multiple-probability fluctuation analysis
ordinary differential equation
paired pulse ratio
- • Endogenous Ca2+ binding proteins such as calbinding-D28k (CB) and parvalbumin (PV) are considered important regulators of short-term synaptic plasticity.
- • Cerebellar Purkinje neurons express large amounts of CB and PV and are laterally connected by inhibitory synapses that show paired-pulse facilitation (PPF) during high-frequency activation.
- • We report quantal synaptic release parameters of these synapses in wild-type and in CB and PV knock-out mice; evidence is provided that these synapses operate at nanodomain influx-release coupling.
- • We find that PPF is independent of CB and PV, using a combination of paired electrophysiological recordings, synaptic Ca2+ imaging and numerical computer simulations.
- • Our results suggest that PPF during high-frequency activation results from slow Ca2+ unbinding from the sensor for transmitter release, which is reminiscent of the ‘active Ca2+’ mechanism of PPF suggested by Katz and Miledi in 1968.
Abstract Paired-pulse facilitation (PPF) is a dynamic enhancement of transmitter release considered crucial in CNS information processing. The mechanisms of PPF remain controversial and may differ between synapses. Endogenous Ca2+ buffers such as parvalbumin (PV) and calbindin-D28k (CB) are regarded as important modulators of PPF, with PV acting as an anti-facilitating buffer while saturation of CB can promote PPF. We analysed transmitter release and PPF at intracortical, recurrent Purkinje neuron (PN) to PN synapses, which show PPF during high-frequency activation (200 Hz) and strongly express both PV and CB. We quantified presynaptic Ca2+ dynamics and quantal release parameters in wild-type (WT), and CB and PV deficient mice. Lack of CB resulted in increased volume averaged presynaptic Ca2+ amplitudes and in increased release probability, while loss of PV had no significant effect on these parameters. Unexpectedly, none of the buffers significantly influenced PPF, indicating that neither CB saturation nor residual free Ca2+ ([Ca2+]res) was the main determinant of PPF. Experimentally constrained, numerical simulations of Ca2+-dependent release were used to estimate the contributions of [Ca2+]res, CB, PV, calmodulin (CaM), immobile buffer fractions and Ca2+ remaining bound to the release sensor after the first of two action potentials (‘active Ca2+’) to PPF. This analysis indicates that PPF at PN–PN synapses does not result from either buffer saturation or [Ca2+]res but rather from slow Ca2+ unbinding from the release sensor.
The use-dependent enhancement of transmitter release following the second of two successive action potentials (APs) separated by a millisecond time interval, termed paired-pulse facilitation (PPF), was discovered more than 70 years ago (Eccles et al. 1941). Yet its mechanisms remain controversial and may differ between synapses (Zucker & Regehr, 2002). Originally, it was suggested that ‘Ca2+ remaining attached to specific sites on the inner axon membrane’ (‘active Ca2+’) causes facilitation (Katz & Miledi, 1968). In a simpler form of the ‘residual Ca2+ hypothesis’, a residue of free Ca2+ ([Ca2+]res) from the first AP adds to the free Ca2+ ([Ca2+]i) from the second AP, thereby causing amplified release. However, it was soon recognized that the decay of [Ca2+]res deviates from the time course of facilitation, such that [Ca2+]res cannot fully account for facilitation (Blundon et al. 1993). Additionally, due to the large amplitude difference between [Ca2+]res (∼100 nm) and nano- or microdomain [Ca2+]i at the release site during the second AP (tens to 100 μm) simple Ca2+ summation has been considered unlikely as exclusive source of facilitation (Zucker & Regehr, 2002). Consequently, at different synapses different ideas were developed to account for facilitation. These include slow Ca2+ relaxation of the bound sensor (Yamada & Zucker, 1992; Bertram et al. 1996; Matveev et al. 2002), separate sites for release and facilitation (Atluri & Regehr, 1996), elevated release site [Ca2+]i during the second pulse (Geiger & Jonas, 2000; Felmy et al. 2003; Bollmann & Sakmann, 2005) or buffer effects (Neher, 1998a; Rozov et al. 2001).
Ca2+ buffers are considered important modulators of release and short-term plasticity (STP). Buffers with slow binding kinetics can suppress facilitation by reducing [Ca2+]res while fast, high-affinity sites may saturate during the first Ca2+ influx, resulting in increased [Ca2+]i during the second AP and amplified release (‘pseudofacilitation’; Neher, 1998a; Rozov et al. 2001; Zucker & Regehr, 2002). Specifically, it has been shown that parvalbumin (PV) can act as anti-facilitating buffer (Caillard et al. 2000; Müller et al. 2007; Eggermann & Jonas, 2012) and calbinding-D28k (CB) as saturable buffer (Blatow et al. 2003). PV can act via different mechanisms. It can either reduce [Ca2+]res due to its Mg2+-induced slow Ca2+ binding kinetics (Caillard et al. 2000; Müller et al. 2007) or prevent saturation of an unidentified high-affinity buffer in a complex process recently described as ‘metabuffering’ (Eggermann & Jonas, 2012).
Purkinje neurons (PNs) strongly express both ‘anti-facilitating’ PV and ‘pro-facilitating’ CB. Neighbouring PNs contact each other via inhibitory synapses (Orduz & Llano, 2007; Watt et al. 2009) that show moderate PPF during high-frequency activation (Orduz & Llano, 2007), making this synapse an interesting target to study details of transmitter release and the mechanisms of PPF. We quantified quantal release parameters of wild-type (WT), CB−/− and PV−/− synapses and propose a mechanistic explanation of PPF during high-frequency activation. Using paired whole-cell recordings, we confirm moderate PPF in WT during 200 Hz activity. Unexpectedly, PPF was not significantly affected by the absence of either CB or PV. Combining multiple-probability fluctuation analysis (MPFA), presynaptic Ca2+ imaging and numerical simulations of WT and mutants, we find that, although CB influenced the average initial release probability (pr), neither CB, PV nor [Ca2+]res appeared to be the main determinants of PPF. Rather, our analysis indicates that a residue of Ca2+ remaining bound to the release sensor (Schneggenburger & Neher, 2000; Sakaba, 2008) after the first AP is the probable main cause of PPF at PN to PN synapses.
All experiments were carried out in accordance with institutional guidelines for animal experiments, and were approved by the state directorate of Saxony, Germany.
Electroporation and electrophysiology
Mice were decapitated under deep isoflurane (Curamed) inhalation anaesthesia and the vermis region of the cerebellum was excised. Parasagittal slices (300 μm thick) were prepared (HM 650 V vibratome; Microm, Waltham, MA, USA) from cerebellar vermis of 7–12-day-old C57Bl6 WT, CB−/− (Airaksinen et al. 1997) or PV−/− mice (Schwaller et al. 1999) as described previously (Schmidt et al. 2003) and transferred to a recording chamber continuously perfused at 3 ml min−1 by artificial cerebrospinal fluid (ACSF) containing (in mm): 125 NaCl, 2.5 KCl, 1.25 NaH2PO4, 26 NaHCO3, 1 MgCl2, 2 CaCl2 and 20 glucose, equilibrated with 95% O2 and 5% CO2 (pH 7.3–7.4). Unless stated otherwise, chemicals were from Sigma-Aldrich (St Louis, MO, USA). Recordings were performed at 32 ± 1°C.
Pipette solutions were prepared with purified water and contained for presynaptic cells (in mm): 150 potassium gluconate, 10 NaCl, 3 Mg-ATP, 0.3 GTP, 0.05 EGTA, 10 Hepes, 10 GABA and 0.1 Atto-594 (Atto-Tec, Siegen, Germany). The pH was adjusted to 7.3 with KOH. The same intracellular solution was used for electroporation but with 0.4 mm Atto-594 replacing EGTA and GABA. The postsynaptic solution contained (in mm): 130 CsCl, 10 NaCl, 1.25 CaCl2, 4.5 Mg-ATP, 0.3 GTP, 10 EGTA, 10 Hepes and 0.1 Atto-488. The pH was adjusted to 7.3 with CsOH.
For rapid identification of intact axon collaterals, PNs were electroporated using voltage pulses of −4 V repeated at 200 Hz for 2 s from an offset voltage of −0.7 V. Thereafter, two-photon image stacks were collected at focus intervals of 2 μm. The fluorescence was filtered (SDM 570, 700-SP/610-SP) and detected by the two internal photomultiplier tubes of the imaging system. The whole-cell configuration was established in putative pairs of connected PNs under optical control (BX50WI; Olympus), using an EPC10/2 amplifier (HEKA, Pfalz, Germany) and Patchmaster 2.6 software and connectivity was tested for by using a brief step depolarization to the presumed presynaptic PN. Postsynaptic currents (PSCs) were recorded at a holding potential (Vhold) of −80 mV, filtered at 5 kHz and sampled at 10 kHz. The liquid junction potential (15 or 4 mV) was corrected for; the series resistance (Rs) and the leak current (Ileak) were monitored continuously and experiments were rejected if either Rs exceeded 30 MΩ or Ileak fell below −400 pA. Typically, 70–80%Rs compensation could be achieved. PSC amplitudes (I) were corrected for the remaining Rs offline according to the following equation:
where k is the uncompensated fraction of Rs. Distances between connected cells and axonal lengths (Table 1) were measured using the ‘segmented line tool’ of ImageJA 1.43q software (NIH, Bethesda, MD, USA).
|WT (n= 71)||CB−/− (n= 47)||PV−/− (n= 30)|
|Cells projecting from apex to base||78%||85%||80%|
|Distance between connected PNs (μm)||89 ± 9||81 ± 10||77 ± 12|
|Distance to first bifurcation (μm)||181 ± 7||193 ± 15||161 ± 17|
|Collateral length (μm)||373 ± 13||374 ± 20||351 ± 25|
|Putative presynaptic axosomatic boutons||3 ± 1||2 ± 1||4 ± 1|
Quantification of synaptic responses
PSCs were analysed using Patchmaster 2.6 and custom written routines in Igor Pro 6.21 (Wavemetrics, Lake Oswego, OR, USA). Paired pulse ratios (PPRs) were calculated by dividing average second amplitudes of a given interstimulus interval (ISI) by the first amplitude averaged over all ISIs. The amplitudes were determined by fitting a product of two exponential functions to the baseline-subtracted currents, which allows for independent adjustment of the time constants of the rising and falling phases (cf. Schmidt et al. 2003, 2013). The amplitude of the second PSC was determined as the difference between its peak and the decay of the first PSC, which subtracts the effect of electrical summation on the second amplitude (Fig. 1E). Prior to PPR calculation, fit amplitudes were converted to absolute amplitudes by analytical calculations and inspected in histograms for all recordings. PSCs were classified as failures if their amplitude was <10 pA, i.e. 2-fold root mean square (RMS) noise. It cannot be excluded that some PSCs with smaller amplitude remained undetected. The consistency between initial synaptic failure rates (F1) estimated based on the 2-fold RMS noise criterion and an estimate based on the quantal parameters (see below) indicates that the error in counting failures is unlikely to be substantial.
Quantal synaptic parameters were determined from PSCs recorded at different [Ca2+]e (0.5–15 mm, ≥ 50 repetitions per concentration) and a 5 s interval between paired stimulations. In most experiments [Ca2+]e of 2 mm was used for starting and final recordings. No significant difference was observed between these two data sets (Fig. 2), indicating that the 5 s interval was sufficient to prevent induction of longer lasting plasticity. In indicated experiments 1 mm tetraethylammonium chloride (TEA) was added to the bath to increase the release probability.
For MPFA, which assumes the applicability of binominal statistics and corrects for non-uniform quantal size (Quastel, 1997; Silver et al. 1998; Clements & Silver, 2000; Scheuss et al. 2002; Silver, 2003; Saviane & Silver, 2006a), noise-corrected variances (σ2) were plotted against mean PSC amplitudes (I) and fitted by a parabola of the form:
where q is the quantal size, N a binominal parameter, and CVI and CVII the coefficients of intrasite and intersite quantal variability, assumed to be 0.3 (Clements & Silver, 2000). The synaptic failure rate predicted from the quantal parameters (F1 = (1 –pr)N) agreed well with the measured failure counts (based on the 10 pA criterion): WT: 0.015–0.32; CB−/−: 0–0.6; PV−/−: 0–0.32. In addition, PSC amplitudes calculated from the median quantal parameters (Fig. 2D–F; PSC = qNpr; WT: 125 (60–316) pA; CB−/−: 169 (40–433) pA; PV−/−: 286 (72–712) pA) were consistent with the amplitudes determined by fitting exponentials.
Presynaptic Ca2+ imaging
For Ca2+ imaging, EGTA, Atto-594 and GABA of the presynaptic pipette solution were replaced by 200 μm Oregon Green-488 BAPTA-1 (OGB1; Invitrogen, Carlsbad, CA, USA). Imaging was performed between 30 and 90 min after the whole-cell configuration had been established. Two-photon excitation was achieved with a mode-locked Ti:sapphire laser (Tsunami; Spectra Physics, Santa Clara, CA, USA) at a centre wavelength of 770 nm fed into a modified laser-scanning microscope (Fluoview-300; Olympus, Tokyo, Japan) equipped with a 60×/0.9 NA water immersion objective. The laser intensity was modulated with a Pockels cell (model 350–80 KDP*/302 RM controller; Conoptics, Danbury, CT, USA), controlled via the EPC10/2 A/D converter. Presynaptic fluorescence signals were elicited by somatically induced APs (1–3 nA current injection for 1 ms; 100% bridge compensation, Vm−70 to −80 mV, Ihold < 300 pA) and recorded in line-scans at 500 Hz. The fluorescence was filtered (HC525/50, 720-SP, AHF, Tübingen, Germany), detected by two external photomultiplier tube modules (H7422–40, Hamamatsu, Iwata City, Japan; PMT-02M/PMM-03, NPI; monitoring epi- and trans-fluorescence, respectively), and digitized via the Fluoview A/D converter. The Ca2+-dependent fluorescence was background corrected and expressed as ΔF/F0.
Ca2+ dynamics and transmitter release were simulated as described in detail previously (Schmidt et al. 2003, 2013) by numerically solving a system of ordinary differential equations (ODEs) using NDSolve of Mathematica 8.04 (Wolfram, Long Hanborough, UK). Spatial resolution was achieved by placing the ODEs in concentric half-shells (5 nm thickness) covering a total radius of 500 nm (Chan-Palay, 1971; Watt et al. 2009). AP-mediated Ca2+ influx was placed in the central hemi-shell and represented by a Gaussian with half duration of 0.6 ms (Bischofberger et al. 2002). Ca2+ binding to buffers was simulated by second (ATP, CB, PV, OGB-1, EGTA) or higher order (CaM) kinetics. For PV, binding to Mg2+ was also included. Radial diffusion of all species was implemented using published diffusion coefficients. Ca2+ was cleared by a surface-based extrusion mechanism with Michaelis–Menten kinetics, balanced by a Ca2+ leak that generated a resting [Ca2+]i of 45 nm (Schmidt et al. 2007; Schmidt & Eilers, 2009). A five-site allosteric sensor model for Ca2+-dependent vesicle fusion (Schneggenburger & Neher, 2000) was modified for priming (Sakaba, 2008) and placed at varying distances from the Ca2+ influx, i.e. in different shells. Other sensor models were tested in addition (Bollmann et al. 2000; Schneggenburger & Neher, 2000; Lou et al. 2005b; Sakaba, 2008). Model parameters are given in Supplementary Tables S1 and S2.
Data summaries and statistics
Unless denoted otherwise, data are presented as median ± interquartile ranges (IQRs). Whiskers in box plots indicate last data points within 1.5-fold IQR. Outliers are included as individual data points, and mean values as dashed lines. MPFA data are given as mean and variances with the variance of variance shown as error bars. Distributions of PPRs and pr were estimated by non-parametric bootstrap analysis (Efron & Tibshirani, 1994). Bootstrap samples were drawn from the data with replacement until their size equalled the size of the data set. This procedure was repeated 10,000 times to calculate a sufficient standard error (SE) estimate of the bootstrap replicates (Fig. S3). Since the original data samples were small and normal distribution could not be assumed, we used the bootstrap 25% trimmed mean, which is close to the median, and the bootstrap SE to determine the coupling distance at PN–PN terminals (Fig. 5D). Unless stated otherwise, statistical significance was tested for either with the Mann–Whitney rank sum test (two groups) or with a one-way analysis of variance on ranks (ANOVA on ranks; for more than two groups).
Short-term plasticity at recurrent PN synapses is unaltered in CB−/− and PV−/−
The axonal arborizations of individual PNs were visualized by two-photon microscopy after single-cell electroporation with red Atto-594 dye (Fig. 1A; see Methods). The morphology of axon collaterals yielded data for the WT that were consistent with previous descriptions (Orduz & Llano, 2007; Watt et al. 2009) and were not altered in CB−/− and PV−/− mice (Table 1). Dual whole-cell recordings were established on the dye-filled presynaptic cell and the putative postsynaptic PN identified with brightfield optics. In total we recorded from 128 pairs of connected PNs (WT and mutants). In the WT, presynaptic APs elicited PSCs strongly scattering in amplitude (Fig. 1B and C) with a median amplitude of 90 pA (IQR 52–299 pA, n= 37 pairs) and a median fraction of synaptic failures in response to the first AP (F1) of 0.12 (0.02–0.36; Fig. 1D). The amplitude histograms were skewed towards larger values with no indication of discrete groups of amplitudes (Fig. 1E). Quantal peaks were not clearly evident, which precluded determination of miniature PSC amplitudes from the histograms. Frequency-dependent STP was evident at a 5 ms ISI with PPRs covering a range from moderate paired pulse depression (PPD) to PPF (n= 8; Fig. 1F). On average (n= 37), moderate PPF prevailed at the 5 ms ISI (PPR = 1.21, 1.00–1.49). PPF was of presynaptic nature, since it was associated with fewer failures in the second response (F2, 0.07, 0–0.23), indicating increased release probability for the second release process (cf. Orduz & Llano, 2007). PPR showed no dependency on recording time; rather, it was essentially stable over 100 min whole-cell recording time (Fig. 1G; r=−0.076 ± 0.089, n= 5; P > 0.05).
To test the idea that saturation of CB underlies PPF (Blatow et al. 2003; Orduz & Llano, 2007) we focused on the 5 ms ISI and performed paired-pulse experiments in pairs of connected PNs from CB−/− mice. The amplitude distributions of PSCs were similar to the WT with a median value of 114 pA (61–447 pA, n= 34) that was statistically not different from the WT (Fig. 1C; P= 0.26). Unexpectedly, also the PPR in CB−/− was not significantly different from the WT, i.e. moderate PPF was present at the 5 ms ISI (1.32, 1.03–1.51; n= 34, P= 0.2; Fig. 1H). In addition, neither F1 (0.16, 0.01–0.38; P= 0.66; Fig. 1D) nor F2 (0.08, 0–0.27; P= 0.94) were altered compared to the WT, which argues against the idea of CB saturation as causing PPF.
Buffering of [Ca2+]res by PV (Caillard et al. 2000) or its interference with saturation of unidentified fixed buffers (Eggermann & Jonas, 2012) could have been another factor in PPF. This was tested by paired-pulse experiments in PV mutants at the 5 ms ISI. However, again neither PSC amplitudes (208 pA, 72–712 pA; P= 0.26, n= 23, Fig. 1C), PPR (1.05, 0.89–1.37; P= 0.2; Fig. 1H) nor failure rates (F1: 0.10, 0–0.38, P= 0.66; F2: 0.07, 0–0.37, P= 0.94; Fig. 1D) were significantly affected by the absence of PV. At the Calyx of Held it has been observed that PV does not affect the amount of PPF at 4 ms ISI but does at longer ISI, resulting in a prolonged time-course of facilitation (Müller et al. 2007). Therefore, we also compared PPF between PV−/− and WT at ISIs of 10 and 20 ms but again found no significant difference between the two groups (ISI 10 ms: WT, PPR 1.0, 0.46–1.18, PV−/− 1.07, 0.9–1.3; P= 0.4; ISI 20 ms: WT, PPR 1.1, 0.9–1.2, PV−/− 0.98, 0.86–1.2; P= 0.7). These findings provide evidence against an involvement of PV in PPF and also argue against a significant involvement of [Ca2+]res (Caillard et al. 2000; Müller et al. 2007) or saturation of a fixed high-affinity Ca2+ buffer (Eggermann & Jonas, 2012) in PPF.
Taken together, we confirm moderate PPF at PN–PN synapses during high-frequency activation. Surprisingly, however, we found no evidence for a substantial contribution of the endogenous buffers CB and PV to PPF.
Lack of CB but not of PV increases the initial release probability
Quantitative estimates of pr, a major determinant of STP, were obtained by MPFA of peak PSC amplitudes recorded at different extracellular Ca2+ concentrations (Silver, 2003). Amplitudes were displayed in variance–mean plots (V–M plots) and fitted by a parabolic function that inferred quantal parameters under consideration of intra- and intersite variability. Despite high [Ca2+]e we found almost linear V–M relationships in all WT pairs (n= 7), indicating small pr in the WT. Due to the limited solubility of Ca2+, we partially blocked potassium currents by bath-applied TEA to increase pr further, assuming that increasing Ca2+ influx by either raising [Ca2+]e or by broadening actions potentials by TEA application has similar effects on intrinsic release sites (Huang et al. 2010; Schmidt et al. 2013). With TEA, V–M plots yielded parabolic fits in 6 out of 7 WT cells (Fig. 2A). On average, the fluctuation analyses yielded a quantal size (q) of 66 pA (43–125 pA, n= 14; pooled with values from the linear relationships, which were statistically not different, P= 0.5) and a binominal parameter N of 11.9 (8.6–15.8; n= 6). For 2 mm[Ca2+]e in the absence of TEA, pr was 0.16 (0.09–0.27).
Fluctuation analyses from CB−/− pairs yielded parabolic V–M plots in 6 out of 8 pairs (Fig. 2B) without application of TEA, indicating an increased pr in the mutant. Indeed, MPFA revealed a pr of 0.30 (0.24–0.43; n= 6), a value significantly larger than in the WT (P= 0.046). Increased pr was accompanied by a significant increase in q (217 pA, 112—278 pA, n= 8; P= 0.004), while N showed a tendency towards lower values that, however, did not reach the level of statistical significance (2.6, 1.2–5.2, P= 0.1). The significant alteration in q possibly reflects postsynaptic compensation, corresponding to spine enlargement in CB−/− PNs (Vecellio et al. 2000). For MPFA of PV−/− connections, TEA supplement was again required and none of the quantal parameters was statistically different from the WT (pr= 0.19, 0.14–0.30; N= 13.6, 6.0–26.0; n= 4; q= 111 pA, 80–193 pA; n= 7; P= 0.6, 0.1, 0.2; Fig. 2C–F).
The pr values might be considered upper limits because the MPFA may be distorted by postsynaptic saturation or desensitization at higher pr (Meyer et al. 2001). However, a substantial postsynaptic involvement appears unlikely because, even in the presence of TEA or high [Ca2+]e, PSC amplitudes remained strongly scattered with some large amplitudes (Fig. 2A–C). In addition, average amplitudes calculated from the quantal parameters were in good accordance with those recorded during the basal characterization of the connections (cf. Methods). Finally, a comparison of second PSCs following a release failure to those following a success revealed no significant difference, with respect to either amplitudes or decays (Fig. 3; Saviane & Silver, 2006b). Taken together, while PV did not significantly influence pr the MPFA data show an almost 2-fold increased pr in CB−/− compared to WT.
Increased presynaptic Ca2+ in CB−/− terminals and model construction
To obtain a deeper understanding of the Ca2+ transients that drive and facilitate vesicular release, we quantified volume-averaged Ca2+ signals in putative presynaptic boutons (Fig. 4A and B) that would serve as templates for adjusting constrained, spatially resolved, kinetic simulations of presynaptic Ca2+ dynamics and transmitter release (Fig. 4C).
PNs were equilibrated for 30 min in the whole-cell configuration with the indicator dye Oregon Green 488 BAPTA-1 (OGB1). Single APs typically did not reliably increase fluorescence above noise level due to their small amplitude of only ∼0.08 ΔF/F0 in WT (cf. Orduz & Llano, 2007) but were previously shown to sum linearly from 1 to 10 APs (Orduz & Llano, 2007). Therefore, to monitor the buffering action of CB and PV, we focused on the robust fluorescence signals that could be elicited by 10 APs at 200 Hz and analysed the transients in boutons of the collaterals. Trains of APs in a given bouton were recorded 3–5 times at different whole-cell times and showed stable signals. The median amplitude in WT was 0.72 ΔF/F0 (0.46–1.32; n= 23 boutons from 7 PNs), corresponding to a volume-averaged [Ca2+]i elevation of only ∼110 nm (Schmidt et al. 2003), which gives an approximate upper limit for [Ca2+]res after 10 APs. Based on linearity (Orduz & Llano, 2007) the upper limit for elevation in [Ca2+]res between the first and the second AP would be 11 nm, an unlikely source for PPF. As expected from our previous work on dendritic Ca2+ signals in the same mutants (Airaksinen et al. 1997; Schmidt et al. 2003), in CB−/− boutons Ca2+ amplitudes were significantly increased (ΔF/F0= 1.58, 1.23–2.20, n= 18/7; P < 0.001), while the absence of PV had no statistical influence on the amplitude compared to the WT (ΔF/F0= 0.51, 0.42–0.71, n= 21/10; Fig. 4D).
The average WT signal was used to adjust numerical simulations that were highly constrained by published parameters (Fig. 4C, D; Supplementary Table S1). The model considered known endogenous buffers (CB, PV, CaM, ATP), the indicator dye or otherwise EGTA, non-linear effects such as buffer competition and saturation, diffusion (including CB, PV, CaM, ATP, dye or EGTA), and a correction for experimental whole-cell wash-out of endogenous proteins. Fixed buffers were represented by the 20% immobilized fractions of CB (Schmidt et al. 2005) and CaM (Lee et al. 1999; Schmidt et al. 2007), with immobile CB being present throughout the terminal, while CaM was immobilized only at the site of the influx, reflecting an upper limit for CaM bound to Ca2+ channels (Lee et al. 1999). Together, the buffer capacity (κ) of the simulated proteins (with the wash-out correction omitted, κnative, Table S1) accounts for κ published for PNs of the age analysed here (Fierro & Llano, 1996) with the uncertainty, however, that Fierro & Llano (1996) did not consider wash-out effects during their experiments.
Ca2+ influx was assumed to occur at the central hemi-shell (cf. Bucurenciu et al. 2008; Eggermann & Jonas, 2012; Schmidt et al. 2013). While this may represent an oversimplification, a Ca2+ point source predicts the maximal local Ca2+ increase and buffer saturation possible; that is, if under these conditions buffer saturation does not occur, it cannot occur with more distributed influx since this would be associated with smaller local [Ca2+]i (Schmidt et al. 2013). The amplitude of the Ca2+ influx and the pump velocity were the only free parameters during model adjustment; all other parameters were taken from the literature and kept invariant. A further demand on the model was that it needed to fit data from the buffer mutants with the complete parameter set (including influx and pump) kept invariant compared to WT, except removal of CB or PV to mimic the mutant. Notably, this demand was excellently fulfilled by the simulations (Fig. 4D), indicating that major Ca2+ signalling processes were reproduced well by the model.
To account for recent findings that, in pyramidal neurons, the concentrations of PV (Eggermann & Jonas, 2012) or CaM (Faas et al. 2011) are higher than previously expected, we also tested models with increased PV and CaM concentrations (500 and 100 μm, respectively). However, under our constrained conditions simulations with a higher PV and/or CaM concentration did not reproduce the experimental Ca2+ transients accurately (Fig. S1).
Following model adjustment, paired AP-evoked Ca2+ transients were simulated under conditions reflecting the paired electrophysiological recordings, i.e. in particular the Ca2+ indicator dye was replaced by EGTA which was present in the pipette solution during paired recordings (Fig. 4E). In these simulations spatially resolved changes in free Ca2+ and in the Ca2+ occupancies of all buffers were analysed. The fractional Ca2+ occupancy of PV, mobile CaM, mobile CB and ATP showed no signs of saturation during both APs (defined as ≥50% occupancy; Schmidt, 2012), even close to the site of Ca2+ influx (Fig. 4Eb–d). The immobile fractions of CB and CaM became saturated with Ca2+ already during the first AP (Fig. 4Ec,e). However, this did not result in increased [Ca2+]i during the second AP, either in the volume average or at any distance from the site of influx (Fig. 4Ea,f). The reason for this is mainly that additional free Ca2+ ions were readily buffered by the large amount of mobile binding sites. In consequence, [Ca2+]i had virtually identical amplitudes during both pulses and declined to 50 nm between APs. Thus, [Ca2+]res was elevated by only ∼5 nm above the resting level of 45 nm (Wilms et al. 2006) prior to the second AP. A more substantial [Ca2+]res of ∼ 100 nm will build up only after 10 APs.
The simulations are in line with the experimental findings and support the notion that in particular neither CB saturation nor a substantial [Ca2+]res underlies PPF. If, nevertheless, a more substantial [Ca2+]res from the first AP were responsible for PPF, at least excess amounts of EGTA should interfere with PPF (Caillard et al. 2000; Rozov et al. 2001). We therefore performed paired-pulse experiments on pairs of connected WT PNs that were dialysed for 60–70 min with 10 mm EGTA. We estimate that after this time 70–80% of the pipette concentration was reached in the terminal (Schmidt et al. 2003; Bucurenciu et al. 2010), which corresponds to an added buffer capacity (κB) of ∼40,000. Even under these conditions of strong exogenous buffering, PPF remained unaltered compared to controls (PPREGTA= 1.18, 0.98–1.31, PPRcontrol= 1.23, 0.78–1.40, n= 5, P= 0.5; Fig. 5A), substantiating the notion that [Ca2+]res is not causal for PPF here.
To obtain further insight into the interplay between facilitation and depletion, we plotted PPR versus pr values for different [Ca2+]e (Fig. 5B; cf. Valera et al. 2012). The plot shows a decline in PPR with increasing pr, which is in accordance with reports from other synapses (e.g. Murthy et al. 1997; Valera et al. 2012). The relationship between pr and PPR was similar in WT and PV−/− and shifted towards higher PPR in CB−/−. As deduced from a simple calculus for maximum PPR (PPRmax= (1 –pr)pr,2/pr; with a max. pr,2= 1) and consistent with the above similarity of second PSC amplitudes following a release failure to those following a success (Fig. 3A), no signs of compensation for vesicle depletion (e.g. by replenishment or extra sites, Valera et al. 2012) were evident at near physiological [Ca2+]e. To address this point further, we analysed the variance of second PSC amplitudes recorded at 2 mm[Ca2+]e for all genotypes and included their V–M relationship into the V–M plots for the first amplitudes (Fig. 5C). If recruitment of extra release sites were involved in PPF, the corresponding V–M relationship of the second amplitudes could deviate from the initial parabola towards larger variances (Valera et al. 2012), whereas an increased second pr in the absence of significant depletion compensation results in data points falling close to the initial parabola (Clements & Silver, 2000). We found that for all three genotypes and all pairs recorded the V–M relationships of the second PSCs lay close to the parabolic fits to the V–M relationships of the first amplitudes. This substantiates the above notion that depletion compensation or extra release sites are unlikely to make a strong contribution to PPF at 2 mm[Ca2+]e. At high pr settings, by contrast, some compensation for the loss of vesicles during the first AP probably occurred, as experimental PPR slightly exceeded the theoretical PPRmax for a given pr (Fig. 5B). Taken together, the data presented so far do not suggest substantial contributions of depletion or its compensation or extra release sites (at [Ca2+]e of 2 mm) of CB, PV and [Ca2+]res to PPF.
Facilitated release sensor as a source for PPF
A remaining possibility for explaining PPF is a slow relaxation of the vesicular release sensor from its Ca2+-occupied states. We will refer to a partially occupied sensor as facilitated release sensor, which is reminiscent of the ‘active Ca2+’ hypothesis by Katz & Miledi (1968). To test the hypothesis that PPF could result from a facilitated release sensor we used the estimated Ca2+ transients to drive four different five-site release sensor models (Bollmann et al. 2000; Schneggenburger & Neher, 2000; Lou et al. 2005a; Sakaba, 2008). In all models (Table S2), release rate and pr dropped rapidly with increasing influx–release coupling distance, with best matches between experimental and theoretical values being obtained at coupling distances between 20 and 35 nm (Fig. S2), indicating that PN–PN synapses operate at nanodomain coupling similar to other inhibitory synapses (Bucurenciu et al. 2008; Eggermann & Jonas, 2012) or the excitatory cerebellar parallel fibre synapse (Schmidt et al. 2013).
In all models we found varying degrees of STP due to differences in the durability of their Ca2+ bound states (Fig. S2). The experimental data were best matched by the models of Schneggenburger & Neher (2000) and Sakaba (2008) (models 2 and 3 in Table S3, respectively). These models generated PPF due to long-lived Ca2+ bound states, thereby facilitating the sensor for the second release process during the 5 ms ISI. Model 2 gave a good description of the data at 2 mm[Ca2+]e (Fig. S2B), but underestimated PPR at 10 mm[Ca2+]e since it did not include a vesicle replenishment mechanism. Model 3 was developed to describe release at cerebellar basket cell terminals and included Ca2+-dependent vesicle replenishment (Sakaba, 2008). While such a replenishment step was not required to describe the data at 2 mm[Ca2+]e, we found that it was necessary to account for PPR recorded at the higher pr settings in 10 mm[Ca2+]e (Fig. 5B). With a slightly increased sensor off-rate (koff) and for CB−/− also an increased refilling rate (kfill) the model accounted well for PPR from high to low [Ca2+]e for WT and mutant PNs (Fig. 5B, D–F; model 5 in Table S2). The adjusted simulations reproduced the experimental pr and PPR values at a coupling distance of 24–29 nm under consideration of the data scatter by bootstrap analysis (Fig. 5E, Fig. S2). They show PPF in the absence of substantially elevated [Ca2+]i in the second pulse and indicate that PPF can indeed result from long-lived Ca2+-bound states of the release sensor.
In summary, experiments in mutant mice and whole-cell dialysis of terminals with or without EGTA show that high-frequency PPF is largely independent of the major endogenous Ca2+ buffers CB and PV and of [Ca2+]res at PN–PN synapses. Numerical simulations indicate that a release sensor facilitated by a residue of the active Ca2+ could provide an explanation for PPF here.
STP is considered important in CNS information processing (Zucker & Regehr, 2002). PPF, one form of STP, may arise from different sources, including saturation of CB, [Ca2+]res and/or ‘active Ca2+’, i.e. here long-lived Ca2+ bound states of the release sensor. Here we provide evidence that PPF in PN–PN synapses is based on the last-named mechanism, despite their strong expression of CB and PV.
Role of CB, CaM and immobile fractions
CB is the dominating endogenous buffer in PNs. Its Ca2+ binding kinetics is rather rapid (Faas et al. 2011) and an 80% fraction of CB is mobile (Schmidt et al. 2005). These characteristics make CB a major determinant in shaping dendritic and spineous Ca2+ dynamics (Airaksinen et al. 1997; Schmidt et al. 2003) and, as we show here, also of the amplitude of presynaptic Ca2+ signals (Fig. 4D). In addition, we show here that in the absence of CB pr is increased almost 2-fold (Fig. 2), indicating that CB is capable of buffering the nanodomain triggering Ca2+ release.
It was hypothesized that saturation of CB underlies PPF at PN–PN synapses (Orduz & Llano, 2007), similar to input-specific synapses on pyramidal neurons (Blatow et al. 2003). We tested this hypothesis by directly analysing PPF in CB−/− synapses and found that it was not significantly altered compared to WT (Fig. 1H). This is inconsistent with the hypothesis of saturated CB being the cause of PPF. It is unlikely that the finding is substantially biased by wash-out of CB as PPR was stable over the recording time (Fig. 1G). In addition, pr (Fig. 2) and Ca2+ signals in presynaptic terminals (Fig. 4) recorded under comparable whole-cell conditions were significantly increased in CB−/−. Finally, the small amplitude of volume-averaged presynaptic Ca2+ signals (Fig. 4D; Orduz & Llano, 2007) is incompatible with saturation of CB. We estimate that the fraction of Ca2+ bound to mobile CB at the presumed site of the release sensor increased to only ∼18% during each AP of the paired-pulse experiments and, due to its kinetics, was increased by ∼2% between APs. The 20% immobile fraction of CB, by contrast, becomes strongly saturated near the sensor (60–80%). A potential non-linearity in [Ca2+]i, however, is damped by mobile CB, such that the overall CB occupancy is only ∼35% and [Ca2+]i is essentially the same during both APs. Similar considerations apply to the 20% immobile fraction of CaM (Lee et al. 1999; Schmidt et al. 2007). In consequence, CB plays only a subsidiary role in facilitation at PN–PN synapses.
Role of PV and residual free Ca2+
PNs also express PV, which can act as an anti-facilitating buffer by different mechanisms. PV–Mg2+ complexes could act as a slow Ca2+ buffer that affects [Ca2+]res without affecting peak [Ca2+]i in the release domain (Caillard et al. 2000; Müller et al. 2007). Alternatively, rapid Ca2+ binding by PV may prevent saturation of unidentified high-affinity Ca2+ buffers (Eggermann & Jonas, 2012). The latter is mediated by the ∼5% metal-free fraction of PV that acts as a rapid, high-affinity Ca2+ buffer (KD∼9 nm; Lee et al. 2000) and is replenished by PV–Mg2+ complexes in this process, termed ‘metabuffering’ (Eggermann & Jonas, 2012). Predominant buffering of [Ca2+]res by PV (‘slow’ buffering) would be evident by a reduction in PPR without an effect on pr, while its anti-saturating action (‘metabuffering’) would reduce PPR and could be accompanied by altered pr. As a consequence, both mechanisms would lead to increased PPF in PV−/− at least at longer ISIs (Müller et al. 2007). However, in our experiments neither pr (Fig. 2) nor PPR (Fig. 1H; at 5, 10 or 20 ms ISI) was significantly altered in PV−/−. This suggests that [Ca2+]res is not a factor in PPF at PN–PN synapses. The conclusion is supported by the finding that also a high concentration of intracellularly infused EGTA (κB∼ 40,000) did not reduce PPF (Fig. 5A).
Facilitated influx or sensor
The relationship between AP number and Ca2+ signal amplitude at PN terminals has been shown to be linear between 1, 2 and 10 pulses (Orduz & Llano, 2007). This argues against facilitation of Ca2+ influx (Geiger & Jonas, 2000; Bollmann & Sakmann, 2005) as causative for PPF. As also no indications for recruitment of extra release sites were evident (Fig. 5C; Valera et al. 2012), we explored a release sensor facilitated by active Ca2+ (Katz & Miledi, 1968) as the potential mechanism of PPF. We addressed this possibility in constrained reaction–diffusion simulations (Schmidt et al. 2013) using published cooperative release models (Bollmann et al. 2000; Schneggenburger & Neher, 2000; Lou et al. 2005a; Sakaba, 2008). All of the sensor models agreed regarding pr at a similar coupling distance. Two of the models did not reproduce PPF due to their rapid dissociation of Ca2+-occupied states (Bollmann et al. 2000; Lou et al. 2005a). They would require an elevated release site [Ca2+]i in the second pulse to generate PPF (cf. Felmy et al. 2003; Bollmann & Sakmann, 2005). Similar to the GABAergic cerebellar basket cell to PN synapse (Sakaba, 2008) the model which gave the best overlap with our experimental data was adapted from the five-site model by Schneggenburger & Neher (2000) using modifications similar to those for the basket cell terminal (Sakaba, 2008). This model indicated that facilitation at the 5 ms ISI could indeed result from Ca2+ remaining bound to the release sensor after the first AP.
At the Calyx of Held the relationship between Ca2+ signal ratio and PPR has been explored in Ca2+ uncaging experiments (Bollmann & Sakmann, 2005). It was found that a ΔF/F0 ratio > 1 is required to produce PPF at an ISI ≥20 ms. For an ISI of 5 ms, however, ΔF/F0 ratios ≤ 1 were sufficient to produced a moderate PPF (cf. fig. 5d,h in Bollmann & Sakmann, 2005). Notably, in this latter case the experimental data were not well reproduced by the model of Bollmann et al. (2000), which requires increased release site [Ca2+]i for PPF (see above). It was concluded that the release machinery relaxes to resting Ca2+ occupancy within 20 ms. This is highly comparable to the situation here and gives further support to the view that PPF at 200 Hz results from slow Ca2+ unbinding from the sensor in the absence of elevated nanodomain [Ca2+]i at PN–PN synapses.
To estimate the coupling distance, we followed our approach based on quantification of pr in WT and endogenous buffer mutants (Schmidt et al. 2013). We extended this approach here by using PPR in addition to pr to estimate the coupling distance. PN–PN synapses appear to operate at nanodomain coupling (<100 nm Eggermann et al. 2012), similar to other inhibitory central synapses (Bucurenciu et al. 2008; Eggermann & Jonas, 2012). To our knowledge all inhibitory central terminals investigated in this respect to date operate at nanodomain coupling, i.e. it might be that this is the typical coupling configuration for this type of synapse. Note, however, that the proposed role of active Ca2+ as a cause of PPF does not depend on the absolute correctness of our estimates of pr and coupling distance (Fig. 5E).
While [Ca2+]i of ∼20 μm at the sensor estimated here could be reached by multiple Ca2+ channels with some distance from the vesicle (Neher, 1998b; Meinrenken et al. 2003) it can also be reached by a single Ca2+ channel at a distance of ∼20 nm (Weber et al. 2010). To our knowledge nothing is known about the distribution and number of Ca2+ channels in terminals formed by PN collaterals. Therefore, we used the simplest assumption of a single influx point in the simulations. Similar strategies have previously proven reasonable in modelling release with no substantial deviations for the conclusions compared to models with more distributed channel topologies (Bucurenciu et al. 2008, 2010; Eggermann & Jonas, 2012; Schmidt et al. 2013). In addition, the small size of the Ca2+ signals (Fig. 4; Orduz & Llano, 2007) is more in line with few channels triggering release in a nanodomain coupling regime, similar to inhibitory hippocampal synapses (Bucurenciu et al. 2010) since [Ca2+]i at the sensor has to reach amplitudes of >10 μm to trigger release (Neher, 1998b; Meinrenken et al. 2003; Neher & Sakaba, 2008).
Use of a facilitation mechanism based on active Ca2+ may be advantageous for synapses with a large buffer capacitance such as the PN–PN synapses. First, due to the high concentration of endogenous Ca2+ buffers a substantial amount of [Ca2+]res can build up only during prolonged bursting. Second, active Ca2+ allows for facilitation without the need to saturate endogenous buffers. Both are favourable in terms of energy expenses, as they lower the amount of post-AP ATP consumption required for Ca2+ clearance from the cytosol. Hence, a PPF mechanism based on active Ca2+ promotes energy-efficient CNS information processing.
The authors declare no conflict of interests.
G.B., O.A. and S.B. performed the experiments and made the figures. G.B., O.A., S.B., J.E. and H.S. analysed the data and H.S. performed the modelling. S.H., J.E. and H.S. designed the study. G.B., S.H., J.E. and H.S. wrote the manuscript. All authors read and approved the final submission.
This work was supported by a DFG grant to J.E. and H.S. (EI 342/4-1).
We thank B. Schwaller for supply of mutant mice, and G. Bethge for technical assistance.