Bassoon Speeds Vesicle Reloading at a Central Excitatory Synapse

Summary Sustained rate-coded signals encode many types of sensory modalities. Some sensory synapses possess specialized ribbon structures, which tether vesicles, to enable high-frequency signaling. However, central synapses lack these structures, yet some can maintain signaling over a wide bandwidth. To analyze the underlying molecular mechanisms, we investigated the function of the active zone core component Bassoon in cerebellar mossy fiber to granule cell synapses. We show that short-term synaptic depression is enhanced in Bassoon knockout mice during sustained high-frequency trains but basal synaptic transmission is unaffected. Fluctuation and quantal analysis as well as quantification with constrained short-term plasticity models revealed that the vesicle reloading rate was halved in the absence of Bassoon. Thus, our data show that the cytomatrix protein Bassoon speeds the reloading of vesicles to release sites at a central excitatory synapse.

(patch pipette out of focus, on the right, scale bar 5 µm).
(B) Stimulus response curve showing the mean EPSC amplitude including (black) or excluding failures (grey) versus stimulus intensity. The small number of synapses onto the granule cell (~4) and the diffuse network of mossy fibres in the granule cell layer allowed the activation of single mossy fibre synapses with an electrode placed in the surrounding tissue (Silver et al., 1996). Insets: Infrared differential interference contrast microscopic image of an acute cerebellar brain slice superimposed with an illustration of the pipettes. The white matter (wm) is indicated. The other layers are indicated as in panel A (scale bar 50 µm). Consecutive EPSCs elicited at the indicated stimulus intensities are shown (stimulus artefact blanked for clarity, scale bar: 50 pA, 1 ms).
(D) Average phasic EPSC amplitude versus time for a 20, 100 and 300 Hz stimulation for control (black; n = 23) and Bsn ΔEx4/5 mice (grey; n = 17; normalized to the 1st EPSC within the train; error bars indicate SEM; asterisks indicate significant differences; note the logarithmic scale).
(E) The steady-state EPSC amplitude (see brackets in panel D) of phasic and tonic EPSC amplitudes for control (black; n = 23) and Bsn ΔEx4/5 mice (grey; n = 17). Bsn -/mice (right) recorded at 23°C. Bi-exponential fits to the current decays are superimposed (single components: red and blue; sum: green dashed).

Figure S3 (related to Figure 3)
Evoked EPSC amplitudes recover more slower from synaptic depression in Bsn ΔEx4/5 at 23°C and Bsn -/at 37 °C than control mice (A) 20 consecutive current traces elicited by a 300 Hz train followed by test stimuli of increasing intervals (the first 2 out of 6 are shown) recorded in a control mouse. The average is superimposed in black.
(B) Average phasic EPSC amplitude of the first two EPSCs elicited after the 300 Hz train versus time for control (black; n = 23) and Bsn ΔEx4/5 mice (grey; n = 17; asterisks indicate significant differences). Bi-exponential fits (solid lines; constrained to reach 100 %) are superimposed.
(C) Example traces from a control mouse including EPSCs during the trains and the entire 5 s lasting recovery phase of stimuli with increasing intervals following the train. The stimulus sequence is illustrated above each trace.
(D) Average EPSC amplitudes during the recovery from 20, 100 and 300 Hz stimulation for control (black; n = 23) and Bsn ΔEx4/5 mice (grey; n = 17). Mono-(20 Hz) and a bi-exponential fits (100 and 300 Hz) to the average time courses are shown with the corresponding time constants and amplitude proportion of the 1st component. Fits were constrained to reach 100 %.
(E) Corresponding fits to the time course of recovery measured in Bsn -/mutants and control mice at 37°C. (B) Parameters of the models 1, 2, and 3 are plotted in green, blue, and red, respectively, versus time during the 300 Hz train experiments. For model 2, the resting reloading rate of 8 0.5 s -1 is indicated. Below, the assumed residual intra-terminal calcium concentration and the quantal size are plotted in black.  Figure 7A and C are highlighted in pink. Linear fits (constrained to go through the origins) had slopes (s) as indicated in the graphs. The correlations were significant (non-parametric Spearman correlation coefficient, r > 0.8 and > 0.3 for quantal content and CV; P < 0.05 throughout). (E and F) Corresponding data for model 3.
Whole-cell patch-clamp recordings were performed from granule cells with an EPC10/2 amplifier (HEKA Electronics, Lambrecht/Pfalz, Germany). Granule cells were identified as previously described (capacitance of < 5 pF; (Silver et al., 1996)). Recordings were discarded if access resistance was >35 MΩ (in some recordings series resistance compensation was enabled with <90 % correction and 10 µs lag). Most granule cells were from lobe V, but there was no obvious correlation between the degree of synaptic depression and the localization of the granule cell within the cerebellum or the age of the animal. The pipette solution contained (in mM): 150 K-gluconate, 10 NaCl, 3 Mg-ATP, 0.3 Na-GTP, 10 Hepes (pH 7.3). In some experiments, 100 µM Alexa 488 was added to the patch solution and the epifluorescence signal was viewed with a CCD camera (iXon DU 897, Andor, Belfast, United Kingdom).
Single mossy fibres were stimulated as described previously (Silver et al., 1996) with a patch electrode filled with ACSF placed on the surface of the surrounding tissue ( Figure S1B; 0.1-10 V, duration 100 µs). In some experiments, bipolar stimulation with a theta-glass pipette was used. To facilitate finding mossy fibre inputs, in some experiments, stimulation pipettes were guided near dendritic glomeruli apparent in the fluorescence signal of Alexa 488 filled granule cells.
EPSCs were recorded at -80 mV (corrected for the liquid junction potential of 13 mV), sampled at 200 kHz (EPSCs at 1 Hz) and 20 kHz (trains of EPSCs) and filtered at 10 kHz.
The amplitude and the kinetic properties of EPSCs were analyzed from the averages of about 20 EPSCs elicited at 1 Hz. The stimulus artefacts of EPCSs recorded at 37°C were removed by subtracting a double-exponential fit to the decay of the artefact current (Saviane and Silver, 2006b). The coefficient of variation (CV) was calculated as the standard deviation of the peak EPSC amplitude divided by the mean EPSC amplitude. The decay was fitted with the sum of two exponentials (baseline constrained to zero) and t = 0 was defined as the peak of the EPSC. Amplitude-weighted decay time constants, τ w , were calculated as (A 1 τ 1 + A 2 τ 2 )/(A 1 + A 2 ), where A 1 and A 2 are amplitudes and τ 1 and τ 2 are time constants of the components.
At each investigated MF-GC connection, the size of the spontaneous EPSCs was estimated with a template matching algorithm under resting conditions (Clements and Bekkers, 1997) implemented in Neuromatic software (www.neuromatic.thinkrandom.com). Exponential fits ( Figure 3 and S3) were weighted with the reciprocal of the standard deviation of the experimental errors (note that the error bars represent the standard errors in the figures). The estimated errors of the fit parameters were taken from Igor Pro and represent standard deviation.

Analysis of pre-and postsynaptic mechanisms of short-term plasticity with EPSC fluctuation analysis
In a subset of the investigated MF-GC connections, in which more than five 300 Hz trains were elicited at >30 s intervals, the variance of the phasic EPSC amplitude was calculated from sequential trains. To account for quantal jitter, the phasic EPSC amplitude was determined as the difference of the mean amplitude within an 100 µs window directly before the stimulus and at the time of the peak of the average EPSCs (Sargent et al., 2005;Saviane and Silver, 2006a). The variance of the variance was calculated according to eq. 50 in Saviane and Silver (2006a) and the error bars in Figure 5C represent the corresponding standard deviation, which were used to weight the linear fit. Based on a binomial model for synaptic transmission, the variance of the EPSC amplitude depends on the quantal size (q; defined as the mean quantal size at the time of the peak of the EPSC), the number of release sites (N), and the release probability per site (p r ), resulting in a parabolic dependence of the EPSC variance on the average EPSC amplitude. To estimate the reduction in q during 300 Hz trains, the relationship between the variance (σ I 2 ) and the mean (I) of the steady state EPSCs at the end of the train (the last 15 of 20 EPSCs) were fit with the linear function: CV QI and CV QII are the coefficients of variation of intrasite and intersite quantal variability, respectively (Silver, 2003). CV QI includes the variance arising from jitter in the quantal events at the peak of the mean EPSC. CV QI and CV QII were constrained to values previously obtained at MF-GC connections [0.39 and 0.31, respectively (Sargent et al., 2005)]. We here adopt the concept that the effective release probability consists of the product of the probability that a vesicle is release ready at a release site (which also can be considered as occupancy of a release site) and the release probability of such a release ready vesicle (Scheuss et al., 2002).
Thus, eq. 1 is based on the assumption that during steady-state depression at the end of the train, the effective release probability per site is low because the occupancy is reduced due to depletion while p r per occupied site (i.e. per vesicle) might still be high (as apparent in the model calculations, cf. p r1 and p r2 in Figure S4B). Next, N was estimated by fitting the 1 st EPSC of the train in the variance-mean relationship with the function (2) q fix was determined independently from the mean peak amplitude of spontaneous EPSCs (q) recorded at the corresponding MF-GC connection (cf. Figure 2C-E) and includes a scaling factor to account for jitter in the latency of quantal release, where q fix = q (15.8pA/18.4pA) corresponding to the previously determined ratio of the stimulus aligned and rise aligned quantal responses (Sargent et al., 2005). The resting p r was calculated by dividing the mean amplitude of the 1 st EPSC by N q fix . To correct for contributions arising from glutamate spillover at MF-GC connections, q determined during the train was increased by 20 % and N was decreased by 28 % (Sargent et al., 2005).

Analysis of vesicle reloading at MF-GC synapses
At each investigated MF-GC connection, at least one but in most cases 3 trains of stimuli at 20, 100 and 300 Hz each (100,100, and 20 stimuli, respectively) were recorded interleaved with intervals of >30 s. Each train was followed by stimuli of increasing intervals (Magleby, 1987): 25, 50, 100, 300, 1000, 3000 ms (after 20 Hz trains the 25 and 50 ms interval were skipped).
To estimate the rate of vesicle reloading at individual MF-GC connections in control and Bassoon mutant mice, we used three established mechanistic models of vesicle recruitment to describe simultaneously the time course of the phasic EPSC amplitudes elicited during and after 20, 100, and 300 Hz stimulations ( Figure 6). In model 1, a MF-GC connection was characterized by N readily releasable vesicles with a release probability (p r ) at N tot release sites (assuming 100% occupancy under resting conditions). Each release site can be reloaded from an infinite pool of releasable vesicles with the rate constant, k, resulting in the following differential equation for the number of ready releasable vesicles (N): In model 2, the rate of vesicle reloading was assumed to depend on the elevation of the intraterminal calcium concentration (Dittman and Regehr, 1998;Hosoi et al., 2007). Thus, in eq. 3, k was replaced with k defined according to eq. 5 of Dittman and Regehr (1998): where k 0 is a Ca 2+ -independent component of reloading, k Ca is the maximal rate of vesicle reloading and K D is the residual calcium (ΔCa 2+ ) at which the Ca 2+ -dependent component reaches its half-maximal value. A linear build up of ΔCa 2+ was assumed, where each AP leads to a constant increase in ΔCa 2+ by 0.4 µM (Trommershäuser et al., 2003) and decays mono-exponentially with a time constant of 12 ms (Saviane and Silver, 2006b; see [Ca 2+ ] in Figure   S4B). In a recent study, slower residual calcium transients were observed in cerebellar MF terminals of turtles (Thomsen et al., 2010), however, the transients were probably distorted by the high-affinity calcium indicator used at an ill-defined concentration. We also tested a model with linear dependence on intra-terminal calcium concentration (data not shown ;Hosoi et al., 2007), however, the predicted depression during 300 Hz stimulation was too small. Finally in model 3, a MF-GC connection is characterized by N 2 readily releasable vesicles with a high release probability (p r2 ) and N 1 readily releasable vesicles with a lower release probability (p r1 ). N 2 is limited by N 2,tot release sites, which are refilled with the rate constant k 2 . N 1 is defined by the equilibrium with a pool of releasable vesicles (N 0 ) with a refilling rate constant k +1 and the back-rate k -1 (thus, at the beginning of the simulation, t = 0, N 1 (0) = N 0 (0) k +1 / k -1 ). N 1 (0) might be considered as the number of functional release sites with low release probability [referred to as low p r sites in the following; see e.g. Weis et al. (1999) for discussion of vesicle state models versus release site models]. Finally, N 0 is refilled from an infinite pool of reserve vesicles with a refilling rate constant k +0 and the back-rate k -0 (thus, N 0 (0) = k +0 / k -0 ). The number of vesicles in the three pools (N 2 , N 1 and N 0 ) is defined by the following differential equations: In all three models, the release probability p r changed according to short-term facilitation in an activity-dependent manner. In model 1 and 2, a simple model of short-term facilitation was implemented (Markram et al., 1998;Saviane and Silver, 2006b): starting from a resting release probability (p r,rest ), each action potential increases p r by the amount p r,rest (1-p r ). p r then decays mono-exponentially back to p r,rest with a time constant of 12 ms (Saviane and Silver, 2006b). To describe the release probabilities of both pools in model 3 with a single free parameter, p r1 and p r2 were defined according to a biophysical model of facilitation assuming different distances of the vesicles to the calcium channels (Trommershäuser et al., 2003). All other parameters describing the intracellular calcium dynamics were taken from Trommershäuser et al. (2003) only the exponential decay of the intracellular residual calcium after an action potential was constrained to 12 ms (Saviane and Silver, 2006b). α was used as a single free parameter to define p r1 and p r2 , which approximately obeyed the relation p r1 ≈ 0.5 p r2 . Note that both models of facilitation led to similar results when implemented in model 1, 2 and 3, i.e., using either the biophysical-based facilitation (Trommershäuser et al., 2003) with model 1 and 2 (neglecting p r1 ) or using the phenomenological facilitation (Markram et al., 1998) with model 3 (assuming p r1 = 0.5 p r2 ) led to similar EPSC amplitudes during and after the trains and consequently similar values of p r , N, and k for each investigated MF-GC connection (data not shown).
For the simulation, we assumed the following changes of the quantal size (q) during shortterm plasticity: (1) Based on the spontaneous EPSCs (Figure 4) Hz experiments (Figure 4). The resulting time course of q is shown in Figure S4B for the 300 Hz train and the recovery.
We tested how strongly our conclusions depend on the exact assumptions of the quantal size during and after the train. Small spontaneous EPSCs at the end of the train might be missed with the template detection method. We therefore increased the steady state depression of q by 14 % for all frequencies, resulting in a steady-state q of 51, 59 and 85 % during 300, 100 and 20 Hz trains. The average resulting best-fit parameters of model 3 were: k = 117 ± 30 and 50 ± 12 s -1 (P < 0.05), p r2 = 0.86 ± 0.06 and 0.84 ± 0.05, N 2 = 1.9 ± 0.2 and 2.3 ± 0.3, n = 13 and 11 for control and Bsn -/at 37°C, respectively. In addition, no postsynaptic component was assumed. The average resulting best-fit parameters of model 3 were: k = 38 ± 6 and 21 ± 2 s -1 (P < 0.05), p r2 = 0.80 ± 0.04 and 0.75 ± 0.04, N 2 = 1.9 ± 0.2 and 2.1 ± 0.2, n = 13 and 11 for control and Bsn -/at 37°C, respectively. In summary, the absolute rate of vesicle reloading depends on the assumed degree of postsynaptic depression, however, under all tested conditions, the rate of vesicle reloading was significantly lower in Bsn -/and Bsn ΔEx4/5 compared with corresponding controls. Finally, the models were constrained to go through the first point of the trains (i.e. N or N 2 was not a free parameter but was a function of the release probability to result in a 1 st EPCS amplitude which was equal to the average of the 1 st EPSC amplitudes of the 20, the 100 and the 300 Hz trains). However, while the underestimation of the 1 st EPSC amplitude in model 1 (see green lines in Figure 6B-D) was removed with this constrain, the best-fit parameters of model 2 and 3 were very similar to the values without that constrain (data not shown).

Estimation of model parameters
To obtain robust parameter estimates from individual MF-GC connections, the slow component of recovery after depression was constrained to 2 s as found on average in control and Bassoon mutant mice at 23 and 37°C (see Figure S3). Thus, in model 2, k 0 , which defines the slow recovery after the trains (when ΔCa 2+ ≈ 0), was constrained to 0.5 s -1 .
Correspondingly in model 3, k 2 , which defines the slow recovery after the trains in model 3, was constrained to 0.5 s -1 per release site N 2 . For model 2, K D was first used as a fourth free parameter for fitting the average control data. The obtained value of 168 nM was fixed in subsequent simulations to increase the robustness of the fit results. The MF synaptic contact is one of the smallest in the brain (160 nm diameter; Hamori and Somogyi, 1983) with an area threefold smaller than those at climbing and parallel fibres, which have 7-8 docked vesicles (Xu-Friedman and Regehr, 2003). Therefore, in model 3, the number of low p r sites was constrained to the limiting case of four per high p r site [i.e. N 1 (0) = 4 N 2,tot and thus k -1 = N 0 (0) k +1 /(4 N 2,tot )], which would correspond to a vesicle density twice that at climbing and parallel fibre synaptic contacts (Saviane and Silver, 2006b). Finally, in model 3, the number of releasable vesicles, N 0 (0), was constrained to 300 per low p r site (Saviane and Silver, 2006b) and the refilling rate, k +0 , was constrained to 8 vesicles s -1 (Saviane and Silver, 2006b) [i.e.
The remaining three free parameters, p r,rest , N tot , and k in model 1, p r,rest , N tot , and k Ca in model 2, and p r2,rest , N 2,tot , and k +1 in model 3 were determined for each investigated MF-GC connection (see below). For simplicity, the suffixes rest and tot were omitted in the main text and Figs. 6, 7 and S6 [i.e. p r,rest , N tot , p r2,rest , and N 2,tot are referred to as p r , N, p r2 , and N 2 , respectively]. Furthermore, note that for a direct comparison of all models the rate k +1 is referred to as the rate per release site and not per vesicle in pool N 0 [i.e. as 300 k +1 ].
Since in model 3, the effective rate of vesicle reloading depends on the rate per releasable vesicle (k +1 ) and the number of releasable vesicles (N 0 ), we aimed to dissect whether the effective rate of vesicle reloading is reduced due to a slower rate of reloading per vesicle (k +1 ) or due to fewer releasable vesicles [N 0 ; cf. reduced number of clustered vesicles found in Bassoon and Piccolo double knockout mice (Mukherjee et al., 2010)]. To this end, we repeated the simulations without constraining the releasable vesicles per low p r site to 300 but instead used N 0 (0) as a fourth free parameter. The following parameters were obtained from the average data: N 0 (0) = 1258 and 778 (127 and 78 per low p r site), k +1 = 0.45 and 0.35 s -1 , p r2 = 0.78 and 0.72, and N 2 = 2.46 and 2.49, for control and Bsn -/at 37 °C (fits to the average as in Figure S6E). Comparable parameters were obtained from the individual MF-GC connections. Although the variability in the four parameters estimated from individual MF-GC connections was too high to result in statistically significant differences between control and Bsn -/-(P > 0.5), the resulting effective rate of vesicle reloading per low p r site was on average significantly different (N 0 (0) k +1 / [4 N 2,tot ] = 54 ± 14 and 26 ± 4 s -1 , n = 13 and 11, for control and Bsn -/at 37 °C, respectively; P < 0.05; cf. similar values obtained with model 3, see Figure 8A). Comparable results were obtained with Bsn ΔEx4/5 and controls at 23 °C.
These data thus indicate that the impaired vesicle reloading in MF-GC connections of Bassoon deficient mice might in part be due to less available vesicle for release, which might also explain the delayed depression during the trains in Bsn -/and Bsn ΔEx4/5 ( Figure S6).
However, the mathematical description of the reloading rate as the product of a rate per vesicles and the number of releasable vesicles is most likely a simplification. Vesicles near the release site are probably reloaded more rapidly compared with more remote vesicles.
Thus, our finding that already the 2 nd EPSC in 300 Hz trains was significantly reduced in Bsn -/and Bsn ΔEx4/5 (Figure 1 and S1) indicates that rapid reloading processes near the AZ (which are probably independent of the number of remote vesicles) were severely impaired in Bassoon deficient mice. Alternatively, a slight increase in the release probability, which was not detected with fluctuation analysis nor with the short-term plasticity models, could contribute to the rapid onset of depression in Bsn -/-.
To further address the robustness of the estimated model parameters, the experimentally determined quantal content and the CV of the peak EPSC amplitude under resting conditions ( Figure 2E and B) were compared with the values estimated from the models on the basis of the train experiments for each MF-GC connection (Figure 7 and S6). The CV was calculated as CV = σ/mean, where σ 2 was defined as (Silver, 2003): and the mean as N q p r . The intrasite and intersite quantal variability CV QI and CV QII were constrained to values previously obtained at MF-GC connections [0.39 and 0.31, respectively (Sargent et al., 2005)]. The quantal size was calculated from the amplitudes of the spontaneous EPSCs as described above [i.e. 14% reduction (Sargent et al., 2005)]. For model 3, CV was defined as the square root of the sum of the variance of pool 1 and pool 2 divided by the mean (N 2 q p r2 + N 1 q p r1 ), assuming uncorrelated linearly adding variances of pool 1 and pool 2.

Implementation of the simulations
Starting from the analytical solution of the differential equations, the number of vesicles within the pools were numerically calculated with a fifth-order Cash-Karp Runge-Kutta method with adaptive step-size control (Hallermann et al., 2010;Press et al., 2002). The change in p r was calculated analytically (Markram et al., 1998;Saviane and Silver, 2006b) or numerically (Trommershäuser et al., 2003). The phasic EPSC amplitude was calculated by the number of released vesicles per stimulus [p r (t) N(t) and for model 3, p r2 (t) N 2 (t) + p r1 (t) N 1 (t)] multiplied by the quantal size [q(t); see Figure S4B], assuming linear summation of the quanta (Sargent et al., 2005;Saviane and Silver, 2006b).
Simulations were implemented in C++ (XCode 3.0, Developer Tool, OS X, Apple, Cupertino, CA, USA). A simplex algorithm (Press et al., 2002) was used to optimize the free parameters for each MF-GC connection consecutively. Subsequently, the three trains of all investigated MF-GC connections were plotted with the predictions of the model superimposed using Mathematica 5.0 (Wolfram Research, Champaign, IL, USA) for visual inspection. Simulation and plotting lasted only several seconds on a conventional 2.7 GHz dual core computer, which allowed to gain a better understanding of the reliability and the constrains of the parameters. After the fit was completed, internal estimates of the errors of the best-fit parameters were calculated as the square roots of the diagonals of the covariance matrix (Colquhoun et al., 2003). To confirm that the global minimum was reached, the best-fit parameters were shown to be independent of the starting values within a plausible range.

III. SUPPLEMENTAL DISCUSSION OF THE SHORT-TERM PLASTICITY MODELS
As a starting point, we used the simplest possible model, in which a synaptic connection is characterized by a number of readily releasable vesicles (N) with a release probability (p r ) and a rate of vesicle reloading at an empty release site (k) from an inexhaustible reserve pool (model 1, Figure 6 green, see Supplemental Experimental Procedures for more details). Fitting this simple model, simultaneously, to the EPSC amplitudes during and after the 300, 100 and 20 Hz data in controls gave an estimate of ~10 N with an p r of 0.37 and a k of 26 s -1 .
The average phasic EPSC amplitudes are compared with these best fit predictions of model 1 in green for control mice ( Figure 6B-D). During the 300 Hz train ( Figure 6B), N was depleted to 25 %, but the p r was increased to 0.61 from 0.37 according to a simple model of facilitation (Markram et al., 1998;see [Ca 2+ ] trace in Figure S4 and Supplemental Experimental Procedures). This model of facilitation in combination with the kinetics of vesicles reloading predicted the presynaptic overshoot after the high-frequency stimulations (cf. green line in Figure 4C), which is not apparent in Figure 6 because the postsynaptic component of shortterm plasticity (see q trace in Figure S4) was included in the calculations. However, the model could not account for the recovery at intermediate times following 20 Hz stimulation, or the prominent slow component of the presynaptic recovery. Moreover, p r predicted by the model was lower than estimates from fluctuation analysis both here ( Figure 5D) and in previous studies (Sargent et al., 2005;Saviane and Silver, 2006b). We therefore applied a more sophisticated plasticity model that included Ca 2+ -dependent vesicle replenishment.
In the second model ( Figure 6, blue), the rate of vesicle reloading, k 0 , was accelerated by residual calcium concentration in the terminal in a Michaelis-Menten-type manner (see eq. 4 in Supplemental Experimental Procedures; Dittman and Regehr, 1998). The rate k 0 was set to 0.5 s -1 to reproduce the slow component of the recovery (~2 s; Figure S3D and E) and K D and k Ca were used as free parameters. The data were best described with K D = 168 nM and k Ca = 41 s -1 (see Figure S4 and Supplemental Experimental Procedures for details on the assumed calcium dynamics; to fit individual MF-GC connections, K D was constrained to 168 nM while k Ca remained a free parameter). During the 300 Hz trains the assumed calcium reached values of ~1 µM and, thus, the rate of vesicle reloading was accelerated to ~40 s -1 .
Since Ca 2+ -dependent vesicle reloading is difficult to disentangle from the Ca 2+ dependences of release and facilitation and from postsynaptic saturation (where present), we examined whether the time courses of depression and recovery at the different frequencies could be accounted for by a Ca 2+ -independent vesicle reloading mechanism. To account for the steadystate depression, the slow component of the depression at 20 Hz, together with the fast and slow components of the recovery following trains, we developed a model with a pool of vesicles that could be recruited and a subsequent maturation step that increased the release probability of a fraction of the vesicles. In this third model (Figure 6, red), release at a MF-GC connection was described by N 2 ready releasable vesicles with a high release probability, p r2 , and N 1 release sites with a lower release probability, p r1 . The vesicles in N 1 are in equilibrium with a large pool of N 0 releasable vesicles [N 0 ;Saviane and Silver, 2006b]. Thus, releasable vesicles in pool N 0 become release competent in pool N 1 with a rate of k +1 .
Subsequently, some vesicles can transit with a slower rate, k 2 , to the pool N 2 . This rate was set to 0.5 s -1 to reproduce the slow component of the recovery (~2 s; Figure S3D and E) and might represent a slow maturation of vesicles closer to calcium channels (Bucurenciu et al., 2008;Sakaba and Neher, 2001;Young and Neher, 2009). During fitting, k +1 , p r2 and N 2 were free parameters, while the remaining parameters in the model were constrained (see Supplemental Experimental Procedures). The average control data ( Figure 6B-D) were best described by 2.3 and 10 vesicles in pool N 2 and N 1 with an initial release probability of 0.8 and 0.5, respectively. The rate of reloading (k +1 ) was ~60 s -1 , consistent with previous estimates (Saviane and Silver, 2006b).