Developmental transformation of Ca2+ channel-vesicle nanotopography at a central GABAergic synapse

The coupling between Ca2+ channels and release sensors is a key factor defining the signaling properties of a synapse. However, the coupling nanotopography at many synapses remains unknown, and it is unclear how it changes during development. To address these questions, we examined coupling at the cerebellar inhibitory basket cell (BC)-Purkinje cell (PC) synapse. Biophysical analysis of transmission by paired recording and intracellular pipette perfusion revealed that the effects of exogenous Ca2+ chelators decreased during development, despite constant reliance of release on P/Q-type Ca2+ channels. Structural analysis by freeze-fracture replica labeling (FRL) and transmission electron microscopy (EM) indicated that presynaptic P/Q-type Ca2+ channels formed nanoclusters throughout development, whereas docked vesicles were only clustered at later developmental stages. Modeling suggested a developmental transformation from a more random to a more clustered coupling nanotopography. Thus, presynaptic signaling developmentally approaches a point-to-point configuration, optimizing speed, reliability, and energy efficiency of synaptic transmission.


In brief
Chen et al. combine paired recordings, structural analysis, and modeling to examine the coupling between presynaptic Ca 2+ channels and release sensors in an inhibitory GABAergic synapse at different developmental time points.The results reveal a developmental transformation from more random organization to precise point-topoint synaptic transmission at the nanometer scale.

INTRODUCTION
2][3][4] Although all synapses are assembled from similar building blocks, their functional properties differ substantially.However, the mechanisms underlying synaptic diversity are incompletely understood.6][7] Experiments with exogenous Ca 2+ chelators 8 indicated that the average coupling distance varies among synapses, with tighter ''nanodomain'' coupling at many inhibitory GABAergic synapses 6,9 and looser ''microdomain'' coupling at several excitatory glutamatergic synapses. 7,10,11Nanodomain coupling conveys various functional advantages, including speed and efficacy of synaptic transmission.Conversely, microdomain coupling permits the regulation of release probability via presynaptic plasticity. 7hus, channel-vesicle coupling sets the speed, efficacy, and plasticity of synaptic signaling. 3lthough the Ca 2+ chelator approach allows precise biophysical measurement of the average coupling distance, 8 the exact topography and stoichiometry of channel-vesicle coupling remains unknown.At the calyx of Held, a biophysically well-char-acterized synapse, several topographies have been proposed based on freeze-fracture replica labeling (FRL), serial-section electron microscopy (EM), and modeling data.These include random localization of Ca 2+ channels and synaptic vesicles, 12 random placement of Ca 2+ channels with an exclusion zone around synaptic vesicles, 13 ring models in which Ca 2+ channels surround synaptic vesicles, 14 and perimeter models in which synaptic vesicles are positioned near clusters of Ca 2+ channels. 15Recent work suggested different coupling topographies at cerebellar parallel fiber synapses (exclusion zone coupling) and stellate cell synapses (perimeter coupling) in the same circuit. 16However, whether these topographies represent canonical coupling motifs used in other synapses remains unclear.
ings between synaptically connected BCs and PCs.We first compared the basic transmission properties at three developmental age groups, postnatal day (P) 7-9, P14-16, and P21-23 (Figure 1; Table S1).During development, the peak amplitude of unitary inhibitory postsynaptic currents (IPSCs) declined (Figure 1D), consistent with previous observations. 25In parallel, both synaptic latency and 20%-80% rise time of IPSCs significantly shortened (p = 0.0079 and 0.0072, respectively; Figures 1E and 1F), indicating an increase in speed and temporal precision of synaptic transmission.Furthermore, paired-pulse ratio (IPSC 2 /IPSC 1 ) and multiplepulse ratio (IPSC 10 /IPSC 1 ) increased during synaptic maturation (Figures 1G, 1H, and S1), demonstrating increased reliability of transmission during repetitive activity.In contrast, IPSC half-duration and decay time constant changed minimally, suggesting constant properties of postsynaptic GABA A receptors (p = 0.38 and 0.45, respectively; Table S1).These results demonstrate that both efficiency and kinetic properties of BC-PC synapses change during development.
At all previously investigated synapses, transmitter release relies on P/Q-, N-, and R-type channels early in development but switches to P/Q-type channels at later time points. 19,23,29herefore, we examined the reliance of transmitter release on different types of presynaptic Ca 2+ channels at the BC-PC synapse (Figures 1I-1N).To determine the contribution of P/Q-type Ca 2+ channels, we applied 1 mM of the selective P/Q-type Ca 2+ channel blocker u-agatoxin IVa, a concentration expected to completely block both P-and Q-type channels. 30Surprisingly, u-agatoxin IVa almost completely blocked synaptic transmission at all developmental stages.The residual evoked IPSC 10-20 min after toxin application was 3.4% ± 1.6% of the control value at P7-9, 4.5% ± 2.0% at P14-16, and 3.1% ± 1.0% at  S1 and S3.
Changes in release probability, number of functional release sites, and vesicle pool size According to the quantal theory of synaptic transmission, the average amplitude of single IPSCs is given as IPSC = p R 3 N 3 q, where p R is release probability, N is number of functional release sites, and q is quantal size. 31To determine how quantal parameters at the BC-PC synapse change during development, we performed nonstationary fluctuation analysis of evoked IPSCs at different developmental time points (Figure 2). 32The extracellular Ca 2+ concentration was changed between 0.7 mM and 10 mM.
Variance and mean of IPSC peak amplitudes were determined from stationary periods after the Ca 2+ concentration change, and variance was plotted against mean for individual experiments.In a subset of experiments with 10 mM Ca 2+ , the K + channel blockers tetraethylammonium (TEA, 1 mM) and 4-aminopyridine (4-AP, 0.05 mM) were added to maximally enhance release. 33,34ariance-mean analysis revealed that release probability at 2 mM extracellular Ca 2+ decreased from 0.52 ± 0.06 at P7-9 to 0.27 ± 0.04 at P14-16, and 0.09 ± 0.02 at P21-23 (6, 6, and 5 pairs, respectively; p = 0.0013; Figure 2D).Consistent with a reduction of p R , the Ca 2+ dependence of transmitter release shifted to higher concentrations during synaptic maturation (Figure S1).The number of functional release sites increased in parallel, from 12.8 ± 2.9 at P7-9 to 14.3 ± 2.4 at P14-16, and 43.3 ± 6.5 at P21-23 (p = 0.0061; Figure 2E).These results suggest a major reorganization of the release mechanism at BC-PC synapses during development.While p R decreased, N became progressively larger during synaptic maturation.In parallel, the quantal size significantly declined during synaptic maturation (from 338.5 ± 46.6 pA at P7-9 to 327.1 ± 49.0 pA at P14-16, and 177.3 ± 22.2 pA at P21-23; p = 0.0066; Figure 2F).In contrast, the quantal content (p R 3 N) was only slightly but not significantly reduced, implying that the changes in p R and N largely compensated for each other (p = 0.13; Figure 2G).
To probe developmental changes in the vesicular pool, we performed cumulative release analysis (Figure S2). 35,36Synapses were stimulated repetitively, normalized IPSC peak amplitude values were cumulatively plotted against stimulus number, and the size of the readily releasable pool (RRP) was determined by linear regression (STAR Methods).RRP size increased during development, from 37.4 ± 5.3 quanta at P7-9 to 51.6 ± 8.1 quanta at P14-16, and 72.6 ± 13.1 quanta at P21-23 (p = 0.028; Figure S2).Thus, the vesicular pool size was developmentally upregulated.
To exclude that TEA and 4-AP affected our quantal parameter estimates, we compared the results from variance-mean analysis at P7-9 synapses in the absence and presence of TEA and 4-AP.No significant differences were detected, validating the use of these blockers in our analysis (p > 0.2; Figures S3A-S3F).To exclude the possibility that saturation or desensitization of postsynaptic receptors confounded the variance-mean analysis, additional experiments were performed in the presence of a low-affinity competitive GABA A receptor antagonist (1,2,5,6-tetrahydropyridin-4-yl) methylphosphinic acid (TPMPA; 300 mM) 37 and a GABA B receptor antagonist (CGP 55845; 1 mM); CGP 55845 was added to rule out possible effects of TPMPA on presynaptic GABA B receptors. 38In the presence of TPMPA and CGP 55845, q significantly decreased (p = 0.016), showing the effectiveness of the GABA A receptor antagonist, whereas p R and N remained constant (Figures S3G-S3L).Thus, postsynaptic receptor saturation or desensitization are unlikely to affect our measurements.These results corroborate our observations of reciprocal changes in p R and N during development.

Shortening of the presynaptic action potential (AP) in BC terminals
To obtain insight into the mechanisms underlying developmental changes in p R , we analyzed the shape of the presynaptic AP that initiates transmitter release (Figures 2H-2K).A somatic whole-cell recording was obtained from a BC, the neuron was filled with Alexa Fluor 488, and the axon arbor including presynaptic terminals surrounding PC somata was visualized using confocal microscopy (Figure 2H).Subsequently, a cell-attached recording was obtained from a BC presynaptic terminal.Analysis of the peak-to-peak duration of the presynaptic action current, a proxy of the half-duration of the presynaptic AP (Figures S4A-S4C), revealed a marked change in duration, from 2.24 ± 0.33 ms at P7-9 to 0.99 ± 0.11 ms at P14-16, and 0.59 ± 0.07 ms at P21-23 (5 presynaptic recordings per age group; p = 0.0025; Figure 2K).In contrast, the half-duration of the somatic AP decreased less prominently, from 1.11 ± 0.05 ms at P7-9 to 0.78 ± 0.03 ms at P14-16, and 0.75 ± 0.02 ms at P21-23 (15 somatic recordings per age group; p < 0.001; Table S1).Thus, the presynaptic AP undergoes substantial shortening during development.Together with the constant reliance of transmitter release on P/Q-type Ca 2+ channels (Figures 1I-1N), these results suggest a reduced efficacy of opening of these channels by the presynaptic AP.
To further test this hypothesis, we measured presynaptic Ca 2+ transients in BC terminals (Figure S5).BCs were filled with Fluo-5F (200 mM) and Alexa Fluor 594 (80 mM), Ca 2+ transients were evoked by single APs, and ratiometric imaging was performed.Peak amplitudes of Ca 2+ transients became significantly smaller during development (Figure S5C).In parallel, decay time constants became shorter, suggesting that the amplitude reduction was generated by reduced Ca 2+ inflow rather than increased Ca 2+ buffering. 39Consistent with this conclusion, application of K + channel blockers significantly increased the peak amplitude of Ca 2+ transients at P21-23, but not in the P7-9 and the P14-16 age groups (Figure S5E).These results provide converging evidence that the efficacy of presynaptic Ca 2+ channel opening decreases during development.

Tightening of coupling between Ca 2+ channels and release sensors
8][19][20][21] However, in all of these cases, reliance on the Ca 2+ channel subtype changes during maturation, making it difficult to distinguish direct effects of coupling from indirect effects of changes in Ca 2+ channel subtype.To probe the channel-sensor coupling distance at the BC-PC synapse at different developmental time points, we infused 10 mM of the slow Ca 2+ chelator ethyleneglycol-bis(b-aminoethylether)-N,N,N 0 ,N 0 -tetraacetic acid (EGTA) into the presynaptic terminals by pipette perfusion (Figure 3). 6,21Pipette perfusion provides a quantitatively controlled way of probing the chelator sensitivity, minimizing any confounding effects of wash-in of anions 40 or wash-out of mobile endogenous buffers, such as parvalbumin (PV). 27,41In P7-9 synapses, infusion of 10 mM EGTA gradually suppressed synaptic transmission (Figures 3B-3D).In contrast, at P21-23 synapses, infusion of 10 mM EGTA had only minimal effects (p = 0.0127; Figures 3E and  3F; Table S1).In P14-16 synapses, the effects of EGTA were also minimal, confirming the previous conclusion that transmitter release at this developmental stage is triggered by nanodomain coupling (Figures 3E and 3F). 9In contrast to EGTA, infusion of 10 mM of the fast Ca 2+ chelator ethylenedioxybis-(o-phenylenenitrilo)-N,N,N 0 ,N 0 -tetraacetic acid (BAPTA) strongly suppressed synaptic transmission at all developmental stages (Figures 3G and  3H; Table S1).Taken together, our results suggest developmental tightening of channel-sensor coupling 3 independently of any switch in Ca 2+ channel subtype.

Changes in bouton and AZ numbers and in nanoscopic AZ structure
We next attempted to obtain insight into the mechanisms underlying changes in the number of functional release sites, N.Although   S1.
3][44] To examine the structural properties of BC-PC synapses during synaptic maturation, we combined light microscopy (LM) and EM analysis (Figure 4; Table S2).Analysis was performed at P7-9, P14-16, and P21-23, developmental time points identical to those used in our biophysical experiments.We first determined the number of boutons per connection, using a triple labeling procedure (Figures 4A and 4B).BCs were filled with biocytin via whole-cell recording and labeled with Alexa Fluor-conjugated streptavidin (5, 5, and 6 biocytin-filled BCs, respectively).Synaptic boutons were identified using antibodies against vesicular GABA transporters (VGAT) and postsynaptic GABA A receptor alpha-1 subunits (GABA A a1). LM analysis including both somata and proximal dendrites of PCs revealed that the number of boutons per connection increased from 6.55 ± 0.64 at P7-9 to 8.40 ± 1.09 at P14-16, and 9.00 ± 0.95 at P21-23 (11, 10, and 10 PCs; p = 0.1126).Thus, the BC-PC synapse is a multi-bouton connection throughout development (Figure 4E).
Next, we determined the number of AZs per bouton, using serial-section EM on perfusion-fixed brain samples (Figures 4C,  4D, and 4F).BC-PC synapses were unequivocally identified, based on their morphological characteristics and location.(legend continued on next page) Evaluation of the AZ number in fully reconstructed boutons revealed 1.87 ± 0.22 AZs per bouton at P7-9, 2.00 ± 0.33 AZs per bouton at P14-16, and 2.16 ± 0.19 AZs per bouton at P21-23 (15, 10, and 19 fully reconstructed boutons; p = 0.5371).Thus, the majority of GABAergic boutons contained one to three AZs, independently of the developmental stage (Figure 4F).Finally, we analyzed the nanoscopic structure of the AZs in more detail (Figures 4G-4K).To accurately determine the number of docked vesicles, we performed cryo-fixation of acute brain slices, which avoids confounding effects of chemical fixation, 45 and reconstructed entire AZs using serial section EM.The number of docked vesicles per AZ substantially increased during development, from 10.2 ± 1.4 at P7-9 to 14.1 ± 2.8 at P14-16, and 25.1 ± 2.0 at P21-23 (16, 10, and 14 AZs; p < 0.0001).The AZ area also significantly increased, from 0.15 ± 0.02 mm 2 at P7-9 to 0.17 ± 0.04 mm 2 at P14-16, and 0.21 ± 0.02 mm 2 at P21-23 (9, 8, and 22 AZs; p = 0.0474).Thus, the overall AZ area at BC-PC synapses appeared larger than at excitatory synapses 46 and other inhibitory synapses. 47n parallel, the density of docked vesicles significantly increased from 48.0 ± 5.1 mm À2 at P7-9 to 64.9 ± 10.1 mm À2 at P14-16, and 90.9 ± 10.0 mm À2 at P21-23 (p = 0.0082).This indicates that the increase in the total number of docked vesicles per AZ is caused by a combination of both increase in AZ area and increase in vesicle density.Finally, we found that the diameter of synaptic vesicles decreased slightly, but significantly, during synaptic maturation (Figure 4K), which may explain the declining quantal size (Figure 2F).
To determine the distribution of docked vesicles within AZs, we analyzed nearest neighbor distance (NND) distributions of docked synaptic vesicles and compared them to simulated random distributions (Figure S6).NND analysis revealed that vesicles were non-randomly distributed at all three developmental stages (p < 0.001; Figures S6A-S6D).To distinguish between clustering and dispersion, we performed Ripley's H(r) function analysis (Figures 4L and 4M). 16,48At both P7-9 and P14-16, maximal H(r) values were not significantly different in measured and randomized data (15 and 9 AZs; p = 0.39 and 0.59, respectively), and the proportion of individual AZs with significant maximal H(r) was small (13.3% for P7-9 and 22.2% for P14-16).In contrast, at P21-23 synapses, maximal H(r) values were significantly higher than in randomized data (15 AZs; p = 0.04), and the proportion of individual AZs with significant vesicle clustering was much larger (60.0%; p < 0.05; Figure 4M).These results suggest that the distribution of docked synaptic vesicles at AZs changes from a more random to a more clustered configuration during development.

Clustering of presynaptic Ca 2+ channels
0][51] BC-PC synapses were ideal for this analysis because transmitter release was exclusively mediated by P/Q-type Ca 2+ channels (Figures 1I-1N).This allowed us to quantitatively analyze presynaptic Ca 2+ channel numbers and localization by immunolabeling with anti-Ca v 2.1 a 1A antibodies, 16 which labeled presynaptic Ca 2+ channels with high efficiency (77.6%;STAR Methods and Li et al. 52 ) and specificity (minimal labeling in Ca v 2.1 a 1A À/À mice; Figure S7).GABAergic synapses were identified by immunolabeling for VGAT, which was detected, albeit with low density, in the plasma membrane of GABAergic terminals (Figures 5A-5C). 53This was particularly important early in development, when glutamatergic axons occasionally form synapses with PC somata. 54For identification of AZs, we applied antibodies against the AZ marker proteins Rab3a-interacting molecule (RIM); E-, L-, K-, and S-rich protein (ELKS); and neurexin in a mix (STAR Methods).AZs were delineated drawing a polygon around the outermost immunoparticles for both Ca v 2.1 and the AZ marker proteins (Figure S8). 51FRL analysis revealed that the number of Ca v 2.1 particles per AZ significantly increased during maturation (Figure 5D).In parallel, the AZ area increased as well (Figure 5E), resulting in similar particle densities throughout development (Figure 5F).These results reveal a largely constant Ca 2+ channel density in AZs of GABAergic BC-PC synapses.FRL analysis further revealed that immunoparticles for Ca v 2.1 in AZs of BC terminals were non-randomly distributed (Figures 5G, 5H, and S9).The measured NND was significantly smaller than the corresponding simulated value, suggesting clustering of the channels (p < 0.001; Figure S9). 51To further evaluate this, we performed Ripley's H(r) function analysis (Figures 5G   (C) Transmission electron micrograph of a BC bouton at P14. Left, low-magnification view; contact area color-coded in pink, AZ area in green.Right, highmagnification view of AZs (white arrows in left panel).PC soma color-coded in yellow.(D) 3D reconstruction of a BC bouton at P9. Contact area between BC terminal and PC soma is depicted in pink, AZ area in green.View from top, side, and bottom, respectively.(E and F) Summary bar graphs of the number of boutons emerging from a single BC and terminating in the perisomatic area of a single PC (from confocal immunohistochemistry analysis; E) and the number of AZs per bouton (from serial section EM analysis; F).S2 and S3. and 5H). 16,48Population analysis revealed a prominent positive peak and a significant difference from the null model for all developmental stages (67, 69, and 81 AZs; p = 0.007, 0.001, and 0.002, respectively; Figure 5G).Analysis of null model rejection rate in individual AZs corroborated this conclusion (rejection for >80% of AZs at three developmental stages; p < 0.05; Figure 5H).Thus, presynaptic Ca 2+ channels in BC-PC synapses were significantly clustered at all developmental time points.
To determine the number of Ca 2+ channel clusters and analyze their properties, we used a ''density-based spatial clustering of applications with noise'' (DBSCAN) algorithm (Figure 6).We found that the number of clusters per AZ increased significantly during development (    6O).In contrast, the distance between adjacent clusters was much wider, 143.7 ± 3.5 nm at P7-9, 146.2 ± 2.7 nm at P14-16, and 159.8 ± 3.1 nm at P21-23 (Figure 6P).Thus, whereas individual channels within a given cluster were tightly packed, clusters within the same AZ were widely separated.
Analysis of EM and FRL data allowed us to further compute the stoichiometric ratios of the channel-vesicle coupling.On average, the number of docked vesicles associated with a Ca 2+ channel cluster was 3.50 at P7-9, 3.22 at P14-16, and 5.42 at P21-23.Hence, BC-PC synapses show an increasing excess of the number of docked synaptic vesicles over the number of Ca 2+ channel clusters.S2. (legend continued on next page) together, these data constrain the coupling configuration.To fully exploit this information, we generated a realistic model of Ca 2+ diffusion and sensor activation at BC terminals (Figure 7).7][58][59] Buffered diffusion of Ca 2+ was modeled by numerical solution of the full set of partial differential equations in three dimensions, assuming a fixed Ca 2+ buffer, a lowaffinity endogenous mobile Ca 2+ buffer, and a high-affinity exogenous mobile Ca 2+ buffer (EGTA or BAPTA; see STAR Methods). 3,6,7,15,60][63] First, we simulated Ca 2+ domains around Ca 2+ channels assuming realistic distributions, including their non-random localization (Figure 7A).Intracellular Ca 2+ concentration was plotted in two dimensions parallel to the AZ.Presynaptic Ca 2+ flux was represented by Gaussian functions with standard deviations s of 1.38 ms, 0.56 ms, and 0.3 ms, to account for differences in presynaptic AP shape (Figure S4E).Peak open probability of presynaptic Ca 2+ channels was assumed as 1, 0.3, and 0.1, respectively (Figures S4F and S5).Whereas Ca 2+ domains around individual Ca 2+ channels and Ca 2+ channel clusters merged in young synapses, individual Ca 2+ domains were much better separated in mature synapses (Figures 7D-7F).On average, the width of Ca 2+ domains at half-maximal amplitude decreased from 83.4 ± 4.5 nm (P7-9) to 58.5 ± 10.2 nm (P14-16), and 19.6 ± 2.1 nm (P21-23; p < 0.0001; Figure 7G).These results indicate a switch from merged Ca 2+ microdomains, which cover the entire AZ, to isolated Ca 2+ nanodomains, which are spatially more confined.Thus, the assumed reduction of Ca 2+ channel open probability, suggested by the reduction in presynaptic AP duration, markedly changed the shape of the Ca 2+ domains (Figures 7D-7F, bottom).
Next, we simulated the effects of these different Ca 2+ domains on transmitter release (Figures 7H and 7I).Vesicles were put at random locations at Ca 2+ channel clusters (corresponding to a cluster area ''CA'' model, see below), and the Ca 2+ concentration at the corresponding location was used to drive the release sensor model (Figure 7H). 55Simulations were performed in control conditions (0.1 mM EGTA) and in the presence of 10 mM EGTA and 10 mM BAPTA to predict the effects of the Ca 2+ chelators. 15Furthermore, the simulated release rates with 0.1 mM EGTA were used to estimate release probability, delay, and decay time constant of transmitter release.Although the model was highly constrained, it reasonably predicted both EGTA sensitivity and release probability (Figures 7J and 7K).

Developmental transformation of coupling nanotopography
To infer the coupling topography, we quantitatively compared the ability of several Ca 2+ channel-vesicle coupling models to describe our experimental observations (including experimental EGTA, BAPTA, p R , delay, and decay time constant of release data; Figure 8).In particular, we examined a cluster area model (''CA'') in which vesicles were put on top of Ca 2+ channel cluster areas, a cluster perimeter model (''CP'') in which the vesicles were positioned along cluster perimeters, 21 a model in which vesicles were randomly positioned over the entire AZ (''RAZ''), and a model in which vesicles were randomly assigned to the entire presynaptic membrane (''RPM'').Furthermore, we tested three different exclusion zone models (''CAEZ,'' ''RAZEZ,'' and ''RPMEZ''; Figure 8A). 13To assess the ability of the models to reproduce the experimental data, we selected a representative AZ from each age group and simulated 100 AZ configurations with stochastic Ca 2+ channel activation and random vesicle positioning.We then compared the distributions of the minus log-likelihood values, providing a metric of the ability of the model to describe the experimental observations.Whereas the CP model resembles the previously described perimeter model, 21 the RAZEZ model shows similarities to the previously used exclusion zone model. 13,16n the representative AZ from the P7-9 age group, the RAZEZ model best described the experimental data, followed by RAZ, CP, CAEZ, CA, RPM, and RPMEZ models (p < 0.001; Figure 8B, left; Figure S11).In contrast, in the AZ from the P21-23 age group, the CP model produced the best fit, followed by CA, CAEZ, RAZ, RAZEZ, RPM, and RPMEZ models (p < 0.001; Figure 8B, right; Figure S11).In the P14-16 age group, the distribution was more similar to the P21-23 than to the P7-9 age group (Figure 8B, center), suggesting that a substantial transformation in coupling topography may occur between the young and medium age groups (i.e., in the range P10-13).
(D-F) Intracellular Ca 2+ concentration 5 nm away from the plasma membrane and 0.2 ms after the peak of the presynaptic Ca 2+ inflow for P7-9 (D), P14-16 (E), and P21-23 (F) AZs.Top, ''line scans'' of Ca 2+ concentration through all Ca 2+ channels in the x direction (y = 0, z = 5 nm), with x = 0 corresponding to the channel center.Different colors indicate different Ca 2+ channels.Center, 3D plots of Ca 2+ domains.Bottom, contour plots of Ca 2+ concentration; points indicate Ca 2+ channels (red, closed; green, activated).Standard deviation s of presynaptic Ca 2+ flux: 1.38 ms, 0.56 ms, and 0.3 ms; open probability of presynaptic Ca 2+ channels: 1, 0.3, and 0.1, respectively.(G) Summary bar graph of width of Ca 2+ domains at half-maximal amplitude for the example AZs from the P7-9, P14-16, and P21-23 age groups.Circles, individual Ca 2+ domains; bars, mean ± SEM (n = 49, 38, and 16).(H and I) Random positioning of synaptic vesicles opposite to Ca 2+ channel clusters explains nanodomain coupling and developmental changes.Transmitter release rate was computed using the Ca 2+ sensor-release model of Lou et al. 55 (H).Release rate was computed in control (I, top) and in 10 mM EGTA (I, bottom) for a representative synapse from the P21-23 age group.Different colors represent release rates for individual vesicles at different locations.(J and K) Summary bar graphs of simulated EGTA effects (J) and release probability (K) for representative AZs from the P7-9, P14-16, and P21-23 age groups.Data in P7-9 were generated by 100 random vesicle placement patterns; data in P14-16 and P21-23 were generated by 10 random channel activation patterns combined with 10 random vesicle placement patterns (CA model).Circles, individual instances of random positioning; bars, mean ± SEM.Red dashed lines, mean experimental values; light red shaded area, 95% confidence band.See also Figure S10 and Table S4.
The results derived from three representative AZs suggest a developmental change in the coupling configuration.To test this hypothesis more generally, we simulated Ca 2+ domains and transmitter release in all morphologically analyzed AZs and determined the best-fit model in each case (67, 69, and 81 AZs, respectively; Figure 8C).In the P7-9 age group, the RAZEZ often provided the best fit, whereas the other models did less frequently (Figure 8C, left).In the P21-23 age group, the CP showed highest frequency (Figure 8C, right).In the P14-16 age group, the distribution was more similar to the P21-23 than to the P7-9 age group.Distributions of best-fit models were significantly different among age groups (p < 0.001; c 2 test).Collectively, structural and modeling results suggest that developmental processes not only result in a reduction in average coupling distance [17][18][19][20][21] but also a change in coupling nanotopography.
Modeling also allowed us to determine the topographical coupling distance between Ca 2+ channels and synaptic vesicles in the three age groups (Figures 8D and 8E).For each channelvesicle pair in each model, we first determined the coupling distance in x-y dimension, resulting in a ''distance matrix''.We then determined the contribution of each channel to the release of each vesicle by channel silencing or activation, resulting in a ''release relevance matrix'' (Figure 8D, right).Finally, we determined the mean topographical coupling distance, multiplying each distance value with the corresponding release relevance as a weight factor.We found that the average topographical coupling distance was 63.5 ± 0.5 nm at P7-9, 36.4 ± 0.4 nm at P14-16, and 26.3 ± 0.5 nm at P21-23 (p < 0.001 for all models; Figure 8E).Thus, our combined functional-structural-computational approach directly demonstrates shortening of the topographical coupling distance during development.(E) Estimates of topographical coupling distance for the three age groups and all tested models.Same color code as in (A).See also Figure S11 and Table S4.

DISCUSSION
To determine the nanotopography and stoichiometry of coupling at an inhibitory synapse, we combined biophysical analysis (paired recording, presynaptic recording, and pipette perfusion), structural measurements (serial-section EM and FRL), and modeling of Ca 2+ diffusion and release sensor activation.This combined approach offered unprecedented insights into the relation between structure and function of a central synapse.
Our results suggest that developmental processes not only result in a reduction of the source-sensor coupling distance, but also a transformation in the coupling nanotopography from more random to more clustered.Thus, presynaptic signaling developmentally approaches a point-to-point configuration, optimizing speed, reliability, and energy efficiency of synaptic transmission.
Ca 2+ channel subtype and activation during development Direct recording from BC terminals revealed that the presynaptic AP undergoes substantial shortening during synaptic maturation.This is reminiscent of previous results at the calyx of Held. 22In contrast, transmitter release at BC-PC synapses constantly relies on P/Q-type Ca 2+ channels.This is different from several other synapses, including the calyx, in which early in development, transmitter release depends on P/Q-, N-, and R-type Ca 2+ channels, whereas later in development, release only relies on P/Q-type channels. 19,23,29Thus, at BC-PC synapses, presynaptic APs of decreasing duration act on the same Ca 2+ channel subtype, implying a reduction in the efficacy of activation of presynaptic Ca 2+ channels during synaptic maturation. 52,57However, as the peak amplitude of the presynaptic AP may also change during development, 34,64 the efficacy of Ca 2+ channel activation can only be roughly estimated (Figure S4F).Our results suggest that the high efficacy of Ca 2+ channel activation in young BC-PC synapses may be similar to that in the calyx of Held and the hippocampal mossy fiber bouton, 56,57 whereas the low efficacy of Ca 2+ channel activation in mature BC-PC synapses more closely resembles the squid giant synapse or the frog neuromuscular junction. 65,66As a corollary, in the immature synapse Ca 2+ channels are opened largely deterministically, whereas in the mature synapse Ca 2+ channels are activated more stochastically. 6719]21 This has been interpreted as a decrease in the average coupling distance between Ca 2+ source and release sensor. 3However, our results reveal that the developmental changes in the coupling are more complex.We found that presynaptic Ca 2+ channels were clustered in the AZ at all developmental time points, as reported for other synapses. 21,51Synaptic vesicles were also non-randomly distributed, but clustering was only significant in mature synapses.
To determine the precise coupling configuration, we compared different nanotopography models against the experimental data (Figure 8).In mature synapses, the CP model, in which vesicles were attached to cluster perimeters, provided the best fit to our experimental observations, although the variability among AZs was substantial.Models in which vesicles were positioned to entire active zones were statistically inferior, and exclusion zones did not improve the fit.In contrast, in young synapses the RAZEZ model, in which vesicles were put to entire AZs with an exclusion zone, was superior (Figure 8C). 13Taken together, our results suggest that developmental processes not only result in a reduction of the coupling distance [17][18][19]21 but rather in a transformation in the coupling topography from more random to more clustered. In ntermediate synapses, the distribution was more similar to the P21-23 than to the P7-9 age group, implying that the transformation occurs between P10 and P13.Recent work suggested exclusion zone coupling at cerebellar parallel fibers versus perimeter coupling in stellate cell synapses.16 Our results highlight the importance of these coupling configurations 13,21 and extend the previous findings by showing not only synapse-specific differences but also developmental regulation.
Our findings have implications for the molecular interactions between Ca 2+ channels and release sensors.The CP model (best-fit model at P21-23) implies attraction between channels and sensors, while the RAZEZ model (best-fit model at P7-9) may suggest repulsion.Thus, intermolecular interactions may switch from repulsive to attractive during development.Attractive forces may be explained by the abundant presynaptic protein RIM, which binds to the vesicle protein Rab3 via zinc-finger domains and to the C terminus of presynaptic Ca 2+ channels via PDZ domains. 71,72Furthermore, RIM-binding proteins (RIM-BPs) bind to both RIM and the Ca 2+ channel C terminus.Additionally, Munc13-3 may tighten the coupling complex. 73Recent work suggested different machineries for clustering of Ca 2+ channels and synaptic vesicles.Whereas RIM and RIM-BP are critically important for Ca 2+ channel clustering, Liprin-a and the protein tyrosine phosphatase PTPs seem to be more relevant for vesicle docking and priming. 74Thus, a developmental sequence of expression of these proteins may contribute to the transformation of the coupling configuration.
Repulsive forces are more difficult to explain.It was suggested that septin 5 may increase the coupling distance, acting as a spacer that separates source and sensor from each other. 75owever, whether septin 5 is expressed at BC-PC synapses and whether it is downregulated during development is, at present, unclear. 76Other molecular factors generating repulsion remain to be identified.

Developmental change in the number of functional release sites
The number of functional release sites, N, is a key factor that determines the efficacy of the synapse. 31But what is the structural correlate of N? 44 Our combined functional and structural analysis provides a tentative answer to this fundamental question.Traditionally, it was thought that synaptic boutons per connection represent the structural correlates of functional release sites. 42,77However, it has also been suggested that the AZ represents the structural correlate. 78Furthermore, there are welldocumented examples of multi-vesicular release from single AZs, 79 raising the possibility of additional substructure of the AZ.At the BC-PC synapse, the number of functional release sites greatly exceeds the number of synaptic boutons per connection (Table S3).Early in development, the functional N agrees with the total number of AZs.However, later in development, the functional N exceeds the number of AZs and coincides better with the number of presynaptic Ca 2+ channel clusters (Table S3).Thus, the structural correlate of the functional N is not constant but may change during development.
How do the changes in the structural correlates of functional N relate to the changes in the coupling configuration?Early in development, the loosely coupled vesicles may ''see'' Ca 2+ channel inflow throughout the entire AZ, so that the AZ may act as a unit (Figure 7D).In contrast, later in development, the tightly coupled vesicles may selectively detect Ca 2+ inflow from the nearest Ca 2+ channels, so that the release process in the AZ is more fragmented (Figure 7F).A corollary of our results is that the interpretation of the number of functional release sites may differ between excitatory synapses (which often show microdomain coupling) 7 and inhibitory synapses (which frequently employ nanodomain coupling). 3Combined biophysical and structural analysis at other synapses will be needed to test this hypothesis.
Whether release units at BC-PC synapses are aligned with clusters of postsynaptic GABA A receptors to form ''nanocolumns'' 80 remains to be determined.If so, our results may call for a redefinition of the term ''synapse.''This term was classically used, based on physiological studies, to describe the entire junction between two neurons, 81 and later, based on anatomical work, for a presynaptic terminal attached to its somatodendritic target element. 42,77Our results suggest that a new definition based on nanotopographical criteria (e.g., presynaptic Ca 2+ channel clusters with attached vesicles, or Ca 2+ nanodomains) may be more appropriate.

Functional significance of coupling nanotopography for inhibitory synaptic transmission
Inhibitory synapses play a key role in several higher network functions, such as feedforward and feedback inhibition, pattern separation by winner-takes-all computations, 82 and fast rhythmic activity, such as network oscillations in the gamma frequency range. 83For all these functions, the speed of inhibition is critically important.Furthermore, speed and efficiency have to be maintained during high-frequency activity, a hallmark property of GABAergic neurons in vivo. 84,85How the requirements for speed and efficacy at inhibitory synapses can be integrated into single AZs remains enigmatic.
Our results suggest that the coupling nanotopography may explain how these requirements are implemented.In the mature synapse, clustered configurations (CA and CP) may offer functional advantages over random configurations (RPM and RPMEZ).The clustered nanotopography enables tight coupling between vesicles and the nearest neighbor Ca 2+ channels, which maximizes the speed of inhibitory synaptic transmission. 6urthermore, the clustered nanotopography allows accommodation of a large number of vesicles to their docking sites, lead-ing to a high vesicle-to-channel stoichiometric ratio.Large numbers of docked vesicles will be important to ensure fast and sustained transmitter release during in vivo-like repetitive activity at GABAergic synapses. 84,85Additionally, stochastic Ca 2+ channel activation in combination with low Ca 2+ channel numbers will minimize multivesicular release at single AZs or single Ca 2+ channel clusters. 79This may save vesicles, contributing to both sustained efficacy and energy efficiency of synaptic transmission. 24Finally, stochastic Ca 2+ channel activation will minimize presynaptic Ca 2+ inflow, further contributing to the energy efficiency.Thus, clustered nanotopography at mature GABAergic synapses provides unique functional advantages to inhibitory synaptic transmission, explaining its critical contribution to higher-order network computations.

Materials availability
This study did not generate new unique reagents.

Data and code availability
Original data, analysis programs, and computer code were stored in the scientific repositories of the Institute of Science and Technology Austria (ISTA).Any additional information required to reanalyze the data reported in this work paper is available from the lead contact upon request.

EXPERIMENTAL MODEL AND STUDY PARTICIPANT DETAILS
C57BL/6J mice were used for this study.Experiments were performed in strict accordance with institutional, national, and European guidelines for animal experimentation and were approved by the Bundesministerium f€ ur Bildung, Wissenschaft und Forschung (A.Haslinger, Vienna).

METHOD DETAILS Cerebellar slice preparation
Paired recordings were performed between synaptically connected BCs and PCs in the cerebellum at three developmental time points (P7-9, P14-16, and P21-23).The BC-PC synapse was particularly suitable for the combined biophysical and structural analysis of developmental changes.First, it is highly amenable to a mechanistic analysis of synaptic transmission, because of perisomatic location and high synaptic connectivity. 9Second, in comparison to hippocampus and neocortex, interneuron diversity in the cerebellum is more limited, making it easier to trace developmental changes.Finally, it undergoes substantial functional changes during development. 25lices were cut from the cerebellum of C57BL/6 mice of either sex in the three age groups.After decapitation, the brain was rapidly dissected out and immersed in ice-cold slicing solution containing: 87 mM NaCl, 25 mM NaHCO 3 , 2.5 mM KCl, 1.25 mM NaH 2 PO 4 , 10 mM D-glucose, 75 mM sucrose, 0.5 mM CaCl 2 , and 7 mM MgCl 2 (pH 7.4 in 95% O 2 /5% CO 2 , $325 mOsm).Parasagittal 250-mmthick cerebellar slices from the vermis region were cut using a VT1200 vibratome (Leica Microsystems).After $20 min incubation at $35 C, the slices were stored at room temperature (RT).Slices were used for maximally 5 h after dissection.Experiments were performed at 21 C-24 C.

Paired recordings
During experiments, slices were superfused with a bath solution containing: 125 mM NaCl, 2.5 mM KCl, 25 mM NaHCO 3 , 1.25 mM NaH 2 PO 4 , 25 mM D-glucose, 2 mM CaCl 2 , and 1 mM MgCl 2 (pH 7.4 in 95% O 2 /5% CO 2 , $325 mOsm).To investigate the relationship between IPSC peak amplitude and [Ca 2+ ] o , different combinations of [Ca 2+ ] o /[Mg 2+ ] o were used (0.7/2.3, 2/1, 4/1, and 10/1 mM).In the age group of 21-23 days, 1 mM TEA and 0.05 mM 4-AP were added to the 10/1 mM combination of [Ca 2+ ] o /[Mg 2+ ] o to further enhance release probability.27]88 Intracellular solution used for presynaptic BCs contained: 125 mM K-gluconate, 20 mM KCl, 10 mM HEPES, 10 mM phosphocreatine, 2 mM MgCl 2 , 0.1 mM EGTA, 2 mM ATP, 0.4 mM GTP, and 0.2% biocytin (pH adjusted to 7.28 with KOH, $310 mOsm).For experiments using Ca 2+ chelators, 0.1 mM EGTA was replaced by 10 mM EGTA or 10 mM BAPTA; the concentration of K-gluconate was reduced accordingly to maintain osmolarity.Presynaptic pipette resistance was 8-10 MU.Intracellular solution for postsynaptic PCs contained: 140 mM KCl, 10 mM HEPES, 2 mM MgCl 2 , 10 mM EGTA, 2 mM ATP, and 2 mM QX-314 (pH adjusted to 7.28 with KOH, $313 mOsm).To achieve minimal postsynaptic series resistance, leaded glass (PG10165-4, WPI) was used to fabricate large tip-sized recording pipettes.Postsynaptic pipette resistance was 0.8-1.5 MU, resulting in a series resistance of 3-8 MU.Experiments in which series resistance changed by > 3 MU were discarded.BCs were recorded under current clamp conditions.For P7-9 synapses, no holding current was applied.For P14-16 and P21-23 age groups, a hyperpolarizing holding current of $ -50 pA was injected to maintain the resting membrane potential at $-65 mV and to avoid spontaneous AP generation.PCs were recorded in the voltage-clamp configuration with a holding potential of À70 mV.To evoke presynaptic APs, single pulses or trains of 10 pulses at 50 Hz (400 pA, 4 ms) were injected into the presynaptic BC every 4 s or 20 s, respectively.In a subset of variance-mean analysis experiments (Figure S3), 300 mM of the low-affinity competitive GABA A receptor antagonist TPMPA was added to the bath solution.As TPMPA has fast binding and unbinding rates (k on $ 5 3 10 6 M À1 s À1 ; k off $ 2000 s À1 ), this is expected to minimize receptor saturation and desensitization. 37Miniature IPSCs (mIPSCs, Table S1) were recorded in pharmacological isolation in the presence of 1 mM TTX, 10 mM CNQX, and 20 mM D-AP5.Peptide toxins were applied using a recirculation system with a peristaltic pump (Ismatec, Germany).The total volume of the system was $5 mL, and the solution was equilibrated with 95% O 2 /5% CO 2 .Bovine serum albumin (BSA, Sigma-Aldrich, St. Louis, MI) was added at a concentration of 0.5 mg mL À1 to prevent adsorption of peptides to the surfaces of the perfusion system.u-agatoxin IVa and u-conotoxin GVIa were from Bachem (Switzerland), and SNX-482 was from Peptides International.
Presynaptic recordings from GABAergic terminals BC boutons were patched using the following experimental strategy. 89,90First, a somatic whole-cell recording was obtained, using BC internal solution containing Alexa Fluor 488 (100 mM, Invitrogen).Second, after $20 min of recording, the fluorescently labeled boutons were visualized in the PC layer with a Leica TCS SP5 confocal microscope (equipped with a DFC365FX camera, a Leica HCX APO L 20x/1.0W objective, and an argon laser, excitation wavelength of 488 nm).Exposure time was minimized to avoid phototoxicity and photobleaching.The bouton pipettes were coated with BSA Alexa Fluor 488 conjugate (0.02%, Invitrogen) solution for $20 s while keeping a positive intrapipette pressure during vertical dipping to prevent the pipette tips from clogging.Finally, confocal and infrared differential interference contrast (IR-DIC) images were compared and boutons were patched in the cell-attached configuration guided by confocal images.

Immunohistochemistry
After recording, slices were fixed by immersion in phosphate buffer (PB; 0.1 M, pH 7.4) containing 4% formaldehyde at 4 C overnight.After 3 times wash in PB, slices were embedded in 4% agarose and further sectioned into 50-mm-thick slices.For cryo-protection, slices were immersed in 30% sucrose in PB for 2 h at 4 C. Slices were further frozen above liquid nitrogen and thawed in PB to increase penetration of reagents.For immunolabeling, slices were first washed 3 times in PB and immersed in 10% normal goat serum (NGS) and 0.4% Triton X-100 in PB for 1 h at RT to block nonspecific binding.The slices were then incubated in rabbit polyclonal anti-GABA A receptor a1 primary antibody (5 mg mL À1 , Synaptic Systems, cat# 224 203) and guinea pig polyclonal anti-VGAT primary antibody (1:200, Synaptic Systems, cat# 131 004) for 48 h at 4 C in PB with 5% NGS and 0.4% Triton X-100.After washing 3 times in PB, slices were further incubated in PB containing 5% NGS, 0.4% Triton X-100, streptavidin Alexa Fluor 647 conjugate (4 mg mL À1 , Invitrogen, cat# S32357), goat anti-rabbit Alexa Fluor 488 (10 mg mL À1 , Invitrogen, cat# A-11034), and goat anti-guinea pig Alexa Fluor 405 (10 mg mL À1 , Abcam, cat# ab175678) for 2 h at RT. Slices were then washed in PB and mounted in Prolong Gold antifade embedding medium (Invitrogen).Fluorescence images were acquired using a Zeiss LSM 800 inverted microscope with sequential scanning of fluorescence signals using an oil objective (63x/1.4).Confocal images were analyzed with Fiji open source software.

Patch pipette perfusion
Ca 2+ chelators were loaded into presynaptic BCs by pipette perfusion, as described previously, 6 using a custom-made two-port pipette holder and parts of the 2PK + pipette perfusion kit (ALA Scientific Instruments, Westbury, NY).Presynaptic pipettes were filled with a small volume (2-4 mL) of intracellular solution.Chelators were applied through one port via a flexible quartz tubing (100 mm outer diameter) coated with polyamide.To minimize exchange times, the end of the tubing was positioned closely to the pipette tip.The other end was connected to a $0.6 mL reservoir with chelator-containing solution.To deliver the chelators to the pipette, positive pressure was applied to the reservoir and a compensatory negative pressure was applied at the second port of the pipette holder (which was also used for suction during seal formation and transition from cell-attached into whole-cell mode).Both positive and negative pressure were generated by a pressure/vacuum pump system and precisely controlled using two independent pressure regulators (2-5 mm Hg).To ensure stable long-term recordings, 3 mM GABA was added to the presynaptic internal solution. 91Control experiments with mock application of a solution with 0.1 mM EGTA revealed that the rundown of evoked IPSCs during long-lasting recordings was only minimal (to 100.4% of control value; Figures 3C and 3D).Given the small magnitude of rundown, no correction was made.To minimize diffusion time, pipette perfusion experiments were made from closely spaced pairs (BC-PC intersomatic distance <50 mm).

Bouton Ca 2+ imaging
Imaging of BC boutons (Figure S5) was performed using a Leica TCS SP5 confocal microscope (equipped with a Leica HCX APO L 20x/1.0W objective).First, BCs were filled with Fluo-5F (200 mM) and Alexa Fluor 594 (80 mM) via somatic whole-cell patch pipettes.To allow for a proper equilibration of the dyes, fluorescent signals were measured $40 min after break-in.Excitation wavelength was 488 nm (argon laser, intensity was set at 0.5%) for Fluo-5F and 561 nm for Alexa Fluor 594 (diode pumped solid state laser, intensity was set at 0.05%).Fluorescence signals were detected by two photomultiplier tubes (PMTs) at fixed PMT voltages, and detection range was 500 nm-550 nm for Fluo-5F and 600 nm-650 nm for Alexa Fluor 594.Boutons were searched in the PC layer and were identified as varicosities with diameter >2 times that of the adjacent axons.Line scan imaging was performed in the center of boutons, and the zoom factor was set such that pixel size was 90 nm.To enable simultaneous measurements from boutons at slightly different focal planes, the pinhole size was increased to 2 Airy units.Fluorescent transients were elicited by single APs evoked by brief somatic current pulses and recorded in line scans at 700 Hz temporal resolution.Each bouton was recorded 3 to 5 times.
Intracellular Ca 2+ transients were extracted with Fiji 92 and further analyzed with custom-made MATLAB code (Matlab 2020, Mathworks).The Ca 2+ -dependent green fluorescence was normalized to the Ca 2+ -insensitive red fluorescence and expressed as DG(t)/R, where G(t) is the fluorescence in the green channel for each time point and R is the mean fluorescence signal in the red channel over each recording epoch.Baseline fluorescence was measured in a 50-ms time window before stimulation, and peak fluorescence was determined in a 10-ms time window after stimulation.Care was taken to avoid phototoxic damage; experiments in which the resting green fluorescence increased by > 20% during recording were excluded from analysis.As background was minimal, no correction was performed.Ca 2+ transients shown in figures represent averages of 5 individual consecutive line scans.The decay phase of the Ca 2+ transients was fit by a double-exponential function, and the time constant was given as amplitude-weighted average decay time constant; components with negative amplitudes were set to 0. The average decay time constant of the Ca 2+ transients was $100 ms, consistent with the relatively low affinity of Fluo-5F (Figure S5). 93ta acquisition and analysis Data were acquired with a Multiclamp 700B amplifier (Axon Instruments/Molecular Devices), low-pass filtered at 10 kHz, and sampled at 20 or 50 kHz using a CED 1401plus interface (Cambridge Electronic Design).Data were analyzed with Stimfit 0.15.8,Igor Pro 6.3 (Wavemetrics), Mathematica 13.2 (Wolfram Research), or R 4.1.0(the R project for statistical computing).For BC recording, resting membrane potential was determined immediately after transition into the whole-cell configuration.Single AP parameters (peak amplitude, half-duration, and maximal rate of rise and decay) were measured from the AP threshold determined as the first point in the voltage trajectory in which the slope exceeded 20 V s À1 .Membrane potentials reported in the text were not corrected for liquid junction potentials.For BC-PC recording, functional properties of unitary IPSCs were determined from averages of 10-50 individual traces including failures.Synaptic latency (from the peak of the presynaptic AP to the onset of the IPSC), rise time (20%-80% of IPSC peak amplitude), and the proportion of failures were determined from 100 to 800 traces using Stimfit software.86 The IPSC decay time constant (single-exponential fit) was determined from single IPSCs.To quantify multiple-pulse depression, traces were averaged and the amplitude of each IPSC in a train was measured from the baseline directly preceding the rising phase.mIPSCs (Table S1) were detected using a template matching algorithm and verified by visual inspection.94 For analysis of quantal parameters, multiple probability fluctuation analysis was used.32 Mean and variance of IPSC peak amplitude were determined from stationary epochs.Variance-mean data were then fit with the equation where s 2 is variance, I is mean current, q is quantal size, and N is the number of functional release sites.Variance-mean data were also fit with equations including type 1 (intrasite) and type 2 (intersite) quantal variability where CV q1 and CV q2 represent the coefficients of variation of type 1 and type 2 variability, respectively. 95Thus, the basic structure of the variance-mean relation was maintained, with linear scaling factors for q (1 + CV q1 2 + CV q2 2) and N ((1 + CV q2 2) À1 ).As corrections were relatively small for plausible values of CV, and N was only affected by CV q2 , Equation 1a was used for final analysis.Additionally, variance-mean data were also fit with equations using a baseline noise term.As introducing this term gave only minimal differences in the estimated parameters and the best-fit value was close to 0, it was omitted in the final analysis.Finally, release probability at 2 mM [Ca 2+ ] o was computed as p R = I 2 mM /(N q).To determine the time course of quantal release, average unitary IPSCs were deconvolved from average quantal IPSCs. 9,96Quantal events were detected in the decay phase after a train of 10 APs using the template matching procedure, and converted into an idealized waveform with instantaneous rise and exponential decay.Time course of quantal release was computed by dividing the Fourier transforms of unitary and quantal IPSCs, and computing the inverse Fourier transform (Figure S1C).
To determine vesicular pool size and refilling rate, IPSC amplitudes during a 100-Hz train of 50 stimuli were subjected to cumulative release analysis. 35IPSC peak amplitude values were normalized by IPSC 1 , averaged across cells, and cumulatively plotted against stimulus number.The last ten data points were fit by linear regression.The size of the RRP was determined from intersection of the regression line with the ordinate, whereas refilling rate was determined from the slope. 35For obtaining absolute numbers of RRP size and refilling rate, estimated values were multiplied by the quantal content of IPSC 1 .For P7-9 and P14-16 synapses, the depression under control conditions was >50%, fulfilling a previously specified criterion for this analysis. 97For P21-23 synapses, however, the extent of depression was less; thus, pool analysis was performed in high-p R conditions with 4 mM extracellular Ca 2+ (Figure S2).

Serial section EM and image analysis
For the analysis of the number of AZs per bouton, brains of animals (C57BL/6 mice P7-9, n = 4; P14-16, n = 4; P21-23, n = 4) were perfusion-fixed with PB containing 2% formaldehyde, 2.5% glutaraldehyde, and 15% saturated picric acid solution.Serial sagittal sections from cerebellum were sliced at 50 mm with a VT1200 vibratome and processed according to a previously published protocol 98 with modifications.Briefly, sections were washed in PB and treated with 0.2% tannic acid in PB two times 45 min each at RT.Sections were postfixed and stained with 2% osmium tetroxide in PB for 40 min at RT and 1% uranyl acetate in water overnight at 4 C.They were further contrast-enhanced with Walton's lead aspartate for 30 min at 60 C, dehydrated in graded ethanol and anhydrous acetone, and embedded in epoxy resin following the manufacturer's instructions (Durcupan ACM, Sigma-Aldrich).
For the analysis of the number of docked vesicles per AZ, high-pressure freezing (HPF) of acute slice preparations was performed with a Leica EM ICE high-pressure freezing apparatus (Leica Microsystems) as previously described. 99After slicing and recovery, slices were mounted in sapphire-metal ring sandwiches.For mounting, a bottom sapphire disk (diameter 6 mm, thickness 120 mm; Wohlwend, Sennwald, Switzerland) was placed on the middle plate of a clear cartridge.Next, a spacer ring (outer diameter 6 mm, inner diameter 4 mm; thickness 200 mm) was put on top of the sapphire disk, adding a drop of extracellular bath solution containing 15% of the cryoprotectant polyvinylpyrrolidone. Subsequently, the tissue sample was transferred using a paintbrush.Finally, a second sapphire disk with identical dimensions was put on top to form a sandwich.Freeze substitution and embedding were done as previously described. 99or serial sectioning, samples were sliced at either 40 nm (number of docked vesicle analysis in cryofixed samples) or 80 nm (number of AZ analysis in chemically fixed samples) using a UC7 ultramicrotome (Leica Microsystems) and a 4-mm Ultra 35 diamond knife (Diatome).Ribbons of sections were mounted onto Formvar-coated copper slot grids, and examined in a Tecnai 10 transmission electron microscope (T10 TEM; Thermo Fisher Scientific) operated at 80 kV accelerating voltage.Images were recorded with a Megaview III CCD camera and Radius acquisition software (both EMSIS).
BC boutons and AZs were selected for three-dimensional reconstruction from serial section electron micrographs based on completeness and optimal angle of sectioning.Serial images were aligned and relevant structures were traced and measured with Fiji/TrakEM2 software. 100Perimeters of AZs were drawn according to close and parallel apposition of the pre-and postsynaptic membrane, and presence of amorphous electron-dense material in the cleft.Three-dimensional reconstruction of AZs was performed using custom-made MATLAB software.Vesicles were classified as docked when the distance between vesicular and presynaptic plasma membrane was <5 nm, consistent with previous criteria for classification of vesicular pools. 99Three-dimensional reconstruction of boutons was performed using the ETomo software of the IMOD software package, version IMOD 4.11. 87For model scaling, the z scale was set as the section thickness divided by the pixel size of the respective electron micrograph.For calculation of the AZ surface area, the object was meshed within the 3Dmod software using the standard parameters.
Freeze-fracture replica labeling (FRL) FRL was performed with some modifications to the original method. 101,102Brains of animals (C57BL/6 mice P7-9, n = 3; P14-16, n = 3; P21-23, n = 3) were perfusion-fixed with PB containing 2% formaldehyde and 15% saturated picric acid solution.Sagittal sections from cerebellum were cut at 140 mm with a VT1200 vibratome and cryoprotected by immersion in 30% glycerol in PB overnight at 4 C. Samples were rapidly frozen by use of the high-pressure freezing machine HPM 010 and fractured by a double-replica method in the freeze-etching device BAF 060 (Leica Microsystems) as described before. 103In brief, fractured faces were replicated by evaporation of carbon (rotating) by means of an electron beam gun positioned at a 90 angle to a thickness of 5 nm for immobilization of macromolecules.They were then shadowed unidirectionally with platinum-carbon at a 60 angle (thickness 2 nm) and strengthened by evaporation of carbon to a thickness of 20 nm from a 90 angle (rotating).Samples were brought to atmospheric pressure and thawed to RT in Tris-buffered saline (TBS; 50 mM, 0.9% NaCl, pH 7.4).Tissue not immobilized in the replica membrane was solubilized in a medium containing 2.5% sodium dodecyl sulfate (SDS) and 20% sucrose in 15 mM TBS, pH 8.3, on a shaking platform for 48 h at 60 C. Replicas were treated for another 12 h at 37 C and kept at RT in the same solution.
For immunolabeling, replicas were washed in TBS and incubated in 5% BSA in TBS for 1 h at RT to block nonspecific binding.Subsequently, antibodies were applied sequentially in TBS containing 2% BSA.Replicas were first incubated with guinea pig polyclonal anti-Ca v 2.1 a 1A primary antibodies (2 mg mL À1 ; Synaptic Systems, cat# 152 205), and reacted with goat anti-guinea pig secondary antibodies conjugated to 10-nm gold particles.Replicas were then incubated with a cocktail of AZ marker proteins including rabbit polyclonal anti-RIM1/2 antibodies (2 mg mL À1 ; Synaptic Systems, cat# 140 203), rabbit polyclonal anti-ELKS antibodies (2 mg mL À1 ; provided by Akari Hagiwara and Toshihisa Ohtsuka, Yamanashi University Medical School, Japan), and rabbit polyclonal anti-neurexin antibodies (1 mg mL À1 ; provided by Masahiko Watanabe, Hokkaido University School of Medicine, Japan), and reacted with goat anti-rabbit secondary antibodies conjugated to 2-nm gold particles. 51Finally, replicas were incubated with mouse monoclonal anti-VGAT antibodies (4 mg mL À1 ; Synaptic Systems cat# 131 011), and reacted with goat anti-mouse secondary antibodies conjugated to 15-nm gold particles.All primary antibodies and gold-conjugated secondary antibodies (1:30, BBI Solutions) were each applied overnight at 15 C. The specificity of the Ca v 2.1 antibody was confirmed by testing cerebellar tissue samples from Ca v 2.1 a 1A À/À mice (Figure S7).Replicas were then washed in water, mounted onto Formvar-coated 100-line copper grids, and examined in a Tecnai 12 TEM (Thermo Fisher Scientific) operated at 120 kV and equipped with a Veleta CCD camera (EMSIS).Images were acquired and analyzed using Radius (EMSIS) and Fiji software (distributed under the General Public License, GPL).For identification of BC AZs, we set the following criteria: (1) presence of immunoparticles labeling AZ marker proteins (2 nm) and VGAT (15 nm; minimum 2 particles), (2) aggregates of intramembrane particles, and (3) direct proximity to postsynaptic PC plasma membrane.AZs were delineated according to the following principles: (1) demarcation of AZs drawing a polygon based on the outmost immunoparticles for Ca v 2.1 (10-nm gold particles) and RIM-ELKS-neurexin (2-nm gold particles; Miki et al., 2017).
(2) Inclusion of an outer rim of 20 nm as antibodies can freely rotate around the epitope. 102The dimension of this rim results from the size of antibodies applied (IgGs with approximately 8 nm each) and the size of the immunoparticle itself (radius of the gold particle).(3) Elimination of cases where a single gold particle or the center of an individual particle cluster was >100 nm away from the nearest particle cluster to avoid spurious delineation of AZs by isolated RIM-ELKS-neurexin particles.The threshold of 100 nm was derived from the longest distance between neighboring RIM-ELKS-neurexin clusters inside AZs.Distances were calculated using macros in R 4.1.0(the R project for statistical computing).The x and y coordinates of immunoparticles were recorded and extracted in Fiji, the distances from each particle to every other particle were calculated, and the smallest value was assigned as the NND for each particle.
Clustering of particles was analyzed by comparing cumulative distributions of NNDs between real data from experimental measurements and simulated data generated by a random point process.Statistical significance was assessed using a Wilcoxon-Mann-Whitney test.In addition, clustering of particles was analyzed using the Ripley method. 16,48Ripley's K function was computed as: KðrÞ = l À 1 X isj u i;j À 1 Iðd i;j < rÞ N; (Equation 2) where l is average point density, u i,j is a weight factor for edge correction, I is an indicator function that counts the number of points within a radius r (taking a value of 1 if its operand is true and 0 otherwise), and N is number of points in the pattern.After correction for edge effects, H(r) was computed from K(r) as HðrÞ = ffiffiffiffiffiffi ffi KðrÞ p q À r.Values H(r) > 0 may indicate clustering, while values H(r) < 0 may suggest dispersion.H(r) curves were first obtained for individual AZs and then pooled for all AZs of each developmental time period.Statistical significance was assessed using a maximum deviation test, comparing experimental against Monte Carlo-simulated data. 16To specifically test for clustering, only positive deviations were considered.For random positioning of Ca 2+ channels, points were simulated on the AZ plane with 10 nm minimal distance.For random positioning of vesicles, spheres were distributed within single sections with 30 nm minimal distance.
To define clusters of particles, we applied DBSCAN to our replica data. 104To obtain quantitative criteria for separating particles in the same versus different clusters, we plotted, for each particle, the 2-nearest neighbor graph for an individual AZ, and then identified the onset point of each graph as e.We found that most of the e were located in the range between mean +2 SD and mean +3 SD of the NND.The mean e was 40.3 nm, 41.1 nm, and 40.9 nm for the P7-9, P14-16, and P21-23 age groups, respectively.The minimal number of points in each cluster was set to 3, based on the Ca v 2.1 particle background labeling on knockout mice tissue (Figure S7). 51The NND between clusters was estimated by determining the shortest distance between cluster centers.
Labeling efficacy of the Ca v 2.1 antibody used in the present study was estimated in control experiments at hippocampal mossy fiber synapses, in which direct presynaptic Ca 2+ current recordings, 52 serial-section EM data, 46 and FRL data (O.K., unpublished) are all available. 105Functional analysis revealed 2007 Ca 2+ channels of all types and 1324 P/Q-type Ca 2+ channels per mossy fiber terminal. 52Serial-section EM gave a total AZ area of 3.33 mm 2 , a total presynaptic surface area of 75.5 mm 2 , and an extrasynaptic surface area of 72.2 mm 2 (75.5 mm 2 À 3.33 mm 2 ; P28). 46Finally, FRL analysis revealed Ca v 2.1 particle densities of 279 mm À2 inside the AZ and 1.36 mm À2 outside the AZ (O.K., unpublished).Taken together, this gives a total number of P/Q immunoparticles of 1027 per mossy fiber terminal (AZ density 3 AZ area + extrasynaptic density 3 extrasynaptic area), corresponding to a labeling efficiency of 77.6% (1027/1324).This is higher than a previous estimate based on optical fluctuation analysis ($40%). 16deling of nanodomain coupling based on realistic coupling topographies Ca 2+ diffusion and binding to buffers was modeled solving the full set of partial differential equations of the reaction-diffusion problem in three dimensions, including all necessary boundary and initial conditions. 3,6,7,15,60

Figure 2 .
Figure 2. Reciprocal changes in release probability, functional release site number, and presynaptic AP duration during development (A-C) Example variance-mean measurements of evoked IPSC amplitudes at varying outer Ca 2+ concentrations ([Ca 2+ ] o ) in BC-PC synapses at P9 (A), P14 (B), and P21 (C).Curves represent fits with Equation 1a (STAR Methods).(D-G) Summary bar graphs of release probability at 2 mM [Ca 2+ ] o (D), number of functional release sites (E), quantal size (F), and quantal content (G).(H-K) Changes in presynaptic AP duration during development.(H) Confocal maximum intensity projection of BC filled with Alexa Fluor 488 during recording through a somatic patch pipette.Somatic recording electrode is located on the top right, presynaptic recording electrode is visible at the bottom.(I) Cell-attached voltage-clamp recordings from putative presynaptic terminals.Gray, individual traces; black, average trace.10 individual traces superimposed.(J) Reconstruction of BC after recording.ML, molecular layer; PCL, Purkinje cell layer, GCL, granule cell layer.(K) Summary bar graph of AP half-duration measured from presynaptic terminal.Half-duration of the presynaptic AP was quantified as the time difference between negative and positive peaks of presynaptic action current.Data are from 5 (P7-9), 5 (P14-16), and 5 (P21-23) bouton recordings.See also Figures S1-S5 and TablesS1 and S3.

2 Figure 4 .
Figure 4. Number of boutons, active zones (AZs), and docked vesicles at BC-PC synapses during development (A) Confocal maximum intensity projection of BC at P14 filled with biocytin during recording and labeled using Alexa Fluor-conjugated streptavidin.(B) Example confocal fluorescence micrographs of biocytin-labeled BC terminals and immunolabeling for VGAT and GABA A a1 subunit in a BC-PC synapse at P14. White arrows indicate two boutons.Individual fluorescent signals were converted into red, green, and blue pseudocolors to improve clarity.Dashed lines indicate pixels used for intensity profile plots (right).
(G) Transmission electron micrographs (left) and corresponding reconstruction of docked vesicle distribution from serial sections (right, blue circles) of an AZ of a BC-PC synapse at P21.Sections (left) correspond to arrows g1 and g2 (right).(H-K) Summary bar graphs of number of docked synaptic vesicles per AZ (H), AZ area (I), docked synaptic vesicle density (J), and docked synaptic vesicle diameter (K) at P7-9, P14-16, and P21-23 respectively.Circles represent data from individual connections, boutons, AZs, or vesicles.Bars indicate mean ± SEM. (L) Ripley H-function analysis of docked vesicle distribution in individual AZs for P7-9 (left), P14-16 (center), and P21-23 age group (right) AZs.Gray, red, and cyan curves represent the edge-corrected H(r) function for 15, 9, and 15 AZs, respectively.The black line represents the mean H(r) function calculated from 100 null model point pattern simulations from each AZ.The gray shaded area represents the 95% confidence envelope (CE).Population p value was calculated using a maximum difference test.(M) Ripley H-function analysis of docked vesicle distribution in individual AZs revealed that the null model was rejected (maximum difference test) for 13.3% of P7-9, 22.2% of P14-16, and 60.0% of P21-23 AZs.Data in (C)-(F) and (I) were obtained from chemically fixed tissue; data in (G), (H), (J), and (K)-(M) were obtained from cryofixed tissue.See also Figure S6 and Tables

Figure 5 .
Figure 5. Nanoclusters of presynaptic Ca 2+ channels in AZs of BC terminals revealed by freeze-fracture replica labeling (FRL) (A-C) FRL of presynaptic Ca 2+ channels in AZs at P9 (A), P14 (B), and P23 (C), respectively.15-nm gold particles represent VGAT immunoreactivity; 10-nm gold particles label presynaptic Ca v 2.1 Ca 2+ channels.BC terminals were identified by location near PC soma and VGAT expression.Putative AZ boundaries are indicated by yellow dashed lines.Right panels show zoomed images from the black rectangular boxes in left panels.(D-F) Summary bar graphs of number of Ca v 2.1 particles per AZ (D), putative AZ area (E), and corresponding particle density in AZs (F).Circles represent data from individual AZs; bars indicate mean ± SEM. (G) Ripley H-function analysis of Ca v 2.1 gold particle distribution across the population of P7-9 (left), P14-16 (center), and P21-23 AZs (right).Gray, red, and cyan curves represent the edge-corrected H(r) function for 67, 69, and 81 AZs, respectively.The black line represents the mean H(r) function calculated from 100 null model point pattern simulations from each AZ.The gray shaded area represents the 95% confidence envelope (CE).Population p value was calculated using a maximum difference test.(H) Ripley H-function analysis of Ca v 2.1 gold particle distribution in individual AZs revealed that the null model was rejected (maximum difference test) for 82.1% of P7-9, 91.3% of P14-16, and 88.9% of P21-23 AZs.See also Figures S7-S9 and TableS2.

Figure 6 .
Figure 6.Developmental changes in number and properties of presynaptic Ca 2+ channel clusters (A-F) Distributions of Ca v 2.1 clusters in representative AZs from the P7-9 (A and B), P14-16 (C and D), and P21-23 age groups (E and F).Original EM micrographs are shown in (A), (C), and (E) and positions of gold particle labeling Ca v 2.1, color-coded according to cluster allocation in (B), (D), and (F).Single scattered particles not allocated to clusters were omitted from the analysis.(G-I) Distribution histograms for the number of Ca v 2.1 clusters per AZ at P7-9 (G), P14-16 (H), and P21-23 age groups (I).(J-L)Plots of Ca v 2.1 gold particle number per cluster against cluster area at P7-9 (J), P14-16 (K), and P21-23 age groups (L).Gray, red, and cyan filled circles indicate mean values.(M and N) Cumulative distributions of the number of Ca v 2.1 clusters per AZ (M) and the number of Ca v 2.1 particles per cluster (N) for P7-9 (gray), P14-16 (red), and P21-23 age groups (cyan).(O and P) Cumulative distributions of nearest neighbor distance (NND) values between Ca v 2.1 particles within a cluster (O) and between the centers of Ca v 2.1 clusters (P) for P7-9 (gray), P14-16 (red), and P21-23 age groups (cyan), respectively.The NND between the centers of clusters was calculated by averaging coordinates of all particles in individual clusters.See also Figures S7 and S8 and TableS2.

Figure 7 .
Figure 7. Sharpening of Ca 2+ domains in cerebellar BC terminals during development (A) Topography of three representative AZs from the P7-9, P14-16, and P21-23 age groups.Blue, AZ area; red, presynaptic Ca 2+ channels.(B) Schematic illustration of simulations of buffered diffusion of Ca 2+ .The full set of partial differential equations was solved assuming a three-dimensional spatial grid with 5-nm resolution.Gray cube, simulated volume.For details, see STAR Methods.(C)Model of AZ in which vesicles were attached to the presynaptic membrane opposite to nanoclusters of presynaptic Ca 2+ channels.Spheres, synaptic vesicles; red dots, presynaptic Ca 2+ channels; green areas, convex hull around Ca 2+ channel clusters.Vesicles were attached at 5 nm vertical distance from the plasma membrane, consistent with the distance of docked vesicles.

Figure 8 .
Figure 8. Change of Ca 2+ channel-vesicle coupling from random to clustered nanotopography during development (C) Histograms of the best-fit model in P7-9 (left), P14-16 (center), and P21-23 age groups (right).Histograms show the distribution for the entire set of reconstructed active zones (67, 69, and 81 AZs).For each AZ, 5 random synaptic vesicle placement patterns were simulated.Insets on top show the models with the highest abundance in the histograms.(D) Direct estimation of ''topographical coupling distance.''Left, schematic illustration of the approach.Topographical coupling distance was computed as the mean of the pairwise distance matrix multiplied with the release relevance matrix to define weights.For details, see STAR Methods.Right, release relevance matrix for a synapse from the P21-23 age group and the CA model.Color scale indicates fractional contribution (red, high contribution; blue, low contribution).
2.91 ± 0.19 at P7-9, 4.38 ± 0.23 at P14-16, and 4.64 ± 0.23 at P21-23; 67, 69, and 81 AZs; p < 0.001; Figures 6G-6I and 6M), whereas the average number of particles The main partial differential equations were Ca] is the free Ca 2+ concentration, t is time, x, y, and z are spatial coordinates, and D Ca is the diffusion coefficient for Ca 2+ .Furthermore, ½B i is the free mobile buffer concentration, k on the binding rate, k off the unbinding rate, ½B i tot the total mobile buffer concentration, and D B the diffusion coefficient of the buffer.Finally, [B fix ] is the free fixed buffer concentration, and [B fix ] tot is the total fixed buffer concentration.Near the Ca 2+ sources, the boundary conditions were given as where s(t, x, y) is the flux density.Otherwise, the boundary conditions were v½Ca vx = v½B i vx = 0 for x/x min or x max ; (Equation 7a)