0 mV. Cells were identified by adding biocytin (0.4%) to the pipette solution for morphological analysis.

Extracellular potentials were recorded using two types of electrodes: field recordings were made with glass micropipettes (GC120TF-10, Clark Electromedical Instruments) filled with ACSF (1-5 M); and to record multiunit activity (MUA), we used tungsten wire electrodes (diameter: 50 µm, California Fine Wire, Grover Beach, CA). Recording electrodes were positioned in a pyramidal cell layer of CA3 subfield, and signals were amplified using a custom-made DAM-8A amplifier (WPI, GB; low filter: 0.1 Hz; high filter: 3 kHz; x1,000). Electrical stimulations were made with a bipolar electrode (10-20 V, 40 µs). Synaptic responses were acquired using an A/D converter (Digidata 1440A, Axon Instruments). Axoscope and Clampfit 10.1 (Axon Instruments) and Origin 7.0 (Microcal Software) programs were used for the acquisition and analysis of the synaptic activities. Group measures are expressed as means ± SD, error bars also indicate SD. Statistical significance of differences was assessed with the Student's t-test, the level of significance was set at P < 0.05. Drugs used were purchased from Sigma [tetrodotoxin (TTX), bumetanide, gramicidin],

Tocris [bicuculline, gabazine, 6-cyano-7nitroquinoxaline-2,3 dione (CNQX), D-2-amino-5phosphopentanoate (APV)] and Molecular Probes (biocytin).

RESULTS

Bumetanide reduces the excitatory GABA action and blocks GDPs in naïve neurons

We first tested the actions of bumetanide on activity of immature hippocampal neurons with simultaneous extracellular and gramicidin perforated patch-clamp recordings (Fig. 1). Neuronal activity at early developmental stages is characterized by spontaneous networkdriven discharges, so-called giant depolarizing potentials (GDPs) [START_REF] Ben-Ari | Giant synaptic potentials in immature rat CA3 hippocampal neurones[END_REF], consisting predominantly of GABAergic postsynaptic currents (PSCs) and bursts of MUA in field potential recordings (Fig. 1Aa). As in earlier observations [START_REF] Sipila | The Na-K-Cl cotransporter (NKCC1) promotes sharp waves in the neonatal rat hippocampus[END_REF], bumetanide (10 µM) blocked spontaneous and evoked GDPs (Fig. 1Ba). In control, single-electrical stimulation evoked a burst of action potentials and large GDPs (Fig. 1Aa). Addition of bumetanide strongly reduced both the number of action potentials (from 65.7 ± 16.9 to 8 ± 2.6 spike, n = 17) and the amplitude of evoked PSCs(Fig. 1, Ba and C). In the presence of APV (40 µM) and CNQX (10 µM), evoked PSCs were considerably reduced, but a few spikes (5.1 ± 1.7 spike, n = 17) were still present (Fig. 1, Ab andC). These spikes were blocked by further addition of bicuculline (Fig. 1, Ac andC), confirming the contribution of excitatory GABAergic synapses in their generation. While bicuculline-sensitive spikes could be generated in the presence of glutamate receptors antagonists, they were not generated in the presence of bumetanide (Fig. 1Bb). Therefore bumetanide was as efficient as bicuculline in blocking the GABA-mediated spiking activity.

Relying on I-V relations of single NMDA and GABA channels (Fig. 2A), we then determined the alterations in DF GABA produced by bumetanide. As shown in Fig. 2, B and C (left), bumetanide did not change E m (-78.5 ± 2.3 and -79.8 ± 3.2 mV, n = 9 and n = 13, respectively, P = 0.5). However, bumetanide decreased DF GABA (from 13.7 ± 11.6 to 2.02 ± 4.8 mV, n = 8 and n = 10, respectively, P < 0.01) and thus negatively shifted E GABA . Therefore bumetanide reduced [Cl -] i leading to a less depolarized DF GABA and blockade of GDPs.

Bumetanide does not block generation and propagation of kainateinduced seizures

We then tested the effects of bumetanide on the generation and propagation of seizures induced by unilateral application of kainate using the IIHF in three-compartment chamber Fig. 3A (left). In keeping with our earlier observations [START_REF] Khalilov | In vitro formation of a secondary epileptogenic mirror focus by interhippocampal propagation of seizures[END_REF], a single application of kainate (300-400 nM) generated recurrent ictal events that propagated from the kainate-treated hippocampus to the contralateral one (Fig. 3A). As shown in Fig. 3A (right), these paroxysmal discharges included high-frequency oscillations (HFOs; 50-150 Hz) in both treated (not shown) and naïve hippocampi. As long as the two hippocampi were connected, continuous application of bumetanide (10 µM) to the contralateral naïve hippocampus-in parallel with recurrent applications of kainate to the treated sidedid not reduce the severity of ictal events in both hippocampi as indicated by the HFOs (Fig. 3B, right) and power spectrum (Fig. 3D; n = 7). In fact, continuous application of bumetanide to both hippocampi while kainate was applied to one hemisphere also failed to reduce seizure severity in both kainate treated and contralateral side (not shown, n = 3). Higher concentrations of bumetanide (50 µM) failed to reduce seizure severity (not shown, n = 3) as well.

Bumetanide does not prevent formation of a mirror focus but blocks seizure generation in the mirror focus

To form an epileptogenic mirror focus, we used recurrent applications of kainate (15 times) to one hippocampus (ipsilateral, ipsi-) that generated an epileptic focus in the connected hippocampus (contralateral, contra-) [START_REF] Khalilov | In vitro formation of a secondary epileptogenic mirror focus by interhippocampal propagation of seizures[END_REF][START_REF] Khalilov | Epileptogenic actions of GABA and fast oscillations in the developing hippocampus[END_REF]. With this protocol, naive hippocampus (contra-) became epileptic and generated seizures after disconnection from the kainate treated side for 2 days [START_REF] Khalilov | In vitro formation of a secondary epileptogenic mirror focus by interhippocampal propagation of seizures[END_REF][START_REF] Khalilov | Epileptogenic actions of GABA and fast oscillations in the developing hippocampus[END_REF]. In these experiments, in parallel with recurrent kainate applications, bumetanide was continuously applied to the contralateral hippocampus. Following repeated applications of kainate, both hippocampi generated spontaneous and synchronous ictal-like seizures in spite of the presence of bumetanide (Fig. 4A). Interestingly, analyses of the inter-hemispheric latencies revealed that each spontaneous ictal event always originated initially from the ipsilateral hippocampus (Fig. 4Ab, n = 5) that was not the case during tonic-clonic and clonic phases of the event (Figs. 4A, c andd, n = 40).

We then disconnected the two hippocampi by severing the commissural fibers (not shown) or by applying TTX to the commissural chamber (Fig. 4B) while the contralateral hippocampus was still exposed to bumetanide. We observed that seizures were generated in the kainate-treated hippocampus only. The bumetanidetreated side failed to generate the epileptiform activity (Fig. 4B, n = 4), generating instead the synchronized events reminiscent to GDPs (named further as epileptic GDPs, EGDPs). However, after washing out of bumetanide, spontaneous and evoked seizures reappeared (Fig. 4C). In additional experiments, continuous application of bumetanide to both hippocampi while kainate was repeatedly applied to only one, failed also to prevent the formation of epileptogenic foci in both hippocampi (n = 4, not shown). Therefore bumetanide prevented neither the long-term effects of kainate nor transformation by propagating seizures the naive hippocampus to one generating seizures.

Bumetanide restores GDP-like recurrent population bursts in the mirror focus

We then investigated the electrical properties of the disconnected mirror focus more detail. Field and patch-clamp recordings were made from the isolated mirror focus in intact hippocampi and in slices prepared from such hippocampus, which also were able to generate spontaneous epileptiform events [START_REF] Khalilov | In vitro formation of a secondary epileptogenic mirror focus by interhippocampal propagation of seizures[END_REF]. The isolated intact hippocampus generated spontaneously ictal and interictal events that were fully blocked by bumetanide (Fig. 5 A, n = 7). Similar observations were made in slices prepared from the mirror foci (Fig. 5B, n = 9). In the presence of bumetanide, the disconnected mirror focus generated EGDPs (see following text and Fig. 6). Bumetanide also blocked the induction of stimuli-induced epileptiform oscillations in the mirror focus (not shown, n = 10). After washout, spontaneous and evoked epileptiform oscillations reappeared after various delays, suggesting that the permanent network alterations in the mirror focus were not abolished by bumetanide (Fig. 5B). Therefore bumetanide blocked seizure generation in the mirror focus but neither prevented formation of the mirror focus nor reversed the chronic epileptic features of the tissue. After addition of bumetanide, interictal activity was completely suppressed and replaced by recurrent population bursts of activity, EGDPs, that had a number of similar features with physiological patterns, GDPs, including (Fig. 6): both types of events were characterized by a few hundred millisecond increase in MUA with a relatively small delta-wave-like deflection of local field potentials in the pyramidal cell layer and without population spikes (Figs. 6Ba and 7A, *); both population events had much smaller amplitudes than those of interictal events (110 ± 18.9 mV for GDPs; 71.3 ± 1.2 mV for EGDPs, and 553.2 ± 12.4 mV for interictal events, n = 24, n = 27, and n = 48 events, respectively, P < 0.01; Fig. 6D); in gramicidin perforated-patch recordings, both types of events had similar reversal potential (60.9 ± 3.1; 59.6 ± 1.5 mV, and 36.9 ± 4.6 mV for interictal events, n = 10; Fig. 6, a and b); and estimated in cell-attached recordings, the number of spikes in CA3 pyramidal cells was similar during GDPs (Fig. 6Ac) and EGDPs (Cc) but much bigger during interictal (Bc) activity (1-2 spikes for control or EGDPs and 4-5 for interictals; Fig. 6E).

Thus in spite of the fact that bumetanide eliminated epileptiform activity in the mirror focus some population activity, EGDPs, still remained, presumably due to a NKCC1-independent increase of [Cl - ] i in epileptic neurons.

NKCC1 underlies only partially excitatory GABA action in epileptogenic neurons

Formation of the mirror focus is associated with a permanent in E GABA [START_REF] Khalilov | In vitro formation of a secondary epileptogenic mirror focus by interhippocampal propagation of seizures[END_REF]. This and other observations [START_REF] Cohen | On the origin of interictal activity in human temporal lobe epilepsy in vitro[END_REF][START_REF] Fujiwara-Tsukamoto | Distinct types of ionic modulation of GABA actions in pyramidal cells and interneurons during electrical induction of hippocampal seizure-like network activity 2[END_REF][START_REF] Jin | Impaired Cl extrusion in layer V pyramidal neurons of chronically injured epileptogenic neocortex[END_REF][START_REF] Rivera | Mechanism of activity-dependent downregulation of the neuron-specific K-Cl cotransporter KCC2[END_REF]; for review, see [START_REF] Ben-Ari | GABA: a pioneer transmitter that excites immature neurons and generates primitive oscillations[END_REF]) suggest that recurrent seizures produce a permanent accumulation of chloride and therefore enhance the excitatory action of GABA.

As shown in Fig. 7, A-D, the excitatory actions of GABA in the mirror focus were reduced but not blocked by combined applications of bumetanide, APV, and CNQX. Bumetanide transformed stimuliinduced epileptiform oscillations to EGDPs (Fig. 7, A andB). Evoked bursts of action potentials were still observed after application of APV and CNQX (Fig. 7C) and were completely blocked following application of bicuculline (D), suggesting that in the presence of bumetanide, GABA still exerts an excitatory action mediated by NKCC1-independent mechanism(s).

To clarify this effect, we measured E m and DF GABA in epileptic neurons. E m was not significantly different in naïve neurons and neurons (Fig. 7E) in the mirror focus (-78.1 ± 1.8 and -74,8 ± 2.3 mV, n = 14 and n = 10, respectively, P = 0.08.

Bumetanide or glutamate receptor antagonists (CNQX+APV) blocked seizures but did not alter E m . In neurons of epileptic mirror foci, however, DF GABA was significantly increased (from 13.2 ± 12.2 FIG. 3. Bumetanide does not block generation and propagation of kainate-induced seizures. Left: experimental design and the 3-compartment chamber. Two hippocampi and commissural connections have independent inlets and a common outlet. Kainate was applied to 1 hippocampus [ipsilateral (ipsi-)] and electrical activity recorded in ipsi-and contralateral hippocampus (contra-). A: kainic acid (300-400 nM) was applied briefly (3 min) to 1 compartment (ipsi-), whereas the contralateral compartment was perfused with normal ACSF. Seizures induced in the ipsilateral hippocampus propagate to the contralateral side. High-frequency oscillations (HFOs, 50-150 Hz) were observed in the contralateral hippocampus. These high-frequency activities were visualized by timefrequency (TF) representations using Wavelet analysis. Here field power is coded in colors so that red corresponds to higher frequency (right). B: kainate was applied to one hippocampus (ipsi-) and bumetanide (10 µM) to the naïve contralateral hippocampus (contra-). Bumetanide did not block ictal-like events and HFOs in the contralateral hippocampus (TF representations and power spectrogram). C: perforated-patch recordings from a neuron in the contralateral treatment (red trace). Cb: integral currents calculated from Ca. D: power spectrum of field potentials during ictal events in control and in the presence of bumetanide.

to 37.3 ± 8.1 mV, n = 8 and n = 33, respectively, P < 0.001) that resulted in a positive shift in E GABA (Fig. 7F). Bumetanide significantly reduced this shift (from 37.3 ± 8.1 to 14.2 ± 7.6 mV, n = 33 and n = 17, respectively, P < 0.001), although values of DF GABA remained bigger than those in naïve neurons (14.2 ± 7.6 vs. 2.02 ± 4.8 mV in naïve neurons in the presence of bumetanide; Figs. 7F and2C). Increasing the bumetanide concentration (50 µM, n = 8) or blockade of ongoing seizures by CNQX+APV failed to block this persistent increase of DF GABA .

Therefore in the presence of bumetanide, DF GABA remained by 10 mV bigger in the epileptic neurons comparing with those in control, and this difference was independent of ongoing epileptiform activity.

DISCUSSION

The principal finding of the present study is that bumetanide reduces DF GABA and blocks seizures in the mirror focus, suggesting that the excitatory action of GABA, mediated at large by NKCC1, is critically important for the generation of epileptiform activity. However, bumetanide does not prevent the seizure-dependent transformation of a naïve network to the epileptic one, suggesting that seizures beget seizures even when NKCC1 is not functioning. In addition, a residual increase in DF GABA in the presence of bumeta-FIG. 4. Bumetanide does not prevent the formation of an epileptogenic mirror focus. A: simultaneous field recordings in the ipsilateral hippocampus exposed 15 times to kainate and contralateral hippocampus continuously exposed to bumetanide. Both hippocampi were connected and spontaneous seizures were synchronous. Aa: an epileptiform ictal-like activity depicted at larger scale. A, b and c: epileptiform events at the start and at the end (tonicclonic phase) of the ictal-like activity. Note that seizures originated always (n = 5) from ipsilateral hippocampus as shown in Ab at expended scale. During the tonic-clonic phase (Ac), this is not the case, as quantified in Ad. Ad: quantification of the inter-hemispheric latencies ( t). B and C: simultaneous field recordings following disconnection of 2 hemispheres by applying TTX onto commissural connections. B: bumetanide is still present in the contralateral side. Seizures are not generated; however, GDP-like population activity still exists. C: after washing bumetanide out, both sides generate seizures that are not synchronous.

nide indicates that a persistent elevation of [Cl -] i in the epileptic neurons is only partially mediated by NKCC1.

Bumetanide is an anticonvulsive but not an antiepileptogenic agent

The effects of bumetanide on seizures are quite controversial depending on the type of model and convulsive agent used. Bumetanide reduced seizures generated by high K + [START_REF] Dzhala | NKCC1 transporter facilitates seizures in the developing brain[END_REF][START_REF] Kilb | Model-specific effects of bumetanide on epileptiform activity in the in-vitro intact hippocampus of the newborn mouse[END_REF], reduced [START_REF] Dzhala | Bumetanide enhances phenobarbital efficacy in a neonatal seizure model[END_REF] or increased [START_REF] Kilb | Model-specific effects of bumetanide on epileptiform activity in the in-vitro intact hippocampus of the newborn mouse[END_REF]) seizures generated by low Mg 2+ , and augmented the frequency of seizures generated by kainate [START_REF] Kilb | Model-specific effects of bumetanide on epileptiform activity in the in-vitro intact hippocampus of the newborn mouse[END_REF]. Delpire and colleagues [START_REF] Zhu | NKCC1 and KCC2 prevent hyperexcitability in the mouse hippocampus[END_REF]) suggested that NKCC1 antagonists aggravate 4-aminopyridine-induced seizures and enhance neuronal excitability, albeit at a later developmental stage (P10-P13), and also suggested that NKCC1 actually reduces hyperexcitability.

We found that bumetanide neither reduced nor aggravated the severity of seizures in both kainate-treated hippocampus and contralateral hippocampus to which these seizures propagated and failed also to prevent formation of the epileptogenic mirror focus. Bumetanide did not block the high-frequency components of seizures (>40 Hz), which are critically important for the formation of mirror focus [START_REF] Khalilov | Epileptogenic actions of GABA and fast oscillations in the developing hippocampus[END_REF]. It also did not alter GABAmediated PSCs during ictal events generated by the propagation of seizures from the kainate-treated hippocampus. In contrast, GABA receptor antagonists block the HFOs and mirror focus formation [START_REF] Khalilov | Epileptogenic actions of GABA and fast oscillations in the developing hippocampus[END_REF] confirming that functional GABA signaling is essential for these events.

In spite of a DF GABA reduction by bumetanide in naïve neurons of to the levels close to E m , the dynamic accumulation of chloride during severe seizures is not fully controlled by NKCC1.

Therefore it is likely that during recurrent seizures the severity of ictal events and the GABA-mediated massive influx of chloride overcome the inhibitory effect of bumetanide on NKCC1 and [Cl -] i accumulation. Dynamic effects of seizures on DF GABA , that is likely neuronal type dependent, and the mechanisms of chronic alteration of DF GABA by seizures remain to be further investigated.

In contrast, bumetanide fully blocked generation of seizures in the disconnected mirror focus although the GDP-like pattern, EGDPs, still remained. Its properties, however, differed significantly from those of interictal events.

Determining the mechanisms underlying the chronic alterations of [Cl -] i in epileptic tissues is important because most antiepileptic drugs (AEDs) have been developed using adult experimental models that do not possess the unique properties of immature neurons and networks [START_REF] Connell | Clinical and EEG response to anticonvulsants in neonatal seizures[END_REF][START_REF] Painter | Phenobarbital compared with phenytoin for the treatment of neonatal seizures[END_REF][START_REF] Staley | Does Plasticity of the GABA(A) reversal potential contribute to epileptogenesis?[END_REF]. It has been suggested that drugs that reduce [Cl -] i such as bumetanide may constitute a novel family of AEDs adapted to developmental epilepsies [START_REF] Dzhala | Bumetanide enhances phenobarbital efficacy in a neonatal seizure model[END_REF]Kahle and Staley 2008b). Our observations, however, suggest that although bumetanide blocks the expression of seizures, it may not be efficient in preventing the longlasting sequels of recurrent seizures. This is particularly important because seizures in neonates can cause long-lasting deteriorate effects [START_REF] Ben-Ari | Limbic seizure and brain damage produced by kainic acid: mechanisms and relevance to human temporal lobe epilepsy[END_REF][START_REF] Hauser | Risk of recurrent seizures after two unprovoked seizures[END_REF][START_REF] Levene | The clinical conundrum of neonatal seizures 15[END_REF][START_REF] Massingale | Survey of treatment practices for neonatal seizures[END_REF][START_REF] Mizrahi | Neonatal seizures: early-onset seizure syndromes and their consequences for development[END_REF][START_REF] Moshe | Kindling in developing rats: persistence of seizures into adulthood[END_REF][START_REF] Tremblay | Maturation of kainic acid seizure-brain damage syndrome in the rat. I. Clinical, electrographic and metabolic observations[END_REF].

NKCC1 is partly responsible for the persistent increase of DF GABA in epileptic neurons

Previous studies consistently showed that bumetanide reduces [Cl -] i and the excitatory actions of GABA in immature neurons [START_REF] Dzhala | NKCC1 transporter facilitates seizures in the developing brain[END_REF][START_REF] Sipila | The Na-K-Cl cotransporter (NKCC1) promotes sharp waves in the neonatal rat hippocampus[END_REF][START_REF] Yamada | Cluptake promoting depolarizing GABA actions in immature rat neocortical neurones is mediated by NKCC1[END_REF]. However, these studies used invasive recording techniques-whole FIG. 5. Bumetanide blocks seizures in the mirror focus. Field recordings in the separated contralateral intact hippocampus (A) and slices obtained from the contralateral hippocampus (B) after mirror focus formation. Note that seizures have been blocked by bumetanide and replaced by spontaneous (GDP-like) population events (see Fig. 6).

cell and perforated-patch recordings-that strongly alter resting membrane potential [START_REF] Tyzio | Membrane potential of CA3 hippocampal pyramidal cells during postnatal development[END_REF]). Here we used for the first time single channel recordings to determine the actions of bumetanide on both E m and E GABA and thus the driving force of GABA DF GABA . Our results indicate that bumetanide clearly reduces significantly E GABA leading to an important fall in the driving force of GABA and confirming the actions of the diuretic compound on intracellular chloride and E GABA . The small change of E m in epileptic neurons when compared with controls as determined with single NMDA channel recordings may be due to tonic GABA A current [START_REF] Sipila | Depolarizing GABA acts on intrinsically bursting pyramidal neurons to drive giant depolarizing potentials in the immature hippocampus[END_REF]) that causes increased membrane depolarization due to depolarizing DF GABA . But we did not investigate further this issue. We also did not investigate possible distal actions of bumetanide on the dendrites of pyramidal neurons or on other neuronal populations.

Enhancement of [Cl -] i in the mirror focus neurons was significantly reduced by bumetanide However, under action of bumetanide, DF GABA in the epileptic neurons was still bigger than in control (>10 and 2 mV, respectively). Although the upregulation of NKCC1 expression in epileptic mirror focus neurons cannot be excluded [START_REF] Okabe | Amygdala kindling induces upregulation of mRNA for NKCC1, a Na(+), K(+)-2Cl(-) cotransporter, in the rat piriform cortex[END_REF], the increase in bumetanide concentration has not reduced [Cl - ] i further, suggesting that other mechanisms are involved. One possible candidate is the KCC2 that is thought to play a fundamental role in Cl -extrusion [START_REF] Hubner | Disruption of KCC2 reveals an essential role of K-Cl cotransport already in early synaptic inhibition[END_REF][START_REF] Lee | KCC2 expression in immature rat cortical neurons is sufficient to switch the polarity of GABA responses[END_REF][START_REF] Rivera | The K + /Cl-co-transporter KCC2 renders GABA hyperpolarizing during neuronal maturation[END_REF]. It is well documented that KCC2 expression in rodents is low at birth in the forebrain and increases steadily during the first 2-3 wk of postnatal life [START_REF] Clayton | Ontogeny of cation-Clcotransporter expression in rat neocortex[END_REF][START_REF] Dzhala | NKCC1 transporter facilitates seizures in the developing brain[END_REF][START_REF] Lu | Developmental regulation of the neuronalspecific isoform of K-Cl cotransporter KCC2 in postnatal rat brains[END_REF][START_REF] Mikawa | Developmental changes in KCC1, KCC2 and NKCC1 mRNAs in the rat cerebellum[END_REF][START_REF] Rivera | The K + /Cl-co-transporter KCC2 renders GABA hyperpolarizing during neuronal maturation[END_REF][START_REF] Wang | Developmental changes in KCC1, KCC2, and NKCC1 mRNA expressions in the rat brain[END_REF]. Seizures and other insults can induce a downregulation of KCC2 expression [START_REF] De | Subiculum network excitability is increased in a rodent model of temporal lobe epilepsy[END_REF][START_REF] Fiumelli | Modulation of GABAergic transmission by activity via postsynaptic Ca 2+ -dependent regulation of KCC2 function[END_REF][START_REF] Palma | Anomalous levels of Cl-transporters in the hippocampal subiculum from temporal lobe epilepsy patients make GABA excitatory[END_REF][START_REF] Payne | Cation-chloride co-transporters in neuronal communication, development and trauma[END_REF][START_REF] Rivera | Mechanism of activity-dependent downregulation of the neuron-specific K-Cl cotransporter KCC2[END_REF]).

However, to the best of our knowledge, little information is available on the functionality of KCC2 at an early developmental stage. We cannot also exclude a participation of voltage-gated Cl - channels to the chloride homeostasis [START_REF] Farrant | The cellular, molecular and ionic basis of GABA(A) receptor signalling[END_REF][START_REF] Huguenard | Whole-cell voltage-clamp study of the fading of GABA-activated currents in acutely dissociated hippocampal neurons[END_REF][START_REF] Ling | Activity-dependent depression of monosynaptic fast IPSCs in hippocampus: contributions from reductions in chloride driving force and conductance[END_REF][START_REF] Mccarren | Use-dependent depression of IPSPs in rat hippocampal pyramidal cells in vitro[END_REF][START_REF] Payne | Cation-chloride co-transporters in neuronal communication, development and trauma[END_REF][START_REF] Staley | Alteration of GABA A receptor function following gene transfer of the CLC-2 chloride channel[END_REF][START_REF] Thompson | Activity-dependent disinhibition. I. Repetitive stimulation reduces IPSP driving force and conductance in the hippocampus in vitro[END_REF].

In conclusion, our study with the use of noninvasive single channel recordings in chronic epileptic tissue, confirms the importance of evaluation of DF GABA and E m to examine the effects of seizures and putative anticonvulsive agents on neuronal network functioning. Our observations are in favor of using bumetanide for blocking seizures in neonates but also call for studies of other regulators of intracellular chloride and their effects on seizures.

Although a strict comparison with the clinical situation is difficult because of the large variety of epilepsy types and longlasting duration required for seizures to evoke their neurological sequels, we consider the mirror focus as an "epileptic" tissue because it generates spontaneously recurrent ictal and interictal seizures for hours and up to 2 days [the longest period this preparation could be kept [START_REF] Khalilov | In vitro formation of a secondary epileptogenic mirror focus by interhippocampal propagation of seizures[END_REF]]. It has been suggested that a combination of phenobarbital and bumetanide is more efficient for treating refractory infantile epilepsies because bumetanide reduces DF GABA and phenobarbital augments the efficacy of inhibitory GABA signaling [START_REF] Dzhala | Bumetanide enhances phenobarbital efficacy in a neonatal seizure model[END_REF]Kahle and Staley 2008b). The validity of this attractive hypothesis will depend, however, on the contribution of NKCC1 to positive DF GABA in epileptic conditions.

FIG. 1 .

 1 FIG. 1. Bumetanide blocks GABA-mediated excitation and GDPs in neonatal rat hippocampus. Dimultaneous extracellular and gramicidin-perforated patch-clamp recordings in the CA3 pyramidal layer of hippocampus in artificial cerebrospinal fluid (ACSF, A) and ACSF + bumetanide (Bum; B). Ab and Bb: similar recordings in the presence of 6-cyano-7nitroquinoxalene-2,3-dione (CNQX) and D-2amino-5-phosphopentanoate (APV). Note that glutamatergic receptor antagonists blocked 100% of the evoked (arrows) multiunit activity (MUA) in the bumetanide treated slices and only 90% in control. Ac and Bc: the remaining activity was completely blocked by the GABAergic receptor antagonist bicuculline (Bicu) confirming the excitatory action of GABA in naïve neurons. C: summary plot of the mean number of units evoked by a single stimulus (15-20 stimuli per slice) in 4 independent experiments.

FIG. 2 .

 2 FIG. 2. Bumetanide strongly reduces the depolarizing driving force of GABA-mediated currents (DF GABA ). A: cell-attached recordings of single GABA(A; left) and N-methyl-Daspartate (NMDA) receptor channels (right) in CA3 pyramidal cells in control ACSF. B: I-V relationships of single GABA A and NMDA receptor channels in ACSF ( ) and bumetanide-treated ( ) slices. C: summary plot of the resting membrane potential (E m ) and driving force of GABA-mediated currents (DF GABA = E GABA -E m ) in control ( ) and in bumetanide ( ). Each circle corresponds to 1 CA3 pyramidal cell. Error bars indicate SD.

  FIG.. 6. Bumetanide transforms seizure activity into the GDP-like recurrent population bursts. Simultaneous extracellular and gramicidine perforated-patch recordings of spontaneous synchronized network activity in control slices (A), mirror focus slices (B), and mirror focus slices in the presence of bumetanide (C). Ab, Bb, and Cb: I-V relations of perforated-patch currents. Ac, Bc, and Cc: simultaneous extracellular and cell-attached recordings of spontaneous network activity in control, mirror focus slices, and mirror focus slices in the presence of bumetanide. D: summary plot of mean amplitudes of field potentials during synchronized network events. E: the mean number of cell-attached recorded spikes during this synchronized activity.

J Neurophysiol -VOL 101 -JUNE 2009 -www.jn.org

ACKNOWLEDGMENTS We thank Dr. Yuri Zilberter, Dr. Rustem Khazipov and Dr. Matthew T. Colonnese for their suggestions and criticism. GRANTS We are indebted for financial support to Institut National de la Santé et de la Recherche Médicale, Ligue Francçaise contre l'épilepsie Conseil Régional Provence Alpes Côte d'Azur. Fédération de la recherche médicale, and the Assistance Publique des Hôpitaux de Paris to Y. Ben-Ari and the Fédération de la recherche sur le cerveau. FIG. 7. Bumetanide reduces only partially the positive DF GABA in epileptogenic focus. A-D: simultaneous extracellular and whole cell recordings of evoked and spontaneous activities in epileptic slices obtained from the contralateral hippocampus after mirror focus formation. Note that bumetanide blocked interictal-like epileptiform events (B) but did not completely block the excitatory action of GABA (C and D). Resting membrane potentials (E m ) measured with single NMDA receptor channels (E) and DF GABA measured with single GABA A receptor channels (F) in control and epileptic slices.


GABAergic Hub Neurons Orchestrate Synchrony in Developing Hippocampal Networks P. Bonifazi,1 * M. Goldin, 1 * M. A. Picardo, 1 I. Jorquera, 1 A. Cattani, 1 G. Bianconi,2 A. Represa, 1 Y. Ben-Ari, 1 R. Cossart 1 † Brain function operates through the coordinated activation of neuronal assemblies. Graph theory predicts that scale-free topologies, which include "hubs" (superconnected nodes), are an effective design to orchestrate synchronization. Whether hubs are present in neuronal assemblies and coordinate network activity remains unknown. Using network dynamics imaging, online reconstruction of functional connectivity, and targeted whole-cell recordings in rats and mice, we found that developing hippocampal networks follow a scale-free topology, and we demonstrated the existence of functional hubs. Perturbation of a single hub influenced the entire network dynamics. Morphophysiological analysis revealed that hub cells are a subpopulation of g-aminobutyric acid-releasing (GABAergic) interneurons possessing widespread axonal arborizations. These findings establish a central role for GABAergic interneurons in shaping developing networks and help provide a conceptual framework for studying neuronal synchrony.

T he coordinated activation of neuronal assemblies features in most physiological brain functions and influences proper network wiring during development [START_REF] Buzsáki | Rhythms of the Brain[END_REF][START_REF] Katz | [END_REF](3). In addition to cellular excitability, synaptic efficacy, and the balance of excitation and inhibition, the architec-ture of network connectivity may be central to the production of synchronous neuronal activity (4)(5)(6)(7). The relationship between network dynamics and topology has been studied using concepts from graph theory and statistical physics (7)(8)(9). Smallworld and scale-free organizations are particularly appealing models for brain connectivity because they offer a compromise between computational needs, wiring economy, and robustness [START_REF] Buzsáki | Rhythms of the Brain[END_REF][START_REF] Amaral | Proc. Natl. Acad. Sci. U.S.A[END_REF][START_REF] Buckner | [END_REF](12)(13)(14). These complex topologies have been found in contexts as diverse as the Internet, social sciences, or biology (8,15). When applied to neuronal circuits, both models share one common feature: Although most neurons are connected locally, a few "hub" neurons possess long-range connections that link large numbers of cells, thereby bestowing network-wide synchronicity. It has been proposed that neuronal hubs orchestrate behaviorally relevant activity in cortical assemblies, as well as being causal in producing pathological oscillations (4)(5)(6)16). However, the existence of neuronal hubs is still speculative, perhaps because of the conceptual and technical difficulties of investigating them, including the rarity of high-connectivity (HC) as compared to low-connectivity (LC) cells. Additionally, definitive functional confirmation that neuronal hubs play a key role in synchroni- zation processes requires testing the causal influence of HC cells on network dynamics, something that cannot be achieved with post hoc data analysis (13,17,18).

To find cells involved in the synchronization of neuronal networks, we designed a method to map functional connectivity (FC) in real time in living brain slices, based on the analysis of multineuron calcium activity. Here we use the term FC to denote the statistical relationship between the activities of neurons (19), which should not be confused with the effective connectivity of functional synapses (20,21). This enabled us to perform targeted electrophysiological recordings and stimulation of neurons with a known degree of FC, while imaging network dynamics. We analyzed the developing hippocampal network because it provides an ideal circuit in which to investigate the existence of hub cells. First, as in most developing brain structures, network activity is concentrated in rhythmic synapse-driven synchronizations, the giant depolarizing potentials (GDPs) (3,22). Second, the network topology underlying the generation of GDPs is confined to local CA3 circuits in slices (23)(24)(25), which substantially simplifies the experimental approach. Last, understanding the cellular basis of synchronization in developing circuits is important, because several maturation processes rely on early network oscillations (22).

Using multibeam two-photon excitation of hippocampal slices from rats and GAD67-green fluorescent protein (GFP) knockin (KI) mice [5 to 7 days old; see the supporting online material (SOM)] loaded with the calcium indicator Fura-2AM (26), spontaneous multineuron activity was recorded with a temporal resolution of 50 to 150 ms (Fig. 1 and fig. S1). The FC of the hippocampus was first investigated at a large scale (with a ×10 objective, Fig. 1A). Focusing on the CA3 region, the activity of 806 T 155 cells (n = 4 slices), distributed across the dentate gyrus to the CA1 region, were simultaneously imaged. Focusing on temporal correlations, a functional connection directed from neuron A to neuron B was established if the activation of A consistently preceded that of B (SOM and fig. S1B). An FC map was thus constructed for all recorded neurons (Fig. 1). In all slices imaged at low magnification, the average distribution of the number of output links per neuron was best fitted by a power-law function with an average scaling power of -1.3 T 0.1 (n = 4 slices, Fig. 1 and SOM). Power-law distributed connectivity is the signature of a scale-free topology, in which hubs are rare neurons with a high connectivity index (8). Neurons with the highest connectivity tended to concentrate more often in the CA3c region (Fig. 1A3,inset). Previous studies have reported that this particular area is a preferential site of initiation for spontaneous GDPs (25,27).

To increase the chances of finding hub neurons, we next performed experiments in the CA3c area at higher magnification (with a ×20 objective, Fig. 1B). As previously reported (26), we were able to combine targeted electrophysiological recordings with calcium imaging. Out of 142 neurons recorded while imaging, only 45 were included in the following analysis because estimation and probing of network topology required very stable experimental conditions (SOM). The connectivity of the networks imaged at x20 was also distributed as a power law with an average scaling factor of -1.1 T 0.1 (n = 45 slices; Fig. 1 andSOM). HC neurons were preferentially located in the stratum oriens and lucidum at the two borders with the pyramidal cell layer (Fig. 1B3 and fig. S3B3). To test the contribution to network dynamics of neurons with different degrees of connectivity, we targeted cells covering the entire connectivity range (Figs. 2 and3, n = 20 HC and 25 LC neurons). Neurons were recorded in current-clamp conditions and stimulated while imaging population activity. Two stimulation protocols were applied for each neuron (SOM): (i) a phasic stimulation [short suprathreshold current pulses The total axonal lengths of HC and LC interneurons were statistically different (P < 0.01).

repeated at 0.1 to 0.2 Hz (the frequency range of GDPs occurrence)]; and (ii) tonic stimulation (continuous positive or negative current injections, bringing the cell to a membrane potential where it fired continuously or was completely silenced, respectively). Cell/network interaction was estimated using three metrics (SOM): (i) the frequency of occurrence of spontaneous network synchronizations (GDPs) during the stimulation relative to the resting condition; (ii) the peristimulus histogram plotting the average fraction of cells activated by the phasic stimulation; and (iii) the phase precession/ succession of GDPs relative to a harmonic oscillator mimicking GDPs' rhythm in resting conditions; in this way, the number of observed versus expected GDPs was estimated over time (SOM). A cell was considered as affecting network dynamics significantly if it satisfied any of the above criteria. About a third (8 out of 20 neurons) of the targeted HC cells exhibited a significant cell/ network interaction (Figs. 2B and3). In contrast, no LC neuron but one showed any significant cell/network interaction (24 out of 25 neurons; Fig. 2A and fig. S2A). The effects of neurons significantly affecting network dynamics (n = 9) could be summarized as follows (Fig. 3): (i) in four cases, tonic or phasic stimulation induced sustained action potential (AP) firing that significantly decreased the occurrence of GDPs to 48 T 13% of resting conditions (P < 0.05; Figs. 2B and 3C and movie S1); (ii) in three cells, phasic stimulation triggered network synchrony in the form of GDPs in 37 T 4% of the trials within 1 s after the stimulus (P < 0.05; Fig. 3A and fig. S5); (iii) in three cells, phasic stimulations induced a phase succession of GDPs as compared to resting conditions (Fig. 3B, P < 0.05). Our evidence suggests that these neurons may act like functional hubs. We will henceforth refer to these as hub neurons.

The developing hippocampal network comprises two major cell types: pyramidal glutamatergic cells and g-aminobutyric acid-releasing (GABAergic) interneurons. In adult cortical structures, network function is strongly modulated by the action of GABAergic interneurons that represent a minority of the total population but include a variety of subtypes (28). Half of the experiments were performed in GAD67-GFP KI mice (29) to selectively identify GABAergic neurons. All hub neurons recorded in GAD67-GFP KI mice, based on their HC index, were GFP-positive (fig. S3, n = 4). Accordingly, the fraction of GFP-positive cells was four times higher in the HC region than in the total cell population (22% of HC neurons versus 6% of all neurons, n = 46 movies in GAD67-GFP KI mice). Therefore, hub neurons are GABAergic, and we next examined whether they represented a specific morphological population. While being recorded, cells were filled with biocytin. All nine hub cells were aspiny neurons and often possessed multipolar dendrites and a cell body located at the border between the pyramidal cell layer and the stratum oriens or lucidum. All HC neurons that were not hubs were morphologically identified as pyramidal cells (fig. S2; 4 cells reconstructed). LC cells not influencing network dynamics exhibited either interneuronal or pyramidal cell morphology (Fig. 2 and fig. S2). All hub neurons had distinctive morphological features, displaying a widespread axonal arborization that most often crossed subfield boundaries, running parallel to principal cell layers toward both the dentate gyrus and CA1 region (n = 6 of 9 neurons, Figs. 2 and3). Three of the hub cells exhibited dense preferential innervation of the CA3 principal cell layer, suggesting a perisomatic, basketlike (28) interneuron subtype (Fig. 3A and fig. S3B2). We Given their extended morphology, it seems probable that hub neurons have a higher probability of being severed in brain slices than other cells and thus probably represent a higher fraction of neurons in vivo [but see (20)]. We conclude that functional hubs are GABAergic interneurons with a long axonal arborization. Hub neurons therefore have the features required to activate many postsynaptic targets.

In order to determine the nature of the functional link between hub neurons and other cells, we first asked whether stimulation of hub neurons could directly trigger a calcium response in other neurons, even in the case where the net effect of stimulation was to desynchronize activity. We thus compared functional and effective connectivity maps (SOM and fig. S4). We found that there was a large overlap between the two maps in the case of HC interneurons (53 T 6% on average, n = 5), whereas stimulation of HC pyramids activated only 8 T 1% of functionally connected neurons (n = 5), indicating that these were effectively not connected to follower cells. We next performed targeted paired recordings from HC and follower neurons (n = 16 pairs). In the case of HC interneurons, we observed a 37% probability of finding a monosynaptic GABAergic connection between neurons (n = 8 pairs, fig. S5). This was significantly different from the case of HC pyramidal cells, because no direct connection could be revealed when recording from them (n = 8 pairs, P < 0.05, Wilcoxon-Mann-Whitney two-sample rank test). This is in agreement with the imaging data and comparable to the highest synaptic connectivity rates reported for interneurons in the adult cortex (21). It therefore represents a high value given the fact that all the monosynaptically connected neurons were more than 100 mm apart (the average distance between recorded neurons was 130 T 20 mm, n = 16 pairs, fig. S5) and that the connection probability is very likely to increase with age (30,31). We conclude that the functional connectivity of hub neurons is supported by an effective synaptic connectivity and propose that HC pyramidal neurons are more likely to operate within assemblies (32).

Because hub function may depend on differences in cellular excitability or synaptic strength (33,34), we next examined the basic electrophysiological properties of hub neurons as compared to LC interneurons (Table 1). Of the basic features analyzed (SOM), hub neurons received more spontaneous excitatory postsynaptic potentials (EPSPs) and had a lower threshold for AP generation (Student's t test, P < 0.05). A lower AP threshold could indicate a more advanced maturation stage for hub neurons (35). Both properties should result in a more efficient activation of hub neurons by synaptic inputs.

Finally, because stimulation of hub neurons significantly affected the occurrence of GDPs, we examined their specific involvement in the spontaneous synchronization process. In agreement with previous estimates (36), the dynamic of a single GDP was characterized by a buildup of activity lasting on average 350 ms (Fig. 4, n = 8 slices, SOM). Using cluster analysis (SOM), a stereotypical spatiotemporal synchronization pattern accounted for one-third of the GDPs within the recording period (33 T 2%, n = 45, Fig. 4). For each neuron, we estimated the average correlation and time of activation relative to all other cells in GDPs that clustered together (Fig. 4 and SOM). In almost half of the movies (n = 20 out of 45), the time correlation graph presented a bimodal distribution (Fig. 4B), indicating that GDPs repetitively started synchronizing neurons plotted on the left side of the distribution, whereas neurons on the right were activated last. By pooling the data from different slices (n = 7588 neurons, 45 movies), we found that the majority of functional hubs clustered on the upper left region of the graph, indicating a more reliable activation at the onset of GDPs (Fig. 4B); this is in agreement with the lower AP threshold and higher synaptic drive described above. Other recorded neurons were evenly distributed across the correlation plot. Cell-attached and whole-cell recordings confirmed that cells activated at the buildup of synchronization indeed fired APs before the occurrence of GDPs (n = 14 neurons, fig. S1C). AP firing in hub neurons thus predicts network synchronization in the developing CA3 region.

This study shows that a scale-free topology can underlie synchronous network patterns in living cortical networks. We suggest that hub neurons, composed of a subpopulation of GABAergic interneurons, orchestrate spontaneous network synchronization. Two different morphological types of hub neurons could be distinguished within our sample data set: (i) cells displaying a long axon spanning regions with sparse collaterals, and (ii) basketlike neurons with a dense but more local arborization pattern. Network synchronization could be triggered by phasic stimulation only in basketlike hub neurons (Fig. 3A and fig. S5). In the adult hippocampus, long-range projecting GABAergic hippocampal interneurons have been described (37) and their hub function has been suggested but never been probed (4). Perhaps the long-axon hub neurons act as connector hubs, whereas basketlike hubs have a local hub function (19). Regardless, the present results confirm the crucial role of GABAergic transmission in shaping network patterns at early developmental stages, when GABA exerts a complex excitation/ shunting inhibition action (38,39). The spontaneous activation, before synchrony, of hub neurons with many direct postsynaptic connections is compatible with excitatory actions of GABA. However, hub cell stimulation also often slowed down network oscillations and in some extreme cases completely desynchronized activity. One possible explanation is that the shunting actions of GABA retard or prevent synchronization. However, other possibilities cannot be excluded, including a phase-resetting effect by which a hub cell can either advance or delay bursting in intrinsically oscillating neurons (39), depending on their phase at the time of the hub input (40).

Single neurons can trigger population synchronization in the disinhibited adult CA3 region (41) or elicit a chain of cell activation in the cortex that can translate into behavior or switch the global brain state (42)(43)(44). Therefore, the demonstration that hub neurons functionally operate in the brain helps bridge the gap between single-cell and network activity. This finding should facilitate the investigation of the mechanisms by which many physiological and pathological network oscillations are generated.

D

isruption of the delicate balance between proliferation and differentiation in cerebellar granule neuron precursors (GNPs) underlies medulloblastoma, the most common pediatric tumor of the nervous system (1, 2). A class of particularly aggressive medulloblastomas associated with very poor prognosis show high expression of Atoh1 (3), a transcription factor highly expressed in GNPs also known as Math1 (4), and recent in vitro studies proposed that Atoh1 might be involved in neoplastic proliferation (5,6). Given that deletion of Atoh1 in mice results in perinatal death (7), the function of this transcription factor in the developing postnatal cerebellum has remained opaque.

To delete Atoh1 in the postnatal developing cerebellum, we crossed Atoh1 flox/flox mice (8) with mice carrying the gene coding for a tamoxifeninducible Cre recombinase in the Rosa locus (R26CreER) (9) and a null allele of Atoh1 [START_REF] Amaral | Proc. Natl. Acad. Sci. U.S.A[END_REF][START_REF] Buckner | [END_REF]. After activation of Cre by tamoxifen, Rosa CreER ;Atoh1 +/flox animals (designated here as Atoh1 wt ) maintain one functional allele of Atoh1, whereas Rosa CreER ;Atoh1 -/flox mice (designated here as Atoh1 D ) lose Atoh1 expression. We injected postnatal day 3 (P3) animals and analyzed their cerebella 3 days later. Nissl staining of matching sections of the external granule layer (EGL), the neuroepithelium formed by GNPs, revealed that Atoh1 D animals had a much thinner EGL than that of their Atoh1 wt littermates (fig. S1). Using phospohistone H3 staining to visualize the M phase of the cell cycle and Tuj1 for neural differentiation, we found that the EGL of Atoh1 D mice had been depleted of cycling immature precursors (Fig. 1, A and B, and fig. S2). Staining for active caspase 3 did not reveal any apoptosis in the EGL of Atoh1 D mice (fig. S1, E andF). We thus investigated whether deletion of Atoh1 triggers the GNP differentiation to granule neurons or induces these cells to transdifferentiate to other cell types. Shown in fig. S2

Fig. 1 .

 1 Fig. 1. Analysis of multineuron calcium activity reveals a scale-free topology in the developing hippocampus. (A) (1) Two-photon calcium fluorescence image of a rat hippocampal slice loaded with Fura-2AM and visualized with multibeam excitation at ×10 magnification. Scale bar, 100 mm. DG, dentate gyrus. (2) Detected contours of the cells from the fluorescence image shown in (1). Red dots are the 10 highest-connectivity neurons in the represented network based on the analysis of calcium event onsets; gray lines mark the output links of one HC neuron. (3) Probability distribution plot of the fraction of output links over the total population of active neurons imaged with ×10 magnification (gray line, n = 3224 neurons in four slices; SOM). The graph is plotted on a loglog scale, and a power-law distribution with a slope (g) of 1.3 T 0.1 (n = 4) is indicated in black (SOM). The inset shows the location of the 30 highest-connectivity neurons (~1% of the population, red dots) on a schematic representation of the hippocampus. The dashed rectangle indicates the size of the area of a x20 movie. Scale bar, 100 mm. (B) (1) Same as (A1) but at x20 magnification. The imaged region corresponds to CA3b/c; that is, around the dotted area in (A1). Arrow indicates the direction of the dentate gyrus. Scale bar, 100 mm. (2) Same as (A2) but for the movie taken in B1. (3) Same as (A3) but for a population of 7588 neurons. The probability distribution of output links from smaller CA3 regions also follows a power law with a similar scaling power (g = 1.1 T 0.1, n = 45). The probability threshold for HC neurons was fixed to 40% (red-shaded area). The inset indicates the location of HC neurons (red dots) on a schematic representation of the CA3b/c region of the hippocampus. HC neurons represented 5 T 1% (n = 45) of all functionally connected cells. This value was not significantly different from that calculated in subfields from ×10 data sets of the same size as ×20 images, because HC neurons represented 4 T 1% of the connected cell population in ×10 movies (n = 4, P > 0.05, Student's t test). sl, stratum lucidum; sp, stratum pyramidale; so, stratum oriens. Scale bar, 100 mm.

Fig. 2 .

 2 Fig. 2. Stimulation of HC but not LC neurons affects network dynamics. (A) Data from a representative LC interneuron. (1) The green arrow indicates the position in the pooled power-law distribution of output links (Fig. 1B) of the recorded neuron. Red-shaded area indicates the HC region, considering a 40% probability threshold. The right contour plot shows the position (solid red dot) and output connections (gray lines) of the illustrated LC interneuron. sl, stratum lucidum; so, stratum oriens. Scale bar, 100 mm. (2) Phasic currentclamp stimulation (200-ms pulses of 75-pA current every 10 s, gray area) of the LC interneuron while being imaged did not affect the occurrence of GDPs (detected from the calcium activity). The interval between GDPs as a function of time is plotted. Values are expressed relative to the average interval between GDPs calculated before the stimulation period. (3) Neurolucida reconstruction of the recorded cell on a schematic representation of the hippocampus reveals an interneuron-like morphology displaying a local axonal arborization (green). Dendritic arborization is black. The black rectangle marks the imaged region. Scale bar, 500 mm. This is a color-coded representation of the functional connectivity map [same as (A1)] (SOM) overlaid with the axonal morphology (green) of the cell. The asterisk indicates the cell body position. Red represents high cell density (a.u., arbitrary units). (B) Same as (A) but for a representative HC interneuron. Phasic stimulation of the HC interneuron [same protocol as (A2)] significantly decreased GDP frequency [(2), P < 0.05]. The recorded cell displayed a widespread axonal arborization (red) spanning locally toward the cells functionally connected [(3), right panel] and further toward the dentate gyrus and the CA1 region [(3), left panel]. (C) (1) Cluster analysis tree of the morphological variables describing the 16 recorded and imaged interneurons (Ward's method, Dlink: Euclidian distances, see SOM). Distances were normalized. Most HC and LC interneurons (based on the analysis of the imaging data) segregated in two different groups. (2) The total axonal lengths of HC and LC interneurons were statistically different (P < 0.01).

3 CFig. 3 .

 33 Fig. 3. Perturbations of network dynamics induced by the stimulation of HC interneurons. (A) Data obtained from a HC interneuron triggering network synchrony (P < 0.05). Frame rate, 10 Hz. (1) The red arrow indicates the position in the pooled power-law distribution of output links (Fig. 1B) of the recorded neuron. (2) Fraction of cells active as a function of time after repetitive phasic stimulation (200-ms pulses of 100-pA current every 10 s) of the HC interneuron (16 consecutive trials). The peristimulus time histogram shows the average across different trials. Red traces are current-clamp recordings from the stimulated HC neuron for six consecutive stimulations (gray). Four out of six trials (indicated by red asterisks in lower panel) triggered GDPs appearing as polysynaptic membrane potential depolarizations.(3) Neurolucida reconstruction of the recorded HC cell on a schematic drawing of the hippocampus. Axonal arborization is in color; dendrites are black. The dashed rectangle indicates the imaged region. Scale bar, 500 mm. (B) Same as (A) but for a HC interneuron inducing a phase succession of GDPs when stimulated (P < 0.05). Phase succession is illustrated in the top graph of (2) plotting the number of GDP cycles skipped during phasic stimulation (gray) as a function of time. The number of expected GDPs was calculated during resting conditions (white) based on the average interval between GDPs. Arrows indicate transitions between oscillatory regimes. Current-clamp recordings from five consecutive stimulation trials for the period marked by (i) show the progressive delay in the occurrence of a GDP (black asterisks) after stimulation (gray). (C) Same as (A) but in a HC interneuron preventing GDPs when stimulated. Graphs in[START_REF] Katz | [END_REF] show the fraction of active cells (top histogram), as well as the cell firing frequency (middle), as a function of time. Peaks of synchronous activity (GDPs) disappear when the membrane potential of the cell (bottom) is depolarized by continuous positive current injection (40 pA; SOM). Current-clamp traces show the activity in the HC neuron in resting (i and iii) and stimulated (ii, gray) conditions. The black arrow indicates the time when a significant effect on network dynamics starts (P < 0.05).

Fig. 4 .

 4 Fig. 4. Hub neurons are activated at the onset of spontaneous network synchronizations. (A) (1) Raster plot of the onsets of calcium events in a representative movie (frame rate, 20 Hz). There are many spontaneous GDPs appearing as broken vertical lines in the raster plot. The middle raster plot shows GDP1 on an expanded time scale. The right plot represents the average temporal profile of the fraction of cells sequentially activated in all GDPs recorded in the same network. The peak of cell coactivation was used as zero time reference. Error bars indicate SDs. (2) Contour plots showing cells activated during the buildup [region a in (1)] and at the peak (b) for the three GDPs marked by arrows in the raster plot in (1). Note the similarity between the patterns of cells. Color-coded contour plots on the right quantify how many times a cell is recruited in one of the two temporal windows over 25 representative GDPs. (B) Time-correlation graph (SOM), plotting for each imaged neuron (7588 neurons) the average correlation and average time of activation relative to all other cells. Red dots indicate targeted functional hubs and dark gray dots indicate all other recorded neurons. (C) (1) Raster plot [calculated as in (A1)] of the network activity (frame rate, 6.67 Hz) while recording an HC hub neuron (red dots) in current-clamp mode (bottom trace). Calcium events (top trace) reflect spiking activity (bottom trace). (2) Same timecorrelation graph as in (B) but only for the recorded slice shown in (C1). The red dot marks the HC hub neuron. Red traces show current-clamp recordings of spontaneous activity in the hub neuron at the time of two different GDPs [marked by arrowheads; dashed rectangles in (C1), lower panel]. AP firing occurs in the hub neuron about 200 ms before GDPs.

  , cells still populating the surface of Atoh1 D cerebellum that had deleted Atoh1 still expressed Zic1, a marker of differentiating postmitotic EGL cells and mature granule neurons, making transdifferentiation unlikely. Proliferating GNPs express Pax6 at low levels, whereas differentiating postmitotic precursors show high expression of Pax6 and turn on the neural differentiation marker NeuN. The cells residing on the surface of the cerebellum of Atoh1 D expressed high levels of 1 Department of Molecular and Human Genetics, Baylor College of Medicine, Houston, TX 77030, USA. 2 Howard Hughes Medical Institute, Baylor College of Medicine, Houston, TX 77030, USA. 3 Departments of Neuroscience and Pediatrics, Baylor College of Medicine, Houston, TX 77030, USA. 4 Program in Developmental Biology, Baylor College of Medicine, Houston, TX 77030, USA.*To whom correspondence should be addressed. E-mail: hzoghbi@bcm.edu

Fig. 1 .

 1 Fig. 1. Atoh1 deletion disrupts GNP proliferation and induces differentiation. (A and B) Phosphohistone H3 staining of cerebella of animals injected with tamoxifen. (Left) Nissl staining of cerebella of animals injected with tamoxifen. The boxed regions represent the images to their right, showing the staining for phosphohistone H3. The arrow in (B) indicates a single cycling cell in the Atoh1 D EGL. (C and D) Pax6 and NeuN staining shows the immature GNPs [(C), white bar] not expressing NeuN and the differentiating population [(C) and (D), between the yellow dotted lines] coexpressing both markers. The colocalization pattern is shown on the bottom right.

Table 1 .

 1 Comparison of basic electrophysiological properties of hub neurons and LC interneurons. Measurements were obtained from whole-cell recordings in eight hub and eight LC interneurons (see SOM methods). V rest , resting membrane potential (corrected value; SOM); R input , input resistance; V threshold , AP threshold (corrected value; SOM); AP width, AP width measured at halfmaximal amplitude. Asterisks indicate significant differences. P < 0.05 was considered significant. The right column indicates the P value given by Student or Mann-Whitney tests.

	Properties	Hub interneurons	LC interneurons	P value
	V rest (mV)	-66 T 5	-64 T 5	0.33
	R input (megohms)	379 T 85	423 T 67	0.69
	Capacitance (pF)	65 T 15	54 T 15	0.64
	V thresh (mV)	-53 T 5*	-39 T 4	0.04
	AP width (ms)	2.05 T 0.5	1.8 T 0.5	0.74
	AP amplitude (mV)	45 T 6	3 9 T 5	0.43
	EPSP frequency (Hz)	4.5 T 1.5*	1.0 T 0.4	0.03
	EPSP amplitude (mV)	2.1 T 0.3	2.6 T 0.5	0.51

www.sciencemag.org SCIENCE VOL 326 4 DECEMBER 2009

Institut de Neurobiologie de la Méditerranée, INSERM U901, Université de la Méditerranée, Parc Scientifique de Luminy, Boîte Postale 13, 13273 Marseille Cedex 9, France.

Department of Physics, Northeastern University, Boston, MA 02115, USA.

DECEMBER 2009 VOL 326 SCIENCE www.sciencemag.org

Adriano Flora, 1 Tiemo J. Klisch, 1,2 Gabriele Schuster, 1 Huda Y. Zoghbi 1,2,3,4 * Granule neuron precursors (GNPs) are the most actively proliferating cells in the postnatal nervous system, and mutations in pathways that control the GNP cell cycle can result in medulloblastoma. The transcription factor Atoh1 has been suspected to contribute to GNP proliferation, but its role in normal and neoplastic postnatal cerebellar development remains unexplored. We show that Atoh1 regulates the signal transduction pathway of Sonic Hedgehog, an extracellular factor that is essential for GNP proliferation, and demonstrate that deletion of Atoh1 prevents cerebellar neoplasia in a mouse model of medulloblastoma. Our data shed light on the function of Atoh1 in postnatal cerebellar development and identify a new mechanism that can be targeted to regulate medulloblastoma formation.


Sloven Dubois
email: sloven.dubois01@univ-lr.fr

Renaud Péteri
email: renaud.peteri@univ-lr.fr

Michel Ménard
email: michel.menard@univ-lr.fr

Decomposition of dynamic textures using Morphological Component Analysis: a new adaptative strategy

The research context of this work is dynamic texture analysis and characterization. Many dynamic textures can be modeled as a large scale propagating wave and local oscillating phenomena. The Morphological Component Analysis algorithm (MCA) is used to retrieve these components using a well chosen dictionary. We define a new strategy for adaptive thresholding in the MCA framework, which greatly reduces the computation time when applied on videos. Tests on synthetic and real image sequences illustrate the efficiency of the proposed method and future prospects are finally exposed.

Introduction

The study of Dynamic Textures (DT) is a recent research topic in the field of video processing. A DT can be described as a time varying phenomenon with a certain repetitiveness in both space and time. A flag in the wind, ripples at the surface of water, smoke or an escalator are all examples of DT. Rather than a simple extension of static textures to the time domain, a DT is a more complex phenomenon resulting from several dynamics. Their study is an active research topic with many applications such as synthesis [START_REF] Filip | Fast synthesis of dynamic colour textures[END_REF], segmentation [START_REF] Doretto | Dynamic texture segmentation[END_REF] or characterization [START_REF] Zhao | Dynamic texture recognition using local binary patterns with an application to facial expressions[END_REF]. The context of our work is the indexation of DT for automatic video retrieval [START_REF] Dubois | A comparison of wavelet based spatio-temporal decomposi-tion methods for dynamic texture recognition[END_REF].

Each DT has its own characteristics, such as stationary, repetitiveness, velocity . . . On Figure 1 showing an image sequence of a river surface, two motions can be observed: a high frequency motion (2) carried by an overall motion [START_REF] Aujol | Dual norms and image decomposition models[END_REF]. Many DT can be decomposed into one or several local oscillating motions carried by far range waves. In order to better characterize these two sets of components, it is necessary to extract them separately.

In this article, the Morphological Component Analysis (MCA) is used for decomposing and analyzing image sequences of natural scenes. To our knowledge, the only existing work using MCA and video is recent and focuses on the inpainting of a cartoon sequence [START_REF] Woiselle | Inpainting with 3D sparse transforms[END_REF].

In Section 2, the MCA is briefly described. The dictionaries selected in the MCA, adapted to the model used for DT, are then presented. A key issue is the computation time of MCA that is related to the thresholding strategy. We propose in Section 3 a new adaptive thresholding strategy that reduced the computation time by a factor of four compared to the original algorithm. Results on synthetic and real sequences of DT are presented and future prospects are discussed in Section 4. 1 2 Decomposing a DT using MCA According to researches on synthesis [START_REF] Finch | GPU Gems: Programming Techniques, Tips, and Tricks for Real-Time Graphics[END_REF] and observations made on a large DT database [START_REF] Péteri | Dyn-Tex: a comprehensive database of Dynamic Textures[END_REF], a DT can be modelled as a sum of local oscillations carried by longer range waves. Recent works for decomposing images and videos [START_REF] Starck | Image decomposition via the combination of sparse representations and a variational approach[END_REF][START_REF] Chan | The digital TV filter and nonlinear denoising[END_REF][START_REF] Aujol | Dual norms and image decomposition models[END_REF] seem relevant for extracting these components. We have chosen the MCA because of the richness of the available dictionnary, which is crucial regarding the complexity of DT.

Given a signal y described as a linear superposition of morphological components K disturbed by a noise ε: y = K i=1 y i + ε. The M CA approach allows to find an acceptable solution to the inverse problem of decomposing a signal on a given vectorial basis, i.e. to extract components (y i ) i=1,...,K from a degraded observation y according to a sparsity constraint. The M CA approach assumes that each component y i can be represented sparsely in the associated basis Φ i : ∀i = 1, . . . , K, y i = Φ i α i . Algorithm 1 describes the main steps of the MCA. A detailed description can be found in [START_REF] Starck | Image decomposition via the combination of sparse representations and a variational approach[END_REF].

Algorithm 1 Morphological Component Analysis 1. while y - K j=1 ỹ(k-1) j 2 σ do 2.
// For each component 3.

for i = 1 à K do 4.
// Compute the marginal residual 5.

r(k)

i = y - i-1 j=1 ỹ(k) j - K j=i+1 ỹ(k-1) j 6. // Projection of r(k) i on basis Φ i 7. α (k) i = Φ T i r(k) i 8.
// The new estimation of y i 9.

ỹ(k

) i = Φ i δ λ (k) α (k) i 10.
end for 11.

// Update of the threshold λ 12.

λ (k+1) = update(λ (k) , strategy)

13. end while A crucial point in the MCA approach is the dictionary definition. An unsuitable choice of transformations will lead to non sparse and irrelevant decompositions of the different dynamical phenomena present in the sequence. As mentioned previously, we model DT as a sum of local oscillations carried by long range waves. It is therefore necessary to associate each component with the most representative basis. In [START_REF] Dubois | A 3D discrete curvelet based method for segmenting dynamic textures[END_REF], the authors show that the curvelet transform [START_REF] Candès | Fast discrete curvelet transforms[END_REF] is relevant for extracting non-local phenomena propagating temporally. It thus seems particularly interesting to model long range waves present in a DT.

The second part of the model is composed of locally oscillating phenomena that will be extracted using the local cosine transform.

The dictionary that we use in the MCA algorithm is then composed of the curvelet transform Φ 1 and the local cosine transform Φ 2 .

Thresholding strategy

Context

The computation time of decomposition algorithms represents a major challenge for sequence analysis (indexing and browsing). Some transforms require several minutes of computation on a short image sequence. A recent work [START_REF] Bobin | Morphological component analysis : An adaptive thresholding strategy[END_REF] has shown that a hundred of iterations is necessary to establish a good separation of the different components when a linear thresholding strategy (LTS) is used. In our case, the total computational time for a 5 second sequence is given by: 100

* [T (Φ T 1 ) + T (Φ 1 ) + T (Φ T
2 ) + T (Φ 2 )] = 20 hours, where T () measures the execution time of one projection on Φ i during one cycle of the algorithm.

If we extend this result to the entire DT database DynTex [START_REF] Péteri | Dyn-Tex: a comprehensive database of Dynamic Textures[END_REF], 583 days of calculation are required. Recently Bobin et al. [START_REF] Bobin | Morphological component analysis : An adaptive thresholding strategy[END_REF] have proposed a thresholding strategy 'Mean of Max' (MOMS) that enables to obtain similar results but with fewer iterations (25 in average instead of 100). It represents a computation time of approximately 7 hours 30 for a 5 second video, resulting in approximately 219 days for the whole database.

For indexing the DynTex database, the computation time of the MOMS is still acceptable, since it is always possible to divide the workload on several processors. In the case where one searches for a particular texture using a query sequence, these calculations are acceptable only on sequences of limited duration and of low resolution. One goal of this work is to reduce these limitations by proposing a new thresholding strategy.

An adaptive thresholding strategy

The quality of the results from the decomposition of a signal using the MCA algorithm strongly depends on the evolution of the threshold λ (k) in one iteration (in one f or loop). Figure 2 shows two different evolutions of λ (k) corresponding to two strategies (1) and ( 2). The evolution of λ (k) is slower in case (1) than in [START_REF] Bobin | Morphological component analysis : An adaptive thresholding strategy[END_REF]. In this example, evolution [START_REF] Aujol | Dual norms and image decomposition models[END_REF], respectively (2), leads to select 5% of the coefficients, respectively 25%, in the two bases. If we consider that evolution [START_REF] Aujol | Dual norms and image decomposition models[END_REF] gives an optimal threshold here, a failure to control the value of λ (k) (in case 2) will lead to a rapid allocation of too many coefficients in the two bases, degrading the final decomposition. The linear thresholding strategy (LTS) leads to the optimum λ (k) for 100 iterations [START_REF] Bobin | Morphological component analysis : An adaptive thresholding strategy[END_REF]. In a large number of natural textures, this number of iterations can be greatly reduced, depending on the texture itself. LTS is then no longer optimum. However, the threshold evolution using LTS can be considered as a minimum slope below which the evolution of λ (k) is sub-optimal. A good strategy for the calculation of λ (k) must lead to a slope greater than or equal to the one obtained using LTS. The 'Mean of Max' strategy (MOMS) is interesting as it can adaptively change the evolution of λ (k) . However, on natural texture sequences, this strategy tends to reduce too drastically this slope, or even almost cancel it.

We propose to combine these two strategies into a new so-called adaptive thresholding strategy (ATS), which defines λ (k) as the minimum value of λ (k) calculated using strategies LTS and MOMS.

The λ (k) update using ATS is formalized as follows: 1) λ min 100 with :

λ (k) = min 1 2 (m 1 + m 2 ), λ (k) - λ (
m 1 = max i Φ T i r (k) ∞ , m 2 = max j =i Φ T j r (k) ∞ r (k) = y - K j=1 ỹ(k) j
is the residual term Using this strategy, we are sure to change the value of λ (k) corresponding to the steepest slope. In other words, when MOMS leads to values of λ (k) evolving slowly, λ (k) follows the LTS 1) λ min 100 . Otherwise, λ (k) follows the MOMS, reducing the number of f or loops in the algorithm and the computation time.

λ (k) = λ (k) - λ (

Applications

Figure 3.a shows a video of water generated by our DT model (not detailed here due to a lack of space, see [START_REF] Dubois | Modèle de Textures Dynamiques et décomposition par l'approche MCA[END_REF]). After our MCA decomposition scheme, we are able to retrieve the long term wave (fig. 3.b) and the local oscillations (fig. 3.c) used in the synthesis. This reinforces the choice of the chosen dictionary composed of the curvelet and local cosine transforms. Let us point out that the use of ATS enables a significant gain in computation time. Indeed, in average for one video sequence, the computation time is about 4 hours 30 (instead of 7h30), which leads to 131 days for the whole DynTex database.

Conclusion and prospects

This paper deals with the decomposition of DT in videos into different dynamical components. We show that the MCA algorithm is well suited for this decomposition in a well chosen basis, but suffers from significant computation time. We propose a new thresholding strategy which leads to a significant gain in the algorithm speed.

Other thresholding strategies are being studied to further improve this computation time. It is particularly necessary to develop strategies that take better into account our proposed model and the features of natural DT. The extracted components of DT can later be used as features for video retrieval applications.

Figure 1 .

 1 Figure 1. 2D+T slices of a dynamic texture: local oscillating phenomenon (2) and long range propagating wave (1).

Figure 2 .

 2 Figure 2. Two thresholding strategies leading to different evolutions of the threshold value (in one f or loop).

Figure 3 .

 3 Figure 3. MCA decomposition of a synthetic video (a) on the curvelet basis (b) and the local cosine basis (c)

Figure 4 .

 4 Figure 4. MCA decomposition of a real video (a) on the curvelet basis (b) and the local cosine basis (c)

This video and other results are visible at:http://mia.univ-larochelle.fr/demos/dynamic_textures/