Properties of AMPARs in immature Purkinje cells
Our primary aim was to estimate the number of AMPA receptors (AMPARs) bound by the quantal transmitter packet, and their density in the postsynaptic membrane. We therefore chose experimental conditions that would provide sufficiently high resolution of miniature and spontaneous EPSCs to allow us to apply peak-scaled non-stationary fluctuation analysis (PS-NSFA, Traynelis et al. 1993; Silver et al. 1996). Furthermore, it was essential to examine cells in which a single type of excitatory input was present. Immature Purkinje cells fulfil these requirements for the following reasons. During the first postnatal week, excitatory synaptic inputs onto Purkinje cells arise solely from climbing fibres (Altman, 1972; Crépel et al. 1981). Synaptic transmission at these sites is mediated entirely by non-NMDA receptors (Konnerth et al. 1990; Farrant & Cull-Candy, 1991) although young Purkinje cells do also possess a population of extrasynaptic NMDA receptors (Momiyama et al. 1996a). In 2- to 4-day-old rats, most of the climbing fibre (CF) contacts occur on the soma, or on the primary dendrite within 10 μm of the Purkinje cell apex (Robain et al. 1981; Chedotal & Sotelo, 1993), allowing high-resolution whole-cell recording of synaptic currents in the visually identified cells in thin cerebellar slices. When Purkinje cells in slices (Fig. 1A) were filled with fluorescent dye via the patch pipette, the highly restricted arborisation of dendrites was confirmed in these immature cells (Fig. 1B).
As channel open probability cannot be obtained directly from PS-NSFA of synaptic currents, we have examined the extrasynaptic channels to provide an estimate of this parameter. It was therefore necessary, in the initial experiments, to determine whether synaptic and extrasynaptic receptors exhibited similar functional properties.
As shown in Fig. 2A and B, we compared the pharmacological properties of synaptic AMPA receptors with whole-cell AMPA responses. In P2–4 Purkinje cells, CF EPSCs were evoked in the presence of blockers for GABAA, glycine and NMDA receptors. In these conditions, CF EPSCs could be blocked by the selective non-NMDAR antagonist, NBQX (5 μm; n= 4 cells). The AMPAR-selective blocker GYKI 52466 also exhibited blocking effects on CF EPSCs (94 ± 3 % block at 50 μm, n= 4; 99 ± 1 % block at 100 μm, n= 3), suggesting that virtually all non-NMDARs at CF synapses are AMPARs at this stage.
Figure 2. Pharmacological identification and similarity in Ca2+ permeability of synaptic and extrasynaptic AMPARs in immature Purkinje cells
A, CF-evoked EPSCs recorded from a P3 Purkinje cell. Averaged traces at stimulation frequency of 0.1 Hz, before and 1 min after NBQX (5 μm) application are superimposed. B, whole-cell current response to bath-applied glutamate (1 mm) in another P3 Purkinje cell. NBQX blocked 88 % of the glutamate-induced steady-state current. C, averaged CF EPSCs in the same cell as in A at Vh=+40 and −40 mV. Stimulus artifact was subtracted using records obtained at Vrev= 0 mV. Stimulation frequency, 0.1 Hz. Intracellular solution contained 50 μm spermine. D, current-voltage relationship of AMPA (10 μm)-induced steady-state current obtained by applying voltage-ramp pulses. P4 Purkinje cell. Bathing solution contained TTX (1 μm), bicuculline (10 μm), strychnine (1 μm), AP-5 (100 μm), cyclothiazide (30 μm) and CPCCOEt (100 μm). Averaged currents of 10 trials in the absence of AMPA were subtracted from that in the presence of AMPA. Vrev, +2.6 mV. Calibration for the inset, 1 nA and 0.1 s.
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Since the peak concentration of glutamate at synapses is estimated to be in the millimolar range (Clements, 1996; Diamond & Jahr, 1997), we used a high concentration (1 or 5 mm glutamate) to activate receptors both in whole-cell recordings and in our later experiments where brief pulses of glutamate were applied to isolated patches (see below). We therefore examined the effect of NBQX on whole-cell currents evoked by bath-application of 1 mm glutamate (Fig. 2B). These currents, which presumably reflect the activation of both extrasynaptic and synaptic populations of receptors, rose slowly and desensitised to a plateau level (Fig. 2B, Vh=−70 mV). The currents could be largely suppressed by 50 μm NBQX (90 ± 3 %; n= 5), confirming they were mediated by non-NMDARs. We will refer to these as AMPARs, as our experiments in outside-out patches suggested that functional kainate receptors did not contribute to the extrasynaptic response (see later section). The small residual whole-cell current, remaining in the presence of 50 μm NBQX (apparent in Fig. 2B), disappeared on removal of glutamate (Fig. 2B) indicating that it was glutamate mediated. It may therefore reflect a small fraction of incompletely blocked non-NMDARs under these conditions, or the activation of mGluR1 receptors in these cells (Shigemoto et al. 1992). We did not examine the residual current further in the present study. However, to avoid possible activation of mGluRs, we used AMPA as the agonist to examine the rectification index (see below and Fig. 2D).
It has previously been shown that non-NMDARs that lack edited subunits display a high Ca2+ permeability and pronounced inward rectification (see review by Dingledine et al. 1999). Studies from our laboratory and others (reviewed by Bowie et al. 1999) have found that spermine is the intracellular factor that confers inward rectification on non-NMDARs that lacked edited subunits. Further, it has recently been shown that, in cerebellar stellate cells, synaptic and extrasynaptic AMPA receptors can differ in their rectification properties, and hence in their subunit composition (Liu & Cull-Candy, 2000). We therefore compared the I–V relationship of CF EPSCs with that generated by the whole-cell AMPA current (arising from a mixture of synaptic and extrasynaptic receptors); 50 μm spermine was included in the patch pipette solution. To allow an estimation of the rectification index (RI, see Methods) CF EPSCs were evoked at +40 and −40 mV, and average peak amplitude and reversal potential (0.6 ± 0.3 mV, n= 6) was measured. We obtained an RI value of 0.93 ± 0.04 (n= 6, Fig. 2C) for AMPAR-mediated synaptic currents. This was not significantly different from the value of 0.90 ± 0.20 (P= 0.52; n= 6) obtained for whole-cell responses to 10 μm AMPA (Fig. 2D). These results suggest that at this stage both synaptic and extrasynaptic AMPAR channels include the GluR2 subunit, as described for these cells in older animals (Tempia et al. 1996; Zhao et al. 1998).
Climbing fibre miniature EPSCs
We next compared the channel conductance of synaptic and extrasynaptic AMPARs. To estimate the synaptic channel conductance, we applied peak-scaled non-stationary fluctuation analysis (PS-NSFA: Traynelis et al. 1993; Silver et al. 1996), to miniature and spontaneous EPSCs arising from CF terminals. Figure 3A illustrates typical examples of MEPSCs recorded from a P3 Purkinje cell. In many of the cells examined in 2 mm extracellular Ca2+, the frequency of MEPSCs was too low to allow an accurate quantitative analysis. We therefore increased extracellular Ca2+ to 5 mm, which gave an average MEPSC frequency of 1.5 ± 0.6 Hz (range 0.4–3.3 Hz, n= 5). The 10–90 % rise time of miniature or spontaneous EPSCs was fast (0.38 ± 0.02 ms; n= 7) and the mean amplitude of MEPSCs was −21.2 ± 2.1 pA (n= 5) at −70 mV, giving a quantal size of 294 ± 28 pS (calculated from the measured reversal potential). Furthermore, the coefficient of variation (CV) of quantal size was 0.32 ± 0.05 (n= 5, room temperature, Fig. 3B). This latter value was not significantly different (P= 0.39) from that obtained for CF-derived quantal events recorded in Sr2+ from P12–14 Purkinje cells (see Silver et al. 1998).
Figure 3. Climbing fibre MEPSCs in an immature Purkinje cell
A, examples of MEPSCs recorded from a P3 Purkinje cell in the presence of 5 mm Ca2+ and 0.3 μm TTX. Vh, −70 mV. B, amplitude histogram of 636 MEPSCs recorded from the cell in A. Noise histogram is scaled for clarity. CV of MEPSC amplitude was calculated after subtracting the noise variance. C, averaged waveform of MEPSCs fitted with a double-exponential function (superimposed continuous line). Dotted lines indicate fast and slow components.
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These CF MEPSCs are likely to be originating from multiple sites, and their amplitude distribution was skewed in common with that at other central synapses (Fig. 3B; Silver et al. 1992; Jonas et al. 1993; see Silver et al. 1996; Auger & Marty, 1997; Forti et al. 1997 for events from single sites). The decay times of MEPSCs and spontaneous EPSCs were well fitted by a double-exponential function with time constants of: τf= 1.59 ± 0.15 ms and τs= 7.29 ± 1.35 ms (proportion of τf= 73.7 ± 6.4 %; n= 7). The decay time of the fast component, which accounted for a majority of the current, approached the deactivation time obtained with brief 5 mm glutamate pulses applied to isolated patches (see below).
Estimating synaptic channel conductance from peak-scaled non-stationary fluctuation analysis of CF EPSCs
Several precautions were taken to guard against potential errors in estimating channel conductance using PS-NFSA of synaptic currents. First, we ensured time stability by testing for time-dependent changes in the amplitude and the weighted decay time (Fig. 4A; Spearman's R range: amplitude, −0.22 to 0.06; decay, −0.15 to 0.20; amplitude, P= 0.35± 0.10; decay, P= 0.36± 0.11, n= 7). Second, we tested whether there were correlations between amplitude and rise time (Fig. 4A, Spearman's R range −0.21 to 0.10, P= 0.29± 0.10, n= 7) and between amplitude and weighted decay time (Fig. 4B, Spearman's R range −0.21 to 0.15, P= 0.38± 0.11, n= 7), to test the assumption that all currents from a particular cell have a mean current waveform that differed only in scaling (see Traynelis et al. 1993; Silver et al. 1996). This is illustrated in Fig. 4C, which shows that when averages generated from the smallest, middle and largest amplitude MEPSCs were scaled, their waveforms were similar. The lack of correlation between rise and decay times was also confirmed (figure not shown, Spearman's R range: −0.08 to 0.15, P= 0.33± 0.10, n= 7).
Figure 4. Stability analysis of CF EPSCs
Analysis of spontaneous EPSCs recorded from a P3 Purkinje cell. Vh, −70 mV. External Ca2+, 5 mm. A, stability plots of amplitude (top) and weighted decay time (middle), and plot of 10–90 % rise time against the amplitude (bottom) of 153 consecutive EPSCs. Straight lines indicate linear regression. The lack of correlation between plotted parameters was confirmed by Spearman's rank test. B, the amplitudes and decay times of EPSCs were not correlated. C, EPSCs were averaged separately according to peak amplitude grouped into three ranges (top). The three separate averages were normalized and superimposed, to illustrate the lack of correlation between decay time course and amplitude (bottom).
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Like conventional non-stationary fluctuation analysis (Sigworth, 1980), PS-NSFA assumes that gating is stochastic and that channels are independent – a condition necessary for binomial statistics to apply. In the case of synaptic currents arising at different release sites, the peak amplitude of EPSCs is expected to vary from event to event, since the number of receptor channels bound by the transmitter packet is likely to vary. The procedure of PS-NSFA therefore involved scaling the mean current waveform to the peak of each individual EPSC (Fig. 5A); the scaled average waveform was then subtracted from the individual EPSC (Fig. 5B), and finally the difference was squared. In this way the fluctuations of amplitude during the EPSC decay are expressed as the binomial variance, arising from random channel gating (closings and re-openings) of channels, all of which were once open at the peak.
Figure 5. Peak-scaled non-stationary fluctuation analysis of CF EPSCs
Procedures of PS-NSFA, applied to 153 spontaneous EPSCs analysed in Fig. 3. A, averaged waveform (red trace) scaled at the peak of an individual EPSC (black trace). Dotted lines indicate binning to 30 fractions. B, subtraction of the peak-scaled average from the individual EPSC shown in A. Arrows indicate the range in which the subtraction was applied. For clarity, data are represented as points. The sum-squared difference was calculated for each bin. The procedure was repeated for each EPSC and cumulated averages are plotted in C. C, the straight red line indicates the fit of the initial one-third of the plot to the theoretical equation (see Methods). The dotted line indicates the baseline variance (2.6 pA2). The weighted mean synaptic channel conductance was 4.6 pS. D, PS-NSFA on randomly re-sampled events was repeated 100 times. Means and s.d.s of the 100 current-variance plots are shown. The individual plot was fitted as in C. E, estimates of the channel conductance obtained by fitting bootstrapped data displayed a normal distribution (red curve). F, relationship of the bootstrap data CV versus the number of events, on simulated current (line-connected symbols) and the real EPSCs (green, pooled data in 5 and 2 mm Ca2+). The bootstrap data CV were also affected by the binning and fitting conditions.
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The relationship between variance and mean current (Fig. 5C) was fitted to the theoretical equation (Methods). When channels open to multiple conductance levels, NSFA gives an estimate of the mean channel conductance weighted towards larger conductance levels (Sigworth, 1980; Cull-Candy et al. 1988), provided that the probability of a channel being in any of the conductance states is small. To meet this condition we obtained our estimates from the initial slope of variance-mean plots, where the channel open probability is low. This gave a weighted mean synaptic channel conductance of 5.4 ± 0.4 pS (n= 7).
Some of the variability in our estimate of the single-channel conductance will arise from a sampling bias, since the number of events available for the PS-NSFA was limited (23–153). To quantify this, we next performed bootstrap analysis (Efron & Tibshirani, 1993; Methods). Balanced re-sampling of events was carried out on the originally analysed event set, and the PS-NSFA was repeated for 100 such event sets (Fig. 5D). When the individual fitted value of the initial slope was collected, the distribution was normal, as expected from the central limit theorem (Fig. 5E). On average, 84 ± 2 % (n= 7) of this distribution represented values within ± 2 pS of the single-channel conductance estimated from the original dataset. The CV of the bootstrap sample data was 0.27 ± 0.06 (n= 7). The validity of the bootstrap analysis was further confirmed by applying it to simulated events, using the kinetic scheme of Purkinje cell AMPARs (Häusser & Roth, 1997). Simulated noise-free EPSCs were generated (Methods), and 100 bootstrap re-samplings were carried out, for varying numbers of events (10, 20, 50, 100 and 200). The relationship between the event number and the variability of bootstrapped data (expressed as bootstrap CV) was thus examined, and the bootstrap CV declined as the event number increased (Fig. 5F). During construction of the current-variance plot from real EPSCs, it was necessary to bin the data (as in Fig. 5C and D), to avoid the fit becoming unevenly weighted by the larger number of data points that resulted from the baseline noise. In noise-free simulated EPSCs, we observed that binning itself increased the bootstrap CV of the fit (Fig. 5F). Similarly, fitted ranges affected the bootstrap CV (Fig. 5F). When simulated data were binned and the fitted range set to be the initial one-third of the current-variance plot, the bootstrap CV of simulated events and of real EPSCs exhibited similar distributions when plotted as a function of the number of events (Fig. 5F). To confirm this similarity, we also repeated bootstrap analysis on 13 sets of simulated EPSCs, using the same number of events as real EPSCs in 13 cells, and the bootstrap CVs were not significantly different (P= 0.61, paired t test). This indicates that, once the current-variance plot is binned, the presence or absence of background noise does not markedly affect the bootstrap CV, nor the error contaminating the fit. This was further supported by our observation that the size of baseline noise and the bootstrap CV were not correlated in our real cell data (P= 0.39, Spearman's test).
In order to determine whether the presence of 5 mm Ca2+ affected our estimate of synaptic channel conductance, we also applied the PS-NSFA to spontaneous EPSCs recorded from cells bathed in 2 mm Ca2+. To enhance the frequency of spontaneous synaptic events in these cells, the climbing fibres were stimulated at a low rate (0.1–1 Hz) during the recording period. Under these conditions we obtained a weighted mean single-channel conductance of 5.8 ± 0.4 pS (n= 6), which was not significantly different (P= 0.52) from the value obtained in 5 mm Ca2+. The background noise levels were not different (P= 0.59) between the two recording conditions (5 mm Ca2+, 3.6 ± 0.6 pA2, n= 7; 2 mm Ca2+, 3.1 ± 0.6 pA2, n= 6). The bootstrap CV in 2 mm Ca2+ was 0.33 ± 0.06 (n= 6), not statistically different from that in 5 mm Ca2+ (P= 0.45).
The PS-NSFA method yields a peak-scaled mean current vs. variance relationship that is parabolic only when no channels open for the first time after the peak of the current (Traynelis et al. 1993). If new channels open after the peak, the relationship is skewed by the presence of additional variance (see Fig. 7 of Traynelis et al. 1993; Traynelis & Jaramillo, 1998). Opening of channels for the first time after the peak is expected either if the transmitter transient within the cleft is slow, or if the latency to first channel opening is long. It was apparent that for AMPAR-EPSCs in Purkinje cells, the peak scaled current-variance plots consistently exhibited some skew in all cells examined. Because the skew was still observed in data derived from MEPSCs, it is unlikely that this is due to asynchronous release of multiple transmitter packets. We next estimated the possible errors associated with fitting the skewed current-variance plots to the parabolic equation of binomial variance, by carrying out simulations.
Figure 7. Effects of filtering on the quantal size and single-channel conductance estimated from PS-NSFA
A, example of a simulated EPSC, in the absence (black) and presence (red) of an RC filter (0.72 kHz) cascaded with a Gaussian filter (2 kHz). The single-channel conductance was 5 pS, the number of channels was 100, and the driving force was −100 mV. The glutamate pulse was set to rise instantaneously to the peak concentration (3.1 mm) and decay as a double-exponential waveform (Clements, 1996), as shown in B. Inset, expansion of the indicated part (dotted line) of currents. B, averaged currents of simulated EPSCs (1000 events averaged in each condition). C, current-variance plots of simulated EPSCs obtained by PS-NSFA. Each plot is derived from 1000 events simulated as in A and B. The initial one-third of the plot was fitted to the theoretical equation (Methods).
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Figure 6 illustrates examples of current-variance plots of simulated EPSCs analysed by PS-NSFA. Even for a homogeneous set of simulated EPSCs, where a fixed number of receptors were exposed to a fixed concentration of glutamate, the current-variance plots exhibited skew with this kinetic scheme (Fig. 6B). The skew was also present when PS-NSFA was applied to the heterogeneous group of events (Fig. 6C). Therefore, if native AMPARs in P2–4 Purkinje cells possess the intrinsic kinetic properties predicted by this model, skew in the current-variance plot is to be expected. Nevertheless, in common with previous studies using simulations (Traynelis et al. 1993), we found that fitting such skewed plots to eqn (2) gave estimated single-channel conductances that exhibited only minor (± 2 %) differences from the expected value, regardless of the peak Po. Furthermore, the conductance value obtained from the slope of the current-variance relationship appeared only marginally affected when estimates were derived by fitting different portions of the plot (33, 50 or 75 %). Thus a comparison of the conductance estimates obtained by fitting either the initial 33 % or 50 % of the current- variance relationship of recorded EPSCs indicated that the values obtained were not significantly different (P= 0.59). Our analysis of simulated currents therefore suggested that the current-variance plots obtained during the tail of the EPSC provided a reasonably accurate estimate of the unitary current.
Figure 6. Skew in the current-variance plot by PS-NSFA is expected from the activation kinetics of the Purkinje cell AMPAR model
Using the kinetic scheme of AMPARs in Purkinje cells (Häusser & Roth, 1997), EPSCs were simulated using four different concentrations of glutamate (0.3 ms, step pulse), as indicated. The single-channel conductance was set at 5 pS, the number of channels was set at 100, and the driving force was −100 mV. A, averages of simulated currents. Upper trace indicates the glutamate pulses. B, current-variance relationships by PS-NSFA (continuous lines) were obtained for an individual set of simulated EPSCs (1000 events each) at indicated peak Po values. Open circles represent current-variance plots obtained by Sigworth-type NSFA, imposed on the Sigworth-type theoretical relationships (dotted curves). C, current-variance relationships of 4000 pooled events by PS-NSFA.
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Estimating possible errors introduced by filtering
Because AMPAR channels display fast kinetics, filtering imposed by whole-cell recording may distort the time course of the EPSC and therefore affect the estimated underlying channel conductance. To minimise this, we used Purkinje cells at a stage when their electrotonic structure is compact. For several reasons the level of filtering imposed by the Purkinje cell-patch pipette circuit would not have been expected to greatly distort our estimate of synaptic channel conductance, or of the number of channels activated by a quantal packet of transmitter at this stage of development. First, there was no significant correlation between the rise and decay time of EPSCs, suggesting that event-to-event variability by dendritic filtering was minimal. Second, there was no statistically significant correlation between the cut-off frequency of RC filtering (fc) in individual cells and the respective estimate of the single-channel conductance (Spearman's R= 0.29, P= 0.54). Third, during examination of the EM structure of immature Purkinje cells, most of the CF synapses were found to be located in the proximity of the soma (J. Tanaka & R. Shigemoto, unpublished observations), in accordance with previous reports (Robain et al. 1981; Chedotal & Sotelo, 1993).
To quantify further the effect of filtering on the single-channel conductance estimated from PS-NSFA, we undertook simulations using the Purkinje cell AMPAR kinetic scheme (Häusser & Roth, 1997). As exemplified in Fig. 7A, filtering attenuation of the current amplitude is dependent on the distribution of open and shut times of channels during the EPSCs. Because these distributions would be influenced by the transmitter waveform, we used a biexponentially decaying pulse for the glutamate waveform at synapses (Clements, 1996) in our EPSC simulations. Representative RC filtering values were taken from our experimental data, and the digital Gaussian filter was further cascaded as a substitute for the Bessel filter used during digitisation of EPSCs. From the fit to the initial one-third of the current-variance plot, attenuation of the single-channel conductance caused by filtering ranged from 22 to 32 % (Fig. 7C). The filtering also attenuated the peak amplitude of EPSCs by 10.9 % (in the best case), 12.2 % (mean) and 17.5 % (in the worst case). Therefore, the level of filtering we encountered during recordings could have been expected to introduce an overestimation of the number of channels activated at the peak of quantal events, by 14.2 % (best case), 15.5 % (mean) or 21.3 % (worst case). Taking this into account, and using the estimate of synaptic channel conductance (5.4 pS, measured in 5 mm Ca2+) together with the measured quantal size (294 pS, measured in 5 mm Ca2+), we calculated that on average ∼ 47 AMPARs were opened by a single quantum of transmitter at these CF terminals.
In order to examine the dependency of filtering on channel open/shut time distributions, we also carried out simulations using other glutamate waveforms (0.3 or 10 ms step pulses, or monoexponential functions with time constants of 0.36 or 2 ms) for the mean level of RC filtering. Despite the wide range in the decay time of such simulated EPSCs (-43 % to +80 % change in time constant, when compared with the biexponential glutamate pulse), the degree of overestimation of the number of activated channels was similar (by 0.4 % to 14.7 %). However, in the absence of detailed data for single-channel currents at the synapse, we cannot rule out that differences in open/shut time distributions may exist between real EPSCs and our simulated examples.
Single-channel conductance and maximum open probability, estimated from non-stationary fluctuation analysis of extrasynaptic receptors
In order to estimate the number of receptors bound by transmitter, rather than the number opened, it was necessary to determine the open probability of the agonist-bound channels (the maximum open probability, Po,max). Examining this property directly for synaptic receptors was not practical, so we next investigated the properties of extrasynaptic receptors under conditions that mimic the activation of synaptic channels in Purkinje cells (Häusser & Roth, 1997; Misra et al. 2000). Brief (1 ms) pulses of 1 or 5 mm glutamate were applied to outside-out membrane patches from the cell soma. The averaged macroscopic current deactivated rapidly with a decay time course that was well described by a double-exponential function. Its mean weighted time constant (1.33 ± 0.42 ms, n= 4, glutamate 5 mm) was comparable to the fast component of MEPSCs and spontaneous EPSCs described above (P= 0.58). The time course of desensitisation (decay in the presence of 5 mm glutamate, 100 ms pulse) could also be fitted to a double-exponential function, but had a markedly slower time course (mean weighted time constant 4.58 ± 1.47 ms, n= 3).
By applying ‘Sigworth-type’ NSFA to the rapidly deactivating currents (see Methods), we obtained an estimate of the weighted mean conductance for extrasynaptic receptors. The mean value of 10.8 ± 3.0 pS (n= 6; pooled from 1 and 5 mm glutamate short-pulse data; Fig. 8A–C) was not statistically different from those obtained for synaptic receptors examined in the presence of 2 mm Ca2+ (t test, P= 0.09). From datasets of weighted single-channel conductances, we calculated the minimum detectable difference, with a statistical power of 0.9 and a confidence limit of 0.05 (one-sample t test). This was 1.5 pS for synaptic channels, while that of extrasynaptic channels was 11 pS, possibly influenced by the presence of one ‘outlier’ patch of 22 pS. However, the bootstrap CV of PS-NSFA data was not significantly different (P= 0.51) from that of Sigworth-type NSFA on short-pulse jump data (0.28 ± 0.06, n= 6). Furthermore, we found no significant difference in estimates of the single-channel conductance between short and long pulse jump data (P= 0.58). Since the attenuation of single-channel conductance by filtering differed between the whole-cell (where attenuation was 24 % with cascaded mean RC and Gaussian filters) and excised patches (12 % with Gaussian filter only), these estimates may become closer once the attenuation due to filtering is removed. Yet, in contrast with the other properties of the synaptic and extrasynaptic AMPARs, the high variability of extrasynaptic channel conductances made it difficult to draw a statistically strong conclusion about the similarity in this feature of synaptic and extrasynaptic AMPARs.
Figure 8. Non-stationary fluctuation analysis of AMPAR-mediated currents in outside-out patches activated by rapid application of glutamate
Data derived from the same patch excised from P4 Purkinje cell. A and D, current-response activated by short (1 ms) or long (100 ms) pulses of glutamate (5 mm). Averaged response and an individual response are superimposed. Top traces indicate the timing of solution exchange measured as changes in liquid junction currents. B and E, stability of peak amplitude of glutamate-activated currents was confirmed by Spearman's rank test. Red lines, linear regression. C and F, open circles are current-variance plots by Sigworth-type NSFA applied to the glutamate-activated currents of extrasynaptic non-NMDARs. The blue dotted lines indicate the fit to the theoretical Sigworth equation (Methods). The red lines in C and F show the current-variance relationship by PS-NSFA. Channel open probability at the peak of the current was 0.57 for the short pulse.
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As is apparent in Fig. 8 (C and F), the current-variance plot obtained by PS-NSFA of AMPAR currents produced by fast application of glutamate also exhibited skew, suggesting that some glutamate-bound receptors open for the first time after the peak. The single-channel conductance values estimated from fitting current-variance plots obtained by Sigworth-type-NSFA and PS-NSFA were not significantly different (P= 0.22).
Provided that the applied glutamate saturates receptors in excised patches, the ‘Sigworth-type’ analysis will yield an estimate of Po,max for these channels. To ensure complete receptor occupancy, we used long pulses (100 ms) of a high concentration of glutamate (5 mm) and estimated Po,max to be 0.72 ± 0.04 (n= 3, Fig. 8D–F). This Po,max value was similar to estimates obtained for AMPARs in more mature (P12–14) Purkinje cells (Häusser & Roth, 1997). Since our data suggest that the synaptic and extrasynaptic AMPARs in these cells show similarities in functional properties, including their I–V relationships and deactivation kinetics, it seemed reasonable to assume that synaptic sites may exhibit a Po,max value similar to that measured for extrasynaptic receptors (0.72). By dividing the number of open channels (47) by Po,max, the average number of transmitter-bound receptors was estimated to be 66. In cases where postsynaptic AMPARs are saturated by transmitter (receptor occupancy = 1), this number of transmitter-bound receptors is equivalent to the number of receptors present in the postsynaptic membrane. If receptors are not saturated by a quantum of transmitter (Silver et al. 1996), this will represent a lower limit for the number of AMPARs present.
Multiple conductance extrasynaptic AMPAR channels
As the conductance level AMPARs enter may be influenced by the concentration of glutamate present (Rosenmund et al. 1998; Smith & Howe, 2000), we tested two different agonist concentrations: a high concentration (1 mm) of glutamate, to approximate that encountered in the synaptic cleft during transmission, or a low concentration (1 μm, with 30 μm cyclothiazide). As illustrated in Fig. 9, bath-application of glutamate to outside-out patches excised from the Purkinje cell soma gave directly resolved channel openings with clear multiple levels in these conditions.
Figure 9. Multiple single-channel conductances of somatic AMPARs in Purkinje cell patches
A and C, examples of single-channel openings in the continued presence of agonist, recorded from outside-out patches of P3 Purkinje cells. Vh, −100 mV. External Ca2+, 5 mm. Baseline (closed) level is indicated as C. B and D, all-point amplitude histograms of single AMPA channel currents. The baseline noise has been subtracted from histograms after fitting Gaussian distributions to the noise components.
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In addition to mRNA for the AMPAR subunits, Purkinje cells at P0 express message for the kainate receptor subunit GluR5, the level of which increases postnatally (Bahn et al. 1994). We obtained no detectable response to the kainate receptor agonist domoate (2 nm) at this age, although patches responded to 5–10 μm AMPA (n= 2, P4, data not shown) and exhibited multiple conductance levels (Momiyama et al. 1996b). It therefore seems likely that the density of functional kainate receptors is low in P4 Purkinje, and the multiple conductance levels activated by glutamate can be ascribed solely to AMPARs.
Estimated receptor density at CF-Purkinje cell synapses
To estimate the minimum packing density of synaptic AMPARs, we next measured the size of the postsynaptic density (PSD) in Purkinje cells from P3 rats. From electron-microscopic examination of ultrathin serial sections of the cerebellum, we collected complete sequences of the PSDs at synaptic inputs onto Purkinje cells (see Fig. 10A). Asymmetrical synapses on these Purkinje cells are generally considered to originate from climbing fibres at this stage (see Altman, 1972).
The size of the PSD exhibited a skewed distribution (skewness = 0.98), with a mean area of 0.074 μm2 (Fig. 10C). The CV of PSD size was 0.63, being 1.3- to 1.6-fold larger than that of the quantal size (0.40 at room temperature, 2135 events pooled from five cells; 0.47 at 33–34 °C, 1112 events pooled from four cells, Fig. 10C). The distribution of quantal size at 33–34 °C was also skewed (skewness = 1.28; skewness = 1.0 at room temperature). At this temperature, even the smallest detected quantal event magnitude was 2.2-fold of the background noise bandwidth (n= 4).
Furthermore, immunogold labelling by an anti-GluR2/3 antibody was observed to be concentrated within PSDs, in contrast with the low level of labelling outside PSDs (Fig. 10B), as reported at the mossy fibre-granule cell synapse (DiGregorio et al. 2002). Thus AMPARs eliciting quantal responses are likely to be localised only at PSDs. Based on this, we calculate the lower limit for the average receptor packing density, from our estimates of the PSD size and the number of channels occupied by the transmitter packet, to be ∼900 receptors μm−2 (after correction for filtering).