New Results

α2δ-2 protein controls structure and function at the cerebellar climbing fiber synapse

Kathleen A. Beeson, Ryne Beeson, Gary L. Westbrook, Eric Schnell
doi: https://doi.org/10.1101/685818

Abstract

α2δ proteins (Cacna2d1-4) are auxiliary subunits of voltage-dependent calcium channels that also drive synapse formation and maturation. Because cerebellar Purkinje cells (PCs) exclusively express one isoform of this family, α2δ-2 (Cacna2d2), we used PCs as a model system to examine roles of α2δ in excitatory synaptic function in a Cacna2d2 knockout mouse. Whole-cell recordings of PCs from acute cerebellar slices revealed altered climbing fiber (CF)-evoked complex spike generation, as well as increased amplitude and decay of CF-evoked excitatory postsynaptic currents (EPSCs). CF terminals in the KO were localized more proximally on PC dendrites, as indicated by VGLUT2+ immunoreactive puncta, and computational modeling demonstrated that the increased EPSC amplitude can be partly attributed to the proximal shifting of CF terminals. In addition, CFs in KO mice exhibited increased multivesicular transmission, corresponding to greater sustained responses during repetitive stimulation, despite a reduction in the measured probability of release. Electron microscopy demonstrated that mutant CF terminals had twice as many vesicle release sites, providing a morphologic explanation for the enhanced glutamate release. Though KO CFs evoked larger amplitude EPSCs, the charge transfer was the same as wildtype as a result of increased glutamate re-uptake, producing faster decay kinetics. Together, the larger, faster EPSCs in the KO explain the altered complex spike responses, which degrade information transfer from PCs and likely contribute to the ataxic phenotype of Cacna2d2 KO mice. Together, our results illustrate the multidimensional synaptic roles of α2δ proteins.

Significance Statement α2δ proteins (Cacna2d1-4) regulate synaptic transmission and synaptogenesis, but co-expression of multiple α2δ isoforms has obscured a clear understanding of how various α2δ proteins control synaptic function. In this study, we focus on roles of the α2δ-2 protein (Cacna2d2), whose deletion causes cerebellar ataxia and epilepsy in mice and humans. Because cerebellar Purkinje cells only expresses this single isoform, we studied excitatory climbing fiber synaptic function onto Purkinje cells in Cacna2d2 knockout mice. Using optical and electrophysiological analysis, we provide the first detailed description of the changes in Purkinje cell output in lacking α2δ-2, and provide a comprehensive mechanistic explanation for how functional synaptic phenotypes contribute to the altered cerebellar output.

Introduction

Synapses are indispensable to neural circuit function, yet our understanding of synapse formation in health and neurological disease is incomplete. Recently, α2δ proteins (Cacna2d1-4) have been recognized as important regulators of synapse formation and plasticity (Dolphin, 2012). In addition to their roles in synaptic transmission as auxiliary subunits of voltage-dependent calcium channels (VDCCs) (Canti et al., 2005; Hoppa et al., 2012), these proteins have multiple postsynaptic roles in driving synapse formation, trans-synaptic communication, and glutamate receptor function (Eroglu et al., 2009; Kurshan et al., 2009; Fell et al., 2016; Wang et al., 2016; Brockhaus et al., 2018; Chen et al., 2018; Geisler et al., 2019). Mutations in human α2δ genes have been associated with epilepsy, movement disorders, and schizophrenia (Edvardson et al., 2013; Pippucci et al., 2013), and α2δ-1/2 proteins are the primary targets of the widely prescribed antiepileptic and analgesic, gabapentin (Gee et al., 1996; Brown and Gee, 1998; Boning Gao, 2000). However, the roles of α2δ proteins in controlling synaptic and network function at any given synapse are still elusive, due in part to expression of multiple isoforms in many neurons.

Purkinje cells (PCs), the primary output pathway from the cerebellar cortex, exclusively express the α2δ-2 isoform (Cacna2d2) (Barclay et al., 2001a; Lein et al., 2007; Dolphin, 2012), thus providing a unique opportunity to determine how this protein affects synaptic transmission. Like the spontaneous ‘ducky’ mouse mutants (du2j/du2j or du/du), deletion of α2δ-2 causes cerebellar ataxia, epilepsy and premature death (Barclay et al., 2001b; Brodbeck et al., 2002; Ivanov et al., 2004; Donato et al., 2006), indicating the importance of α2δ proteins in neurological function.

The climbing fiber (CF) to PC synapse has multiple distinctive features, including the mono-innervation of mature PCs by a single CF (Hashimoto et al., 2009), making this an ideal site to determine how α2δ-2 contributes to synaptic function. CF activity drives complex spike (CpS) generation in PCs, which produces a high-fidelity error prediction signal important to the processing of motor coordination and learning (Yang and Lisberger, 2014; Heffley et al., 2018). CpSs are initiated by a AMPAR-mediated depolarization that drives an initial sodium spike followed by multiple axonally generated ‘spikelets’ (Davie et al., 2008), which correlate with the degree of PC spike rate plasticity and performance during motor learning (Khaliq and Raman, 2005; Yang and Lisberger, 2014; Burroughs et al., 2017). In this manner, CF synaptic activity controls cerebellar command of motor output.

We combined structural and electrophysiological analysis of the CF to PC synapse with Cacna2d2 knockout mice (Ivanov et al., 2004) to elucidate the contribution of α2δ-2 to excitatory synapse formation and transmission. Contrary to positive regulation of excitatory synaptogenesis by α2δ-1 isoform (Li et al., 2004; Eroglu et al., 2009; Chen et al., 2018; Risher et al., 2018), loss of α2δ-2 resulted in increased innervation by CFs. Thus, α2δ-2 KO CFs have elevated glutamate release and clearance compared to WT, resulting in profound deficiencies in the generation of CpS spikelets. Together, these studies demonstrate the critical role of α2δ-2 in proper CF-PC synapse organization and network function, and allude to the wide versatility of α2δ proteins at the synapse.

Materials & Methods

Animals

Cacna2d2 knockout mice (Cacna2d2tm1Svi, MGI = 3055290; generously supplied by Drs. Sergey Ivanov and Lino Tessarollo) were obtained as cryopreserved sperm and re-derived via in vitro fertilization on a C57B/6J background. Breeding mice were kept heterozygous, and genotyping was performed using the following primers: forward 5’-ACTGGTGGGCATCTTACAGC-3’, reverse mutant 5’ - AAAGAACGGAGCCGGTTG-3’, reverse wildtype 5’- TGTTAGCGGGGAGGTCACTA- 3’. This produced a ∼700 bp product from the wildtype allele and a ∼550 bp product from the mutant allele. Mice were born in the Mendelian ratio of 1:2:1; with WT mice having two copies of the intact Cacna2d2 gene, and KO mice as homozygous mutants. Because ∼50% of KO mice die prematurely (Ivanov et al., 2004), all experiments utilized male and female mice between p21-p30, when CF-PC synapses have reached maturity but before significant loss of KO mice.

Cacna2d2 deletion was verified using quantitative PCR. Briefly, mice were deeply anesthetized by inhalation of 4% isoflurane followed by injection of 0.8 ml of 2% avertin (Sigma-Aldrich) and rapidly decapitated. Brain was dissected in ice-cold sterile PBS containing RiboLock RNase Inhibitor (ThermoFisher, 1:200k) and whole cerebella were isolated and homogenized in QIAzol Lysis Reagent (Qiagen) and stored at -80°C. RNA isolation and qPCR were performed by the Oregon Health & Science University Gene Profiling/RNA and DNA Services Shared Resource. In brief, RNA was isolated using the Trizol/RNeasy hybrid protocol with QIAcube automation. SuperScript VILO cDNA synthesis kit (Life Technologies) was used for reverse transcription with 800 ng of input RNA per 100 µl reaction. 2 µl of cDNA was used in the PCR reaction using the TaqMan Universal master mix (Life Technologies), using a single master mix per TaqMan probe set for Cacna2d2 (Mm01230564_g1), and ACTB and RPL7a were used as endogenous controls. Data were acquired using Applied Biosystems QuantStudio 12K Flex Software v1.2.2 (Life Technologies) with settings set to default.

Animals used in these studies were maintained in facilities fully accredited by the Association for Assessment and Accreditation of Laboratory Animal Care and veterinary care was provided by Oregon Health and Science University’s Department of Comparative Medicine. All animal care and experiments were performed in accordance with state and federal guidelines, and all protocols were approved by the OHSU Institutional Animal Care and Use Committee.

Immunohistochemistry

Following deep anesthesia as described above, p21 Cacna2d2 KO and WT littermates were transcardially perfused with 5 ml phosphate-buffered saline (PBS) followed by 4% paraformaldehyde-PBS (PFA-PBS). Mice were decapitated, and brains were removed and post-fixed for 24 hrs in 4% PFA-PBS. Cerebella were cut in sagittal sections at 50 µm on a vibratome and stored in PBS at 4°C. Sections containing vermis lobe VI were permeabilized with 0.4% Triton-PBS containing 10% normal goat serum for 1hr at room temperature, then stained with mouse anti-Calbindin 1:20 (Neuromab #73-452) and guinea pig anti-VGLUT2 1:200 (Synaptic Systems #135404) at 4°C overnight. After rinsing, corresponding fluorescently-labeled secondaries (Invitrogen) were applied at 1:400 and glass coverslips were mounted on glass slides with Fluoromount G (Sigma-Aldrich).

To image VGLUT2+ synapses, 6 µm z-stack images from the vermis lobe VI were acquired at 0.2 µm intervals with a Zeiss LSM780 laser scanning confocal microscope at 40x magnification and 1024 x 1024 pixel density using ZEN software. This produced images of the entire thickness of the molecular layer, including the PC somata. Images were then analyzed in FIJI/ImageJ. VGLUT2+ puncta distribution/density were quantified from maximum projection images as distinct VGLUT2+ puncta of at least 0.2 µm2, after subtracting the background for increased contrast. For each punctum, the y-distance from the top of the PC layer to the terminal was measured. Per image, a minimum of 100 µm of linear PC layer was quantified. VGLUT2+ puncta distributions were then binned into 10 µm distances. VGLUT2+ puncta size and a second measure of density (from whole volume of tissue) were calculated using a masking feature in FIJI/ImageJ that captures puncta between 0.1-5µm2, and this was normalized to the length of PCL imaged to produce a measure of density per µm of PCL. Punctum distribution, density and size data were averaged from 2-3 sections/animal, using 5-6 animals of each genotype. Slides were coded prior to imaging, and image acquisition and analysis were performed by investigators blinded to genotype. Sections were stained side-by-side with the same antibody mixtures, and imaging parameters were kept constant between samples.

Slice Preparation and Electrophysiology

KO or WT littermates were deeply anesthetized as described above, and transcardially perfused with ice-cold sucrose-based solution containing (mM): 87 NaCl, 2.5 KCl, 1.25NaH2PO4, 0.4 ascorbate, 2 Na pyruvate, 25 D-glucose, 25 NaHCO3, 75 Sucrose, 7 MgCl2, 0.5 CaCl2 (osmolarity adjusted to 300-305 mOsm) and equilibrated with 95% O2 and 5% CO2 gas mixture. Acute 300 µm sagittal slices were cut from cerebellum using a vibratome (VT1200, Leica Microsystems), and incubated for 30 minutes in standard artificial cerebral spinal fluid (aCSF) at 34°C.

Whole-cell recordings were obtained using 1-3 MΩ borosilicate glass pipettes filled with either K-gluconate or CsCl2-based internal solution. For current clamp experiments, internal solution contained (in mM): 135 K-gluconate, 10 HEPES, 10 NaCl, 1 MgCl2, 0.1 BAPTA, 0.1 CaCl2, 2 ATP-Mg, and 10 phosphocreatine, pH 7.28 adjusted with KOH (osmolarity adjusted to 289 mOsm). For voltage clamp recordings, the internal solution contained (in mM): 100 CsMeSO4, 35 CsCl, 15 TEA-Cl, 1 MgCl2, 15 HEPES, 0.2 EGTA, 2 ATP-Mg, 0.3 TrisGTP, 10 phosphocreatine, and 2 QX-314, pH 7.3 adjusted with CsOH (osmolarity adjusted to 295 mOsm). External solution contained (in mM): 125 NaCl, 25 NaHCO3, 1.25 NaH2PO4, 3 KCl, 25 Dextrose, 2 CaCl2, 1 MgCl2 (osmolarity adjusted to 300 mOsm) and was continuously perfused via roller pump.

PCs from the vermis, lobe VI were identified by soma size and location in the PC layer using live infrared differential contrast microscopy on an upright Olympus microscope. Inhibition was blocked in all experiments by 10 µM SR95531 (Tocris). Whole-cell patch-clamp recordings were obtained in voltage clamp mode and cell capacitance, series resistance and input resistance were monitored in real time using intermittent -10 mV voltage steps. Signals were amplified with a MultiClamp 700B (Molecular Devices) amplifier and pipette capacitance was compensated for using MultiClamp software. Signals were low-pass Bessel-filtered at 6 kHz and sampled at 10 kHz, and digitized with a National Instruments analog-to-digital board. All recordings were acquired and analyzed using IgorPro-based (Wavemetrics) software. All recordings were performed at room temperature.

Climbing fiber-mediated excitatory postsynaptic currents (EPSCs) were evoked using theta or monopolar glass electrode stimulation in the granule cell layer (0.1 ms, 0- 100 V square pulses; 0.1 or 0.05 Hz stimulation frequency), placed ∼50 µm from the PC, and the stimulation electrode position was adjusted if needed to obtain a CF response. CF responses were identified as large all-or-none EPSCs that appeared during incremental increases in stimulation intensity, as well as through paired-pulse depression when stimulated with 2 pulses 50 ms apart. All cells were first recorded in voltage clamp mode, where a hyperpolarizing step of -10 mV was applied to monitor cell capacitance, series resistance and input resistance. Series resistance was not compensated; cells with series resistance >10 MΩ or a >2 MΩ change in series resistance over the course of the experiment were excluded.

For current clamp experiments, PC resting membrane potential was measured by holding the cell in zero current mode, then a small amount of bias current (approximately-130 pA) was injected to keep the cell near -60 mV for complex spike and current step experiments. Bridge balance was applied to compensate for pipette and series resistance throughout the recording. First, CFs were stimulated at 0.1 Hz and 10 consecutive sweeps of evoked complex spikes were recorded. Then with CF stimulation off, 500 ms steps of current injection from -200 pA– 1 nA were delivered at least 5 times per step. Cells were returned to voltage clamp mode to assess recording stability. For complex spike analysis, sweeps were averaged from which the initial spike amplitude and rise rate were measured. Spikelets were quantified as rapid depolarizations (>1000 V/s) that reached +20 mV from baseline, from which spikelet trough-to-peak amplitudes were measured. Area under the curve was measured by integrating the trace during the first 100 ms following stimulation.

For most voltage clamp experiments, cells were held at -70 mV in the presence of 0.5 µM NBQX (Tocris) to maintain voltage clamp during CF EPSCs. Brief hyperpolarizing steps (-10 mV) were delivered to monitor PC access and input resistance preceding each CF-evoked EPSC. 10 CF EPSC trials were averaged, and these averages were used to determine peak amplitude, 20-80% rise time and tau of decay (from single-exponential fits of the EPSC decay). Then, ten paired-pulse responses with an inter-stimulus interval of 50 ms were collected, followed by 10 Hz trains of CF stimulation or drug wash-in experiments. For DL-TBOA experiments, baseline EPSCs were acquired at Hz before 50 µM DL-TBOA (Tocris) was added to the bath. For kynurenic acid (KYN) experiments, aCSF excluded NBQX and PCs were held at -20 mV to maintain voltage-clamp during 0.1 Hz CF stimulation. After acquiring baseline EPSCs, 1 mM KYN (Sigma-Aldrich) was added to the perfusate. Quantification of EPSC peak amplitude and tau of decay from drug wash-in experiments used averages from 10 sweeps prior to wash-on compared to 10 sweeps after 10 minutes of exposure to drug (For KYN effect: (EPSCControl - EPSCKYN) * 100; For TBOA effect: (τTBOA - τControl) * 100). For asynchronous EPSC (aEPSC) experiments, aCSF was composed of 1.3 mM Sr2+ in replacement of Ca2+ and 3.3 mM Mg2+, and NBQX was omitted. PCs were held at -70 mV and CFs were stimulated at 0.05 Hz. ∼10 trials were used for quantification of aEPSCs, which were sampled from a 500 ms window starting at 150 ms from CF stimulation, and selected manually. For data presentation, aEPSC traces were off-line box-filtered at 1 kHz. To estimate the readily releasable pool, cumulative CF response amplitudes were plotted, and the last third of the train was fit with a linear regression that was extrapolated to time 0 (Schneggenburger et al., 1999).

NEURON Computational PC Model

CF simulations were performed with NEURON version 7.7.0, using source code generously supplied by Dr. Michael Häusser (Roth and Häusser, 2001). The following model parameters were kept constant across all simulations: Rm = 120.2 kΩcm2, Cm = 0.64 µF/cm2 and a residual uncompensated series resistance of 1 MΩ. Because the Model is based on recordings and dimensions of a p21 rat PC (Roth and Häusser, 2001), we normalized our WT measurements for CF distribution to the model cell as control, and adjusted the dendritic innervation by KO CFs based on our VGLUT2+ distribution as a relative decrease in length of coverage (i.e. 0.7x CF length of control). CF EPSCs were simulated using 500 inputs of 1 nS peak conductance (simulated as the sum of two exponentials for rise and decay) with a reversal potential of 0 mV and a constant density per dendritic length distribution. Simulation time step was 10 µs for integration. Waveforms were created in IgorPro8 from simulation output to measure EPSC decay time constants by fitting with a single exponential.

Transmission Electron Microscopy (TEM)

Animals were deeply anesthetized with isoflurane and avertin, as described above, and then transcardially perfused with 10 ml ice-cold heparin (1k usp per ml; Novaplus) followed by freshly prepared 2% glutaraldehyde/2% paraformaldehyde in 0.1M PB solution filtered with #3 filter paper (VWR) and pH to 7.4. Brains were dissected, cerebella were blocked, and post-fixed for 30 minutes in 4% paraformaldehyde. Tissue was transferred to 0.1 M PB for storage at 4°C and 40 µm sagittal slices of vermis lobe VI were made using a Leica microtome. Slices were collected in separate wells to assure TEM would be from slices >100 µm apart. PFA, Glutaraldehyde and microtome blades were all from Electron Microscopy Sciences (EMS).

Tissue samples were coded before processing for TEM by a blinded investigator. Briefly, sections were incubated in 1% osmium tetroxide in PB for 30 minutes, dehydrated through a graded series of ethanols, placed into propylene oxide for 30 min, and then placed in 1:1 propylene oxide:EMBed resin (EMS) rotating at room temperature overnight. Sections were then incubated in 100% resin for 2 hrs, embedded between sheets of Aclar plastic, and incubated at 60°C for 48 hrs. Cerebellum sections were then glued to resin blocks and ultrathin sections (50 nm) were collected onto 400 mesh copper grids (EMS). The ultrathin sections were then counterstained with uranyl acetate and Reynolds lead citrate and examined using a FEI Tecnai 12 electron microscope (Hillsboro, OR) and images were captured using an Advanced Microscopy Techniques digital camera.

CF terminals were imaged from the most highly innervated region of the molecular layer (20-60 µm from PC somata) and identified at 6800x magnification by the following criteria: proximity (<3 µm) to PC primary dendrites, dense-packing of round vesicles, and when synaptic contacts were present, asymmetric Gray’s type-1 excitatory synaptic markers. Images were taken at 18500x magnification and CF terminals with clearly delineated membranes that met the criteria described above were analyzed using Fiji/ImageJ software by a separate blinded investigator. Terminal area, total SV density, the length and number of synaptic contacts made by each terminal (as determined by the opposing postsynaptic density), as well as the number of SVs within 100 nm of each synaptic contact as a proxy for the readily releasable pool were measured. Quantifications from ∼10-15 CF images/animal were averaged (n = animal).

Statistics

Data was tested for Gaussian distribution using the Kolmogorov-Smirnov normality test with Dallal-Wilkinson-Lilliefor P value. Differences between genotypes in VGLUT2+ puncta distribution and TEM total synaptic contacts/terminal were tested for significance using Kolmogorov-Smirnov test. For other nonparametric data, the Mann-Whitney test was used (i.e. CpS spikelet number). Immunofluorescence, TEM, and electrophysiology data with normal distributions were analyzed using Student’s t-tests. Normalized and cumulative amplitude responses during repetitive CF stimulation were compared between genotypes using Multiple t-tests with Holm-Sidak correction. For morphology data, multiple images per animal were averaged and n = mice. For electrophysiology, all experiments utilized at least 4 animals per genotype, and n = cells. Data were graphed in Prism GraphPad version 8 and are reported as the mean ± SEM. *p<0.05, **p<0.01, ***p<0.001, ****p<0.0001.

Results

α2δ-2 controls Purkinje cell spiking patterns in response to climbing fiber activation

To examine how the loss of α2δ-2 affects cerebellar output, we performed whole-cell recordings from PCs in acutely prepared cerebellar slices from α2δ-2 knockout (KO) mice and their wildtype (WT) littermates at p21-p30, after CF innervation has reached maturity (Hashimoto et al., 2009). We focally stimulated CFs in the granule cell layer and unitary CF-mediated EPSCs were identified by their large amplitude, all-or-nothing nature and paired-pulse depression (Dittman and Regehr, 1998; Hashimoto and Kano, 1998; Liu and Friel, 2008; Rudolph et al., 2011). CF-evoked CpSs were then recorded in current clamp mode.

The voltage envelope of CpS waveforms was comparable between WT and KO (Figure 1A; Integral of CpS between time 0 - 100 ms: WT = 0.96 ± 0.06 V • s, n = 10; KO = 0.81 ± 0.06 V • s, n = 11; p = 0.1; unpaired Student’s t-test), but the number of CpS spikelets was substantially reduced in KO PCs (Figure 1B; WT = 3.2 ± 0.5, n = 10; KO = 1.2 ± 0.4, n = 11; p = 0.002; Mann-Whitney). In addition, the few spikelets that did occur during the KO CpS were of lower trough-to-peak amplitude. All first spikelets in the WT were >30 mV compared to 75% in the KO (Figure 1C), which is consistent with a lower probability of CpS transmission (Khaliq and Raman, 2005) in the α2δ-2 KO. Moreover, though subsequent spikelets were present in 2 of 11 KO cells, none reached 30 mV trough-to-peak amplitude (Mean KO spikelet2 = 16.5 ± 5.7 mV, n = 2; spikelet3 = 7.6 mV, n = 1; spikelet4 = 7.2 mV, n = 1; spikelet5 = 6.5 mV, n = 1). Despite significant differences in CpS spikelet generation between genotypes, initial spike amplitudes (Figure 1D) and rise rates were unchanged between WT and KO (Spike slope: WT = 1790 ± 230 V/s, n = 10; KO = 1660 ± 240 V/s, n = 11; p = 0.69; unpaired Student’s t-test).

Figure 1
Figure 1 Climbing fiber (CF)-evoked complex spikes (CpSs) are altered in the Cacna2d2 KO, but intrinsic PC excitability is unchanged.

(A) Representative CF-evoked complex spikes in WT (left) and KO (right) PCs, arrow indicates CF stimulation. Each trace consists of 10 overlaid traces (lighter color) and the corresponding CpS average (dark color). (B) Average number of spikelets per CpS in WT and KO PCs; **p < 0.01 (Mann-Whitney). (C) Percentage of spikelets exceeding 30 mV trough-to-peak amplitude, ordered by spikelet number. (D) Average CpS initial spike amplitude; p = 0.89 (NS). (E) Average PC membrane potential when in zero current mode; p = 0.60 (NS). (F) Representative single traces of membrane voltage responses to current injection, showing steps of 0, 100, 200 pA injections from Vm = -60 mV; Left WT (black); Right KO (green). Average Istep to initiate spiking WT = 200 ± 39 pA, n = 10; KO = 289 ± 82 pA, n = 9; p = 0.33 (NS). (G) Average spike count during current steps from -0.2 to 1 nA, Vm = -60 mV. WT (black) and KO (green); p = 0.63 (NS; Two-way ANOVA with repeated measures, F(1, 19) = 0.23). Data shown ± SEM, n = cells; unpaired Student’s t-test unless otherwise indicated.

The altered CpS in KO PCs were not associated with changes in the intrinsic excitability of α2δ-2 KO PCs as measured by their resting membrane potentials (Figure 1E), input resistance (WT 140 ± 20 MΩ, n = 8; KO 122 ± 7.8 MΩ, n = 11; p = 0.38, unpaired Student’s t-test), or response to current injection (Figures 1F and 1G). Thus, we explored whether altered CpS patterns might represent differences in CF-mediated synaptic currents.

α2δ-2 knockout mice have larger CF-evoked EPSCs with accelerated decay kinetics

The CF-evoked excitatory postsynaptic current (EPSC) kinetics influence the CpS shape, such that a slow EPSC decay increases the likelihood of spikelet generation (Rudolph et al., 2011). Spikelet generation is also sensitive to the peak synaptic conductance, as an increased phasic conductance can result in depolarization block and failure to generate spikelets (Davie et al., 2008). Thus, we performed whole-cell recordings of CF EPSCs in the presence of low concentrations of the AMPAR antagonist, NBQX (0.5µM), to facilitate voltage clamp control (as in Dittman and Regehr, 1998; Liu and Friel, 2008; Rudolph et al., 2011).

Peak EPSC amplitudes were 37% larger in KO mice (Figures 2A and 2B; WT = 703 ± 63 pA, n = 17; KO = 961 ± 86 pA, n = 19, p = 0.03; unpaired Student’s t-test). WT and KO EPSC decays were well-fit by a single exponential curve, and KO EPSCs exhibited faster decay kinetics (Figures 2C and 2D; WT τdecay = 20.6 ± 1.1 ms, n = 17; KO τdecay = 13.2 ± 0.8 ms, n = 20, p < 0.0001; unpaired Student’s t-test). Despite these two alterations, the EPSC in the KO had an equivalent charge transfer to that of WT EPSCs (Figures 2E), and 20-80% risetimes were similar in WT and KO PCs (Figures 2F and 2G).

Figure 2
Figure 2 CF-evoked EPSCs are larger and faster in Cacna2d2 KO mice, but total charge transfer is conserved.

(A) Representative CF-evoked EPSCs. Left WT average (black); Right KO average (green). (B) Average peak CF EPSC amplitude; *p < 0.05. (C) Peak scaled EPSCs, demonstrating the relative decay time constants for these example traces (τdecay) based on single exponential fits; WT (black) and KO (green). (D) τdecay (ms) for CF EPSCs in WT vs. KO PCs; **** p< 0.0001. (E) Average charge transfer within the first 100 ms of EPSC; p = 0.58 (NS). (F) Peak scaled EPSCs, expanded to display risetime kinetics; WT (black) and KO (green). (G) Average CF EPSC 20-80% risetime (ms); p = 0.83 (NS). Data shown ± SEM, n = cells; unpaired Student’s t-test.

Proximal redistribution of CF synapses in the α2δ-2 knockout partially contributes to larger CF-evoked EPSCs

To examine the larger EPSC in KO mice, we isolated quantal events at CF synapses via desynchronized CF evoked release. We replaced extracellular calcium with strontium (Rudolph et al., 2011; Zhang et al., 2015), and measured the amplitudes of CF- derived asynchronous quantal release events (aEPSCs). The average aEPSC was 24% larger in KO compared to WT PCs (Figures 3A-C; WT = 25.6 ± 1.0 pA, n = 8; KO = 31.8 ± 1.6 pA, n = 8, p = 0.004; unpaired Student’s t-test), indicating that part of the increased CF-evoked EPSC amplitude could be accounted for by a larger unitary response.

Figure 3
Figure 3 Desynchronized CF-evoked vesicle release reveals larger quantal responses in Cacna2d2 KO.

(A) Representative CF-evoked EPSCs in the presence of 1.3 mM Sr2+; Top WT EPSC (black) and example asynchronous EPSC (aEPSC; inset); Bottom KO EPSC (green) and aEPSC (inset). (B) Cumulative aESPC amplitude distribution graphed in 10 pA bins; WT (black) and KO (green); **p < 0.01 for 20 and 30 pA bins, all others NS (Multiple t-tests with Holm-Sidak correction for multiple comparisons). (C) Average aEPSC amplitudes; **p < 0.01. Data shown ± SEM, n = cells; unpaired Student’s t-test.

Therefore, we asked whether there might also be an increase in the number of CF synapses onto PCs using an immunohistochemical approach. CF terminals can be selectively identified as discrete puncta along the primary dendrites of PCs through their expression of VGLUT2 (Miyazaki et al., 2004; Zhang et al., 2015). As is apparent in Figure 4A, VGLUT2+ puncta were significantly closer to PC somata in KO mice than in WTs. CF terminals were a mean distance of 40.8 ± 0.5 µm from the PC soma in WT, whereas α2δ-2 KO mice had a mean CF terminal distance of 30.6 ± 0.3 µm (Figures 4A and 4C; n = 3-5 images from 5 mice of each genotype; p < 0.0001; Kolmogorov-Smirnov test). Moreover, distal CF innervation (beyond 50 µm from the PC soma; Figure 4B) accounted for 23% of puncta in WT, but only 6% in KO. This shift in CF terminal distribution in KO animals was not associated with a change in VGLUT2+ puncta size (Figure 4D) or overall number of puncta within the molecular layer (Figure 4E; Mean number of puncta normalized to length of PCL: WT = 1.91 ± 0.21puncta/µmPCL; KO = 1.81 ± 0.14 puncta/µmPCL, n = 3-5 images from 5 mice of each genotype; p = 0.7; unpaired Student’s t-test). There was no change in the molecular layer width, and the density of PCs was unchanged (Mean molecular layer width; WT = 110 ± 3.8 µm; KO = 106 ± 4.8 µm, p = 0.43; Mean PC density; WT = 0.62 ± 0.08 cells/µmPCL; KO = 0.65 ± cells/µmPCL, p = 0.72; n = 8 images from 3 mice of each genotype; unpaired Student’s t-test).

Figure 4
Figure 4 CF terminal distribution, but not number, is altered in Cacna2d2 KO cerebellum.

(A) Representative images from p21 WT (above) and KO (below) tissue, depicting the Purkinje cell layer (PCL). Calbindin (left/blue in merge) marks PCs, while VGLUT2 immunoreactivity (middle/red in merge) marks CF terminals. Yellow lines demarcate the 50 µm most proximal to PC somata and is the region most highly innervated by climbing fibers. Scale bar = 20 µm. (B) VGLUT2-immunoreactive CF terminals in the outer molecular layer, cropped at the distal yellow line (50 µm), illustrate differences in CF innervation of distal PC dendrites in WT (top) and KO (below) PCs. Scale bar = 20 µm. (C) Cumulative distribution of VGLUT2+ puncta relative to PC somas in WT (black, n = 5 animals) and KO (green, n = 5 animals); ****p < 0.0001 (Kolmogorov-Smirnov test). (D) Average VGLUT2+ punctum size is not significantly different between WT and KO terminals; p = 0.55 (NS). (E) Average VGLUT2+ puncta density per length of PCL (puncta/ µmPCL) is not significantly different between WT and KO; p = 0.72 (NS). Unless otherwise stated, data shown ± SEM, n = animal; unpaired Student’s t-test.

The increased proximity of CF inputs to PC soma in the KO could contribute to both the increased EPSC amplitude and decay rate, due to decreased dendritic filtering (Roth and Häusser, 2001). To ask whether changes in CF synapse localization alone could account for the altered EPSC amplitude and kinetics, we modified the Roth and Häusser (2001) computational model of dendritic integration of CF inputs onto PCs to match our data. This model, based on morphological reconstructions of single PCs and empirical measurements of dendritic filtering (Roth and Häusser, 2001), allowed us to simulate how redistribution of CF inputs would affect the ensemble CF EPSC. Using this model (Figures 5A; For KO, “Model CF70% Control” simulates the empirically observed VGLUT2+ distribution from Figure 4C), a shift from the WT to the KO distribution of CF inputs produced only a 16% increase in simulated EPSC amplitude and a 15% decrease in tau of decay (Figures 5B). Thus, the proximal distribution of CF inputs in the KO augment the quantal response (Figure 5C), consistent with the increase in evoked CF EPSC amplitude.

Figure 5
Figure 5 Computational PC model simulates the impact of proximally shifted CF inputs on EPSC waveform.

(A) Left Model CF input distribution similar to control PCs (dark blue; “Model CFControl”) vs. a similar PC with CF inputs shifted 30% closer (right, light blue, “Model CF70% Control”), which matches the degree of proximal shift in WT vs. KO innervation, respectively. All models conserve the total number of CF quantal inputs (500 inputs with 1 nS conductance), though input density is adjusted to accommodate the shortened region of CF innervation (see inset). (B) Overlay of EPSC output waveforms from Model CFControl simulations (dark blue; 4.7 nA), Model CF70% Control (light blue; 5.4 nA), and peak scaled Model CFControl to compare decay kinetics. For tau of decay; Model CFControl τdecay = 12.0 ms; Model CF70% Control τdecay = 10.2 ms). (C) Predicted increase in EPSC peak amplitude for various degrees of proximally shifted Model CFs (light blue bars, restricted to a zone 100-50% the width of control CFs, all including 500 quantal inputs) compared to Model CFControl (dark blue bar). For comparison, the empirically determined increase in quantal EPSC (aEPSC; hatched green bar) and evoked EPSC (eEPSC; filled-hatched dark green bar) amplitudes in KO PCs are also displayed (derived from Figures 3 and 2, respectively). The orange dotted line demarcates the predicted EPSC increase from the model based on the observed shift in CF location.

Increased multivesicular release from α2δ-2 knockout CFs

CF synapses exhibit multivesicular release, in which individual synapses simultaneously release multiple quanta, increasing the synaptic glutamate concentration (Wadiche and Jahr, 2001; Rudolph et al., 2011). To determine whether KO mice displayed altered multivesicular release, we used the low affinity, competitive AMPAR antagonist, kynurenic acid (KYN), to assay synaptic glutamate concentrations. Because KYN binds and unbinds AMPARs throughout the duration of the CF-evoked glutamate transient, KYN inhibition of the AMPAR-mediated current is inversely proportional to the concentration of glutamate present at postsynaptic receptors (Wadiche and Jahr, 2001). KYN (1µM) inhibited WT EPSC peak amplitudes by 65% (Figures 6A and 6B; Average EPSCPeak amplitude control vs. KYN; WTControl = 1.77 ± 0.41 nA vs. WTKYN = 0.62 ± 0.16 nA, n = 6, p = 0.007; paired Student’s t-test), whereas KO EPSCs were inhibited by only 40% (Average EPSCPeak amplitude control vs. KYN; KOControl = 2.63 ± 0.31 nA vs. KOKYN = 1.57 ± 0.21 nA, n = 8, p = 0.0009; paired Student’s t-test; For relative change in WT vs. KO, p = 0.001; unpaired Student’s t-test), demonstrating enhanced multivesicular release from KO CFs.

Figure 6
Figure 6 Cacna2d2 KO has increased glutamate release and clearance at CF-PC synapses.

(A) Representative CF EPSCs recorded at Vm = -20 mV in the absence of NBQX for WT and KO PCs (relative scales; WT = black; KO = green). For each, traces after exposure to 1 mM kynurenic acid (KYN; blue) are shown normalized to baseline EPSC amplitudes. (B) Percent inhibition of ESPC peak amplitude by KYN; ***p < 0.001. (C) Representative normalized CF-evoked EPSCs recorded at Vm = -70 mV in the presence of 0.5 µM NBQX; Left WT average (black); Right KO average (green). Overlay average peak-scaled traces after exposure to 50 µM DL-TBOA (TBOA; magenta). (D) Average increase in EPSC decay by TBOA; **p < 0.01. Data shown ± SEM, n = cells; unpaired Student’s t-test.

For these experiments, PCs were held at -20 mV to maintain voltage clamp of the CF-evoked EPSC (Harrison and Jahr, 2003; Rudolph et al., 2011) and NBQX was omitted because co-application of NBQX and KYN facilitates AMPAR-mediated responses (Prescott et al., 2006). Interestingly, at this holding potential, KO EPSCs exhibited slower decay kinetics (For τdecay at baseline Vm = -20 mV; WT-20mV = 11.6 ± 1.12 ms, n = 6; KO-20mV = 18.5 ± 1.32 ms, n = 8, p = 0.002; unpaired Student’s t-test). Although this is consistent with a larger glutamate transient due to multivesicular release (Paukert et al., 2010), it is in apparent odds with the faster decay kinetics in KO PCs at more hyperpolarized potentials. One explanation for this discrepancy in decay kinetics could be the voltage-dependence of glutamate re-uptake by PCs. PCs and surrounding Bergmann glia express high levels of glutamate transporters to manage spillover and glutamate clearance, and activity of these transporters shapes the CF-evoked EPSC waveform (Paukert et al., 2010). However, PCs play a dominant role in synaptic glutamate clearance (Auger and Attwell, 2000), and glutamate transporters have decreased efficiency at depolarized voltages (Bergles et al., 1997). In this scenario, the contributions of PC and Bergmann glia glutamate transporters together result in rapid EPSC decay in the KO at hyperpolarized potentials, but prolonged decay expected from multivesicular release dominates the EPSC waveform when KO PCs are held at depolarized potentials.

Faster EPSC decay in α2δ-2 knockout due to enhanced glutamate clearance

We further investigated the role of glutamate transporters in shaping the CF EPSC waveform in WT and KO mice while holding PCs at -70 mV in the presence of low NBQX (0.5 µM), as in our prior voltage clamp experiments (Figure 2). Block of glutamate transporters with the non-selective transport re-uptake inhibitor, DL-TBOA (50 µM), increased WT decay constants by ∼30% (similar to Rudolph et al., 2011) (Figures 6C; WT τdecay control vs. TBOA; WTControl = 13.6 ± 0.9 ms vs. WTTBOA = 17.4 ± 0.9 ms, n = 7, p = 0.001; paired Student’s t-test). In contrast, TBOA increased decay constants of KO EPSCs by 73% (KO τdecay control vs. TBOA; KOControl = 11.1 ± 1.1 ms vs. KOTBOA = 19.1 ± 2.2 ms, n = 7, p = 0.001; paired Student’s t-test). After TBOA exposure, WT and KO had similar decay constants (τdecay WT vs. KO in TBOA; p = 0.48; unpaired Student’s t-test). However, the relative effect of TBOA on decay was significantly greater in KO EPSCs (Figure 6D; % increase in τdecay WT vs. KO, p = 0.003; unpaired Student’s t-test) consistent with enhanced glutamate clearance by surrounding glutamate transporters.

Repetitive stimulation of CFs suggests lower release probability in the α2δ-2 knockout, though cumulative vesicle release is greater

The enhanced multivesicular release in the α2δ-2 KO (Figure 6A-B) suggests a presynaptic contribution to the CF EPSC phenotype. CF synapses have high initial probability of release (PR), which is associated with paired-pulse depression at short interstimulus intervals (Hashimoto and Kano, 1998). However, CF-evoked EPSCs from KO mice showed a consistent increase in the paired-pulse ratio when compared with WT CFs (Figures 7A and 7B; Paired-pulse ratio: WT = 0.41 ± 0.03, n = 17; KO = 0.51 ± 0.02, n = 18, p = 0.01; unpaired Student’s t-test), suggesting CFs have a lower PR when α2δ-2 is deleted. Therefore, we hypothesized that KO CFs might have a substantially greater readily releasable pool of glutamate to exhibit increased multivesicular release while also having a lower PR.

Figure 7
Figure 7 Repetitive stimulation of CF synapses reveals a lower probability of release and greater cumulative release in Cacna2d2 KO.

(A) Representative traces from WT (black) and KO (green) PCs during 50 ms paired-pulse stimulation. Traces are scaled to the first EPSC (EPSC1). Dotted gray line shows paired-pulse depression of the second EPSC (EPSC2) in WT compared to KO. (B) Average paired-pulse ratio (EPSC2 /EPSC1); ** p < 0.01. (C) Representative traces in response to 10 Hz stimulation; WT (black); KO (green). (D) Traces from (C) peak scaled to EPSC1 and overlaid, illustrating different relative steady-state EPSC amplitudes during latter portions of the train. (E) Summary data of EPSC amplitudes normalized to EPSC1 during 10 Hz stimulation in WT (black) and KO (green). *p < 0.05 (Multiple t-tests with Holm-Sidak correction). (F) EPSC amplitudes during 10 Hz stimulation plotted as cumulative amplitude from WT (black) and KO (green). For comparison of cumulative amplitude between WT and KO at various stimulation numbers (stim #); * p < 0.05, ** p < 0.01, *** p < 0.001 (Multiple t-tests with Holm-Sidak correction). Dotted grey lines illustrate a linear fit to cumulative amplitude between stim # 20-30 from WT and KO trains. Data shown ± SEM, n = cells; unpaired Student’s t-test unless otherwise indicated.

To estimate the relative size of the readily releasable pool in WT and KO, we stimulated CFs with a 10 Hz train. WT and KO CF synapses had strikingly different responses during repetitive stimulation. Both genotypes exhibited a delayed facilitation followed by depression, which may indicate multiple pools of vesicles with differing release probabilities (Lu and Trussell, 2016). However, KO EPSCs were larger at every stimulus throughout the train (Figures 7C-E), providing further evidence of enhanced vesicle release compared to WT. A linear fit to the last 10 responses of a cumulative amplitude plot produced a significantly steeper slope (Linear regression using 95% Confidence Intervals; WTslope = 78.7 ± 0.6, n = 5; KOslope = 172.2 ± 0.5, n = 5; p < 0.0001; unpaired Student’s t-test) and a larger y-intercept in KO PCs when compared to WT (Figure 7F). This analysis provided an estimate of the readily releasable pool (Schneggenburger et al., 1999), which was 29% larger in the KO compared to WT (WT y-intercept = 2.08 ± 0.02 nA, n = 5; KO y-intercept = 2.77 ± 0.01 nA, n = 5; p < 0.0001; unpaired Student’s t-test). Thus, both a single stimulus (Figure 6A-B) and repetitive stimulation of CFs produced increased vesicle release in the α2δ-2 KO, suggesting either an enhancement of a low PR pool of vesicles (Lu and Trussell, 2016) and/or more discrete release sites with reduced PR compared to WT.

CF terminals in α2δ-2 knockout have more release sites

Because we did not see an increased density of VGLUT2+ puncta by light microscopy, we hypothesized CF terminals in the KO had either a greater number of release sites or vesicles. CF terminals can be identified with electron microscopy (EM) by their high density of round synaptic vesicles (SVs) and contacts onto PC “thorns” along primary PC dendritic shafts (Palay and Chan-Palay, 1974; Miyazaki et al., 2004). While blinded to genotype, we imaged and quantified CF terminals from WT and KO mice (10-15 images/animal; see Materials and Methods). In agreement with VGLUT2+ puncta size determined by confocal microscopy (Figure 4D), CF terminal cross-sectional area was no different between genotypes when sampled using EM (Figures 8A and 8B). WT and KO CF terminals also had an equivalent density of synaptic vesicles (SVs) (Figure 8C) and no change in number of SVs within 100 nm of the synaptic contact, taken as a proxy for the readily releasable pool (WT = 18.5 ± 2.4 SV/µmContact, n = 5 mice; KO = 20.4 ± 2.7 SV/µmContact, n = 6 mice, p = 0.6; unpaired Student’s t-test).

Figure 8
Figure 8 CF terminals have increased numbers of synaptic contacts in Cacna2d2 KO animals.

(A) Representative transmission electron micrographs of CF terminals (pseudocolored yellow) from p21 WT (left) and KO (right) animals. White arrows indicate postsynaptic densities used to quantify synaptic contacts/terminal. Scale bar = 0.5 µm. (B) Average CF terminal area (µm2); p = 0.55 (NS). (C) Synaptic vesicle (SV) density (SV/ µm2) is not different between WT and KO animals; p = 0.57 (NS). (D) Average number of contacts per CF terminal (# contacts/terminal) is significantly increased in KO animals. ** p <0.01 (Mann-Whitney test). (E) Histogram of all CFs analyzed from WT (black) and KO (green) cerebelli, displaying the number of contacts per sampled CF terminal normalized to total number of CF terminals; p < 0.01 (Kolmogorov-Smirnov test). Data shown ± SEM, n = animals using 15-20 images/animal; unpaired Student’s t-test unless otherwise stated.

However, the number of synaptic contacts made by CF terminals in α2δ-2 KOs was nearly twice that of WT terminals (Figure 8A and 8D; WT = 1.08 ± 0.16 contacts/terminal, n = 5 mice; KO = 2.08 ± 0.17 contacts/terminal, n = 6 mice, p = 0.009; Mann-Whitney test). Moreover, the distribution of the number of contacts made by CF terminals was right-shifted in KO (Figure 8E; p < 0.002; Kolmogorov-Smirnov test). Although quantifying synaptic contacts per terminal using single EM sections likely underestimates the true number of contacts per terminal, the observed doubling of discrete contacts made by KO CFs is consistent with increased multivesicular release in the α2δ-2 KO.

Discussion

We investigated synaptic transmission and morphology at the CF-PC synapse in mice lacking α2δ-2, which is the only α2δ isoform expressed in PCs (Barclay et al., 2001b; Brodbeck et al., 2002; Ivanov et al., 2004; Donato et al., 2006). We observed profound deficiencies in the generation of CF-induced complex spikes (CpS) in the α2δ-2 KO mice, associated with altered underlying EPSC amplitude and kinetics. As demonstrated in Davie et al., enhancement of EPSC-like conductance results in depolarization block of CpS spikelet generation (Davie et al., 2008). Thus, we hypothesize that the increased glutamatergic transmission and accelerated EPSC kinetics (Rudolph et al., 2011) shapes the CpS in the α2δ-2 KO (Figure 9). We found several compelling lines of evidence that each CF terminal in the KO contains more discrete synaptic contacts, leading to increased multivesicular release and consequently larger EPSCs, despite an apparent decrease in probability of release. In addition to the increased number of release sites, the proximal localization of CF terminals influenced the quantal response seen at the PC soma due to reduced dendritic filtering. In fact, the CF70% Control Model PC simulation estimates that >1.4-fold increase in synaptic contact number would be sufficient to reach the magnitude of EPSC enhancement seen in KO. This likely provides an underestimate, as the simulation does not account for the observed decrease in PR.

Figure 9
Figure 9 Summary of CF-PC phenotypes in Cacna2d2 KO mice.

Proximal distribution of CF inputs onto KO Purkinje cells enhances postsynaptic quantal responses to CF glutamate release, and the increased number of synaptic release sites increases total glutamate concentration. Together, this results in a 140% EPSC amplitude in the KO compared to control. Counteracting these effects are a lower CF PR and enhanced glutamate clearance, which doubles the EPSC decay rate. Ultimately, larger synaptic conductances in the KO likely contribute to depolarization block of CF-evoked spikelet generation.

Altogether, these findings may appear surprising as they would seem to contradict expectations based on observations in which synapse formation is positively regulated with α2δ expression (Li et al., 2004; Eroglu et al., 2009; Chen et al., 2018; Risher et al., 2018). Herein, we place our findings at the CF-PC synapse in the context of the known roles of α2δ proteins to better understand the effects described in the α2δ-2 KO.

α2δ-2 proteins as auxiliary Ca2+ channel subunits

α2δ proteins were first identified as auxiliary subunits of voltage-dependent Ca2+ channels (VDCCs), and contribute to surface trafficking of VDCCs in heterologous expression systems (Canti et al., 2005; Cassidy et al., 2014). In cultured hippocampal neurons, knockdown of the α2δ-1 isoform reduces presynaptic Ca2+ influx, decreasing synaptic vesicle release (Hoppa et al., 2012). Additionally, capacitive measurements from inner hair cells of the spontaneous Cacna2d2 mutant, du/du, exhibits reduced exocytosis, presumably due to decreased VDCC abundance (Fell et al., 2016). In agreement with these data, loss of α2δ-2 protein lowered release probability at the CF-PC synapse, as determined by paired-pulse ratio. Thus, some of the phenotypes we observed could be related to altered VDCC localization or abundance in PCs, as well as within the CF terminal. PCs predominantly express Cav2.1 (Barclay et al., 2001a), and α2δ-2 can traffic Cav2.1 in heterologous expression systems (Canti et al., 2005). CF-PC transmission has been extensively characterized in Cav2.1 mutant mice (Matsushita et al., 2002; Miyazaki et al., 2004; Hashimoto et al., 2011), which may provide important clues as to whether our observed phenotypes could be due to altered VDCC function.

For example, the Cav2.1 leaner pore mutation reduces PC calcium currents by 60% and has larger, rapidly decaying CF-evoked EPSCs (Liu and Friel, 2008), similar to the α2δ-2 KO. Leaner CFs do not exhibit any change in PR (Liu and Friel, 2008), though CF vesicle release is mostly (70-90%) regulated by Cav2.1 (Regehr and Mintz, 1994). However, Cav2.1 global and PC-specific KOs exhibit no change in CF EPSC amplitude or decay kinetics (Miyazaki et al., 2004; Hashimoto et al., 2011). Additionally, other Cav2.1 pore mutants have reduced PC calcium currents, but display different CF EPSC phenotypes. For example, rolling Nagoya mutants have a 40% reduction in calcium currents associated with larger EPSC amplitudes but slower decay kinetics, whereas tottering mice have a 40% decrease in calcium currents with no change in EPSC waveform (Matsushita et al., 2002). Thus, although there are some similarities between certain VDCC mutants and the Cacna2d2 KO, some of the roles of α2δ-2 at the CF-PC synapse likely involve other effector mechanisms.

It is important to consider whether alterations in presynaptic morphology alone might influence measures of apparent release probability and the readily releasable pool size by repetitive stimulation (Fekete et al., 2019). For example, it is possible that PR at individual release sites is unchanged, but that the increased number of release sites per terminal could allow for accumulation of [Ca2+]i during repetitive stimulation via inter-site crosstalk. In this scenario, greater recruitment from a low PR vesicle pool can be accessed, sustaining release during subsequent stimuli. Currently, there is no definitive way to distinguish between a heterogeneous population of PR at discrete release sites, or whether the vesicle recruitment from low vs. high PR pools differs (Kaeser and Regehr, 2017). The possibility of multiple vesicle pools in the CF, as seen by the bimodal responses in Figure 7C, further complicates our ability to derive readily releasable pool size and release probability at this synapse (Neher, 2015; Lu and Trussell, 2016). Given the lack of evidence for α2δ-2 expression in inferior olivary cells from which CFs arise (Lein et al., 2007), yet increased number of synaptic contacts per CF terminal in the α2δ-2 KO, it is interesting to speculate whether altered presynaptic function is a consequence of PC-driven morphological changes. Direct experimentation is necessary to understand whether α2δ-2 loss alters calcium dynamics and PR at discrete release sites in the CF.

α2δ-2 proteins as synaptic organizers

More recently, roles for α2δ proteins independent of VDCCs are supported by their ability to regulate synapse formation despite pharmacological block or deletion of VDCCs (Eroglu et al., 2009; Kurshan et al., 2009). α2δ-1 induces excitatory synapse formation in response to glial-secreted thrombospondin (Eroglu et al., 2009), and this is dependent on postsynaptic signaling through NMDARs (Risher et al., 2018). In fact, several studies have suggested that α2δ-1 interacts with NMDARs and regulates NMDAR-mediated currents leading to spinogenesis (Chen et al., 2018; Risher et al., 2018). However, this interaction is unlikely at the mouse CF-PC synapse, where NMDARs are not expressed until late adulthood (Piochon et al., 2007; Renzi et al., 2007).

Studies in C. elegans have proposed a trans-synaptic interaction between presynaptic α2δ-3 and a postsynaptic neurexin (Tong et al., 2017) as a mechanism for synaptic function at the neuromuscular junction. In mammals, neurexin is presynaptically expressed (Missler et al., 2003; Zhang et al., 2015) and has trans-synaptic interactions with postsynaptic neuroligin. Similar to our observations in the Cacna2d2 KO, the neuroligin triple KO mouse (Zhang et al., 2015) has a proximally-shifted CF distribution phenotype, also without a change in VGLUT2+ puncta size or overall density (Zhang et al., 2015). However, the neuroligin tKO does not have changes in CF-PC synaptic function (Zhang et al., 2015), suggesting that although α2δ-2 may act in parallel with neurexin-neuroligin to coordinate features such as synaptic localization, the functional components that depend on α2δ-2 involve other effector mechanisms. Together, our data suggest both VDCC-dependent and -independent roles of α2δ-2 at the CF-PC synapse.

Impacts of α2δ-2 loss on cerebellar function

Of the four α2δ isoforms (Cacna2d1-4), Cacna2d2 loss has the most severe phenotype, as mice and humans with mutations in α2δ-2 have ataxia, epilepsy, and motor control deficits (Barclay et al., 2001b; Brodbeck et al., 2002; Ivanov et al., 2004; Donato et al., 2006; Pippucci et al., 2013). Because PCs provide output from the cerebellum, some of these neurologic phenotypes are likely due to PC dysfunction. PC spike-rate and plasticity are instructed by CF-evoked CpSs, providing error prediction information for motor coordination, presumably graded by number of spikelets generated (Rasmussen et al., 2013; Yang and Lisberger, 2014; Burroughs et al., 2017). Because CpSs evoked by α2δ-2 KO PCs had significantly fewer spikelets, we predict PC information transfer would be degraded, and thus α2δ-2 loss contributes directly to cerebellar dysfunction. As du/du mutants have reduced whole-cell calcium currents in PCs (Donato et al., 2006), we considered whether this is could explain the decreased spikelet generation. However, CpS spikelets originate in the axon and do not require dendritic or somatic VDCCs (Davie et al., 2008; Palmer et al., 2010), suggesting that the CpS phenotype in α2δ-2 mutants is more likely related to functional alterations at the CF-PC synapse.

Particularly surprising were the number and variety of functional and structural alterations at the α2δ-2 KO CF-PC synapse. In addition to those noted above, they also included alterations in glutamate re-uptake and structural redistribution of CF terminals. Though α2δ-2 may have a role in regulating each of these processes, it is likely that some have developed as compensation for a primary derangement directly related to the loss of α2δ-2. Delayed conditional deletion of α2δ may aid in teasing these issues apart. It will also be valuable to address whether postsynaptic α2δ proteins instruct presynaptic development or function, using cell-specific targeted rescue or deletion. Together, our results underscore the critical roles of α2δ-2 in the proper organization and transmission at the CF-PC synapse.

Acknowledgments:

This material was supported in part by the Department of Veterans Affairs, Veterans Health Administration, Office of Research and Development, Biomedical Laboratory Research and Development Merit Review Award I01-BX002949 (ES), a Department of Defense CDMRP Award W81XWH-18-1-0598 (ES), NIH T32NS007466 (KAB), NIH R01-NS080979 (GLW), NINDS 1R21NS102948 (IK/ES), NIH P30NS061800 (Dr. Sue Aicher), and OHSU Innovation Fund (ES) awards. The electron microscope was purchased with funds from the Murdock Charitable Trust awarded to Dr. Aicher.

We thank Dr. Stefanie Kaech-Petrie of the OHSU Advanced Light Microscopy Core for assistance with imaging, and for the electron microscopy expertise of Dr. Sue Aicher, James Carroll, and Jo Hill. We would like to acknowledge Drs. Sergey Ivanov and Lino Tessarollo for generously providing the Cacna2d2 knockout mice; Drs. Michael Häusser and Arnd Roth for necessary files and permission to use the NEURON model; and research associates Arielle Isakharov and Ada Zhang for outstanding technical support. We also thank Dr. Christopher Vaaga and Dr. Laurence Trussell for constructive comments on the manuscript. The contents of this manuscript do not represent the views of the U.S. Department of Veterans Affairs or the United States Government.

References

  1. 1.↵
    Auger C, Attwell D (2000) Fast removal of synaptic glutamate by postsynaptic transporters. Neuron 28:547–558.
    OpenUrlCrossRefPubMedWeb of Science
  2. 2.↵
    Barclay J, Balaguero N, Mione M, Ackerman SL, Letts VA, Brodbeck J, Canti C, Meir A, Page KM, Kusumi K, Perez-Reyes E, Lander ES, Frankel WN, Gardiner MR, Dolphin AC, Rees M (2001a) Ducky Mouse Phenotype of Epilepsy and Ataxia Is Associated with Mutations in the Cacna2d2 Gene and Decreased Calcium Channel Current in Cerebellar Purkinje Cells. The Journal of Neuroscience 21:6095–6104.
    OpenUrlAbstract/FREE Full Text
  3. 3.↵
    Barclay J, Balaguero N, Mione M, Ackerman SL, Letts VA, Brodbeck J, Canti C, Meir A, Page KM, Kusumi K, Perez-Reyes E, Lander ES, Frankel WN, Gardiner RM, Dolphin AC, Rees M (2001b) Ducky Mouse Phenotype of Epilepsy and Ataxia Is Associated with Mutations in the Cacna2d2 Gene and Decreased Calcium Channel Current in Cerebellar Purkinje Cells. The Journal of Neuroscience 21:6095–6104.
    OpenUrlAbstract/FREE Full Text
  4. 4.↵
    Bergles DE, Dzubay JA, Jahr CE (1997) Glutamate transporter currents in bergmann glial cells follow the time course of extrasynaptic glutamate. Proc Natl Acad Sci U S A 94:14821–14825.
    OpenUrlAbstract/FREE Full Text
  5. 5.
    Boning Gao YS, Anton Maximov, Mohamad Saad, Eva Forgacs‡, Farida Latif, Ming H. Wei (2000) Functional Properties of a New Voltage-dependent Calcium Channel The Journal of Biological Chemistry 275:12237–12242.
    OpenUrlAbstract/FREE Full Text
  6. 6.↵
    Brockhaus J, Schreitmuller M, Repetto D, Klatt O, Reissner C, Elmslie K, Heine M, Missler M (2018) alpha-Neurexins Together with alpha2delta-1 Auxiliary Subunits Regulate Ca(2+) Influx through Cav2.1 Channels. J Neurosci 38:8277–8294.
    OpenUrlAbstract/FREE Full Text
  7. 7.↵
    Brodbeck J, Davies A, Courtney JM, Meir A, Balaguero N, Canti C, Moss FJ, Page KM, Pratt WS, Hunt SP, Barclay J, Rees M, Dolphin AC (2002) The ducky mutation in Cacna2d2 results in altered Purkinje cell morphology and is associated with the expression of a truncated alpha 2 delta-2 protein with abnormal function. J Biol Chem 277:7684–7693.
    OpenUrlAbstract/FREE Full Text
  8. 8.↵
    Brown JP, Gee NS (1998) Cloning and Deletion Mutagenesis of the alpha2delta Calcium Channel Subunit from Porcine Cerebral Cortex. The Journal of Biological Chemistry 273:25458–25465.
    OpenUrlAbstract/FREE Full Text
  9. 9.↵
    Burroughs A, Wise AK, Xiao J, Houghton C, Tang T, Suh CY, Lang EJ, Apps R, Cerminara NL (2017) The dynamic relationship between cerebellar Purkinje cell simple spikes and the spikelet number of complex spikes. J Physiol 595:283–299.
    OpenUrlCrossRef
  10. 10.↵
    Canti C, Nieto-Rostro M, Foucault I, Heblich F, Wratten J, Richards MW, Hendrich J, Douglas L, Page KM, Davies A, Dolphin AC (2005) The metal-ion-dependent adhesion site in the Von Willebrand factor-A domain of alpha2delta subunits is key to trafficking voltage-gated Ca2+ channels. Proc Natl Acad Sci U S A 102:11230–11235.
    OpenUrlAbstract/FREE Full Text
  11. 11.↵
    Cassidy JS, Ferron L, Kadurin I, Pratt WS, Dolphin AC (2014) Functional exofacially tagged N-type calcium channels elucidate the interaction with auxiliary alpha2delta-1 subunits. Proc Natl Acad Sci U S A 111:8979–8984.
    OpenUrlAbstract/FREE Full Text
  12. 12.↵
    Chen J, Li L, Chen SR, Chen H, Xie JD, Sirrieh RE, MacLean DM, Zhang Y, Zhou MH, Jayaraman V, Pan HL (2018) The alpha2delta-1-NMDA Receptor Complex Is Critically Involved in Neuropathic Pain Development and Gabapentin Therapeutic Actions. Cell Rep 22:2307–2321.
    OpenUrlCrossRefPubMed
  13. 13.↵
    Davie JT, Clark BA, Hausser M (2008) The origin of the complex spike in cerebellar Purkinje cells. J Neurosci 28:7599–7609.
    OpenUrlAbstract/FREE Full Text
  14. 14.↵
    Dittman JS, Regehr WG (1998) Calcium Dependence and Recovery Kinetics of Presynaptic Depression at the Climbing Fiber to Purkinje Cell Synapse. The Journal of Neuroscience 18:6147–6162.
    OpenUrlAbstract/FREE Full Text
  15. 15.↵
    Dolphin AC (2012) Calcium channel auxiliary alpha2delta and beta subunits: trafficking and one step beyond. Nat Rev Neurosci 13:542–555.
    OpenUrlCrossRefPubMed
  16. 16.↵
    Donato R, Page KM, Koch D, Nieto-Rostro M, Foucault I, Davies A, Wilkinson T, Rees M, Edwards FA, Dolphin AC (2006) The ducky(2J) mutation in Cacna2d2 results in reduced spontaneous Purkinje cell activity and altered gene expression. J Neurosci 26:12576–12586.
    OpenUrlAbstract/FREE Full Text
  17. 17.↵
    Edvardson S, Oz S, Abulhijaa FA, Taher FB, Shaag A, Zenvirt S, Dascal N, Elpeleg O (2013) Early infantile epileptic encephalopathy associated with a high voltage gated calcium channelopathy. J Med Genet 50:118–123.
    OpenUrlAbstract/FREE Full Text
  18. 18.↵
    Eroglu C, Allen NJ, Susman MW, O’Rourke NA, Park CY, Ozkan E, Chakraborty C, Mulinyawe SB, Annis DS, Huberman AD, Green EM, Lawler J, Dolmetsch R, Garcia KC, Smith SJ, Luo ZD, Rosenthal A, Mosher DF, Barres BA (2009) Gabapentin receptor alpha2delta-1 is a neuronal thrombospondin receptor responsible for excitatory CNS synaptogenesis. Cell 139:380–392.
    OpenUrlCrossRefPubMedWeb of Science
  19. 19.↵
    Fekete A, Nakamura Y, Yang YM, Herlitze S, Mark MD, DiGregorio DA, Wang LY (2019) Underpinning heterogeneity in synaptic transmission by presynaptic ensembles of distinct morphological modules. Nat Commun 10:826.
  20. 20.↵
    Fell B, Eckrich S, Blum K, Eckrich T, Hecker D, Obermair GJ, Munkner S, Flockerzi V, Schick B, Engel J (2016) alpha2delta2 Controls the Function and Trans-Synaptic Coupling of Cav1.3 Channels in Mouse Inner Hair Cells and Is Essential for Normal Hearing. J Neurosci 36:11024–11036.
    OpenUrlAbstract/FREE Full Text
  21. 21.↵
    Gee NS, Brown JP, Dissanayake VUK, Offord J, Thurlow R, Woodruff GN (1996) The Novel Anticonvulsant Drug, Gabapentin (Neurontin), Binds to the The Journal of Biological Chemistry 271:5768–5776.
    OpenUrl
  22. 22.↵
    Geisler S, Schopf CL, Stanika R, Kalb M, Campiglio M, Repetto D, Traxler L, Missler M, Obermair GJ (2019) Presynaptic alpha2delta-2 Calcium Channel Subunits Regulate Postsynaptic GABAA Receptor Abundance and Axonal Wiring. J Neurosci 39:2581–2605.
    OpenUrlAbstract/FREE Full Text
  23. 23.↵
    Harrison J, Jahr CE (2003) Receptor Occupancy Limits Synaptic Depression at Climbing Fiber Synapses. The Journal of Neuroscience 23:377–383.
    OpenUrlAbstract/FREE Full Text
  24. 24.↵
    Hashimoto K, Kano M (1998) Presynaptic origin of paired-pulse depression at climbing fibre-Purkinje cell synapses in the rat cerebellum. J Physiol 506 (Pt 2):391–405.
    OpenUrlCrossRefPubMedWeb of Science
  25. 25.↵
    Hashimoto K, Ichikawa R, Kitamura K, Watanabe M, Kano M (2009) Translocation of a “winner” climbing fiber to the Purkinje cell dendrite and subsequent elimination of “losers” from the soma in developing cerebellum. Neuron 63:106–118.
    OpenUrlCrossRefPubMedWeb of Science
  26. 26.↵
    Hashimoto K, Tsujita M, Miyazaki T, Kitamura K, Yamazaki M, Shin HS, Watanabe M, Sakimura K, Kano M (2011) Postsynaptic P/Q-type Ca2+ channel in Purkinje cell mediates synaptic competition and elimination in developing cerebellum. Proc Natl Acad Sci U S A 108:9987–9992.
    OpenUrlAbstract/FREE Full Text
  27. 27.↵
    Heffley W, Song EY, Xu Z, Taylor BN, Hughes MA, McKinney A, Joshua M, Hull C (2018) Coordinated cerebellar climbing fiber activity signals learned sensorimotor predictions. Nat Neurosci 21:1431–1441.
    OpenUrlCrossRefPubMed
  28. 28.↵
    Hoppa MB, Lana B, Margas W, Dolphin AC, Ryan TA (2012) alpha2delta expression sets presynaptic calcium channel abundance and release probability. Nature 486:122–125.
    OpenUrlCrossRefPubMedWeb of Science
  29. 29.↵
    Ivanov SV, Ward JM, Tessarollo L, McAreavey D, Sachdev V (2004) Cerebellar Ataxia, Seizures, Premature Death, and Cardiac Abnormalities in Mice with Targeted Disruption of the Cacna2d2 Gene. American Journal of Pathology 165:1007–1018.
    OpenUrlCrossRefPubMedWeb of Science
  30. 30.↵
    Kaeser PS, Regehr WG (2017) The readily releasable pool of synaptic vesicles. Curr Opin Neurobiol 43:63–70.
    OpenUrlCrossRefPubMed
  31. 31.↵
    Khaliq ZM, Raman IM (2005) Axonal propagation of simple and complex spikes in cerebellar Purkinje neurons. J Neurosci 25:454–463.
    OpenUrlAbstract/FREE Full Text
  32. 32.↵
    Kurshan PT, Oztan A, Schwarz TL (2009) Presynaptic alpha2delta-3 is required for synaptic morphogenesis independent of its Ca2+-channel functions. Nat Neurosci 12:1415–1423.
    OpenUrlCrossRefPubMedWeb of Science
  33. 33.↵
    Lein ES et al. (2007) Genome-wide atlas of gene expression in the adult mouse brain. Nature 445:168–176.
    OpenUrlCrossRefPubMedWeb of Science
  34. 34.↵
    Li CY, Song YH, Higuera ES, Luo ZD (2004) Spinal dorsal horn calcium channel alpha2delta-1 subunit upregulation contributes to peripheral nerve injury-induced tactile allodynia. J Neurosci 24:8494–8499.
    OpenUrlAbstract/FREE Full Text
  35. 35.↵
    Liu S, Friel DD (2008) Impact of the leaner P/Q-type Ca2+ channel mutation on excitatory synaptic transmission in cerebellar Purkinje cells. J Physiol 586:4501–4515.
    OpenUrlCrossRefPubMed
  36. 36.↵
    Lu HW, Trussell LO (2016) Spontaneous Activity Defines Effective Convergence Ratios in an Inhibitory Circuit. J Neurosci 36:3268–3280.
    OpenUrlAbstract/FREE Full Text
  37. 37.↵
    Matsushita K, Wakamori M, Rhyu IJ, Arii T, Oda S-i, Mori Y, Imoto K (2002) Bidirectional Alterations in Cerebellar Synaptic Transmission of tottering and rolling Ca2. The Journal of Neuroscience 22:4388–4398.
    OpenUrlAbstract/FREE Full Text
  38. 38.↵
    Missler M, Zhang W, Rohlmann A, Kattenstroth G, Hammer RE, Gottmann K, Sudhof TC (2003) a-Neurexins couple Ca21 channels to synaptic vesicle exocytosis. Nature 423:939–948.
    OpenUrlCrossRefPubMedWeb of Science
  39. 39.↵
    Miyazaki T, Hashimoto K, Shin HS, Kano M, Watanabe M (2004) P/Q-type Ca2+ channel alpha1A regulates synaptic competition on developing cerebellar Purkinje cells. J Neurosci 24:1734–1743.
    OpenUrlAbstract/FREE Full Text
  40. 40.↵
    Neher E (2015) Merits and Limitations of Vesicle Pool Models in View of Heterogeneous Populations of Synaptic Vesicles. Neuron 87:1131–1142.
    OpenUrlCrossRefPubMed
  41. 41.↵
    Palay SL, Chan-Palay V (1974) Cerebellar Cortex: Cytology and Orgnaization. Berlin, Heidelberg, New York: Springer.
  42. 42.↵
    Palmer LM, Clark BA, Grundemann J, Roth A, Stuart GJ, Hausser M (2010) Initiation of simple and complex spikes in cerebellar Purkinje cells. J Physiol 588:1709–1717.
    OpenUrlCrossRefPubMed
  43. 43.↵
    Paukert M, Huang YH, Tanaka K, Rothstein JD, Bergles DE (2010) Zones of enhanced glutamate release from climbing fibers in the mammalian cerebellum. J Neurosci 30:7290–7299.
    OpenUrlAbstract/FREE Full Text
  44. 44.↵
    Piochon C, Irinopoulou T, Brusciano D, Bailly Y, Mariani J, Levenes C (2007) NMDA receptor contribution to the climbing fiber response in the adult mouse Purkinje cell. J Neurosci 27:10797–10809.
    OpenUrlAbstract/FREE Full Text
  45. 45.↵
    Pippucci T, Parmeggiani A, Palombo F, Maresca A, Angius A, Crisponi L, Cucca F, Liguori R, Valentino ML, Seri M, Carelli V (2013) A novel null homozygous mutation confirms CACNA2D2 as a gene mutated in epileptic encephalopathy. PLoS One 8:e82154.
  46. 46.↵
    Prescott C, Weeks AM, Staley KJ, Partin KM (2006) Kynurenic acid has a dual action on AMPA receptor responses. Neurosci Lett 402:108–112.
    OpenUrlCrossRefPubMed
  47. 47.↵
    Rasmussen A, Jirenhed DA, Zucca R, Johansson F, Svensson P, Hesslow G (2013) Number of spikes in climbing fibers determines the direction of cerebellar learning. J Neurosci 33:13436–13440.
    OpenUrlAbstract/FREE Full Text
  48. 48.↵
    Regehr WG, Mintz IM (1994) Participation of Multiple Calcium Channel Types in Transmission at Single Climbing Fiber to Purkinje Cell Synapses. Neuron 12:605–613.
    OpenUrlCrossRefPubMedWeb of Science
  49. 49.↵
    Renzi M, Farrant M, Cull-Candy SG (2007) Climbing-fibre activation of NMDA receptors in Purkinje cells of adult mice. J Physiol 585:91–101.
    OpenUrlCrossRefPubMedWeb of Science
  50. 50.↵
    Risher WC, Kim N, Koh S, Choi JE, Mitev P, Spence EF, Pilaz LJ, Wang D, Feng G, Silver DL, Soderling SH, Yin HH, Eroglu C (2018) Thrombospondin receptor alpha2delta-1 promotes synaptogenesis and spinogenesis via postsynaptic Rac1. J Cell Biol 217:3747–3765.
    OpenUrlAbstract/FREE Full Text
  51. 51.↵
    Roth A, Häusser M (2001) Compartmental models of rat cerebellar Purkinje cells based on simultaneous somatic and dendritic patch-clamp recordings. Journal of Physiology 535:445–472.
    OpenUrlCrossRefPubMedWeb of Science
  52. 52.↵
    Rudolph S, Overstreet-Wadiche L, Wadiche JI (2011) Desynchronization of multivesicular release enhances Purkinje cell output. Neuron 70:991–1004.
    OpenUrlCrossRefPubMedWeb of Science
  53. 53.↵
    Schneggenburger R, Meyer AC, Neher E (1999) Released Fraction and Total Size of a Pool of Immediately Available Transmitter Quanta at a Calyx Synapse. Neuron 23:399–409.
    OpenUrlCrossRefPubMedWeb of Science
  54. 54.↵
    Tong XJ, Lopez-Soto EJ, Li L, Liu H, Nedelcu D, Lipscombe D, Hu Z, Kaplan JM (2017) Retrograde Synaptic Inhibition Is Mediated by alpha-Neurexin Binding to the alpha2delta Subunits of N-Type Calcium Channels. Neuron 95:326–340 e325.
    OpenUrl
  55. 55.↵
    Wadiche JI, Jahr CE (2001) Multivesicular release at climbing fiber-Purkinje cell synapses. Neuron 32:301–313.
    OpenUrlCrossRefPubMedWeb of Science
  56. 56.↵
    Wang T, Jones RT, Whippen JM, Davis GW (2016) alpha2delta-3 Is Required for Rapid Transsynaptic Homeostatic Signaling. Cell Rep 16:2875–2888.
    OpenUrlCrossRefPubMed
  57. 57.↵
    Yang Y, Lisberger SG (2014) Purkinje-cell plasticity and cerebellar motor learning are graded by complex-spike duration. Nature 510:529–532.
    OpenUrlCrossRefPubMedWeb of Science
  58. 58.↵
    Zhang B, Chen LY, Liu X, Maxeiner S, Lee SJ, Gokce O, Sudhof TC (2015) Neuroligins Sculpt Cerebellar Purkinje-Cell Circuits by Differential Control of Distinct Classes of Synapses. Neuron 87:781–796.
    OpenUrlCrossRefPubMed
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Posted June 28, 2019.
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α2δ-2 protein controls structure and function at the cerebellar climbing fiber synapse
Kathleen A. Beeson, Ryne Beeson, Gary L. Westbrook, Eric Schnell
bioRxiv 685818; doi: https://doi.org/10.1101/685818
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