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

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1 J Physiol (27) pp Kinetics of both synchronous and asynchronous quantal release during trains of action potential-evoked EPSCs at the rat calyx of Held V. Scheuss, H. Taschenberger and E. Neher Max Planck Institute for Biophysical Chemistry, Department of Membrane Biophysics, Göttingen, Germany 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 (2 ms, 1 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.2 to 15.2 vesicles ms 1 (ves ms 1 ) with a mean of 2.3 ±.6 ves ms 1. On average, asynchronous release accounted for less than 14% of the total number of about 367 ± 35 vesicles released during 2 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. (Received 2 July 27; accepted after revision 29 September 27; first published online 4 October 27) Corresponding author E. Neher: Max Planck Institute for Biophysical Chemistry, Am Fassberg 11, D-3777 Göttingen, Germany. eneher@gwdg.de 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. 22; von Gersdorff & Borst, 22). At the developmental stage, at which such measurements are most readily performed (postnatal days (P) 8 1) 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 V. Scheuss and H. Taschenberger contributed equally to this work. procedures to characterize separately synchronous release, asynchronous release, and residual glutamate currents. At many inhibitory (Vincent & Marty, 1996; Lu & Trussell, 2; Kirischuk & Grantyn, 23; Hefft & Jonas, 25) as well as excitatory (Goda & Stevens, 1994; Cummings et al. 1996; Otis et al. 1996; Kinney et al. 1997; DiGregorio et al. 22; Oleskevich & Walmsley, 22; Singer et al. 24) 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. 25). 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 DOI: /jphysiol

2 362 V. Scheuss and others J Physiol for studying synaptic transmission using dual voltage clamp (Neher & Sakaba, 21b,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. 21; Scheuss et al. 22) 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 2 ms-long 1 Hz trains. Methods Electrophysiological recordings Brainstem slices were prepared from P8 1 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 2 μm-thick slices were cut on a VT1S vibratome (Leica, Germany). Slices were maintained at 35 C for 3 4 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, NaHCO , ascorbic acid.4, myo-inositol 3, sodium pyruvate 2, CaCl 2 2, MgCl 2 1 and d-aminophosphonovalerate (d-ap5).5 (ph7.4). Bicuculline (1 μm) and strychnine (2 μm) were routinely included in the bath solution to suppress inhibitory postsynaptic currents. In some experiments 1 μm cyclothiazide (CTZ) was added to reduce AMPAR desensitization. EPSCs were evoked by afferent fibre stimulation (1 μs, 3 V) using a bipolar stimulating electrode and recorded at a holding potential (V h )of 7 or 8 mv with EPC-9 or EPC-1 patch-clamp amplifiers (Heka, Lambrecht, Germany). The pipette solution contained (mm): caesium gluconate 13, TEA-Cl 2, Hepes 1, sodium phosphocreatine 5, Mg-ATP 4, GTP.3 and 5 EGTA (ph 7.2, 31 mosmol l 1 ). Open tip resistance was M. 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 3M. R s values typically ranged from 3.5 to 8 M before compensation. Currents were sampled at 2 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. 21). Artifacts associated with afferent fibre stimulation were blanked by linear interpolation. Short ( 2 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 2 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. 22). Discrete ensemble fluctuation (DEF) analysis Non-stationary ensemble fluctuation analysis was performed according to Scheuss et al. (22). 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, 1 Hz, repetitions at 1 s intervals, n = 9 synapses) as well as long EPSC trains (2 stimuli, 1 Hz, repetitions at 15 s intervals, n = 28 synapses) were analysed. The intersweep intervals allowed for > 9% recovery from synaptic depression. Data sets showing > 3% 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. 22) to minimize the influence of trends and drifts in the data (Clamann et al. 1989; Scheuss & Neher, 21). Since recruitment of new vesicles between individual stimuli is negligible during 1 Hz trains, the quantal size q i for EPSC i can be estimated from the mean (Ī i ), variance (Var i ), and covariance (Cov i ) (eqn (9) in Scheuss et al. 22). Assuming all covariances to be of postsynaptic origin, a lower estimate for q i is obtained from q ilower = Var i/ī i. (1) Assuming all covariance derives from vesicle depletion, an upper estimate for q i is obtained from q iupper = Var i/ī i Cov i,i+1 /Ī i+1. (2)

3 J Physiol Release kinetics at the calyx of Held 363 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. 25) 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 3 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, 21a). 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, 21a; Sakaba & Neher, 21a), 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 (λ 2 (t)) is also an estimator for ξ(t). A scaled version of λ 2 (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 22 repetitions, on average 96), which provide more accurate variance estimates. Additionally, we introduced a sidelobe correction (see below) to improve the time resolution of λ 2 (t) estimates. (iii) We allowed quantal size to be a slowly varying quantity q(t), which was calculated piecewise from a comparison of varianceand deconvolution-derived release rates. We first calculated an apparent deconvolution rate ξ (t) from the mean EPSC, assuming a constant quantal size q (Neher & Sakaba, 21a). 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 λ 2 (t) = 1 2(N 1) N 1 n=1 ( y n (t)) 2 where y n (t) represent the nth difference trace y n (t) = y n (t) y n+1 (t) after band-pass filtering. Band-pass filtering of the difference traces was performed as previously described (Neher & Sakaba, 21b) using two-stage box filters, except that we used longer time windows (.5 ms instead of.3 ms) for the box filters. The lower frequency band used here (peak of the pass-band shifted from 174 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 (21b). 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 f c 1/(3T box ). 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 λ 2,i ( indicates correction for background and AMPAR channel variance) and release rate ξ o,i 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 q i = λ 2,i H V (4) q o ξ o,i (eqn (B8) in Neher & Sakaba, 23) where λ 2,i and ξ o,i represent variance- and deconvolution-derived rates, respectively, associated with the phasic release transient evoked by the ith stimulus and H V 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 = (by filling in values of q 1 ) 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 2 ms EPSC trains, which showed strong desensitization, q estimates were small during the second half of the trains and fluctuated strongly from one (3)

4 364 V. Scheuss and others J Physiol 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. Aa C b 'Unfiltered' halfwidth (ms) c 1ms ms 2 ms Ba b Filtered halfwidth (ms) filtered original rate 2. ξ Vraw ξ V ξ D 2 ms 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 2 EPSCs was generated. The original, unfiltered release function had a half-width of.45 ms. Aa, mepsc waveform before (black) and after (grey) band-pass filtering. Ab, 2nd central moment λ 2 (t) ofthe 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 (21b). 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.36 ms was expanded in time by various factors to obtain release transients with half-width values ranging between.36 and 1.2 ms. These waveforms were low-pass filtered at 48 Hz and their half-widths measured. The resulting relationship was used to translate filtered into corrected waveforms (Table 1). 1 ves/ms 5 na With the time course of q(t), we then calculated two new estimates for ξ(t). One was based on deconvolution: ξ D (t) = ξ o (t) q o q(t). (5) A second one was based on corrected variance λ 2 (t) (Neher & Sakaba, 21b, 23): ξ V (t) = λ 2 (t)h V /q2 (t). (6) As stated above, the goal of the fitting procedure is to find a set of parameters for which ξ D (t) and ξ V (t) 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). To quantify asynchronous release in-between late stimuli of long trains (2 stimuli, 1 Hz), we calculated a mean ξ V trace by averaging peak-aligned 1 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 1 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 <.5 ms (<.88 ms after band-pass filtering) for P8 1 calyx synapses (Schneggenburger & Neher, 2). In this case, ξ async equals (M total M initial )/6.4 ms, where M total is the total quantal content within the 1 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 λ 2 (t) 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

5 J Physiol Release kinetics at the calyx of Held 365 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 (.47 ms A half-width) which was flanked by two smaller sidelobes (1.7% and.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 A 12 9 control 1 μm CTZ Ba 2 ves/ms 5 na q CEF (pa) q DEF (pa) 9 12 B 6 b 1 ves/ms q (pa) 45 3 C Quantal size (pa) Time (ms) Figure 2. CEF analysis of 5 ms EPSC trains evoked by afferent fibre stimulation (1 Hz, 5 stimuli) recorded in the presence of 1 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, 1 Hz). Stimulation artifacts have been blanked for clarity during a period of.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 =.153 ms, τ decay(fast) = 1.64 ms, τ decay(slow) = 8.76 ms, fraction of slow decay component was.697. The bar below the first release transient indicates the time window, which was used to calculate the average quantal size for EPSC 1. Bb, low release rate range expanded to illustrate build-up of asynchronous release during the 5 ms EPSC train. C, quantal amplitude for individual EPSCs ( ) and the interpolated curve, which was used to calculated release rates C q(pa) control 1 1 μm Ctz Stimulus no. 3 Stimulus no. 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 5 ms EPSC trains plotted against stimulus number for 5 synapses recorded in the absence (B) and 4 synapses recorded in the presence (C) of 1 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)

6 366 V. Scheuss and others J Physiol in well-resolved λ 2 (t) traces (see ξ Vraw in Fig. 1Bb). When CTZ was omitted from the bath solution, mepscs decayed with a faster time constant (.5 ms), and the late sidelobe was as large as 15% of the central peak and occurred only.9 ms later. To eliminate such sidelobes from the variance traces, λ 2 (t) 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 = 67 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 = 48 Hz (Fig. 1C). After convolving λ 2 (t) 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 48 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, 21b). 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 q(t) = H λ 4 (t) 4 (7) λ 3(t) ξ cum (t) = Z λ 4 3 (t) 4 (8) λ 3 4(t) where λ 3 (t) and λ 4 (t) are 3rd and 4th cumulants of the band-pass-filtered ensemble and H 4 and Z 4 are calibration factors calculated from the filtered mepsc waveform and the amplitude distribution of mepscs (Neher & Sakaba, 23). In addition, we calculated the variance contributions of asynchronously released quanta (Var m ) according to Neher & Sakaba (23) Var m = λ 2 3 H 3. (9) λ 4H 4 Alternatively, when q is known, Var m can be obtained from: Var m = λ 3 H 3 /q (1) (Neher & Sakaba, 23; eqns (B13), (B7a) and (B1)), where H 3 is a calibration factor in analogy to H 4 (Neher & Sakaba, 23). 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, 21b). 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) (2) in Neher & Sakaba, 21b); 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 Var c from AMPAR channel gating (Neher & Sakaba, 23; eqn (B14)) Var c = λ 2 λ 2, Var m, (11) where Var m is calculated from 3rd and 4th cumulants according to either eqn (9) or eqn (1) and λ 2, is the background variance (see below). Var c 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 1 μm d-ap5 (see Fig. 5). For current amplitudes of 5to 1 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

7 J Physiol Release kinetics at the calyx of Held 367 cumulant of currents larger than 5 na had positive values significantly different from zero corresponding to an apparent release rate of 1 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). 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 1 pa) and variance Var L (typically 1 2 pa 2 ) 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 1 2% to Var L. The difference between Var L and the variance due to spontaneous release Var m (eqn (9)) provided an estimate for the background variance λ 2,. 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. 21; Scheuss et al. 22), 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 5 ms-long trains (1 Hz, 5 stimuli, n = 4 synapses without (w/o) CTZ, n = 5 synapses with (w) CTZ) or 2 ms-long trains (1 Hz, 2 stimuli, n = 9 synapses w/o CTZ, n = 19 synapses w CTZ). A typical experiment in which 5 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 λ 2 (t) was calculated from band-pass-filtered EPSCs and corrected for background and AMPAR channel variance. The corrected variance λ 2 (t) 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 ratesshown 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, 21a). In order to evaluate the influence of such ambiguities, we repeated the analysis of 5 ms stimulus trains while restricting the kinetic parameters of the assumed quantal

8 368 V. Scheuss and others J Physiol 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 (EPSC 1 ) 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.6 ±.1 na and 8.5 ± 2.4 to 2.4 ±.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 5 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 4 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, 21). Under control conditions, q declined strongly to 3% 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. When synaptic stimulation was extended from 5 ms to 2 ms (Fig. 4), EPSC amplitudes decreased further (on average from 6. ± 1. na to.2 ±.1 na and 11.9 ± 1.2 na to 1.3 ±.2 na in the absence and presence of CTZ, respectively). Thus, steady-state EPSCs (EPSC 16 to EPSC 2 ) were strongly depressed (5 ± 1% of EPSC 1 in the absence (n = 9) and 12 ± 2% of EPSC 1 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 EPSC 16 to EPSC 2, n = 9) during 2 ms EPSC trains in the absence of CTZ. This compared well to a mean of 1 ± 1 pa obtained for q DEF for the same experiments. By contrast, when CTZ was included in the bath, q CEF dropped by 2 4% 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 ± 3pAversus 25 ± 3 pa, respectively, n = 18). 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 2 ms 1 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. (25) 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 1 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,

9 J Physiol Release kinetics at the calyx of Held 369 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, 21). 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 5%, that caused by CTZ 3% (Table 1). In contrast to the release transient, EPSC half-widths were prolonged about 1-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. Aa control 1 μm Ctz b 2 na 4 na 5 ms Figure 4. Kinetics of EPSCs and synchronous release transients during 2 ms EPSC trains (1 Hz, 2 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 1 μm CTZ. Ab, averages for the initial (EPSC 1 ) 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 EPSC 16 to EPSC 2 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 (83 Hz instead of the usual 48 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 1 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 1 Hz stimulus trains (2 ms, 1 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 2 ms trains, peak rates of the synchronous release transients decreased from 449 ± 64 (EPSC 1 )to7± 6 ves ms 1 (average of EPSC 16 to EPSC 2 ) (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 EPSC 1 (grey trace) with the average of EPSC 16 to EPSC 2 (black trace) after scaling to the same peak rate. c 4 ves/ms B Halfwidth from CEF (ms) Halfwidth from deconvolution (ms) Da b Halfwidth (ms) C ms 2 ves/ms 1 μm CTZ (n = 19) from deconvolution from CEF ms 1 ves/ms 5 ms 15 Stimulus no. 2

10 37 V. Scheuss and others J Physiol Table 1. Half-width of initial and late release transients Half-width Control Corrected With CTZ Corrected CTZ/control (ms) (n = 14) (n = 23) 1st stim..85 ±.1.42 ±.4.93 ±.2.58 ± th stim..98 ±.2.68 ± ±.4.82 ± th/1st th stim ±.9.99 ± ±.4.99 ± th/1st Mean half-widths for the 1st, 5th and 2th 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. Table 2. Parameters describing the variance of whole-cell currents elicited by application of exogenous glutamate Slope/values Axis intercept Range/value (mean ± S.D.) (mean ± S.D.) (na) (1 14 A) (na) Fit to low range: w/o CTZ to ± 1.4 <.5 1 μm CTZ to ± 1 <.15 Fit to medium range w/o CTZ.5 to ± ±.7 1 μm CTZ 2 to ± ±.12 Error of extrapolation w/o CTZ at.225 na.8 ±.5 1 μm CTZ at 9 na.135 ±.7 Summary data from 5 MNTB principal neurons recorded in the absence of CTZ (w/o CTZ) and 7 neurons recorded in the presence of 1 μm CTZ. Glutamate concentration in the application pipette ranged from 1 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. 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 2 ms trains, peak rates of the synchronous release transients decreased from 449 ± 64 ves ms 1 (EPSC 1 )to 7 ± 6 (average of EPSC 16 to EPSC 2 ) (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 1 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 ±.7 na) towards the end of 2 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

11 J Physiol Release kinetics at the calyx of Held 371 by channel gating, Neher & Sakaba (21a) 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, 21a). 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 < 5 pa (w/o CTZ) and < 2 na (w CTZ) were, however, consistently smaller by 3% 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). 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)). A control 1 μm Ctz 15 pa 2.5 na 2 s 1 s 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 1 μm CTZ Principal neurons of the MNTB were voltage clamped at 8 mv and 1 μm glutamate was repeatedly (3 7 times) applied for approximately.4 s by a short puff ( 4 ms) from a nearby glass pipette. The distance from application pipette to postsynaptic neuron was adjusted to elicit peak currents between.3 and.8 na or 1 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. B C 9 3 Variance (pa 2 ) A A A Current (pa) A A A Current (na) variance 3rd cumulant 4th cumulant 12

12 372 V. Scheuss and others J Physiol How accurate is a linear extrapolation from the fitting window defined above (typically covering current ranges between 5 and 15 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 1 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 2 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 5% in the synapse shown in Fig. 6A and in both synapses ξ V was < 1 ves ms 1 within 5 ms of cessation of stimulation. The average time course of the last release transient of the 2 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). On average, asynchronous release rate during the last five EPSCs of 2 ms trains was 2.3 ±.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 3% when measured 5 1 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 =.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 (5 ms trains) and 6 out of 9 synapses (2 ms trains) under control conditions. In the presence of CTZ, this fraction amounted to 2 out of 4 (5 ms trains) and 7 out of 19 (2 ms trains) synapses. Given the well-documented changes in synaptic properties with development (Taschenberger & von Gersdorff, 2; Iwasaki & Takahashi, 21; Joshi & Wang, 22; Taschenberger et al. 22; Puente et al. 25; Renden et al. 25; Hermida et al. 26) 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, 25; Leao et al. 26) 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, 21b). 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, 23 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) (eqns (8) and (9)) (Neher & Sakaba, 21b). 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.