Tony Barbay

Emilie Pecchi

Myriam Ducrocq

Nathalie Rouach

Frédéric Brocard

Rémi Bos
email: remi.bos@univ-amu.fr

Astrocytes regulate locomotion by orchestrating neuronal rhythmicity in the spinal network via potassium clearance

Keywords: Locomotion, Spinal cord, Astrocytes, Neuronal Oscillations, Potassium uptake, Kir4

INTRODUCTION

Mammalian locomotion relies on repeated sequences of muscle contractions triggered by a rhythmic central pattern generator (CPG) network, which is mainly located in the ventromedial part of the lumbar spinal cord [START_REF] Grillner | Current Principles of Motor Control, with Special Reference to Vertebrate Locomotion[END_REF][START_REF] Kiehn | Decoding the organization of spinal circuits that control locomotion[END_REF]. Activation of the spinal CPG network is triggered by descending inputs releasing neuromodulators such as glutamate, serotonin and dopamine. Several populations of CPG interneurons -V0, V2a and Hb9 -display conditional rhythmic oscillations in response to neuromodulators [START_REF] Grillner | Current Principles of Motor Control, with Special Reference to Vertebrate Locomotion[END_REF][START_REF] Kiehn | Decoding the organization of spinal circuits that control locomotion[END_REF]. No single population of ventromedial interneurons appears to act alone or to orchestrate the entire CPG pattern. The spinal rhythmogenesis emerges from the synchronization of individual neurons with intrinsic bursting properties [START_REF] Brocard | Do Pacemakers Drive the Central Pattern Generator for Locomotion in Mammals?[END_REF]. Despite decades of research, the functional organization of the locomotor CPG remains still unclear.

In the spinal locomotor CPG, physiological variation in extracellular K

+ ([K +

] e ) coincides with the emergence of the oscillatory pattern of intrinsic bursting neurons [START_REF] Brocard | Activity-Dependent Changes in Extracellular Ca2+ and K+ Reveal Pacemakers in the Spinal Locomotor-Related Network[END_REF], and thus powers up the motor output [START_REF] Bos | Kv1.2 Channels Promote Nonlinear Spiking Motoneurons for Powering Up Locomotion[END_REF][START_REF] Bracci | Extracellular K+ Induces Locomotor-Like Patterns in the Rat Spinal Cord In Vitro: Comparison With NMDA or 5-HT Induced Activity[END_REF]. At rest, [K + ] e is kept close to 3 mM in serum levels [START_REF] Kofuji | Potassium buffering in the central nervous system[END_REF]Verkhratsky et al., 2018). The maintenance of K + homeostasis is one of the crucial supportive functions mediated by astrocytes [START_REF] Ben Haim | Elusive roles for reactive astrocytes in neurodegenerative diseases[END_REF][START_REF] Sibille | The neuroglial potassium cycle during neurotransmission: role of Kir4.1 channels[END_REF]. In addition, to display a high resting K + conductance that facilitates the uptake of neuron released K + , astrocytes have a hyperpolarized resting membrane potential (RMP).

Both parameters rely on the activity of the weakly inwardly rectifying Kir4.1 K + channel, which in the nervous system is expressed exclusively in glial cells, with the highest expression in astrocytes [START_REF] Kelley | Kir4.1-Dependent Astrocyte-Fast Motor Neuron Interactions Are Required for Peak Strength[END_REF]. Astrocytic Kir4.1 channels have been described in many CNS regions, including the spinal cord [START_REF] Olsen | Functional expression of Kir4.1 channels in spinal cord astrocytes[END_REF][START_REF] Ransom | Biophysical and pharmacological characterization of inwardly rectifying K+ currents in rat spinal cord astrocytes[END_REF]. Studies using genetic, pharmacological and modeling approaches in the brain networks identified Kir4.1 as the main astrocytic inwardly rectifying K + channel regulating [K + ] e and thus influencing neuronal excitability [START_REF] Nwaobi | The role of glial-specific Kir4.1 in normal and pathological states of the CNS[END_REF][START_REF] Sibille | The neuroglial potassium cycle during neurotransmission: role of Kir4.1 channels[END_REF].

Astrocytes display ramified processes enwrapping synapses, placing them in an ideal position to (i) sense synaptic activity [START_REF] Panatier | Astrocytes Are Endogenous Regulators of Basal Transmission at Central Synapses[END_REF] and (ii) adjust network activity by releasing gliotransmitters [START_REF] Araque | Gliotransmitters Travel in Time and Space[END_REF][START_REF] Savtchouk | Gliotransmission: Beyond Black-and-White[END_REF]. Rhythmic oscillations are strongly affected in the brain networks when gliotransmission is genetically or pharmacologically modified [START_REF] Lee | Astrocytes contribute to gamma oscillations and recognition memory[END_REF][START_REF] Sheikhbahaei | Astrocytes modulate brainstem respiratory rhythm-generating circuits and determine exercise capacity[END_REF]. In the spinal motor network, the locomotor oscillatory rhythm is correlated with enhanced calcium (Ca

2+

) transients in astrocytes [START_REF] Broadhead | Bi-Directional Communication Between Neurons and Astrocytes Modulates Spinal Motor Circuits[END_REF], which likely triggers ATP release [START_REF] Witts | Adenosine-mediated modulation of ventral horn interneurons and spinal motoneurons in neonatal mice[END_REF], modulating excitatory synaptic transmission [START_REF] Carlsen | Purines released from astrocytes inhibit excitatory synaptic transmission in the ventral horn of the spinal cord[END_REF]. Thus, growing evidence point to the contribution of gliotransmission in modulating neuronal rhythmogenesis [START_REF] Montalant | Role of astrocytes in rhythmic motor activity[END_REF]. Astrocytes can also respond to neurotransmitters and neuromodulators [START_REF] Paukert | Norepinephrine Controls Astroglial Responsiveness to Local Circuit Activity[END_REF][START_REF] Rosa | Neuron-glia signaling in developing retina mediated by neurotransmitter spillover[END_REF] by modifying [K + ] e , which greatly impact brain oscillations (Bellot-Saez et al., 2017; Ding et al., 2016; Sibille et al., 2015). However, the mechanisms underlying the contribution of astrocytic K + homeostasis to rhythmogenesis remain incompletely understood.

Here we investigated whether astrocyte K + uptake modulates neuronal oscillations patterns in the spinal CPG network. We demonstrate that most of the ventromedial astrocytes are active during neuronal oscillations, and that the inwardly-rectifying Kir4.1 channels are crucial for maintaining neuronal oscillations, which ultimately influence the locomotor activity. This study places astrocytes as central elements of the spinal cord locomotor CPG.

RESULTS

Astrocytes respond to changes in extracellular ions underlying neuronal oscillations in the spinal CPG. Astrocytes from the ventromedial part of upper lumbar segments (L1-L2), the main locus of was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this preprint (which this version posted July 7, 2022. ; https://doi.org/10.1101/2022.07.07.498974 doi: bioRxiv preprint 4 the locomotor CPG [START_REF] El Manira | Dynamics and plasticity of spinal locomotor circuits[END_REF][START_REF] Kiehn | Decoding the organization of spinal circuits that control locomotion[END_REF], were recorded from transgenic mice expressing GFP under the control of the astrocytic Aldh1L1 promoter (Tsai et al., 2012) (Fig 1A). This spinal region contains interneurons endowed with two types of inherent membrane oscillations at a frequency range similar to stepping rhythms: (i) one is TTX-sensitive dependent on the persistent sodium current (INaP) [START_REF] Tazerart | The Persistent Sodium Current Generates Pacemaker Activities in the Central Pattern Generator for Locomotion and Regulates the Locomotor Rhythm[END_REF]

2+

] e ) (Brocard et al., 2013), (ii) the other is TTX-insensitive dependent on the Ca

2+

currents and triggered by a neuromodulator cocktail composed of 5-HT, dopamine and NMDA, in presence of the voltage-dependent sodium channels blocker, tetrodotoxin (TTX) [START_REF] Masino | TTX-resistant NMDA receptor-mediated membrane potential oscillations in neonatal mouse Hb9 interneurons[END_REF][START_REF] Wilson | Conditional Rhythmicity of Ventral Spinal Interneurons Defined by Expression of the Hb9 Homeodomain Protein[END_REF][START_REF] Ziskind-Conhaim | Persistent sodium current contributes to induced voltage oscillations in locomotor-related hb9 interneurons in the mouse spinal cord[END_REF]. This neuromodulator cocktail mimics the effect of descending inputs from the hindbrain for inducing a locomotor rhythmicity [START_REF] Grillner | Current Principles of Motor Control, with Special Reference to Vertebrate Locomotion[END_REF]. In recording conditions required to generate bursting cells, all astrocytes displayed a reversible depolarisation of their membrane potentials: (i) when [K + ] e was increased to 6mM and [Ca

2+

] e decreased to 0.9mM (Fig. 1 B-C) or (ii) when the neuromodulator cocktail was applied in presence of TTX (Fig. 1 D-E).

We observed that in absence of neuronal activity, neuromodulators increased [K + ] o to ~6mM (Fig. S1). To explore the temporal dynamics of the astrocytic response compared to neuronal oscillations, we performed dual recordings of a ventromedial Hb9 GFP+ interneuron which is known to display the two types of bursting properties [START_REF] Tazerart | The Persistent Sodium Current Generates Pacemaker Activities in the Central Pattern Generator for Locomotion and Regulates the Locomotor Rhythm[END_REF][START_REF] Ziskind-Conhaim | Persistent sodium current contributes to induced voltage oscillations in locomotor-related hb9 interneurons in the mouse spinal cord[END_REF] and an adjacent astrocyte from the upper lumbar segments (L1-L2) (Fig. 1F). In 13 pairs, astrocytic depolarization in response to the TTX-sensitive

[K + ] e /[Ca 2+
] e variations (Fig. 1 G) or the TTX-insensitive neuromodulator cocktail (Fig. 1H) either preceded (69%) or followed (31%) the onset of the neuronal rhythmic bursting of the adjacent GFP+ pacemaker interneurons (Fig. 1I), suggesting that astrocytes play an active role in spinal rhythmogenesis.

Enhanced astrocytic Ca 2+ transients occur during neuronal oscillations in the ventral spinal cord. To better locate and characterize the dialogue between neurons and astrocytes during spinal oscillations, we performed two-photon Ca

2+

imaging of neuronal and astrocyte signals in the locomotor CPG area. Mice were injected at birth with adeno-associated virus serotype 9 (AAV9) (Fig. S2A) designed to express GCaMp6f in astrocytic processes under the gfaABC1D promoter and jRGECO1a in neurons under the Syn.NES promoter (Fig. S2B). We simultaneously imaged the chromophores in lumbar slices (L1-L2) of post-natal mice (day [START_REF] Mu | Glia Accumulate Evidence that Actions Are Futile and Suppress Unsuccessful Behavior[END_REF][14][15][16]) and first confirmed that neuronal signals were prevented by TTX, in contrast to the signals recorded astrocyte processes that remain intact (Fig. S2C-D).

We next explored the spatio-temporal dynamics of the astrocytic transients and compared it to the neuronal transients. In response to changes in extracellular K

2+

transients during neuronal oscillations (Fig. 2A). Quantification showed that the occurrence of Ca

2+

transients preceded the neuronal oscillations in ~64% of astrocytes, whereas in ~36% of them the Ca

2+

transients occurred during neuronal oscillations (Fig. 2D). These data confirmed our electrophysiological dual recordings (Fig. 1I). We also observed that most of the astrocytes (~70%) showing Ca

2+

signal increases in response to ionic variations or perfusion of the neuromodulator cocktail were located in the ventromedial part of the spinal cord (Fig. 2E). Altogether, these data suggest that ventromedial astrocytes are functionally coupled with neuronal rhythmicity in the spinal CPG area.

The astrocytic Ca 2+ transients regulate the Kir4.1-mediated inwardly rectifying K + current.

+

] e in hippocampus (Wang et al., 2012a) and cerebellum (Wang et al., 2012b), we then investigated whether the increase in astrocytic Ca 2+ transients related to

was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

neuronal oscillations in the spinal CPG area (Fig. 2) stimulates K + uptake. We first recorded the passive membrane properties of the ventromedial GFP+ astrocytes from upper lumbar slices (Fig. 3A-B) and then isolated the Ba 2+ -sensitive Kir4.1 current underlying K + uptake in standard artificial cerebro-spinal fluid (aCSF) (Fig. 3C-D). We then switched to oscillatory aCSF by increasing [K + ] e to 6mM and reducing [Ca

2+

] e to 0.9mM, which leads to neuronal bursting (Fig. 1G and Fig. 2A-B) and intracellular astrocytic Ca 2+ transients (Fig. 2A and2C). In this condition, we observed that preventing the astrocytic Ca

2+

transients with BAPTA (30mM) inside the patch pipette significantly reduced the barium (Ba

2+

)-sensitive current driven by Kir4.1 channels (Fig. 3 E-F). These data strongly suggest that the increase in intracellular Ca 2+ from ventromedial astrocytes observed during neuronal oscillations modulates K + uptake via Kir4.1 channels.

Kir4.1 channels are expressed in astrocytes from the spinal locomotor CPG region. We next investigated whether Kir4.1 channels are expressed in the spinal locomotor CPG. Using Hb9-eGFP mice which express GFP+ interneurons with intrinsic bursting properties [START_REF] Tazerart | The Persistent Sodium Current Generates Pacemaker Activities in the Central Pattern Generator for Locomotion and Regulates the Locomotor Rhythm[END_REF][START_REF] Ziskind-Conhaim | Persistent sodium current contributes to induced voltage oscillations in locomotor-related hb9 interneurons in the mouse spinal cord[END_REF], we found that ventromedial GFP+ interneurons were enwrapped by Kir4.1 labeling, which is diffusely expressed in the grey matter of the upper lumbar segments (Fig. S3A). To confirm that Kir4.1 channels in the locomotor CPG area are exclusively expressed in glial cells with a highest expression in astrocytes, we used the Aldh1L1-eGFP astrocyte-specific reporter mice [START_REF] Cahoy | A Transcriptome Database for Astrocytes, Neurons, and Oligodendrocytes: A New Resource for Understanding Brain Development and Function[END_REF]. We examined co-expression of Aldh1L1-eGFP with immunolabeling of Kir4.1 channels and neuronal marker NeuN in lumbar slices. We observed that 100% of the GFP+ astrocytes expressed Kir4.1 channels contrary to NeuN+ cells, which lacked Kir4.1 staining (Fig. S3B-C).

The Ba 2+ -sensitive inwardly rectifying K + (Kir4.1) current is crucial for maintaining neuronal oscillations and locomotor-like activity in the CPG. We next studied the role of Kir4.1 channels in the lumbar rhythmogenesis. We first induced rhythmic oscillations in the GFP+ ventromedial interneurons from Hb9-eGFP mice in response to [K + ] e /[Ca 2+ ] e variations (Fig. 4A) or bath perfusion of the neuromodulator cocktail in presence of TTX (Fig. 4B). In both conditions, pharmacological blockade of Kir4.1 channels with Ba 2+ (100 µM) caused a shift in the spiking pattern from bursting to tonic firing in ~70% of the TTX-sensitive neuronal oscillations (Fig. 4C) or resulted in a cessation of bursting activity (~85%) of the TTX-insensitive neuronal oscillations (Fig. 4D). Interestingly, we noticed that before totally preventing the neuronal oscillations, Ba

2+

progressively decreased the rhythmic bursting frequency accompanied with an increase in burst amplitude and duration in both conditions (Fig. S4). We next confirmed the Ba 2+ effect on preventing neuronal oscillations at a larger scale by two-photon Ca

2+

imaging of cell populations. We observed a progressive loss of Ca 2+ oscillations in the vast majority of neurons in response to Ba 2+ in presence of the oscillatory aCSF (n=25/28) or the neuromodulator cocktail (n=7/9) (Fig. 4E-F). Bath application of Ba 2+ also induced a significant rise in amplitude of the astrocytic Ca 2+ signal in both conditions (Fig. 4G).

To confirm the functional role of the inwardly rectifying K + (Kir4.1) current in the integrated rhythmogenesis, we investigated the contribution of Kir4.1 in the locomotor rhythm-generating network by using ex vivo whole-mount spinal cords. Since rostral lumbar segments (L1-L2) have a more powerful rhythmogenic capacity than the caudal ones, we recorded locomotor-like activities from the contralateral L2 ventral roots (Fig. 5A) in response to ionic variations (Fig. 5B) or bath application of a neuromodulator cocktail composed of N-methyl-DL aspartate (NMA) and 5 hydroxytryptamine (5-HT) (Fig. 5C). In both conditions, Ba was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

Loss-of-function of Kir4.1 decreases the probability for ventromedial CPG interneurons to oscillate

To further explore the functional role of Kir4.1 channels in spinal rhythmicity, we performed their targeted loss-of function by using a short hairpin RNAs (shRNAs). We injected intrathecally at birth at T13-L1 level an AAV9 virus encoding the Kir4.1-shRNA with a eGFP reporter (Fig. 6A-B). The viral transfection led to a decrease of ~40% in Kir4.1 membrane protein expression in the lumbar spinal cord (Fig. 6C). Concomitantly, a strong expression of eGFP in the ventromedial part of the spinal cord was observed from T1 to L5-S1 (Fig. 6D, Fig. S5). We first examined the effect of Kir4.1-shRNA on glial and neuronal electrophysiological properties. In the virally transfected GFP+ astrocytes (Fig.

S6A-B), we observed in whole-cell configuration a more depolarized RMP (Fig. S6C), a higher input resistance (Fig. S6C), a marked change in the current-voltage (I-V) relationship and a reduced Ba 2+ sensitive current in mice transduced with Kir4.1-ShRNA compared to Ctrl-ShRNA mice (Fig. S6D-I).

We also observed that the RMPs of ventromedial interneurons surrounded by the virally transfected GFP+ astrocytes (Fig. 6E) from mice transduced with Kir4.1-ShRNA were overall more depolarized than the RMPs of interneurons from mice infected with Ctrl-ShRNA (Fig. 6E-F), suggesting that knockdown of Kir4.1 in astrocytes had a widespread impact on the excitability of neighbouring neurons.

We then tested the ability of the ventromedial interneurons to oscillate after the viral transfection of the spinal cord. We found a significant lower proportion of rhythmic bursting in ventromedial interneurons surrounded by GFP+ astrocytes in mice transduced with Kir4.1-ShRNA compared to Ctrl-ShRNA in response to both ionic variations (~24% vs 80%) (Fig. 6G and6I) or bath perfusion of the neuromodulator cocktail in presence of TTX (~ 23% vs 75 %) (Fig. 6H and6J). Altogether, these data demonstrate the pivotal role of astrocytic Kir4.1 channels in the oscillatory pattern of ventromedial interneurons from the CPG.

Loss-of-function of Kir4.1 slows down the in vivo locomotor pattern and decreases the locomotor performances. We then tested whether the knockdown of Kir4.1 in the spinal cord has a functional impact on the locomotor behaviors. We thus injected intrathecally at birth an AAV9 encoding either the Kir4.1-shRNA or the Ctrl-shRNA. From 12 to 18 days after the viral injection, we performed a set of behavioural locomotor tests on freely moving mice (Fig. 7A). We first used footprint analysis to evaluate the locomotor pattern (Fig. 7B). Mice transduced with Kir4.1-shRNA displayed an increase in both swing and stand phases compared to Ctrl-ShRNA mice (Fig. 7C-D) related to a slower speed of locomotion and a decrease in regularity index without any modification of the base of support (Fig. 7D). We next tested whether Kir4.1 channels also modulate locomotor behaviours in more challenging tasks. We thus assayed motor coordination using the rotarod and swimming forced test without practice sessions to avoid any compensatory learning mechanisms. Consistently, mice transduced with Kir4.1-shRNA failed to adapt to accelerated speed (Fig. 7E) and displayed a lower swimming performance (Fig. 7F). Importantly, we did not observe any modification of the motoneuronal soma size in mice transduced with Kir4.1-ShRNA compared to Ctrl-ShRNA mice (Fig. S7). In sum, the Kir4.1-mediated inwardly rectifying K + current appears to play a key role for locomotor coordination and the maintenance of the locomotor pattern in freely moving mice.

DISCUSSION

This study demonstrates that astrocytic regulation of extracellular K + plays a critical role in maintenance of neuronal rhythmogenesis in the spinal cord motor circuitry. We report that spinal astrocytes from neonatal mice display Ca We also demonstrated that knockdown of Kir4.1 decreases the ability of the ventromedial interneurons to oscillate. This perturbation results in an alteration of the locomotor pattern and in lower locomotor performances in challenging tasks.

was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

Functional coupling of astrocytic Ca 2+ signals and neuronal oscillations. Recent studies have highlighted unexpected contribution of astrocytic Ca 2+ signals in regulating rhythmic behaviours including respiration [START_REF] Sheikhbahaei | Astrocytes modulate brainstem respiratory rhythm-generating circuits and determine exercise capacity[END_REF], mastication [START_REF] Morquette | An astrocyte-dependent mechanism for neuronal rhythmogenesis[END_REF] and locomotion [START_REF] Broadhead | Bi-Directional Communication Between Neurons and Astrocytes Modulates Spinal Motor Circuits[END_REF]. However, it is still incompletely understood whether the increased astrocytic Ca

2+

transient is a prerequisite or a consequence of neuronal oscillations. Here, we reveal that ventromedial astrocytes depolarize and display an increase in Ca 2+ signals both before and in response to ions and neuromodulator changes related to neuronal oscillations. Our two-photon Ca

2+

imaging data reveal a functional coupling between spinal cord astrocytes and CPG interneurons. The simultaneous imaging of neuronal and astrocytic activity led to the characterization of distinct subsets of active astrocytes in the spinal CPG area. In one subset, the response precedes neuronal oscillation. This active role of astrocytes in rhythmicity has been suggested in the trigeminal sensorimotor circuit [START_REF] Morquette | An astrocyte-dependent mechanism for neuronal rhythmogenesis[END_REF] or in cortical areas where the increase in astrocytic Ca 2+ events precedes the switch to the slow-oscillation state [START_REF] Poskanzer | Astrocytes regulate cortical state switching in vivo[END_REF]. In another group, the responses are concomitant to neuronal bursting. In line with this, in Drosophila astrocyte Ca 2+ transients are driven by rhythmic firing of the octopaminergic neurons [START_REF] Ma | Neuromodulators signal through astrocytes to alter neural circuit activity and behaviour[END_REF]. A recent study also demonstrated such a dynamics in fish radial astroglia (analogs of the mammalian astrocyte), where the noradrenergic neuronal activity precedes the Ca

2+

wave observed in radial astroglia [START_REF] Mu | Glia Accumulate Evidence that Actions Are Futile and Suppress Unsuccessful Behavior[END_REF]. However, we cannot totally rule out that one astrocyte may belong to both groups. Altogether, our data highlight a bi-directional coupling between astrocytic Ca 2+ signal and neuronal oscillations.

The Ca 2+ -dependent K + uptake in spinal astrocytes. Astrocytic Ca 2+

transients are often associated to gliotransmission [START_REF] Araque | Gliotransmitters Travel in Time and Space[END_REF]). Here we propose that an alternative mechanism to the classical gliotransmission operates for spinal rhythmogenesis. Previous works demonstrated that GPCR-mediated Ca

2+

signalling in astrocytes is linked to an increase of K + uptake in hippocampus (Wang et al., 2012a) and cerebellum (Wang et al., 2012b). This astrocytic Ca Kir4.1 current from a U251 cell line [START_REF] Ratto | Squaring the Circle: A New Study of Inward and Outward-Rectifying Potassium Currents in U251 GBM Cells[END_REF]. Because (i) the locomotor-like activity is associated with [K + ] e homeostasis (Brocard et al., 2013), and (ii) the astrocytic K + uptake is activated by intracellular Ca 2+ transients (Wang et al., 2012a), we assume that the Ca 2+ dependent astrocytic K + homeostasis plays a key role in the spinal rhythmicity.

Astrocytic-dependent K + regulation of the spinal rhythmogenesis. The maintenance of K + homeostasis by astrocytes is crucial in modulating neuronal excitability [START_REF] Dallérac | How do astrocytes shape synaptic transmission? Insights from electrophysiology[END_REF][START_REF] Neprasova | High extracellular K(+) evokes changes in voltage-dependent K(+) and Na (+) currents and volume regulation in astrocytes[END_REF]. However, whether spinal astrocytes may exert a "ionostatic control" of neuronal bursting, as suggested by [START_REF] Ding | Changes in the composition of brain interstitial ions control the sleep-wake cycle[END_REF], is still unclear. Here, we evaluated the consequence of blocking the astrocytic inwardly rectifying K + (Kir4.1) channels on neuronal oscillations in the locomotor CPG. Blocking the Kir4.1-mediated astrocytic K + uptake with Ba 2+ (100 µM) [START_REF] Cui | Astroglial Kir4.1 in the lateral habenula drives neuronal bursts in depression[END_REF][START_REF] Djukic | Conditional Knock-Out of Kir4.1 Leads to Glial Membrane Depolarization, Inhibition of Potassium and Glutamate Uptake, and Enhanced Short-Term Synaptic Potentiation[END_REF][START_REF] Ransom | Biophysical and pharmacological characterization of inwardly rectifying K+ currents in rat spinal cord astrocytes[END_REF] decreases the frequency of neuronal oscillations until progressively preventing them. In line with this effect, injection of Kir4.1-ShRNA resulting in the decrease in Kir4.1 astrocytic membrane expression also significantly reduces the probability of driving neuronal oscillations. These results highlight the key role of astrocytic K + uptake in maintaining the neuronal oscillatory pattern. Although the astrocytic Kir4.1 channels are not homogeneously expressed among and within brain structures [START_REF] Higashi | An inwardly rectifying K1 channel, Kir4.1, expressed in astrocytes surrounds synapses and blood vessels in brain[END_REF], we showed a strong Kir4.1 expression in astrocytes enwrapping the ventromedial bursting interneurons and lamina IX motoneurons. This strategic distribution of Kir4.1 channels surrounding the bursting spinal neurons may be viewed as a powerful mechanism to rapidly modulate network rhythmicity.

Moreover, since glutamate tunes the CPG network by exerting a speed control of locomotor-like

was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this preprint (which this version posted July 7, 2022. ; https://doi.org/10.1101/2022.07.07.498974 doi: bioRxiv preprint 8 activity [START_REF] Talpalar | Dual-mode operation of neuronal networks involved in left-right alternation[END_REF] and that [K + ]e provides the driving force for glutamate uptake [START_REF] Nwaobi | The role of glial-specific Kir4.1 in normal and pathological states of the CNS[END_REF]Verkhratsky and Nedergaard, 2018) the effective K + uptake from the extracellular space through Kir4.1 is thus crucial for tuning the neuron oscillations. In line with this, previous works highlighted the importance of [K +

] e for rhythmogenesis in hippocampal (Jensen et al. 1994) or cortical [START_REF] Bellot-Saez | Astrocytic modulation of cortical oscillations[END_REF] networks. Furthermore, the increase in [K + ] e induced by neuromodulators may promote the shift between neuronal oscillatory states in cortical slices electrically silenced by TTX [START_REF] Ding | Changes in the composition of brain interstitial ions control the sleep-wake cycle[END_REF]. A computational work also demonstrated that extracellular K + dynamics can cause transition between fast tonic spiking and slow bursting in neocortical networks [START_REF] Frohlich | Slow state transitions of sustained neural oscillations by activity-dependent modulation of intrinsic excitability[END_REF] in the same range than the spinal locomotor network.

The ventromedial astrocytes regulate the locomotor pattern in vivo. A dense literature pointed out that during locomotion, mice display enhanced Ca 2+ signals in astrocytes of the cerebellum [START_REF] Nimmerjahn | Motor Behavior Activates Bergmann Glial Networks[END_REF][START_REF] Paukert | Norepinephrine Controls Astroglial Responsiveness to Local Circuit Activity[END_REF], visual cortex [START_REF] Paukert | Norepinephrine Controls Astroglial Responsiveness to Local Circuit Activity[END_REF], or somatosensory cortex [START_REF] Bojarskaite | Astrocytic Ca(2+) signaling is reduced during sleep and is involved in the regulation of slow wave sleep[END_REF][START_REF] Dombeck | Imaging Large-Scale Neural Activity with Cellular Resolution in Awake, Mobile Mice[END_REF]. On the other hand, silencing astrocyte Ca 2+ activity in brainstem with optogenetics or chemogenetics can modulate the rhythmic respiratory behaviour [START_REF] Gourine | Astrocytes Control Breathing Through pH-Dependent Release of ATP[END_REF][START_REF] Sheikhbahaei | Astrocytes modulate brainstem respiratory rhythm-generating circuits and determine exercise capacity[END_REF]. In this study, we used genetic tools with ShRNA to knockdowns Kir4.1 in the locomotor CPG and demonstrate that the astrocytic regulation of K + homeostasis plays a key role in controlling the locomotor speed and challenging locomotor tasks in vivo. Mice transduced with Kir4.1-ShRNA showed striking locomotor deficits compared to Ctrl-ShRNA mice. Kir4.1 had been reported to contribute to the maintenance of the soma size of large αmotoneurons and peak strength in adult mice [START_REF] Kelley | Kir4.1-Dependent Astrocyte-Fast Motor Neuron Interactions Are Required for Peak Strength[END_REF].

We demonstrated that the Further studies will be needed to decipher the importance for spinal rhythmicity of the astrocytic syncytium mediating K + buffering in the locomotor CPG.

was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

EXPERIMENTAL PROCEDURES

Further details and an outline of resources used in this work can be found in the Supplemental Procedures.

Mice. Two-photon Ca 2+ imaging. Two-photon excitation of Gcamp6f and jRGECO1a was simultaneously evoked with a laser tuned to 960 nm. Imaging was done at 30.5202 Hz. The microscope was equipped with two detection channels for fluorescence imaging. See the Supplemental Experimental Procedures for more details.

shRNA constructs. Specific shRNA sequence designed to knockdown Kir4.1 transcript was incorporated into an adeno-associated viral (AAV) vector (serotype 9), which features a H1 promoter to drive shRNA expression and a CAG promoter to drive eGFP expression for identification of transduced cells [START_REF] Cui | Astroglial Kir4.1 in the lateral habenula drives neuronal bursts in depression[END_REF]. See the Supplemental Experimental Procedures for more details.

Intrathecal vector delivery. A minimally-invasive technique was used to micro-inject adenoassociated viral (AAV) vectors into the T13-L1 intervertebral space. A total volume of 2 µL /animal was injected. See the Supplemental Experimental Procedures for more details.

Kir4.1 protein quantification. Kir4.1 expression was analyzed using the 12-230 kDa separation module (SM-W004 ProteinSimple) on an automated capillary western blotting system ('Jess' ProteinSimple). See the Supplemental Experimental Procedures for more details.

was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

Immunohistochemistry. was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. Oscillatory aCSF TTX+cocktail

Oscill. aCSF+ Ba 2+ TTX+cocktail+ Ba 2+ +Ba 2+

Figure 5 was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this preprint (which this version posted July 7, 2022. was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this preprint (which this version posted July 7, 2022. ; https://doi.org/10.1101/2022.07.07.498974 doi: bioRxiv preprint

  and 0.15 ± 0.01 Hz, respectively) (Fig.2A-B), which correlated with enhanced astrocytic Ca 2+ transients in processes (Fig.2A and 2C). Interestingly, we distinguished distinct subsets of astrocytic Ca 2+ signals. Some astrocytes showed increased Ca 2+ transients before the onset of the neuronal Ca 2+ oscillations, in contrast to others, which displayed Ca

2+(

  100 µM) slowed down the locomotor rhythm by increasing the locomotor burst duration and decreasing the burst frequency without apparent effect on burst amplitude (Fig 5B-D). We also observed a decrease in the cross-correlogram coefficient in presence of Ba 2+ related to a decreased rhythmic alternation (Fig 5E-F) confirming the role of Kir4.1 channels in modulating rhythmogenesis at the network level.

  in a transient decrease in [K + ] e . In our study, we provide for the first time evidence that a blockade of the Ca 2+ transients from ventromedial lumbar astrocytes significantly reduces the Ba 2+ -sensitive current mediated by Kir4.1. This result is in line with observations showing that menthol-induced Ca 2+ transients in astrocytes increases the Ba 2+ -sensitive

  . Indeed, we did not observe any modification of the motoneuronal soma size in mice transduced with Kir4.1-ShRNA compared to Ctrl-ShRNA mice.[START_REF] Tong | Astrocyte Kir4.1 ion channel deficits contribute to neuronal dysfunction in Huntington's disease model mice[END_REF] observed that the Kir4.1 expression decrease in the striatal network of a mouse model of Huntington disease, results in altered locomotor pattern[START_REF] Tong | Astrocyte Kir4.1 ion channel deficits contribute to neuronal dysfunction in Huntington's disease model mice[END_REF]. We did not observe any Kir4.1-ShRNA expression in brain or brainstem structures involved in the locomotor control. This result is in line with the restricted diffusion to the thoraco-lumbar segments of the AAV9-ShRNA injected intrathecally at birth in the lumbar segments[START_REF] Bos | Trpm5 channels encode bistability of spinal motoneurons and ensure motor control of hindlimbs in mice[END_REF]. Thus we assume that the behavioural consequence of Kir4.1 knockdown on locomotor performances is due to Kir4.1 decrease in the spinal locomotor networks.Overall this study defines the contours of a new concept for the spinal locomotor CPG. We propose that the astrocytic Ca 2+ transients which occurs during the neuronal oscillations likely maintains extracellular K + homeostasis, which in turn adjusts the locomotor pattern (Graphical abstract).

Figure 1 .

 1 Figure 1. Astrocytes respond to variations in [K + ] e and [Ca 2+ ] e related to neuronal oscillations in the spinal CPG. A. Confocal image of endogenous GFP from a lumbar slice of a P8 Aldh1L1-eGFP mouse. White inset represents the patch-clamp recording area of the ventromedial GFP+ astrocytes. The recording glass microelectrode is in white. CC stands for central canal, GM for grey matter and WM for white matter. B. Representative voltage trace of a GFP+ astrocyte in response to [K + ] e rise to

Figure 2 .

 2 Figure 2. Increase in astrocytic Ca 2+ transients is correlated to neuronal oscillations A. Top. Examples of neuronal jRGECO1a Ca 2+ transients (ΔF/Fo) oscillating in response to K + rise and Ca 2+ decrease (left) or in response to the neuromodulator cocktail in presence of TTX (right). Middle, bottom. Examples of the increase of the astrocytic Gcamp6f Ca 2+ signals (ΔF/F0) before (middle) or during (bottom) the neuronal oscillations (top) from the same field of view. B. Quantification of the mean amplitude (left), duration and frequency (right) of the neuronal jRGECO1a Ca 2+ transients in

Figure 3 .

 3 Figure 3. Spinal astrocytes display a Ba 2+ -sensitive Kir4.1 current modulated by intracellular Ca 2+ . A. Left. DIC image of a lumbar slice from a P8 Aldh1L1-eGFP mouse superimposed with the

Figure 4 .

 4 Figure 4. K + homeostasis maintenance through Kir4.1 channels is crucial for neuronal oscillations. A-B. Representative voltage traces of a lumbar GFP+ ventromedial interneuron from a P6 Hb9-eGFP mouse before (left) and during (middle) ionic variations ([K + ] e = 6mM, [Ca 2+ ] e = 0.9mM) on which Ba 2+ (100 µM) is added (right) (A) or in presence of TTX (left) and following application of the neuromodulator cocktail (middle) on which Ba 2+ is added (right) (B). C-D. Quantification of the proportion of GFP+ interneurons oscillating in response to ionic variations (C, left) or to the neuromodulator cocktail (D, left) and following bath application of Ba 2+ for more than 5 minutes (C-

Figure 5 .

 5 Figure 5. Modulation of astrocytic Kir4.1 channels alters the locomotor-like activity pattern. A. Schematic representation of the whole-mount spinal cord (ventral side up) with two contralateral recording glass electrodes. VRL2L stands for ventral root lumbar segment 2 left. VRL2R stands for ventral root lumbar segment 2 right. B-C. Extracellular recordings of alternating rhythmic activities of L2 segment ventral roots (integrated signals) in response to [K + ] e rise and [Ca 2+ ] e decrease (B, left) or in response to the neuromodulator cocktail (C, left) and in the presence (B-C, right) of Ba 2+ . D.

Figure 6 .

 6 Figure 6. Targeted decrease in Kir4.1 channels reduces the occurrence of neuronal oscillations. A. Schematics of the AAV vector engineered to overexpress shRNA or dominant-negative Kir4.1. H1, human H1 promoter; CAG, CMV early enhancer/chicken Actb promoter. B. Schematic representation of the experimental design. WT for wild-type, INs for interneurons and P for postnatal day. C. Left: Kir4.1 pseudo-gel images from Capillary Western Blot of lumbar segments from P14 intrathecally injected at birth with an adeno-associated virus (AAV9) encoding either a scramble shRNA (n = 5 mice) or a Kir4.1-targeting shRNA (n = 5 mice). One mouse per lane. Right: group mean quantification of the ~168 kDa band normalized to scramble-injected controls. D. Representative image of GFP in lumbar slices from P10 mice after intrathecal injection at birth of an adenoassociated virus (AAV9) encoding a Kir4.1-targeting shRNA (Kir4.1-ShRNA). E. DIC image of the ventromedial part of a lumbar slice and the corresponding one-photon GFP signal (right) of a P10 mouse injected with AAV9-Ctrl-ShRNA (left) or AAV9-Kir4.1-ShRNA (right). CC means central canal. Scale bars, 20µm. F. Quantification of the mean RMP (left), input resistance (middle) and cocktailevoked membrane depolarisation (right) of ventromedial interneurons from wild-type mice injected with AAV9 encoding for Ctrl-ShRNA (left, n = 18 neurons from 4 mice) or Kir4.1-ShRNA (right, n = 30 neurons from 5 mice). G-H. Representative voltage traces of one interneuron of a mouse injected with AAV9-Ctrl-ShRNA (left) or AAV9-Kir4.1-ShRNA (right) in response to ionic changes (E) or in response to the neuromodulator cocktail in presence of TTX (F). I-J. Proportion of oscillatory interneurons (blue) or not (grey) from mice injected at birth with an AAV9 encoding either a Luciferase shRNA (Ctrl-ShRNA, n = 4 mice) (left) or a Kir4.1-targeting shRNA (Kir4.1-ShRNA, n = 7 mice) (right) in presence of high [K + ] e and low [Ca 2+ ] e (H) or in presence of the neuromodulator cocktail + TTX (I). ns, no significance, **P < 0.01, ***P < 0.001 (two-tailed Mann-Whitney test for C and F, two-tailed Fisher test for I and J). Mean ± SEM. For detailed P values, see Source data file.

Figure 7 .

 7 Figure 7. Astrocytic Kir4.1 channels influence the locomotor behaviour. A. Schematic representation of the experimental design. WT for wild-type and P for postnatal day. B. Top. Bottom view of P18 mice injected at birth with AAV9 encoding either for the Ctrl-ShRNA (left) or the Kir4.1-ShRNA (right) freely walking on a glass platform (Catwalk). Bottom. Side view of the same P18 mice. C. Representative footfall diagrams during CatWalk locomotion of a Ctrl-ShRNA P18 mouse (blue, top) or Kir4.1-ShRNA P18 mice (green, bottom). The stance phase is indicated by horizontal bars and the swing phase by open spaces. RF for Right Forelimb, RH for Right Hindlimb, LF for Left Forelimb, LH for Left Hindlimb. D. Comparative quantification of the normalized step cycle phases (stance, swing) (left), regularity index (middle left), body speed (middle right) and hind limb base of support (right) between Ctrl-ShRNA mice (blue, n = 14 mice) and Kir4.1-ShRNA mice (green, n = 14 mice). Each circle represents an individual mouse. E. Latency to fall from a rod rotating at accelerated speed (4-40 rpm) during 300s of wild-type mice transduced either with the Ctrl-ShRNA (blue, n = 14 mice) or with Kir4.1-ShRNA (green, n = 14 mice). F. Left: Heatmaps illustrate the swimming activity of two wild-type mice transduced either with the Ctrl-ShRNA (top) or with the Kir4.1-shRNA (bottom). Scale bar, 10 cm. Middle: Comparison of the mean swimming distance (middle left) and the mean velocity (middle right) between Ctrl-shRNA (blue, n = 9 mice) and Kir4.1-shRNA (green, n = 9 mice)

  Figure 1

  Figure4was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.The copyright holder for this preprint (which this version posted July 7, 2022. ; https://doi.org/10.1101/2022.07.07.498974 doi: bioRxiv preprint

  Figure 6

  and triggered by a rise in [K

		+ ] e with a concomitant
	decrease in extracellular Ca 2+	levels ([Ca

  Transverse spinal cord sections at the lumbar L1-L2 level were processed for immunohistochemistry using antibodies against Kir4.1, NeuN. Tissue processing and staining are detailed in the Supplemental Experimental Procedures.

	Behavioral tests. Assessment of motor behaviour were performed on neonatal mice with three
	different tests: walking, rotarod and swimming. See the Supplemental Experimental Procedures for
	more details.
	Statistical Analysis. Group measurements were expressed as means ± S.E.M. All statistical analyses
	are indicated in Figure legends. The level of significance was set at p < 0.05. Statistical analyses were
	performed using Graphpad Prism 9 software. See the Supplemental Experimental Procedures for
	more details.

  mice. Each circle represents one individual mouse. Right: Percentage of mobility and immobility for Ctrl-shRNA mice (blue, n = 9 mice) and Kir4.1-shRNA mice (green, n = 9 mice) during the swimming forced test. ns, no significance, *P < 0.05, **P < 0.01, ***P < 0.001 (Mann-Whitney test for D, E right and F, Two-way ANOVA with Sidak's multiple comparisons test for E left). Mean ± SEM. For detailed P values, see Source data file.

ACKNOWLEDGMENTS

This work was mainly funded by the CNRS and "Fonds d'Investissement de l'INT jeunes chercheuses, jeunes chercheurs" (FI_INT_JCJC_2019) (to R.B.) and a small part by the Agence National de la Recherche Scientifique (CalpaSCI, ANR-16-CE16-0004) (to F.B.). We thank Ivo Vanzetta, Pascal Weber and Sebastien Roux for their technical advices in imaging sessions, Anne Duhoux for animal care, Cécile Brocard for genotyping and Jérémy Verneuil for providing the Matlab script. We also gratefully acknowledge Eduardo Gascon, Florence Jaouen, Catherine Lepolard and Ana Borges-Correia from Neuro-Vir platform of the Neuro-Bio-Tools facility (Institut de Neurosciences de la Timone, UMR 7289, Marseille, France) for their advices, support and assistance in the design and production of vectors used in this work. We also thank Geneviève Rougon for her critical insights on the manuscript.

AUTHOR CONTRIBUTIONS

DECLARATION OF INTERESTS

The authors declare no conflict of interest.


C Lapeyronie
email: cedric.lapeyronie@cea.fr

M.S Alfonso

B Viala

J.-H Tortai

Superior dielectric properties of epoxy-based photoresist thin film nanocomposites with carbon-coated Cu@C nanoparticles

Keywords: Metal Polymer Nanocomposites (MPCs), dielectric spectroscopy, nanoparticles, surface functionalization

Superior dielectric properties of epoxy-based photoresist thin film nanocomposites with carbon-coated Cu@C nanoparticles

C Lapeyronie, M Alfonso, B Viala, J-H Tortai

INTRODUCTION

In recent decades, the microelectronics community has shown great interest in high dielectric constant nanocomposite (high-k) for the implementation of new nanocomposite materials for integrated capacitors [START_REF] Shimoga | High-k Polymer Nanocomposite Materials for Technological Applications[END_REF][START_REF] Toor | Dielectric properties of ligand-modified gold nanoparticle/SU-8 photopolymer based nanocomposites[END_REF] . For instance, Metal Polymer Composites (MPCs) have received considerable attention due to their wide versatility to address the different needs and constraints of such applications [START_REF] Xu | High dielectric constant SU8 composite photoresist for embedded capacitors[END_REF][START_REF] Mendes-Felipe | High dielectric constant UV curable polyurethane acrylate/indium tin oxide composites for capacitive sensing[END_REF] . In these materials the filling volume fraction, chemical composition, homogeneity of dispersions and shape of the nanoparticles (NPs) dictate the dielectric properties.

Previous studies stated that MPCs following Percolation Theory can exhibit high permittivity value at the vicinity of percolation threshold [START_REF] Stauffer | Introduction to percolation theory[END_REF][START_REF] Yuan | Percolation of carbon nanomaterials for high-k polymer nanocomposites[END_REF] . However, the values of the reported dielectric losses are often irreconcilable to allow their practical applications [START_REF] Liao | A surfacemodified TiO 2 nanorod array/P(VDF-HFP) dielectric capacitor with ultra high energy density and efficiency[END_REF][START_REF] Cao | Mussel-inspired polydopamine functionalized silicon carbide whisker for PVDF composites with enhanced dielectric performance[END_REF][START_REF] Wang | Flexible multi-walled carbon nanotubes/polydimethylsiloxane membranous composites toward high-permittivity performance[END_REF][START_REF] Li | Dielectric behavior of a metal-polymer composite with low percolation threshold[END_REF] . In fact, percolative nanodielectrics usually present a large increase in conductivity causing high dielectrics losses and making them not eligible as dielectric film capacitors [START_REF] Wang | Flexible multi-walled carbon nanotubes/polydimethylsiloxane membranous composites toward high-permittivity performance[END_REF][START_REF] Li | Dielectric behavior of a metal-polymer composite with low percolation threshold[END_REF] . This latter undesirable effect is subordinate to the fact that nanoparticles tend to stay packed as aggregates and thus are complex to uniformly disperse in the polymeric matrix [START_REF] Liu | Nanoparticle Dispersion and Aggregation in Polymer Nanocomposites[END_REF][START_REF] Rishi | A thermal model to describe kinetic dispersion in rubber nanocomposites: The effect of mixing time on dispersion[END_REF] . Consequently, the achievement of a homogenous dispersion of NPs in a polymeric host is the crucial challenge to allow a fine tuning of these materials to combine high permittivity and low dielectric losses. For example, Lu et al. [START_REF] Lu | Synthesis and dielectric properties of novel high-K polymer composites containing in-situ formed silver nanoparticles for embedded capacitor applications[END_REF] drew the conclusion that metallic silver (Ag) nanoparticles incorporated in carbon black/polymer composites enhance the dielectric constant of nanocomposite with value of 2260 at 10 kHz with dissipation factor of only 0.45 at 3.7%wt. Dang et al. [START_REF] Dang | Novel Ferroelectric Polymer Composites with High Dielectric Constants[END_REF] have reported a percolative nanocomposite based on metallic nickel (Ni) nanoparticles randomly dispersed in PVDF showing a dielectric constant of 400 at 100 Hz and losses of 0.18 approaching percolation around 17%vol. Meeporn et al. [START_REF] Meeporn | Improved dielectric properties of poly(vinylidene fluoride) polymer nanocomposites filled with Ag nanoparticles and nickelate ceramic particles[END_REF] claimed that ceramic nickelated Ag-MLSNO/PVDF nanocomposites can be used as a high-k material for energy storage applications with a dielectric constant of 62 at 1 kHz and low losses of 0.027 at a nanoparticle/polymer volume fraction of 17%vol. However, the reported values in literature vary over a wide range depending on the size of the nanoparticles, degree of nanostructuring and filling volume fraction percentage. Furthermore, most of the presented devices are millimetre thick and cannot be considered as suitable candidates for integrated capacitors.

Regarding all previous works, nanocomposites based on photolithographic resists seem to be the best suited materials to fit the needs of the microelectronics community in thin films with high dielectric constant. Following after this highly potential approach, this work aims to establish a wafer-scale film fabrication process using commercial carbon-coated copper nanoparticles (Cu@C), embedded in epoxy-based photoresist SU8™, to obtain a 15 µm thick capacitor with 100. The particles used were firstly chosen for their carbon shell, which will prevent the oxidation of the metallic core and thus, preserve the electrical properties of Cu. Secondly, the shell allow a non-covalent surface functionalization onto its graphene-like structure with a pyrene-terminated agent [START_REF] Alfonso | Core-Shell Percolative Nanodielectric for High Voltage Integrated Capacitors Journées nationales sur les technologies émergentes en micro-nano fabrication[END_REF][START_REF] Takacs | New Approach to Closely Spaced Disordered Cobalt-Graphene Polymer Nanocomposites for Non-Conductive RF Ferromagnetic Films[END_REF] . The manufacturing process developed to obtain the nanocomposite thin films is subdivided into five steps: NPs powder deagglomeration, surface functionalization, dispersion into the polymeric resist, spin-coating and photo-developement of the formulated thin film nanocomposites, local gold electrode deposition. For the steps of deagglomeration, functionalization and dispersion, sono-mechanical treatments were performed [START_REF] Dieringa | Processing of Magnesium-Based Metal Matrix Nanocomposites by Ultrasound-Assisted Particle Dispersion[END_REF] . The dielectric properties of the formulated nanocomposite films were investigated by using broadband dielectric spectroscopy. Moreover, the effect of DC bias voltage on the dielectric properties was investigated. C-V loops highlighted a processable voltage window in which no evidence of electrical aging or dielectric breakdown was encountered. In the meantime, two mechanisms of electron field emission were observed as the filling volume fraction increases. The mentioned results were also modelled by using the percolation theory (PT) indicating a high dielectric constant of 124 in the vicinity of the percolation threshold (close to 3.2%vol).

Material and Methods

Chemicals

Nanopowders Cu@C with a nanoparticle mean diameter of 25 nm were purchased from Nanostructured & Amorphous Materials, Inc. Poly(styrene), Ω-(1-Pyrenyl)-Terminated ( 1.3) (PyrPS) supplied by Polymer Source was used as surface agent. Negative i-line epoxy photoresist SU8™2050, composed of epoxy resin, propylene carbonate, triaryl sulfonium initiator and cyclopentanone was supplied by Microresist Corp. Propylene glycol methyl ether acetate >99% (PGMEA) was purchased from Microposit™ EC Solvent.

Nanocomposites preparation

The aim of this manufacturing process is to produce film nanocomposites with a targeted thickness of 15 µm, in which nanoparticles are uniformly dispersed at different volume fractions (%vol). Thus, thin dielectric films are obtained through spin-coating deposition of formulated nanocomposites onto 4-inch Si Boron p-doped wafers (0.001-0.005 Ohm.cm) to make Metal-Insulator-Semiconductor (MIS) devices. Obtaining a homogeneous dispersion of nanopowders in high viscosity resist remains the main challenge of the nanofabrication process. Previous studies claimed that Van der Walls attraction and electrostatic repulsion are competing for the agglomeration of nanoparticles also during spin-coating deposition step. As a matter of fact, during the spin-coating step the NPs are driven into two directions enforced by two forces: (1) the centrifugation force that will align the particles radially and (2) the solvent evaporation force that will tend to stack particles vertically [START_REF] Ogi | Fabrication of a large area monolayer of silica particles on a sapphire substrate by a spin coating method Colloids and Surfaces A[END_REF] . The first force controls the thickness obtained via the rotation speed of the spinner, while the second one depends on the casting solvent vapour pressure in regards with temperature and humidity. To limit the packing issue of the NPs, we developed a nanoformulation procedure involving ultrasonication of the nanoparticles in the PGMEA solvent, which entails a non-covalent surface functionalization prior to films deposition.

The functionalisation step was performed by adding Polystyrene Pyrene-terminated (PyrPS) under bath sonication, in order to adsorb a thin insulating nanometric layer onto the Cu@C nanoparticles. This step was also used to improve the dispersibility of the nanoparticles in the SU8™ photoresist host as demonstrated by previous studies [START_REF] Alfonso | Enhanced dielectric properties of epoxy-based photoresist nanocomposites using carboncoated nickel nanoparticles for high voltage integrated capacitors[END_REF][START_REF] Takacs | Non -conductive ferromagnetic carbon-coated (Co, Ni) metal/polystyrene nanocomposites films[END_REF] .

Preliminary tests have given to the nanoparticles a concentration of 0.1 g/mL as the threshold limit to the achievement of a stable over time colloidal dispersion. Simultaneously, obtaining a targeted 15 µm thickness of the deposited nanocomposite films was achieved through coherent dilutions of the colloidal dispersion (Cu@C-PyrPS in PGMEA) and the photoresist. These dilutions allowed to maintain the same viscosity of the nanoformulations at different concentrations of nanoparticles. The complete fabrication of each nanocomposite consists in a five steps process as shown in Figure 1.

Step 1: Deagglomeration of Cu@C nanoparticles and surface functionalization with PyrPS in PGMEA in sonication bath Fisherbrand FB15055 at the power of 90 W. Nanoparticles and surface agent are added by small quantities, in alternation, to ensure good dispersion and functionalization. The totality of NPs powder is added in three times, as the PyrPS powder. Each addition of powder is followed by a 10 min sonication bath.

Step 2: Functionalized NPs are added into SU8™2050 photoresist and sono-mechanically dispersed by tip sonication for 30 minutes with QSONICA Sonicators Q500 at 100 W. In this step the SU8™2050 photoresist is diluted into a SU8™2010 photoresist.

Step 3: Spin-coating of 4 mL of nanocomposite resin onto a 4-inch wafer were performed by POLOS SPIN 200i at 1,500 rpm (with an acceleration of 5,000 rpm.s -1 ) for 30 seconds to obtain a 15 µm thick film.

Step 4: Pre-bake, UV exposure and bake are performed on the spin-coated nanocomposite film.

The two baking steps are performed with POLOS hotplate 200S (230 V AC ) at 95°C for 3 minutes and the UV exposure (λ = 365 nm) was done with a home-built mask aligner at a dose of 135 mJ/cm². Finally, the photodefinable nanocomposite is developed in PGMEA for 3 minutes.

Step 5: Deposition of 100 nm thick gold electrodes by using Physical Vapor Deposition (PVD) with PLASSYS Evaporation HV/UHV and a home-built mask for the implementation of MIS devices. Film thickness was measured for each capacitor with a stylus profilometer (Bruker DektakXT).

Characterizations

To ensure the structure of the as received carbon-coated nanoparticles, Raman spectroscopy was performed on the raw powder. For this purpose, a beam of λ=532 nm was used to verify the absence of copper(II) oxide (CuO) and the nature of the carboneous shell coating the nanoparticles [START_REF] Ebnesajjad | Surface and Material Characterization Techniques Handbook of Adhesives and Surface Preparation[END_REF] . Moreover, the morphology and chemical composition of the nanoformulated nanocomposite films were analysed by SEM/EDS cross sectional images and elemental mapping with ZEISS GeminiSEM. These characterisations allow to verify the dispersion homogeneity of nanoparticles in the overall thickness of films and the effective chemical composition of the formulated films.

The dielectric behaviour of the nanoformulated nanocomposites thin films was investigated by using broadband dielectric spectroscopy (10 2 -10 6 Hz) at room temperature using Novocontrol Alpha series ZG2 through a sinusoidal stimulation of ±3V AC . The effects of DC voltage on the C-V and I-V characteristics were analysed by using Aixacct TF2000E at the frequency reference of 5 kHz. These measurements aimed to investigate the ageing, the occurrence of dielectric breakdown and the influence of NPs amount on the conduction mechanisms with an imposed DC bias voltage. Furthermore, to facilitate the comparison of these features, the obtained data were standardized over true electrodes thicknesses and surfaces.

RESULTS AND DISCUSSION

Nanocomposites structure a) Raman spectroscopy

In order to verify the structure of the carbon shell and its integrity during the deagglomeration step, Raman spectroscopy was performed on sono-mechanically dispersed as-received Cu@C nanoparticles. The damaging of this protective shell during the manufacturing process could lead to the oxidation of the metallic copper core that can worsen the dielectric properties of nanocomposites. It can be noted that the thin carbon shell may be deteriorated also by the power of the beam used. For this reason, different laser powers were used to investigate the carbon structure. Firstly, the raw nanoparticles were excited with a beam power of 0.2 mW at a wavelength of 532 nm. The result shown in Figure 2.a presents the characteristic peaks of CuO which can be seen at 290 cm -1 , 340 cm -1 and 630 cm -1 [START_REF] Xu | Raman spectra of CuO nanocrystals[END_REF] . Furthermore, the specific peaks for the graphene-like carbon [24] located at 1587 cm -1 (G band) and 2700 cm -1 (2D band) are still visible, suggesting that the fragile carbon shell was partially destroyed due to the beam power. Thus, in order to avoid this damaging effect, the measurement was performed on another sample of the same composition at the same wavelength (532 nm) but at a lower laser power of 0.01 mW. In this case, Raman spectrum (Figure 2.b) does not reveal CuO peaks while the characteristic G band and 2D band are more intense. It can be concluded that the ultrasonicated as-received NPs exhibit no detectable oxidation and that the morphology of the carbon shell corresponds to a graphene-like structure. Despite the presence of a D band indicating the presence of defects inside the graphene crystalline structure, the carbon shell is efficient to protect the metal core from oxidation. Moreover, the widen of the 2D band and the ratio of specify that we do not have a monolayer of graphene.

b) Morphology of the nanocomposite films

To reach a manufacturing processing level, achieving a homogeneous dispersion of nanoparticles along the whole film thickness is essential. To ensure this goal, cross-sectional SEM micrograph coupled with EDS elemental mapping were performed on previously dielectric characterized MIS devices and are shown in Figure 3.

Dielectric characterization a) Dielectric spectroscopy

The dielectric behaviour of the (Cu@C)-PyrPS//SU8 (MIS) devices were characterized using a sinusoidal stimulation of 3 V AC between 10 2 Hz and 10 6 Hz at room temperature. The frequency dependence of the characteristic dielectric features is shown in Figure 4.

The results have been averaged over 20 capacitors. Sampling on different locations of the deposited films on the same sample allowed to verify the distribution of Cu@C nanoparticles on it. No significant variation of the dielectric properties was detected confirming an equal distribution in the entire surface of the films. As frequently reported in literature, high-permittivity is often associated to high dielectric losses. Phase shift response was analysed to ensure the capacitive behaviour of formulated nanocomposites. Figure 4.a shows no significant variation of the phase angle with the volume fraction, up to 2.4%vol. In details, the phase angle remains close to -90° (pure capacitive behaviour) in the whole frequency range Hence, in this condition, the device can be modelled as a CPE (Constant Phase Element) at low volume fraction (lesser than 2.4%vol) and a RC parallel circuit exhibiting a typical frequency dependence of phase shift at higher volume fraction [START_REF] Gompf | Impedance spectroscopy and equivalent circuits of metal-dielectric composites around the percolation threshold[END_REF] . Indeed, for the formulation at 3.0%vol of Cu@C the phase shift is close to -60° (mainly capacitive behaviour) at high frequencies ( 1 kHz) then abruptly rises close to 0° (resistive behaviour) at low frequency. As shown in Figure 4.b, dielectric losses increase with volume fraction of Cu@C NPs. Nonetheless all the devices present losses inferior to the threshold value of 1 between 400 Hz and 10 6 Hz. However (Cu@C)-PyrPS//SU8 3.0%v

shows an increase of below 400 Hz with a maximum value of 4.30. This critical variation of losses is in agreement with the previously discussed phase shift frequency dependence. It can be attributed to the low inversion of electric field applied that facilitates charges mobility, thus, preventing the storage of charges. The frequency dependence of AC conductivity is shown in Figure 4.c. A linear response of AC conductivity was measured for all formulated nanocomposites except for the highest loaded composite which exhibits a constant value of AC conductivity at low frequency, typical of a resistive behaviour. Finally, it is shown in Figure 4.d an increment of the relative permittivity of the formulated nanocomposites as the volume fraction increases. The highest permittivity obtained at the reference frequency value of 5 kHz was measured for the sample at the highest concentration, with a permittivity value of 124. This value is one order of magnitude higher of pure SU8™ polymer. In Table 1 below are reported the values of the previously discussed dielectric parameters at the reference frequency of 5 kHz. This variation of permittivity could be explained by the Maxwell-Wagner-Sillars theory (MWS) [START_REF] Van Beek | The Maxwell-Wagner-Sillars effect, describing apparent dielectric loss in inhomogeneous media[END_REF][START_REF] Perrier | Polystyrene-glass bead composites: Maxwell-Wagner-sillars relaxations and percolation[END_REF] . The MWS theory also known as interfacial polarization takes place when two phases present an and different. Under the influence of an external electric field, electrical charges accumulate at the interface between the matrix and the fillers. In this study, the charges accumulate at the interface between the SU8™ and the functionalized (Cu@C)-PyrPS.

Consequently, increasing the filling volume fraction of nanoparticles rise the quantity of charges inside the material leading to an enhancement of capacitance, and thus relative permittivity.

However, this is only true before electrical percolation. Once electrical percolation is reached current can flow through the material and the capacitance drops while the losses rise drastically.

The results are also supported by the percolation theory stating that permittivity and losses follow a power law with an exponential increase at the vicinity of the percolation threshold [START_REF] Yuan | Percolation of carbon nanomaterials for high-k polymer nanocomposites[END_REF] .

Indeed, as the number of nanoparticles in the matrix increases, the interparticular distance lowers easing conduction mechanisms. Considering the values presented in Table 1 the variation of all four dielectric parameters suggests that none of the presented nanocomposites reached the percolation threshold. The large variation of permittivity between 2.4%vol and 3.0%vol on the contrary seems to indicate percolation threshold is not reached yet.

By Comparing the obtained experimental results with the literature, the capacitive nanocomposites produced does not exhibit giant permittivity in the proximity of percolation threshold. However, at the reference frequency of 5 kHz the dielectric losses is 0.65. This obtained value for the highest capacitive nanocomposite (3.0%vol) is not so low but still usable in practical applications. As a comparison, Wang et al. [START_REF] Wang | Flexible multi-walled carbon nanotubes/polydimethylsiloxane membranous composites toward high-permittivity performance[END_REF] presented PDMS filled with carbon nanotube with of 60 and of 10 (@ 10 kHz) for MWCNTs/PDMS 2%wt and Cao et al. [START_REF] Cao | Mussel-inspired polydopamine functionalized silicon carbide whisker for PVDF composites with enhanced dielectric performance[END_REF] showed a SiC-PVDF 20%wt nanocomposite with of 200 and of 8 (@ 5 kHz). In consequence, our most charged formulation presents a direct improvement of nanocomposite thin film, as capacitor, with high permittivity and low losses.

b) Percolation Theory and percolation threshold estimation

The value of percolation threshold was estimated by using the generalized power laws of percolation as shown below in equation 1 and 2. Equation 1 details the variation before percolation threshold while equation 2 details the variation after percolation threshold:

(eq. 1)

(eq. 2)

Where is the effective relative permittivity, is the relative permittivity of the polymeric matrix, is the effective conductivity, is the conductivity of the matrix, is the conductivity of a nanoparticle, and are the critical exponents for permittivity and conductivity respectively. In Figure 5 is shown the obtained values at 5 kHz of AC conductivity and relative permittivity with the fit obtained with the percolation theory power laws. agreement with what is reported in literature although these values slightly vary according to the specific conductivity of nanostructured system [START_REF] Yacubowicz | Dielectric behavior of carbon black filled polymer composites[END_REF][29][START_REF] Clarkson | Electrical conductivity and permittivity measurements near the percolation transition in a microemulsion[END_REF] . In agreement with the estimation of percolation threshold the highest loaded sample of 3.0%vol displays all the dielectric features of a classic behaviour of a near percolated system. That is why samples at higher volume fraction

were not investigated in this study.

c) Effect of Bias DC voltage on dielectric properties

The dielectric responses of the formulated Cu@C based nanocomposites in response to an applied DC electric field obtained with AIXACCT TF2000E are reported on Figure 6. In details, the maximum value of sustained DC electric field is represented for each nanocomposite. It is worthy to note that above these reported values, the conduction mechanisms of charges transport increase significantly turning the devices into highly leaky capacitors. As a matter of fact, above these values it is prevented to make measurements with this technique due to the abrupt increase of dissipative current.

The obtained relative permittivity values obtained through C-V loop measurements are in accordance with the previously characterized ones obtained by dielectric spectroscopy (@ 5 kHz) as shown in Figure 6.a. No variations of permittivity are visible on the range of electric field applied. DC voltage do not seem to have an impact on the polarisation of the material. However, the sustained DC voltage is dependent of the filling volume fraction. Particularly, the high loaded nanocomposite (Cu@C)-PyrPS//SU8 3.0%vol can stand an electric field of 6.01 kV/cm while the (Cu@C)-PyrPS//SU8 0.8%vol can withstand an electric field of 33.88 kV/cm.

The effects of a DC bias electric field are highlighted in the evolution of dielectric losses as shown in Figure 6.b. Indeed, for the formulation at 3.0%vol the dielectric losses response assumes a flat trend with a value of 0.68, in accordance to dielectric spectroscopy, at low applied DC electric field up to the threshold value of 3.51 kV/cm where the dielectric losses suddenly increase leading to a leaky capacitor. This effect is present in all formulated nanocomposites with the DC electric field threshold value decreasing with the increase of volume filling fraction. In order to evaluate the conduction mechanisms involved in this dramatically increase of dielectric losses under the application of an DC electric field, the charge transport regimes were investigated. Figure 7.a. shows the non-linear dependence of current density under DC applied electric field, following the same trend as dielectric losses.

A greater level of understanding can be achieved through the representation of logarithm of current density over electric field as a function of the inverse of applied electric field [START_REF] Zhang | The Role of Field Electron Emission in Polypropylene/Aluminum Nanodielectrics Under High Electric Fields[END_REF][START_REF] Ikuno | Electron transport properties of Si nanosheets: Transition from direct tunneling to Fowler-Nordheim tunneling[END_REF] . This The conduction mechanisms which takes place in the material are dependant of the nanostructured system. In details, the mobility of charges that flow through the nanofillers is function of the distance between them and thus depending on their distribution and quantity. Indeed, at low applied DC electric field the energy given to the charges is enough to go through small energy barrier. As a result, the displacement of charges will only be on close fillers (Direct Tunnelling).

However, above the threshold E Trans determined by the inflection of the curves as shown in Thus, with the increase of volume filling fraction the energy barrier length through the nanofillers decrease with the occurrence of the Fowler-Nordheim tunnelling at lower applied DC electric field. The obtained E Trans values determined for each nanocomposite is summarized in Table 2.

CONCLUSION

This article presents a reliable fabrication path for the achievement of homogeneous Metal Polymer Composites (MPCs) thin films based on Cu@C nanoparticles embedded in SU8™ photoresist with a controlled thickness of 15 µm. Raman spectroscopy performed on the asreceived Cu@C nanoparticles showed the graphene-like structure necessary for the surface functionalization by Polystyrene Pyrene terminated (PyrPS). The dielectric properties determined by broadband dielectric spectroscopy showed an 31 times higher than pure SU8™ with reasonable losses of 0.65 at 5 kHz for the highest filled formulation (3.0%vol). The Percolation Theory used on the dielectrical parameters allowed to establish the percolation threshold of the system to be at the vicinity of 3.2%vol. Superior capacitive behaviour was observed for the (Cu@C)-PyrPS//SU8 3.0%vol up to an applied DC electric field of 3.51 kV/cm and no breakdown appeared until 6.01 kV/cm. Finally, it was observed two conduction mechanisms depending on the intensity of the electric field: Direct tunneling and Fowler-Nordheim tunneling.

Figure 1 :

 1 Figure 1 : Schematic of nanocomposite fabrication from commercial nanoparticles to the measurement of electrodes thickness.

Figure 2 :

 2 Figure 2 : Raman analysis of sono-mechanically dispersed as-received Cu@C nanoparticles at λ = 532nm and at different powers. Raman spectrum at a beam power of (a) 0.2 mW and (b) at 0.01 mW.

Figure 3 .

 3 Figure3.a presents a cross-sectional micrograph of the films, cut along the diameter of the circular electrodes. The images in Figure3show a low surface roughness with a highly nanostructured nanoparticles distribution, with different NPs size and shape in the overall film thickness. Moreover, a thickness of 15 µm film was measured, agreeing with the profilometry technique. This further elemental characterization confirms the efficiency of the sono-dispersion process on the homogenisation of the functionalised nanoparticles in the polymeric host (Figure3 b and c).

Figure 3 :

 3 Figure 3: SEM micrograph coupled with EDS elemental mapping of (Cu@C)-PyrPS//SU8 2.4%vol. (a) Cross-sectional SEM micrograph of the targeted 15µm film thickness, (b) EDS elemental mapping superimposed to the SEM micrograph and (c) EDS elemental mapping.

Figure 4 :

 4 Figure 4 : Frequency dependence of the (a) phase angle , (b) dielectric losses expressed as , (c) AC conductivity and (d) relative permittivity of (Cu@C)-PyrPS//SU8 nanocomposites with different filling volume fraction.

Figure 5 :

 5 Figure 5 : Percolation theory applied to the experimental values. Fit of experimental data at 5 kHz and 3 VAC on: (a) Conductivity, (b) Relative permittivity

Figure 6 :

 6 Figure 6: (a) Relative permittivity and (b) losses as as function of DC electric field at 5 kHz for formulated (Cu@C)-PyrPS//SU8 nanocomposite thin films

  representation (Figure 7.b) allows to distinguish a minimum value that correspond to a transition between two different conduction mechanisms. These phenomena are the Direct Tunnelling and Fowler-Nordheim Tunnelling conduction.

Figure 7 :

 7 Figure 7: (a) Current density as function of DC electric field, (b) Logarithm of current density over DC electric field as a function of the inverse of DC electric field at 5 kHz for formulated (Cu@C)-PyrPS//SU8 nanocomposite thin films

Figure 7 .

 7 Figure 7.b, charges which are intrinsic of the metallic nanofillers are emitted on long distances (Fowler-Nordheim Tunnelling) brutally increasing the current density of the nanocomposites.

Table 1 :

 1 Dielectric properties of the (Cu@C)-PyrPS//SU8 nanocomposites measured at 5 kHz and 3 VAC

		Ψ (°)	σ (S/m)		tan δ	εr
	SU8	-89.539	1.026 x 10	-8	0.0089	4.053
	0.8%v	-86.091	1.309 x 10	-7	0.0683	6.697
	1.2%v	-79.266	5.444 x 10	-7	0.1896	10.046
	2.4%v	-73.880	1.319 x 10	-6	0.2891	15.920
	3.0%v	-56.762	2.294 x 10	-5	0.6561	123.669

Table 2 :

 2 Values of transition electric field between Direct tunnelling and Fowler-Nordheim tunnelling for all formulated nanocomposites

	@ 5 kHz	0.8%v		1.2%v		2.4%v		3.0%v
	1/ETrans (cm/MV)	62.008		128.016		174.910		221.888
	ETrans (MV/cm)	1.613 x 10	-2	7.812 x 10	-3	5.717 x 10	-3	4.507 x 10	-3

AKNOWLEDGEMENT

This work was funded by the French IPCEI NANO 2022 Murata program and was partly supported by PTA (Upstream Technological Platform), cooperated by CNRS RENATECH and CEA Grenoble, France. The Raman spectroscopy was performed by LE Van-Hoan (DRT/LETI/DPFT/SMCP/LPMS) CEA Grenoble, France.