Efficacy and Stability of Quantal GABA Release at a Hippocampal Interneuron–Principal Neuron Synapse

Unitary IPSPs and IPSCs at the BC–GC synapse

We examined inhibitory synaptic transmission between pairs of monosynaptically connected BCs and GCs in slices from mature rats (18–25 d old) at physiological temperatures (34°C). This synapse has several technical advantages (Fig. 1). First, interneurons and principal neurons in this circuit can be distinguished by morphological criteria (Fig. 1A) and by the ability of the presynaptic interneuron to generate high-frequency trains of action potentials during sustained current injection (Fig. 1B). Second, paired recordings from synaptically connected interneurons and principal neurons can be obtained with relatively high probability, because the axonal arborization of BCs is extensive (Fig. 1A) (Freund and Buzsáki, 1996; Geiger et al., 1997). Third, although unitary IPSPs and IPSCs have small amplitudes at physiological intracellular Cl⁻ concentrations (Fig.1C,D), the amplitude of unitary IPSCs with high intracellular Cl⁻ concentration (149 mm) is substantially larger, with excellent signal-to-noise ratio under these conditions (Fig.1E). Fourth, the voltage-clamp conditions of the unitary IPSCs are ideal, because of the mainly perisomatic location of synaptic contacts and the favorable electrotonic properties of postsynaptic granule cells. Finally, synaptic transmission in the paired recording configuration is stationary over long periods of time, with a stimulation frequency of ≤0.25 Hz (Fig.1F).

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Fig. 1.

Unitary IPSPs and IPSCs at the BC–GC synapse in the paired recording configuration. A, Schematic illustration of the BC–GC microcircuit in the dentate gyrus.B, High-frequency train of action potentials evoked in a putative BC by a current pulse (200 msec, 1.4 nA). C, Unitary IPSPs recorded from a BC–GC pair at −30 mV with 6 mm intracellular Cl⁻ concentration. Single presynaptic action potential evoked by a depolarizing current pulse in the BC is shown on top, single IPSPs are shown superimposed in the center, and average IPSP is depicted at the bottom. D, Unitary IPSCs in a BC–GC pair with 6 mm intracellular Cl⁻concentration. Single presynaptic action potential is shown ontop, single IPSCs at −100 and −50 mV are shown superimposed in the center, and average IPSCs at −100 to −50 mV (10 mV increment) are depicted at the bottom.E, Unitary IPSCs in a BC–GC pair with 149 mm intracellular Cl⁻ concentration. Single presynaptic action potential is shown on top, single IPSCs at −100 and +30 mV are shown superimposed in thecenter, and average IPSCs at −70 to +30 mV (20 mV increment) are depicted at the bottom. F, Unitary IPSC peak amplitude plotted against recording time. Note that the amplitude was stationary (correlation coefficientr = 0.05, p > 0.1). Averages are from 30–100 single synaptic events. Data inC–F are from different pairs. Pair shown in F is pair #1 in Table 2.

Figure 2 shows the properties of unitary IPSCs in high intracellular Cl⁻ in an individual pair, and Figure 3 summarizes the results from 78 BC–GC pairs. The mean synaptic latency, measured from the steepest point in the rising phase of the presynaptic action potential to the onset of the IPSC, was 1.1 msec. The rise of the synaptic events was almost instantaneous (average 20–80% rise time 0.26 msec). The mean unitary IPSC peak amplitude (including failures of transmission) was 504 pA at −70 mV. Because the mean reversal potential of unitary IPSCs is +4.2 mV (Table1), this corresponds to a peak conductance change of 6.8 nS. The decay of the unitary IPSCs was better fitted with the sum of two exponentials than with a single exponential in the majority of pairs; the average values of the time constants were 1.9 msec (38% amplitude contribution) and 9.4 msec, respectively. Synaptic transmission at the BC–GC synapse was very reliable; the mean percentage of failures was 6.5%. Thus BC-mediated inhibition shows shortlatency, rapid onset, large peak-conductance change, long duration, and high reliability (Table 1).

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Fig. 2.

Amplitude and time course of the unitary postsynaptic conductance change at the BC–GC synapse. Data are from a single pair. A, Presynaptic action potential (top), single unitary IPSCs (9 sweeps superimposed), average IPSC (from 60 sweeps), and sum of two exponentials fitted to the average IPSC (bottom, with individual components) are depicted. B, Latency, measured from the steepest point in the rising phase of the presynaptic action potential to the onset of the first IPSC in a trace. C, Rise time (20–80%) of unitary IPSCs. D, Peak amplitude of unitary IPSCs. Thirty-one failures are not displayed. E, Decay time constants of unitary IPSCs: fast decay time constant τ₁ (open bars); slow decay time constant τ₂ (filled bars). F, Amplitude contribution of the fast component of decay (A₁) obtained by biexponential fit. Extracellular Ca²⁺ and Mg²⁺ concentrations were 2 and 1 mm, respectively. Holding potential was −70 mV; intracellular Cl⁻ concentration in the postsynaptic GC was 149 mm. All data are from the same BC–GC pair.

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Fig. 3.

Amplitude and time course of the unitary postsynaptic conductance change at the BC–GC synapse. Summary graphs of data from 78 pairs. A, Percentage of failures of transmission. B, Mean first latency. C, Mean 20–80% rise time. D, Mean peak amplitude of average IPSCs (including failures). E, Mean decay time constants: fast decay time constant τ₁ (open bars); slow decay time constant τ₂(filled bars). F, Mean amplitude contribution of the fast component of decay (A₁). Extracellular Ca²⁺ and Mg²⁺ concentrations were 2 and 1 mm, respectively. Holding potential was −70 mV; intracellular Cl⁻ concentration in the postsynaptic granule cells was 149 mm in all experiments.

Direct recording of quantal IPSCs at the BC–GC synapse

Rigorous analysis of the transmitter release process requires direct recording of quantal currents (Katz, 1969; Isaacson and Walmsley, 1995). We therefore examined quantal BC–GC IPSCs in conditions of low release probability with a reduced Ca²⁺/Mg²⁺concentration ratio in the bath solution (Fig.4). Figure 4, A andB, shows unitary IPSCs in a pair at two different Ca²⁺/Mg²⁺concentrations. When the Ca²⁺/Mg²⁺concentration ratio was reduced, the amplitude of the unitary IPSC decreased, and the number of failures increased substantially, to >80% with Ca²⁺ concentrations <0.5 mm (Fig. 4C). Under these conditions, the amplitude of the successful unitary IPSCs excluding failures reached an asymptotic value corresponding to the quantal size (Fig.4D). The mean peak amplitude of these putative quantal IPSCs was 129 ± 19 pA at −70 mV. With the mean reversal potential of unitary IPSCs of +4.2 mV, this corresponds to an apparent quantal conductance change of 1.7 ± 0.3 nS. The mean CV of the putative quantal IPSC in conditions of low release probability, including both intrasite and intersite components, was 33.7 ± 1.0% (five pairs at Ca²⁺ concentrations of 0.1–0.3 mm, corrected for baseline noise). Thus direct recording of quantal IPSCs at the BC–GC synapse reveals a large quantal size and a moderate variability of the quantal amplitude.

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Fig. 4.

Direct recording of quantal IPSCs at the BC–GC synapse. A, B, Unitary IPSCs at physiological Ca²⁺/Mg²⁺concentrations (A) (2 mmCa²⁺, 1 mm Mg²⁺) and after reduction of release probability (B) (0.5 mm Ca²⁺, 2.5 mmMg²⁺). Six traces are shown superimposed ontop; average IPSCs including failures are shown at thebottom. C, Percentage of failures plotted against the extracellular Ca²⁺ concentration.D, Mean peak amplitude of successful IPSCs (excluding failures) plotted against extracellular Ca²⁺ concentration. Error bars indicate SD of IPSC amplitudes. Open circles indicate experiments in which the Mg²⁺ concentration was kept constant (3 or 4 mm); filled circles represent experiments in which the sum of Ca²⁺ and Mg²⁺concentrations was maintained (3 mm). As the Ca²⁺ concentration was reduced, the number of failures increased, but the amplitude of the successful IPSCs approached asymptotically a minimal value. This suggests that IPSCs at Ca²⁺ concentrations below 0.5 mm are mainly quantal IPSCs. Data in C and D are from 11 pairs; data obtained from the same pair were connected bydashed lines.

The time course of quantal release

Asynchrony of transmitter release can provide a significant contribution to the time course of the average postsynaptic conductance change at various synapses (Diamond and Jahr, 1995; Isaacson and Walmsley, 1995; Geiger et al., 1997). To determine the time course of quantal release at the BC–GC synapse, we used the approach of first latency measurements (Barrett and Stevens, 1972) (Fig.5). The time course of quantal release (open bars), determined from the distribution of first latencies (filled bars) in conditions of reduced Ca²⁺/Mg²⁺concentration ratio, rose and decayed within a time window of ∼1 msec, indicating that GABA release was highly synchronized (Fig.5A). To test the validity of the first latency approach, single quantal events in low Ca²⁺/Mg²⁺concentration ratio were aligned to their onset, averaged, and reconvolved with the time course of quantal release in the same pair. The time course of the reconvolved IPSC was almost indistinguishable from that of the averaged unitary IPSC (four pairs), suggesting that quantal contributions superimposed independently (Fig. 5B). The logarithmic plot of the mean time course of release from four pairs illustrates that the release period decayed approximately exponentially, with a time constant of 0.23 msec (Fig. 5C). Thus quantal release at the BC–GC synapse showed high synchrony, comparable to that of fast excitatory synapses (Isaacson and Walmsley, 1995; Geiger et al., 1997).

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Fig. 5.

Time course of quantal release at the BC–GC synapse. A, First latency distribution (filled bars) and time course of quantal release (open bars) in a BC–GC pair, calculated from first latencies using the correction method of Barrett and Stevens (1972). Data were obtained with 0.5 mm Ca²⁺ and 2.5 mm Mg²⁺ in the bath; data are from 299 IPSCs (401 failures). B, Average unitary IPSC in 0.5 mm Ca²⁺, 2.5 mmMg²⁺, average quantal IPSC (obtained after aligning single events on their rising phase), and a simulated IPSC generated by reconvolution of the time course of quantal release with the time course of the quantal conductance change are shown superimposed. Thethree traces were normalized to the same peak value.C, Mean time course of quantal release. Histograms of the time course of release were aligned to the bin with the maximal number of events (n_max, which is represented as time 0 in the graph). Numbers of events were normalized by n_max and plotted logarithmically. The line represents the results of linear regression of the decay, yielding a decay time constant of 0.23 msec. Data are from four pairs. D, Average unitary IPSCs in 2 mm Ca²⁺/1 mmMg²⁺ and 0.5 mmCa²⁺/2.5 mm Mg²⁺, normalized to the same peak amplitude value, are shown superimposed. The absolute peak amplitudes were 612 and 164 pA, respectively.E, Plot of the decay time constants against extracellular Ca²⁺ concentration: fast decay time constant τ₁ (open symbols), slow decay time constant τ₂ (filled symbols); different symbol shape indicates different pairs (12 total). Thegraph illustrates that the decay time course of the IPSCs is only weakly dependent on extracellular Ca²⁺concentration. F, Plot of the decay time constants (mean value of the two time constant values weighted with the respective amplitude contribution) of single unitary IPSCs in four pairs against the peak amplitudes. Both weighted time constant and amplitude were normalized to the mean value in the recorded ensemble.Line represents the results of linear regression. No significant correlation between time constant and amplitude was apparent (p > 0.1). Data inA, B, and D are from the same pair.

To further examine the possibility of cross talk (Barbour and Häusser, 1997) or multivesicular release (Auger et al., 1998) at higher release probabilities, we tested whether the decay time course of average unitary IPSCs became slower as the Ca²⁺/Mg²⁺concentration ratio was increased. IPSCs in conditions of normal and reduced Ca²⁺/Mg²⁺concentration ratio, normalized to their respective peak current amplitudes, showed almost identical time courses (Fig. 5D). The mean decay time constant was very similar for Ca²⁺ concentrations between 0.1 and 2 mm, with only a slight prolongation at higher concentrations (Fig. 5E; 2–12 pairs per Ca²⁺ concentration). Furthermore, as indicated by the scatter plot from individual evoked IPSCs, the decay time constant was independent of the IPSCs amplitude (Fig.5F; four pairs). Thus the analysis of the decay time course of IPSCs provides no evidence for cross talk or increase in the number of fused vesicles with increasing Ca²⁺concentration at this synapse.

Number of functional release sites and release probability

Because a decrease of the Ca²⁺/Mg²⁺concentration ratio reduced the amplitude of the IPSCs excluding failures (Fig. 4), it appeared likely that the BC–GC synapse comprises multiple functional release sites. To determine the number of functional release sites and the probability of release at individual sites quantitatively, we fitted IPSC peak amplitude distributions at different Ca²⁺/Mg²⁺concentration ratios with compound binomial models of release (MP-CBA; see Materials and Methods) (Fig. 6) (Redman, 1990). Failures were also included in the fit because (1) they could be unequivocally distinguished from successful IPSCs because of the favorable recording conditions and (2) they appeared to be entirely failures of synaptic transmission (stimulation failures were not present in the paired recording configuration, and conduction failures appeared unlikely; see Discussion).

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Fig. 6.

Estimation of the number of functional release sites and the release probability using multiple probability compound binomial analysis. A, Peak amplitude distributions from a pair in 2 mm Ca²⁺/1 mmMg²⁺ (a) and 0.5 mm Ca²⁺/2.5 mmMg²⁺ (b). The thick curve represents the total probability density function (ΣP_i(x)); thethin curves represent individual components (P₁(x) −P₇(x)) as obtained by maximum-likelihood fit. For model parameters, see Table 2, pair #1. Failures are not depicted; measured numbers of failures were 1 (a) and 430 (b), and predicted numbers of failures were 1 (a) and 429 (b). B, Similar analysis for a different pair (#3) in 2 mm Ca²⁺/1 mm Mg²⁺ (a) and 0.5 mm Ca²⁺/2.5 mmMg²⁺ (b). Measured numbers of failures were 13 (a) and 731 (b), and predicted numbers of failures were 8 (a) and 729 (b).C, Results of bootstrap analysis for the number of functional release sites (left) and the release probabilities in the two conditions (right) for pair #1 (a) and pair #3 (b). Bootstrap replications (100) of the original data set were fitted in a manner identical to the original data set, and the distributions of estimated number of release sites and release probabilities (in 2 mm Ca²⁺/1 mmMg²⁺ and 0.5 mmCa²⁺/2.5 mm Mg²⁺, respectively) were plotted. For details, see Materials and Methods.D, Plot of estimated mean release probability <p> against extracellular Ca²⁺concentration for the five pairs shown in Table 2. Data were fitted with a Hill equation f(c) =p_max [1 + (EC₅₀/c)ⁿ]⁻¹, with maximal release probability p_max = 0.79, EC₅₀ = 1.5 mm, and apparent Hill coefficient n = 2.4, where c denotes the extracellular Ca²⁺ concentration.

Two examples are shown in Figure 6, with amplitude distributions in 2 mm Ca²⁺/1 mmMg²⁺ on top and in 0.5 mmCa²⁺/2.5 mmMg²⁺ at the bottom. The estimated number of functional release sites was seven and five, and the mean release probability in 2 mm Ca²⁺/1 mm Mg²⁺ was 0.61 and 0.57, respectively. Bootstrap analysis further indicated that the errors in the estimates of number of functional release sites and release probability were small for both pairs (Fig. 6C, Table2).

In five pairs in which IPSC amplitudes, rise times, and series resistance were stationary and the total number of traces was >700, the number of functional release sites estimated by MP-CBA ranged from three to seven, and the mean release probability in physiological divalent concentrations was between 0.41 and 0.63 (Table 2). In all pairs both intrasite (Liu and Tsien, 1995a) and intersite (Nusser et al., 1997) components of quantal variability appeared to be present. Although the compound binomial model accounted for inhomogeneity of release probability in principle, the high value of the shape parameter α_p (10^1.4 − 10²) (Table 2) indicated that the release probability was relatively uniform among sites (Silver et al., 1998).

MP-CBA further allowed us to investigate the dependence of the estimated mean release probability on extracellular Ca²⁺ concentration, as shown in Figure6D. Fitting the data with a Hill equation revealed a half-maximal release probability at a Ca²⁺concentration of 1.5 mm, an apparent Hill coefficient of 2.4, and an extrapolated maximal release probability of 0.79. Fitting the data at the low-concentration limit (≤1mm) in double logarithmic representation gave similar results (apparent Hill coefficient 2.5; fit results not illustrated). In conclusion, single action potentials in the presynaptic BC trigger powerful inhibition of the postsynaptic GC, attributable to a large quantal size, a high release probability at physiological Ca²⁺ concentrations, and the presence of multiple functional release sites.

Depression induced by paired-pulse stimulation

In the intact hippocampal network, BCs can generate high-frequency trains of action potentials (Penttonen et al., 1998; Csicsvari et al., 1999). This raises the question of whether dynamic changes of transmission occur at BC–GC synapses during repetitive stimulation. We first examined paired-pulse modulation (Fig.7). When two action potentials were elicited in the BC, separated by intervals of variable duration, the amplitude of the second IPSC was smaller than that of the first (Fig.7A). The maximal paired-pulse depression, measured for 10 msec interpulse intervals, was 37 ± 6%. Recovery from PPD was complete after 5 sec; when fitted with a single exponential function, the time constant of recovery was 1.97 sec (Fig. 7B) (3–11 pairs).

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Fig. 7.

Properties of PPD of IPSCs at the BC–GC synapse. A, IPSCs evoked by pairs of action potentials in the presynaptic BC, separated by intervals of variable duration.Traces shown are averages of 30 unitary IPSCs and were normalized to the same amplitude for the first average IPSC (absolute values of A₁ were 1393, 1180, and 1216 pA, respectively). B, Time course of recovery from PPD. The ratio of amplitudes of the second (A₂) and the first (A₁) unitary IPSC, both measured from their respective baselines as indicated in A, was plotted against the interpulse interval. The curverepresents a fitted exponential function with a time constant of 1.97 sec. Number of pairs is indicated in parentheses above the data points. C, Coefficient of variation analysis suggests a presynaptic locus of PPD. The inverse of the square of the coefficient of variation of A₂(CV⁻²) was plotted against the mean peak amplitude; data were normalized by the CV⁻² and mean, respectively, of A₁ . Data are from 10 pairs. Intervals between presynaptic action potentials were 100 msec (▾), 500 msec (▿), 1 sec (▪), 2 sec (■), and 3 sec (♦).Curve a represents the prediction of Equation 8 of Silver et al. (1998) for a pure change in release probability psuperimposed on the data points (number of release sites = 5, release probability = 0.53, CV₁ = 0.18, CV₂ = 0.34; no variation in p).Curve e represents the prediction of a pure change in quantal size q, and curves b–d show predictions for mixed changes (75, 50, and 25% contribution of changes in p, withp = x^aand q =x^1-a, where a is the fractional contribution of the change in p andx is the normalized mean). D, PPD appears to be independent of presynaptic GABA_B receptor activation.Left, Average IPSCs in control conditions (top) and in the presence of 5 μmCGP55845A in the bath solution (center) are depicted, together with a superposition of both traces (bottom).Right, Summary bar graph of meanA₂/A₁ in control conditions and in the presence of CGP55845A. Extracellular Ca²⁺ and Mg²⁺ concentrations were 2 and 1 mm, respectively. Interpulse interval, 100 msec. Failures included in all averages. Number of pairs indicated inparentheses above the bars.

To determine whether the depression was presynaptic or postsynaptic in origin, we examined the variation of peak current amplitudes during the first and second IPSC for interpulse intervals of ≥100 msec. Figure7C shows a summary plot of the inverse of the square of the CV (CV⁻²) against the mean amplitudes of the second IPSC (nine pairs); both CV⁻² and mean were normalized to the values of the first IPSC (Malinow and Tsien, 1990). The data points were superimposed with the predictions of a model with variable presynaptic and postsynaptic contributions to PPD, using Equation 8 of Silver et al. (1998) and mean values forN_r, <p>, CV₁, and CV₂ as obtained by MP-CBA (Table 2). A comparison of data points and model curves suggests that the results were more consistent with a reduction in <p> than a reduction in <q>, implying that PPD was mainly presynaptic in origin.

If PPD was caused by the activation of presynaptic GABA_B receptors (Deisz and Prince, 1989; Lambert and Wilson, 1994) after release of GABA from a single BC, it should be blocked by the selective, high-affinity GABA_Breceptor antagonist CGP55845A (Kaupmann et al., 1997); however, PPD for 100 msec intervals was not significantly different in the absence and presence, respectively, of 5 μm CGP55845A (Fig.7D) (p > 0.2), indicating that PPD is independent of presynaptic GABA_B receptor activation.

If PPD was caused by depletion of the releasable pool of synaptic vesicles (Stevens and Tsujimoto, 1995; Debanne et al., 1996; Dobrunz and Stevens, 1997), its extent should be dependent on the average release probability. In contrast to this prediction, the extent of PPD at the BC–GC synapse was not significantly different in various Ca²⁺/Mg²⁺concentration ratios (Fig.8A) (p > 0.2). Furthermore, if PPD was caused by depletion, the peak amplitude of the second IPSC evoked by paired stimulation should be inversely related to that of the first (Debanne et al., 1996); however, amplitudes of IPSCs evoked by paired stimuli were not significantly correlated at the BC–GC synapse (Fig.8B). Thus PPD at the BC–GC synapse was presynaptic in origin, but unexpectedly appeared to be independent of both extracellular Ca²⁺ concentration and previous release.

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Fig. 8.

PPD at the BC–GC synapse appears to be independent of release probability and previous exocytosis.A, PPD is independent of extracellular Ca²⁺ concentration. Left, Average IPSCs in 4 mm Ca²⁺/0.5 mmMg²⁺ (top) or 0.5 mmCa²⁺/4 mm Mg²⁺(center) are depicted (failures included), together with a superposition of both traces after normalization to give the same peak amplitude for the first average IPSC (bottom).Right, Mean A₂ /A₁(open bars) and percentage of failures (filled bars) for 0.5 and 3 mm  Ca²⁺/3 mm Mg²⁺. Interpulse interval, 100 msec. Number of pairs indicated in parentheseson top. B, PPD appears to be independent of previous release. Plot of A₂ againstA₁ for individual events is shown. Amplitudes were normalized to the mean A₁ in the recorded ensemble. Line represents the results of linear regression. No significant correlation between IPSC peak amplitudes was apparent (p > 0.05); interpulse interval, 100 msec. Data were from 10 pairs; different pairs are represented by different symbols.

Depression induced by multiple-pulse stimulation

We then examined dynamic changes of transmission at the BC–GC synapse during 1–50 Hz trains of 900–1000 action potentials (Fig.9). Evoked IPSCs at the BC–GC synapse showed a marked depression during high-frequency stimulation, as reported previously for inhibitory synapses in the neocortex (Galarreta and Hestrin, 1998; Varela et al., 1999). The onset of depression was biexponential, with time constants of 61 msec and 17.6 sec for a stimulation frequency of 20 Hz (Fig. 9C) (23 pairs). The steady-state depression increased with the frequency of stimulation; half-maximal depression occurred at 5.0 Hz (Fig. 9D). After a 20 Hz train of action potentials, recovery from depression was biexponential, with time constants of 1.3 and 31.7 sec (Fig.9E) (23 pairs).

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Fig. 9.

Depression of IPSCs at the BC–GC synapse during multiple-pulse stimulation. A, Unitary IPSCs during a 20 Hz train of 1000 action potentials; stimulation frequency before and after the train was 0.25 Hz. Presynaptic action potentials (top) were truncated. B, Unitary IPSCs at an expanded time scale from the same pair as shown in Ain control conditions (top), at the end of the 20 Hz train (center), and after recovery (bottom). C, Onset of depression during a 20 Hz train. Each data point represents the mean IPSC peak amplitude in 23 pairs, normalized to the mean peak amplitude at 0.25 Hz before the train. D, Plot of mean unitary IPSC peak amplitudes (action potentials 851–900, failures included) against stimulation frequency, normalized to the control value (at 0.25 Hz). Number of pairs indicated in parentheses above the data points.E, Recovery from depression induced by a 20 Hz train. Each data point represents the mean peak amplitude from one (first point) or three (all following points) consecutive IPSCs in 23 pairs, normalized to the mean peak amplitude at 0.25 Hz after complete recovery from depression (which, on average, was 1.05-fold larger than that before the train, indicating a slight post-tetanic potentiation).F, Coefficient of variation analysis of short-term depression. The inverse of the square of the CV of the peak amplitude of unitary IPSCs (action potentials 851–900) was plotted against the mean peak amplitude for different frequencies; data were normalized by the CV⁻² and mean, respectively, of IPSCs evoked at 0.25 Hz. Stimulation frequency was 1 Hz (●), 2 Hz (○), 10 Hz (▾), 20 Hz (▿), 40 Hz (▪), and 50 Hz (■).Curve a represents the prediction of Equation 8 ofSilver et al. (1998) for a pure change in p superimposed on the data points (with same parameters as in Fig. 7). Curve e represents the prediction of a pure change inq, and curves b–d show predictions for mixed changes (75, 50, and 25% contribution of changes inp). G, Onset of depression during a 20 Hz train in the presence of 5 μm CGP55845A. Each data point represents the mean peak amplitude in seven pairs, normalized to the mean peak amplitude at 0.25 Hz before the train. H, The slow component of depression appears to be dependent on release probability. Onset of depression during 20 Hz trains in 0.5 mm Ca²⁺/2.5 mmMg²⁺ (9 pairs, ○) and 2 mmCa²⁺/1 mm Mg²⁺ (●). Each data point represents the mean peak amplitude, normalized to the mean peak amplitudes at 0.25 Hz before the train. I, Correlation of peak amplitudes of consecutive IPSCs in the late portion of 20 Hz trains (last 500 action potentials) in 2 mmCa²⁺/1 mm Mg²⁺. Peak amplitudes A_n+1 of IPSCs (or failures) were plotted against the amplitudes A_n of the directly preceding IPSCs (or failures), both normalized to the mean amplitude of the data set. Eleven of 11500 points are located outside the plot range. Line represents the results of linear regression. A slight but significant negative correlation between IPSC peak amplitudes was apparent (slope −0.054; p < 0.001). Extracellular Ca²⁺ and Mg²⁺concentrations were 2 and 1 mm, respectively, in all cases except H. Time 0 in C, E,G, and H indicates the time of change in frequency. SEMs in C, G, andH were not shown for clarity. Continuous curves in C–E and Hrepresent the predictions of a two-pool model with activity-dependent reduction in release probability fitted to the data points (Fig.10).

To determine whether the depression was presynaptic or postsynaptic in origin, CV⁻²was plotted against the mean unitary IPSC in steady-state conditions at a given frequency; both CV⁻² and mean were normalized to the control values at 0.25 Hz (Fig.9F). The data points were superimposed with the predictions of a model with variable presynaptic and postsynaptic contributions to depression (Fig. 7C). Similar to PPD, comparison of data and predictions suggests that multiple-pulse depression was mainly presynaptic in origin. In the presence of 5 μm CGP55845A, the time course of depression was qualitatively similar, but the steady-state IPSC amplitude was significantly larger (33 ± 6% vs 21 ± 2%,p < 0.01) (Fig. 9G) (seven pairs), suggesting a small contribution of GABA_Breceptors to multiple-pulse depression.

Frequency-dependent depression is often interpreted as a depletion of the releasable pool of synaptic vesicles (Liley and North, 1953;Stevens and Tsujimoto, 1995). If this were the case, its extent would depend on the average release probability (Dittman and Regehr, 1998), and amplitudes of consecutive IPSCs in the train may be correlated (Matveev and Wang, 2000). We therefore examined depression during 20 Hz trains at different Ca²⁺/Mg²⁺concentration ratios (Fig. 9H). In conditions of reduced release probability (0.5 mmCa²⁺), the fast component of depression was comparable, but the slow component showed a reduced amplitude and a slower time course (Fig. 9H, open symbols). The ratio of currents at the end of the train to those before the train was significantly larger in 0.5 mmCa²⁺ (0.55 ± 0.08) than in 2 mm Ca²⁺ (0.27 ± 0.03; p < 0.001). Furthermore, amplitudes of subsequent IPSCs in the second portion of the train were negatively correlated (Fig. 9I). These results are consistent with the hypothesis that the slow component of depression is caused by depletion of the vesicular pool (Matveev and Wang, 2000).

To understand the interactions between fast and slow depression, we examined the quantitative predictions of pool models with different forms of activity dependence (Betz, 1970; Kusano and Landau, 1975). Figure 10 illustrates the predictions of a two-pool model with constant release probability and replenishment (Fig. 10, model a) and two alternative models with either activity-dependent reduction in release probability (modelb) or activity-dependent increase in replenishment (modelc). In the absence of evidence for multivesicular release (Fig. 5), we implemented a univesicular release constraint (Korn et al., 1982; Matveev and Wang, 2000). Among the alternatives tested, the model with the activity-dependent reduction in release probability would be most consistent with the experimental observations. Unlike the other models, it predicts the biexponential time course of multiple-pulse depression (Fig. 10B) very closely. Furthermore, the model predicts the approximate extent of PPD and the independence of PPD on release probability (Fig. 10, legend). If this model is used to fit the depression data in Figure 9,C–E and H, with release probabilities constrained to the mean values obtained by MP-CBA (Fig.6D, Table 2), we estimate that the capacity of the releasable pool is 51 vesicles per release site at the BC–GC synapse (see Discussion and continuous curves in Fig. 9 for quantitative predictions).

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Fig. 10.

Activity-dependent gating of release may prevent depletion of the releasable pool of synaptic vesicles.A, Schematic illustration of different vesicular pool models. Univesicular release constraint. The capacity of the releasable pool (N_v0) was assumed as 50, the initial release probability (p_R at time 0) as 0.5, and the refilling rate as k = 0.01 sec⁻¹. a, Two-pool model with constant rates. b, Two-pool model with activity-dependent reduction in release probability (Betz, 1970). Activity-dependent reduction of p_R was defined by a_max = 1, α = 0.2, and β = 2 sec⁻¹, yielding a half-maximal activating frequency at 10 Hz and a maximal time constant of 0.5 sec. c, Two-pool model with activity-dependent refilling of the releasable pool (Kusano and Landau, 1975). Activity-dependent increase of k was defined bya_max = 4, α = 0.2, and β = 2 sec⁻¹. The frequency dependence of the reduction and enhancement factor, respectively, in steady-state conditions is illustrated adjacent to the affected rate.B, Mean release probabilityp_R during 20 Hz trains, normalized to the initial value. Dotted curve indicates modela; continuous curve, modelb; dashed curve, model c. The shaded area indicates the gain of IPSC amplitude in the late phase of the train, generated by redistribution of release events from the early to the late phase. Note that the prediction of model b is consistent with the time course of onset of multiple-pulse depression. Furthermore, model bpredicts a maximal paired-pulse depression of 1-(N_v0 −p_R)/N_v0exp(−α) = 0.19, whereas models a andc give a much smaller depression 1-(N_v0 −p_R)/N_v0= 0.01. Model b was also used to fit the experimental data in Figure 9, C–E andH. The initial release probabilitiesp_R were constrained to 0.526 and 0.049, respectively, which were the mean release probabilities in 2 mm Ca²⁺/1 mmMg²⁺ and 0.5 mmCa²⁺/2.5 mmMg²⁺ during low-frequency stimulation (Fig.6D, Table 2). The best-fit parameters were as follows: capacity of the releasable poolN_v0 = 51 vesicles per site, refilling rate k = 0.059 sec⁻¹, maximal activity-dependent modification a_max = 0.59, and rates of α = 0.36 and β = 3.9 sec⁻¹, yielding a half-maximal inhibitory frequency of 10.7 Hz and a maximal time constant of 0.26 sec of the activity-dependent process. For details, see Materials and Methods.

Quantal size at the BC–GC synapse

The estimated quantal conductance at the BC–GC synapse in high intracellular Cl⁻ concentration was 1.7 nS (Fig. 4D). If the single-channel conductance of postsynaptic GABA_A receptors is assumed to be 30 pS at 34°C (Brickley et al., 1999; Perrais and Ropert, 1999), this would imply the opening of 57 GABA_AR channels at the peak of a quantal IPSC. If the current flow through GABA_ARs expressed in GCs follows the Goldman-Hodgkin-Katz equation, the quantal conductance in physiological Cl⁻ concentrations would be predicted to be ∼0.5 nS [chord conductance at +10 mV calculated using the Goldman-Hodgkin-Katz current equation for 6 mmintracellular Cl⁻ (Hille, 1992; also seeBormann et al., 1987)]. Considering that the resting input conductance of a GC is approximately 2 nS (Spruston and Johnston, 1992), this suggests that a quantal event has considerable shunting effects under physiological conditions.

Our values of the quantal conductance at the BC–GC synapse are larger than previous estimates for inhibitory synapses on hippocampal granule cells [0.2–0.4 nS, high intracellular Cl⁻ (Edwards et al., 1990); 0.4 nS, low intracellular Cl⁻ (Nusser et al., 1998)]. Differences in recording temperature (34°C in this paper vs 21−23°C in the other studies) certainly contribute to this apparent difference but are unlikely to explain it entirely. It is possible that different presynaptic interneuron subtypes were activated in the different studies. Presynaptic interneurons in the present experiments were selected according to fast spiking during sustained current injection, which will bias the sample toward parvalbumin-positive basket cells (Freund and Buzsáki, 1996; Cauli et al., 1997; Lübke et al., 1998). In contrast, interneurons activated in the other studies by minimal extracellular axonal stimulation may also include CCK/VIP-positive basket cells or HICAP cells with axons coaligned with the commissural-associational pathway (Freund and Buzsáki, 1996;Cauli et al., 1997; Lübke et al., 1998).

Release probability and Ca²⁺ dependence

The mean release probability at the BC–GC synapse in physiological divalent concentrations, determined by compound binomial analysis, was ∼0.4–0.6 (Fig. 6). The dependence of release probability on extracellular Ca²⁺concentration at the BC–GC synapse is consistent with the cooperative binding of >2 Ca²⁺ ions to the putative Ca²⁺ sensor, probably synaptotagmin (Südhof, 1995). The apparent Hill coefficient (2.4) is lower, however, than that at the frog neuromuscular junction (∼3.8) (Dodge and Rahamimoff, 1967) or at glutamatergic autapses (3.3) (Reid et al., 1998). This may reflect a difference between inhibitory or excitatory terminals (e.g., in the synaptotagmin isoforms present). Alternatively, the lower Hill coefficient of inhibitory synapses may be attributable to intersite differences in the EC₅₀values among terminals of the same connection, which will result in reduction of the apparent Hill coefficient.

The maximal release probability that is approached at high Ca²⁺ concentrations (extrapolated value ∼0.8) (Fig. 6D) indicates a high efficacy of coupling of Ca²⁺ inflow to exocytosis at the BC–GC synapse. Furthermore, the high maximal release probability suggests that axonal conduction of a single spike is reliable, despite the extensive arborization of the BC axon (Freund and Buzsáki, 1996). The proportion of conduction failures in physiological divalent concentrations is probably much less than 0.2 (1 - maximal release probability), because an increase in Ca²⁺ concentration is likely to reduce the safety factor of transmission, for example, caused by screening of surface charges (Frankenhaeuser and Hodgkin, 1957).

The BC–GC synapse is a multi-site connection

The present results indicate that synaptic events at the BC–GC synapse are generated at three to seven functional release sites (Fig.6, Table 2). This value appears to be in approximate agreement with the estimated number of anatomical release sites at inhibitory synapses in the hippocampus determined by electron microscopic analysis [10–12 inhibitory contacts between basket cells and pyramidal neurons in the CA1 subfield; eight inhibitory contacts between axo-axonic cells and GCs (Buhl et al., 1994); two to six inhibitory contacts between perisomatic inhibitory cells and pyramidal neurons in the CA3 region (Miles et al., 1996); two to four inhibitory contacts between BCs and GCs (Geiger et al., 1997; J. Lübke, personal communication). It remains to be determined whether BC–GC synaptic contacts comprise a single release site or multiple release sites, as reported previously for dendrite-targeting interneurons in the neocortex (Tamás et al., 1997).

The locus of PPD is upstream of the exocytotic step

Synaptic depression has been attributed to desensitization of postsynaptic receptors (Jones and Westbrook, 1995, 1996), negative feedback by presynaptic metabotropic receptors (Deisz and Prince, 1989;Lambert and Wilson, 1994), synaptic refractoriness (Stevens and Wang, 1995), or depletion of the releasable pool of synaptic vesicles (Debanne et al., 1996; Dobrunz and Stevens, 1997). None of these factors, however, appears to be primarily responsible for PPD of unitary IPSCs at the BC–GC synapse.

Desensitization of postsynaptic GABA_Areceptors is not the major factor underlying PPD, because CV analysis suggested that the primary locus of PPD is presynaptic. Presynaptic receptors do not appear to be involved, because PPD at the BC–GC synapse was unaffected by the high-affinity GABA_B receptor antagonist CGP55845A (Kaupmann et al., 1997). Synaptic refractoriness is not expected to contribute to PPD, because recovery from refractoriness is thought to be complete within ∼10 msec (Stevens and Wang, 1995). Finally, pool depletion was unlikely, because the extent of PPD was independent of extracellular Ca²⁺ concentration, and a negative correlation between the amplitudes of first and second IPSCs was not observed (Fig. 8). The independence of PPD on extracellular Ca²⁺ concentration and previous release further argues against both desensitization of postsynaptic GABA_A receptors and activation of presynaptic GABA_B receptors. More generally, this independence argues against the involvement of any type of presynaptic receptor activated by modulators coreleased with GABA.

Although desensitization does not underlie PPD, it is possible that it is involved in the generation of the slow component of IPSC decay (9 msec in this study), which may reflect transitions of postsynaptic GABA_A receptors from desensitized to open states (Jones and Westbrook, 1995, 1996). If this were the case, postsynaptic GABA_A receptors may have largely recovered from desensitization at times when PPD is still substantial (e.g., at 100 msec).

On the basis of this evidence, we conclude that PPD at the BC–GC synapse is generated by a mechanism located upstream of the exocytotic step. Candidate mechanisms include (1) increased probability of axonal conduction failures after the first spike (Lüscher and Shiner, 1990), (2) changes in duration of the presynaptic spike resulting in reduced Ca²⁺ inflow (Geiger and Jonas, 1999), (3) inactivation of presynaptic Ca²⁺ channels (Patil et al., 1998), (4) Ca²⁺ depletion in the extracellular space (Borst and Sakmann, 1999), and (5) reduction of release probability after the first spike (Betz, 1970; Faber et al., 1998), which may reflect desensitization of the Ca²⁺ sensor that triggers release or direct voltage-dependent inactivation of the release machinery. Evidence for release-independent forms of PPD has also accumulated recently for other synapses (Dobrunz et al., 1997; Bellingham and Walmsley, 1999; Geiger et al., 1999; Thomson and Bannister, 1999).

The slow component of multiple-pulse depression: depletion of the releasable pool?

During a train of presynaptic action potentials, unitary IPSC peak amplitudes at the BC–GC synapse decline biexponentially (Fig.9C). The fast component of depression may correspond to PPD, whereas the slow component appears to be distinct. Desensitization of postsynaptic GABA_A receptors is unlikely to be the main factor underlying the slow component of depression, because CV analysis suggested a mainly presynaptic origin. Presynaptic autoreceptors provide a small contribution to slow depression, as indicated by the slight reduction of multiple-pulse depression by CGP55845A (Jensen et al., 1999; this paper); however, depletion of the releasable pool of synaptic vesicles (Liley and North, 1953) is the most likely mechanism for this slow depression. This is supported by the dependence of slow depression on release probability (Fig.9H) and the negative correlation between amplitudes of consecutive IPSCs (Fig. 9I) (Matveev and Wang, 2000).

Assuming that the two phases of multiple-pulse depression are shaped by a fast depression mechanism upstream of the release machinery and a slow depression mechanism corresponding to depletion of the readily releasable pool, we estimate that the capacity of the releasable pool at the BC–GC synapse is ∼50 per release site. It is not clear whether this pool corresponds to the “readily releasable pool” (Stevens and Tsujimoto, 1995) or comprises both a readily releasable and a “reserve” pool (Liu and Tsien, 1995b). If our pool corresponds to the readily releasable pool, it would be larger than that at excitatory synapses in cultured neurons (∼20) (Stevens and Tsujimoto, 1995).

Activity-dependent gating of release may stabilize inhibition

The possible coexistence of a fast depression generated by a gating mechanism upstream of the exocytotic event and a slow depression caused by depletion of the releasable pool raises the question of how these two forms of depression interact during high-frequency activity. One possibility is that activity-dependent reduction in release probability, somewhat counter-intuitively, protects against depletion of the releasable pool of synaptic vesicles, thus conferring stability of transmission (Betz, 1970; Brenowitz et al., 1998). As shown in Figure 10B, the predicted IPSC amplitudes during a high-frequency train for the model with constant rates and the model with activity-dependent reduction of release probability show crossover, implying that vesicles saved in the early phase can be released in the late phase of the train (shaded area). Because GABAergic interneurons in the hippocampus in vivogenerate action potentials over a wide range of frequencies with mean values of 10–20 Hz (Penttonen et al., 1998; Csicsvari et al., 1999), redistribution of synaptic efficacy within a train may contribute to the stability of transmission at GABAergic synapses in the hippocampal network of the behaving rat.