Reduced endogenous Ca2+ buffering speeds active zone Ca2+ signaling.

Fast synchronous neurotransmitter release at the presynaptic active zone is triggered by local Ca(2+) signals, which are confined in their spatiotemporal extent by endogenous Ca(2+) buffers. However, it remains elusive how rapid and reliable Ca(2+) signaling can be sustained during repetitive release. Here, we established quantitative two-photon Ca(2+) imaging in cerebellar mossy fiber boutons, which fire at exceptionally high rates. We show that endogenous fixed buffers have a surprisingly low Ca(2+)-binding ratio (∼ 15) and low affinity, whereas mobile buffers have high affinity. Experimentally constrained modeling revealed that the low endogenous buffering promotes fast clearance of Ca(2+) from the active zone during repetitive firing. Measuring Ca(2+) signals at different distances from active zones with ultra-high-resolution confirmed our model predictions. Our results lead to the concept that reduced Ca(2+) buffering enables fast active zone Ca(2+) signaling, suggesting that the strength of endogenous Ca(2+) buffering limits the rate of synchronous synaptic transmission.

At presynaptic nerve terminals, the opening of voltage-gated Ca2+ channels during action potentials (APs) leads to a brief Ca2+ influx. The resulting microdomain Ca2+ signals reach several tens of micromolar amplitude near open Ca2+ channels and trigger neurotransmitter release at presynaptic active zones (1, 2). After Ca2+ channel closing, the binding to endogenous Ca2+ buffers and diffusion of Ca2+ within the cytosol lead to collapse of the microdomain, increasing the residual [Ca2+] in the presynaptic terminal to not more than a fraction of micromolar. During this equilibration with Ca2+ buffers, the majority of entering Ca2+ ions are bound to endogenous Ca2+ buffers (3). The strength of intracellular Ca2+ buffering can be characterized by the Ca2+-binding ratio defined as the ratio of buffer-bound Ca2+ to free Ca2+ (4). It is established that strong Ca2+ buffering limits the spread of Ca2+ ions at active zones and thus restricts neurotransmitter release to the vicinity of Ca2+ channels (5). Rapid removal of calcium from the active zone is essential to sustain synchronous release during repetitive activity. However, the mechanisms controlling the speed of active zone Ca2+ signaling during repetitive synaptic transmission and the clearance of Ca2+ from the active zone in between APs remain elusive.

The cerebellar mossy fiber bouton (cMFB) to granule cell synapse is ideally suited to analyze Ca2+ signaling during repetitive synaptic transmission because of the synchronous neurotransmitter release at exceptionally high frequencies (6–8). Understanding rapid active zone Ca2+ signaling requires knowledge about the Ca2+ dynamics and the strength, mobility, and binding kinetics of endogenous Ca2+ buffers. In particular, a dissection of fixed and mobile buffers (9, 10) is needed, which is technically challenging and requires access to the presynaptic terminal.

Here, we perform quantitative two-photon Ca2+ imaging in cMFBs, which are dialyzed with the pipette solution, and in remote cMFBs along the same axon, which are minimally perturbed, to separately characterize fixed and mobile Ca2+ buffers. We show that rapid active zone Ca2+ signaling is achieved by a low Ca2+-binding ratio of endogenous fixed buffers with low affinity and mobile buffers with high affinity. Our data explain how a central synapse achieves the speed of active zone Ca2+ signaling required for fast and synchronous transmitter release and suggest that the strength of endogenous Ca2+ buffering limits the precision and synchronicity of repetitive synaptic activity.

Results

Quantitative Two-Photon Ca2+ Imaging in cMFBs.

Quantitative knowledge about presynaptic Ca2+ dynamics is crucial to understanding the mechanisms of active zone Ca2+ signaling. Here, we combined direct patch-clamp recordings from en passant cMFBs (6, 8) (Fig. 1 ) with quantitative two-photon Ca2+ imaging. Single APs produced distinct and reproducible fluorescence transients (Fig. 1 ), consistent with previous measurements in mice and turtles (11, 12). Presynaptic recordings permit quantifying Ca2+ transients using a dual-indicator method (13) (Fig. 1). For each combination of Ca2+-sensitive (green) and Ca2+-insensitive (red) dye, the signals were calibrated with presynaptic recordings by adding 10 mM EGTA or 10 mM CaCl2 to the intracellular solution (). The Ca2+ concentration at rest ([Ca2+]rest) was 57 ± 7 nM in cMFBs based on recordings with the Ca2+ indicator OGB-1 (n = 30; Fig. S1), consistent with other presynaptic terminals (14–16). Establishing quantitative two-photon Ca2+ imaging in combination with in-cell calibration measurements at cMFBs (Figs. S1 and S2) enabled us to analyze the Ca2+ dynamics at these presynaptic terminals in detail.

Fig. 1.

Quantitative two-photon Ca2+ imaging in cMFBs. (A) Illustration of the cellular connectivity within cerebellar cortex. Mossy fibers (magenta) send information to the cerebellar cortex. Presynaptic cerebellar mossy fiber boutons (cMFBs) transmit signals to postsynaptic granule cells (GC, green), which excite Purkinje cells (PC, gray) via parallel fibers. Purkinje cell axons represent the sole output of the cerebellar cortex. Patch-clamp pipette illustrates presynaptic recording configuration. (B) (Left) Infrared image of a cMFB in an acute cerebellar slice during patch-clamp process. Arrow indicates membrane dimpling before seal formation. (Right) Same bouton after gaining whole-cell access. Asterisks indicate patch-pipette. (C) Two-photon image of a patched bouton filled with 10 µM Atto594 and 50 µM Fluo-5F (maximum z-projection of a stack of images over 45 µm; z-step, 2.5 µm). Line scan position is indicated. (D) cMFB APs elicited by current injection (200 pA, 3 ms). (Inset) APs on expanded time scale; superposition of 15 consecutive APs (gray) with average (black). (Scale bars, 200 µs and 20 mV.) (E) Two-photon line scans for the green and red channel. Arrowheads denote time point of AP. (F) Change in fluorescence intensity within the cMFB (ΔF/F) for the green and red channel. Colored traces are averages of 15 sweeps (gray). (G) Corresponding calculated Ca2+ concentration.

Low Ca2+-Binding Ratio of Endogenous Fixed Buffers.

The Ca2+-binding ratio of endogenous fixed buffers (κE,fixed) can be estimated by loading a cellular compartment with various amounts of Ca2+ indicator dye (4, 17), as direct whole-cell recording from a small subcellular compartment leads to substantial wash-out of mobile Ca2+ buffers. We used Ca2+-sensitive dyes of different affinities to measure Ca2+ transients evoked by single APs (Fig. 2 ). Increasing the Ca2+-binding ratio of the added Ca2+ indicator (κB), which also acts as a Ca2+ buffer, reduced the amplitude and prolonged the decay of Ca2+ transients (Fig. 2 and Fig. S3). According to the single compartment model, the inverse of the amplitude (A–1) and the decay time constant (τ) were linearly related to κB (4, 14) (Fig. 2 ). Hence, the Ca2+ transient without added buffer was estimated by linear extrapolation, yielding amplitude of 204 nM and τ of 50.3 ms. The Ca2+-extrusion rate (γ) was determined as 267 s−1 and κE,fixed as 17.1 and 12.5 from A–1 and τ extrapolation, respectively, resulting in a mean estimate of ∼15 (Fig. 2 ). The product of A and τ was independent of κB (18) (Fig. 2). Statistical reliability was addressed with a bootstrap method, resulting in κE,fixed of 17.5 ± 7.5 and 12.7 ± 7.2 from A–1 and τ extrapolation, respectively (mean ± SEM, corresponding to a 16–84% CI based on 152 experiments; and Fig. S3).

Fig. 2.

Low Ca2+-binding ratio of endogenous fixed buffers. (A) Example traces of Ca2+ transients in response to single APs recorded with different indicators (color-coded). Traces are averages of 25–30 sweeps and were digitally filtered for display (Fluo-4FF and OGB-5N examples were filtered to 100 Hz; remaining traces to 170 Hz). Black lines are exponential fits; arrowhead denotes time point of AP. The affinity (KD) and Ca2+-binding ratio (κB) of Ca2+ indicators are specified. (B) Example trace of Ca2+ transient in response to a single AP recorded with Fura-2 (average of 20 sweeps). (C) Inverse of the amplitude of AP-evoked Ca2+ transients recorded using different dyes plotted vs. Ca2+-binding ratio of the indicator (κB). The line represents a linear fit. Extrapolation to the abscissa gave an estimate of the Ca2+-binding ratio of endogenous fixed buffers (arrow). Color-coding is identical to A and B. (D) Corresponding analysis of the decay time constant (τ) of Ca2+ transients. Resulting parameters are indicated. (E) Product of A and τ plotted vs. κB. The line represents a linear fit.

These results depend on correct quantification of presynaptic [Ca2+]. To confirm that our two-photon imaging with dual-indicator calibration reliably estimates [Ca2+], we recorded Ca2+ transients in response to a single AP using the Ca2+ indicator Fura-2 and epifluorescence illumination with two alternating wavelengths (n = 12; Fig. 2). The amplitude and decay time constant were in close agreement to the measurements with two-photon imaging (Fig. 2 ). Furthermore, a single-indicator method applicable for high-affinity Ca2+ dyes (being independent of intrabouton calibration measurements) (19) yielded very similar amplitudes (Fig. S3). Thus, these data demonstrate that at cMFBs the Ca2+-binding ratio of endogenous fixed buffers is very low compared with other presynaptic terminals (14, 15, 20–22).

Ca2+ Transients in Remote Boutons Indicate Wash-Out of Mobile Buffers.

To analyze a potential wash-out of endogenous mobile buffers during presynaptic recordings, we measured Ca2+ transients in remote boutons along the mossy fiber axon of patched cMFBs (Fig. 3). There, Ca2+ transients elicited by single APs became smaller in amplitude and decayed more slowly during dye loading (Fig. 3). Intrabouton concentration and Ca2+-binding ratio κB of Fluo-5F were calculated from the fluorescence intensity (Fig. 3 ). For quantification of Ca2+ signals, we corrected for a faster loading of Atto594 compared with Fluo-5F (). Linear extrapolation of A–1 and τ vs. κB resulted in low and sometimes negative estimates of κE (Fig. 3 ). These results indicate a wash-out of slow mobile Ca2+ buffers, because slow buffers speed the decay of Ca2+ transients and the initial presence of slow buffers consequently leads to an underestimation of κE (23). Indeed, simulating the wash-in of Fluo-5F and simultaneous wash-out of mobile buffers with slow binding kinetics reproduced well our observations (Fig. 3).

Fig. 3.

Ca2+ transients in remote boutons indicate wash-out of a mobile buffer. (A) Two-photon image of a patched bouton filled with 10 µM Atto594 and 200 µM Fluo-5F (maximum z-projection of a stack of images over 80 µm; z-step, 4 µm; patch-pipette is illustrated schematically). Dotted lines indicate line scan positions in the patched and remote bouton. (B) Example traces of Ca2+ transients during dye loading in a remote bouton elicited by single APs at different time points after gaining whole-cell access. Time and estimated dye concentration are indicated; black lines represent exponential fits. (C) Red and green fluorescence at a remote bouton increase with time during whole-cell recording. Fluorescence was background subtracted and calculated over the whole trace (600 ms, red channel) or 90 ms of baseline before stimulation (green channel). Black lines are fits of Eq. . (D) Ca2+-binding ratio of added buffer (κB) vs. time. Dye concentration was calculated from the fit in C, and κB was computed using Eq. . (E) Inverse of the amplitude (Upper) and time constant τ (Lower) of Ca2+ transients recorded during dye loading are plotted vs. κB. Lines represent linear fits; same experiment as in B. (F) Histograms of extrapolated κE values obtained from extrapolation of A–1 (Upper) and τ (Lower) in 26 dye loading experiments. Mean value is indicated in gray. (G) Simulating Ca2+ transients during dye loading and simultaneous washout of a slow endogenous buffer (100 µM mobile buffer with EGTA-like kinetics, red circles). Wash-out of the slow buffer impacts on τ-extrapolation, resulting in a negative κE estimate (dashed lines indicate linear extrapolation).

To gain additional evidence that unperturbed cMFBs contain mobile Ca2+ buffers, we analyzed Ca2+ transients at the beginning of dye loading experiments. If a remote bouton was rapidly detected and recorded from, the initial concentration of added Ca2+ indicator was low (κB < 15; mean κB = 9.0 ± 1.3; n = 8). Ca2+ transients at the beginning of these experiments decayed with a time constant of 51.2 ± 12.5 ms. Despite the presence of the Ca2+ indicator, the time constant is comparable to what the extrapolation to κB = 0 predicted for patched boutons (τ = 50 ms; Fig. 2). This observation again indicates that slow mobile buffers speed the decay of residual Ca2+ in cMFBs. We thus infer that cMFBs contain a substantial amount of endogenous mobile buffers.

Mobile Buffers at cMFBs Have Slow Bindings Kinetics.

To gain insights into the properties of the mobile buffers, we compared Ca2+ transients in remote and patched boutons at identical dye concentration. In the dye loading experiments (Fluo-5F pipette concentration, 200 µM), we selected transients measured at ∼50 µM Fluo-5F concentration (48.2 ± 2.1 µM, n = 24) during dye loading in remote cMFBs to compare with Ca2+ transients recorded using 50 µM Fluo-5F in separate experiments in patched cMFBs (Fig. 4). The amplitudes were similar (P = 0.75), but the decay was significantly faster in remote compared with patched cMFBs (P < 0.001; Fig. 4). This result is consistent with the presence of a mobile buffer with slow binding kinetics in remote boutons, because slow buffers speed the initial decay of the Ca2+ transient with little effect on amplitude (24). Note that the limited duration (500 ms) of our recordings precluded a detailed analysis of the slower exponential component resulting from the slow buffer, as discussed previously (25). However, including 100 µM EGTA in the patch-pipette reproduced the speeding of the initial decay time constant observed in remote boutons (Fig. 4 ). Furthermore, simulating the effect of mobile buffers with EGTA-like kinetics on the Ca2+ transient replicated well our results (Fig. S4 ). These data indicate that the endogenous mobile buffers at cMFBs have slow binding kinetics, high affinity, and are equivalent to ∼100 µM EGTA (9).

Fig. 4.

Mobile buffers at cMFBs have slow bindings kinetics. (A) Example traces of Ca2+ transients evoked by a single AP. (Top) Ca2+ transient at a patched bouton recorded with 50 µM Fluo-5F. (Middle) Ca2+ transient recorded with 46 µM Fluo-5F in a remote bouton at the beginning of dye loading (200 µM Fluo-5F in the pipette solution). (Bottom) Ca2+ transient at a patched bouton measured with 50 µM Fluo-5F and 100 µM of the slow Ca2+ buffer EGTA. Traces are single sweeps. (B) Decay time constant (τ) and amplitude of Ca2+ transients evoked at patched (green) or remote boutons (blue) and with EGTA added to the pipette solution (red). The estimated concentration of Fluo-5F at remote boutons in the initial phase of dye loading was 48.2 ± 2.1 µM (n = 24), which is comparable to the Fluo-5F concentration in patched cMFBs (50 µM).

Buildup of Residual Ca2+ During High-Frequency Firing.

In vivo, cMFBs fire bursts of APs with exceptionally high frequencies (6, 26), where vesicular transmitter release is remarkably synchronous (8, 27). To understand which mechanisms enable synchronous high-frequency release, we measured the buildup of Ca2+ during high-frequency bursts (20 APs at 300 Hz). First, we analyzed the Ca2+ influx per AP during train stimulation by pharmacologically isolating the Ca2+ current elicited by AP-like stimuli (200 µs to 0 mV; Fig. 5). Ca2+ currents displayed facilitation during 300-Hz bursts (Fig. 5), consistent with P/Q-type voltage-gated Ca2+ channels at cMFBs (8). Next, we used Ca2+ imaging to measure the increased spatially averaged residual [Ca2+] by 300-Hz train stimulations (Fig. 5). The increase caused by individual APs could be resolved well and appeared constant for the first APs of the train (Fig. 5). Peak residual [Ca2+] during the train in the absence of Ca2+ indicators was estimated as 3.8 µM by back-extrapolation (Fig. 5; [3.1–5.5 µM], bootstrap 16–84% CI based on 40 experiments). The amplitude of 3.8 µM indicates that the Ca2+ transients from single APs (amplitude, 0.20 µM; Fig. 2) summate markedly during short high-frequency bursts, resulting in high peak [Ca2+] during trains. The estimates for τ, κE, and γ from train stimulation (τ = 86 ± 26 ms; κE = 13 ± 5 and 17 ± 7 for A–1 and τ extrapolation, respectively; γ = 210 ± 27 s–1; bootstrap SEM based on n = 40) were comparable to estimates from single APs (Fig. 2 and Fig. S3). However, analysis of stronger stimuli such as 100-ms depolarizations to 0 mV suggests a speeding of Ca2+ extrusion at higher [Ca2+], as previously described (28). To investigate the contribution of mobile buffers, we added 100 µM of EGTA to the intracellular solution (Fig. S4), which reduced the average peak amplitude by ∼30% (P = 0.046; Fig. S4). In excellent agreement, adding 100 µM EGTA in simulations predicted a 31% reduction (Fig. S4 ). The fast Ca2+-extrusion mechanisms in cMFBs prevent a summation of the slow component of residual Ca2+ transients caused by mobile buffers, which can evoke delayed release at some synapses (29, 30). These data demonstrate that endogenous mobile buffers reduce the buildup of residual Ca2+ during high-frequency bursts at cMFBs.

Fig. 5.

Buildup of residual Ca2+ concentration during high-frequency firing. (A) (Top) Ca2+ concentration measured during the first five stimuli of 300-Hz AP firing in a cMFB with 50 µM Fluo-5F (3-kHz temporal resolution) superimposed with the prediction of our model. (Middle) Voltage command. (Bottom) Corresponding presynaptic Ca2+ currents. Note the facilitation of the peak Ca2+ current amplitude. (B) Average peak Ca2+ currents amplitude during high-frequency trains normalized to the first amplitude and plotted vs. stimulus number (n = 5 cells). (C) Example traces of Ca2+ transients in response to a train of 20 APs at a frequency of 300 Hz measured with different Ca2+ indicators. Traces are averages of two to five sweeps; black lines represent exponential fits. (D) Inverse of the amplitude and time constants (τ) of Ca2+ transients in response to 20 APs at 300 Hz vs. κB. Lines represent linear fits; color-coding is identical to C.

Modeling Ca2+ Transients in an Unperturbed Bouton.

Because Ca2+ indicators perturb intracellular [Ca2+], we used back-extrapolation to κB = 0 in Figs. 2 and 5. Extrapolation, however, does not address wash-out of mobile buffers. We therefore developed a detailed model to analyze residual Ca2+ (Fig. 6) and active zone Ca2+ (Fig. 7) of the unperturbed terminal. The model cMFB included the experimentally determined endogenous buffers (Figs. 2–5), Ca2+ current amplitude (8), and Ca2+ current facilitation (Fig. 5). The predicted free [Ca2+] was calculated from Ca2+ indicator occupancy, similarly as experimentally performed (). Kinetic parameters of endogenous buffers were taken as experimentally determined values (see below). The remaining free parameters were optimized to reproduce the experimental data for single APs and trains of APs at 300 Hz with a single set of parameters (Fig. 6 ). With this model, we then analyzed Ca2+ transients in unperturbed boutons (without dyes, including mobile buffers), neglecting the possible influence of the intracellular solution on Ca2+-extrusion mechanisms. Adding a mobile buffer (corresponding to 100 µM EGTA) markedly speeded Ca2+ transients to a decay time constant of ∼26 ms (Fig. 6 ). Thus, our data suggest that residual Ca2+ decays with a time constant of ∼26 ms and summates to a few micromolar during high-frequency firing in unperturbed boutons.

Fig. 6.

Modeling Ca2+ transients in an unperturbed bouton. (A and B) Ca2+ transients elicited by a single AP (A) and a train of 20 APs at 300 Hz (B) recorded with different dyes superimposed with the corresponding model prediction (magenta). Bold lines are grand averages; gray shaded areas represent ±SD. The model was optimized to best reproduce all traces with a single set of parameters. (C and D) Simulation of a Ca2+ transient in response to a single AP (C) and a train of 20 APs at 300 Hz (D) at an unperturbed bouton (containing 100 µM of mobile buffer and no indicator dye).

Fig. 7.

Weak endogenous fixed buffers accelerate active zone Ca2+ signaling. (A) Visualization of the active zone model. The active zone contained 12 Ca2+ channels (red) spaced at 30 nm. The model simulated the influx, 3D buffered diffusion, and extrusion of Ca2+. For one point at a distance of 20 nm from the channel (cross), the [Ca2+] is shown during a train of 20 APs at 300 Hz (Upper Right). Note that the increase in peak amplitude is mainly due to the implemented Ca2+ current facilitation (Fig. 5 ). The collapse of the free [Ca2+] microdomain is illustrated for three time points after the first AP (t = 0 µs, 50 µs, and 1 ms; end of the AP defined as t = 0). Within 50 µs, the Ca2+ domains of individual Ca2+ channels collapsed to a microdomain Ca2+ signal, which itself collapsed within 1 ms. (B) Peak amplitude of local [Ca2+] at a distance of 20 nm from the Ca2+ channel during the 1st and 20th AP at 300 Hz was reduced by increasing κE,fixed (light and dark gray), but remained unaltered by increasing the concentration of mobile buffer (light and dark blue). The Ca2+ channel opening and the resulting local [Ca2+] are illustrated on the left. (C) Active zone Ca2+ clearance (defined as the time until the local [Ca2+] at 20 nm distance from the Ca2+ channel reaches 20% of its peak amplitude) was considerably slowed by increasing κE,fixed, being approximately fivefold longer for κE,fixed = 100 than for κE,fixed = 15. Active zone Ca2+ clearance was independent of the amount of mobile buffer between 0 and 200 µM. (D) Relative Ca2+ buildup during repetitive firing (defined as the [Ca2+] before the 20th AP normalized to the peak [Ca2+] of the 1st AP) was reduced by increasing κE,fixed up to 50 and by increasing concentrations of mobile buffer. (E) The spatial extent of active zone Ca2+ (defined as FWHM of a line profile through the center of the active zone 50 µs after the AP) decreased with increasing κE,fixed but was unaffected by the amount of mobile buffer.

Weak Endogenous Fixed Buffers Accelerate Active Zone Ca2+ Signaling.

How can cMFBs sustain synchronous vesicular release despite the substantial summation of residual Ca2+ during high-frequency firing? To address this question, we investigated the spatiotemporal dynamics of Ca2+ at the active zone and the influence of endogenous fixed and mobile buffers. We simulated active zone Ca2+ diffusion and buffering based on the model established above () during a train of 20 APs at 300 Hz. The local [Ca2+] of the 1st and 20th AP was analyzed at a distance of 20 nm from a channel (Fig. 7). We focused our analysis on four functionally important parameters: First, the local peak [Ca2+] of the 1st and 20th AP, which was markedly decreased with increasing κE,fixed, but increasing the slow mobile buffer concentration (0–200 µM), had little effect (Fig. 7). Second, the local Ca2+ clearance was defined as the time needed for [Ca2+] to decrease to 20% of the peak during the AP. Clearance was much faster for lower κE,fixed (fivefold acceleration with κE,fixed of 15 compared with 100), but depended little on the amount of mobile buffer (Fig. 7). Third, the relative Ca2+ buildup during repetitive firing was defined as the [Ca2+] before the 20th AP normalized to the peak [Ca2+] of the 1st AP. Increasing κE,fixed up to 50 reduced the relative buildup by a factor of ∼2, and increasing κE,fixed above 50 had no further effect. Increasing the mobile buffer concentration up to 200 µM reduced the relative buildup by a factor of ∼3 (Fig. 7). Fourth, the spatial extent of active zone Ca2+ was measured as full-width at half-maximum (FWHM) of a line profile through the center of the active zone 50 µs after the AP. FWHM was markedly enlarged with lower κE,fixed, but remained unaltered by changing the amount of mobile buffer (Fig. 7), consistent with previous analytical calculations of the length constant (mean distance a Ca2+ ion diffuses before being captured by a buffer molecule) (31, 32). To investigate the sensitivity of our results on the parameters of the model, we varied these parameters and obtained similar results to those shown in Fig. 7, revealing the robustness of our modeling approach ().

These data demonstrate that a low κE,fixed enables active zone Ca2+ signals with high amplitude, large spatial extent, and rapid decay. Furthermore, a high concentration of mobile buffer reduces the buildup of Ca2+ between APs. Thus, fixed endogenous buffers with low affinity and low Ca2+-binding ratio in combination with mobile buffers with high affinity seem ideally suited to speed active zone Ca2+ clearance and thus enable synchronous and reliable high-frequency transmission.

Ca2+ Signals at Different Distances from Active Zones.

The rapid clearance of Ca2+ from the active zone suggests that during an AP, Ca2+ rapidly diffuses from active zones into the center of the presynaptic terminal. One might therefore expect that [Ca2+] rises slightly slower at the center of the cMFB than at the edge where active zones are located. To experimentally confirm this prediction, we performed measurements with the low-affinity dye OGB-5N and with increased spatial and temporal resolution. High-resolution point and line measurements (5- to 10- and 1- to 3-kHz sampling rate, respectively) revealed extremely rapid rise kinetics at the edge of cMFBs (0.143 ± 0.01 ms; n = 20; average distance to edge, 278 ± 42 nm), significantly faster than at the center (2.20 ± 0.37 ms, n = 20; P < 0.001, unpaired t test; Fig. 8 ). The resolved difference in Ca2+ kinetics is most likely caused by equilibration of Ca2+ microdomains within cMFBs. In our cMFB model, the Ca2+ influx is restricted to the surface of the cylinder, representing the ∼300 active zones at the surface of cMFBs (Fig. 8). The model nicely reproduced the high-resolution Ca2+ measurements (Fig. 8), providing an independent validation of our modeling approach.

Fig. 8.

Ca2+ signals at different distances from active zones. (A) Example of a two-photon point scan (sampling rate, 10 kHz) close to the edge of a cMFB (230 nm). (Left) Two-photon image of bouton filled with 10 µM Atto594 and 200 µM OGB-5N. (Center) In response to an AP (arrowhead), a rapid rise of [Ca2+] was observed. Unfiltered data trace; average of 34 traces. (Right) Rise of [Ca2+] on expanded time scale superimposed with exponential fit (blue dotted line; time constant, 120 µs). (B) Example of two-photon line scan at 3-kHz resolution at the center and close to the edge of boutons. (Left) Two-photon image of a bouton filled with 10 µM Atto594 and 200 µM OGB-5N. (Right) In response to an AP (arrowhead), a faster rise of [Ca2+] was observed close to the edge of the cMFB compared with the center. Average of 49 traces each; blue and orange dotted lines are exponential fits, time constants are indicated. (C) Average rise time constants (n = 20 each, P < 0.00001, unpaired t test). (D) Illustration of the cylindrical cMFB model. Ca2+ influx occurs at the surface of the cylinder, where active zones are located. (E) Grand averages of subbouton Ca2+ signals superimposed with the model predictions at two distances from the surface (edge, 275 nm; center, 0.9 µm) as illustrated in D. Data were peak normalized and binned with 0.2-ms (edge, n = 20) or 0.3-ms bin duration (center, n = 20); error bars represent SEM.

From the high-resolution data at the edge of cMFBs, we additionally determined limits for the binding kinetics of the endogenous fixed buffers. The analyses (Fig. S5) revealed that koff must be >10,000 s–1, KD > 20 µM, and kon < 6 × 109 s–1⋅M–1, which is close to the upper diffusion limit. Our boundaries for koff and KD are similar to previous approximations at the calyx of Held presynaptic terminal (20, 33) and at chromaffin cells (34) and indicate that the endogenous fixed buffers at cMFBs are of low affinity with fast binding kinetics.

Weak Endogenous Fixed Buffers Enable Highly Synchronous Release.

To investigate whether the rapid clearance of Ca2+ from the active zone caused by weak endogenous fixed buffers promotes synchronous neurotransmitter release, we simulated the time course of release rate for a single AP (Fig. 9). The duration and amplitude of the vesicular release rate were highly dependent on κE,fixed. With κE,fixed = 15, the FWHM of the release rate was 114 µs, similar to previously measured values (27). With κE,fixed = 100, however, the FWHM was prolonged 2.8-fold (Fig. 9). These results had little dependence on the implementation of the release scheme (Fig. S6). Thus, the strength of endogenous fixed Ca2+ buffers limits the synchronicity of release.

Fig. 9.

Weak endogenous fixed buffers enable highly synchronous release. (A) Visualization of the active zone model (Fig. 7). Ca2+ channel to vesicle coupling distance was 20 nm. The release scheme was based on ref. 75; see Fig. S6 for details. (B) Comparison of the local [Ca2+] at the position of the vesicle (Middle) and release rate (Bottom) for a single AP (Ca2+ channel opening illustrated at Top) with different binding ratios of fixed buffer (κE,fixed = 15 and 100). Low κE,fixed leads to highly synchronous release.

Discussion

In this study, we identified the mechanisms controlling the speed of active zone Ca2+ signaling using quantitative two-photon Ca2+ imaging with submillisecond temporal and subbouton spatial resolution at central presynaptic terminals. We found a surprisingly low Ca2+-binding ratio of endogenous fixed buffers. Our experimentally constrained model revealed that such weak Ca2+ buffering enables rapid diffusional removal of Ca2+ from the active zone. Thus, our study provides a framework of presynaptic Ca2+ signaling explaining how central synapses can sustain fast and synchronous neurotransmitter release.

Low Ca2+-Binding Ratio.

Dissection of fixed and mobile Ca2+ buffers requires efficient control of the cytosolic solution. This procedure has been performed at few preparations such as chromaffin cells (23, 35) and dendrites dialyzed via somatic recordings (18, 36–39). Previous studies investigating κE at presynaptic terminals provided estimates ranging from ∼20 at hippocampal mossy fiber boutons (15), ∼56 at boutons of cerebellar granule cells (21), and ∼140 at boutons of layer 2/3 neocortical pyramidal cells (22), to up to ∼1,000 at the crayfish neuromuscular junction (40). Due to somatic or axonal loading in these studies, however, mobile buffers might have contributed, leading either to overestimation of κE,fixed or, as demonstrated in Fig. 3, to underestimation of κE,fixed. To our knowledge, a rigorous dissection of mobile and fixed buffers at presynaptic terminals has only been possible at preloaded and whole-cell dialyzed calyx of Held synapses (9) and at somatically loaded presynaptic terminals of retinal bipolar cells (10). At the calyx of Held, values for κE,fixed of ∼22 (25), ∼40 (14, 20), or ∼46 (41) have been determined. By systematic dialysis of cMFBs with Ca2+ indicators of different affinity, we demonstrate a Ca2+-binding ratio of the fixed buffers of ∼15 (Fig. 2). Thus, our data show that κE,fixed at cMFBs is lower than all previously determined values.

Because the estimate of κE,fixed depends on correct quantification of [Ca2+], we used three independent quantification approaches: two-photon Ca2+ imaging with dual-indicator quantification based on intrabouton calibration; two-photon Ca2+ imaging with single-indicator quantification based on an independent calibration approach (Figs. S1 and S2); and ratiometric Ca2+ imaging with Fura-2 using UV-epifluorescence excitation. The three independent methods were in excellent agreement, demonstrating the reliability of our quantification.

In addition, our high-resolution experiments revealed that the endogenous fixed buffers have low affinity (KD > 20 µM; Fig. S5), consistent with estimates at the calyx of Held (20, 33), indicating that fixed buffers are present at >300 µM concentration in cMFBs (calculated from κE = 15 and KD > 20 µM; Fig. S5).

Mobile Ca2+ Buffers with Slow Binding Kinetics.

By comparing remote and dialyzed boutons we demonstrate that—in addition to the background of fixed buffers—there is a small but substantial contribution of mobile Ca2+ buffers with slow, EGTA-like kinetics (Figs. 3 and 4). These high-affinity mobile buffers speed the decay of residual Ca2+ in cMFBs (Fig. 4) in a strikingly similar way to mobile buffers at the calyx of Held (9). In contrast, we found that mobile buffers had little impact on active zone Ca2+ clearance (see below). Simple calculation of the Ca2+-binding ratio of mobile buffers (κB = [B]/KD) results in ∼500. However, the concept of a binding ratio is only useful if Ca2+ and buffers are in kinetic equilibrium and if the equilibration time constant between slow buffers and Ca2+ is faster than the Ca2+-extrusion rate (23). At cMFBs, though, extrusion and equilibration time constant are both in the range of 100 ms (Figs. 2 and 5).

The molecular identity of endogenous mobile buffers is unknown at cMFBs, but Ca2+-binding proteins including parvalbumin, calretinin, and calbindin-D28k are obvious candidates (3, 42). Kinetically, parvalbumin seems a likely candidate for a slow buffer (9, 43). However, we found very weak expression levels of parvalbumin, calretinin, and calbindin-D28k assessed with immunohistochemistry in cMFBs, indicating that none of these proteins is a dominant Ca2+ buffer in cMFBs. Because Ca2+ transients were very similar in patched boutons in the presence of EGTA and in remote boutons in the presence of mobile buffers (Fig. 4), we used a mobile buffer with kinetics of EGTA in our simulations and did not implement any cooperativity (44, 45).

Speeding Active Zone Ca2+ Signaling.

We show that a low Ca2+-binding ratio of endogenous fixed buffers is essential for Ca2+ microdomains with high amplitudes, large spatial extent, and rapid clearance (Fig. 7). Although one could assume that a high κE,fixed has the potential to efficiently remove Ca2+ from the active zone, our results show the opposite, namely that a low κE,fixed speeds active zone Ca2+ clearance (Fig. 7). This finding can be explained by the acceleration of the apparent Ca2+ diffusion by reduced fixed buffers (46) and, intuitively, by less unbinding of Ca2+ from the fixed buffers in-between APs.

In addition, slow mobile buffers help to prevent facilitation of intracellular [Ca2+] during high-frequency firing but have little impact on active zone Ca2+ signals at cMFBs (Fig. 7 and Fig. S4). In contrast, mobile buffers seem to influence active zone Ca2+ signals at hippocampal mossy fiber boutons (47) and ribbon-type synapses (10, 48, 49). In these preparations, however, the mobile buffers have faster kinetics and/or the Ca2+ channel to vesicle coupling is less tight compared with cMFBs (8). Under these conditions, binding to the slow buffer and an acceleration of the apparent Ca2+ diffusion by mobile buffers (37, 46, 50) are expected to impact active zone Ca2+ signals. Furthermore, our data argue against substantial saturation of mobile buffers causing facilitation of release (38, 51). The low affinity of fixed buffers at cMFBs (Fig. S5) also prevents substantial saturation, which would allow slow buffers to impact local Ca2+ signals (43).

Thus, our results establish that active zone Ca2+ signaling is mainly accelerated by the lack of a large amount of fixed buffers allowing rapid diffusional collapse of local Ca2+ signals and by mobile buffers with slow kinetics that bind Ca2+ during fast repetitive firing. This concept of active zone Ca2+ signaling is consistent with the low κE,fixed found in cMFBs and the synchronous release of cMFBs during high-frequency transmission (8). The previously determined larger presynaptic κE,fixed and the slower firing regimes of the respective synapses corroborate the concept that the strength of endogenous fixed buffers limits the maximum synchronous transmission frequency.

Resolving Intrabouton Ca2+ Diffusion During Single APs.

In this study, we resolved local Ca2+ signals during the equilibration of microdomain Ca2+ at a mammalian central synapse (Fig. 8). Recently, local Ca2+ signals at synaptic and nonsynaptic regions were resolved with different rise time and initial amplitude at the calyx of Held synapse (20). Furthermore, local Ca2+ signals with long-lasting differences in amplitude were recorded at hippocampal mossy fiber boutons (52). In contrast, we measured complete Ca2+ equilibration within the first few milliseconds of a single AP. The fast rise time (∼140 µs) argues that our local Ca2+ signals were recorded very close to the Ca2+ entry site. The small size of cMFBs with active zones that are small (diameter, 160 nm) (53) and closely spaced (∼400 nm) (54) can explain the rapid equilibration (model prediction in Fig. 8).

Experimental high-resolution analysis of intrabouton Ca2+ diffusion is essential to understand Ca2+ dynamics at the active zone and to constrain computer simulations. Previously, comparable analyses of local Ca2+ signals have also been performed at neuromuscular junctions (2, 55), cerebellar synaptosomes (56), chromaffin cells (57), and inner hair cells (58). Our results at bona fide central synapses are consistent with the previous studies and extend our understanding of microdomain signaling by elucidating the differential role of endogenous fixed and mobile buffers for active zone Ca2+-signals.

Conclusion

The fixed endogenous Ca2+ buffers of cerebellar mossy fiber boutons are of low affinity and have a very low binding capacity. The buffering properties of cMFBs are ideal for rapid clearance of Ca2+ from the active zone, which allows synchronous release at high repetition rates. These data pinpoint the mechanisms allowing highly synchronous, fast neurotransmitter release at central presynaptic terminals.

Materials and Methods

Electrophysiology.

Cerebellar slices were prepared from P21–P61 CD-1, or C57BL/6 mice of either sex. Animals were treated in accordance with the German Protection of Animals Act and with the guidelines for the welfare of experimental animals issued by the European Communities Council Directive. Mice were anesthetized with isoflurane and killed by rapid decapitation; the cerebellar vermis was quickly removed and mounted in a chamber filled with chilled extracellular solution. Parasagittal 300-µm-thick slices were cut using a Leica VT1200 microtome (Leica Microsystems), transferred to an incubation chamber at 35 °C for ∼30 min, and then stored at room temperature until use. The extracellular solution for slice cutting, storage, and experiments contained (in mM) the following: NaCl 125, NaHCO3 25, glucose 20, KCl 2.5, CaCl2 2, NaH2PO4 1.25, MgCl2 1 (310 mOsm, pH 7.3 when bubbled with Carbogen [5% (vol/vol) O2/95% (vol/vol) CO2]). Presynaptic patch-pipettes were pulled to open-tip resistances of 6–16 MΩ (when filled with intracellular solution) from borosilicate glass (Science Products) using a DMZ Puller (Zeitz-Instruments). The intracellular solution contained (in mM) the following: K-Gluconate 150, NaCl 10, K-Hepes 10, Mg-ATP 3, and Na-GTP 0.3 (pH adjusted to 7.3 using KOH). Atto594 (10–20 µM) and one of the following Ca2+-sensitive dyes were added to the intracellular solution: OGB-1 (50 or 100 µM), Fluo-5F (50 or 200 µM), Fluo-4FF (100 µM), or OGB-5N (200 µM). Experiments were performed at 34–37 °C. We purchased Atto594 from Atto-Tec, Ca2+-sensitive fluorophores from Life Technologies, and all other chemicals from Sigma-Aldrich.

Cerebellar mossy fiber boutons were visualized with oblique illumination and infrared optics. Whole-cell patch-clamp recordings from cMFBs were made using a HEKA EPC10/2 amplifier (HEKA Elektronik). Presynaptic cMFBs were identified as previously described (8). Measurements were corrected for a liquid junction potential of +13 mV. Series resistance was typically <40 MΩ. APs were evoked in current-clamp mode by brief current pulses (amplitude 50–500 pA; duration 1–3 ms). For train stimulations (20 stimuli at a frequency of 300 Hz), brief depolarizations (0 mV, 200 µs) were applied in voltage-clamp mode. Ca2+ transients recorded in response to current injections (current-clamp) or short depolarizations (voltage-clamp) did not differ in amplitude or decay time constant (Fig. S1). In voltage-clamp experiments, the holding potential was −80 mV.

Quantitative Two-Photon Ca2+ Imaging.

Two-photon Ca2+ imaging was performed with a Femto2D laser-scanning microscope (Femtonics) equipped with a pulsed Ti:Sapphire laser (MaiTai, SpectraPhysics) tuned to 810 nm, a 60×/1.0 NA objective (Olympus) or 100×/1.1 NA objective (Nikon), and a 1.4 NA oil-immersion condenser (Olympus). Data were acquired in line scan mode, typically at a 1-kHz sampling rate. In a subset of experiments, we performed line- and point-scan measurements with a sampling rate of 3–10 kHz (Figs. 5 and 8 and Figs. S4 and S5). Background was measured outside of boutons in a neighboring area and subtracted. Imaging data were acquired and processed using Mes software (Femtonics).

We calculated the ratio (R) of green-over-red fluorescence to quantify intracellular [Ca2+] with Ca2+ indicators of different affinity. Using green and red indicators, [Ca2+] can be calculated as (13)

Minimum (Rmin) and maximum (Rmax) fluorescence ratios were determined with 10 mM EGTA or 10 mM CaCl2 in the intracellular solution, respectively. We performed these measurements in situ, i.e., in cMFBs or cerebellar granule cells to account for possible different dye properties in cytosol (17). Details of the calibration are described in . For the high-affinity dye OGB-1, we also compared single- and dual-indicator quantification methods, which gave very similar results ( and Figs. S1 and S3).

The decay of the Ca2+ concentration (C) was fit with an exponential function

where A0 was constrained to the baseline level calculated for 20–90 ms before stimulation. For display purposes, Ca2+ transients in the figures were digitally filtered using Igor Pro software (Wavemetrics; −3-dB filter cutoff frequency, 170 Hz) unless stated otherwise (Figs. 2, 5, and 8 and Fig. S5).

The two-photon signal is a convolution of the imaged structure and the microscope’s point-spread function. Typical dimensions of two-photon point-spread functions are <1 µm radially and <2 µm axially (59). Because most cMFBs have a diameter >3 µm (54), the heterogeneous fluorescence signal within boutons (Fig. 8) cannot be explained by artifacts due to partial overlap of the point-spread function with boutons but rather represents kinetic differences of the intrabouton [Ca2+].

Ratiometric Fura-2 Ca2+ Imaging.

In addition, presynaptic Ca2+ transients were recorded using Fura-2 (100 µM) and a Ca2+-imaging system (TILL-Photonics) with an excitation light source (Polychrome V) coupled to the epifluorescence port of the microscope (FN-1 with 100×/1.1 NA objective; Nikon) via a light guide, following previous descriptions (18, 33, 60). Fluorescence was measured with a back-illuminated electron-multiplying frame-transfer charge coupled device camera (iXon DU897; Andor Technology). Fura-2 fluorescence at both 350 and 380 nm was sampled every 10–30 ms; camera binning was 8 × 8. Background was measured in an area close to the patched bouton and subtracted. In these experiments, [Ca2+] was calculated as previously described (18, 33, 60)

and the effective dissociation constant (Keff) as

where α is the isocoefficient, KD the dissociation constant of Fura-2 (0.286 µM) (36), and R = F1/F2, where F1 and F2 are the background-subtracted fluorescence intensities at 350 and 380 nm, respectively. For Fura-2 experiments, Rmax and Rmin were measured in cells using 10 mM CaCl2 or 10 mM EGTA, respectively. The isocoefficient α was determined by adjusting α to obtain a Ca2+ independent sum of F1 + αF2 as previously described (35), resulting in a value of ∼0.05.

Estimation of Endogenous Buffer Ratio.

We used the “added buffer method” to estimate the endogenous buffering capacity at cMFBs (17). The incremental Ca2+-binding ratio of exogenous buffers (κB) was calculated as (14)

where [B] is the concentration of the exogenous buffer, [Ca2+]rest is the free Ca2+ concentration under resting conditions, and [Ca2+]peak = [Ca2+]rest + Δ[Ca2+]AP, where Δ[Ca2+]AP is the baseline subtracted amplitude of the AP-evoked Ca2+ transient. According to the single-compartment model, the decay time constant (τ) and the inverse of the amplitude (A–1) of the Ca2+ transient depend linearly on κB of the added buffer (4, 36)

where QCa is the charge flowing into the presynaptic terminal, F is the Faraday constant, V is the accessible volume of the terminal, and γ is the Ca2+-extrusion rate. We plotted A–1 and τ obtained from experiments vs. κB. Extrapolation of the linear regression line to κB = 0 yields an estimate of the Ca2+ transient without added exogenous buffer; the x axis intercept equals –(1 + κE) (4). Gluconate and nucleotides in the intracellular solution contribute an additional κ of ∼4.5 (61). We therefore added 4.5 to all κB values of the intracellular solutions in our analysis.

Confidence intervals of κE, A, τ, and γ estimates by back-extrapolation (Figs. 2 and 5) were determined by bootstrap procedures (62) implemented in Mathematica 10. An artificial dataset was taken from the original dataset, with replacement. Ten thousand datasets were generated and analyzed as the original dataset.

Dye Loading in Remote Boutons.

CMFBs were filled with 10–20 µM Atto594 for visualization and 200 µM Fluo-5F to record Ca2+ transients at remote boutons. Immediately after gaining whole-cell access, the red channel was used to locate a remote bouton along the same axon. Ca2+ transients were subsequently recorded at this remote bouton with APs evoked in current-clamp mode every 15–30 s. To describe the diffusion of dyes and endogenous mobile buffers, the mossy fiber axon was approximated by a semi-infinite cylinder. Consequently, the intensity of fluorescence reflecting the increasing dye concentration over time was fit using the following equation (63):

where F0 denotes the fluorescence at maximum dye concentration during steady state, x is the distance (constrained to the measured distance between patched and remote bouton in every experiment), D is the diffusion coefficient of the dye, and erfc is the complementary error function given as

Red and green fluorescence (i.e., 90-ms baseline before AP) was plotted vs. dye-loading time (Fig. 3) and fit using Eq. .

In all experiments, the resulting apparent diffusion coefficients were higher for Atto594 than for Fluo-5F (35.4 ± 7.0 and 20.5 ± 4.0 µm2⋅s−1, respectively). Therefore, we determined the concentration of the dyes separately from the fit with Eq. , referred to as [Atto] and [Fluo] in the following. For each time point of the dye loading, we calculated a corrected green-over-red ratio R* as

where [Atto]pipette and [Fluo]pipette are the red and green dye concentrations in the pipette, respectively. κB was determined with Eq. using the [Fluo] and Ca2+ transient amplitude. At the end of dye loading experiments, Ca2+ transients in remote boutons had a slightly faster decay and higher amplitude than in patched boutons (τ: 494 ± 55 vs. 681 ± 47 ms, P = 0.02; amplitude: 24.3 ± 3.4 vs. 19.7 ± 1.1 nM, P = 0.1; n = 26 and 57, respectively). This difference is consistent with lower dye concentrations in remote compared with patched boutons, as expected from Eq. and the limited time course of these experiments. In our analysis, we did not correct for differences in z-depth between patched and remote boutons, as fluorescence ratios were <20% different up to 100-µm depth measured with sealed pipettes.

Ca2+ Current Recordings.

In some experiments (Fig. 5 ), we pharmacologically isolated presynaptic Ca2+ currents during cMFB whole-cell patch-clamp recordings as previously described (8). Ca2+ currents were elicited by step depolarizations of 200-µs duration from −80 to 0 mV. Ca2+ currents were corrected for leak and capacitance currents using the P/4 method. In these experiments, the extracellular solution consisted of (in mM) the following: NaCl 105, KCl 2.5, NaH2PO4 1.25, NaHCO3 25, glucose 25, CaCl2 2, MgCl2 1, TTX 0.001, 4-AP 5, and TEA 20. The presynaptic patch pipette contained (in mM) the following: CsCl 135, TEA-Cl 20, MgATP 4, NaGTP 0.3, Na2phosphocreatine 5, Hepes 10, and EGTA 0.2.

Modeling of Spatiotemporal Ca2+ Diffusion and Buffering.

The model simulated the time course of Ca2+ influx and buffered diffusion in a cMFB, using a finite-difference scheme (51, 64–66). Previous electrophysiological experiments (8) and our Ca2+-imaging measurements constrained key parameters of the model (Table S1). Simulations were implemented in CalC 7.7.4 (67); further evaluations were performed with Wolfram Mathematica 10. All calculations were executed on a MacBook Pro computer with 2.7-GHz Intel Core i7 processor and 16-GB RAM operating on Mac OS X 10.8.

When simulating Ca2+ dynamics in the whole cMFB (Figs. 6 and 8), we assumed a cylindrical morphology, 1.8 µm in diameter and 24.8 µm in length, to reproduce the Ca2+ transients recorded with the various dyes (Fig. 6) and the diffusional properties within cMFBs (Fig. 8). Grid size of the model was set to 20 points in radial and longitudinal dimensions (increasing grid size did not change the results). The AP-evoked Ca2+ current influx at the surface of the cylinder was approximated by a Gaussian of 99-µs FWHM and 543-pA peak amplitude (8). The simulations included fixed endogenous buffers, ATP, gluconate (Table S1), and the following Ca2+ extrusion pump mechanism, which was implemented with the Ca2+ flux, J, defined as

where γ = 0.14 µm⋅ms–1, Vmax = 0.25 µM⋅µm⋅ms–1, n = 2.5, and KD = 3.7 µM. J has units of µM⋅µm⋅ms–1 = 10−6 mol⋅m–2⋅s–1. The second nonlinear component of the definition describes the speeding of Ca2+ extrusion at higher [Ca2+], e.g., during 100-ms depolarization to 0 mV, and is based on previous analyses of Ca2+ extrusion mechanisms (28). The parameters Vmax, n, and KD were adjusted to reproduce the measured Ca2+ transients elicited by single APs and trains of APs (Fig. 6 ). The model did not include an axon, but diffusion of Ca2+ into the mossy fiber axon would be pooled in the implemented extrusion mechanism.

When modeling Ca2+ dynamics on a fine spatial scale at a single active zone (Fig. 7), we represented the active zone with a rectangular box (65). To reduce simulation time we took advantage of the assumed symmetry with respect to two perpendicular planes and considered only a quarter of this volume comprising three Ca2+ channels. The x-y dimensions were 0.23 µm (corresponding to half of the distance between neighboring active zones) (54), and the z dimension was 1.0 µm. The active zone model had a spatial grid of 50 × 50 × 30 points (x,y,z), with slight stretching implemented in the corner containing the channels (51). Boundary conditions on all side surfaces were set to be no flux and on the top surface to Dirichlet (boundary value clamped to background [Ca2+]). On the bottom surface (Ca2+ channel plane), the Ca2+ extrusion pump (Eq. ) was added. Parameters used in the simulations are given in Table S1. Binding rates of EGTA were taken from ref. 68, which were estimated at physiological temperature and pH 7.3. The resulting KD was 200 nM, which is similar to commonly used parameters estimated at room temperature (69, 70). To analyze unperturbed active zone Ca2+ signaling, active zone simulations included ATP and fixed and mobile buffers as stated (Fig. 7) without gluconate.

Per active zone, 12 open Ca2+ channels with a single channel current of 0.15 pA (71) and a duration of 105 µs (8) were assumed. The number of Ca2+ channels is thus constrained by the measured Ca2+ influx per AP in cMFBs (macroscopic Gaussian-like Ca2+ current with half-duration of 99 µs, and peak amplitude of 543 pA) (8), assuming 300 active zones per cMFB (54). The distance between Ca2+ channels was 30 nm, consistent with freeze-fracture replica labeling (8). Channel open times were fixed for all channels, and single channel open probability was set to 1. Stochastic implementation of an open probability < 1 (71) would result in a larger number of channels per simulated active zone due to the constraint by the measured Ca2+ influx. A larger number would increase the net distance between open channels, which was addressed in the following sensitivity analysis.

To investigate the sensitivity of simulations on model parameters, we systematically varied the number of open Ca2+ channels (range, 4–36), single channel conductance (range, 0.05–0.4 pA), distance between Ca2+ channels (range, 10–60 nm), and the distance of the position where the local Ca2+ concentration was sampled to the nearest Ca2+ channel (range, 10–60 nm). Furthermore, the number of x-y grid points (range, 10–80) and CalC accuracy parameter (range, 10−1–10−7) were varied. As expected from previous studies investigating the impact of Ca2+ distribution on synaptic release (20, 65, 66, 72–74), the peak local [Ca2+] was different when we varied the model parameters (range, 12–122 µM). However, the main finding of this study—the speeding of active zone Ca2+ signaling with low κE,fixed—was very robust with all tested parameters (fold-change of clearance time for κE,fixed of 15 and 100 as indicated in Fig. 7 ranged from 3.2 to 8.9).

Modeling of the Release Time Course.

To simulate the time course of vesicular release rate at cMFBs, we used the described model of the active zone and included a release sensor at 20-nm distance from the nearest Ca2+ channel. The release scheme was taken from ref. 75 and was adjusted for physiological temperature and a release probability of 0.3 (76). To test the sensitivity of our findings on the used release scheme, we systematically compared several release schemes as explained in detail in Fig. S6.

Data Analysis.

Statistical comparisons were performed via two-sided paired or unpaired Student t tests; P < 0.05 was considered significant. Means are expressed ± SEM except where stated.