Kinetics of both synchronous and asynchronous quantal release during trains of action potential-evoked EPSCs at the rat calyx of Held

Abstract

We studied the kinetics of transmitter release during trains of action potential (AP)-evoked excitatory postsynaptic currents (EPSCs) at the calyx of Held synapse of juvenile rats. Using a new quantitative method based on a combination of ensemble fluctuation analysis and deconvolution, we were able to analyse mean quantal size (q) and release rate (ξ) continuously in a time-resolved manner. Estimates derived this way agreed well with values of q and quantal content (M) calculated for each EPSC within the train from ensemble means of peak amplitudes and their variances. Separate analysis of synchronous and asynchronous quantal release during long stimulus trains (200 ms, 100 Hz) revealed that the latter component was highly variable among different synapses but it was unequivocally identified in 18 out of 37 synapses analysed. Peak rates of asynchronous release ranged from 0.2 to 15.2 vesicles ms⁻¹ (ves ms⁻¹) with a mean of 2.3 ± 0.6 ves ms⁻¹. On average, asynchronous release accounted for less than 14% of the total number of about 3670 ± 350 vesicles released during 200 ms trains. Following such trains, asynchronous release decayed with several time constants, the fastest one being in the order of 15 ms. The short duration of asynchronous release at the calyx of Held synapse may aid in generating brief postsynaptic depolarizations, avoiding temporal summation and preserving action potential timing during high frequency bursts.

The glutamatergic (Grandes & Streit, 1989) axosomatic calyx of Held synapse in the medial nucleus of the trapezoid body (MNTB) allows simultaneous voltage clamp of both the pre- and the postsynaptic compartments (Borst et al. 1995; Takahashi et al. 1996). It therefore offers unique possibilities to study mechanisms of transmitter release and its short-term plasticity (Schneggenburger et al. 2002; von Gersdorff & Borst, 2002). At the developmental stage, at which such measurements are most readily performed (postnatal days (P) 8–10) three kinds of interesting phenomena exist, which challenge the analysis of EPSCs. (i) Synaptic activity induces strong desensitization of postsynaptic AMPA receptors (AMPARs). (ii) This is primarily caused by residual glutamate accumulating in the synaptic cleft. If desensitization is attenuated pharmacologically, the residual glutamate elicits significant postsynaptic currents. (iii) Superimposed on residual glutamate currents, asynchronous release builds up during EPSC trains. Here we present analysis procedures to characterize separately synchronous release, asynchronous release, and residual glutamate currents. At many inhibitory (Vincent & Marty, 1996; Lu & Trussell, 2000; Kirischuk & Grantyn, 2003; Hefft & Jonas, 2005) as well as excitatory (Goda & Stevens, 1994; Cummings et al. 1996; Otis et al. 1996; Kinney et al. 1997; DiGregorio et al. 2002; Oleskevich & Walmsley, 2002; Singer et al. 2004) synapses, asynchronous release as well as postsynaptic current components elicited by residual transmitter are important elements of information processing. Our new quantitative method provides a valuable tool for the detailed study of these signal components and their developmental changes, which we reported previously for the calyx of Held synapse (Taschenberger et al. 2005). Furthermore, such tools are needed for the correct interpretation of EPSCs in the presence of residual glutamate current and asynchronous release, when studying the molecular mechanisms of transmitter release and vesicle pool dynamics.

We use a combination of ensemble fluctuation analysis and deconvolution to analyse AP-evoked EPSCs. We adapt and improve a method, which was originally developed for studying synaptic transmission using dual voltage clamp (Neher & Sakaba, 2001b,a) and apply it to EPSC trains evoked by afferent fibre stimulation. First, we compare the results with those of a variant of multiple probability fluctuation analysis (Silver et al. 1998; Meyer et al. 2001; Scheuss et al. 2002) and find good agreement of quantal size (q) estimates between both methods. Next, we apply this method to extract the time course of the release rate ξ(t) during EPSC trains. Finally, we concentrate on asynchronous release, which builds up during high-frequency stimulation simultaneously with residual glutamate currents. We show that in some synapses the contribution of asynchronous release can match that of synchronous release towards the end of 200 ms-long 100 Hz trains.

Methods

Electrophysiological recordings

Brainstem slices were prepared from P8–10 Wistar rats as previously described (von Gersdorff et al. 1997). Experiments were performed according to the ethical guidelines of the state of Lower Saxony. After decapitation, the brainstem was quickly removed and 200 μm-thick slices were cut on a VT1000S vibratome (Leica, Germany). Slices were maintained at 35°C for 30–40 min, and kept at room temperature for ≤ 4 h. The standard external recording solution was artificial cerebral spinal fluid containing (mm): NaCl 125, KCl 2.5, NaHCO₃ 1.25, ascorbic acid 0.4, myo-inositol 3, sodium pyruvate 2, CaCl₂ 2, MgCl₂ 1 and d-aminophosphonovalerate (d-AP5) 0.05 (pH 7.4). Bicuculline (10 μm) and strychnine (2 μm) were routinely included in the bath solution to suppress inhibitory postsynaptic currents. In some experiments 100 μm cyclothiazide (CTZ) was added to reduce AMPAR desensitization. EPSCs were evoked by afferent fibre stimulation (100 μs, ≤ 30 V) using a bipolar stimulating electrode and recorded at a holding potential (V_h) of −70 or −80 mV with EPC-9 or EPC-10 patch-clamp amplifiers (Heka, Lambrecht, Germany). The pipette solution contained (mm): caesium gluconate 130, TEA-Cl 20, Hepes 10, sodium phosphocreatine 5, Mg-ATP 4, GTP 0.3 and 5 EGTA (pH 7.2, 310 mosmol l⁻¹). Open tip resistance was 2.5–4 MΩ. During whole-cell recording, series resistance (R_s) was automatically determined before each sweep and appropriate compensation was applied, such that the remaining uncompensated R_s never exceeded 3 MΩ. R_s values typically ranged from 3.5 to 8 MΩ before compensation. Currents were sampled at 20 kHz and low-pass filtered at 6 kHz. All experiments were carried out at room temperature (22–24°C).

Data analysis

All analysis routines were written and executed with the software IgorPro (version 5, WaveMetrics, Lake Oswego, OR, USA). Digitized current traces were corrected off-line for remaining uncompensated R_s (Traynelis, 1998; Meyer et al. 2001). Artifacts associated with afferent fibre stimulation were blanked by linear interpolation. Short (≤ 200 μs) electrical artifacts, which were sometimes present in long continuous records, were removed by interpolation if they occurred in flat sections of the traces (typically one artifact every 20 traces). EPSC amplitudes were determined as the difference between peak and baseline current. The latter was derived from the extrapolation of double exponential fits to the decay phase of the preceding response in the case of slowly decaying EPSCs recorded in the presence of CTZ. Miniature EPSCs (mEPSCs) were recorded during interstimulation intervals for comparison of their mean amplitudes with quantal size estimates derived from fluctuation analysis. mEPSCs were detected using a template-matching algorithm and analysed as previously described (Clements & Bekkers, 1997; Scheuss et al. 2002).

Discrete ensemble fluctuation (DEF) analysis

Non-stationary ensemble fluctuation analysis was performed according to Scheuss et al. (2002). We refer to this analysis method as ‘discrete’ because it analyses EPSC peak amplitudes, unlike the ‘continuous’ ensemble fluctuation analysis, described below, which analyses fluctuations for all samples along a trace. Relatively short EPSC trains (5 stimuli, 100 Hz, 23–104 repetitions at ≥ 10 s intervals, n = 9 synapses) as well as long EPSC trains (20 stimuli, 100 Hz, 14–220 repetitions at ≥ 15 s intervals, n = 28 synapses) were analysed. The intersweep intervals allowed for > 90% recovery from synaptic depression. Data sets showing > 30% run-down of initial EPSC amplitudes were rejected from analysis. Mean, variance and covariance of the ith EPSC in the train (EPSC_i) or the successive EPSCs i and i + 1, respectively, were calculated segment-wise using maximum overlap and applying the minimum possible segment size of n = 2 (eqns (1)–(3) in Scheuss et al. 2002) to minimize the influence of trends and drifts in the data (Clamann et al. 1989; Scheuss & Neher, 2001).

Since recruitment of new vesicles between individual stimuli is negligible during 100 Hz trains, the quantal size q_i for EPSC_i can be estimated from the mean , variance (Var_i), and covariance (Cov_i) (eqn (9) in Scheuss et al. 2002). Assuming all covariances to be of postsynaptic origin, a lower estimate for q_i is obtained from

(1)

Assuming all covariance derives from vesicle depletion, an upper estimate for q_i is obtained from

(2)

The symbol * indicates that these estimates are not corrected for variability of quantal amplitudes and dispersion of quantal latencies. Because a recent study (Taschenberger et al. 2005) showed that such corrections nearly cancel each other, we used uncorrected q_i* values for comparison with estimates derived by other methods.

Continuous ensemble fluctuation (CEF) analysis

The same ensembles of EPSC trains were used to obtain time-resolved estimates for quantal amplitude q(t) and the release rate ξ(t) with a resolution of ∼300 μs. In case q is known and constant, the mean ξ(t) can readily be calculated by deconvolving the average waveform of the EPSC trains using an algorithm which incorporates a diffusion model to account for residual glutamate currents (Neher & Sakaba, 2001a). During simultaneous pre- and postsynaptic voltage clamp, the required model parameters characterizing mEPSC shape as well as glutamate diffusion can be obtained from ‘fitting protocols’ applied to the presynaptic terminal. In previous studies (Neher & Sakaba, 2001a; Sakaba & Neher, 2001a), analysis had to be limited to EPSC sections where all model parameters including quantal size were constant which was achieved by pharmacologically preventing desensitization and saturation of AMPARs.

We now extended this analysis method in three ways. (i) It was applied to AP-evoked EPSC trains elicited by afferent fibre stimulation, i.e. only the postsynaptic compartment was voltage clamped. We determined the model parameters required for deconvolving EPSCs of a given synapse by considering that the time-resolved EPSC variance (λ₂(t)) is also an estimator for ξ(t). A scaled version of λ₂(t) should superimpose onto ξ(t) estimated by deconvolution and the task is reduced to finding model parameters (such as quantal size, time constants of rise and decay of the quantal current, and those describing the residual glutamate current), for which the release rate estimates derived from variance agree with those derived from deconvolution. (ii) We used larger ensembles of EPSCs (14–220 repetitions, on average 96), which provide more accurate variance estimates. Additionally, we introduced a sidelobe correction (see below) to improve the time resolution of λ₂(t) estimates. (iii) We allowed quantal size to be a slowly varying quantity q(t), which was calculated piecewise from a comparison of variance- and deconvolution-derived release rates.

We first calculated an apparent deconvolution rate ξ₀(t) from the mean EPSC, assuming a constant quantal size q₀ (Neher & Sakaba, 2001a). Next, the continuous band-pass-filtered variance λ′₂(t) (2nd central moment, the prime indicates band-pass filtering) was calculated from the N − 1 difference traces between successive repetitions in order to optimally eliminate trends and drifts

(3)

where represent the nth difference trace after band-pass filtering. Band-pass filtering of the difference traces was performed as previously described (Neher & Sakaba, 2001b) using two-stage box filters, except that we used longer time windows (0.5 ms instead of 0.3 ms) for the box filters. The lower frequency band used here (peak of the pass-band shifted from 1074 Hz to 644 Hz) emphasizes noise-power generated by release events relative to that caused by AMPAR channel gating. The rationale for applying this type of filter and its characteristics are given in Neher & Sakaba (2001b). For low-pass filtering the deconvolution result, the same two-stage box filter algorithm was used. The resulting cut-off frequency f_c of such low-pass depending on the duration of the box window T_box was found empirically to be given by .

We then obtained estimates of the actual q_i for each EPSC in the train by appropriately scaling the average of the band-pass-filtered variance (* indicates correction for background and AMPAR channel variance) and release rate derived from deconvolution over short time windows around each EPSC_i. Time windows were selected starting at the onset of EPSC_i and covering the time during which ξ is significantly above background (see Fig. 2B for an example). The estimate for q_i was calculated as the ratio

(4)

(eqn (B8) in Neher & Sakaba, 2003) where and represent variance- and deconvolution-derived rates, respectively, associated with the phasic release transient evoked by the ith stimulus and is a calibration factor including corrections for filtering. This approach assumes that q(t) varies slowly during the stimulus train and is nearly constant for a given EPSC. In this sense the quantal size estimate is not ‘time-resolved’ but remains ‘discrete’, although continuous (sample point by sample point) q(t) estimates may be obtained from large ensembles of traces with low noise. The complete time course q(t) was obtained by linear interpolation between the discrete q_i values and extending the traces to t = 0 (by filling in values of q₁) and to the end of the record (by filling in the quantal size of the last response) (see Fig. 2C for an example). This procedure disregards the expectation that q(t) should recover after the last stimulus. However, this error should be small as long as residual glutamate is present. For some of the 200 ms EPSC trains, which showed strong desensitization, q estimates were small during the second half of the trains and fluctuated strongly from one stimulus number to the next. In such cases, late q_i were replaced by their mean or by approximations derived from linear or exponential fits to q_i versus i.

Figure 2. CEF analysis of 50 ms EPSC trains evoked by afferent fibre stimulation (100 Hz, 5 stimuli) recorded in the presence of 100 μm CTZ.

A, mean waveforms for EPSC train (black trace) and residual glutamate current (grey trace) derived from an ensemble of 81 EPSCs (5 stimuli, 100 Hz). Stimulation artifacts have been blanked for clarity during a period of 0.6 ms before each EPSC. Ba, release rate derived from variance ξ_V (eqn (6), dashed trace) superimposed on that derived from deconvolution ξ_D (eqn (5), continuous trace) for the same synapse as shown in A. For deconvolution, the following kinetic parameters determining mEPSC waveform were used: τ_rise = 0.153 ms, τ_decay(fast) = 1.64 ms, τ_decay(slow) = 8.76 ms, fraction of slow decay component was 0.697. The bar below the first release transient indicates the time window, which was used to calculate the average quantal size for EPSC₁. Bb, low release rate range expanded to illustrate build-up of asynchronous release during the 50 ms EPSC train. C, quantal amplitude for individual EPSCs (⋄) and the interpolated curve, which was used to calculated release rates.

With the time course of q(t), we then calculated two new estimates for ξ(t). One was based on deconvolution:

(5)

A second one was based on corrected variance (Neher & Sakaba, 2001b, 2003):

(6)

As stated above, the goal of the fitting procedure is to find a set of parameters for which and agree. This is achieved iteratively by trial and error. However, in many cases the partitioning of the current decay into components derived from residual glutamate and those derived from quantal release events is not unique (see Discussion). The deconvolution-derived estimate ξ_D is less noisy and more accurate during episodes of high release rates. For estimating the lower rates in-between stimuli (late or asynchronous release), ξ_D depends critically on the choice of the diffusion model parameters. For this reason, evaluation of asynchronous release was exclusively based on ξ_V which is less sensitive to the accuracy of the diffusion model parameters but depends critically on a correct separation between variance originating from release and that generated by AMPAR channel gating (see below). It should be pointed out that the data processing implies low-pass filtering of the release function, which causes the peaks of the release transients to be broadened (Fig. 1C).

Figure 1. CEF analysis of simulated EPSCs.

The mEPSC waveform which was found to describe the experimental data shown in Fig. 2 was used in this simulation and an ensemble of 200 EPSCs was generated. The original, unfiltered release function had a half-width of 0.45 ms. Aa, mEPSC waveform before (black) and after (grey) band-pass filtering. Ab, 2nd central moment λ′₂(t) of the filtered mEPSC. Ac, expanded version of λ′₂(t) to illustrate the two smaller sidelobes flanking the mean peak. Ba, individual simulated EPSCs and mean EPSC waveform. Bb, release rate estimates from deconvolution (ξ_D) and CEF analysis (ξ_V, ξ_Vraw) compared to the filtered original release function (grey). The variance-based rate estimate is shown before (ξ_Vraw) and after (ξ_V) sidelobe correction. The release rate estimates ξ_V and ξ_D are similar. Their peaks are broadened, compared to the original, unfiltered release function due to the filtering operations which are applied either explicitly (for ξ_D) or implicitly in the sidelobe correction (for ξ_V). Simulations were performed as in Neher & Sakaba (2001b). C, relationship between the half-width estimate from CEF analysis and the original, unfiltered half-width of the release transient. A ‘model’ release transient with a half-width of 0.36 ms was expanded in time by various factors to obtain release transients with half-width values ranging between 0.36 and 1.2 ms. These waveforms were low-pass filtered at 480 Hz and their half-widths measured. The resulting relationship was used to translate filtered into corrected waveforms (Table 1).

To quantify asynchronous release in-between late stimuli of long trains (20 stimuli, 100 Hz), we calculated a mean ξ_V trace by averaging peak-aligned 10 ms windows of ξ_V(t), which corresponded to the last five EPSCs. We separated synchronous from asynchronous release by making the simplifying assumptions that: (1) the average asynchronous release rate ξ_async remains nearly constant during the 10 ms interstimulus window, and (2) phasic release contributes only during the first 3.6 ms. This latter assumption seems reasonable given that the half-width of the release transient is < 0.5 ms (< 0.88 ms after band-pass filtering) for P8–10 calyx synapses (Schneggenburger & Neher, 2000). In this case, ξ_async equals (M_total − M_initial)/6.4 ms, where M_total is the total quantal content within the 10 ms window and M_initial is that during the initial 3.6 ms.

Sidelobe correction of continuous variance traces

To further improve the time resolution of the filtered variance and thereby ξ_V, we introduced an additional step of data processing. We shall first explain the rationale for such a step and then describe the algorithm for its implementation. Band-pass filtering of the EPSCs, as described above, converts the variance contributed by a single release event into a very short spike. This is illustrated in Fig. 1 for the example of a slowly decaying mEPSC (Fig. 1Aa), as typically recorded in the presence of CTZ. The 2nd moment calculated from such a filtered mEPSC (Fig. 1Ab) consisted of a main peak (0.47 ms half-width) which was flanked by two smaller sidelobes (1.7% and 0.4% of the main peaks amplitude) occurring 2.8 ms before and 1.1 ms thereafter (Fig. 1Ac). Although being small, such sidelobes could also be clearly observed in well-resolved traces (see ξ_Vraw in Fig. 1Bb). When CTZ was omitted from the bath solution, mEPSCs decayed with a faster time constant (∼0.5 ms), and the late sidelobe was as large as 15% of the central peak and occurred only 0.9 ms later.

To eliminate such sidelobes from the variance traces, was convolved with an appropriately designed filter kernel calculated in the frequency domain (using FFT routines) as the ratio of two impulse functions: the desired single peak response and the original impulse function (the variance trace of a filtered mEPSC). The ratio was transformed into the time domain by inverse FFT. We applied low-pass filtering at various stages to avoid oscillation of the filter kernel. First, we used as the desired single peak impulse response a filtered version (f_c = 1.7 kHz) of the main peak in the original impulse response. In addition, a Gaussian low-pass filter was applied in the frequency domain (f_c = 670 Hz) and spectral amplitudes beyond 4 times this frequency were zeroed before inverse FFT transformation. This resulted in a final filter characteristic of the kernel equivalent to a low-pass filter with f_c = 480 Hz (Fig. 1C). After convolving with this filter kernel, the result was time-shifted by a small amount for optimal alignment of ξ_V with ξ_D. To facilitate comparison between ξ_V and ξ_D, the latter was low-pass filtered using the f_c of 480 Hz, as implicitly applied in deriving ξ_V (Fig. 1Bb).

Estimating quantal parameters from 3rd and 4th cumulants

For sufficiently low release rates, both q(t) and ξ(t) can be estimated from 3rd and 4th cumulants of filtered records (Fesce, 1999; Neher & Sakaba, 2001b). This method has the advantage that it is only weakly influenced by AMPAR channel noise and by slowly varying residual glutamate currents. However, its resolution is typically an order of magnitude lower than that of the variance-based method described above. We analysed the decay of EPSC ensembles following the stimulus train, when both residual glutamate current and asynchronous release declined slowly, up to 5 s after stimulus onset.

We calculated quantal size q(t) and cumulant-derived release rates ξ_cum(t) according to

(7)

(8)

where and are 3rd and 4th cumulants of the band-pass-filtered ensemble and and are calibration factors calculated from the filtered mEPSC waveform and the amplitude distribution of mEPSCs (Neher & Sakaba, 2003). In addition, we calculated the variance contributions of asynchronously released quanta according to Neher & Sakaba (2003)

(9)

Alternatively, when q is known, can be obtained from:

(10)

(Neher & Sakaba, 2003; eqns (B13), (B7a) and (B10)), where H′₃ is a calibration factor in analogy to H′₄ (Neher & Sakaba, 2003). To minimize effects of non-stationarities ‘local means’ of the ensemble (i.e. the means of typically 5 consecutive repetitions surrounding a given EPSC) were subtracted from individual records (Neher & Sakaba, 2001b). Due to the non-linear mathematical operations involved the sequence of signal processing matters: first, mean subtraction and filtering; second; calculation of 2nd, 3rd and 4th moments; third, low-pass filtering of the moments; fourth, calculation of 4th cumulant as the difference between the 4th moment and 3 times the square of the 2nd moment; fifth, correction for the subtraction of local means (eqns (18)–(20) in Neher & Sakaba, 2001b); sixth, evaluation of eqns (7) and (8). The low-pass filter for the higher moments (step 3) has to be chosen such that the maximum local fluctuations in 3rd and 4th cumulants are smaller than about half their mean values, in order to avoid excessive non-linear distortions, when calculating the ratios of eqns (7)–(9).

We evaluated q(t) and ξ(t) according to eqns (7) and (8) after low-pass filtering between 7 Hz and 16 Hz. We also estimated the variance contribution from AMPAR channel gating (Neher & Sakaba, 2003; eqn (B14))

(11)

where is calculated from 3rd and 4th cumulants according to either eqn (9) or eqn (10) and is the background variance (see below). is used later to correct for AMPAR channel variance, when estimating asynchronous release.

This analysis relies on the assumption that current fluctuations due to AMPAR channel gating by residual glutamate do not contribute to 3rd and 4th cumulants because they represent the superposition of a large number of single-channel openings. According to the central-limit theorem, the distributions of such current fluctuations should be Gaussian with very small skew and kurtosis. To test this assumption, we analysed AMPAR whole-cell currents elicited by puff application of glutamate and recorded in the presence of 100 μm d-AP5 (see Fig. 5). For current amplitudes of −5 to −10 nA in the presence of CTZ, which is close to the amplitudes of typically recorded residual glutamate currents, the 3rd cumulant was small, although contaminated by large noise. However, the 4th cumulant of currents larger than −5 nA had positive values significantly different from zero corresponding to an ‘apparent release rate’ of 10 events ms⁻¹ at about −9 nA. Since the estimates for 3rd and 4th cumulants become very noisy in the presence of large residual glutamate currents, the calculations according to eqns (7)–(11) become reliable only after a short time window following stimulation, once the residual glutamate current has decayed sufficiently (see Results).

Figure 5. Variance, 3rd and 4th cumulants of whole-cell currents elicited by application of exogenous glutamate and recorded in the absence (left) and presence (right) of 100 μm CTZ.

Principal neurons of the MNTB were voltage clamped at −80 mV and 100 μm glutamate was repeatedly (3–7 times) applied for approximately 0.4 s by a short puff (∼400 ms) from a nearby glass pipette. The distance from application pipette to postsynaptic neuron was adjusted to elicit peak currents between −0.3 and −0.8 nA or −10 and −15 nA in the absence and presence of CTZ, respectively. These peak amplitudes exceed the maximum residual glutamate currents observed during afferent fibre stimulation. A, glutamate application elicited whole-cell currents. B, variance, 3rd and 4th cumulants. All traces were low-pass filtered at 6.7 Hz. C, variance plotted versus whole-cell current. Lines represent linear fits to the lower (dotted lines) and medium (dashed lines) current regions. Summary results of the line fits are given in Table 2.

Correction for background variance and leak currents

Our analysis required accurate estimates of whole-cell leak current and background variance for the correct separation between variance resulting from stochastic vesicle release and variance originating from stochastic channel opening. To obtain these, we first calculated the ensemble mean current I_P without prior mean subtraction and filtering, together with variance, and 3rd and 4th cumulants of the filtered traces. We applied low-pass filtering at 3 Hz to the results and measured mean (typically –100 pA) and variance (typically 1–2 pA²) of the leak current on sections of traces without evoked release and residual glutamate current. Spontaneous release occurred at an average rate of ∼1 ves s⁻¹, which is too little to add significantly to the mean leak current but contributes ∼10–20% to . The difference between and the variance due to spontaneous release (eqn (9)) provided an estimate for the background variance .

Results

Discrete and continuous ensemble fluctuation analyses yield similar estimates for quantal size

The principal aim of this study was to obtain time-resolved estimates for quantal parameters and release rates during repetitive synaptic activity by applying a newly developed method, which we termed continuous ensemble fluctuation (CEF) analysis. To establish that CEF analysis is applicable to AP-evoked EPSCs at the calyx of Held we first compared results obtained by this new method to those obtained by discrete ensemble fluctuation (DEF) analysis (Meyer et al. 2001; Scheuss et al. 2002), a variant of multiple probability fluctuation analysis (Silver et al. 1998). We recorded EPSC trains in the absence or presence of CTZ and applied two different stimulus protocols: either 50 ms-long trains (100 Hz, 5 stimuli, n = 4 synapses without (w/o) CTZ, n = 5 synapses with (w) CTZ) or 200 ms-long trains (100 Hz, 20 stimuli, n = 9 synapses w/o CTZ, n = 19 synapses w CTZ). A typical experiment in which 50 ms trains were recorded in the presence of CTZ is illustrated in Fig. 2. An average waveform of the EPSC train was obtained from an ensemble of 81 repetitions (black trace Fig. 2A). The continuous ensemble variance was calculated from band-pass-filtered EPSCs and corrected for background and AMPAR channel variance. The corrected variance is proportional to the release rate and to the square of the quantal size at a given time. The average EPSC waveform was subjected to deconvolution analysis (see Methods). The residual glutamate current estimated by the diffusion model of the deconvolution algorithm is shown superimposed on the mean current for comparison in Fig. 2A (grey trace). The deconvolution result is proportional to the product of release rate and quantal size. Thus combining the variance and deconvolution results allowed the derivation of estimates for the release rate (Fig. 2B) and quantal size (Fig. 2C). The latter estimates for the time course q(t) were obtained by forming an appropriately scaled ratio of variance and deconvolution (eqn (4)). For time points around the peaks of EPSCs, the ratios are well defined because both variance- and deconvolution-derived rates are large. However, such ratios are not very accurate and also noisy for time points in-between stimuli, when both quantities are small. We therefore averaged variance and deconvolution results during appropriately chosen intervals around EPSC peaks (bar in Fig. 2B) and derived quantal size estimates for individual EPSCs (Fig. 2C, diamonds) from the ratios of such averages. By interpolation (see Methods) we arrived at the estimated continuous evolution of quantal amplitude q(t) during the EPSC train (Fig. 2C, continuous line), which was used to calculated release rates shown in Fig. 2B. A comparison of variance-derived rates (ξ_V, Fig. 2B dashed trace) with those derived from deconvolution (ξ_D, Fig. 2B, continuous trace) shows that both estimates agree closely.

In the analysis above, deconvolution of the average EPSC waveforms was performed without restricting the parameters determining the kinetics of the assumed quantal event. For most synapses analysed this way, rise and initial decay of the mEPSC waveform (obtained from spontaneous quantal EPSCs recorded in-between stimulus trains) corresponded well to the model parameters found during deconvolution. However, the mEPSC decay beyond the half-decay point sometimes disagreed, particularly for experiments in the presence of CTZ. Such deviations between assumed and measured mEPSC waveform may be caused by the fact that the diffusion model of the deconvolution algorithm allows some freedom in assigning the model parameters because a fraction of the slow EPSC decay can be regarded either as residual glutamate current or else as a slowly decaying component of the mEPSCs (Neher & Sakaba, 2001a).

In order to evaluate the influence of such ambiguities, we repeated the analysis of 50 ms stimulus trains while restricting the kinetic parameters of the assumed quantal event such that its shape agreed with that of the measured mEPSC to within 5% of its peak value for times up to the half-decay. Applying this restriction, we could obtain agreement between the release rate estimates ξ_D and ξ_V to within ∼5% of the peak rate in all experiments. However, some traces which fulfilled the 5% criterion still showed systematic deviations between the two rate estimates, such as differing slopes during the interstimulus intervals and small fluctuations of ξ_D below the zero-line. Relaxing the restriction and allowing deviations from the measured mEPSC waveform resulted in much better agreement between ξ_D and ξ_V (≤ 2% deviation) (Fig. 2B).

The same experimental data were also subjected to DEF analysis. Mean peak current I_i for each of the five stimuli, variance Var_i, and covariance Cov_i were calculated. From these three quantities upper and lower bounds for the quantal size q_i were derived for each EPSC_i (eqns (1) and (2)).

Figure 3A shows a scatterplot of quantal size estimates for the initial EPSCs (EPSC₁) in the trains derived by CEF analysis (q_CEF) versus those derived by DEF analysis (q_DEF). Data points are spread around the identity line indicating that both q estimates generally agreed well. During such short trains, EPSC amplitudes decreased on average from −4.9 ± 1.2 to −0.6 ± 0.1 nA and −8.5 ± 2.4 to −2.4 ± 0.6 nA in the absence and presence of CTZ, respectively. The stronger depression in the absence of CTZ suggests a contribution of AMPAR desensitization. This is corroborated by both DEF and CEF analysis. Figure 3B and C summarizes the changes in quantal size observed during short-term depression in 50 ms EPSC trains recorded in the absence (Fig. 3B) and presence (Fig. 3C) of CTZ showing good agreement between the estimates derived by CEF and DEF analysis. Average values for DEF-derived q*_i,lower and q*_i,upper are plotted together with q_CEF and mean amplitudes of spontaneous quantal EPSCs for both recording conditions. Upper and lower bounds for q*₁ were −45 and −29 pA (w/o CTZ) and −45 and −40 pA (w CTZ), bracketing the respective mean mEPSC amplitudes obtained under the same experimental conditions. Upper and lower bounds for q* estimates were similar, particularly when postsynaptic desensitization was reduced by including CTZ in the bath, suggesting that covariance and, implicitly, release probability were small (Scheuss & Neher, 2001). Under control conditions, q declined strongly to ∼30% of its initial value (Fig. 3B). With CTZ present in the bath, the decrease of q was lessened but not completely prevented (Fig. 3C). Under both experimental conditions (w and w/o CTZ), q_CEF fell between the lower-bound and upper-bound estimates of DEF analysis for the first three EPSCs. In the presence of CTZ (Fig. 3C), q_DEF for the fourth and fifth EPSC were, however, larger compared to q_CEF. Presumably, this was caused by large residual glutamate currents. CEF analysis showed that AMPAR channel gating by residual glutamate contributed significantly to variance. In contrast to q_DEF, estimates derived from CEF analysis were corrected for this contribution.

Figure 3. Comparison of quantal size estimates derived from DEF and CEF analysis.

A, scatter plot of q estimates for the initial EPSCs of the trains derived from CEF analysis (q_CEF) versus those derived from DEF analysis (q_DEF) for a total of 37 cells. Note that the data points are scattered around the identity line (dotted line). B and C, mean quantal size estimates during 50 ms EPSC trains plotted against stimulus number for 5 synapses recorded in the absence (B) and 4 synapses recorded in the presence (C) of 100 μm CTZ. In addition, the mean amplitude of spontaneously occurring mEPSCs for the same experiments is shown (diamonds). Estimates from CEF analysis (eqn (4), squares) are compared to lower (eqn (1)) and upper (eqn (2)) bounds of q estimates derived from DEF analysis (circles).

When synaptic stimulation was extended from 50 ms to 200 ms (Fig. 4), EPSC amplitudes decreased further (on average from −6.0 ± 1.0 nA to −0.2 ± 0.1 nA and −11.9 ± 1.2 nA to −1.3 ± 0.2 nA in the absence and presence of CTZ, respectively). Thus, steady-state EPSCs (EPSC₁₆ to EPSC₂₀) were strongly depressed (5 ± 1% of EPSC₁ in the absence (n = 9) and 12 ± 2% of EPSC₁ in the presence (n = 19) of CTZ). Most of this depression was caused by AMPAR desensitization because q_CEF decreased to only −8 ± 1 pA (average of EPSC₁₆ to EPSC₂₀, n = 9) during 200 ms EPSC trains in the absence of CTZ. This compared well to a mean of −10 ± 1 pA obtained for q_DEF for the same experiments. By contrast, when CTZ was included in the bath, q_CEF dropped by 20–40% during the first five EPSCs and remained constant thereafter or recovered slightly. Quantal size estimates for late EPSCs often fluctuated from one stimulus number to the next due to their small peak amplitudes. Again, q_CEF was on average slightly smaller than q_DEF for the steady-state EPSCs (−22 ± 3 pA versus −25 ± 3 pA, respectively, n = 18).

Figure 4. Kinetics of EPSCs and synchronous release transients during 200 ms EPSC trains (100 Hz, 20 stimuli).

Aa, average waveforms for EPSCs (black traces) and residual glutamate currents (grey traces) obtained from ensembles of 37 (left) and 29 (right) EPSCs recorded in the absence (left) and presence (right) of 100 μm CTZ. Ab, averages for the initial (EPSC₁) and the last five EPSCs in the trains superimposed for comparison. Ac, corresponding average release functions for the initial and the steady-state EPSCs. Dashed lines in Ab and Ac represent averages of steady-state responses after normalizing their peak amplitude to those of the initial responses. The average release rate for EPSC₁₆ to EPSC₂₀ estimated by deconvolution is shown for comparison (grey traces). In order to better preserve kinetic features, analysis of the two synapses shown in A was performed at a higher bandwidth (830 Hz instead of the usual 480 Hz). Stimulus artifacts have been removed for clarity. B, scatter plot of half-width values of initial release transients estimated by deconvolution versus those estimated by CEF analysis for synapses recorded in the absence (open grey circles) and presence (filled grey circles) of 100 μm CTZ. The large black circles represent average values and the dotted line indicates the identity line. C, comparison of half-width values for release transients underlying the individual EPSCs elicited by 100 Hz stimulus trains (200 ms, 100 μm CTZ) and measured by deconvolution (filled circles) and CEF analysis (open circles). Half-width values obtained from CEF analysis are corrected for the effect of low-pass filtering in B and C. Continuous lines represent exponential fits, yielding time constants of 2.9 stimuli (CEF analysis) and 4.3 stimuli (deconvolution). Da, average release time course obtained from CEF analysis of a total of 19 synapses in the presence of CTZ. During the 200 ms trains, peak rates of the synchronous release transients decreased from 449 ± 64 (EPSC₁) to 70 ± 6 ves ms⁻¹ (average of EPSC₁₆ to EPSC₂₀) (peak rates not corrected for low-pass filtering). Broadening of the synchronous release transient during EPSC trains is evident in Db which compares release functions for EPSC₁ (grey trace) with the average of EPSC₁₆ to EPSC₂₀ (black trace) after scaling to the same peak rate.

The time course of synchronous release measured by CEF analysis

Having established that CEF analysis reliably estimates q associated with individual EPSCs during trains, we set out to analyse the time course of the synchronous release transients ξ(t) for synapses stimulated with 200 ms 100 Hz trains in the absence (Fig. 4A, left) and presence (Fig. 4A, right) of CTZ. For both recording conditions, average waveforms of the EPSC train and residual glutamate current are shown in Fig. 4Aa for two representative synapses. Residual glutamate currents were small in the absence of CTZ due to strong AMPAR desensitization (Fig. 4Aa, left).

As described by Taschenberger et al. (2005) for very young synapses (P5–7), we observed a broadening of EPSCs during stimulus trains (Fig. 4Ab). Calculation of ξ(t) by CEF analysis allowed us to study this broadening in more detail. Figure 4B shows a scatter plot of half-width estimates for the release transients of the initial EPSCs derived from CEF analysis versus those derived from deconvolution demonstrating good agreement between the two methods. Both synaptic delays (data not shown) and the widths of the release transients (Fig. 4C, Table 1) increased during trains. During 100 Hz stimulation, the increase in half-width was well approximated with a single exponential function (Fig. 4C). The relative broadening of the release transient was variable among different synapses as was the width of the initial release transients. However, the mean half-width of the release transients tended to be longer in the presence of CTZ consistent with a broadening of presynaptic APs by CTZ (Ishikawa & Takahashi, 2001). Table 1 provides raw half-width values along with values corrected for the effect of low-pass filtering (Fig. 1C) for comparison. The corrected half-width of the 5th response under CTZ is about twice the width of the 1st response in the absence of the drug. The broadening during the train is on average ∼50%, that caused by CTZ ∼30% (Table 1). In contrast to the release transient, EPSC half-widths were prolonged about 10-fold in the presence of CTZ indicating that the slow EPSC decay in the presence of CTZ is primarily caused by more slowly decaying mEPSCs and a build-up of residual glutamate current.

Table 1.

Half-width of initial and late release transients

Half-width (ms)*	Control (n = 14)	Corrected	With CTZ (n = 23)	Corrected	CTZ/control
1st stim.	0.85 ± 0.01	0.42 ± 0.04	0.93 ± 0.02	0.58 ± 0.03	1.4
5th stim.	0.98 ± 0.02	0.68 ± 0.04	1.08 ± 0.04	0.82 ± 0.05	1.2
5th/1st		1.62		1.41
20th stim.	1.22 ± 0.09	0.99 ± 0.10	1.20 ± 0.04	0.99 ± 0.05	1.0
20th/1st		2.4		1.7

^*Mean half-widths for the 1st, 5th and 20th EPSC within a train in the absence and presence of cyclothiazide (CTZ). In each case a second value is given, which is the mean corrected for the effect of low-pass filtering according to the relationship illustrated in Fig. 1.

The average time course of the release rate estimates ξ_V obtained from CEF analysis of a total of 19 synapses in the presence of CTZ is shown in Fig. 4Da. During the 200 ms trains, peak rates of the synchronous release transients decreased from 449 ± 64 ves ms⁻¹ (EPSC₁) to 70 ± 6 (average of EPSC₁₆ to EPSC₂₀) (rates not corrected for low-pass filtering). Broadening of the synchronous release transient during EPSC trains is particularly evident in Fig. 4Db which compares the average release transients for the initial and steady-state EPSCs after normalizing and aligning their peaks.

Estimation of low release rates in the presence of large residual glutamate currents

Closer inspection of the sample traces in Fig. 4Ac reveals that in one synapse (Fig. 4A right, w CTZ) asynchronous release of ∼5–10 ves ms⁻¹ developed during the train, while hardly any asynchronous release was detectable in the other synapse (Fig. 4A left, w/o CTZ). Such prominent asynchronous release was not a property conveyed by CTZ, but it rather displayed synapse-to-synapse variation. However, when AMPAR desensitization was reduced pharmacologically, postsynaptic current fluctuations elicited by synchronous and asynchronous release were superimposed on large residual glutamate currents (−1.6 to −11.9 nA, on average −6.6 ± 0.7 nA) towards the end of 200 ms EPSC trains. How accurately can release rates be estimated in the presence of such large residual glutamate currents? Rates of asynchronous release are about two orders of magnitude smaller than peak rates of synchronous release and therefore require very precise estimation of the influence of residual glutamate currents. For the calculation of ξ(t) in-between stimuli we relied on variance, using q estimates derived from CEF analysis. To separate the measured variance into components originating from the stochastics of the release process and those generated by channel gating, Neher & Sakaba (2001a) assumed the contribution of the latter to be proportional to the mean EPSC. Analysis of whole-cell currents elicited by application of AMPA supported the assumption of linearity for currents within a certain amplitude range (Neher & Sakaba, 2001a). Here we reinvestigated this issue by repetitively applying exogenous glutamate both in the absence and presence of CTZ (Fig. 5). We calculated the mean (Fig. 5A) and variance (Fig. 5B) of the ensemble exactly as during CEF analysis. When variance (low-pass filtered at f_c = 7–17 Hz) was plotted versus mean current, we found a roughly linear relationship between both quantities over the most relevant current range (Fig. 5C). The slope of this relationship can be considered as a measure for the filtered version of the single-channel current. The limiting slopes for currents < 50 pA (w/o CTZ) and < 2 nA (w CTZ) were, however, consistently smaller by ∼30% than slopes at larger currents (dotted lines in Fig. 5C, Table 2). This is in line with the observation obtained from single-channel recording that sublevels of lower conductance are populated more frequently at lower than at higher agonist concentration (Rosenmund et al. 1998). In addition, we observed some variability in the relationship between variance and mean glutamate current among different cells as indicated by the large s.d. of the average slopes (Table 2).

Table 2.

Parameters describing the variance of whole-cell currents elicited by application of exogenous glutamate

	Range/value (nA)	Slope/values (mean ± s.d.) (10−14 A)	Axis intercept (mean ± s.d.) (nA)
Fit to low range:
w/o CTZ	0 to −0.05	−4.1 ± 1.4	< 0.05
100 μm CTZ	0 to −2	−3.4 ± 1	< 0.15
Fit to medium range
w/o CTZ	−0.05 to −0.15	−5.1 ± 1.6	−0.012 ± 0.007
100 μm CTZ	−2 to −6	−5.3 ± 1.4	−0.82 ± 0.12
Error of extrapolation
w/o CTZ	at −0.225 nA	−0.08 ± 0.05*
100 μm CTZ	at −9 nA	−0.135 ± 0.07*

Summary data from 5 MNTB principal neurons recorded in the absence of CTZ (w/o CTZ) and 7 neurons recorded in the presence of 100 μm CTZ. Glutamate concentration in the application pipette ranged from 100 μm to 1 mm. Peak amplitudes of evoked whole-cell currents were adjusted by varying the distance of the application pipette from the recorded neuron.

^*Relative error of extrapolation (mean ± s.e.m.), measured as the relative difference between the measured variance at the indicated current and the medium-range linear fit.

In order to more accurately estimate the contribution of channel gating to the ensemble variance of EPSCs, it was thus necessary to measure the relationship between mean glutamate current and its variance for each synapse individually by analysing the decaying residual glutamate currents after stimulus trains. Immediately after cessation of synaptic stimulation, the variance of residual glutamate currents was often strongly contaminated by noise from asynchronous release. However, the analysis of 3rd and 4th cumulants (see below) indicated that in most experiments variance contributed by asynchronous release was small during the time when residual glutamate currents decayed from 66% to 33% of their amplitude measured at the end of the EPSC trains. In the subsequent analysis of asynchronous release, we therefore used extrapolated line fits to this current range as our estimate for channel variance and calculated release rates according to eqn (6). In five experiments the 3rd cumulant appeared to be slightly negative in part of this current range. In these cases we corrected variance before the line fit by a small amount calculated on the basis of the measured 3rd cumulant and the quantal size at the end of the train (eqn (11)).

How accurate is a linear extrapolation from the fitting window defined above (typically covering current ranges between −50 and −150 pA and between −2 and −6 nA in the absence and presence of CTZ, respectively) to current amplitudes measured between stimuli and shortly after stimulus trains? Figure 5C shows that line fits in the respective current ranges applied to glutamate-elicited whole-cell currents approximated the relationship between variance and current quite well, even for currents larger than the fitting window. Extrapolating the line fit to 1.5-fold larger current values resulted in an underestimate of variance of not more than 10–15% (Table 2). We assume that a similar relative error of the extrapolation also applies for measurements on synapses and take this for estimating the reliability of our values for asynchronous release (see below).

Variable contribution of asynchronous release to the total release during EPSC trains

Prominent asynchronous release was apparent in some but not all experiments. Figure 6 illustrates results from two representative synapses with either significant (Fig. 6A) or very small (Fig. 6B) amounts of asynchronous release. Both synapses were recorded in the presence of CTZ and stimulated using 200 ms trains. Figure 6Aa and Ba shows average waveforms for the EPSC trains and residual glutamate currents. The corresponding release functions ξ_V are displayed in Fig. 6Ab and Bb. Peak amplitudes of EPSCs and synchronous release transients were comparable in both synapses, but the rates of asynchronous release measured towards the end of the EPSC trains were remarkably different (Fig. 6Ab, 5.5 ves ms⁻¹; Fig. 6Bb, 1.2 ves ms⁻¹). Within approximately 15 ms, asynchronous release decreased by ∼50% in the synapse shown in Fig. 6A and in both synapses ξ_V was < 1 ves ms⁻¹ within 50 ms of cessation of stimulation. The average time course of the last release transient of the 200 ms trains is shown in Fig. 6C. Within the first 25 ms after its peak, the release rate decayed in a double exponential fashion with fast and slow time constants of ∼589 μs and ∼15 ms, respectively. Presumably, the former represents the decay of the synchronous release transient whereas the latter accounts for the initially rapidly decreasing asynchronous release. On a longer time scale, however, asynchronous release did not decay with a single exponential to the level of spontaneous release but on several time scales (see below).

Figure 6. Asynchronous release during and shortly after 200 ms EPSC trains (100 Hz, 20 stimuli).

Illustrated are two representative synapses recorded in the presence of 100 μm CTZ showing either prominent (A) or little asynchronous release (B). Aa and Ba, average waveforms for EPSC trains and residual glutamate currents obtained from ensembles of 207 (A) and 70 (B) EPSCs. Ab and Bb, average release functions obtained by CEF analysis. Insets, average release rate of the last 10 EPSCs in the train shown at expanded scales for a comparison of asynchronous release following the synchronous release transients. Scale bars in B also apply to A. Stimulus artifacts have been blanked for clarity. C, average time course of the final release transient of the trains (EPSC₂₀) obtained from 27 synapses recorded in the absence (n = 9) or presence (n = 18) of 100 μm CTZ plotted on a semilogarithmic scale illustrating the biphasic decay of the release rate. The decay of the release transient was fitted by a double exponential function (grey line) with fast and slow time constants as indicated. D, scatter plot of average asynchronous release rate at the end of 200 ms EPSC trains versus the peak rate of the initial EPSCs recorded in the absence (⋄) and presence (♦) of CTZ. Average rates of asynchronous release varied strongly among MNTB synapses. Continuous and dotted lines represent linear fit and 95% confidence intervals, respectively. No correlation with the initial peak rate was found (r = 0.014). One synapse (shown in Fig. 8A) with exceptionally high asynchronous release is not included in this plot.

On average, asynchronous release rate during the last five EPSCs of 200 ms trains was 2.3 ± 0.6 ves ms⁻¹ (n = 27). The average rate of asynchronous release correlated neither with the initial peak amplitude of the synchronous release transient (Fig. 6D) nor with the amount of synaptic depression (not shown). To estimate the fraction of synapses with clearly identifiable asynchronous release, we selected all synapses in which the total variance exceeded our estimate for channel variance by more than 30% when measured 5–10 ms after the last stimulus (twice the value for reliability derived from Table 2). This ‘limit of resolution’ corresponded typically to an equivalent rate of ξ = 0.4 ves ms⁻¹ for experiments in the absence of CTZ and 2.4 ves ms⁻¹ in its presence. Using this criterion, we detected asynchronous release unequivocally in 3 out of 5 (50 ms trains) and 6 out of 9 synapses (200 ms trains) under control conditions. In the presence of CTZ, this fraction amounted to 2 out of 4 (50 ms trains) and 7 out of 19 (200 ms trains) synapses. Given the well-documented changes in synaptic properties with development (Taschenberger & von Gersdorff, 2000; Iwasaki & Takahashi, 2001; Joshi & Wang, 2002; Taschenberger et al. 2002; Puente et al. 2005; Renden et al. 2005; Hermida et al. 2006) it seems possible that the changes in asynchronous release reflect different maturational states of the synapses. Alternatively there could be gradients in these parameters within the MNTB due to its tonotopic organization (Brew & Forsythe, 2005; Leao et al. 2006) in which case ‘high-frequency synapses’ and ‘low-frequency synapses’ would differ in the relative contribution of phasic versus asynchronous release for a given stimulation frequency.

Estimation of release rate and quantal size from 3rd and 4th cumulants in the presence of residual glutamate current

The release rate estimates presented above assumed a constant quantal size for a short time after the stimulus train. Thus, so far we neglected the recovery of q(t) after desensitization. In principle, q estimates might be calculated according to eqn (4). In this case, however, these would be unreliable being based on the ratio between two small quantities (variance and deconvolution rate), both of which are likely to have large relative errors due to inaccuracies in the estimation of residual glutamate current and its associated channel variance. Alternatively, higher cumulants can be used to estimate quantal sizes and release rates (Fesce, 1999; Neher & Sakaba, 2001b). Cumulants are linear combinations of the higher moments of the current fluctuations and have the convenient property of being additive for independently fluctuating signals (see Neher & Sakaba, 2003 for an introduction to their properties and use in synaptic research). Because the release rate is expected to be sufficiently low after cessation of stimulation, the 3rd and 4th cumulants can provide well-resolved estimates for q(t) and ξ(t) (eqn (8) and (9)) (Neher & Sakaba, 2001b). However, immediately after trains and particularly in the presence of CTZ, residual glutamate currents are very large and introduce excessive noise into the measurement of cumulants and also a bias for the case of the 4th cumulant.

We analysed the higher cumulants of the large whole-cell currents evoked by glutamate application as illustrated in Fig. 5. Third and 4th cumulants were calculated, filtered at 6.7 Hz bandwidth and plotted alongside variance (Fig. 5B). For absolute current amplitudes > 200 pA (w/o CTZ) or > 5 nA (w CTZ) both 3rd and 4th cumulants displayed large fluctuations. While the 3rd cumulant fluctuated symmetrically around zero, the 4th cumulant often showed a bias towards positive values. The observed fluctuations follow the predictions by Heinemann & Sigworth (1991). They are in the same order of magnitude as the standard deviation (s.d.) of cumulant estimates in the presence of Gaussian noise (eqn (32) in Heinemann & Sigworth, 1991) and the s.d. of 3rd and 4th cumulants changes roughly with the 3rd and 4th power of the variance, respectively. The mean values of 3rd and 4th cumulants measured in the current ranges between −0.20 and −0.25 nA (w/o CTZ) and between −8 and −10 nA (w CTZ) from 13 experiments are summarized in Table 3. Within these current ranges, the mean 3rd cumulant is smaller than or similar to its standard error. The mean 4th cumulant is positive, but of the same order of magnitude as its s.d. Given the steep dependence of the s.d. of both cumulants on variance (and implicitly on current) it is obvious why they are deeply buried in the noise for larger currents, while smaller residual glutamate currents of, e.g., half the size will allow the resolution of 16-fold smaller signals. It should be noted, though, that the fluctuations of the cumulants in EPSC recordings are expected to be smaller than the values in Table 3 because of the larger ensemble sizes.

Table 3.

Parameters describing 3rd and 4th cumulants of whole-cell currents elicited by application of exogenous glutamate

	Mean ± s.d.a	Equivalent release rateb (ves ms−1)	Assumed quantal size (pA)
3rd cumulant (in A3)
w/o CTZ	(−0.06 ± 0.1) × 10−35	0.016 ± 03	−10
100 μm CTZ	(−38.4 ± 32) × 10−35	1.7 ± 1.4	−18.5
4th cumulant (in A4)
w/o CTZ	(1.2 ± 0.42) × 10−46	0.6 ± 0.2	−10
100 μm CTZ	(289 ± 130) × 10−46	12.4 ± 5.6	−18.5

^aValues were measured during decaying phases of glutamate-evoked currents (or else around the peak) in the range −0.2 to −0.25 nA (w/o CTZ, n = 5) or −8 to −10 nA (w CTZ, n = 7). Three out of 13 experiments in this series were performed at V_h = −70 mV (instead of the usual −80 mV). Skew values of these were corrected by a factor (8/7)³ = 1.5 and kurtosis values by (8/7)⁴ = 1.7. Results were low-pass filtered at 6.7 Hz, 3–6 traces each.

^bThe release rate, which would produce the measured 3rd and 4th cumulants, calculated in analogy to eqn (B7a) of Neher & Sakaba (2003), assuming a quantal size (last column) as measured by CEF analysis towards the end of 200 ms 100 Hz EPSC trains.

What is the magnitude of the errors introduced by residual glutamate currents on release rate estimates derived from the 3rd and 4th cumulants? To address this question, we converted cumulants of glutamate application-evoked currents and their s.d.s into ‘equivalent release rates’ using eqn (B7a) in Neher & Sakaba (2003) and assuming quantal amplitudes as they are typically observed at the end of 100 Hz stimulus trains (last column of Table 3). Third and fourth cumulants are proportional to ξ and to the 3rd and 4th power of q, respectively. It turns out that the influence of fluctuations is much smaller when analysing 3rd cumulants compared to results from 4th cumulants. Also, experiments in the absence of CTZ are much less afflicted by residual glutamate current than those in its presence. This, obviously is due to the much smaller residual glutamate currents in spite of the fact that resolving power is reduced as a consequence of a smaller q. The numbers for equivalent release rates range from 0.016 to 12.4 events ms⁻¹ (Table 3), which is from negligible to exceedingly large considering that the peak asynchronous release rates typically observed at the end of a stimulus train were on average 2.3 ± 0.6 ves ms⁻¹ (see above).

Asynchronous release rates estimated from 3rd and 4th cumulants

Figure 7A shows the average trace of EPSCs evoked by 20 stimuli at 100 Hz in the presence of CTZ and the 3rd and 4th cumulants during their decay. During the first 100 ms period following the train, while the absolute amplitude of residual glutamate current (Fig. 7Aa, grey trace) is larger than −4 nA, both cumulants (Fig. 7Ab) show strong fluctuations and the 4th cumulant has a positive bias as expected from the analysis of glutamate-evoked currents described above. Within a time window from 10 to 60 ms after the train the magnitude of both cumulants (3rd, −1.1 × 10⁻³⁴ ± 0.8 × 10⁻³⁴ A³; 4th, 5.9 × 10⁻⁴⁵ ± 2.6 × 10⁻⁴⁵ A⁴) were within the range of values expected for residual current effects (Table 3). Therefore we cannot distinguish asynchronous release from residual glutamate current during the early phase of the EPSC decay. Later, however, as residual glutamate current decreases from −2 nA to −1 nA (≥ 200 ms after the end of the train), the 3rd cumulant fluctuated around a constant mean of −5.5 × 10⁻³⁶ A³ until the end of the record. This is larger than the 3rd cumulant of glutamate-induced currents. Once residual glutamate current decreases below −1 nA, both 3rd and 4th cumulants should reflect spontaneous release. Some large spikes in both records (see Fig. 7Ac for an example) could be traced to individual large EPSCs in the original record, which, within a 5 ms time window, dominate the mean of the ensemble in spite of averaging over 143 repetitions. While such large events (−128 pA in the case of the largest spike in Fig. 7Ac) dominate 3rd and 4th cumulants, they were only barely recognizable in variance. According to eqn (7) and (8) the mean cumulants indicate a rate of spontaneous release of 2.7 ves s⁻¹ and a quantal amplitude of −45 pA (Fig. 7Ad).

Figure 7. Analysis of higher cumulants in two synapses stimulated with 200 ms (A) and 50 ms (B) 100 Hz trains and recorded in the presence of 100 μm CTZ.

Aa and Ba, average waveforms for EPSCs (black trace) and residual glutamate currents (grey trace) obtained from ensembles of 144 (A) and 81 (B) EPSCs. Ab, decay of 3rd (top) and 4th (bottom) cumulants after the EPSC train for the same synapses and plotted on the same time scale as in Aa. Higher cumulants were large and fluctuating during stimulation and were therefore blanked up to 6 ms after the peak of the last EPSC for clarity. Ac, expanded section (time window from 200 ms to 1 s after the last EPSC) from the traces as shown in Ab. Ad, time course of release rate (top) and quantal size (bottom). Time scale of Ad applies also to Ac. Bandwidth was 67 Hz. B, a different experiment using 50 ms stimulus trains. Ba, average EPSC waveform. Bb, time course of release rate (top) and quantal size (bottom) for the same synapses and plotted on the same time scale as in Ba. Higher cumulants were filtered at 6.8 Hz. The traces were blanked for times earlier than 100 ms after the end of the EPSC train. Rates and quantal size in Ad and Bb were estimated from 3rd and 4th cumulants according to eqn (8) and (9). Bc, average EPSC waveform (black trace) and estimated residual glutamate current (grey trace) shown on expanded time scale.

Figure 7B shows another example, in which an ensemble of 81 EPSCs was recorded for almost 5 s after trains. It too had a constant rate of spontaneous release throughout the time window from 200 ms after the train to the end. Here ξ(t) and q(t) were calculated (eqn (7) and (8)) after low-pass filtering 3rd and 4th cumulants at 6.7 Hz demonstrating the resolution in the determination of these two quantities that can be obtained with an ensemble of this size.

Another synapse with exceptionally large asynchronous release allowed us to compare rate estimates obtained from variance with those derived from higher cumulants (Fig. 8A). The cumulant analysis according to eqn (7) and (8) resulted in a decaying ξ(t) after the end of the train and a nearly constant quantal amplitude as early as 80 ms after the end of the stimulus train (not shown). In this time window, the amplitudes of higher cumulants were large enough to exceed effects from residual glutamate: 15 ms after the end of the stimulus train the 3rd cumulant (−1.5 × 10⁻³³ A³) was an order of magnitude higher compared to those values expected exclusively from residual gluamate (Table 3). The 4th cumulant (2 × 10⁻⁴⁴ A⁴), however, may well include a contribution from residual glutamate currents. This led to exceedingly large values in quantal amplitude during the first 80 ms and to large fluctuations in ξ(t) (not shown). The conclusion that the 3rd cumulant faithfully represents quantal release (in this example) while the 4th cumulant is compromised by contributions from AMPAR channel fluctuations is corroborated by Fig. 8Ab. Here ξ(t) obtained from corrected variance was plotted against time together with the apparent rates calculated directly from 3rd and 4th cumulants according to eqn (B7a) of Neher & Sakaba (2003). To do so, we assumed a constant value of q = −21 pA, which is the mean quantal amplitude in that experiment in a window from 0.4 to 0.8 s after the train. The rate derived from the 3rd cumulant agreed well with that from variance, while the 4th cumulant-derived rate shows fluctuations clearly deviating from the other two curves.

Figure 8. Decay of asynchronous release after 200 ms following 100 Hz trains.

A, analysis of an experiment performed in the presence of 100 μm CTZ, in which the rate of asynchronous release was exceptionally high. Aa, average waveform for EPSC train and residual glutamate current obtained from an ensemble of 30 EPSCs. Ab, release rate estimates during an early time window from 10 to 140 ms after the last stimulus calculated from variance (continuous noisy trace, low-pass filtered at 670 Hz), 3rd cumulant (continuous smooth trace, low-pass filtered at 17 Hz), and 4th cumulant (dashed trace, low-pass filtered at 17 Hz) individually, assuming a quantal amplitude of −21 pA (see text). Note the similar time course of the different estimates. An exponential fitted to the variance-derived release rate in that time window yielded a decay time constant of ∼20 ms. Early sections of the traces were truncated at those time points where influences from the last stimulus due to filtering rendered them unreliable. B, average time course of the rate of asynchronous release (Ba, black trace) calculated from 3rd cumulants and quantal size (Bb) calculated from 3rd and 4th cumulants after 200 ms EPSC trains during a time window from 0.1 to 1.0 s after the last stimulus. On average, asynchronous release decayed with an exponential time constant of ∼80 ms in that time window (Ba, grey trace) while q(t) fluctuated around a nearly constant value of −27 pA. Summary data from 27 synapses.

In this experiment, the average asynchronous release rate during trains measured by CEF analysis was 10–20 ves ms⁻¹ and decayed by a factor of ∼2 within 5 ms after the trains. Figure 8Ab shows that over an intermediate range the time course can be fitted with an exponential having a time constant of ∼20 ms. From > 80 ms after the train it further decayed with a slower time constant of ∼45 ms. It should be emphasized, though, that this synapse had exceptionally high spontaneous release and that the rate still seemed to decay slowly at the end of the record. The average decay time constant during the time interval from 80 ms to 1 s after the stimulus train was 79.3 ± 22.7 ms (excluding this and 2 more synapses, which had similarly decaying rates late in the record). The average rate of spontaneous release ≥ 1 s after the 200 ms trains was 2.98 ± 0.85 ves s⁻¹. The average q, as measured by 3rd and 4th cumulants, was −27.3 ± 3.4 pA (n = 15, Fig. 8B). This was ∼27% lower than the average quantal size of the first EPSC in the trains, as measured by CEF analysis for the same set of experiments. Differences in the two methods of analysis which may well account for the discrepancies are discussed below.

Discussion

The main goal of our study was to reconstruct, with high resolution, the time course of phasic and asynchronous quantal release during and after repetitive afferent fibre stimulation of the calyx of Held synapse in juvenile (P8–10) rats. Applying a new quantitative method based on a combination of ensemble fluctuation analysis and deconvolution, we find that release transients evoked by calyceal APs were very brief with an average half-width of 0.42 ms under control conditions and 0.58 ms in the presence of CTZ. During repetitive high-frequency stimulation, the half-width of the phasic release transients gradually increased by about 66% and significant asynchronous release built up during stimulus trains in a subset of synapses. Peak rates of asynchronous release ranged from 0.2 to 15.2 ves ms⁻¹ with a mean of 2.3 ves ms⁻¹. On average, asynchronous release accounted for less than 14% of the total number of about 3670 vesicles released during 200 ms 100 Hz trains. Following such trains, asynchronous release decayed with several time constants, the fastest one being in the order of 15 ms.

Several methods are available to study the rate of quantal release. Each of these is suited best under certain experimental conditions: at synapses with low average quantal content, individual quanta can either be counted directly (Katz & Miledi, 1965; Zucker, 1973) or the release rate can be inferred from quantal latency distributions (Barrett & Stevens, 1972; Isaacson & Walmsley, 1995; Taschenberger et al. 2005). At synapses with high average quantal content and especially during repetitive high-frequency stimulation, deconvolution analysis provides an alternative option for estimating the release time course from average EPSC waveforms, provided that both amplitude and time course of the underlying quantal event are invariant and known (Van der Kloot, 1988; Diamond & Jahr, 1995; Vorobieva et al. 1999; Hefft & Jonas, 2005). Complications arise, however, if quantal size cannot be assumed to be constant and/or if additional current components such as ‘spillover currents’ or ‘residual transmitter currents’ contribute to the postsynaptic response, such as was shown to be the case for strong stimulation of the calyx of Held synapse (Neher & Sakaba, 2001a; Sakaba & Neher, 2001b; Wong et al. 2003; Taschenberger et al. 2005).

For such a scenario, the combined data from the mean time course and the fluctuations in an ensemble of EPSCs provide detailed information on the quantal parameters and time course of release. In particular, combining deconvolution of the mean EPSC with variance analysis allowed us to track changes in both quantal size q and release rate ξ during trains of stimuli. Residual glutamate currents due to a slow clearance of released transmitter can be corrected for in the analysis. However, large residual glutamate currents may lead to several adverse affects which, as we show, need detailed consideration. Applying this method we find asynchronous release to build up during 100 Hz trains in a subset of synapses.

Comparison of different methods of ensemble fluctuation analysis

Discrete ensemble fluctuation (DEF) analysis represents one option for the analysis of EPSC fluctuations (Scheuss et al. 2002). It evaluates peak amplitudes of repetitively evoked EPSCs and, essentially, is a variant of multiple-probability fluctuation analysis (Silver et al. 1998). During trains, peak EPSC amplitudes vary because of the stochastics of the release process and the interplay of facilitation and depression. When the resting calyx of Held synapse is stimulated repetitively, short-term depression dominates and usually leads to a strong reduction of EPSCs during trains (von Gersdorff et al. 1997; Scheuss et al. 2002; Taschenberger et al. 2005). Additional current fluctuations due to channel gating by residual glutamate are not considered in DEF analysis. Continuous ensemble fluctuation (CEF) analysis, on the other hand, separates noise according to its sources. It derives estimates for q and ξ point by point along a trace, similar to ensemble fluctuation analysis of voltage-activated records (Sigworth, 1980). Quantal amplitudes are derived from a comparison of ensemble variance with the deconvolution-derived release rate ξ_D. The effects of residual glutamate currents are allowed for by explicit modelling as part of the deconvolution routine and – with regard to variance – by a correction procedure. For calculating the quantal size q associated with a given EPSC in the train, we average results over a certain time window, which includes the phasic part of the respective EPSC. In this way, we can obtain estimates for the average q and also for the quantal content of all EPSCs within a stimulus train. Comparing results from DEF and CEF analysis, we find that the estimates from the latter lie within the bounds of the former (except for some special cases with identifiable sources of error) and that they favourably compare with q estimates derived from analysing spontaneously occurring mEPSCs. Both DEF and CEF analysis show a strong reduction in quantal size during stimulus trains. The decrease in q was not completely eliminated by adding CTZ to the bath solution, which agrees with earlier studies (Partin et al. 1994; Meyer et al. 2001; Scheuss et al. 2002).

Detection of asynchronous release

Asynchronous release between stimuli and after stimulus trains can be estimated by CEF analysis, even in the presence of substantial residual glutamate current. Furthermore consideration of the higher (3rd and 4th) cumulants of the fluctuations provides a convenient way to measure quantal amplitudes and rates during episodes of low and slowly changing release (Fesce, 1999). We have previously examined the theoretical resolution of these methods both by dual voltage-clamp experiments and by simulation (Neher & Sakaba, 2001b). In the present study we apply them to AP-evoked EPSCs and consider some systematic deviations, which result from large residual glutamate currents. We compare currents in the presence and absence of CTZ. CTZ and structurally related drugs have been used extensively at glutamatergic synapses for the purpose of eliminating or delaying desensitization (Yamada & Rothman, 1992; Patneau et al. 1993; Trussell et al. 1993). We have shown previously (Sakaba & Neher, 2001b) that a combination of CTZ and the low-affinity AMPAR antagonist kynurenic acid delays desensitization and avoids saturation of AMPARs (Wadiche & Jahr, 2001), such that EPSCs can indeed be considered as linear indicators of quantal release even during strong stimuli. In the present study, we use either none of these drugs or only CTZ, because kynurenic acid reduces q. This is a disadvantage when aiming at the study of variance and higher cumulants, which vary with the square or higher powers, respectively, of quantal amplitude. We find that CTZ alone can keep quantal amplitude constant to within ∼60–80% during our stimulation protocols (up to 20 stimuli at 100 Hz), while w/o CTZ, q drops to ∼25% of its initial value. We consider our estimates for q reliable, since four different methods (analysis of spontaneous mEPSCs, DEF analysis, CEF analysis, and analysis of higher cumulants) lead to consistent results. On the other hand, the presence of CTZ leads to sizable residual glutamate currents, which at the end of 100 Hz trains can be as large as the maximum EPSC in a train.

In spite of such large residual glutamate currents and in spite of the fact that the decay of evoked EPSCs as well as that of mEPSCs is significantly slowed in the presence of CTZ, deconvolution analysis recovers the time course of release and shows that the release function is only slightly broadened by CTZ in contrast to the half-width of EPSCs, which is increased 10-fold. A slight broadening of the release transient by CTZ is probably caused by a broadening of presynaptic APs (Ishikawa & Takahashi, 2001). Likewise, we observed broadening of release transients during trains (Taschenberger et al. 2005) both in the presence and absence of CTZ. Parameters describing neurotransmitter release, such as the width of the release transient, the relative reduction of quantal content during trains and the development of asynchronous release during trains (see below) were variable between synapses and possibly reflect the fact that synapses are not fully mature yet at the age of P8–10. It will be interesting to study such changes during development in a systematic way.

One of the most variable aspects that we encountered is asynchronous release. In some synapses hardly any asynchronous release could be detected, even after 20 stimuli at 100 Hz, similar to the case of more mature synapses (P12–14; Taschenberger et al. 2005). In other synapses it reached high levels during trains, such that, integrated over a 10 ms period between two successive stimuli, it contributed almost as much as synchronous release. Following trains, asynchronous release decayed over three orders of magnitude from maximum rates of a few thousand events per second, which is close to the maximum rate of vesicle recruitment at steady state (Neher & Sakaba, 2001a), to an average of 5.8 vesicles per second. The decay occurred over several time scales, with an initial half-decay time in the order of 10 ms. This was followed by an episode in which decays can be fitted by exponentials, with time constants in the range 20–50 ms (see also Taschenberger et al. 2005; Erazo-Fischer et al. 2007) and by a very slow decay towards the level of spontaneous release in the seconds range. Presumably, this time course is related to the decline of [Ca²⁺]_i near active zones due to buffered diffusion and Ca²⁺ extrusion. Interestingly, the decay of asynchronous release after stimulus trains follows a very similar rapid time course in parvalbumin-expressing hippocampal interneurons (Hefft & Jonas, 2005). The decay of release from 100 ves s⁻¹ to resting conditions is conveniently analysed by studying the higher cumulants. Unfortunately, however, during a time window from ∼10 to 100 ms after the end of trains, residual glutamate currents in the presence of CTZ are very large such that estimates from 3rd and 4th cumulants are not reliable. On the other hand, the release rate is too small to be measured by variance. It seems, that quantal amplitude, which is reduced at the end of the train by desensitization, recovers partially within this short time. In any case, q estimates, which are provided by the analysis of 3rd and 4th cumulants are constant to within 20% from the earliest time they can be obtained (∼100 ms after the end of the trains) up to ∼5 s later.

The complicating effects of residual glutamate current on estimates of quantal parameters

As discussed above, relative constancy of q can be achieved by adding CTZ to the bath solution. However, under those conditions, residual glutamate currents can reach amplitudes of −10 to −15 nA presumably because of reduced desensitization and higher apparent affinity of AMPARs for glutamate (Partin et al. 1996). Such large residual glutamate currents turned out to be a problem for fluctuation analysis in two respects. (1) The variance of residual glutamate current is large and no longer proportional to current over the entire amplitude range. (2) Large residual glutamate currents contaminate the signals of 3rd and 4th cumulants by large noise as predicted by Heinemann & Sigworth (1991). In addition, they contribute to the 4th cumulant. Such contributions are large enough not to be neglected with respect to those contributed by release events. As a consequence, the resolution of 3rd and 4th cumulant-derived estimates for q(t) and ξ(t) immediately at the end of the EPSC trains is lower than that in the absence of CTZ, when amplitudes of residual glutamate currents are < 400 pA (see Table 3). This holds in spite of the fact that w/o CTZ, quantal amplitudes are smaller by a factor of two to three and consequently 4th cumulants are reduced by factor of 2⁴ to 3⁴.

Non-linearities in the relationship between variance and residual glutamate current can be expected on several grounds. First of all, standard ensemble noise analysis, as introduced by Sigworth (1980), expects a parabolic relationship, in which the linear approximation holds only for low opening probabilities of channels. Thus we would expect that the linear approximation, which we used to correct total variance, overcompensates for the contributions of open–close fluctuations of the residual glutamate currents. For glutamate currents an additional complication arises: Rosenmund et al. (1998) have shown that the probability with which sublevels of conductance are visited depends on the occupancy state of the glutamate receptors. One would therefore expect a lower apparent single channel conductance at low current levels, and correspondingly a lower slope of the variance–current relationship. Applying glutamate to postsynaptic neurons we found such a lower slope for the late phase of current decays. We therefore measured the relationship between variance and current over ranges which covered those of recorded residual glutamate currents (both w and w/o CTZ). We identified amplitude ranges for which linear approximations hold and allow extrapolation into the typical range of residual glutamate currents during and after 100 Hz stimulus trains. The uncertainty in the extrapolation sets limits to the resolution of the variance-based estimates for ξ(t), which again were more severe in the experiments including CTZ compared to those w/o CTZ (thresholds for reliable detection of asynchronous release were determined as 2.9 events ms⁻¹ and 0.9 events ms⁻¹, respectively).

Nevertheless, we would not advise against the use of CTZ in general. In its absence, q may change by up to 50% from one EPSC to the next (see Fig. 3). This raises difficult questions about the analysis of evoked release and the meaning of q. As long as release is less than one quantum per active zone during an AP there will be little mutual desensitization among quanta during a given AP. Therefore, our approach to determine a quantal amplitude for each AP in a train seems valid and represents the average state of desensitization of AMPARs at the time of a given AP. However, for stronger stimulation, either at higher extracellular [Ca²⁺] or else during longer-lasting presynaptic voltage-clamp depolarizations, quanta may interact with respect to desensitization, and residual glutamate may rapidly desensitize AMPAR channels at neighbouring active zones and thereby change the time course of their quantal responses. Therefore, the approach taken in most of our previous studies was to work under conditions of relatively constant quantal size (i.e. with both CTZ and kynurenic acid added).

Furthermore, there is a severe systematic problem in cases with strongly varying quantal sizes, i.e. in the absence of CTZ. The procedure of CEF analysis described in the Methods handles changes in quantal size by a posteriori correction: in a first pass a deconvolution is performed with the assumption of constant q, which is later corrected on the basis of a comparison with variance (eqn (5)). The problem remains, however, that during the first pass a release rate based on constant q also underlies the calculation of residual glutamate. Thus we underestimate residual glutamate concentration late in the record, when q is reduced. This underestimate is partly compensated for by neglecting the decreased postsynaptic glutamate sensitivity in the estimation of the residual glutamate current. The final outcome of this partial compensation depends on the non-linearities in the glutamate dose–response curve. For this reason we applied an iterative procedure in a few cases. First, we performed CEF analysis as described. Then we repeated the deconvolution using a variable quantal size, as determined in the first cycle. In this second run we adjusted the parameters of the diffusion model and of the mEPSC for best agreement between ξ_D and ξ_V values. It turned out that the required adjustments were minor. However, the linear interpolation between q_i values, used so far as an approximation to the q(t) function, had to be replaced in some cases by a more smoothly varying polynomial or by an exponentially changing amplitude function, in order to avoid discrete breaks in slope of the estimates for the residual current.

In conclusion, the approach taken here allowed us to extract information about the time course of neurotransmitter release from EPSCs in the presence of complicating factors, such as residual glutamate and postsynaptic desensitization. Unfortunately, these adverse effects are very severe in the calyx of Held at the particular age which is otherwise most suitable for dual whole-cell voltage clamp (P8–10), such that the analysis requires careful consideration of several potential sources of error. Effects of residual glutamate current and desensitization are greatly reduced at synapses of older animals, which are, however, less easily accessible to presynaptic recordings. Nevertheless, even for younger calyx synapses, release evoked by afferent fibre stimulation can be determined quite precisely, both with respect to quantal amplitude and quantal content, if excessive residual glutamate currents are avoided. We expect that the methods developed here will be more readily applicable in the study of asynchronous release in other preparations, where its relationship to residual transmitter current is more favourable, such as at inhibitory synapses (Vincent & Marty, 1996; Lu & Trussell, 2000; Kirischuk & Grantyn, 2003; Hefft & Jonas, 2005). The possibility of analysing the time course of synchronous and asynchronous release will allow the study of biochemical processes underlying different modes of synaptic vesicle fusion and transmitter release.