Diversity of excitatory release sites

The molecular mechanisms underlying the diversity of cortical glutamatergic synapses is still only partially understood. Here, we tested the hypothesis that presynaptic active zones (AZs) are constructed from molecularly uniform, independent release sites (RSs), the number of which scales linearly with the AZ size. Paired recordings between hippocampal CA1 pyramidal cells and fast-spiking interneurons followed by quantal analysis demonstrate large variability in the number of RSs (N) at these connections. High resolution molecular analysis of functionally characterized synapses reveals highly variable Munc13-1 content of AZs that possess the same N. Replica immunolabeling also shows a 3-fold variability in the Munc13-1 content of AZs of identical size. Munc13-1 is clustered within the AZs; cluster size and density are also variable. Our results provide evidence for quantitative molecular heterogeneity of RSs and support a model in which the AZ is built up from variable numbers of molecularly heterogeneous, but independent RSs.


Introduction
Computational complexity of neuronal networks is greatly enhanced by the diversity in synaptic function (Dittman et al., 2000;O'Rourke et al., 2012). It has been known for decades that different types of central neurons form synapses with widely different structure, molecular composition, and functional properties, resulting in large variations in the amplitude and kinetics of the postsynaptic responses and the type of short-and long-term plasticity. When the mechanisms underlying distinct functions were investigated among synapses made by distinct pre-and postysynaptic cell types (e.g. hippocampal mossy fiber vs. Schaffer collateral vs. calyx of Held vs. cerebellar climbing fiber etc. synapses), most studies converged to the conclusion that different pre-(e.g. different types of Ca channels, Ca sensors) and postsynaptic (e.g. different types of AMPA receptor subunits) molecule isoforms underlie the functional variability (reviewed by Sudhof, 2012).
Robust differences in synaptic function were also found when a single presynaptic cell formed synapses on different types of postsynaptic target cells. Such postsynaptic target cell type-dependent variability in vesicle release probability (Pv) and short-term plasticity was identified in cortical and hippocampal networks (Koester and Johnston, 2005;Losonczy et al., 2002;Pouille and Scanziani, 2004;Reyes et al., 1998;Rozov et al., 2001;Scanziani et al., 1998;Thomson, 1997). Studies investigating the underlying mechanisms revealed not only different molecules (e.g. mGluR7, kainate receptors in the active zone (AZ) and Elfn1 in the postsynaptic density (PSD), Shigemoto et al., 1996;Sylwestrak and Ghosh, 2012), but distinct densities of the same molecules were also suggested as key molecular features (Eltes et al., 2017;Rozov et al., 2001).
Probably even more surprising is the large structural and functional diversity of synapses that are established by molecularly identical pre-and postsynaptic neuron types (e.g. synapses among cerebellar molecular layer interneurons (INs), Pulido et al., 2015;among hippocampal CA3 PCs, Holderith et al., 2012), suggesting that qualitative molecular differences are unlikely to be responsible for the functional diversity. What could then be responsible for the large diversity in function in such synapses ? Pulido (2015) investigated so called simple synapses where the synaptic connection is mediated by a single presynaptic AZ and the opposing PSD. Their results revealed that the number (N) of functional release sites (RSs) varied from 1 to 6 per AZ and it showed a positive correlation with the quantal size (q).
Because in these synapses q is largely determined by the number of postsynaptic GABAA receptors and because the GABAA receptor number scales linearly with the synapse area (Nusser et al., 1997) they concluded that the N linearly scales with the synaptic area. Previous results from our laboratory showed that the probability with which release occurs (PR) from a CA3 PC axon terminal correlates with the size of the synapse. As this probability is the function of both Pv and N [PR = 1-(1-Pv) N ], our results are also consistent with the model that N scales with synaptic area (Holderith et al., 2012). This view was further supported by a recent paper (Sakamoto et al., 2018), which concluded that in synapses of cultured hippocampal neurons the number of Munc13-1 macromolecular clusters shows a linear correlation with the N. Thus, the following model emerged: presynaptic AZs are composed from an integer number of uniform, independent RSs, which are built from the same number of identical molecules (molecular units). The more RSs there are, the larger the size of the AZ is, which face a correspondingly larger PSD containing proportionally more receptors. This model is supported by a number of molecular neuroanatomical studies showing that the number of presynaptic AZ molecules (e.g. Cav2.1, Cav2.2, Rim1/2; Holderith et al., 2012;Kleindienst et al., 2020;Miki et al., 2017) or postsynaptic molecules (e.g. PSD-95, AMPA receptors; Fukazawa and Shigemoto, 2012;Kleindienst et al., 2020) scales linearly with the synapse area. However, a recent study using superresolution imaging of release from cultured neurons concluded that the RSs are functionally heterogeneous and RSs with high or low Pv are distributed in a nonrandom fashion within individual AZs (Maschi and Klyachko, 2020).
Here, we performed in vitro paired whole-cell recordings followed by quantal analysis to determine the quantal parameters (N, Pv and q) in synaptic connections between hippocampal CA1 pyramidal cells (PCs) and fast-spiking interneurons (FSINs). Our results demonstrate that the large variability in postsynaptic response amplitude is primarily the consequence of large variations in N. The variability in N is also substantial in individual AZs (1 -17). Multiplexed molecular analysis with confocal and STED superresolution microscopy revealed large variability in the Munc13-1 content of AZs that possess the same number of RSs, indicating that RSs could be formed by variable number of Munc13-1 molecules.
This molecular variability among RSs is supported by our high-resolution electron microscopy replica immunolabeling data, demonstrating highly variable number of gold particles in Munc13-1 clusters in these hippocampal glutamatergic AZs.

Large variability in unitary EPSC amplitudes evoked by CA1 PCs in FSINs
To investigate the variance in unitary EPSC (uEPSC) amplitudes evoked in FSINs by CA1 PC single action potentials (APs), we recorded a total of 79 monosynaptically connected pairs in 2 mM external [Ca 2+ ] from acute slices of adult mice of both sexes (Figure 1). The amplitude of uEPSCs ranged from 3 to 507 pA with a mean of 105.0 pA and a SD of 107.9 pA, yielding a coefficient of variation (CV) of 1.03.
The uEPSCs had a moderate variability in their 10-90% rise times (RT, mean = 0.4 ± 0.2 ms, CV = 0.4) but some had values over 1 ms. To exclude the contribution of differential dendritic filtering to the observed variance in amplitudes, we restricted our analysis to presumed perisomatic synapses by subselecting uEPSCs with 10-90% RTs ≤500 µs. These fast-rising EPSCs had a similar large variability in their amplitudes (113.1 ± 111.0 pA, n = 68; Figure 1D) with a CV of 0.98. The type of short-term plasticity is a widely used feature of postsynaptic responses that is assumed to predict the Pv. Although, some connections displayed initial facilitation followed by depression, most of the connections showed robust depression, and the resulting moderate variability in the paired-pulse ratio (CV = 0.38; Figure 1E) implies that the variability in Pv might not be the major source of variability in EPSC amplitudes. It is well known that FSINs are morphologically diverse (contain perisomatic region-targeting basket and axoaxonic cells and dendrite-targeting bistratified cells) and therefore we tested whether the observed amplitude variance could be the consequence of different morphological identity of the postsynaptic cells.
A total of 50 INs could be categorized into perisomatic region-targeting (n = 35) or bistratified (n = 15) cells, and when uEPSCs amplitudes were compared (perisomatic: 128.1 ± 121.9 pA vs bistratified: 126.4 ± 125.7 pA), no significant difference was found (p = 0.98, Mann-Whitney U-test). Furthermore, the CV within each group was ~1, revealing a similar variance in EPSC peak amplitudes when the postsynaptic cells belong to a well-defined IN category.

Quantal parameters at PC -FSIN connections
To elucidate the basis of the uEPSC amplitude variability, we determined the quantal parameters N, Pv and q of the connections using Multiple Probability Fluctuation Analysis (MPFA, Silver, 2003). For their reliable determination, the Pv must be changed substantially and must have a maximum value >0.5.
Because, Pv in 2 mM [Ca 2+ ] shows a more pronounced correlation with the peak EPSC amplitude (Figure 2-figure supplement 1C), we calculated the relative contribution of the three quantal parameters to the amplitude variance and found that even in 2 mM [Ca 2+ ] the variance in N (63%) has a substantially larger contribution than that of q (25%) or Pv (12%; for CV values in 2 mM [Ca 2+ ] see Because PC -FSIN connections are not mediated by single synapses (Buhl et al., 1997;Molnar et al., 2016), the overall variability in N is not simply the consequence of different Ns per AZs, but also the function of the number of synaptic contacts formed by the presynaptic axon on the postsynaptic cell. To determine the number of synaptic contacts between the connected cells, we carried out high magnification confocal microscopy analysis of the biocytin filled, aldehyde fixed and post hoc developed cells (detailed below). Our data revealed a relatively weak correlation between peak uEPSC amplitude and the N / AZ (rs = 0.37; Figure 2H) and a more robust one between the peak uEPSC amplitude and the synapse number (rs = 0.61; Figure 2I). When we examined their variances, an approximately equal contribution of the synapse number (mean = 2.3 ± 1.6, n = 26, CV = 0.68) and the N / AZ (mean = 4.9 ± 3.7, n = 26, CV = 0.75) to the variance in N (mean = 10.2± 9.8, n = 26, CV = 0.96) was observed.

Correlation of the amounts of synaptic molecules with N
So far, our results demonstrate large variability in the peak amplitude of uEPSCs between CA1 PC and FSINs, which is primarily the consequence of large variability in N among the connections. This variability originates approximately equally from differences in the number of synaptic contacts between the connected cells (ranges from 1 to 7, CV = 0.68) and from variations in the number of RSs within individual AZs (ranges from 1 to 17, CV = 0.75). Why monosynaptic connections between the same preand postsynaptic cell types show variability in the number of synaptic contacts is unknown and answering this question is outside the scope of the present study.
Here we address the question of what the molecular correlates of the variability in the number of RSs within individual presynaptic AZs are. We employ a recently developed high-resolution, quantitative, multiplexed immunolabeling method  to molecularly analyze functionally characterized individual synapses. Following in vitro paired recordings, the slices were fixed, re-sectioned at 70-100 µm, the biocytin-filled cells were visualized with Cy3-coupled streptavidin and the sections were dehydrated and embedded into epoxy resin. As Cy3 molecules retain their fluorescence in the water-free illumination using a high numerical aperture (NA = 1.35) objective lens. Every pair was studied by two independent investigators and all independently found potential contacts were scrutinized by three experts. After obtaining confocal image Z stacks from all potential contacts, the thick sections were re-sectioned at 200 nm thickness, in which we could unequivocally identify the contacts (compare Figure   3F and G). Following their registration with confocal microscopy, multiplexed immunoreactions were carried out on serial sections for presynaptic Munc13-1, vGluT1 molecules and postsynaptic AMPA receptors (with a pan-AMPAR Ab, data not shown) and PSD-95 ( Figure 3H  Since N is the function of how many contacts there are between the cells and how many RSs there are within the AZs, we next dissected their individual contributions. Although, our results revealed positive correlations for both values with Munc13-1 ( Figure 4F and G), we noticed a remarkable variability: synapses with widely different numbers of RSs have similar amounts of Munc13-1 and synapses with similar Ns showed very different amounts of Munc13-1 ( Figure 4G). In summary, our data is consistent with a model in which the size of the presynaptic AZ correlates with the number of RSs, but the observed variance indicates variability in the overall amounts of Munc13-1 in individual RSs. Next, we aimed to investigate this issue with a more sensitive and higher resolution method.

Variable size and molecular content of Munc13-1 clusters in glutamatergic AZs on Kv3.1b+ INs as revealed by SDS-FRL
To investigate the relationship between the size of AZs and the amounts of Munc13-1, we obtained replicas from the CA1 region of age-matched mouse hippocampus. First, we verified the specificity of our labeling using two Munc13-1 antibodies recognizing non-overlapping epitopes (Figure 5-figure   supplement 1). We then performed double immunogold labeling for Kv3.1b and Munc13-1 (Figure 5).
Next we investigated the sub-synaptic distribution of Munc13-1 as it has been suggested to have a clustered distribution in AZs and the clusters represent the RSs (Sakamoto et al., 2018). First, we measured mean nearest-neighbor distances (NND) between gold particles in the AZs and compared them to random particle distributions. The mean NND distances were significantly smaller than those of randomly distributed gold particles (data: 0.026 ± 0.01 µm, random: 0.033 ± 0.009 µm, n = 159, p<0.001, Wilcoxon signed-rank test; Figure 5K). A previous study from our laboratory demonstrated that Ripley's H-function analysis could reveal clustered distribution of synaptic molecules, including Munc13-1 in cerebellar synapses (Rebola et al., 2019). We performed this analysis on 159 AZs and found that in 66% of the AZs the distribution of gold particles was compatible with clustering (p<0.05, MAD-test). Next, we used DBSCAN to identify the Munc13-1 clusters in these 105 AZs and found an average of 5.4 ± 2.5 clusters per AZ. This number is remarkably similar to the number of functional RSs per AZ (4.9 ± 3.7), supporting the notion that Munc13-1 clusters are indeed the molecular equivalents of the functional RSs (Sakamoto et al., 2018). When the number of clusters were plotted against the AZ area, a significant positive correlation was found ( Figure 5L). However, the number of clusters also varied 3-fold in synapses of identical sizes, resulting in a CV of 0.36 in the cluster density (mean: 73 ± 27 clusters / µm 2 AZ area, n = 105). We also noticed that not only the cluster density varies, but the Munc13-1 content of the clusters (4.5 ± 3.0 gold /cluster, CV: 0.67, n = 571) is also highly variable (for individual AZs see Figure 5H).

Quantitative STED analysis reveals highly variable amounts of Munc13-1 in excitatory synapses of identical sizes
Our SDS-FRL experiments reveal large variability in the Munc13-1 content of synapses with identical sizes, which is the consequence of both the variability in the cluster density and the molecular content of the clusters. We believe that the replica labeling is the most appropriate method for quantitative analysis of sub-synaptic distributions of molecules due to its high resolution and sensitivity, but unfortunately it is impossible to perform SDS-FRL in synapses that had been functionally characterized due to the random fracturing of the tissue. Because of this limitation, we developed the above described postembedding, multiplexed immunofluorescent reaction with which we could molecularly characterize functionally tested individual synapses . In our final set of experiments we aimed to compare the results of these postembedding reactions to those obtained with SDS-FRL.
We randomly selected and serially sectioned proximal dendritic segments of two in vitro recorded FSINs (Figure 6). The sections were then immunoreacted for Munc13-1 and PSD-95 in consecutive labeling rounds and their reaction strengths were quantitatively analyzed on the STED images. First, we performed the analysis on 200 nm thick sections (the usual section thickness in our protocol) and focused on en face synapses where the pre-and postsynaptic specializations are present in a single section and therefore no 3D reconstruction is needed from serial sections (Figure 6C). In the two examined cells relative Munc13-1 and PSD-95 intensities show a loose correlation (Figure 6D). More important, the PSD-95 normalized Munc13-1 labeling showed a large variability (Cell 1: CV = 0.42; Cell 2: CV = 0.40) and a slight synapse size-(PSD-95 intensity) dependence, like that obtained with SDS-FRL (compare Figure 5J with Figure 6E). Because the orientation of the functionally characterized synapses related to the sectioning plane is random, i.e. is not always perpendicular or vertical, we repeated these experiments using 70 nm section thickness and performed full 3D reconstruction of the synapses from serial sections (Figure 6-figure supplement 1). As can be seen in the superimposed STED images in  Pulido and Marty, 2017). In the present study, we examined the connections between hippocampal CA1 PCs and FSINs in adult mice and revealed large variability in uEPSC amplitudes (from 3 to 500 pA, CV = 1) evoked by single PC APs. This large amplitude variability is also present in dendritically unfiltered EPSCs and for both morphologically defined basket and bistratified cells. Quantal analysis demonstrated that variability in N has the largest contribution to the variance in uEPSC amplitudes, which is the consequence of an approximately equal variability in the number of synapses per connection (2.3 ± 1.6, CV = 0.68, from 1 to 7) and the N / AZ (4.9 ± 3.7, CV = 0.75, from 1 to 17). PC to FS basket cell synaptic connections are mediated by a remarkably similar number of synapses in human neocortex (mean = 3.3, range: 1-6; Molnar et al., 2016), cat visual cortex (mean = 3.4, range: 1-7; Buhl et al., 1997), rat neocortex (mean = 2.9, range 1-6; Molnar et al., 2016) and mouse hippocampus (mean = 2.3, range: 1-7; present study). It seems that it is not a unique feature of PC -FSIN connections, because a very similar number (mean = 2.8, range: 1-6) was found when CA1 PCs to oriens-lacunosum-moleculare (O-LM) IN connections were examined in juvenile rats . All data taken together demonstrate that multi-synapse connections between PCs and GABAergic local circuit INs is an evolutionary conserved feature of cortical networks. As mentioned above, currently it is unknown why PC to IN connections are mediated by multiple (~3) and variable number (1 -7) of synaptic contacts.

It is well known that synapses made by molecularly identical presynaptic nerve cells on molecularly identical postsynaptic cells can show large structural and functional variability (reviewed by
Unlike the number of synapses per connection, when the mean number of RS per AZ was compared, a much larger variability and a species-specific difference was found. Molnar et al. (2016) reported that the N /AZ was ~4-times larger in human (~6) compared to rat (1.6) cortical PC -FSIN connections. It is 4.9 for the same connection in adult mouse hippocampus, which is very similar to that found in mouse cultured hippocampal neurons (4.9 in Sakamoto et al., 2018 and4.2 in Ariel et al., 2013). The difference in N / AZ between human and rat was accompanied by a larger AZ size in human (0.077 µm 2 ), which is again similar to that obtained in our present study in adult mice (0.071 µm 2 ), indicating that both in human and mice a RS occupy (or need) approximately the same AZ area. The positive correlations between the docked vesicles and the AZ area (Molnar et al., 2016;Schikorski and Stevens, 1999) and between the N / AZ and the average PSD-95 immunoreactivity ( Figure 4C) are consistent with a model in which the N scales linearly with the AZ area and each independent RS is built up from the same number of molecules (Sakamoto et al., 2018). However, when not only the mean, but the variance in the available data is also considered, a more complex picture emerges. First, there is large variability in the number of docked vesicles in AZs with identical sizes ( Figure 3S in Molnar et al., 2016), which might reflect variability in RS density, but an incomplete docking site/RS occupancy cannot be excluded. Such incomplete RS occupancy cannot explain our data showing that AZs with the same amount of PSD-95 (same size) have an over 3-fold variability in N. Thus, it seems that variability in the docking site occupancy might not be the main source of variability, but the actual RS density seem to be variable. A similar large variability is present in the data of Sakamoto et al (Figure 3c in Sakamoto et al., 2018)  One consequence of the variable number of docked vesicles or RS density is that the inter RS distance varies substantially in AZs of identical sizes. One possible consequence of that is that the RSs might not function independently when they are close enough to "see" substantial amounts of Ca 2+ from the neighboring RSs. Our data, showing that the average Pv of the RSs does not depend on the N, together with that of Sakamoto et al (2018), demonstrating that Pv does not depend on the NRRP, strongly indicate that the average Pv does not depend on the size of AZ. A pervious study from our laboratory (Holderith et al., 2012) described that the probability with which release occurs at hippocampal synapses (PR) depends on the AZ size. We would like to stress that this probability (PR) is the function of both the Pv and N [PR = 1-(1-Pv) N ], therefore the synapse size-dependent increase in N fully explains our previous and current results.
What might be the consequence of the variable amounts of Munc13-1 in RSs? Munc13-1 is an evolutionally conserved presynaptic protein that is essential for docking and priming vesicles for release (Augustin et al., 1999;Betz et al., 2001;Brockmann et al., 2020;Imig et al., 2014;Jahn and Fasshauer, 2012;Ma et al., 2011;Varoqueaux et al., 2002) therefore it can be hypothesized that the amount of this molecule might have an effect on the docking site occupancy or the priming state of the vesicles. MPFA only allows the determination of Pv, a probability that depends on the probability of the RS being occupied (Pocc) and on the probability of a docked vesicle being released (Psucc; Neher, 2017). What could be the consequence of the variable amounts of Munc13-1? Two lines of evidence indicate that Pocc is high at neocortical/hippocampal glutamatergic synapses. As mentioned above, Sakamoto et al. (2018) came to this conclusion from the similar NRRP and N. Molnar et al (2016) examined the number of docked vesicles at cortical PC -FSIN synapses and determined N, and found rather similar values for both human and rat synapses, arguing for a Pocc of ~0.8 that is similar to that found at the Calyx of Held (Neher, 2010), but larger than at cerebellar IN synapses (Pulido et al., 2015). Thus it seems that variability in Pocc might not be in hippocampal synapses as well (Hanse and Gustafsson, 2001;Schluter et al., 2006). Whether such highand low-Pv vesicles are intermingled within individual AZs or are segregated to distinct AZs is unknown.
It is just as unknown whether the normally and superprimed vesicles need different amounts of Munc13-1 or not. It is noteworthy that the priming efficacy of Munc13-1 depends on its interaction with RIM and RIM binding protein (Brockmann et al., 2020) therefore predicting the functional consequence of the different amounts of Munc13-1 per RS might require the determination of these molecules in individual Munc13-1 clusters. A recent study using superresolution imaging of vesicle release from cultured hippocampal neurons provided strong evidence for the heterogeneity in Pv among RSs within individual AZs. Maschi and Klyachko (2020) demonstrated that the Pv of centrally located RSs is higher and participate more frequently in multivesicular release (MVR) than those that are located at the periphery of the AZs. These data taken together indicate substantial variability in Pv among RSs, which is more likely to be the consequence of variable Psucc, the relationship of which to the amounts of Munc13-1 molecules remains to be seen.
Our results are also compatible with the concept that individual cortical synapses release more than a single vesicle from an AZ upon the arrival of a single AP (called MVR; Biro et al., 2006;Christie and Jahr, 2006;Maschi and Klyachko, 2020;Pulido et al., 2015;Rudolph et al., 2015;Wadiche and Jahr, 2001). The occurrence of MVR is the function of N / AZ and Pv. All available data indicate that cortical/hippocampal excitatory and inhibitory synaptic AZs contain multiple RSs, the number of which positively correlates with the size of the AZ, fulfilling one essential requirement of MVR. The average Pv, however, is much more heterogeneous. The most compelling evidence for variable Pv in distinct boutons is the postsynaptic target cell type-dependent variability in Pv and short-term plasticity (Eltes et al., 2017;Koester and Johnston, 2005;Losonczy et al., 2002;Pouille and Scanziani, 2004;Reyes et al., 1998;Rozov et al., 2001;Scanziani et al., 1998;Thomson, 1997). A previous study from our laboratory demonstrated that Pv at hippocampal CA1 PC to O-LM cell synapses is so low that the occurrence of MVR is negligible 13 under physiological conditions . However, the Pv at PC -FSIN synapses is almost an order of magnitude higher (~0.4) than that at PC -O-LM synapses and given an average of five RSs per AZ, the probability of MVR is around 70%. We would emphasize that Pv at CA3 to CA1 PC synapses is probably in between these values, indicating that the occurrence of MVR is much less prominent. The degree of postsynaptic receptor occupancy is a key issue when the functional consequence of MVR is considered. If the occupancy is high (e.g. cerebellar climbing fiber to Purkinje cell synapses; Harrison and Jahr, 2003 or at cerebellar molecular layer IN synapses, Auger et al., 1998;Nusser et al., 1997) the effect of simultaneously released multiple vesicles is negligible and the rational of such release mode is debated.
However, more and more evidence indicate that receptor occupancy is relatively low at most central     Data are from n = 18 synapses from 11 pairs from 10 mice. rs, Spearman's rank correlation coefficient, note that linear fits are not part of the correlation analysis.

Animals
Animals were housed in the vivarium of the Institute of Experimental Medicine in a normal 12 h/12 h light/dark cycle and had access to water and food ad libitum. All the experiments were carried out according to the regulations of the Hungarian Act of Animal Care and Experimentation 40/2013 (II.14) and were reviewed and approved by the Animal Committee of the Institute of Experimental Medicine, Budapest.
To quantify the Munc13-1 densities in the AZs of axon terminals targeting Kv3.1b+ dendrites and somata, all experiments were performed using the "mirror replica method" (Eltes et al., 2017;Hagiwara et al., 2005). With this method, replicas are generated from both matching sides of the fractured tissue surface, allowing the examination of the corresponding E-and P-faces of the same membranes. The AZs were delineated on the P-face based on the underlying high density of intramembrane particles.
Analysis of the distribution of Munc13-1 protein within the AZs We used a Python-based open-source software with a graphical user interface, GoldExt (Szoboszlay et al., 2017) to analyze gold particle distributions. Coordinates of the immunogold particles and corresponding AZ perimeters were extracted from EM images. Spatial organization of immunogold particles in presynaptic AZs was analyzed on the population of AZs using mean nearest neighbor distance (NND) and a Ripley analysis (Rebola et al., 2019;Ripley, 1979). For the NND analysis, we calculated the mean of the NNDs of all gold particles within an AZ and that of random distributed gold particles within the same AZ (same number of gold particles, 200 repetitions). The NNDs were then compared statistically using the Wilcoxon signed-rank test. We used a variance stabilized and boundary corrected version of the Ripley's K function, called H-function (Hr) to examine whether particle distributions within individual AZs are clustered or dispersed over a range of spatial scales according to Rebola et al. (2019). To determine the number of clusters in Munc13-1 labeled AZs we used the density-based clustering algorithm, DBSCAN (Ester et al., 1996). DBSCAN requires two user-defined parameters: ε (nm), which is the maximum distance between two localization points to be assigned to the same cluster, and MinPts, the minimum number of points within a single cluster. We systematically changed the ε value from 1 to 100 nm and found the largest difference between the data and the random distributions at ε = 31 nm (Matlab code was kindly provided by Maria Reva). We then determined the mean number of clusters (Nc = 5.4 ± 2.5) with this ε value and a MinPts of 2. We then tested the effects of changing ε and MinPts on Nc (ε = 21, NminP = 2, Nc = 5.7 ± 2.7; ε = 41, MinPts = 2, Nc = 4.0 ± 1.8; ε = 31, MinPts = 3, Nc = 3.8 ± 1.8) and found that changing these parameters within plausible values results in a moderate change Nc.