Bassoon and the synaptic ribbon organize Ca2+ channels and vesicles to add release sites and promote refilling

doi:10.1016/j.neuron.2010.10.027

Neuron. Author manuscript; available in PMC 2011 November 18.

Published in final edited form as:

Neuron. 2010 November 18; 68(4): 724–738.

doi: 10.1016/j.neuron.2010.10.027

PMCID: PMC3005353

NIHMSID: NIHMS249817

Bassoon and the synaptic ribbon organize Ca²⁺ channels and vesicles to add release sites and promote refilling

T. Frank,^1,^2,³ M.A. Rutherford,¹^# N. Strenzke,^4,⁵^# A. Neef,³^# T. Pangršič,¹ D. Khimich,¹ A. Fetjova,⁶ E.D. Gundelfinger,⁶ M.C. Liberman,⁵ B. Harke,⁷ K.E. Bryan,⁸ A. Lee,⁸ A. Egner,⁷ D. Riedel,⁹^* and T. Moser^1,^2,³^*

¹ InnerEarLab, Department of Otolaryngology and Center for Molecular Physiology of the Brain, University of Göttingen Medical Center, 37099 Göttingen, Germany

² International Max Planck Research School for Neurosciences, Göttingen Graduate School for Neurosciences and Molecular Biosciences, 37077 Göttingen, Germany

³ Bernstein Center for Computational Neuroscience, 37073 Göttingen, Germany

⁴ Auditory Systems Physiology Group, Department of Otolaryngology and Center for Molecular Physiology of the Brain, University of Göttingen Medical Center, 37099 Göttingen, Germany

⁵ Eaton Peabody Laboratory, Massachusetts Eye and Ear Infirmary, Boston, MA 02114, USA

⁶ Department of Neurochemistry and Molecular Biology, Leibniz Institute for Neurobiology, 39118 Magdeburg, Germany

⁷ Department of Nanobiophotonics, Max Planck Institute for Biophysical Chemistry, 37077 Göttingen, Germany

⁸ Department of Molecular Physiology and Biophysics, University of Iowa, Iowa City, IA 52242

⁹ Laboratory of Electron Microscopy, Max Planck Institute for Biophysical Chemistry, 37077 Göttingen, Germany

^* Correspondence should be addressed to: Dr. T. Moser, InnerEarLab, Department of Otolaryngology and Center for Molecular Physiology of the Brain, University of Göttingen Medical Center, 37099 Göttingen, Germany, Tel.: +49-551-3922803, Email: tmoser/at/gwdg.de or, Dr. D. Riedel, Laboratory of Electron Microscopy, Max Planck Institute for Biophysical Chemistry, 37077 Göttingen, Germany, Tel.: +49-551-2011913, Email: driedel/at/gwdg.de

^#These authors contributed equally to the work

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Summary

At the presynaptic active zone, Ca²⁺ influx triggers fusion of synaptic vesicles. It is not well understood how Ca²⁺-channel clustering and synaptic vesicle docking are organized. Here we studied structure and function of hair cell ribbon synapses following genetic disruption of the presynaptic scaffold protein Bassoon. Mutant synapses - mostly lacking the ribbon - showed a reduction in membrane-proximal vesicles, with ribbonless synapses affected more than ribbon-occupied synapses. Ca²⁺-channels were also fewer at mutant synapses and appeared in abnormally shaped clusters. Ribbon absence reduced Ca²⁺-channel numbers at mutant and wild-type synapses. Fast and sustained exocytosis were reduced notwithstanding normal coupling of the remaining Ca²⁺-channels to exocytosis. In-vitro recordings revealed a slight impairment of vesicle replenishment. Mechanistic modeling of the in-vivo data independently supported morphological and functional in-vitro findings. We conclude that Bassoon and the ribbon (1) create a large number of release sites by organizing Ca²⁺-channels and vesicles, and (2) promote vesicle replenishment.

Introduction

Sensory encoding in the auditory and visual system of vertebrates relies on transformation of graded receptor potentials into rates of neurotransmitter release at ribbon synapses. The synaptic ribbon, an electron-dense structure anchored at the active zone, tethers a halo of synaptic vesicles (Glowatzki et al., 2008; Nouvian et al., 2006; Sterling and Matthews, 2005). Aside from its major component RIBEYE/CtBP2 (Khimich et al., 2005; Schmitz et al., 2000; Zenisek et al., 2004) the ribbon also contains scaffold proteins such as Bassoon and Piccolo (Dick et al., 2001; Khimich et al., 2005; tom Dieck et al., 2005). Genetic disruption of Bassoon perturbs the anchoring of ribbons to the active zones (AZs) of photoreceptors (Dick et al., 2003) and cochlear inner hair cells (IHCs) (Khimich et al., 2005). At the IHC synapse, where the functional effects of Bassoon disruption and ribbon loss are best studied, fast exocytosis is reduced (Khimich et al., 2005) and sound encoding by the postsynaptic spiral ganglion neurons impaired (Buran et al.). Moreover, IHCs of these Bassoon mouse mutants (Bsn^ΔEx4/5) show smaller Ca²⁺ currents. However, matching Ca²⁺ currents by reducing the driving force for Ca²⁺ in wild-type IHCs does not equalize fast exocytosis between wild-type and mutant IHCs. This, together with an unaltered rate constant of fast exocytosis in mutant IHCs – indicating a normal vesicular release probability – led to the previous hypothesis, that the defect primarily reflects a reduction of the readily releasable pool of vesicles (RRP) due to the loss of the ribbon (Khimich et al., 2005).

However, the exact structural and functional correlates of the RRP reduction remained unclear. For example, potential differences between mutant AZs that still have a ribbon (ribbon-occupied) and their ribbonless counterparts have not yet been investigated. Moreover, it is not known to which degree and by which mechanism Ca²⁺ influx is affected at the level of individual synapses and how this might contribute the exocytic deficit. Several mechanisms may explain the impairment of fast exocytosis in IHCs of Bsn^ΔEx4/5 mutants. First, mutant AZs may contain fewer vesicular docking sites and/or closely co-localized Ca²⁺ channels. Together, they have been suggested to constitute the numerous release sites of the IHC AZ at which vesicle fusion is controlled by the Ca²⁺ nanodomain of one or few nearby active Ca²⁺ channels (Brandt et al., 2005; Moser et al., 2006; Goutman and Glowatzki, 2007). Vesicles docked and primed in these “slots” probably constitute the RRP, of which the released fraction but not the release kinetics depends on the number of slots recruited by a given stimulus (Brandt et al., 2005; Furukawa and Matsuura, 1978; Wittig and Parsons, 2008). Therefore, fewer release sites, due to fewer Ca²⁺ channels (Neef et al., 2009) and/or fewer docking sites, could explain impaired fast exocytosis as a deficit of RRP size. Second, even if the number of release sites was unchanged, the standing RRP would be diminished if vesicle occupancy at each of these sites was reduced in Bsn^ΔEx4/5 IHCs, e.g. due to impaired replenishment or enhanced undocking of vesicles. Third, the coupling between Ca²⁺ influx and Ca²⁺ sensors of the exocytosis machinery could be altered, such that not all vesicles can contribute to fast exocytosis, even after proper docking and biochemical priming. This point subsumes changes in diffusion, buffering or homeostasis of [Ca²⁺]_i, as well as an increased distance between channels and Ca²⁺-sensors (“positional priming”, (Neher and Sakaba, 2008) as it was reported at the Drosophila neuromuscular junction after disruption of the presynaptic scaffold protein Bruchpilot (Kittel et al., 2006). Finally, the intrinsic Ca²⁺ sensitivity of exocytosis could be altered.

The availability of a number of novel techniques such as improved stimulated emission depletion (STED) microscopy and fast confocal imaging of Ca²⁺ influx, as well as of a new Bassoon-deficient mouse line (Bsn^gt) now allowed us to address these questions. Here we used in vitro and in vivo physiology in combination with light and electron microscopy and computational modeling to study in detail structural and functional effects of Bassoon disruption, at both ribbon-occupied and ribbonless AZs. Our results indicate that both functional inactivation of Bassoon and ribbon loss reduce the number of synaptic Ca²⁺ channels. Membrane-tethering of vesicles was improved but not fully normal at ribbon-occupied mutant AZs suggesting a partial function of these ribbons. Mutant IHCs showed a reduction in the number of release sites while maintaining an intact coupling of Ca²⁺ influx to exocytosis. Vesicle replenishment was slightly impaired in in-vitro experiments. We conclude that the multiprotein complex of the synaptic ribbon and Bassoon organize Ca²⁺ channels and synaptic vesicles at the AZ, thereby creating a large number of release sites.

Results

The most prominent morphological phenotype of IHCs associated with the disruption of Bassoon function in mouse mutants with partial gene deletion (Bsn^ΔEx4/5) is the loss of synaptic ribbons from their AZs (Buran et al., 2010; Khimich et al., 2005). In IHCs of immunolabeled whole-mounted organs of Corti from 3-week-old mice, we used confocal microscopy to count ribbon synapses as juxtaposed spots of presynaptic CtBP2/RIBEYE (labeling ribbons) and postsynaptic GluR2/3 (labeling glutamate receptor clusters). Per IHC in Bsn^ΔEx4/5 we found on average 2.5 ribbon-occupied synapses (22 % of 1240 synapses, N = 112 IHCs) instead of 11.9 ribbon-occupied synapses in Bsn^wt (97 % of 1028 synapses, N = 84 IHCs). Consistent with observations at retinal photoreceptor ribbon synapses (Dick et al., 2003), we detected expression of the N-terminal Bassoon fragment in IHCs of Bsn^ΔEx4/5 mice (Fig. S1A) but found that it was not localized to afferent IHC synapses, arguing against a residual function at the AZ. This observation and the absence of an auditory deficit in 8-week old heterozygous Bsn^ΔEx4/5 mice (data not shown) do not support the idea of a dominant negative effect of the N-terminal Bassoon fragment. We also observed fewer ribbon-occupied synapses in IHCs of the newly generated Bassoon-deficient mouse line Bsn^gt (4.8 vs. 9.6 ribbon-occupied synapses per IHC in wild-type) which, like Bsn^ΔEx4/5 mice, showed a mild hearing impairment (threshold increase by 23 dB for click stimuli in 4 Bsn^gt mice compared to 3 wild-type littermates vs. 37 dB increase in Bsn^ΔEx4/5 (Pauli-Magnus et al., 2007)). A weak Bassoon immunolabeling was observed at a small subset (approximately 10%) of synapses in Bsn^gt IHCs (Fig. S1B), potentially explaining the higher number of ribbon-occupied AZs in Bsn^gt IHCs.

Reduction of membrane-proximal vesicles at hair cell synapses of Bassoon mutants

We studied effects of Bassoon disruption and ribbon loss on synaptic ultrastructure in electron micrographs of 80 nm sections (Fig. 1A-B). Membrane-proximal vesicles at apparently ribbonless Bsn^ΔEx4/5 AZs showed an altered distribution. When measuring their lateral position relative to the presynaptically projected center of the postsynaptic density, we observed a broad and seemingly random distribution of those vesicles at the AZ (Fig. 1C, gray bars). In contrast, membrane-proximal vesicles at AZs of Bsn^wt IHCs fell into two categories: ribbon-associated (red open bars) and non-ribbon-associated (black open bars). The latter population was indistinguishable from membrane-proximal vesicles at ribbonless Bsn^ΔEx4/5 AZs (p = 0.27, Kolmogorov-Smirnov test). We then counted the total number of those vesicles in single 80 nm sections, and observed significantly fewer vesicles at apparently ribbonless (1.5 ± 0.2 vesicles, 53 AZs) and ribbon-occupied Bsn^ΔEx4/5 synapses (2.0 ± 0.4 vesicles/AZ section; 10 AZs) than at ribbon-occupied Bsn^wt synapses (4.2 ± 0.4 vesicles/AZ section; 26 AZs; p < 0.01 for both comparisons).

Figure 1

Synaptic ultrastructure and vesicle distribution in the presence and absence of the synaptic ribbon

Because the absence of a synaptic ribbon cannot unequivocally be concluded from not seeing a ribbon in a single 80 nm synaptic section, we used EM tomography to address potential differences between ribbon-occupied and ribbonless AZs in Bsn mutant mice (Fig. 1E-H). We used Bsn^gt mice for these experiments due to their larger fraction of ribbon-occupied AZs. In electron tomography, we counted vesicles that were tethered to the plasma membrane by filamentous linkers (see Fig. 1D for examples; Fernandez-Busnadiego et al., 2010). Indeed, we found a trend towards more membrane-tethered vesicles when a ribbon was present (6.4 ± 0.8, n = 10 vs. 3.7 ± 1.1, n = 6 at ribbonless Bsn^gt AZs, p = 0.1), likely reflecting the addition of a ribbon-associated vesicle population. As in the analysis of 80 nm sections of Bsn^ΔEx4/5 AZs, vesicle numbers at ribbon-occupied Bsn^gt AZs did not reach Bsn^wt levels (10.6 ± 0.7, n = 5, p < 0.01). We also observed that, unlike at Bsn^wt synapses, ribbons of Bsn^gt tended to be farther away from the plasma membrane (Fig. 1I). In fact, we found a spectrum of ribbon-anchorage phenotypes: from wild-type like proximity to loosely anchored ribbons (often accompanied by a second detached ribbon) to complete ribbon absence. It is tempting to speculate that loosely anchored ribbons may not fully promote membrane-tethering of vesicles. We note that even in the 250 nm tissue sections that were used for tomography, the reported vesicle numbers represent underestimates of the full complement of membrane-proximal vesicles because synapses were not completely included along one dimension. However, this error equally affected each synapse type, and tomograms fully contained the synapse in the other two dimensions. Noteworthy, we found that the electron-dense material lining the presynaptic plasma membrane (presynaptic density) was longer and thicker at ribbon-occupied Bsn^wt AZs than the spot-like presynaptic densities at Bsn^gt AZs (regardless of ribbon presence; Fig. 1E2-H2, Table S1), which sometimes harbored more than one density (Fig. 1F2, H2).

Finally, we also studied AZs in IHCs of mouse mutants which contain fewer Ca²⁺ channels due a lack of the β₂ subunit (Ca_Vβ₂, Neef et al., 2009). Ca_Vβ₂-deficient IHCs display a 70% reduction of both Ca²⁺ influx and RRP exocytosis despite the presence of synaptic ribbons. Number (Fig. 1J, data from wild-type littermates of Bsn^ΔEx4/5 and Ca_Vβ₂ mutants were pooled) and distribution (data not shown) of membrane-proximal vesicles were unaltered in 80 nm sections, suggesting that proteins of the macromolecular ribbon complex, but not Ca²⁺-channels, are required for the formation of vesicle docking sites.

Fewer Ca²⁺ channels and altered shape of Ca²⁺ channel clusters

Voltage-gated Ca²⁺ influx is decreased in IHCs of Bsn mutants (Bsn^ΔEx4/5; Khimich et al., 2005). Here we explored changes of synaptic Ca²⁺ signaling by morphological and functional imaging. First, we studied synaptic Ca²⁺ channel clusters by confocal and stimulated emission depletion (STED) microscopy following immunolabeling of Ca_V1.3 Ca²⁺ channels. Images of Bsn^ΔEx4/5 and Bsn^wt organs of Corti that had been processed for immunohistochemistry in parallel and following the same protocol were acquired with identical microscope settings and analyzed for intensity and shape of Ca_V1.3 immunofluorescent spots (Fig. 2). We estimated the short and long axes of the elliptic fluorescent objects by fitting two-dimensional Gaussian functions to the background-subtracted images (see Supplemental Experimental Procedures). The fluorescence integral within this region served as a proxy of the abundance of synaptic Ca²⁺ channels. In Bsn^wt organs of Corti the synaptic location of Ca_V1.3 clusters (Fig. 2A) was readily confirmed by the co-localization with synaptic ribbons (Brandt et al., 2005; Meyer et al., 2009) and Bassoon (Fig. S1B). In addition, some lower intensity spot-like immunofluorescence was present in IHCs (Fig. 2). In Bsn^ΔEx4/5 and Bsn^wt IHCs the synaptic localization of Ca²⁺ channel clusters was identified by co-staining for postsynaptic glutamate receptors (GluR2; Fig. S1C). This confirmed that Ca²⁺ channels remained clustered at synapses despite both the disruption of Bassoon and, in most cases, absence of the ribbon. In comparison to Bsn^wt, the immunofluorescence of Ca_V1.3 clusters colocalized with GluR2 was reduced at Bsn^ΔEx4/5 synapses (Figs. 2B, S1D).

Figure 2

Decreased immunofluorescence and altered shape of Ca_V1.3 clusters

In experiments co-labeling for Ca_V1.3 and the synaptic ribbon marker RIBEYE/CtBP2 we were able to separate ribbon-occupied AZs from ribbonless AZs in Bsn^ΔEx4/5 and Bsn^wt mice. Because of the absence of an additional synaptic marker at ribbonless Bsn^ΔEx4/5 AZs, and to exclude non-synaptic Ca_V1.3 immunofluorescent spots from analysis, we considered only the ten brightest spots in each cell for both genotypes. This approach was justified by knowledge of cochlear location (10 synapses per cell in apical turn; Meyer et al., 2009) and the observation that 92.2% and 89.4% of the 10-brightest Ca²⁺ channel clusters were juxtaposed to GluR2 immunofluorescent spots in Bsn^ΔEx4/5 and Bsn^wt IHCs, respectively. In confocal images, Ca_V1.3 immunofluorescence was reduced by 42% at Bsn^ΔEx4/5 AZs (Fig. 2B, p < 1e-20). As quantified in Figure 2B-C and Table 1, the Ca_V1.3 immunofluorescence decreased in the order: ribbon-occupied Bsn^wt > ribbonless Bsn^wt > ribbon-occupied Bsn^ΔEx4/5 > ribbonless Bsn^ΔEx4/5. Ca_V1.3 channel clusters of ribbon-occupied Bsn^ΔEx4/5 AZs were also more similar to Bsn^wt AZs in shape than those of ribbonless Bsn^ΔEx4/5 AZs. The altered shape of the latter was evident in a smaller long-to-short axis ratio (standard STED, Fig. 2D-E and Table 1).

Table 1

Summary of IHC physiology in Bsn wild-type and mutant mice

To resolve a potential substructure within Ca_V1.3 clusters, we used a custom-built STED microscope (STED*; lateral point spread function (PSF) less than 100 nm at a tissue depth of 15 to 25 μm, yellow range in Fig. 2E). Ca²⁺ channel clusters of Bsn^wt AZs typically displayed one to three stripes of Ca_V1.3 immunofluorescence (Fig. 2F). Parallel confocal observation of the associated CtBP2/RIBEYE immunofluorescence suggested that these synapses featured one ribbon regardless of the number of stripes, although two closely-spaced ribbons may fall within the confocal PSF and thus may not be resolved as individual ribbons. In contrast, Bsn^ΔEx4/5 AZs showed Ca_V1.3 immunofluorescence spots rather than stripes (Fig. 2F, full width at half maximum of long and short axes: 120 ± 7.9 nm and 95 ± 5.5 nm, n = 13) with ribbon-occupied AZs typically harboring more spots than ribbonless AZs. Ca_V1.3 immunofluorescent stripes and spots were reminiscent of the patterns of presynaptic density observed in electron tomography (Fig. 1E2-H2). In summary, the abundance of synaptic Ca²⁺ channels and the cluster shape are altered upon Bassoon disruption, which might reflect the loss of a direct Bassoon action on Ca²⁺ channel clustering or of the Bassoon-mediated ribbon anchorage. To test for a potential role of Bassoon in the direct synaptic anchoring of Ca²⁺ channels, we determined if Bassoon and the Ca_V1.3 channel interacted in a heterologous expression system. We did not find evidence that Bassoon coimmunoprecipitated or co-localized with Ca_v1.3 in transfected HEK293T cells (Fig. S4). Therefore, the role of Bassoon in recruiting Ca²⁺ channels to the AZ may not involve a direct association of the two proteins.

Reduced synaptic Ca²⁺ influx results from fewer channels and lower open probability

To study synaptic Ca²⁺ influx in Bsn^ΔEx4/5 IHCs we performed whole-cell patch-clamp recordings of Ca²⁺ current (I_Ca) and confocal imaging of presynaptic Ca²⁺ microdomains (Frank et al., 2009). We found a reduction of peak whole-cell I_Ca amplitude in Bsn^ΔEx4/5 IHCs of 3-week-old mice (Fig. 3, Table 1, Fig. S2, Table S1). It ranged between 62% (ruptured-patch, 5 mM [Ca²⁺]_e; Fig. 3A, Table 1) and 69% (perforated–patch, 10 mM [Ca²⁺]_e; Fig. S2, Table S1) of Bsn^wt amplitude. The difference from Bsn^wt was alleviated in the presence of the dihydropyridine agonist BayK8644 (77%, ruptured-patch, 10 mM [Ca²⁺]_e; Fig. 3B, Table 1), suggesting that Ca²⁺ channel open probability is reduced in Bsn^ΔEx4/5 IHCs in the absence of BayK8644. Moreover, we found that Ca²⁺ current activation was slowed in Bsn^ΔEx4/5 IHCs (Figs. 3C, S2), while it was indistinguishable from wild-type IHCs in the presence of BayK8644 (Fig. 3D). Finally, Ca²⁺ currents in Bsn^ΔEx4/5 IHCs inactivated slightly more (Fig. 3E; Table S1).

Figure 3

Biophysical properties of voltage-dependent whole-cell Ca²⁺ current (I_Ca)

To test whether the observed reduction in I_Ca was caused by changes in channel number (N_Ca), unitary current (i_Ca), or open probability (p_open), we performed a non-stationary fluctuation analysis on Ca²⁺ tail-currents ([BayK8644]_e = 5 μM; Brandt et al., 2005). In line with the observed reduction in I_Ca amplitude, both variance and mean were reduced in Bsn^ΔEx4/5 IHCs (Figs. 3F, G). The analysis indicated a ≈20% decrease in the number of functional Ca²⁺ channels, but statistically indistinguishable single channel currents and maximal open probabilities in the presence of BayK8644 (Tables 1, S1). We note that due to uncertainties associated with the channel property estimates from fluctuation analysis (Tables 1, S1), which also deviate from those obtained from single channel recordings in immature IHCs (Zampini et al., 2010), emphasis is on comparison between the genotypes rather than on absolute values (see also Supplemental Experimental Procedures).

Synaptic Ca²⁺ microdomains, primarily reflecting Ca²⁺ influx at the AZ (Frank et al., 2009), were visualized using the low affinity Ca²⁺ indicator Fluo-5N (400 μM, K_d = 95 μM) in conjunction with the slow Ca²⁺ chelator EGTA (2 mM). The Ca²⁺ microdomain amplitude (ΔF) measured under these conditions likely reflects a linear summation of the Ca²⁺ influx contributed by the individual synaptic Ca²⁺ channels (Frank et al., 2009). Consistent with the finding of Ca_V1.3 channel clusters in immunohistochemistry, we readily observed Ca²⁺ microdomains also in Bsn^ΔEx4/5 IHCs (Fig. 4A). However, their average amplitude (ΔF_avg; Table 1), measured at −7mV in spot-detection experiments at the center of the Ca²⁺ microdomains, was reduced to 36% of control (Fig. 4B, C), exceeding the reduction of whole-cell I_Ca (to 60–70%, Fig. 3) and Ca_V1.3 immunofluorescence (to 58%, Fig. 2). Augmenting influx through Ca_V1.3 Ca²⁺ channels (5 μM BayK8644) alleviated the amplitude reduction of synaptic Ca²⁺ influx in Bsn^ΔEx4/5 IHCs (to 52% of control; Fig. 4D, Table 1) and increased amplitude variability among the Bsn^ΔEx4/5, but not the Bsn^wt synapses (Figs. 4E, F). Kinetics (Figs. 4C, D, S3, Table S1), voltage dependence (Figs. 4G, S3, Table S1), and spatial extent (Fig. 4H, Table S1) of the Ca²⁺ microdomains in Bsn^ΔEx4/5 IHCs were similar to control. There was however, a tendency towards faster kinetics and more negative activation of Bsn^ΔEx4/5 Ca²⁺ microdomains (Table S1). While the former may reflect differences in Ca²⁺ buffering and/or diffusion, the latter may indicate an altered gating of synaptic Ca²⁺ channels in the absence of Bassoon and/or the ribbon.

Figure 4

Reduced presynaptic Ca²⁺ influx

In a second set of experiments we studied Ca²⁺ signaling at ribbonless and ribbon-occupied AZs in separation using a fluorescent RIBEYE-binding peptide to identify ribbon-occupied AZs (Frank et al., 2009, Zenisek et al., 2004) in both Bsn^ΔEx4/5 and Bsn^wt IHCs. While Ca²⁺ microdomains at ribbon-occupied AZs had larger amplitudes than ribbonless synapses in Bsn^wt IHCs, there was no significant difference between ribbonless and ribbon-occupied AZs in Bsn^ΔEx4/5 IHCs (Fig. 4I). The latter finding was unexpected given their difference in Ca_V1.3 immunofluorescence, but could reflect limited sensitivity of functional Ca²⁺ imaging, precluding detection of very dim Ca²⁺ signals at Bsn^ΔEx4/5 ribbonless synapses. In summary, the reduced amplitude of Ca²⁺ microdomains and its partial alleviation upon the BayK8644-mediated increase in open probability led us to conclude that Bsn^ΔEx4/5 synapses contain fewer Ca²⁺ channels with a lower open probability. The reduction of synaptic Ca²⁺ influx beyond the decrease observed in whole-cell I_Ca indicates a higher proportion of extrasynaptic channels in Bsn^ΔEx4/5 IHCs.

Reduced RRP and sustained exocytosis, but intact Ca²⁺ influx – exocytosis coupling

How does the reduction of Ca²⁺ channels and membrane-proximal vesicles – as well as a potential mislocalization of these two elements – affect hair cell exocytosis? We addressed this question in Bsn^ΔEx4/5 IHCs by measuring exocytic membrane capacitance changes (ΔC_m) in response to short (20 ms, ΔC_{m, 20 ms}) and longer (100 ms, ΔC_{m, 100 ms}) depolarizations to the maximum Ca²⁺ current potential in native buffering conditions (perforated-patch configuration, Fig. 5). Based on previous work (Goutman and Glowatzki, 2007; Li et al., 2009; Meyer et al., 2009; Neef et al., 2009; Rutherford and Roberts, 2006; Schnee et al., 2005), we interpret ΔC_{m, 20 ms} as fast (synchronous) exocytosis, representing release of a standing RRP, and the difference between ΔC_{m, 100 ms} and ΔC_{m, 20 ms} as sustained exocytosis, reflecting vesicle supply to the RRP and subsequent fusion. In this set of experiments, ΔC_{m, 20 ms} was reduced to 60% (Fig. 5A, Table 1) and sustained exocytosis to 56% (Fig. 5B, Table 1). These results are consistent with a model in which RRP size and sustained exocytosis rate are related to the number of physical docking/release sites at the AZ (reduction of membrane-proximal vesicles: ~50%, Fig. 1J). To test whether the intrinsic Ca²⁺ dependence of exocytosis differed between genotypes, we used flash photolysis of caged Ca²⁺, but found comparable time constants of the fast component of the ΔC_{m, flash} for elevations of [Ca²⁺]_i to 25–37 μM (Bsn^ΔEx4/5: 2.4 ± 0.4 ms, mean post-flash [Ca²⁺]_i: 29.0 ± 1.9 μM, N = 6 vs. Bsn^wt: 2.6 ± 1.1 ms, mean post-flash [Ca²⁺]_i: 31.5 ± 2.5, N = 4; Fig. 5C, Table S1) suggesting an unaltered biochemical Ca²⁺ sensitivity of exocytosis. Notably, despite the lack of ribbons from most synapses in Bsn^ΔEx4/5 IHCs the amplitude of their flash-evoked C_m rise was statistically indistinguishable from Bsn^wt.

Figure 5

Reduced exocytosis but normal Ca²⁺ influx-exocytosis coupling

The observation that the reduction of Ca²⁺-influx-triggered exocytosis did not exceed the reduction in the number of membrane-proximal and -tethered vesicles (Fig. 1) suggests that the remaining docking sites are equipped with nearby Ca²⁺ channels (reduction of synaptic Ca²⁺ channels: ≈ 50 %, Table 1; estimated from Bsn^ΔEx4/5 vs. Bsn^wt synaptic Ca²⁺ microdomain amplitude in the presence of BayK8644). Yet, a looser coupling between Ca²⁺ channels and vesicle docking sites than implied for the Ca²⁺ nanodomain regime suggested for wild-type IHC AZs could not be excluded (Brandt et al., 2005; Goutman and Glowatzki, 2007; Moser et al., 2006). Therefore, we studied the sensitivity of exocytosis to the slow Ca²⁺ chelator EGTA (Fig. 5F). Consistent with the preservation of nanodomain -controlled vesicle fusion in Bsn^ΔEx4/5 IHCs, their ΔC_{m, 20 ms} in the presence of 5 mM [EGTA]_i was reduced to 58% of control levels (Table 1) – closely resembling the reduction in the presence of endogenous Ca²⁺-buffers (see above). Additionally, we probed RRP exocytosis as a function of Ca²⁺ influx at different membrane potentials (Fig. 5D, E). Changing the membrane potential manipulates open probability and single channel current in opposite directions. Thus, exocytosis can be tested for the same absolute Ca²⁺ influx through either few open channels with high single channel current (mild depolarizations), or more open channels with low single channel current (strong depolarizations). If exocytosis of a given vesicle was under control of a population of several Ca²⁺ channels (Ca²⁺ microdomain control), exocytosis should be identical for the same Ca²⁺ current independent of the membrane potential. In case of a Ca²⁺ nanodomain control, more exocytosis is expected for more open Ca²⁺ channels, i.e. at more depolarized potentials (‘hysteresis’; Zucker and Fogelson, 1986). This was indeed observed in Bsn^wt IHCs (Figs. 5E1, S5), as described before (Brandt et al., 2005), but also in Bsn^ΔEx4/5 IHCs (Figs. 5E1, S5), further arguing that Ca²⁺ nanodomain control of exocytosis is maintained at mutant AZs. As a further consistency check, we scaled the exocytosis-Ca²⁺ current integral relationship of Bsn^ΔEx4/5 IHCs by experimentally derived factors to normalize the data to the lower number of membrane-proximal vesicles and synaptic Ca²⁺ channels. This resulted largely in an overlap with the wild-type data (Fig. 5E2). In summary, the data indicate that the coupling of Ca²⁺ channels to release sites remains intact despite Bassoon disruption, but that the rates of initial and sustained exocytosis are reduced to a similar extent as the number of membrane-proximal vesicles.

In vitro and in vivo analysis of synaptic vesicle replenishment

Traditionally, the synaptic ribbon has been assigned a “conveyor belt” and/or “attractor” function (Holt et al., 2004; Sterling and Matthews, 2005), according to which, it is responsible for rapid supply of vesicles to the RRP and enables high rates of tonic neurotransmitter release (Gomis et al., 1999; Johnson et al., 2008; Moser and Beutner, 2000; Rutherford and Roberts, 2006; Schnee et al., 2005; Spassova et al., 2004). Hence, we tested whether the rate of RRP refilling was reduced in the absence of the ribbon and functional Bassoon protein. Here, we explored vesicle replenishment in vitro by measuring relative ΔC_m in paired-pulse protocols, with the stimuli (20 ms or 100 ms long depolarizations) being separated by various time intervals (98, 198, and 398 ms; Fig. 6). The ratio of Ca²⁺ current integrals was close to one in both genotypes (marginally smaller in Bsn^ΔEx4/5 IHCs; Fig. 6C, D; Table S1) indicating that the Ca²⁺ signals that drive exocytosis were mostly comparable between both pulses. For 20 ms stimuli at short inter-pulse-intervals (IPI: 98 ms) we observed stronger depression of the exocytic response in Bsn^ΔEx4/5 IHCs, indicating a slower recovery of the RRP at Bsn^ΔEx4/5 synapses (p < 0.01). For longer recovery times (IPI: 198, 398 ms), the difference did not reach statistical significance. While both Bsn^wt and Bsn^ΔEx4/5 IHCs showed depression for short stimuli, Bsn^wt IHCs exhibited a tendency towards facilitation for long depolarizations (100 ms). In contrast, Bsn^ΔEx4/5 IHCs also showed depression when challenged with long stimuli (p < 0.01 for 98, 198, and 398 ms IPI).

Figure 6

Slowed vesicle replenishment kinetics

In vivo, we measured the recovery of the auditory nerve fiber response following a “masking” sound as a proxy of the recovery of the presynaptic RRP (Spassova et al., 2004). We used a forward masking paradigm (Harris and Dallos, 1979; Spassova et al., 2004) in which a 100 ms masking stimulus was separated from a 15 ms probe stimulus by a variable silent interval ranging between 2 and 512 ms (Fig. 7A). Onset spike rates and adapted spike rates in response to the masking stimulus were reduced by a factor of 1.7 and 1.4, respectively, in Bsn^ΔEx4/⁵ (poststimulus time histograms [PSTHs], Fig. 7B). We found an enhanced forward masking effect in Bsn^ΔEx4/⁵ fibers when comparing each probe response to its masker response (lower ratio of spike rates probe/masker [averaged over the first 5 ms of the probe and the masker] at 4–32 ms interval for mutants, p < 0.05 each). There was also a trend towards longer time of half-recovery from masking in Bsn^ΔEx4/⁵ (34.9 ± 5.0 ms in mutant and 23.3 ± 4.9 ms in wild-type, p = 0.13).

Figure 7

Comparison of sound-evoked spike rates in vivo for Bsn^wt and Bsn^ΔEx4/5 mice

Taken together, the in vitro and in vivo results suggest a disturbed replenishment of fusion-competent synaptic vesicles in Bsn^ΔEx4/⁵ IHCs. To what degree is the impaired sound coding phenotype in Bsn^ΔEx4/⁵ IHCs caused by a reduction in the number of release sites or by their deficient re-filling? To answer this question, we quantified the forward masking data by a novel model of sound-dependent RRP fusion and replenishment combined with auditory nerve fiber refractoriness. The core parameters of this model are the number of release sites, sound-dependent rates (fusion rate constants and refilling rate constants per release site in the presence and absence of sound), and absolute and relative refractory periods (Supplemental Experimental Procedures). As those parameters are biophysically accessible quantities, the model can be used for quantitative, mechanistic data analysis of auditory nerve fiber responses in the context of cellular physiology.

A single set of parameters accurately reproduced PSTHs for all 9 recovery periods (Figs. 7B and S6). The very same set of parameters also predicted the ratio of spike counts (probe/masker) for analysis windows of 5 ms and 13 ms following sound onset (Fig. 7C). Importantly, the dominating difference between the parameter sets for the two genotypes was a 35 % reduction in release site number for Bsn^ΔEx4/5 (i.e. the maximal capacity of the RRP; see dotted line in Fig. 7B for a simulation with wild-type release site number), while the fusion rates and vesicular release probability remained virtually unchanged (Table S2; consistent with capacitance measurements [Fig. 5]). Additionally, refilling rate constants were slightly reduced. When assuming wild-type vesicle replenishment kinetics for Bsn^ΔEx4/5 fibers – while keeping all other model parameters for this genotype – the adapted spike rates were accordingly slightly improved (see dashed line in Fig. 7B).

In summary, using the model as a quantification of the in-vivo results allowed us to draw conclusions about pre-synaptic quantities from post-synaptic measurements. Generally, the model validated our structural and functional findings, made independently in vitro. Additionally, it advanced our mechanistic understanding by permitting the discrimination between a reduction in the number of (1) generally available release sites and the reduction in the (2) occupancy of those release sites: the parameters suggest that the reduced response amplitude in Bsn^ΔEx4/5 fibers is primarily due to a reduction in the total number of release sites (35 %) and to a lesser degree caused by a reduction in their occupancy. These two effects combine such that in the model the number of release sites occupied at rest is reduced to 50% of wild-type, which is in agreement with the 55% reduction in number of membrane-proximal vesicles observed in electron micrographs of Bsn^ΔEx4/5 AZs (Fig. 1J).

Discussion

In this study, we examined effects of genetic Bassoon disruption at several structural and functional levels. EM tomography revealed a spectrum of synapse morphologies: from wild-type like, to loosely anchored ribbons, to ribbonless. Intriguingly, we found that Bsn mutant synapses with a partially anchored ribbon (ribbon-occupied) exhibited an intermediate phenotype between wild-type AZs and mutant ribbonless AZs. While fewest synaptic Ca²⁺ channels were found at ribbonless AZs in Bsn^ΔEx4/5 IHCs, the ribbon-occupied Bsn^ΔEx4/5 AZs harbored more, but still fewer Ca²⁺ channels than wild-type AZs – similar to the quantification of membrane-proximal vesicle number. Fast and sustained exocytosis was reduced in proportion to the overall reduction in membrane-proximal vesicle and Ca²⁺ channel number, while the Ca²⁺ sensitivity of exocytosis remained normal. Moreover, vesicle replenishment was impaired. A mechanistic computational model of synaptic transfer, used to fit the in vivo data, independently supported morphological and functional in-vitro findings. We conclude that Bassoon disruption and the associated ribbon loss reduces the number of functional release sites, impairs their refilling, and consequently lowers the RRP.

Structural consequences of Bassoon disruption and ribbon loss

The most prominent phenotype of Bassoon disruption is the loss of synaptic ribbons from a majority of AZs (Khimich et al., 2005; tom Dieck et al., 2005). In contrast to retinal photoreceptors (Specht et al., 2007), mature hair cells of Bsn mutants exhibited some (although few) ribbon-occupied synapses at typical locations (Figs. 1–2). Together with observations at Bsn^wt synapses without a ribbon, study of these ribbon-occupied mutant synapses helped to test the role of the synaptic ribbon. Both semi-quantitative immunofluorescence microscopy (Fig. 2B-C) and confocal imaging of synaptic Ca²⁺ influx (Fig. 4I1) revealed that ribbon presence was associated with an increase in the number of Ca²⁺ channels at Bsn^wt AZs. Using STED microscopy we furthermore observed a stripe-like arrangement of the Ca²⁺ channel cluster(s) at ribbon-occupied Bsn^wt AZs. These structures were reminiscent of the electron-dense material seen in electron tomograms of AZs in mouse IHCs (Fig. 1E2-H2) and frog saccular hair cells (Lenzi et al., 2002), and the row-like arrays of intra-membrane particles observed in freeze-fracture electron micrographs (Roberts et al., 1990; Saito and Hama, 1984). At all Bsn^ΔEx4/5 synapses, this Ca_V1.3 cluster geometry was dissolved into a pattern of small spots (Fig. 2F), similar to alterations of presynaptic densities seen in electron tomography (Fig. 1E2-G2). This coincidence supports the view that the Ca_V1.3 clusters are an integral part of the presynaptic density (Lenzi et al., 2002). While this difference in cluster geometry could, in principle, reflect a direct effect of Bassoon loss, we did not find evidence for direct interactions between Bassoon and Ca_V1.3 (heterologous expression; Fig. S4). The observation of spots rather than stripes at ribbon-occupied Bsn^ΔEx4/5 synapses might also reflect a decreased organizational impact of the ribbon when its anchorage is loosened. It is interesting to note that the CAST/ELKS1 homologue Bruchpilot has been implicated in clustering of presynaptic Ca²⁺ channels at the Drosophila neuromuscular junction (Kittel et al., 2006). Bruchpilot is an integral component of presynaptic electron-dense projections (T-bars, which were absent in Bruchpilot mutants) and physically interacts with presynaptic Ca²⁺ channels, at least in vitro (Fouquet et al., 2009).

Our finding of abnormal clustering of synaptic Ca²⁺ channels upon Bassoon disruption is supported by a comparison between the associated reduction in whole-cell (≈20 %) and synaptic Ca²⁺ influx (≈ 50 %; both in the presence of BayK8644). The stronger decrease in synaptic Ca²⁺ influx indicates an increased fraction of extrasynaptic Ca²⁺ channels in mutant IHCs. Similar to Ca²⁺ channels, the number of membrane-proximal vesicles appears to be greater when the ribbon is present. At least by trend, ribbonless mutant AZs showed the fewest vesicles, whereas the presence of a ribbon increased this figure, but not to wild-type levels.

Functional consequences of Bassoon disruption and ribbon loss

How do these findings relate to synaptic function? Specifically, how are the number of release sites – formed by vesicle docking sites and closely colocalized Ca²⁺ channels – and synaptic exocytosis affected by Bassoon disruption? First, when probing fast and sustained exocytosis in Bsn^ΔEx4/5 IHCs, we observed a decrease in amplitude that was roughly comparable to the observed reduction in vesicle number and synaptic Ca²⁺ channel number. Second, both intrinsic and apparent Ca²⁺ cooperativity of exocytosis was normal in Bsn^ΔEx4/5 IHCs. Together, these observations suggest that the coupling between Ca²⁺ influx through the remaining Ca²⁺ channels and the fusion of the remaining vesicles was unaffected. Yet, one faces the caveat that a static technique such as EM cannot distinguish between fewer physical docking sites or their lower occupancy due to impaired replenishment. Thus, distinguishing between these two scenarios is aided by probing vesicle re-supply, which was slightly impaired in Bsn^ΔEx4/5 mice (Fig. 6). This finding stands in agreement with the study of Hallermann and colleagues (Hallermann et al., 2010), which shows that vesicle reloading at a central synapse is impaired in Bsn mutants, evident by enhanced synaptic depression during sustained high-frequency trains. However, our study of a ribbon synapse revealed additional defects; fitting a mechanistic computational model to our in vivo data (Figs. 7, S6), indicated that synaptic transmission at the IHC synapse of Bsn^ΔEx4/5 was impaired primarily due to a reduced number of functional release sites (in accordance with our morphological and functional in vitro data) and, to a lesser extent, their slower refilling – under the given stimulus protocol (Fig. 7).

Towards disentangling the interplay between Bassoon and the synaptic ribbon

Bassoon, via interaction with RIBEYE (tom Dieck et al., 2005) contributes to ribbon anchorage. In hair cells some residual and partial ribbon anchorage is observed, probably involving additional anchoring proteins. Those “ribbon-occupied” Bsn mutant synapses were inferior to their wild-type counterparts with regard to both Ca²⁺ channel clustering and membrane-tethering of vesicles. These observations could either be explained by (1) a direct effect of functional Bassoon loss, or (2) by a limited capacity of sick ribbons to perform their task(s). Several recent studies at conventional synapses show that Bassoon is not required for synaptic transmission per se but is involved in clustering (Mukherjee et al., 2010) and replenishment of synaptic vesicles (Hallermann et al., 2010). Our results are generally consistent with these findings; however, ribbon synapses do require Bassoon also for basic synaptic transmission. It is likely that the more severe synaptic phenotype found in IHCs reflects the perturbation of ribbon-supported functions. For example, in contrast to (Hallermann et al., 2010) we do find a substantial reduction in the number of release sites in Bsn mutant IHCs. Additionally, the trend towards less membrane-tethered vesicles in general, but more vesicles at ribbon-occupied than ribbonless Bsn mutant synapses (while no evidence for a reduced quantal content in [Hallermann et al., 2010]) could, for example, be explained by a combinatorial effect of primary Bassoon loss and secondary Piccolo loss (Mukherjee et al., 2010) in the case of ribbonless synapses. However, the complex nature of interactions between the numerous members of the cytomatrix of the active zone (Schoch and Gundelfinger, 2006), demand careful evaluation of one-protein, one-function hypotheses. The absence of detectable direct effects of Bassoon disruption on basal synaptic transmission at conventional synapses (Hallermann et al., 2010; Mukherjee et al., 2010) and the intermediate phenotypes seen in ribbon-occupied mutant synapses might favor a hypothesis of sick ribbons over direct Bassoon effects underlying the majority of observed synaptic and auditory phenotypes in Bsn mutants. Future studies including silencing of ribbon components such as Piccolo and RIBEYE are required to further our understanding of the roles of the synaptic ribbon and Bassoon for active zone structure and function, and also their dynamic regulation.

Experimental Procedures

A more detailed version of the Experimental Procedures is published in Supplemental Information. Unless stated otherwise, all chemicals were obtained from Sigma-Aldrich.

Animals

Mice with deletion of exons 4/5 of the Bassoon gene (Bsn^ΔEx4/5; (Altrock et al., 2003) or carrying a gene-trapped allele (Bsn^gt, Lexicon Pharmaceuticals, Inc.), and wild-type littermates were used. All experiments were approved by the University of Göttingen Board for Animal Welfare and the Animal Welfare Office of the State of Lower Saxony.

Immunohistochemistry

Apical cochlear turns were fixed in methanol for 20 min. at −20°C and prepared as previously described (Khimich et al., 2005; Meyer et al., 2009). The following antibodies were used: mouse anti-CtBP2 (BD Biosciences), rabbit anti-GluR2/3 (Chemicon), rabbit anti-Ca_V1.3 (Alomone Labs), mouse anti-GluR2 (Chemicon), mouse anti-Sap7f407 to Bassoon (Abcam), rabbit anti-BSN1.6 to Bassoon (E.D. Gundelfinger).

Confocal and STED microscopy

Confocal image stacks were acquired with a Leica SP5 microscope and 100x oil immersion objective. For STED-imaging, two different microscopes were used: the Leica TCS STED (Fig. 2D-E), and a custom apparatus (Harke et al., 2008) with a resolution of around 80 nm. For size/shape analysis of Ca²⁺ channel clusters, XY scans were acquired after finding the fluorescence maximum with a XZ-scan.

Electron microscopy and Tomography

Cochleae were processed for electron microscopy as described (Meyer et al., 2009 and Pangrsic et al., 2010). Thin sections were examined using a Philips CM120 BioTwin transmission electron microscope (Philips Inc.) with a TemCam F224A camera (TVIPS) at 20,000x magnification. Images were subsequently analyzed using iTEM software (Olympus). Tilt series from 250 nm sections were recorded at 27,500x magnification in the range of 129°, then calculated using Etomo (http://bio3d.colorado.edu/).

Patch-clamp and confocal Ca²⁺ imaging of IHCs

IHCs from apical coils of freshly dissected organs of Corti (P20 through P31) were patch-clamped as described (Moser and Beutner, 2000) and fluctuation analysis (FA) was performed similarly as previously described (Meyer et al., 2009). Currents were low-pass filtered at 8.5 kHz or 5 kHz and sampled at 100 kHz (FA) or 40 kHz (Ca²⁺ currents, ΔC_m measurements), respectively. Cells with holding current > −50 pA were discarded. Ca²⁺ currents were further isolated using a P/n protocol. In FA and Ca²⁺ current activation recordings, series resistance was compensated online (20–50 %; τ= 10 μs). Residual series resistance averaged 4.4 ± 0.4 MΩ (wt; n = 35 ensembles) and 4.3 ± 0.3 MΩ (mut; n = 33 ensembles) in FA experiments. Flash photolysis was performed essentially as described in Beutner et al, 2001. Confocal Ca²⁺ imaging was performed as described (Frank et al., 2009).

Single unit recordings

Single unit recordings from auditory nerve fibers of 6–10 week old Bsn^wt and Bsn^ΔEx4/5 mice (N=7 each) were performed as described by (Taberner and Liberman, 2005) and (Buran et al., 2010).

Data analysis

Data analysis was performed using Matlab (Mathworks), Igor Pro (Wavemetrics), and ImageJ software and is described in more detail in supplemental information. Two-tailed t-tests or the Mann-Whitney-Wilcoxon test were used for statistical comparisons between two samples. * p < 0.05, ** p < 0.01, *** p < 0.001

Highlights

Few membrane-tethered synaptic vesicles upon Bassoon disruption, fewer without ribbon
Ribbon promotes clustering of Ca²⁺ channels at the synapse
Altered Ca²⁺ channel gating in mutants, but Ca²⁺-coupling to exocytosis unaffected
Synaptic transmission is impaired by fewer release sites and their slowed refilling

Supplementary Material

Click here to view.^{(3.5M, doc)}

Acknowledgments

The study was designed by T.M., T.F., N.S., A.N. and D.R. The experimental work was performed by T.F. (Ca²⁺ imaging, Ca²⁺ current and C_m recordings), N.S. (single unit recordings under supervision of M.C.L.), M.A.R. (confocal and STED microscopy), T.P. (flash photolysis), D.K. (confocal microscopy), and D.R. (electron microscopy). A.E. and B.H. contributed to STED microscopy and A.E. contributed to image analysis. A.N. performed modeling and contributed to data analysis. A.F. and E.D.G. provided the mice (gene trap mutant in collaboration with Lexicon Pharmaceuticals) and discussion. K.E.B and A.L. performed protein-protein interaction experiments. T.M., T.F., N.S., A.N. and M.A.R. prepared the MS. We thank S. Blume, N. Dankenbrink-Werder, A. Gonzalez, M. Köppler, and B. Kracht for expert technical assistance. This work was supported by grants of the Max Planck Society (Tandem-Project grant to Nils Brose and T.M.), the German Research Foundation: Fellowship to N.S., Center for Molecular Physiology of the Brain grant FZT-103 to T.M. and A.E., the German Federal Ministry of Education and Research (Bernstein Focus for Neurotechnology to T.M. and A.E.), the State of Saxony-Anhalt/European Structural Funds (EFRE-IfN C2/1) to E.D.G., and by the National Institutes of Health (grant to M.C.L., DC009433 and HL087120 to A.L. and T32 AI 07260 to K.E.B). M.A.R. and T.P. were supported by fellowships of the Alexander von Humboldt foundation. A.N. is a Fellow of the Bernstein Center for Computational Neuroscience Göttingen.

Footnotes

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