Karima Ait Ouares

Marco Canepari
email: marco.canepari@univ-grenoble-alpes.fr

The origin of physiological local mGluR1 supralinear Ca 2+ signals in cerebellar Purkinje neurons

In mouse cerebellar Purkinje neurons (PNs), the climbing fibre (CF) input provides a signal to parallel fibre (PF) synapses triggering PF synaptic plasticity. This signal is given by supralinear Ca 2+ transients, associated with the CF synaptic potential and co-localised with the PF Ca 2+ influx, occurring only when PF activity precedes the CF input. Here, we unravel the biophysical determinants of supralinear Ca 2+ signals associated with paired PF-CF synaptic activity. We used membrane potential (V m ) and Ca 2+ imaging to investigate the local CF-associated Ca 2+ influx following a train of PF synaptic potentials, in two cases: 1. when the dendritic V m is hyperpolarised below the resting V m ; and 2. when the dendritic V m is at rest. We found that supralinear Ca 2+ signals are mediated by type-1 metabotropic glutamate receptors (mGluR1s) when the CF input is delayed by 100-150 ms from the first PF input in both cases. When the dendrite is hyperpolarised only, however, mGluR1s boost neighbouring T-type channels providing a mechanism for local coincident detection of PF-CF activity. The resulting Ca 2+ elevation is locally amplified by saturation of endogenous Ca 2+ buffers produced by the PF-associated Ca 2+ influx via the mGluR1-mediated non selective cation conductance. In contrast, when the dendritic V m is at rest, mGluR1s increase dendritic excitability by inactivating A-type K + channels, but this phenomenon is not restricted to the activated PF synapses. Thus, V m is likely a crucial parameter in determining PF synaptic plasticity and the occurrence of hyperpolarisation episodes is expected to play an important role in motor learning.

Significance statement

In Purkinje neurons, parallel fibre synaptic plasticity, determined by coincident activation of the climbing fibre input, underlies cerebellar learning. We unravel the biophysical mechanisms allowing the CF input to produce a local Ca 2+ signal exclusively at the sites of activated parallel fibres. We show that when the membrane potential is hyperpolarised with respect to the resting membrane potential type-1 metabotropic glutamate receptors locally enhance Ca 2+ influx mediated by T-type Ca 2+ channels and that this signal is amplified by saturation of endogenous buffer also mediated by the same receptors. The combination of these two mechanisms is therefore capable of producing a Ca 2+ signal at the activated parallel fibre sites, suggesting a role of Purkinje neuron membrane potential in cerebellar learning.

Introduction

In cerebellar Purkinje neurons (PNs), short-and long-term synaptic plasticity of the parallel fibre (PF) inputs can be induced by pairing PF excitatory synaptic potentials (EPSPs) with a climbing fibre (CF) EPSP [START_REF] Wang | Coincidence detection in single dendritic spines mediated by calcium release[END_REF][START_REF] Brenowitz | Associative short-term synaptic plasticity mediated by endocannabinoids[END_REF][START_REF] Safo | Endocannabinoids control the induction of cerebellar LTD[END_REF]. These forms of plasticity, that are believed to underlie associative motor learning and control behaviours [START_REF] Ito | Cerebellar long-term depression: characterization, signal transduction, functional roles[END_REF], are homosynaptic and they require local Ca 2+ elevation at the site of activated PF synapses. Precisely, the Ca 2+ transient triggered by a CF-EPSP alone is not local [START_REF] Knöpfel | Climbing Fibre Responses in Olivo-cerebellar Slice Cultures. II. Dynamics of Cytosolic Calcium in Purkinje Cells[END_REF][START_REF] Miyakawa | Calcium transients evoked by climbing fiber and parallel fiber synaptic inputs in guinea pig cerebellar Purkinje neurons[END_REF][START_REF] Canepari | Dendritic spike saturation of endogenous calcium buffer and induction of postsynaptic cerebellar LTP[END_REF][START_REF] Ouares | Two Distinct Sets of Ca 2+ and K + Channels Are Activated at Different Membrane Potentials by the Climbing Fiber Synaptic Potential in Purkinje Neuron Dendrites[END_REF] since it is caused by a depolarising transient, originating in the soma and in the initial dendritic segment, that spreads to distal dendrites to open voltage-gated Ca 2+ channels (VGCCs). When a CF-EPSP occurs after PF activity, the associated Ca 2+ transient is larger than the summation of the two Ca 2+ transients triggered by PF and CF inputs alone, and it is therefore referred as "supralinear" Ca 2+ signal [START_REF] Brenowitz | Associative short-term synaptic plasticity mediated by endocannabinoids[END_REF]. However, in contrast to the Ca 2+ transient associated with an unpaired CF-EPSP, the supralinear Ca 2+ signal associated with paired PF and CF inputs is localised exclusively at the site of activated PF synapses.

The ability of a spread physiological signal to trigger a local signal, in combination with synaptic activity, exclusively at the sites of activated synapse, is a crucial requirement for coincident detection and associative plasticity in many systems. In hippocampal and neocortical pyramidal neurons, synchronous action potentials and excitatory synaptic activity can potentiate activated synapses (Debanne, 2001). In this case, action potentials transiently depolarising the dendrites can provide a signal localised at activated synapses by unblocking NMDA receptors from Mg 2+ [START_REF] Ascher | Electrophysiological studies of NMDA receptors[END_REF]. In the case of PF synaptic plasticity induced by coincident CF inputs, however, the underlying biophysical mechanism does not involve NMDA receptors but instead type-1 metabotropic glutamate receptors (mGluR1s) which are locally activated by glutamate release from PF terminals [START_REF] Hartell | Induction of cerebellar long-term depression requires activation of glutamate metabotropic receptors[END_REF][START_REF] Wang | Coincidence detection in single dendritic spines mediated by calcium release[END_REF][START_REF] Brenowitz | Associative short-term synaptic plasticity mediated by endocannabinoids[END_REF][START_REF] Safo | Endocannabinoids control the induction of cerebellar LTD[END_REF]. Since mGluR1 activation is not voltage-dependent, the fundamental question is to understand how a CF-EPSP, that alone generates a depolarisation and a Ca 2+ influx everywhere in the dendrite, can trigger a strong localised Ca 2+ elevation, in combination with mGluR1 activation, exclusively at the site of activated PFs.

In a recent study, we have demonstrated that the dendritic depolarisation produced by a CF-EPSP activates two types of VGCCs, namely T-type and P/Q-type VGCCs, and that the activation of both channels is determined by the dendritic membrane potential (V m ) at the beginning of the CF-EPSP (Ait [START_REF] Ouares | Two Distinct Sets of Ca 2+ and K + Channels Are Activated at Different Membrane Potentials by the Climbing Fiber Synaptic Potential in Purkinje Neuron Dendrites[END_REF]. Specifically, at initial hyperpolarised V m , the dendritic Ca 2+ transient is largely mediated by T-type VGCCs while activation of A-type voltage-gated K + channels limits the opening of P/Qtype VGCCs. In contrast, at initial depolarised V m , T and A channels are inactivated and the larger dendritic depolarising transient activates P/Q-type VGCCs that mediate Ca 2+ spikes. It was also shown that both T-type VGCCs [START_REF] Hildebrand | Functional coupling between mGluR1 and Cav3.1 T-type calcium channels contributes to parallel fiber-induced fast calcium signaling within Purkinje cell dendritic spines[END_REF][START_REF] Isope | Contributions of T-type voltage-gated calcium channels to postsynaptic calcium signaling within Purkinje neurons[END_REF] and P/Q-type VGCCs [START_REF] Otsu | Activity-dependent gating of calcium spikes by A-type K+ channels controls climbing fiber signaling in Purkinje cell dendrites[END_REF] can be boosted by mGluR1 activation, providing two potential biophysical mechanisms underlying localised supralinear Ca 2+ signals that are required for coincident detection and PF synaptic plasticity.

In the present study we addressed the question of how a CF-EPSP can generate a supralinear Ca 2+ signal exclusively at the sites of activated PF synapses. We used a protocol of moderate PF stimulation mimicking a physiological burst to reveal the biophysical mechanism that permit a CF-EPSP to trigger a localised signal at the site of activated PF synapses in realistic scenarios. We used ultrafast V m and Ca 2+ imaging, using indicators of different affinity and a series of selective pharmacological manipulations and we performed a detailed analysis to elucidate the different mechanisms underlying supralinear Ca 2+ signals under different conditions.

Materials and methods

SLICE PREPARATION, SOLUTIONS, ELECTROPHYSIOLOGY AND PHARMACOLOGY

Experiments were ethically carried out in accordance with European Directives 2010/63/UE on the care, welfare and treatment of animals. Procedures were reviewed by the ethics committee affiliated to the animal facility of the university (D3842110001). We used 21-35 postnatal days old mice (C57BL/6j) of either sex. Animals were anesthetised by isofluorane inhalation and the entire cerebellum was removed after decapitation. Cerebellar sagittal slices (250 µm thick) were prepared following established procedures (Vogt et al., 2011a;Vogt et al., 2011b;[START_REF] Ouares | A generalised method to estimate the kinetics of fast Ca(2+) currents from Ca(2+) imaging experiments[END_REF] using a Leica VT1200 (Leica, Wetzlar, Germany). Slices were incubated at 37°C for 45 minutes before use. The extracellular solution contained (in mM): 125 NaCl, 26 NaHCO 3 , 1 MgSO 4 , 3 KCl, 1 NaH 2 PO 4 , 2 CaCl 2 and 20 glucose, bubbled with 95% O 2 and 5% CO 2 . The intracellular solution contained (in mM): 125 KMeSO 4 , 5 KCl, 8 MgSO 4 , 5 Na 2 -ATP, 0.3 Tris-GTP, 12 Tris-Phosphocreatine, 20 HEPES, adjusted to pH 7.35 with KOH. In V m imaging experiments, PNs were loaded with the voltage-sensitive dye (VSD) JPW1114 as previously described [START_REF] Canepari | Dendritic spike saturation of endogenous calcium buffer and induction of postsynaptic cerebellar LTP[END_REF] and in some experiments also with the Ca 2+ indicator Fura-2FF (at 1 mM) using a previously described procedure (Vogt et al., 2011a). In experiments of Ca 2+ imaging only, Oregon Green BAPTA-5N (OG5N) was added to the internal solution at 2 mM concentration and, in some experiments, also Fura-2 (Fura2) at 0.4 mM concentration was included. Patch-clamp recordings were made at 32-34°C using a Multiclamp amplifier 700A (Molecular Devices, Sunnyvale, CA) and electrical signals were acquired at 20 kHz using the A/D board of the CCD camera, regardless of the imaging acquisition rate. The measured V m was corrected for junction potential (-11 mV) as previously estimated [START_REF] Canepari | Imaging Inhibitory Synaptic Potentials Using Voltage Sensitive Dyes[END_REF]. PF-and CF-EPSPs were elicited by current pulses of 5-20 µA amplitude and 100 µs duration delivered by separate electrodes. To avoid jitters, the stimulation protocols were precisely controlled with a Master-8 pulse generator (A.M.P.I., Jerusalem, Israel). All recordings were performed at least 30 minutes after establishing whole cell. This minimum time before starting recording was 45 minutes in experiments with Fura2, heparin and ryanodine. In V m imaging experiments, cells were initially loaded with the voltage sensitive dye JPW1114 and re-patched with a solution without this dye to avoid toxicity due to dye overloading. 7-(Hydroxyimino)cyclopropa[b]chromen-1a-carboxylate ethyl ester N-Trimethyl-5-[(tricyclo[3.3.1.1 3,7 ]dec-1-ylmethyl)amino]-1-pentanaminium bromide hydrobromide (IEM1460) were dissolved in exracellular solution and applied to the bath via the perfusion system.

(CPCCOEt), (1S,2S)-2-[2-[[3-(1H-Benzimidazol-2-yl)propyl]methylamino]ethyl]-6-fluoro-1,2,3,4-tetrahydro- 1-(1-methylethyl)-2-naphthalenyl-cyclopropanecarboxylate-dihydrochloride (NNC550396 or NNC) and N,N,
Heparin sodium salt, 1H-Pyrrole-2-carboxylic acid (3S,4R,4aR,6S,7S,8R,8aS,8bR,9S,9aS)-dodecahydro-4,6,7,8a,8b,9a-hexahydroxy-3,6a,9-trimethyl-7-(1-methylethyl)-6,9-methanobenzo[1,2]pentaleno [1,6bc]furan-8-yl ester (ryanodine) and 1- 3,amino]hexyl]-1Hpyrrole-2,5-dione (U73122) were dissolved in intracellular solution and applied via the patch recording. DHPG, dissolved in external solution, was applied through a pipette positioned near the PN dendrite using 20 ms pulses of pressure provided by a pressure ejector PDES-2DX (npi, Tamm, Germany). AmmTx, dissolved in external solution, was applied through a pipette positioned near the PN dendrite by continuous gentle pressure application. CPCCOEt, Heparin sodium salt, ryanodine, U73122, NNC550396 and DHPG were purchased from Tocris (Bristol, UK). IEM1460 was purchased from Hello Bio (Bristol, UK). AmmTx was purchased from Smartox Biotechnology (Saint Egrève, France).

OPTICAL RECORDING

OG5N (Invitrogen, Carlsbad, CA) was excited at 470 nm with an OptoLED (Cairn Research, Faversham, UK) as previously described [START_REF] Jaafari | Imaging Fast Calcium Currents beyond the Limitations of Electrode Techniques[END_REF][START_REF] Jaafari | Functional coupling of diverse voltage-gated Ca(2+) channels underlies high fidelity of fast dendritic Ca(2+) signals during burst firing[END_REF][START_REF] Ouares | A generalised method to estimate the kinetics of fast Ca(2+) currents from Ca(2+) imaging experiments[END_REF][START_REF] Ouares | Two Distinct Sets of Ca 2+ and K + Channels Are Activated at Different Membrane Potentials by the Climbing Fiber Synaptic Potential in Purkinje Neuron Dendrites[END_REF]. Fura-2FF (Santa Cruz, Dallas, TX) and Fura-2 (Invitrogen) were excited at 385 nm using the OptoLED. V m and Ca 2+ optical measurements were achieved sequentially (Canepari and Ogden, 2008) by alternating excitation of Fura-2FF excitation and the excitation of the voltage sensitive dye JPW1114 (Invitrogen) at 528 nm using a LDI laser (89 North, Williston, VT). OG5N Ca 2+ fluorescence was recorded at 530 ± 21 nm. Fura-2FF and Fura2 Ca 2+ fluorescence was recorded at 510 ± 41 nm. JPW1114 V m fluorescence was recorded at >610 nm. Image sequences were recorded using a NeuroCCD-SMQ camera (RedShirtimaging, Decatur, GA). Images were de-magnified by ~0.2X to visualise an area of ~150 µm diameter and acquired at 5 kHz or at 20 kHz with a resolution of 26 X 26 pixels or 26 X 4 pixels respectively. In all experiments, four trials with a 20 s interval between two consecutive trials, were obtained to assess the consistency of the signals and averaged to improve the signal-to-noise ratio. The number of averaged trials was nine in 20 kHz recordings. However, in all figures, the somatic V m recording used in the illustrations was from a single trial, corresponding to the first trial of the series. Fluorescence was corrected for bleaching using a filtered trial without signal. Ca 2+ fluorescence transients were expressed as fractional changes of fluorescence (∆F/F 0 ), using the average of the first four images of the sequence to calculate F 0 . In the colour-coded images, all pixels with intensity value below twice the minimum are set to 1, to exclude pixels with large photon noise threshold, and only those pixels having signal peak >5 % are illustrated, in order to appreciate the signal localisation. V m fluorescence transients were calibrated in mV using prolonged hyperpolarising steps as described in a previous article (Ait [START_REF] Ouares | Two Distinct Sets of Ca 2+ and K + Channels Are Activated at Different Membrane Potentials by the Climbing Fiber Synaptic Potential in Purkinje Neuron Dendrites[END_REF].

MODEL AND COMPUTER SIMULATIONS OF CALCIUM BINDING TO THE INDICATORS

A simplified version of the model described in Ait [START_REF] Ouares | A generalised method to estimate the kinetics of fast Ca(2+) currents from Ca(2+) imaging experiments[END_REF] was used to estimate the Ca 2+ fluorescence signals in the presence of 2 mM OG5N and 400 µM Fura2. The model consists on a set of 9 equations:

d Ca 2+ dt = ξ Ca - (K ON Bj • B j • Ca 2+ -K OFF Bj • B j Ca 2+ d B j Ca 2+ dt = K ON Bj • Ca 2+ • B j -K OFF Bj • B j Ca 2+ d B j dt = - d B j Ca 2+ dt
This model comprises 4 buffers, with association and dissociation constants K ON Bj and K OFF Bj respectively.

Buffers 1 and 2 are the indicators OG5N and Fura2 respectively, having K ON Fura2 = 570 µM -1 s -1 [START_REF] Canepari | Imaging neuronal calcium fluorescence at high spatio-temporal resolution[END_REF] and K D (K OFF /K ON ) equal to 35 µM and 0.2 µM respectively. Buffers 3 and 4 are the two pairs of binding sites of calbindin D-28k having K ON equal to 217.5 µM -1 s -1 and to 27.5 µM -1 s -1 and K OFF equal to 35.8 s -1 nM and 2.6 s -1 respectively, as used in Ait [START_REF] Ouares | Two Distinct Sets of Ca 2+ and K + Channels Are Activated at Different Membrane Potentials by the Climbing Fiber Synaptic Potential in Purkinje Neuron Dendrites[END_REF], to take into account the difference in temperature and the radial diffusion from the published values [START_REF] Nägerl | Binding kinetics of calbindin-D(28k) determined by flash photolysis of caged Ca(2+)[END_REF].

Calbindin D-28k dominates Ca 2+ binding in the millisecond time scale [START_REF] Schmidt | Spine neck geometry determines spino-dendritic cross-talk in the presence of mobile endogenous calcium binding proteins[END_REF] and has estimated concentration of 120 µM [START_REF] Kosaka | Axons and axon terminals of cerebellar Purkinje cells and basket cells have higher levels of parvalbumin immunoreactivity than somata and dendrites: quantitative analysis by immunogold labeling[END_REF]. The Ca 2+ influx associated with the CF was approximated by a Gaussian function of 15 or 20 µM/ms and 1.5 ms time constant, consistent with the detailed model described in Ait [START_REF] Ouares | Two Distinct Sets of Ca 2+ and K + Channels Are Activated at Different Membrane Potentials by the Climbing Fiber Synaptic Potential in Purkinje Neuron Dendrites[END_REF]. We simulated 200 ms of recording using the function "ode45" in Matlab. In these 200 ms, the Gaussian function approximating the CF associated Ca 2+ influx was delayed by 180 ms from the beginning of the simulation and, in the simulations corresponding to the paired scenarios, it was preceded by a slow Ca 2+ influx approximated by another Gaussian function of 4 µM/ms and 45 ms time constant to estimate the effect of saturating the high affinity buffers. The OG5N ∆F/F 0 signal was extrapolated from the Ca 2+ bound to the indicator using the dynamic range of 15 measured in Ait [START_REF] Ouares | A generalised method to estimate the kinetics of fast Ca(2+) currents from Ca(2+) imaging experiments[END_REF]. The Fura2 -∆F/F 0 signal was extrapolated from the Ca 2+ bound to the indicator using the dynamic range of 0.9 as used in Ait [START_REF] Ouares | Two Distinct Sets of Ca 2+ and K + Channels Are Activated at Different Membrane Potentials by the Climbing Fiber Synaptic Potential in Purkinje Neuron Dendrites[END_REF].

EXPERIMENTAL DESIGN AND STATISTICAL ANALYSIS

Data were processed and analysed using MATLAB. Changes produced by the pairing protocol with respect to the CF stimulation alone, or by the pharmacological action of an agent, were assessed by performing the paired Student's t-test on the signal parameter under the two different conditions. A change in the signal was considered significant when p < 0.01. In all figures, a significant change was indicated with "*". In the specific case of data reported in Fig. 1, the conclusion that the effect of adding CPCCOEt is different when the CF stimulation is delayed by 60 ms from the first PF stimulus, with respect to the cases of 100 ms and 150 ms delays, is supported by a paired t-test performed on the ∆F/F 0 ratios at two different delays that gave a value of p < 0.01.

For the quantitative interpretation of the results of combined Ca 2+ imaging with the low-affinity indicator OG5N and with the high affinity indicator Fura2, we calculated the variable "S" defined as: In the specific case in which the unpaired Ca 2+ signal is the same, i.e. when the initial V m is at the hyp state and the delay of the CF stimulation is either 60 ms or 110 from the first PF stimulus, the ratio S(Fura2)/S(OG5N) provides a comparative estimate of the Fura2 saturation. Indeed, regardless of the contribution of the Ca 2+ influx that is different at the two different delays, the more Fura2 is saturated the smaller S(Fura2) will be and, conversely, the larger S(OG5N) will be. Thus, the smaller S(Fura2)/S(OG5N)

= ∆ / (ℎ ) !" ∆ / (
is, the larger the contribution of Fura2 saturation will be.

Results

Distinct dendritic supralinear Ca 2+ transients associated with paired PF-CF stimulation

Several studies have shown that, at sites of activated PF synapses, the Ca 2+ transient associated with a CF-EPSP is significantly larger when it occurs after PF activation [START_REF] Wang | Coincidence detection in single dendritic spines mediated by calcium release[END_REF][START_REF] Brenowitz | Associative short-term synaptic plasticity mediated by endocannabinoids[END_REF][START_REF] Safo | Endocannabinoids control the induction of cerebellar LTD[END_REF][START_REF] Canepari | Dendritic spike saturation of endogenous calcium buffer and induction of postsynaptic cerebellar LTP[END_REF]. To initially analyse these supralinear Ca 2+ signals, we used a protocol of stimulation for the PF input consisting of 5 stimuli delivered at 100 Hz with an electrode positioned near a PN dendritic site (Fig. 1A), with the initial V m hold between -75 mV and -85 mV, below the average V m recorded in the soma when no current is injected (V rest ), which was always between -65 mV and -50 mV. The intensity of stimulation was set to attain a first EPSP in the range of 1-4 mV of somatic amplitude and the protocol occasionally caused somatic action potentials during the last EPSPs. In cells filled with 2 mM of the low-affinity Ca 2+ indicator OG5N (K D = 35 µM, [START_REF] Canepari | Kinetic, pharmacological and activity-dependent separation of two Ca2+ signalling pathways mediated by type 1 metabotropic glutamate receptors in rat Purkinje neurones[END_REF], this protocol systematically produced a fast fractional change of fluorescence (∆F/F 0 ) signal, raising at each individual PF-EPSP, followed by a slow ∆F/F 0 signal peaking at 100-150 ms after the first PF stimulus. As illustrated by the colour code pictures in Fig. 1A, both signals were localised within the same area of a few microns adjacent to the PF stimulating electrode since the sharp depolarisation associated with PF-EPSPs is also localised [START_REF] Canepari | Dendritic spike saturation of endogenous calcium buffer and induction of postsynaptic cerebellar LTP[END_REF]. At submicron spatial scale, however, the two signals are probably not co-localising, since the fast signal is mediated by VGCCs activated by the PF depolarisation [START_REF] Canepari | Dendritic spike saturation of endogenous calcium buffer and induction of postsynaptic cerebellar LTP[END_REF], whereas the slow signal is mediated by a non selective cation conductance [START_REF] Canepari | Ca2+ ion permeability and single-channel properties of the metabotropic slow EPSC of rat Purkinje neurons[END_REF] which is believed to be formed by TRPC3 channels [START_REF] Hartmann | TRPC3 channels are required for synaptic transmission and motor coordination[END_REF].

The time course of the Ca 2+ transient in the 2X2 pixels (~11X11 µm 2 ) region (R1) adjacent to the PF stimulating electrode is reported together with ∆F/F 0 from a control region (R2) of the same size with no Ca 2+ signal to show the high signal-to-noise ratio of these measurements permitting a precise quantitative analysis of Ca 2+ signals. We investigated the Ca 2+ signal associated with a CF-EPSP unpaired or paired with the PF-EPSPs at delays of 60 ms, 100 ms or 150 ms from the first PF stimulus (Fig. 1B). In all three cases, the Ca 2+ transient associated with the paired CF-EPSP was larger than that associated with the unpaired CF-EPSP and these phenomena were restricted to the area where the two Ca 2+ transients associated with the PF-EPSPs were observed, as illustrated by the colour code frames in Fig. 1B. Addition of the mGluR1 inhibitor CPCCOEt (20 µM) reduced the slow ∆F/F 0 signal associated with PF stimulation (Fig. 1C) and the supralinear Ca 2+ signals associated with the CF-EPSP delayed by 100 ms and 150 ms from the first PF stimulus, but not that associated with the CF-EPSP delayed by 60 ms from the first PF stimulus. In N = 6 cells, we quantified the supralinear Ca 2+ signal by calculating the ratio between the amplitude of the ∆F/F 0 signal associated with the paired CF-EPSP and the amplitude of the ∆F/F 0 signal associated with the unpaired CF-EPSP (∆F/F 0 ratio, Fig. 1D). The ∆F/F 0 ratio significantly (p < 0.01, paired t-test) decreased from 3.40 ± 0.73 to 1.93 ± 0.42 and from 3.38 ± 0.69 to 2.02 ± 0.27 in the cases of 100 ms and 150 ms delay of the CF stimulation respectively. In contrast, it did not significantly (p > 0.1, paired t-test) change (from 2.23 ± 0.47 to 2.19 ± 0.60) in the case of 60 ms delay of the CF stimulation.

We concluded that supralinear Ca 2+ signals associated with CF-EPSPs delayed by 100 ms and 150 ms were mGluR1-dependent, whereas the supralinear Ca 2+ signal associated with the CF-EPSP delayed by 60 ms was mGluR1-independent.

The CF-associated Ca 2+ transient at initial hyperpolarised V m (hyp, ~-80 mV) is mainly mediated by Ca 2+ influx via T-type VGCCs (Ait [START_REF] Ouares | Two Distinct Sets of Ca 2+ and K + Channels Are Activated at Different Membrane Potentials by the Climbing Fiber Synaptic Potential in Purkinje Neuron Dendrites[END_REF]. Thus, we further investigated the supralinear Ca 2+ signal at V rest (rest, ~-60 mV), i.e. when T-type VGCCs are mostly inactivated and the CF-associated Ca 2+

transient is largely mediated by Ca 2+ influx via P/Q-type VGCCs that can be activated because also most of A-type K + channels are inactivated. Again, we used the protocol consisting of 5 PF stimuli at 100 Hz with an electrode positioned near a PN dendritic site (Fig. 2A), followed by a CF-EPSP delayed by 110 ms from the first PF stimulus. In this experiment, however, recordings were performed both at hyp and rest initial V m (Fig. 2B). In both cases, the Ca 2+ transient associated with the paired CF-EPSP was larger than that associated with the unpaired CF-EPSP, and both supralinear Ca 2+ signals were co-localised with the PF active area (see the colour code frames in Fig. 2B). Addition of CPCCOEt reduced both supralinear Ca 2+ signals associated with the CF-EPSP (Fig. 2C). In N = 6 cells, the ∆F/F 0 ratio significantly (p < 0.01, paired t-test) decreased from 3.02 ± 0.61 to 1.88 ± 0.50 and from 2.19 ± 0.38 to 1.46 ± 0.30 in the cases of hyp and rest initial V m respectively (Fig. 2D). We concluded that supralinear Ca 2+ signals associated with CF-EPSPs, delayed by 110 ms from the first PF stimulus, were mGluR1-dependent both at hyp and at rest initial V m , i.e. independently on whether the CF-associated Ca 2+ transient is mediated by T-type or P/Q-type VGCCs.

Kinetics of dendritic supralinear Ca 2+ signals

The three forms of supralinear Ca 2+ signals presented in the previous paragraph are time-correlated with the CF-associated Ca 2+ transients which are mediated by T-type and P/Q-type VGCCs (Ait Ouares et al., 2019). They can be in principle due to the modulation of these Ca 2+ sources, to the activation of other Ca 2+ sources, or to both phenomena. If it is only the original Ca 2+ source to be larger, then the kinetics of the rising phase of the Ca 2+ transient is expected to be the same for the paired and unpaired CF signal.

Thus, useful information can be obtained by analysing the kinetics of the rising phase of the Ca 2+

transients in paired protocols with respect to the Ca 2+ transients associated with unpaired CF-EPSPs, to reveal any possible subsequent component of the Ca 2+ transients. To this aim, we performed Ca 2+

recordings associated with the same stimulation protocols described in the previous paragraph, but in this case at 20 kHz to accurately analyse the kinetics of Ca 2+ transients (Fig. 3A). We then analysed the rising phase of the different Ca 2+ transients exploiting the short relaxation time of OG5N [START_REF] Jaafari | Using simultaneous voltage and calcium imaging to study fast Ca2+ channels[END_REF][START_REF] Jaafari | Functional coupling of diverse voltage-gated Ca(2+) channels underlies high fidelity of fast dendritic Ca(2+) signals during burst firing[END_REF][START_REF] Ouares | A generalised method to estimate the kinetics of fast Ca(2+) currents from Ca(2+) imaging experiments[END_REF]. To quantitatively analyse the fast kinetics of Ca 2+ transients, we averaged 9 recordings for each stimulating protocol (instead of 4). As shown in Fig. 3A, the individual somatic V m signals and the associated Ca 2+ transients were perfectly aligned indicating no jitter in the timing of the CF stimulation. We then normalised the signals to the peak and applied a Savitzky-Golay smoothing filter (Fig. 3B) with 20 points time window, that reduces the noise with minimal distortion of the kinetics of the fluorescence transient [START_REF] Savitzky | Smoothing and differentiation of data by simplified least squares procedures[END_REF], as previously demonstrated [START_REF] Jaafari | Using simultaneous voltage and calcium imaging to study fast Ca2+ channels[END_REF]. Finally, we calculated the time derivative [START_REF] Jaafari | Imaging Fast Calcium Currents beyond the Limitations of Electrode Techniques[END_REF] as shown in Fig. 3C.

The time to peak of the time derivative, from the CF stimulus, is an indirect kinetics measurement of the Ca 2+ source and it is typically longer for T-type VGCCs that principally mediate Ca 2+ influx at hyp states, with respect to P/Q-type VGCCs that principally mediate Ca 2+ influx at rest states (Ait [START_REF] Ouares | Two Distinct Sets of Ca 2+ and K + Channels Are Activated at Different Membrane Potentials by the Climbing Fiber Synaptic Potential in Purkinje Neuron Dendrites[END_REF]. Thus, in the example of Fig. 3C, the time difference between the two peaks (∆t peak ) at the hyp and the rest state, in the case of unpaired CF-EPSPs, was 3 samples (150 µs). We then measured the times to peak in the cases of CF-EPSPs in pairing protocol and compared those with the cases of unpaired CF-EPSPs.

In the example of Fig. 3C, the time to peak of the paired CF signal at the hyp state was the same of that of unpaired CF signal at the hyp state (∆t peak = 0). In contrast, the times to peak of the paired CF signal at the rest state or with the CF stimulation delayed by 60 ms from the first PF stimulus were the same of that of unpaired CF signal at the rest state. We performed this analysis in N = 8 cells and calculated both ∆t peak from the CF signal at hyp (Fig. Yet, several studies have linked PF-triggered activation of mGluR1s to Ca 2+ release from internal stores, in particular via InsP3 receptors (Finch and Augustine, 2018;[START_REF] Takechi | A new class of synaptic response involving calcium release in dendritic spines[END_REF]. To directly test whether Ca 2+ release from internal stores play a role in these supralinear Ca 2+ signals, we performed experiments with the internal solution containing either 1 mg/mL of heparin (Fig. 4A), to inhibit Ca 2+ store release via InsP3 receptors [START_REF] Kim | Transient upregulation of postsynaptic IP3gated Ca release underlies short-term potentiation of metabotropic glutamate receptor 1 signaling in cerebellar Purkinje cells[END_REF], or with the internal solution containing 100 µM ryanodine (Fig. 4B), to inhibit Ca 2+ store release via ryanodine receptors [START_REF] Kano | Ryanodine receptor-mediated intracellular calcium release in rat cerebellar Purkinje neurones[END_REF]. In groups of 6 cells tested with each pharmacological agent, mGluR1-dependent supralinear Ca 2+ transients were consistent with those measured in control internal solution (Fig. 4C). The same result was obtained in a group of 6 cells, tested at hyp states only, injected with 10 µM of the phospholipase-C inhibitor U73122 (data not shown), that was proven to prevent mGluR1-mediated Ca 2+ release from stores in PN dendrites [START_REF] Canepari | Kinetic, pharmacological and activity-dependent separation of two Ca2+ signalling pathways mediated by type 1 metabotropic glutamate receptors in rat Purkinje neurones[END_REF]. Taken together, these results rule out any significant contribution of Ca 2+ release from stores either via InsP3 or ryanodine receptors.

Dendritic V m associated with mGluR1-dependent supralinear Ca 2+ signals

Since Ca 2+ release from internal stores does not contribute to the supralinear Ca 2+ signals reported above, the origin of these phenomena can be an increase in the Ca 2+ influx through the plasma membrane during the CF-EPSP, an increase in free Ca 2+ concentration (and therefore in the Ca 2+ bound to the OG5N) due to a transient saturation of endogenous Ca 2+ buffers or a combination of both phenomena. If the supralinear Ca 2+ signal includes an increase of Ca 2+ influx through the plasma membrane, the additional charge influx is expected to increase the electrical current and therefore the dendritic V m transient associated with the CF-EPSP. We initially measured dendritic V m associated with a paired CF-EPSP delayed by 60 ms from the first PF stimulus using V m imaging from a region adjacent to the PF stimulation electrode. V m fluorescence transients were calibrated on an absolute scale (in mV) using prolonged hyperpolarising pulses as previously described [START_REF] Canepari | Dendritic spike saturation of endogenous calcium buffer and induction of postsynaptic cerebellar LTP[END_REF][START_REF] Ouares | Two Distinct Sets of Ca 2+ and K + Channels Are Activated at Different Membrane Potentials by the Climbing Fiber Synaptic Potential in Purkinje Neuron Dendrites[END_REF], to quantify the depolarisation associated with the CF-EPSP under different conditions. In the experiment reported in Fig. 5A, the initial V m before the CF-EPSP shifted from -80 mV to -62 mV when the PF-EPSP train was applied (Fig. 5B). Consistently with the fact at that this initial V m A-type K + channels are partially inactivated, and activation of P/Q-type VGCCs is boosted (Ait [START_REF] Ouares | Two Distinct Sets of Ca 2+ and K + Channels Are Activated at Different Membrane Potentials by the Climbing Fiber Synaptic Potential in Purkinje Neuron Dendrites[END_REF], the peak V m shifted from -21 mV to -3 mV. Significant shifts in the initial and peak V m were observed in N = 8 cells in which this experiment was performed (Fig. 5C), confirming that the mGluR1-independent supralinear Ca 2+ signal, occurring when the CF-EPSP is at the end of the PF-EPSPs train, is associated with a shift from T-type VGCCs to P/Q-type VGCCs as suggested by the results reported in Fig. 3.

After this first set of V m experiments, we performed combined V m and Ca 2+ imaging recordings with a similar approach recently utilised to characterise the dendritic V m transient associated with the unpaired CF-EPSP (Ait [START_REF] Ouares | Two Distinct Sets of Ca 2+ and K + Channels Are Activated at Different Membrane Potentials by the Climbing Fiber Synaptic Potential in Purkinje Neuron Dendrites[END_REF], to measure dendritic V m associated with mGluR1-dependent supralinear Ca 2+ signals. The cell shown in Fig. 6A was filled with the voltage-sentive dye (VSD) JPW1114

and with 1 mM of the low-affinity Ca 2+ indicator Fura-2FF (K D = 6 µM, [START_REF] Hyrc | Ionic selectivity of low-affinity ratiometric calcium indicators: mag-Fura-2, Fura-2FF and BTC[END_REF], used to localise the area of supralinear Ca 2+ signals both at hyp and rest initial V m (Fig. 6A). Consistently with the observation that PF-ESPSs locally activate VGCCs at hyp initial V m , the depolarisation associated with the PF train was above -30 mV in the region (R1) adjacent to the stimulating electrode, while the depolarisation was comparable with that in the soma in a different region (R2), as shown in Fig. 6B. To excite VSD fluorescence over 160 ms without causing photodamage, we used only 20% of the laser intensity applied for previous CF-associated V m measurements (Ait [START_REF] Ouares | Two Distinct Sets of Ca 2+ and K + Channels Are Activated at Different Membrane Potentials by the Climbing Fiber Synaptic Potential in Purkinje Neuron Dendrites[END_REF]. Using this weaker illumination, the standard deviation of the photon noise was equivalent to ~2.5 mV after calibration and the peak-to-peak noise was equivalent to ~10 mV in R1 (Fig. 6B). Therefore, to allow discrimination of V m changes of less than 3 mV, we applied the following filtering procedures (Fig. 6C). For the unpaired CF recordings, the initial V m was set to the averaged V m signal before CF stimulation. For the paired CF recordings, the initial V m was accurately estimated by applying a 64-points median filter to the original fluorescence signal after the end of the PF stimulation. Finally, for all recordings, a 4-points median filter was applied to the 20 ms fluorescence signal following CF stimulation. Fig. 6D shows a small but detectable additional depolarisation associated with the paired CF-EPSP both at hyp and rest initial V m . In N = 7 cells, in which we successfully performed combined V m and Ca 2+ with filtered signals above the photon noise to discriminate V m changes < 3 mV, the additional depolarisation, calculated as the difference between the paired and unpaired CF-associated V m transients was always detectable in the case of hyp initial V m and corresponded to a significant increase of 5.0 ± 1.6 mV (p< 0.01, paired t-test). In the case of rest initial V m , a detectable increase (>3 mV) was observed only in 4/7 cells. The mean ± SD of the V m was 2.5 ± 2.5 mV (N = 7 cells). We concluded that small additional V m transients are always associated with mGluR1-dependent supralinear Ca 2+ signals at hyp initial V m , a result consistent with the hypothesis that at least part of the supralinear Ca 2+ signal under this condition is due to Ca 2+ influx through the plasma membrane. In the case of rest initial V m , additional V m transients were occasionally observed, suggesting a smaller and possibly highly variable contribution of Ca 2+ influx through the plasma membrane.

Contribution of the saturation of the endogenous buffer to the supralinear Ca 2+ signals

In a previous study we have shown that trains of PF stimuli at 100 Hz produce a local progressive saturation of endogenous Ca 2+ buffers that boosts a Ca 2+ fluorescent transient associated with a CF-EPSP occurring at the end of the PF train [START_REF] Canepari | Dendritic spike saturation of endogenous calcium buffer and induction of postsynaptic cerebellar LTP[END_REF]. Since mGluR1 activation induces a slow Ca 2+ influx, saturation of the endogenous Ca 2+ buffer may occur on a longer time scale and contribute to the mGluR1-dependent supralinear Ca 2+ signals. To test whether this phenomenon occurs, experiments can be performed with the inclusion the high-affinity UV-excitable indicator Fura-2 (Fura2, K D ~200 nM).

We initially tested different Fura2 concentrations (100 µM, 200 µM and 400 µM) and we finally chose the concentration of 400 µM since under this condition the Fura2 signal was not saturated by a CF Ca 2+ transient and the OG5N was still large enough to be accurately analysed. To examine quantitatively how this type of measurement can provide an answer to the question on whether and at which extent the saturation of the endogenous buffer contributes to the supralinear Ca 2+ signals, we run computer simulations using the simple but realistic biochemical model described in the Materials and Methods.

Specifically, we analysed a scenario where the same Ca 2+ influx associated with a CF-EPSP occurs unpaired or paired with a previous slow Ca 2+ influx, and another scenario in which the paired Ca 2+ influx is 25% larger with respect to the unpaired Ca 2+ influx (Fig. 7A). When the simulation is run without Fura2, the putative OG5N ∆F/F 0 exhibits supralinear Ca 2+ signals under paired conditions in both scenarios (Fig. 7B).

When the simulation is instead run with Fura2, while supralinear Ca 2+ signals under paired conditions are still present in the putative OG5N ∆F/F 0 , the putative Fura2 -∆F/F 0 behaves differently in the two scenarios: it exhibits a small supralinear Ca 2+ signal in the case of potentiated Ca 2+ influx, but the paired Ca 2+ signal is smaller than the unpaired Ca 2+ signal when Ca 2+ influx is the same (Fig. 7C). To analyse quantitatively this result, we introduce the variable "S" defined as the ratio of the paired ∆F/F 0 peak against the unpaired ∆F/F 0 peak. The conclusive information that can be obtained, by the analysis of the variable S, is explained in detail in the Experimental design and statistical analysis section of the Materials and Methods. Briefly, when the supralinear Ca 2+ signal is exclusively due to buffer saturation, then the value of S for Fura2 (S Fura2 ) must be less than one (S Fura2 = 0.95 in the case of the simulation of Fig. 7C).

In contrast, a value of S Fura2 larger than 1 indicates that larger Ca 2+ influx contributes to the supralinear Ca 2+ signal (S Fura2 = 1.22 in the case of the simulation of Fig. 7C). Since a supralinear Ca 2+ signal exclusively due to larger Ca 2+ influx (i.e. no buffer saturation) leads to an increase in the absolute ∆F/F 0 signal which is the same for the two indicators, the ratio of S for the two indicators (S Fura2 /S OG5N ) must be 1 in this case. It follows that a lower value of this ratio indicates that buffer saturation contributes to the supralinear Ca 2+ signal (S Fura2 /S OG5N = 0.54 in the case of the simulation of Fig. 7C). Thus S Fura2 /S OG5N also represents a quantitative estimate of the extent of buffer saturation in the two cases. With the premise that the analysis of the saturation of Fura2 provides an estimate for the saturation of the endogenous buffer occurring physiologically, we run experiments by adding 400 µM Fura2 in the patch electrode. In the cell of Fig. 8A, we applied the same stimulation protocols of Fig. 3 and measured separately the absolute fluorescent transients from the two indicators (OG5N ∆F/F 0 and Fura2 -∆F/F 0 ). Under this condition, supralinear OG5N Ca 2+ signals were observed (Fig. 8B), indicating that these signals are not prevented by the presence of Fura2 at this moderate concentration. In contrast, whereas a supralinear Fura2 Ca 2+

signal associated with the paired CF-EPSP delayed by 110 ms at the hyp state was observed, the Fura2

Ca 2+ signal associated with the paired CF-EPSP delayed by 60 ms was smaller than the Ca 2+ signal associated with the unpaired CF-EPSP (Fig. 8B). We then calculated the variable S for the ratios of the ∆F/F 0 peaks in each protocol against the ∆F/F 0 peak associated with the unpaired CF stimulation (Fig. 8C). In N = 8 cells tested, S Fura2 was significantly positive for the mGluR1-dependent supralinear Ca 2+ signal at hyp states (p<0.01 paired t-test, S Fura2 = 2.38 ± 0.05), confirming that larger Ca 2+ influx through the plasma membrane contributes in this case (Fig. 8C). However, S Fura2 was significantly smaller than S OG5N (p<0.01, paired t-test, S Fura2 /S OG5N = 0.58 ± 0.09) indicating that also buffer saturation contributes to this supralinear Ca 2+ signal. Finally, S Fura2 /S OG5N for the mGluR1 independent supralinear Ca 2+ signal (0.31 ± 0.13) was significantly smaller than S Fura2 /S OG5N for the mGluR1-dependent supralinear Ca 2+ signal (p<0.01, paired t-test), indicating that in this case buffer saturation provides a larger contribution. The Ca 2+ increase through P/Q-type VGCCs produced by switching from hyp states to rest states is essentially due to larger Ca 2+ influx (S Fura2 /S OG5N = 0.80 ± 0.23). Thus, as expected, the further mGluR1-dependent Ca 2+ increase includes a significant contribution of buffer saturation (S Fura2 /S OG5N = 0.54 ± 0.19, calculated using the unpaired CF signal at rest states). This analysis, however, does not allow estimating a possible contribution of larger Ca 2+ influx in the case of mGluR1-dependent supralinear Ca 2+ signal at rest states.

Origin of the mGluR1-dependent supralinear Ca 2+ signals at initial hyperpolarised V m

The results presented above demonstrate that mGluR-dependent supralinear Ca 2+ signals at the hyp state are due to a combination of Ca 2+ influx increase through the plasma membrane and to a transient saturation of the endogenous Ca 2+ buffer. The rising phase of the paired CF Ca 2+ signal has the same kinetics of the Ca 2+ signal associated with the unpaired CF input (Fig. 3) which is principally mediated by T-type VGCCs (Ait [START_REF] Ouares | Two Distinct Sets of Ca 2+ and K + Channels Are Activated at Different Membrane Potentials by the Climbing Fiber Synaptic Potential in Purkinje Neuron Dendrites[END_REF]. It has been reported that mGluR1 activation potentiate Cav3.1 Ttype VGCCs in PNs [START_REF] Hildebrand | Functional coupling between mGluR1 and Cav3.1 T-type calcium channels contributes to parallel fiber-induced fast calcium signaling within Purkinje cell dendritic spines[END_REF]. Hence, we finally assessed directly whether the Ca 2+ influx component of the mGluR1-dependent supralinear Ca 2+ signal at hyp states is through these channels. In the cell reported in Fig. 9A, we recorded the Ca 2+ transient associated with a CF-EPSP unpaired or paired with PF stimulation, at hyp or rest initial V m in control conditions with a delay of 110 ms from the first PF stimulus and the CF stimulation. Addition of 30 µM of the Cav3.1 blocker NNC550396 (NNC) inhibited spontaneous firing at rest initial V m and strongly reduced Ca 2+ transients associated both with PF-EPSPs and the CF-EPSP at hyp initial V m (Fig. 9A). In contrast, Ca 2+ transients associated both with PF-EPSPs and the CF-EPSP at rest initial V m were only slightly affected by NNC addition, confirming that dendritic Ttype VGCCs are mostly inactivated at this state (Fig. 9A). As shown in Fig. 9B, the supralinear Ca 2+ transient at hyp initial V m was also strongly inhibited by addition of NNC. In N = 6 cells tested with this experimental protocol, the ratios between the CF Ca 2+ signals in the presence of NNC and in control condition at initial hyperpolarised V m were 0.44 ± 0.18 and 0.32 ± 0.13 for the CF unpaired or paired with PF stimulation respectively (Fig. 9C). In both cases, the Ca 2+ signal associated with the paired CF-EPSP was significantly smaller (p< 0.01, paired t-test). In contrast, the ratios between the CF Ca 2+ signals in the presence of NNC and in control condition at rest initial V m were 0.93 ± 0.13 and 0.91 ± 0.10 for the CF unpaired or paired with PF stimulation respectively, indicating that in this state T-type VGCCs contribute marginally to Ca 2+ signals (Fig. 9C). The results reported in Fig. 9 unambiguously confirm that the Ca 2+ [START_REF] Hildebrand | Functional coupling between mGluR1 and Cav3.1 T-type calcium channels contributes to parallel fiber-induced fast calcium signaling within Purkinje cell dendritic spines[END_REF].

In the example of Fig. 10A, addition of 250 µM of IEM1460 produced a use dependent block of the slow mGluR1-dependent Ca 2+ transient over a period of 20 minutes in which stimulation protocols were repeated every 5 minutes. While a change in the somatic V m recordings was observed after IEM1460 application, the fast PF-mediated Ca 2+ transients did not change indicating that VGCCs were not directly affected by the blocker. Whereas the Ca 2+ transient associated with the unpaired CF-EPSP was also not affected, the Ca 2+ transient associated with the paired CF-EPSP was progressively reduced consistently with the slow mGluR1-mediated Ca 2+ transient that was extrapolated using a simple fitting of the decay phase of the fast PF-mediated Ca 2+ transient (Fig. 10B). We performed this experiment in N = 6 cells, obtaining a significant reduction of the slow mGluR1-mediated Ca 2+ transient (p<0.01, paired t-test), 20 minutes after IEM1460 application, corresponding to a ∆F/F 0 ratio of 0.49 ± 0.16 (Fig. 10C). Consistently with this result, the supralinear Ca 2+ signal, quantified again as the ratio between the paired and the unpaired ∆F/F 0 peaks, significantly (p < 0.01, paired t-test) decreased from 3.37 ± 0.83 to 1.86 ± 0.56 (Fig. 10D). We concluded that the mGluR1-dependent supralinear Ca 2+ signal at hyp states are caused by boosting of T-type VGCCs amplified by endogenous buffer saturation produced by the slow mGluR1dependent PF-mediated Ca 2+ influx.

Origin of the mGluR1-dependent supralinear Ca 2+ signals at V rest

The experiments reported in Fig. 8 and in Fig. 10 suggest that the mGluR1-dependent supralinear Ca 2+ signal also at rest state is largely due to saturation of the endogenous buffer, but the results reported in Fig. 9 further suggest that an increase in Ca 2+ influx may contribute in a variable manner. It has been reported that mGluR1 activation shifts the inactivation curve of A-type K + channels boosting the opening of P/Q VGCCs at initial V m > -65 mV in PNs [START_REF] Otsu | Activity-dependent gating of calcium spikes by A-type K+ channels controls climbing fiber signaling in Purkinje cell dendrites[END_REF]. Thus, consistently with the results of the kinetics analysis reported in Fig. 3, an increase in Ca 2+ influx via P/Q-type VGCCs may contribute to this supralinear Ca 2+ signal. In contrast to the direct local regulation of T-type VGCCs by mGluR1s [START_REF] Hildebrand | Functional coupling between mGluR1 and Cav3.1 T-type calcium channels contributes to parallel fiber-induced fast calcium signaling within Purkinje cell dendritic spines[END_REF], occurring at hyp states, the indirect regulation of P/Q-type VGCCs is produced by a V m modulation and therefore it is not co-localised with mGluR1s. By analysing cells in which V rest was <-60 mV, i.e. where A-type K + channels are not yet fully inactivated, we observed some occasional small supralinear Ca 2+ signals at far-away sites from the PF-activated region at rest states. An example of this wide supralinear Ca 2+ signal is reported in Fig. 11A and Fig. 10B. While this far supralinear Ca 2+ signal was smaller than the supralinear Ca 2+ signal co-localised with the PF-mediated signal (Fig. 11A), the kinetics was qualitatively similar to that of a "supralinear" Ca 2+ signal obtained by blocking A-type K + channels with the toxin AmmTx3 [START_REF] Zoukimian | Synthesis by native chemical ligation and characterization of the scorpion toxin AmmTx3[END_REF][START_REF] Ouares | Two Distinct Sets of Ca 2+ and K + Channels Are Activated at Different Membrane Potentials by the Climbing Fiber Synaptic Potential in Purkinje Neuron Dendrites[END_REF], as shown in the example of Fig. 11C.

Finally, in many studies, physiological mGluR1 activation has been mimicked by bath application of the agonist (S)-3,5-dihydroxyphenylglycine (DHPG, see for example [START_REF] Canepari | The conductance underlying the parallel fibre slow EPSP in rat cerebellar Purkinje neurones studied with photolytic release of lglutamate[END_REF][START_REF] Tempia | Characterization of the mGluR(1)-mediated electrical and calcium signaling in Purkinje cells of mouse cerebellar slices[END_REF][START_REF] Maejima | Synaptically driven endocannabinoid release requires Ca2+-assisted metabotropic glutamate receptor subtype 1 to phospholipase Cbeta4 signaling cascade in the cerebellum[END_REF][START_REF] Otsu | Activity-dependent gating of calcium spikes by A-type K+ channels controls climbing fiber signaling in Purkinje cell dendrites[END_REF]. We examined this artificial stimulation protocol, that in principle can also produce Ca 2+ release from internal stores, by applying 100 µM DHPG, using a pipette positioned near the dendrites, with a short (20 ms) pressure ejection as shown in the example of Fig. 12A.

At hyp state, DHPG application triggered a slow Ca 2+ signal, but in contrast to the physiological PF stimulation a corresponding slow V m depolarisation was observed in the soma (Fig. 12A). Thus, while a substantial supralinear Ca 2+ signal associated with DHPG pairing was observed, the kinetics of the Ca 2+ transient indicates a dominance of Ca 2+ influx via P/Q-type VGCCs (Fig. 12B), consistently with the fact that the initial V m for the CF-EPSP is ~-60 mV. The size of the supralinear Ca 2+ signal associated with DHPG application is comparable to those associated with PF stimulation (Fig. 12C). Nevertheless, since all these phenomena are largely due to transient saturation of the endogenous buffer and the spatial and temporal dynamics of Ca 2+ influx causing this saturation is different in the different protocols, we conclude that experiments using DHPG application cannot realistically mimic the physiological scenarios associated with mGluR1 activation.

In summary, at the rest state, regulation of P/Q-type VGCCs by mGluR1 activation may contribute to the supralinear Ca 2+ signal, but the localisation of this signal, produced by Ca 2+ influx via these channels, is entirely due to the previous Ca 2+ entry that saturates the endogenous buffer.

Discussion

Determinants of the different dendritic supralinear Ca 2+ signals in PNs

In this study we identified the biophysical determinants of the dendritic supralinear Ca 2+ signals, observed when a CF-EPSP is preceded by PF activation, that are believed to trigger PF synaptic plasticity [START_REF] Hartell | Parallel fiber plasticity[END_REF][START_REF] Jörntell | Synaptic memories upside down: bidirectional plasticity at cerebellar parallel fiber-Purkinje cell synapses[END_REF][START_REF] Vogt | On the induction of postsynaptic granule cell-Purkinje neuron LTP and LTD[END_REF]. In a recent report, we have demonstrated that isolated CF-EPSPs essentially trigger Ca 2+ influx via T-type VGCCs when the initial V m < -70 mV and Ca 2+ influx via P/Q-type VGCCs when the initial V m > -60 mV (Ait [START_REF] Ouares | Two Distinct Sets of Ca 2+ and K + Channels Are Activated at Different Membrane Potentials by the Climbing Fiber Synaptic Potential in Purkinje Neuron Dendrites[END_REF]. In both cases these signals are spread throughout the dendritic arborisation at different extent. Here we demonstrate that bursts of PF-EPSPs are capable of locally amplifying these two Ca 2+ signals at the sites of activated PF synapses, driving the CF "error" signal specifically to these inputs [START_REF] Safo | Timing dependence of the induction of cerebellar LTD[END_REF]. The biophysical mechanisms that permit these phenomena of amplification are summarised in Fig. 13. As shown in Fig. 6B, a burst of PF-EPSPs locally depolarises the dendritic area comprising the activated spines. Thus, if a CF-EPSP occurs during this depolarising phase, the Ca 2+ influx associated with the CF-EPSP will be principally mediated by P/Q-type VGCCs, independently of the initial V m . The fast Ca 2+ influx associated with the PF-mediated depolarisation can transiently saturate the endogenous Ca 2+ buffer and therefore a supralinear free Ca 2+ signal is produced in the dendritic region where V m is depolarised. It must be pointed out that this type of supralinear Ca 2+ signal depends on the number and arrangement of activated PFs that determine the spatial pattern of depolarisation, but it is not clearly established whether a scenario of "beams" of PF axons activating spines in close proximity occurs in vivo [START_REF] Bower | The organization of cerebellar cortical circuitry revisited: implications for function[END_REF]. During the short PF-mediated depolarisation, mGluR1s do not affect the Ca 2+ transient associated with the CF-EPSP (Fig. 1D). After the end of the PF train, V m is repolarised and mGluR1 effects take action. In this time window, if the repolarised V m is at the hyp state (< -70 mV) the Ca 2+ influx associated with the CF-EPSP will be principally mediated by T-type VGCCs which are potentiated by mGluR1s (Fig. 9). In addition, the slow mGluR1-mediated Ca 2+ influx is also capable of saturating the endogenous buffer, a mechanism that further amplifies this supralinear free Ca 2+ signal (Fig. 10).

Interestingly, both T channels potentiating and the slow mGluR1-mediated Ca 2+ influx are triggered by the same mGluR1 pathway [START_REF] Hildebrand | Functional coupling between mGluR1 and Cav3.1 T-type calcium channels contributes to parallel fiber-induced fast calcium signaling within Purkinje cell dendritic spines[END_REF] involving a protein tyrosine phosphatase [START_REF] Canepari | Evidence for protein tyrosine phosphatase, tyrosine kinase, G-protein regulation of the parallel fiber metabotropic slow EPSC of rat cerebellar Purkinje neurons[END_REF], suggesting that the two factors contributing to this supralinear Ca 2+ signal co-localise with mGluR1s at submicron scale. Eventually, if the repolarised V m is > -65 mV, the Ca 2+ influx associated with a CF-EPSP will be principally mediated by P/Q-type VGCCs. The Ca 2+ influx via P/Q-type VGCCs can be also boosted by mGluR1s through inhibition of A-type K + channels [START_REF] Otsu | Activity-dependent gating of calcium spikes by A-type K+ channels controls climbing fiber signaling in Purkinje cell dendrites[END_REF], but with two major differences with respect to the T channels boosting discussed above. First, this mechanism is highly variable since at these initial V m range A-type K + channels are already partially inactivated. Second, the potentiated P/Q channels do not co-localise with the site of activated PFs (Fig. 11A and Fig. 11B). Thus, the only mechanism providing co-localisation in this case is saturation of the endogenous buffer produced by the slow Ca 2+ influx that is independent of the initial V m .

Role of the initial V m and implication for synaptic plasticity

The evidence that mGluR1s locally potentiate a specific Ca 2+ source (the T-type VGCC) and concomitantly amplify the same signal suggests that the occurrence of a hyp state episode is important for synaptic plasticity. Yet, in vivo electrode recordings have shown that, in PNs, V rest is similar to that observed in brain slices [START_REF] Kitamura | Dendritic calcium signaling triggered by spontaneous and sensory-evoked climbing fiber input to cerebellar Purkinje cells in vivo[END_REF], indicating that the dendritic V m is normally not at the hyp state. Also, spontaneous bursts of dendritic Ca 2+ spikes are observed by recording Ca 2+ and V m signals simultaneously [START_REF] Roome | Simultaneous dendritic voltage and calcium imaging and somatic recording from Purkinje neurons in awake mice[END_REF], again indicating that depolarising transients occur when the dendrite is relatively depolarised. These observations suggest that the hyp state might occur exclusively during rare but crucial episodes in which synaptic plasticity may occur. Episodes of hyp state can be due, in principle, to synaptic inhibition coactively occurring during activity patterns associated with cerebellar learning [START_REF] Suvrathan | Depressed by Learning-Heterogeneity of the Plasticity Rules at Parallel Fiber Synapses onto Purkinje Cells[END_REF]. Indeed, it was recently demonstrated that optogenetic activation of interneurons in the molecular layer strongly affects PF synaptic plasticity and motor learning, as well as CF-mediated signalling [START_REF] Rowan | Graded Control of Climbing-Fiber-Mediated Plasticity and Learning by Inhibition in the Cerebellum[END_REF][START_REF] Gaffield | Inhibition gates supralinear Ca 2+ signaling in Purkinje cell dendrites during practiced movements[END_REF]. Another possibility is that hyp state episodes are intrinsically generated in PNs by a "priming" signal that hyperpolarises the cell, for instance by activating a K + conductance. Interestingly, in a recent study, it was proposed that PF synaptic depression may physiologically occur when two CF events occur, the first one concomitant with a PF-EPSP burst and the second one after 100 ms [START_REF] Bouvier | Cerebellar learning using perturbations[END_REF]. Notably, the concomitant activation of PF and CF inputs hyperpolarises the PN, as also visible in the examples with 60 ms delay reported here in Fig. 3A and Fig. 8A.

Role of the mGluR1-activated non-selective cation conductance

An mGluR1-activated non-selective cation conductance, permeable to Ca 2+ , is the channel that mediates the slow mGluR1 Ca 2+ influx [START_REF] Canepari | The conductance underlying the parallel fibre slow EPSP in rat cerebellar Purkinje neurones studied with photolytic release of lglutamate[END_REF][START_REF] Canepari | Ca2+ ion permeability and single-channel properties of the metabotropic slow EPSC of rat Purkinje neurons[END_REF]. This channel has been identified as the C3-type transient receptor potential (TRPC3) since in mutant mice lacking this channel all signals associated with the mGluR1-activated non-selective cation conductance are absent [START_REF] Hartmann | TRPC3 channels are required for synaptic transmission and motor coordination[END_REF]. This mouse, as well as another mouse model carrying a point mutation in the TRPC3 channel [START_REF] Becker | A point mutation in TRPC3 causes abnormal Purkinje cell development and cerebellar ataxia in moonwalker mice[END_REF], exhibit severe changes in behavioural cerebellar functions. More recently, it was shown that mGluR1s can also activate GluD2 delta "orphan" glutamate receptors, raising the question of whether the mGluR1-activated non-selective cation conductance is actually composed by different channels (Ady et al., 2008). Notably, critical mutations of GluRD2 impair synaptic plasticity and motor learning and cerebellar behavioral functions [START_REF] Hirano | Cerebellar regulation mechanisms learned from studies on GluRdelta2[END_REF]. Regardless of the identity of the channel underlying the slow mGluR1 Ca 2+ influx, in this study we report a clear role for this conductance.

During the time window of mGluR1 action, Ca 2+ entering the cell after a PF-EPSP burst binds to mobile proteins forming the rich endogenous buffer of PNs [START_REF] Bastianelli | Distribution of calcium-binding proteins in the cerebellum[END_REF]. Therefore, in this critical time window, the buffer capacity of PN dendrites, which is exceptionally high at rest [START_REF] Fierro | High endogenous calcium buffering in Purkinje cells from rat cerebellar slices[END_REF], can locally lower to a level that enables Ca 2+ influx associated with a CF-EPSP to activate molecular pathways that would not be activated by an unpaired CF-EPSP. The transient saturation of the endogenous buffer has been already identified as crucial computational element that allows local integration of Ca 2+ signals [START_REF] Maeda | Supralinear Ca2+ signaling by cooperative and mobile Ca2+ buffering in Purkinje neurons[END_REF]. However, experimental evidence of endogenous buffer saturation was associated with dendritic depolarisation [START_REF] Canepari | Dendritic spike saturation of endogenous calcium buffer and induction of postsynaptic cerebellar LTP[END_REF], co-localised with activated VGCCs which go beyond the spatial pattern of activated spines. In contrast, endogenous buffer saturation caused by the slow Ca 2+ influx can be segregated to activated synapses. In general, the spatial pattern of activated spines [START_REF] Schmidt | Spino-dendritic cross-talk in rodent Purkinje neurons mediated by endogenous Ca2+-binding proteins[END_REF] and their geometry [START_REF] Schmidt | Spine neck geometry determines spino-dendritic cross-talk in the presence of mobile endogenous calcium binding proteins[END_REF]) are expected to be determinants of endogenous buffer saturation in the case of synaptic Ca 2+ influx. Finally, endogenous buffer saturation caused by the slow mGluR1 Ca 2+ influx is likely co-localising with the potentiated T-type VGCCs when the dendrite is at hyp state, since the two mGluR1-mediated mechanisms share the same molecular pathway [START_REF] Hildebrand | Functional coupling between mGluR1 and Cav3.1 T-type calcium channels contributes to parallel fiber-induced fast calcium signaling within Purkinje cell dendritic spines[END_REF].

Perspectives

This study was achieved by monitoring fluorescence simultaneously in large portions of PN dendrites with a spatial resolution of ~10 µM. Thus, the dendritic sites of recording comprise several spines and the parent dendritic segment. A full understanding of the signals in terms of individual spines and dendritic bulks, which is not available in this study, should be achieved in the near future either by reducing the temporal resolution using rapid multisite confocal imaging [START_REF] Filipis | A novel multisite confocal system for rapid Ca2+ imaging from submicron structures in brain slices[END_REF], or by reducing the number of recording spots using 2-photon random access microscopy [START_REF] Otsu | Optical monitoring of neuronal activity at high frame rate with a digital random-access multiphoton (RAMP) microscope[END_REF]. A second question that should be explored in detail is the relation between the initial V m state and the induction of PF synaptic plasticity. Numerous studies have investigated other parameters as crucial determinants of PF synaptic plasticity, including timing, size of Ca 2+ signals, spatial arrangements of synaptic inputs and others [START_REF] Vogt | On the induction of postsynaptic granule cell-Purkinje neuron LTP and LTD[END_REF]. In this study we show that a scenario, where a specific Ca 2+ source (the T-type VGCC) is locally boosted and amplified by mGluR1s, occurs only when the initial initial V m is hyperpolarised, a phenomenon that can translate into an important information processing rule associated with cerebellar function.

Figure 1 .

 1 Figure 1. Timing and localisation of supralinear Ca 2+ signals. A, Reconstruction of PN filled with 2 mM OG5N (left) with position of two stimulating electrodes for the CF and PFs and two regions of interest indicated (R1 and R2). Somatic V m and Ca 2+ ∆F/F 0 signals at R1 and R2 associated PFs stimulated with 5 pulses at 100 Hz with timing indicated by purple lines (right). Spatial distribution of ∆F/F 0 signal corresponding to the 2 nd -5 th PF-EPSPs and to the peak of the slow Ca 2+ signal depicted using a colour code. B, Somatic V m and Ca 2+ ∆F/F 0 signals at R1 and R2 associated with CF stimulation unpaired (light blue traces) or paired (dark blue traces) with PF stimulation at 100 Hz (timing indicated by purple lines) following at 60 ms, 100 ms or 150 ms from the first PF pulse (timing indicated by purple triangle). Spatial distribution of the ∆F/F 0 signal associated with CF-EPSP paired with PF stimulation depicted using a colour code. C, Ca 2+ ∆F/F 0 signals at R1 associated with CF stimulation unpaired or paired with PF stimulation delayed by 60 ms, 100 ms or 150 ms from the first PF pulse in control solution (blue traces) or after addition of 20 µM of the mGluR1 antagonist CPCCOEt (green traces). The time window outlined is reported below. D, Mean ± SD (N = 6 cells) of ∆F/F 0 ratio between the paired and unpaired signals in control solution or after addition of CPCCOEt. "*" indicates significant inhibition of supralinear Ca 2+ signal by CPCCOEt (p< 0.01, paired t-test). The dotted line depicts ∆F/F 0 ratio = 1. All optical signals were from averages of 4 trials.

Figure 2 .

 2 Figure 2. Supralinear Ca 2+ signals at different initial V m . A, Reconstruction of PN filled with 2 mM OG5N (left) with position of two stimulating electrodes for the CF and PFs and a region of interest adjacent to the PF stimulating electrode indicated. B, Somatic V m and Ca 2+ ∆F/F 0 signals at the region of interest associated with CF stimulation unpaired (light blue traces) or paired (dark blue traces) with PF stimulation (timing indicated by purple lines) delayed by 110 ms from the first PF pulse (timing indicated by purple triangle) in the case of hyperpolarised (hyp, ~-80 mV) or V rest (rest, ~-60 mV). Spatial distribution of the ∆F/F 0 signal associated with CF-EPSP paired with PF stimulation depicted using a colour code. C, Same Ca 2+ ∆F/F 0 signals associated with CF stimulation unpaired or paired with PF stimulation in control solution (blue traces) or after addition of 20 µM of the mGluR1 antagonist CPCCOEt (green traces). The time window outlined is reported below. D, Mean ± SD (N = 6 cells) of the ∆F/F 0 ratio between the paired and unpaired signals in control solution or after addition of CPCCOEt. "*" indicates a significant inhibition of supralinear Ca 2+ signal by CPCCOEt (p< 0.01, paired t-test). The dotted line depicts ∆F/F 0 ratio = 1. All optical signals were from averages of 4 trials.

Figure 3 .

 3 Figure 3. Kinetics of supralinear Ca 2+ signals. A, Reconstruction of PN filled with 2 mM OG5N; position of PF stimulating electrode and adjacent region of interest indicated. Somatic V m and Ca 2+ ∆F/F 0 signals in the region of interest associated with different protocols: from left to right a CF-EPSP unpaired at hyp and rest states, paired with a PF-EPSPs train delayed by 110 ms from the first PF stimulus at hyp and rest states, and paired with a PF-EPSPs train delayed by 60 ms from the first PF stimulus. On the bottom, V m

Figure 4 .

 4 Figure 4. Supralinear Ca 2+ signals in the presence of heparin or ryanodine. A, Reconstruction of PN filled with 2 mM OG5N and 1 mg/mL of heparin sodium salt to block InsP3 receptors (left); position of PF stimulating electrode and adjacent region of interest indicated. Somatic V m and Ca 2+ ∆F/F 0 signals in the region of interest associated with different protocols: from left to right a CF-EPSP unpaired at hyp and rest states, paired with a PF-EPSPs train delayed by 110 ms from the first PF stimulus at hyp and rest states, and paired with a PF-EPSPs train delayed by 60 ms from the first PF stimulus. B, Same as A, but with the internal solution containing 100 µM ryanodine to block ryanodine receptors. C, Mean ± SD (N = 6 cells for each group) of ∆F/F 0 ratio between the paired and unpaired signals in the presence of heparin (green columns) or ryanodine (purple columns). Blue columns are mean ± SD of ∆F/F 0 ratios in control conditions already reported in Fig. 1 and Fig. 2. Values for heparin were: 3.17 ± 0.41 for 110 ms CF delay at hyp

Figure 5 .

 5 Figure 5. Dendritic V m associated with mGluR1-independent supralinear Ca 2+ signals. A, Dendrite of PN filled with the voltage-sensitive dye JPW1114 (left); position of PF stimulating electrode and adjacent region of interest indicated. Somatic (top) and dendritic (bottom) V m in the region of interest associated with a CF-EPSP unpaired or paired with a PF-EPSPs train with the CF stimulation delayed by 60 ms from the first PF stimulus. B, On a time window of 20 ms, dendritic V m signals of panel A. V init and V peak indicate the initial and peak V m calibrated in mV. C, Mean ± SD (N = 8 cells) of V init and V peak for the signals associated with an unpaired CF-EPSP (-83 ± 3 mV and -18 ± 5 mV respectively) and for the signals

Figure 6 .

 6 Figure 6. Dendritic V m transients associated with mGluR1-dependent supralinear Ca 2+ signals. A, Dendritic PN area filled with the VSD JPW1114 and 1 mM Fura-2FF (left); position of PF stimulating electrode and two regions of interest (R1 and R2) indicated. Somatic V m and Fura-2FF -∆F/F 0 signals (right) from single trials at R1 and R2 associated with CF stimulation unpaired (light blue traces) or paired (dark blue traces) with PF stimulation in the case of hyp (~-80 mV) or rest (~-60 mV) initial V m , indicating supralinear Ca 2+ signals at R1. B, V m calibrated recordings associated with CF stimulation unpaired (red traces) or paired (pink traces) with PF stimulation at R1 and R2 superimposed to somatic V m, in the case of hyp or rest initial V m . C, V m recordings at R1 shown in panel B filtered as following: for the unpaired CF, average of the signals before the CF stimulation and in the next 20 ms a 4-points median filter is applied; for the paired CF, a 64-points median filter is applied after the PF train and before the CF stimulation and in the next 20 ms a 4-points median filter is applied. D, Same signals of panel C in the outlined time window; the values of the V m transients are indicated. E, Mean ± SD (N = 7 cells) of the V m transient difference between the paired and unpaired CF in the case of hyp or rest initial V m . "*" indicates a significant difference (p< 0.01, paired t-test). All optical signals were from averages of 4 trials.

Figure 7 .

 7 Figure 7. Computer simulations of the Ca 2+ fluorescence signals in the presence of 2 mM OG5N and 400 µM Fura-2. A, Ca 2+ influx used in the computer simulations associated with a CF-EPSP: Gaussian function of 15 µM/ms (left) or 20 µM/ms (right) and 1.5 ms time constant unpaired or paired with a preceding slow Ca 2+ influx approximated by another Gaussian function of 4 µM/ms and 45 ms time constant. B, Computer simulations of the putative OG5N ∆F/F 0 signal in the absence of Fura2 using the model described in detail in the Materials and Methods and the Ca 2+ influx reported in panel A. The ∆F/F 0 signal was extrapolated from the Ca 2+ bound to the indicator using the dynamic range of 15 measured in Ait Ouares et al (2016). C, Computer simulations of the putative OG5N ∆F/F 0 signal (top) and of the putative Fura2 -∆F/F 0 signal (bottom) in the presence of 400 µM Fura2 using the same model and Ca 2+influx as in panel B. The Fura2 -∆F/F 0 signal was extrapolated from the Ca 2+ bound to the indicator using the dynamic range of 0.9 used in Ait[START_REF] Ouares | Two Distinct Sets of Ca 2+ and K + Channels Are Activated at Different Membrane Potentials by the Climbing Fiber Synaptic Potential in Purkinje Neuron Dendrites[END_REF]. The values of the variable S, described in detail in the Experimental design and statistical analysis section of the Materials and Methods are reported for the two indicators.

Figure 8 .

 8 Figure 8. Contribution of saturation of endogenous Ca 2+ buffers to supralinear Ca 2+ signals. A, Dendritic PN area filled with two Ca 2+ indicators (left): OG5N (2 mM, K D = 35 µM) and Fura2 (0.4 mM, K D = 0.2 µM); position of PF stimulating electrode and adjacent region of interest indicated. Somatic V m and Ca 2+ signals

Figure 9 .

 9 Figure 9. Supralinear Ca 2+ signals after blocking T-type VGCCs. A, Dendritic area of a PN filled with 2 mM OG5N (left) with position of PF stimulating electrode and an adjacent region of interest indicated. On the right, somatic V m (black traces) and Ca 2+ ∆F/F 0 (blue or green traces) signals at the region of interest associated with CF stimulation unpaired (light traces) or paired (dark traces) with PF stimulation (timing indicated by purple lines) delayed by 110 ms from the first PF pulse (timing indicated by purple triangle) in the case of hyp or rest initial V m . Signals were acquired in control conditions (blue traces) or after addition of 30 µM of the T-type VGCC blocker NNC (green traces). B, Same Ca 2+ signals in panel A over a 20 ms time window outlined. C, Mean ± SD (N = 6 cells) of the ratios between the ∆F/F 0 peak after addition of NNC and the peak under control condition; dark blue columns are for paired signals; light blue columns are for unpaired CF signals. Ratios are calculated both for unpaired and paired CF signals. "*" indicates a significant reduction of paired Ca 2+ signal after addition of NNC (p< 0.01, paired t-test). The dotted line depicts the ratio = 1. All optical signals were from averages of 4 trials.

Figure 10 .

 10 Figure 10. Use-dependent block of mGluR1 slow Ca 2+ transients and of supralinear Ca 2+ signals. A, Dendritic area of a PN filled with 2 mM OG5N (left) with position of PF stimulating electrode and an adjacent region of interest indicated. Somatic V m and Ca 2+ ∆F/F 0 signals at the region of interest associated with an unpaired CF-EPSP, with PFs stimulated with 5 pulses at 100 Hz or with a CF-EPSP paired with PF stimulation at hyp state. Black and dark blue traces were from recordings in control solution. Traces at different gray or blue tones were from recordings performed a time (t) after addition of 250 µM of the channel blocker IEM1460. B, On the left, same recordings in A for PF stimulation only (PF)in control condition and 20 minutes after addition of IEM1460; the exponential "fit" of the Ca 2+ ∆F/F 0 decay after the 5 th PF-EPSP is also reported with a dotted line. On the right, Ca 2+ transients associated with the slow mGluR1-mediated component calculated as the difference between the Ca 2+ ∆F/F 0 signals associated with PF stimulation and the fit trace on the left. C, Mean ± SD (N = 6 cells) of the ratio between the slow mGluR1-dependent PF-mediated Ca 2+ transients (PF -fit) 20 minutes after addition of IEM1460 and in control condition. "*" indicates a significant reduction of the signal (p< 0.01, paired t-test). The dotted line depicts the ratio = 1. D, Mean ± SD of the ∆F/F 0 ratio between the paired and unpaired signals in control solution or after addition of IEM1460. "*" indicates a significant inhibition of supralinear Ca 2+

Figure 11 .

 11 Figure 11. Wide mGluR1-dependent supralinear Ca 2+ signals at rest states. A, On the left, dendrite of PN filled with 2 mM OG5N; position of PF stimulating electrode and of two regions of interest indicated (R1 and R2); R1 is adjacent to the PF stimulating electrode; R2 is ~60 µm away from the PF stimulating electrode. On the right, somatic V m (top) and dendritic Ca 2+ signals (bottom) in R1 and R2 associated with a CF-EPSP unpaired or paired with a PF-EPSPs train with the CF stimulation delayed by 110 ms from the first PF stimulus at rest state. B, On a time window of 20 ms, somatic V m and dendritic Ca 2+ signals in R2 reported in panel A, exhibiting a supralinear Ca 2+ transient smaller than that in R1. C, Somatic V m (top) and dendritic Ca 2+ signal associated with an unpaired CF-EPSP in control condition or after addition of the A-type K + channel inhibitor AmmTx3. The two supralinear Ca 2+ signals reported in panels A and B are qualitatively very similar. All optical signals were from averages of 4 trials.

Figure 12 .

 12 Figure 12. Supralinear Ca 2+ signals associated with DHPG application. A, On the left, dendrite of PN filled with 2 mM OG5N (left); a region of interest and the position of a pipette delivering 100 µM DHPG dissolved in external solution are indicated; DHPG application was achieved by applying a 20 ms pulse of pressure using a pressure ejector. On the right, somatic V m (top) and dendritic Ca 2+ signals (bottom) in the region of interest associated with a CF-EPSP unpaired (light blue trace) or paired with DHPG application (dark blue trace); the timing of DHPG application and of CF stimulation are indicated with a purple line and a purple arrow respectively; a ∆F/F 0 artefact is observable during the short DHPG application. B, On a time window of 20 ms, dendritic Ca 2+ signals reported in panel A, exhibiting a supralinear Ca 2+ transient.C, First on the left, mean ± SD (2.20 ± 0.80, N = 7 cells) of ∆F/F 0 ratio between the CF-associated signal paired with DHPG application and unpaired. Following on the right, mean ± SD of ∆F/F 0 ratios between CF-associated signals paired with PF stimulation and unpaired; the statistics relative to 60 ms delay between the first PF stimulus and the CF stimulation is the same reported in Fig.1D; the two statistics relative to 110 ms delay between the first PF stimulus and the CF stimulation at hyp and rest states are the same reported in Fig.2D. The dotted line depicts ∆F/F 0 ratio = 1.

Figure 13 .

 13 Figure 13. Illustration of the determinants of the different dendritic supralinear Ca 2+ signals in PNs. On the top, a representative PN dendritic region indicating the position of the PF stimulation electrode and a hand-drawn schematic dendritic V m associated with an unpaired CF-EPSP and the consequent Ca 2+ transient at hyp and rest states. The V m transient opens principally T and A channels at the hyp state (box b), and principally P/Q (and possibly A channels) at the rest state (box a). In both cases, Ca 2+ entering through VGCCs binds to the endogenous Ca 2+ buffer (ECB) without saturating it. On the bottom, a handdrawn schematic dendritic V m associated with paired CF-EPSPs and the consequent Ca 2+ transient. During the PF-EPSPs Ca 2+ entering through both VGCC types saturates the ECB (box c). At 60 ms delay from the first PF-EPSP the CF-Ca 2+ transient principally mediated by P/Q channels produces a supralinear Ca 2+ increase because the ECB is saturated (box d). At 110 ms delay and at hyp state, the CF-Ca 2+

Figure 13

 13 Figure 13

  In contrast, the time to peak of the CF signals (paired and unpaired) at hyp states was significantly (p<0.01 paired t-test) longer (by 2.75 ± 0.71 samples) from the time to peak of the CF signals (paired and unpaired) at rest states. Finally, the time to peak of the CF signals at hyp states was significantly (p<0.01 paired t-test) longer (by 2.38 ± 0.75 samples) than the time to peak of the paired CF signals with the CF stimulation delayed by 60 ms from the first PF-stimulus. We therefore concluded that the fast kinetics of Ca 2+ transients associated with the CF-EPSP is identical in paired and unpaired condition, both at hyp and rest states, when the CF stimulation is delayed by 110 ms from the first PF stimulus. This conclusion suggests that the principal Ca 2+ source of the supralinear Ca 2+ signal with the CF stimulation delayed by 110 ms from the first PF stimulus at hyp states is the T-type VGCC. In contrast, the principal Ca 2+ source of the supralinear Ca 2+ signals with the CF stimulation delayed by 110 ms from the first PF stimulus at rest states, or with the CF stimulation delayed by 60 ms from the first PF stimulus, is likely the P/Q-type VGCC.

3D, top bar diagram) and at rest states (Fig.

3D

, bottom bar diagram). The time to peak of the paired CF signal at hyp states was the same of the unpaired CF signal at hyp states and the time to peak of the paired CF signal at rest states was the same of the unpaired CF signal at rest states.

  As shown in the example of Fig.9A, addition of NNC reduced the fast Ca 2+ transient associated with the PF-EPSP train while it did not affect the slow Ca 2+ transient mediated by mGluR1s. Furthermore, although both unpaired and paired Ca 2+ transients were inhibited by NNC, the paired Ca 2+ transient was still larger (Fig.9A), suggesting that local amplification of the residual component by buffer saturation is still present when T-type VGCCs are blocked. Thus, endogenous buffer is likely saturated by the slow mGluR1-mediated Ca 2+ influx. To test this hypothesis, we measured mGluR1-dependent supralinear Ca 2+ signals at hyp states while blocking the slow mGluR1-mediated Ca 2+ transient with the channel blocker IEM1460 that does not affect the mGluR1-dependent boosting of T-type VGCCs

influx component responsible for mGluR1-dependent supralinear Ca 2+ signals at hyp state is mediated by T-type Ca 2+ channels.

  2. Values for heparin were: 3.17 ± 0.41 for 110 ms CF delay at hyp states; 2.02 ± 0.27 for 110 ms CF delay at rest states; 2.72 ± 0.54 for 60 ms CF delay. Values for ryanodine were: 3.06 ± 0.85 for 110 ms CF delay at hyp states; 1.93 ± 0.56 for 110 ms CF delay at rest states; 2.56 ± 0.80 for 60 ms CF delay. Experiments were performed 45 minutes after whole cell to obtain full equilibration of the internal solution. Used concentrations of heparin and ryanodine were the maximal tolerated by the cells for one-hour recording. All optical signals were from averages of 4 trials.

  OG5N ∆F/F 0 and Fura -∆F/F 0 ) were obtained by alternating the excitation wavelength. B, Same Ca 2+ transients associated with the CF-EPSP in panel A, for the two indicators, superimposed either to the unpaired CF transient at hyp state or to the unpaired CF transient at rest state. C, S is defined as the ratio between the ∆F/F 0 peaks for each protocol and the ∆F/F 0 peak associated with the unpaired CF stimulation. On the left, mean ± SD (N = 8 cells) of S corresponding to Fura2 signals (S Fura2 ) in the different cases as reported in the legend; "*" indicates a significant difference (p< 0.01, paired t-test) between the two ∆F/F 0 peaks used to calculate S Fura2 . On the right, mean ± SD (N = 8 cells) of S Fura2 /S OG5N Fura2 ratios. All optical signals were from averages of 4 trials.

	in the different cases as reported in the legend; "*" indicates a significant difference (p< 0.01, paired t-test)
	between S OG5N and S Fura2 . "**" indicates a significant difference (p< 0.01, paired t-test) between two
	S OG5N /S

signals in the region of interest associated with different protocols: from left to right a CF-EPSP unpaired at hyp and rest states, paired with a PF-EPSPs train delayed by 110 ms from the first PF stimulus at hyp and rest states, and paired with a PF-EPSPs train delayed by 60 ms from the first PF stimulus; signals from the two indicators (

This work was supported by the Agence Nationale de la Recherche through three grants (ANR-14-CE17-0006 -WaveFrontImag; Labex Ion Channels Science and Therapeutics: program number ANR-11-LABX-0015 and National Infrastructure France Life Imaging "Noeud Grenoblois") and by the Federation pour la recherché sur le Cerveau (FRC -Grant Espoir en tête, Rotary France). We thank Dr. Boris Barbour for useful discussions during the project, for reading the manuscript before submission and for advices on improving the clarity of the figures.

transient produces a supralinear Ca 2+ increase because T channels are potentiated by active mGluR1s and the ECB is saturated by Ca 2+ entering through the mGluR1-activated channel (box f). At 110 ms delay and at rest state, the CF-Ca 2+ transient produces a supralinear Ca 2+ increase because the ECB is saturated by Ca 2+ entering through the mGluR1-activated channel and possibly because of a larger Ca 2+ influx via P/Q channels enhanced by stronger inactivation of A channels by mGluR1s (box e).