Quantal amplitude and quantal variance of strontium-induced asynchronous EPSCs in rat dentate granule neurons

Abstract

1. Excitatory postsynaptic currents (EPSCs) were recorded from granule cells of the dentate gyrus in acute slices of 17- to 21-day-old rats (22-25 °C) using tissue cuts and minimal extracellular stimulation to selectively activate a small number of synaptic contacts.

2. Adding millimolar Sr²⁺ to the external solution produced asynchronous EPSCs (aEPSCs) lasting for several hundred milliseconds after the stimulus. Minimally stimulated aEPSCs resembled miniature EPSCs (mEPSCs) recorded in the same cell but differed from them in ways expected from the greater range of dendritic filtering experienced by mEPSCs. aEPSCs had the same stimulus threshold as the synchronous EPSCs (sEPSCs) that followed the stimulus with a brief latency. aEPSCs following stimulation of distal inputs had a slower mean rise time than those following stimulation of proximal inputs. These results suggest that aEPSCs arose from the same synapses that generated sEPSCs.

3. Proximally elicited aEPSCs had a mean amplitude of 6.7 ± 2.2 pA (± s.d., n = 23 cells) at -70 mV and an amplitude coefficient of variation of 0.46 ± 0.08.

4. The amplitude distributions of sEPSCs never exhibited distinct peaks.

5. Monte Carlo modelling of the shapes of aEPSC amplitude distributions indicated that our data were best explained by an intrasite model of quantal variance.

6. It is concluded that Sr²⁺-evoked aEPSCs are uniquantal events arising at synaptic terminals that were recently invaded by an action potential, and so provide direct information about the quantal amplitude and quantal variance at those terminals. The large quantal variance obscures quantization of the amplitudes of evoked sEPSCs at this class of excitatory synapse.

According to the quantal model of synaptic transmission, neurotransmission is a stochastic process with two sources of uncertainty: the probabilistic release of presynaptic vesicles and the variable postsynaptic response to the transmitter contained in each vesicle. Classical treatments (Del Castillo & Katz, 1954) indicate that these two sources of uncertainty can be distinguished in the quantal ‘peaks’ that are apparent in amplitude histograms of evoked synaptic potentials. The relative areas of these peaks reflect the statistics of vesicular release; their separation and breadth reflect the mean amplitude and variability, respectively, of the postsynaptic response to each vesicle (the quantal amplitude, q, and the quantal variance, qv) (Redman, 1990; Bekkers, 1994). Alternatively, q and qv can be estimated from the amplitude distribution of spontaneous miniature synaptic responses, which are thought to arise from the random exocytosis of single vesicles of transmitter (Fatt & Katz, 1952; Frerking & Wilson, 1996a).

The quantal parameters q and qv are central components of many biophysical models of synaptic function. For example, q may represent the minimum unit of information transfer at a synapse, whilst qv might quantify the precision with which that information is conveyed. Both parameters are also relevant to ongoing debate about the concentration of neurotransmitter in the synaptic cleft and the saturation or otherwise of postsynaptic receptors (Clements, 1996; Frerking & Wilson, 1996B). Despite their importance, estimates of quantal amplitude and variance at central synapses remain controversial. Amplitude histograms of evoked excitatory postsynaptic currents (EPSCs), largely obtained in acute slice preparations, have indicated a small to moderate quantal variance (Liao et al. 1992; Jonas et al. 1993; Stricker et al. 1996; Paulsen & Heggelund, 1996). On the other hand, studies of miniature synaptic currents, often done in culture, have suggested that the quantal variance can be large, with a coefficient of variation of 0.5 or greater (Bekkers et al. 1990; Raastad et al. 1992; Bekkers & Stevens, 1995; Liu & Tsien, 1995; Frerking et al. 1995; Isaacson & Walmsley, 1995; Abdul-Ghani et al. 1996). Culture experiments are attractive because they allow precise control over the origin of miniature synaptic currents (Bekkers & Stevens, 1995; Liu & Tsien, 1995; Forti et al. 1997). This is important because miniature currents gathered at random from all synapses on a cell reflect a population variance that may not be relevant to the variance associated with just those synapses that generate action potential-evoked EPSCs (Walmsley, 1993). However, culture experiments are open to the criticism that quantal variance at synapses grown in vitro, which develop in the absence of many of the usual cues found in vivo, may be artefactual. Discrepancies between slice and culture results might thus be resolved if both EPSC amplitude histograms and miniature EPSCs could be measured in slices with the same precise control over their sites of origin as is possible in culture.

This paper explores an approach to measuring both miniature and action potential-evoked EPSCs arising from the same small population of synapses in a hippocampal slice preparation. The method draws upon the classical finding that extracellular strontium provokes a prolonged ‘asynchronous’ release of neurotransmitter at the endplate (Miledi, 1966; van der Kloot, 1994). We show that asynchronous EPSCs (aEPSCs) occur in slices of dentate gyrus and that these are similar to miniature EPSCs (mEPSCs). Differences between aEPSCs and mEPSCs can be explained by the greater range of dendritic filtering experienced by the latter, since they arise in synapses located all over the dendritic tree. We further show that aEPSCs have the same stimulus threshold as synchronous, action potential-evoked EPSCs. This and other evidence suggests that aEPSCs recorded in strontium are equivalent to mEPSCs which originate in a subset of synaptic contacts, namely, those which generate the electrically evoked EPSC.

As stated by Korn & Faber (1991), an important component of a ‘proper’ quantal analysis is information about the miniature events. The classical quantal model states that the amplitude distribution for the miniatures should align with the first quantal peak in the amplitude distribution for evoked events (Del Castillo & Katz, 1954). Subsequent peaks should be spaced at intervals equal to the mean or modal amplitude of the miniatures (Redman, 1990). In order to test this prediction in the slice preparation, different strategies have been adopted for selecting the relevant miniatures. Paulsen & Heggelund (1994) chose a system with a simple morphology (retinogeniculate synapses) in which all miniatures recorded in the postsynaptic cell were likely to have originated from a small population of homogeneous synapses. Jonas et al. (1993) studied mossy fibre inputs onto CA3 pyramidal cells, selecting miniatures with the fastest rise times as being those most likely to have arisen in the proximal mossy fibre synapses. Both of these reports broadly confirmed the classical prediction, at least for a subset of their recordings.

Our strontium data provide another way of addressing this question in slices. Synchronous and asynchronous EPSCs arising from the same synapses were accumulated into amplitude histograms. It was expected that quantal ‘peaks’ would be observed in the synchronous EPSC distribution, and that the first peak would be aligned with the aEPSC distribution. In order to optimize the conditions for observing such peaks, we studied proximal synapses on a small neuron with low intrinsic noise (the granule cell of the dentate gyrus) and accumulated evoked EPSC histograms with large numbers of entries (typically > 1000). Tissue cuts and minimal stimulation were used to minimize the number of active synapses. We found that neurotransmission at this slice synapse was very similar to that observed between pairs of cultured hippocampal pyramidal cells (Bekkers & Stevens, 1995). Quantization was never apparent in the EPSC histograms and the variance of the amplitudes of aEPSCs was large.

Some of this data has been published as an abstract (Bekkers, 1995) and a workshop proceedings (Bekkers, 1998).

METHODS

Slice preparation

Hippocampal slices were prepared using standard techniques that were approved by the Animal Experimentation Ethics Committee of the Australian National University. Following decapitation, transverse or parasagittal hippocampal slices (400 μm thick) were cut from the brains of 17- to 21-day-old Wistar rats in ice-cold artificial cerebrospinal fluid (ACSF) using a Vibratome microslicer (Pelco, Redding, CA, USA). Slices were incubated in ACSF at 34°C for 1 h, and then maintained at room temperature in a holding chamber until use (1-3 h after slicing).

Solutions

The ACSF solution used for slicing and incubation contained (mM): 124 NaCl, 3 KCl, 1.3 MgSO₄, 2.5 CaCl₂, 26 NaHCO₃, 2.5 NaH₂PO₄ and 11 glucose, pH 7.4 when bubbled with carbogen (95 % O₂, 5 % CO₂). The basic external solution for recordings comprised (mM): 110 NaCl, 3 KCl, 2.5 MgCl₂, 26 NaHCO₃, 2.5 NaH₂PO₄ and 10 glucose, pH 7.4 when saturated with carbogen at room temperature. To this was added 2 mM CaCl₂ (2Ca solution), or 8 mM SrCl₂ (8Sr solution), or a mixture of 4 mM SrCl₂ and 1 mM CaCl₂ (4Sr-1Ca solution), depending on the experiment (see Results). In all cases the osmolarity was adjusted to 290 mosmol kg⁻¹ with sorbitol. Bicuculline methiodide was always added at 10 μM to block GABA_A currents. Extracellular Mg²⁺ should have blocked NMDA currents at our holding potential (-70 mV). This was confirmed by checking that 50 μM D-2-amino-5-phosphonopentanoic acid (D-AP5) had no effect on the EPSCs. In some experiments 1 μM CGP 55845 (to block GABA_B currents) was present but also had no effect. Tetrodotoxin (TTX) was sometimes included in the external solution at 0.5 μM, which was sufficient to block all evoked EPSCs. The internal solution contained (mM): 125 caesium gluconate, 5 CsCl, 10 EGTA, 2 Na₂ATP, 2 MgCl₂, 0.4 GTP, 10 Hepes at pH 7.3, to which sorbitol was added to give an osmolarity of 310 mosmol kg⁻¹. All compounds were obtained from Sigma, except D-AP5 (Tocris Cookson, Bristol, UK) and CGP 55845 (a gift of Professor D. R. Curtis).

Whole-cell recording

Hippocampal slices were perfused continuously with carbogen-bubbled external solution at 2 ml min⁻¹. Recordings were usually made from neurons in the lateral blade of the dentate gyrus (Fig. 1A). In an effort to reduce the number of stimulated synaptic inputs, a cut was made across the slice, leaving a tissue bridge ∼50 μm long immediately adjacent to the cell body layer (Fig. 1A). The stimulating electrode was a patch electrode (tip diameter ∼1 μm) filled with external solution and coated with metallic paint; the interior of the electrode was connected to one terminal of an isolated stimulator, the paint to the other terminal. The stimulator was placed 40-160 μm distal to the cut and in stratum moleculare on the boundary of the cell body layer. At this location, commissural inputs from the contralateral hippocampus were preferentially stimulated (Laatsch & Cowan, 1966). The distance from the tissue bridge to the granule cell from which recordings were made was in the range 290-470 μm. Another cut, not illustrated in Fig. 1A, was made between the dentate gyrus and CA3 to abolish epileptic activity. In some experiments a cut was also made to isolate a ∼50 μm tissue bridge abutting the hippocampal fissure (Fig. 8A). This was to enable selective stimulation of distal inputs.

Figure 1. Stimulation, recording and analysis procedures.

A, schematic diagram of the hippocampal slice preparation showing the relative locations of the electrodes and the tissue cut (not to scale). The stimulator was placed at the border of the cell body layer, 290-470 μm from the recording electrode and 40-160 μm from the cut, on the opposite side from the postsynaptic neuron. Region CA3 was also isolated by a cut (not shown) made just distal to the leftmost extent of the dentate cell body layer. B, plot of mean peak amplitude of the electrically evoked EPSC versus stimulus intensity for one cell, showing the existence of a stimulus plateau. Each point is the mean (±s.e.m.) of 4 separate measurements of the mean EPSC amplitude (each an average of 30 episodes) at each stimulus setting. The non-zero mean amplitude below the stimulus threshold is an artefact of the on-line peak detection algorithm used to measure the amplitudes. The arrow indicates the stimulus strength used in this experiment (8.5 μA). C, examples of aEPSCs that were detected by the sliding template algorithm but were rejected by eye because of overlapping events. The second aEPSC in the middle trace was accepted. D, examples of fits of the exponential product function given in Methods, in order to estimate the rise times and decay time constants of accepted aEPSCs. Horizontal lines indicate the intervals over which the baseline was adjusted (2 ms) and the peak was averaged (1 ms).

Figure 8. aEPSCs following stimulation of distal inputs have slower rise times than those following proximal stimulation.

Aa, schematic diagram of the arrangement of the electrodes. In addition to the usual cut isolating a proximal input, a second cut was made, leaving a short (≈50 μm) tissue bridge between the end of the cut and the hippocampal fissure. The distal stimulator was placed close to the fissure. An additional cut, not shown, isolated CA3. Ab, superimposed averages of 200 aEPSCs recorded in the same cell following stimulation of either distal (open symbol) or proximal (closed symbol) afferents. B, plot of the 20-80 % rise time of aEPSCs, obtained from the averaged aEPSCs, versus the series resistance measured in that cell. In two cells (joined by vertical dashed lines) both distal and proximal data were obtained; all other points were from different cells. The horizontal interrupted lines and error bars represent the mean ±s.d. of data from the two kinds of stimulation: 1.04 ± 0.26 ms (distal) and 0.52 ± 0.10 ms (proximal). C, histograms of 20-80 % rise time for aEPSCs following distal and proximal stimulation (left panel) and for spontaneous EPSCs (right panel), all recorded in the same cell. The aEPSC histograms have been corrected by subtracting the histogram for spontaneous EPSCs, after scaling the latter to allow for the different rates of occurrence of the events. The mean rise times (±s.d.) and numbers of entries in the histograms, after correction, were 0.34 ± 0.10 ms and 507 (proximal aEPSCs), 0.99 ± 0.33 ms and 162 (distal aEPSCs), 0.72 ± 0.31 ms and 572 (spon EPSCs).

Whole-cell recordings were made from neurons in stratum granulosum using the blind patch-slice method. In order to minimize the series resistance (R_s), electrode resistances were kept as low as possible (2.5-3.5 MΩ) while still being compatible with the formation of stable seals. Fast capacitance transients were fully compensated in the on-cell configuration prior to going whole cell. Cells were voltage clamped at -70 mV. Granule cells were identified by their capacitance charging transients (Spruston & Johnston, 1992). Occasionally, spiking cells with faster transients were encountered; these were presumed to be interneurons and were excluded.

The afferent stimulus was a 100 μs pulse provided by an isolated constant current stimulator. Stimuli were applied at 0.5 Hz. Synaptic currents were recorded using an Axopatch 1D (Axon Instruments), filtered at 1 kHz with a 4-pole Bessel filter, and digitized at 10 kHz by an ITC-16 interface (Instrutech, Great Neck, NY, USA) running under Igor software (Wavemetrics, Lake Oswego, OR, USA) on a Macintosh computer. Currents were also recorded continuously onto videotape (PCM 200, Vetter, Rebersburg, PA, USA) after filtering at 5 kHz. The series resistance of the electrode and the input resistance of the neuron were continuously monitored by means of a 20 ms, 1 or 2 mV hyperpolarizing voltage step applied before each afferent stimulus (Fig. 3A). A more accurate estimate of R_s was calculated from the peak of the capacitance transient that was periodically recorded during the experiment after switching the Bessel filter to 10 kHz. The latter estimates, which still overestimate the true R_s because of the residual effect of filtering, are given in Fig. 8.

Figure 3. Stability of the stimulus and recording conditions.

All data were obtained from the same granule cell in 4Sr-1Ca external solution. A, eight superimposed episodes recorded near the middle of the experiment, showing raw data before the stimulus artefact is subtracted. The test pulse was 2 mV and the stimulator was set at 6 μA. B, each point is the peak amplitude of the early (synchronous) EPSC in each episode, measured as described in the Methods to correctly include failures. The bars mark intervals during which the stimulus was turned off. C, each point is the series resistance, corrected to the value measured from the peak of the capacitance charging transient with the filter set at 10 kHz, for each episode. D, plot of the input resistance (R_N) versus episode number, where each point is the mean of R_N measured in 10 consecutive episodes. The horizontal line shows the mean input resistance of this cell, 760 MΩ.

With the stimulating electrode placed very close to the cell body layer and less than 500 μm from the postsynaptic neuron, synaptic inputs were only rarely encountered and were readily lost after small movements of the stimulator (< 5 μm). For each input, a stimulus-response plot was constructed (Fig. 1B; Raastad, 1995). Twenty or thirty EPSCs were averaged on-line at a particular setting of stimulus current and the mean peak EPSC amplitude was measured. This was repeated at each stimulus setting over the region of interest, randomly revisiting each setting up to five times. The mean EPSC amplitudes at each stimulus setting were averaged together and the means and s.e.m.s were plotted (Fig. 1A). The stimulator was then set at a current strength corresponding to the plateau of the stimulus-response plot (arrow in Fig. 1A) and left unaltered throughout the experiment. Stimulus settings were in the range 5-20 μA, with two outliers near 40 μA. In several cases the whole procedure was repeated at the end of the experiment to ensure that the stimulus plateau had not varied. However, in all experiments presented here the stability of the stimulus was also evident from the fact that the mean evoked EPSC amplitude was stationary over the duration of the experiment (e.g. Fig. 3A).

In some experiments the external solution was changed by perfusing the bath for at least 10 min. All experiments were done at room temperature (22-25°C).

Data analysis

Analysis was done using AxoGraph (Axon Instruments). In the following discussion, an ‘episode’ means a single sweep of raw data. This is illustrated in Fig. 3A, which shows eight episodes superimposed.

The first step in the analysis was to remove the stimulus artefact, because it may distort the measurement of early EPSCs. This was done by averaging together episodes containing no EPSCs (evoked or spontaneous) and subtracting the average from each episode. This procedure very effectively removed the artefact, without the need for any blanking (e.g. Fig. 4). In order for this procedure to be valid, it was assumed here that the artefact was an extracellular field current that added linearly to the recorded intracellular current without significantly distorting the membrane potential.

Figure 4. Extracellular strontium enhances the appearance of asynchronous EPSCs.

A and B show episodes on two different time bases. In each case the stimulus artefact has been subtracted; the location of the stimulus is shown by the vertical dashed line. A, EPSCs recorded in 2Ca external solution. Spontaneous EPSCs are indicated by the arrows. Same cell as in Fig. 5A. B, EPSCs recorded in another neuron in 8Sr external solution. Same cell as in Fig. 2.

EPSCs were detected automatically using a sliding template algorithm (Clements & Bekkers, 1997). Briefly, a waveform with the time course of a typical EPSC (the template) was slid along the episode and optimally scaled to fit the data at each position. A detection criterion was calculated based on the optimum scaling factor and the quality of the fit. This criterion was closely related to the signal-to-noise ratio for the detected event. The EPSC was detected when the criterion passed a threshold. The template was generated by averaging a number of EPSCs selected by eye. The threshold for the detection criterion was set at 3 or 4, which was optimal for the conditions of these experiments (Clements & Bekkers, 1997). All the detected EPSCs were inspected visually to exclude any which may have been distorted by overlap with neighbouring EPSCs. For example, in Fig. 1A the first EPSC in each episode was excluded, while the second in episode 2 (middle trace) was accepted. At the highest rates of aEPSC activity (∼10 Hz; Fig. 5A) indistinguishably overlapping aEPSCs, defined as those occurring within 2 ms of each other, would have contributed less than 0.1 % of the total population.

Figure 5. Latency frequency histograms vary with different concentrations of external calcium and strontium, and aEPSC amplitude is weakly dependent on latency.

A-C, latency frequency histograms are shown for EPSCs recorded in three different external solutions (2Ca, 4Sr-1Ca and 8Sr). Each panel shows the same data with two different abscissae. The right-hand panels have logarithmic ordinates. The horizontal bar in each panel indicates the 100 ms window over which the rate of occurrence of aEPSCs was measured. The window started at t_c (left panels) or at 750 ms after the stimulus (right panels). The rates for these windows are shown above the bars. The superimposed smooth curves are least-squares fits of a constant (A) or a sum of a single exponential and a constant (B and C), starting at a latency of 20 ms. The results of the fits were: A, constant = 0.58 Hz; B, decay = 61 ms, constant = 0.41 Hz; C, decay = 117 ms, constant = 0.43 Hz. Each panel was from a different cell. n is the number of entries in the histograms. The histogram in 2Ca solution is truncated because data were only sampled to 880 ms after the stimulus. D, the peak amplitude of each EPSC was plotted versus its latency from the stimulus (same cell as in C). The superimposed straight lines are unconstrained fits to the points from t_c (11.0 ms in this cell) to 0.5 s (left) or 1.5 s (right). They have slopes of -1.96 × 10⁻³ and -0.41 × 10⁻³ pA ms⁻¹, respectively.

The analysis yielded a file of excised EPSCs, aligned at the time point where the current first rose out of the noise (the foot), together with the latency from the stimulus to the peak of each EPSC (Fig. 2A, inset). The latency data permitted the sorting of EPSCs into ‘synchronous’ and ‘asynchronous’ categories. For each experiment, latency measurements were accumulated into frequency histograms (Fig. 2). Latencies were first binned at 0.5 ms and the function f(t) =a₁exp(-t/τ₁) +a₂exp(-t/τ₂) +c was fitted from the peak of the histogram to the maximum latency (usually 1.4-1.5 s; Fig. 2A). Here a₁, a₂ and c are constants and τ₁ and τ₂ are the fast and slow decay time constants; c reflects the background rate of mEPSCs in the cell (see Results). The estimate of τ₂ was checked by rebinning the latencies at 10 ms and fitting a single exponential plus a constant from 20 ms to the maximum latency (Fig. 2A). τ₂ found in this way was usually within 10 % of the value estimated from the fit with 0.5 ms bins. The averaged values of τ₂ given in Results were obtained from fits with 10 ms bins.

Figure 2. Definition of asynchronous EPSCs.

Asynchronous EPSCs were identified by means of a latency frequency histogram compiled for each cell. The latency was measured from the time of the stimulus (vertical dashed line, inset) to the peak of each detected EPSC. A, frequency histogram of latencies measured for one cell in external solution containing 8 mM Sr²⁺ (8Sr), compiled with a bin width of 10 ms. The superimposed smooth curve is a least-squares fit of a single exponential plus a constant offset; the fit started at 20 ms latency. The fitted decay time constant is 135 ms and the added constant, which corresponds to the background rate of mEPSCs, is 1.4 Hz. The histogram contains 3754 entries. B, the same data shown with an expanded abscissa and a 0.5 ms bin width. The superimposed continuous curve is a least-squares fit of a sum of two exponentials plus a constant offset. The fit started at the peak of the histogram. The three components of the fit are shown separately as dashed lines superimposed on the histogram. The latency at which the amplitudes of the two fitted exponentials was equal was called the cutoff time, t_c, here 11.7 ms. Events with latencies < =t_c were defined as synchronous, those with latencies > t_c as asynchronous.

Synchronous and asynchronous EPSCs were defined by means of a cutoff time, t_c, defined as the latency at which the amplitude of the fitted fast component equals that of the fitted slow component (Fig. 2A): t_c = (τ₁τ₂/(τ₂ - τ₁))ln(a₁/a₂). EPSCs with latencies ≤t_c were defined as synchronous, while those with latencies > t_c as asynchronous. The mean value of t_c was 11.2 ± 2.9 ms (±s.d., n = 23 experiments). Errors in this assignment of synchronous and asynchronous EPSCs were estimated as follows. The number of sEPSCs incorrectly assigned to the asynchronous category is approximately equal to the area under the fitted fast component to the right of t_c (Fig. 2A). Similarly, the number of incorrectly assigned aEPSCs is approximately equal to the area under the fitted slow component to the left of t_c, after extrapolating the curve to the leftmost edge of the experimental histogram (Fig. 2A). These errors were expressed as percentages of the counted numbers of sEPSCs and aEPSCs, after subtracting the estimated number of background mEPSCs in each interval. The mean errors were 2.9 ± 2.8 and 7.6 ± 5.1 % for sEPSCs and aEPSCs, respectively (±s.d., n = 23). Unless otherwise stated, all histograms of measurements on aEPSCs included EPSCs with latencies ranging from t_c to 350 ms after the stimulus (i.e. up to 3-4 times the estimated value of τ₂; see Results).

EPSC amplitude was measured by baselining each EPSC over a 2 ms window immediately before the foot and then averaging over a 1 ms window around the peak (Fig. 1A). The baseline noise was estimated by applying the same procedure to regions of each episode containing no events, where the separation between the two windows was obtained from the time to peak of the average of all accepted EPSCs. A single Gaussian function was fitted to a histogram of the noise amplitudes, yielding an estimate for the s.d. of the noise for each experiment.

For measuring the amplitudes of synchronous EPSCs, including failures (e.g. Figs 3B, 11A and 12A), a slightly different method was used. The analysis was done on the original episodes, after subtraction of the stimulus artefact. The peak amplitude of each EPSC was measured as above, except that the range of the search for peaks was restricted to that used to define synchronous EPSCs (e.g. latency ≤ 10.7 ms for the cell in Figs 3 and 11). If the measured amplitude fell below 4 times the s.d. of the baseline noise for the cell - that is, if the peak of the current was insufficiently distinct - the amplitude was instead measured at a fixed latency equal to the latency of the mean of all synchronous EPSCs. In the case of failures, then, this method reduced to the procedure for measuring baseline noise. Spontaneous and miniature EPSCs were also analysed as above, after replaying the data from VCR tape, filtering at 1 kHz and digitizing continuously at 10 kHz.

Figure 11. Amplitude histograms for synchronous and asynchronous EPSCs recorded in the same cell are broadly skewed and do not show quantization.

Examples of episodes recorded in this cell are shown at the top right (same cell as in Fig. 3). The arrow indicates the stimulus time, the dashed vertical line the cutoff time between synchronous and asynchonous EPSCs (10.7 ms latency). This was a proximal input in 4Sr-1Ca external solution. Left panels, amplitude histograms for both kinds of EPSC. The sEPSC distribution has a mean of 4.1 ± 5.8 pA (±s.d.) including failures, or 10.3 ± 4.3 pA excluding failures. The data in A are shown on two different vertical scales. The noise histogram is shown in B (thin line; s.d. = 0.83 pA); its vertical scale has been arbitrarily adjusted. Right panels, 20-80 % rise time histograms for the same EPSCs; their mean ±s.d. are 0.68 ± 0.44 ms (synchronous) and 0.63 ± 0.33 ms (asynchronous). Their similarity suggests that the synchronous EPSCs are little distorted by latency jitter in the release of synaptic vesicles. The aEPSC amplitude distribution has a mean of 8.0 ± 3.2 pA and a CV of 0.39 (noise subtracted).

Figure 12. Another example of amplitude histograms for synchronous and asynchronous EPSCs, recorded for a distal input.

Amplitude histograms for sEPSCs and failures (A) and for aEPSCs (B) recorded in the same cell. The noise histogram is shown (thin line, B; s.d. = 0.72 pA); its vertical scale has been arbitrarily adjusted. This was a distal input recorded in 4 Sr-1Ca. The sEPSC distribution has a mean of 2.6 ± 4.1 pA (±s.d.) including failures, or 8.1 ± 3.6 pA excluding failures. The aEPSC amplitude distribution has a mean of 6.7 ± 3.0 pA (±s.d.) and a CV of 0.43 (noise subtracted).

Because the rising phase of EPSCs was noisy, direct measurement of individual rise times was prone to error. For this reason, the function f(t) =a(1 - exp(-t/τ_r))⁵exp(-t/τ_d) was fitted to each EPSC, where a is a constant and τ_r and τ_d are rise and decay time constants. This function, which was used to fit mEPSCs in culture (Bekkers & Stevens, 1996), gave excellent fits to EPSCs (Fig. 1A), as confirmed by visual inspection of the traces. The 20-80 % rise time of each event was calculated from the fitted curve. All histograms of rise times shown in this paper were obtained from such fits. However, because this procedure was time consuming, each estimate of the rise time shown in Fig. 8A was obtained from a single measurement on the averaged aEPSCs obtained in each experiment (e.g. inset to Fig. 8A).

All curve fits were done using the built-in Simplex optimization algorithm implemented in AxoGraph, using the sum of squared errors as the minimization parameter. Statistical comparisons used the Kolmogorov-Smirnov (K-S) test when comparing histogram data, and Student's two tailed t test when comparing means. In most cases errors are given as ±s.d. However, in some instances (e.g. when calculating the rates of occurrence of aEPSCs; Fig. 10) the error was estimated from √n/n, where n is the number of observations (Sigworth & Sine, 1987). For the stimulus-response plots (Figs 1D and 6A) error is given as ±s.e.m. The coefficient of variation (CV) is defined as σ/μ where σ is the standard deviation and μ the mean. Skew is defined as Σ((x_i - μ)/σ)³/N, where the sum is over the N data points x_i. The kth-order gamma function is defined as f(x) =λ^ke^-λxx^k-1/Γ(k), where λ=μ/σ², k =λμ, and Γ(k) = (k - 1)! (McLachlan, 1978).

Figure 10. The rate of aEPSCs is reduced by reductions in transmitter release probability.

Each point was obtained from a single cell in which EPSCs were recorded before and after changing the external solution from 4Sr-1Ca to 2Sr-0.5Ca (○) or from 2Sr-0.5Ca to 1Sr-0.25Ca (□). The mean evoked EPSC amplitude in each solution was measured from the average of 500 consecutive episodes (including failures). The aEPSC rate was measured for the 100 ms window starting at t_c for each cell, and was corrected for the measured rate of spontaneous EPSCs in the cell. Error bars were calculated using either the ensemble s.e.m. (for the EPSC amplitudes), or the rate multiplied by √n/n (for the aEPSC rates), where n is the number of observations (n = 216-520). The diagonal line is the relation expected if aEPSC rate is proportional to transmitter release probability. The experiment shown in Fig. 9 is the second point from the right. One cell, lying on the diagonal near 1, paradoxically showed little effect of the reduction in Sr²⁺ and Ca²⁺ concentrations.

Figure 6. Synchronous and asynchronous EPSCs have the same stimulus threshold.

A, peak amplitude of the mean sEPSC measured at different stimulus settings in the same cell. Each point was obtained by averaging 60 episodes. The error bars represent ± ensemble s.e.m. The horizontal line represents the mean suprathreshold response, 3.6 pA. B, aEPSC rate for a 100 ms window starting at t_c, obtained from the same data set as in A (60 episodes at each stimulus setting). The error bars were obtained by multiplying the average rate by √n/n, where n is the number of events in the window at each stimulus setting (n = 3-72). The horizontal continuous line represents the mean suprathreshold aEPSC rate, 10.8 Hz. The horizontal dashed line is the rate of occurrence of spontaneous EPSCs measured in this cell during a 4 min period without stimulation (0.64 Hz). C, examples of individual episodes recorded at stimulus settings of 4 μA (left) or 6 μA (right). This experiment used 8Sr external solution.

RESULTS

The data set comprised 27 dentate granule neurons with a mean input resistance (R_N) of 702 ± 418 MΩ (±s.d.; range 290-1560 MΩ) at a holding potential of -70 mV. The mean standard deviation of the noise (σ_n), measured at 1 kHz, was 0.67 ± 0.18 pA (±s.d.). These may be compared with the mean values reported in a recent study of the larger CA1 pyramidal neurons that are more typically used for quantal analysis (R_N = 86.7 MΩ, σ_n = 0.8 pA; Stricker et al. 1996).

Recording stability

Three parameters were monitored on-line during each experiment to confirm stability of the recording conditions: peak amplitude of the evoked (synchronous) EPSC, uncompensated series resistance, and input resistance of the cell. Figure 3A shows eight superimposed episodes recorded in an external solution containing a mixture of 4 mM Sr²⁺ and 1 mM Ca²⁺ (4Sr-1Ca solution). Shown below are the corresponding time course scatter plots for this experiment, where each point represents a measurement on a single episode (except in panel D, where averages of 10 consecutive measurements are plotted). The horizontal bars in Fig. 3A indicate periods where the stimulus was turned off. The horizontal line in Fig. 3A represents the mean input resistance for this cell, 760 MΩ. All three parameters were stable over the duration of this experiment (83 min). Each of the 27 granule cells analysed here was similarly stable over the region of analysis.

EPSC latencies in Ca²⁺ and Sr²⁺

When afferents onto a granule cell were stimulated in external solution containing 2 mM Ca²⁺ (2Ca solution), small EPSCs reminiscent of mEPSCs were observed in the cell (Fig. 4A, arrows). These putative miniatures were independent of the stimulus (location indicated by the vertical dashed line, Fig. 4A, left): they occurred at a rate of 0.67 Hz in the interval 10-110 ms after the stimulus and at 0.73 Hz in the interval 750-850 ms after the stimulus (Fig. 5A; same cell as in Fig. 4A). These rates were similar to the rate of spontaneous EPSCs recorded in this cell in the absence of stimulation (0.54 Hz). Note that in other cells it was found that spontaneous EPSCs and true miniature EPSCs (recorded in the presence of 0.5 μM TTX) had identical properties, suggesting that spontaneous EPSCs could be regarded as mEPSCs under our recording conditions (see below). For the cell illustrated in Fig. 4A the mean amplitude (3.7 ± 1.9 pA; ±s.d., n = 63 events) and mean 20-80 % rise time (0.96 ± 0.30 ms) of the EPSCs occurring in the 10-100 ms post-stimulus time window were not significantly different from the corresponding values for spontaneous EPSCs measured in the same cell (amplitude 3.6 ± 2.2 pA, rise time 0.95 ± 0.39 ms; n = 97 events; P = 0.3, K-S test). Similar results were obtained in another cell in which these measurements were made. In summary, the EPSCs occurring >10 ms after a stimulus in 2 mM Ca²⁺ had the properties of miniature EPSCs and presumably arose randomly in synapses located all over the dendritic tree.

The external solution was then changed to one containing 8 mM Sr²⁺ (and no Ca²⁺; 8Sr solution), a concentration that was chosen because it was about as effective as 2 mM Ca²⁺ in supporting neurotransmission, as judged by the mean amplitude of the EPSCs occurring immediately after the stimulus. In the presence of Sr²⁺, a flurry of additional EPSCs appeared at longer latency (Fig. 4A). It is thought that these late EPSCs, which are temporally locked to the stimulus, arise from the same recently activated synapses as produced the early synaptic response (Dodge et al. 1969; Goda & Stevens, 1994; Oliet et al. 1996; Otis et al. 1996). The data presented in this paper confirm this interpretation for excitatory synapses on dentate granule neurons, and strengthen the view that aEPSCs in Sr²⁺, like mEPSCs, are due to the release of single quanta of neurotransmitter.

EPSC latency histograms

The latency from the stimulus to the peak of each EPSC was measured and accumulated into a frequency histogram (Fig. 5). In 2Ca solution, the latency histogram showed a sharp peak within 10 ms of the stimulus, reflecting synchronously evoked EPSCs (Fig. 5A). By 10 ms after the stimulus, the rate of occurrence of EPSCs had declined to near the measured background rate of mEPSCs in the cell (0.54 Hz). In contrast, the latency histograms for solutions containing Sr²⁺ showed an additional, more slowly decaying component of release (Fig. 5A and C). This was quantified by fitting a sum of two exponentials plus a constant offset to the latency histograms measured in Sr²⁺ (Fig. 2, Methods; only the slower exponential component is shown in Fig. 5A and C). The fitted constant offset was similar to the background rate of mEPSCs in the cell; for example, the cell in Fig. 5A had a background rate of 0.28 Hz, compared with a rate of 0.40 Hz obtained from the fit and 0.31 Hz measured over the interval 750-850 ms after the stimulus (Fig. 5A). Similar results were obtained in nine other cells in which this comparison was made.

The slower fitted time constant (τ₂; Methods) had mean values of 97 ± 33 ms (±s.d., n = 6) in 8Sr solution and 81 ± 32 ms (n = 13) in 4Sr-1Ca or 2Ca solutions. These values were not significantly different (P = 0.35, Student's unpaired t test). However, the amplitude of the slow component (a₂) relative to that of the fast component (a₁) was larger in the solution containing the higher Sr²⁺ concentration. The ratio a₂/a₁ had a mean value of 133 ± 57 (× 10⁻³; ±s.d., n = 6) in 8Sr solution and 40 ± 26 (× 10⁻³; n = 13) in 4Sr-1Ca or 2Ca solutions. These values were significantly different (P = 0.0001, unpaired t test). In summary, increasing the concentration of Sr²⁺ increased the frequency of asynchronous EPSCs but did not affect the rate at which their frequency declined following the stimulus.

Identification of asynchronous EPSCs

Asynchronous EPSCs were defined using the result of the fit to the latency histogram of a sum of two exponentials plus a constant offset (Fig. 2; Methods). The time at which the amplitudes of the two exponentials were equal was called the cutoff time, t_c (11.7 ms in Fig. 2A). EPSCs with latencies ≤t_c were classified as synchronous (sEPSCs), while those with latencies > t_c as asynchronous (aEPSCs). This definition gave errors of classification (sEPSCs wrongly classified as aEPSCs and vice versa) estimated at less than 8 % (Methods).

The mean rates of occurrence of spontaneous EPSCs (in the absence of stimulation) and mEPSCs (in TTX), measured in 4Sr-1Ca solution, were 0.69 ± 0.35 Hz (n = 17) and 0.68 ± 0.45 Hz (n = 3; ±s.d.), respectively. This suggests that presynaptic inputs onto granule cells did not spontaneously discharge action potentials under our conditions, because adding TTX made no difference to the spontaneous rate. Thus, spontaneous EPSCs can be regarded as mEPSCs in these experiments.

aEPSCs, which presumably arise from a small subset of recently activated synapses, will be contaminated by ongoing mEPSCs, which presumably arise from all synapses on the cell. The mean rate of occurrence of EPSCs during a 100 ms time window following t_c was 7.7 ± 1.6 Hz (±s.d., n = 4) in 8Sr solution and 5.3 ± 2.5 Hz (n = 15) in 4Sr-1Ca or 2Ca solutions. Thus, the relative amount of contamination by mEPSCs during this 100 ms post-stimulus window was higher in 4Sr-1Ca solution (approximately 0.69/5.3 = 13 % on average) than in 8Sr solution (9 %). In some cases (e.g. Figs 8C and 10) the contamination by spontaneous or miniature EPSCs was estimated and subtracted.

aEPSC amplitude versus latency

If aEPSCs can result from multivesicular release, they should be larger at shorter latencies from the stimulus, where the probability of transmitter release is higher (Barrett & Stevens, 1972; Isaacson & Walmsley, 1995). This is tested in Fig. 5A, which is a scatterplot of the peak amplitude of each EPSC versus its latency (same cell as in Fig. 5A). There was a weak tendency for aEPSC amplitudes to decrease with latency. The straight line in Fig. 5A (left) is an unconstrained fit through all the amplitudes with latencies from t_c (11.0 ms in this cell) to 500 ms, which spans the range of enhanced asynchronous release (Fig. 5A, right). The line has a slope of -1.96 × 10⁻³ pA ms⁻¹. The line in Fig. 5A (right) was fitted over the range 11 ms to 1.5 s and has a slope of -0.41 × 10⁻³ pA ms⁻¹. However, these results do not necessarily indicate that aEPSCs may be multiquantal at shorter latencies. As the latency increases, the population of aEPSCs is increasingly contaminated by spontaneous EPSCs, which have a smaller mean amplitude (see below). Less ambiguous evidence that aEPSCs in Sr²⁺ are uniquantal is given later (Fig. 9).

Figure 9. The mean amplitude of aEPSCs is unaltered by changes in transmitter release probability.

A, each point is the peak amplitude of the synchronous EPSC in each episode, plotted against episode number. The bar marks the interval during which the stimulus was turned off while the bath solution was changed. B, amplitude histograms for the same cell as in A. Left, histograms of EPSCs obtained in 4Sr-1Ca solution. Right, histograms of EPSCs obtained in 2Sr-0.5Ca solution. Also shown in B are the noise histograms, their vertical ranges arbitrarily adjusted (thin lines; s.d. = 0.77 pA). The mean amplitude, excluding failures, of sEPSCs is significantly reduced (from 12.4 ± 6.8 to 9.3 ± 5.0 pA; ±s.d.) but that of aEPSCs is not significantly affected (from 6.8 ± 3.2 to 6.5 ± 3.0 pA) by reducing release probability. This suggests that aEPSCs result from the release of single vesicles of neurotransmitter, their amplitudes being independent of the probability of synchronously evoked release.

A subset of asynchronous EPSCs was collected from episodes containing no synchronous EPSCs. The amplitude distribution and behaviour with latency of these sorted aEPSCs were similar to control, suggesting that the properties of aEPSCs at this synapse were not affected by prior synchronous release of neurotransmitter (such as might occur if desensitization were significant; cf. Otis et al. 1996).

Stimulus threshold of aEPSCs

If aEPSCs are due to delayed release from the synapses which generated sEPSCs, both aEPSCs and sEPSCs should have the same stimulus threshold. This hypothesis is tested in Fig. 6. A stimulus-response plot for the mean sEPSC amplitude shows that the threshold for sEPSCs occurred between 4 and 6 μA in this cell (Fig. 6A). The rate of aEPSCs in the same cell was estimated by counting the number of aEPSCs that occurred in a 100 ms time window starting at t_c. The threshold for the increase in aEPSC rate was the same as that for mean sEPSC amplitude, between 4 and 6 μA (Fig. 6A). At stimulus settings of 4 μA the measured aEPSC rates were close to the mean rate of mEPSCs measured in this cell during a 4 min period without stimulation (0.64 Hz, dashed line, Fig. 6A). At settings of 6 μA the aEPSC rate abruptly increased to a mean value of 10.8 Hz (continuous line, Fig. 6A). Figure 6C shows typical episodes recorded at the subthreshold stimulus setting of 4 μA (left) and the suprathreshold setting of 6 μA (right). Similar results were found in three other cells. These findings suggest that aEPSCs are tightly coupled to activity in the subset of synapses on the cell that are minimally stimulated.

Comparison of asynchronous and miniature EPSCs

If aEPSCs are uniquantal, they should resemble mEPSCs, bearing in mind that they may differ in detail because of differences in cable filtering. Recall that our experiments were designed to preferentially activate a small population of proximal synapses, by using a tissue cut and minimal stimulation (Fig. 1). Figure 7 compares some parameters of aEPSCs and mEPSCs measured in the same cell. The mEPSCs were measured in the presence of 0.5 μM TTX, but identical results were obtained for spontaneous EPSCs (recorded in the same cell in the absence of TTX and without stimulation). Because the rising phase of individual EPSCs was noisy, rise and decay times were measured from the fit to each EPSC of an empirical function (Methods; Fig. 1A). Frequency histograms for peak amplitude (Fig. 7A) and 20-80 % rise time (Fig. 7A) were significantly different for the two kinds of EPSC (P < 0.001, K-S test): the amplitude distribution for aEPSCs had fewer small-amplitude events and the mean (11.6 pA) was larger, and the 20-80 % rise time distribution was narrower and the mean (0.69 ms) was smaller, than those for mEPSCs (means 7.3 pA and 0.87 ms). The skew of the aEPSC amplitude distribution was also smaller than that for mEPSCs in this cell (1.03 cf. 1.53), a result that was also apparent when averaging across many cells (Table 1).

Figure 7. Proximally evoked aEPSCs resemble mEPSCs measured in the same cell, but are less affected by dendritic filtering.

Properties of aEPSCs (left) and mEPSCs (right, in 0.5 μM TTX) recorded in the same neuron. Examples of each kind of EPSC are given in the insets. A, histograms of peak amplitude. The amplitude distribution for aEPSCs is less heavily skewed to small amplitudes than that for mEPSCs, and has a larger mean (11.3 ± 5.0 pA cf. 7.2 ± 3.8 pA; ±s.d.). The noise histogram for the cell is shown (thin line; s.d. = 0.89 pA); its vertical scale has been arbitrarily adjusted. B, histograms of 20-80 % rise time, measured from fits to each EPSC of the exponential product function given in Methods. The rise time distribution is narrower for aEPSCs than mEPSCs, and has a smaller mean (0.69 ± 0.12 ms cf. 0.87 ± 0.19 ms; ±s.d.). C, scatter plots of 20-80 % rise time versus peak amplitude measured from each EPSC. Variability in rise time obscures an expected negative correlation between rise time and amplitude for mEPSCs, if mEPSCs experience a greater range of dendritic filtering because of their more dispersed sites of origin. This experiment used 4Sr-1Ca external solution.

Table 1.

Mean amplitude and amplitude variance of asynchronous and miniature EPSCs

Condition	Amplitude (pA)	Amplitude variance (CV)	Skew
Asynchronous EPSCs, proximal stimulation	6.7 ± 2.2 (23)	0.46 ± 0.08 (23)	1.1 ± 0.2 (23)
Asynchronous EPSCs, distal stimulation	5.8 ± 1.0 (5)	0.34 ± 0.06 (5)	1.1 ± 0.2 (5)
Spontaneous EPSCs	5.4 ± 0.9 (20)	0.45 ± 0.09 (20)	1.6 ± 0.3 (13)

Mean peak amplitude and amplitude variance (given as coefficient of variation, CV = S.D./mean) of EPSCs recorded in one of three different ways: (i) aEPSCs following proximal stimulation in Sr²⁺, or (ii) following distal stimulation in Sr²⁺; and (iii) spontaneous EPSCs without stimulation, with or without TTX. In cases (i) and (ii) the quantities were calculated for all EPSCs occurring in the time window from t_c to 350 ms after the stimulus. Also shown is the skew in the amplitude distributions, defined in Methods. There was no difference in the aEPSCs recorded in 8 Sr, 4 Sr-1 Ca, or 2 Sr-0.5 Ca, so the data have been combined. All entries are given as mean ± S.D. (number of experiments). CVs were corrected by subtracting the noise variance measured in each cell.

These results are expected if aEPSCs originate in proximal synapses but mEPSCs arise in synapses all over the cell and experience a greater range of dendritic filtering. If this is the case, smaller mEPSCs of more distal origin should have slower rise times. However, a plot of 20-80 % rise time versus peak amplitude for individual mEPSCs showed too much scatter for any trend to be apparent (Fig. 7A, right). The same finding has been reported for mEPSCs in CA1 pyramidal cells in both culture and slice preparations (Bekkers & Stevens, 1996; Ghamari-Langroudi & Glavinovi´c, 1998). A plot of decay time constant versus peak amplitude also showed no correlation (not shown). Similar results were obtained for two other cells. The mean 20-80 % rise time and the mean decay time constant of aEPSCs in these three cells were 0.67 ± 0.03 ms and 6.3 ± 0.9 ms, respectively (mean ±s.d.). The corresponding quantities for mEPSCs in the cells were 0.80 ± 0.10 ms and 7.0 ± 0.2 ms.

Proximal and distal aEPSCs

The data in Fig. 7 strengthen the view that aEPSCs arise from the same, recently activated synapses as those responsible for the synchronous EPSCs, because stimulation of proximal synapses produced aEPSCs with faster kinetics than mEPSCs, consistent with a proximal origin of aEPSCs. The next series of experiments tested this idea more rigorously by directly comparing proximal and distal synaptic inputs. The design of the experiment is illustrated in Fig. 8Aa. In addition to the cut made to isolate proximal afferents onto the granule cells (Fig. 1A), a second cut was made across the slice, leaving a short (∼50 μm) tissue bridge between the end of the cut and the hippocampal fissure. The stimulating electrode was placed close to the fissure. A stimulus plateau was found in the usual way, and aEPSCs were collected after the delivery of stimuli to this distal input.

Averages of aEPSCs, recorded in the same cell with distal or proximal stimulation, are shown in Fig. 8Ab. The current following distal stimulation (○) has a slower rise time. This is expected if the aEPSCs arise in the stimulated distal synapses, because they would then experience greater dendritic filtering than aEPSCs arising in proximal inputs. It is surprising that the mean amplitude of distally arising aEPSCs was only slightly less than that of proximal aEPSCs (4.5 pA cf. 5.3 pA; Fig. 8Ab) despite the marked slowing of the averaged distal aEPSCs. This is probably due to signal-to-noise limitations: a larger fraction of smaller aEPSCs of distal origin will be missed by the detection algorithm, leading to an overestimate of the distal mean amplitude (Clements & Bekkers, 1997). On the other hand, aEPSCs of all sizes will experience similar filtering of their rise times, and so this quantity will be estimated more accurately. For this reason our analysis concentrated on comparisons of the 20-80 % rise time distributions.

The results from 18 such experiments are summarized in Fig. 8B. Each point represents the 20-80 % rise time of averaged aEPSCs measured in a single cell following either distal (○) or proximal (•) stimulation. In only two cases (points joined by the vertical dashed lines) was it possible to obtain sufficient data for both distal and proximal inputs onto the same neuron. All other points were obtained from different cells. To test for the possible effect of differing access resistance when comparing between cells, each point was plotted against the measured value of R_s in that cell. R_s appeared to have no systematic effect. The mean 20-80 % rise time for distal aEPSCs was 1.04 ± 0.26 ms (±s.d., n = 5 cells), while that for proximal currents was 0.52 ± 0.10 ms (n = 15 cells; cf. Keller et al. 1991). These means and s.d.s are indicated by the horizontal dashed lines and error bars in Fig. 8B. These values were significantly different (P < 0.001; unpaired t test).

The points in Fig. 8A were obtained from measurements on the average of captured aEPSCs. In the one cell for which sufficient data were obtained for both distal and proximal stimulation (joined points near R_s = 30 MΩ), the rise times of individual EPSCs were measured from the fit of a smooth function to each current (see Methods). Frequency histograms of the 20-80 % rise times of proximal aEPSCs, distal aEPSCs and spontaneous EPSCs, all obtained from the same cell, are shown in Fig. 8C. Contamination of the aEPSC distributions by mEPSCs was corrected by subtracting the spontaneous EPSC rise time histogram, after scaling to allow for the differing rates of the events. The effect of histogram sampling error on the subtraction procedure accounts for the negative-going bins in the tail of the proximal aEPSC histogram (Fig. 8A, left). Pair-wise comparison of the histograms showed that all were significantly different (P < 0.001; K-S test). The histogram for spontaneous EPSCs spans the range from the fastest proximal aEPSC to the slowest distal aEPSC. This supports the view that mEPSCs are a mixture of distal and proximal events.

In three additional cells, sufficient data were obtained to allow comparison between mEPSCs and distal aEPSCs in the same neuron. The results were similar to those in Fig. 8C. In each case the 20-80 % rise time distributions were significantly different (P < 0.003; K-S test), with the mEPSC distribution being broader and more skewed (not illustrated).

Effect of altering the probability of transmitter release

As a further test of the uniquantal nature of aEPSCs, the synchronous synaptic release probability (P_r) was varied by altering the concentrations of external divalent ions. In the experiment shown in Fig. 9, halving the concentrations of Sr²⁺ and Ca²⁺ (and increasing the concentration of Mg²⁺ to keep the total concentration of divalent ions constant) increased the number of failures and reduced synchronous synaptic transmission. The mean evoked EPSC amplitude in 4Sr-1Ca solution (including failures) was 8.9 pA, compared with 3.1 pA in 2Sr-0.5Ca solution, giving an average reduction in P_r of 65 % (Fig. 9A). The mean amplitude of synchronous EPSCs, excluding failures, (the ‘potency’; Stevens & Wang, 1994) was reduced from 12.4 to 9.3 pA when changing from 4Sr-1Ca to 2Sr-0.5Ca (Fig. 9A, upper panels). However, the aEPSCs remained unchanged (Fig. 9A, lower panels). Their mean amplitudes were 6.8 pA before and 6.5 pA after reducing release probability, and their amplitude distributions were not significantly different (P = 0.52, K-S test). This supports the idea that each aEPSC results from the release of a single synaptic vesicle, independent of differences in P_r.

Although the amplitude of aEPSCs did not vary with changes in P_r, their release rate may be expected to change, given that they are due to delayed release from recently active synapses (Fig. 6). Support for this view has already been seen above: the average rate of aEPSCs following stimulation in 8Sr solution was higher than that in 4Sr-1Ca solution, presumably reflecting the higher P_r for asynchronous events in 8Sr solution (Fig. 5). A more rigorous test of this idea is presented in Fig. 10. Each point was obtained from a single cell when changing from 4Sr-1Ca to 2Sr-0.5Ca solution (○) or from 2Sr-0.5Ca to 1Sr-0.25Ca solution (□). The abscissa plots the ratio of mean evoked EPSC amplitudes (i.e. the ratio of P_r values for synchronous events; Stevens & Wang, 1994) and the ordinate the ratio of aEPSC rates in the first 100 ms before and after changing solutions. The rates were corrected for the measured spontaneous EPSC rate in each cell. The diagonal line is the relationship expected if the aEPSC rate strictly reflects P_r. Although the expected trend is apparent, all but one of the points lie above the diagonal, suggesting that distinct processes may underlie evoked synchronous release and asynchronous release in Sr²⁺.

Synchronous and asynchronous EPSC histograms

By recording in Sr²⁺, we can now compare amplitude histograms for both evoked and miniature EPSCs arising in the same population of synapses on a hippocampal granule cell (Fig. 11). Proximal inputs were stimulated in this experiment, and the external solution contained 4Sr-1Ca. Amplitude histograms are shown on the left (with two different vertical scales for synchronous EPSCs) and 20-80 % rise time histograms on the right. The similarity of the rise time distributions for sEPSCs and aEPSCs (Fig. 11 legend) confirms that the amplitude measurements of the former are not distorted by jitter in the release of synaptic vesicles, which would be expected to prolong the average rise times of the EPSCs.

Although there is a clear dip between the failure and ‘successes’ peaks of the sEPSC amplitude distribution (Fig. 11A, left), there is no sign of quantization of sEPSC amplitudes. Conditions for observing such quantization seemed optimal for this cell, because of its long-term stability (Fig. 3) and the large number of entries in the histogram (n = 2296; Fig. 11A). The absence of quantal peaks would be explicable in view of the large variance of aEPSCs arising from the same population of synapses (coefficient of variation, CV = 0.39; Fig. 11A). If such variance were intrinsic to each release site, quantal peaks would merge together in the evoked EPSC amplitude histogram and the quantal structure would be obscured. Similar results were obtained in 22 other experiments under similar conditions. Another example, for a distal input, is illustrated in Fig. 12. A third example is shown in Bekkers (1998) (Fig. 46). In all cases clear quantization of synchronous EPSCs was not observed, and the variance of asynchronous EPSCs was large (Table 1; e.g. for proximal EPSCs, CV = 0.46 ± 0.08, mean ±s.d., baseline noise variance subtracted).

This result was not due to the use of EPSC peak amplitude as a measure of synaptic efficacy. When EPSCs were integrated to give charge (Jack et al. 1981), quantal peaks were still not seen. The variance of the charge carried by aEPSCs was also large (e.g. for proximal EPSCs, CV = 0.49 ± 0.09, n = 17).

DISCUSSION

In this paper we have confirmed for excitatory synapses in the dentate gyrus a classical finding for the endplate, that asynchronous events recorded following synaptic stimulation in Sr²⁺ are produced by delayed release of unitary quanta from the stimulated synapses. In recent years the same basic observation has been reported for a number of other brain slice synapses, including Schaffer collateral inputs onto CA1 pyramidal cells in the rat or guinea-pig hippocampus (Oliet et al. 1996), auditory nerve inputs onto neurons of the chick cochlear nucleus (Otis et al. 1996), cortical projections onto rat striatal neurons (Choi & Lovinger, 1997), and climbing fibre inputs onto Purkinje cells in the rat cerebellum (Silver et al. 1998). Our work confirms and extends these earlier results. We have shown that (i) Sr²⁺ produces an exponentially decaying enhancement of asynchronous release and the initial release rate depends upon the Sr²⁺ concentration (Fig. 5A-C); (ii) synchronous and asynchronous EPSCs have the same stimulus threshold (Fig. 6); (iii) aEPSC amplitude shows little dependence on both the latency from the stimulus (Fig. 5A) and the probability of evoked release (Fig. 9), suggesting that aEPSCs are uniquantal; (iv) the amplitude and rise time distributions of proximally evoked aEPSCs resemble those of mEPSCs recorded in the same cell, but differ from them in ways expected from differences in dendritic filtering (Fig. 7); (v) aEPSCs of distal and proximal origin show kinetic differences explicable by dendritic filtering (Fig. 8); and (vi) the rate of occurrence of aEPSCs is correlated with the probability of synchronous evoked release (Fig. 10). These results together suggest that Sr²⁺-evoked aEPSCs are uniquantal events arising locally at synaptic terminals that were recently invaded by an action potential.

Our experiments were also designed to look for quantal ‘peaks’ in amplitude histograms for synchronously evoked EPSCs, in order to test the prediction of the classical quantal model that the spacing of such peaks is predictable from the amplitude histogram for mEPSCs arising in the same synapses (i.e. aEPSCs). Despite our efforts to minimize the number of active synapses by using tissue cuts and minimal stimulation (Fig. 1), in no case were clear peaks apparent in the histograms for sEPSCs (Figs 11 and 12). One interpretation of this result is that quantal structure is obscured by large intrasite quantal variance. This is consistent with the finding that aEPSC amplitudes exhibited a large amplitude variability (CV ≡ 0.3-0.5; Table 1). Other interpretations will be discussed below.

Sr²⁺-induced asynchronous release of transmitter vesicles as a model for synchronous release

Is it plausible that asynchronous EPSCs collected in the presence of a non-physiological cation, Sr²⁺, accurately reflect normal synchronous release of transmitter vesicles? The connection between aEPSCs and synchronous release may be weakened if, for example, aEPSCs in Sr²⁺ are due to release from a separate pool of vesicles, or if they arise from partial emptying of vesicles that are normally fully discharged when generating synchronous EPSCs.

Several pieces of evidence suggest that Sr²⁺ does not disrupt or misrepresent normal quantal release. At the neuromuscular junction Sr²⁺, like Ca²⁺, supports quantal transmission that can be described by the Poisson model (Miledi, 1966; Dodge et al. 1969). Replacing Ca²⁺ by Sr²⁺ at the squid giant synapse also has no significant effect on the mean amplitude of miniature EPSPs (Augustine & Eckert, 1984). A similar result was obtained here for dentate granule cells: spontaneous mEPSCs have a mean amplitude of 5.4 ± 0.9 pA in 1-8 mM Sr²⁺ (n = 20; Table 1), close to the value of 4.5 ± 1.3 pA obtained in 2 mM Ca²⁺ without Sr²⁺ (n = 8). Further, we have shown that Sr²⁺-evoked aEPSCs are similar to spontaneous mEPSCs in Sr²⁺, apart from the effects of cable filtering (Fig. 7). Asynchronous EPSCs in Sr²⁺ are perhaps even more likely to reflect normal action potential-evoked exocytosis than are mEPSCs, because aEPSCs are temporally locked to the stimulus and have the same stimulus threshold as sEPSCs (Fig. 6). Taken together, these results support the view that both synchronous and asynchronous EPSCs in Sr²⁺ arise from the same vesicle release mechanism, as do miniature and evoked EPSCs in Ca²⁺.

As a further test of the similarities between synchronous and asynchronous release, we compared the change in aEPSC rate with the change in probability of synchronous release when halving the external concentrations of Ca²⁺ and Sr²⁺ (Fig. 10). If sEPSCs and aEPSCs are generated by similar mechanisms, these two measures of release are expected to vary together (diagonal line in Fig. 10). Although there is a strong suggestion of such a correlation, four out of five data points lie significantly above the diagonal. This suggests at least a partial disengagement of synchronous and asynchronous release in Sr²⁺.

The desynchronizing effect of Sr²⁺ is commonly thought to result from increased levels of residual Sr²⁺ in the presynaptic terminal, presumably because Sr²⁺ is less rapidly extruded or sequestered than Ca²⁺ (Abdul-Ghani et al. 1996). According to this hypothesis, the actual mechanism of vesicular release is no different between Sr²⁺ and Ca²⁺. An alternative hypothesis is that asynchronous release requires a distinct mechanism, perhaps involving a different subtype of the putative Ca²⁺ sensor synaptotagmin (Goda & Stevens, 1994). According to this model, Sr²⁺ activates the asynchronous release mechanism more effectively than does Ca²⁺. This would weaken the link between synchronous and asynchronous release, as is also suggested by the data in Fig. 10. However, the similarity of amplitude distributions for mEPSCs in Sr²⁺ and Ca²⁺ suggests that, even if Sr²⁺ produces release by a slightly different mechanism, it does not alter the distribution or amount of neurotransmitter that is released.

Differences between aEPSC and mEPSC distributions

We have shown that the peak amplitude and 20-80 % rise time distributions for proximally evoked aEPSCs and mEPSCs recorded in the same cell are significantly different (Fig. 7). The amplitude distribution for aEPSCs has a smaller skew, and so is more nearly Gaussian, than that for mEPSCs (Table 1). The 20-80 % rise time distribution, obtained from fits of an empirical function to individual EPSCs in order to minimize measurement errors, is narrower for aEPSCs (Fig. 7A). Both of these findings are compatible with the hypothesis that mEPSCs, which arise randomly from synapses all over the cell, experience a greater range of dendritic filtering than the aEPSCs, which arise in proximal synapses. This interpretation is supported by the differences between rise time distributions for spontaneous EPSCs and aEPSCs of distal and proximal origin, all recorded in the same cell (Fig. 8A). Rise times for the spontaneous events span the range from the fastest proximal aEPSCs to the slowest distal aEPSCs. This suggests that spontaneous EPSCs (putative mEPSCs) are a combination of distal and proximal uniquantal events.

If the kinetics of mEPSCs are determined by dendritic filtering, it is expected that the rise time of individual events will vary inversely with their amplitude (Bekkers & Stevens, 1996). Such a correlation was not observed (Fig. 7A, right). Lack of correlation has been reported in many other studies (e.g. Mennerick et al. 1995; Bekkers & Stevens, 1996; Ghamari-Langroudi & Glavinovi´c, 1998). The general conclusion from the above work is that, whilst averaged mEPSCs arising at different electrotonic distances exhibit the expected correlation (e.g. Bekkers & Stevens, 1996), individual events are too variable for such a trend to be readily apparent. The small size of most mEPSCs (mode = 4.5 pA, cf. noise s.d. = 0.89 pA; Fig. 7A, right) may also have compromised our ability to resolve such a correlation.

Previous applications of Sr²⁺ to central synapses have reported that aEPSC and mEPSC amplitude distributions are identical, both for Schaffer collateral-CA1 pyramidal cell inputs (Oliet et al. 1996) and cortical inputs to the striatum (Choi & Lovinger, 1997). However, neither of these studies used minimal stimulation. By using metal bipolar stimulating electrodes to evoke large EPSCs (tens of picoamps), it is likely that aEPSCs were elicited from synapses all over the dendritic tree, like mEPSCs. Estimates of amplitude variability obtained from these aEPSCs would therefore have been distorted by dendritic filtering. In contrast, our experiments were designed to selectively activate a small number of proximal synapses, in an effort to estimate intrinsic quantal variance uncontaminated by artefacts due to differential cable filtering.

Intersite and intrasite quantal variance

We have found that amplitude distributions of aEPSCs following minimal stimulation have a large variability (CV = 0.46 for proximal inputs; Table 1). To what extent can this variability be taken to reflect quantal variance (qv) at these synapses? Quantal variance might arise in one of two ways.

(1) Intersite variance

Each synaptic contact generates a narrow, but different, amplitude distribution. Large apparent qv arises when a population of active contacts is sampled. That is, the variance intrinsic to each release site (the true qv) is small, and the mEPSC or aEPSC distribution yields an overestimate of the true qv. The response at each contact may be determined by the number of postsynaptic receptors (Frerking & Wilson, 1996B).

(2) Intrasite variance

Each functionally distinct synaptic contact is able to generate the full range of quantal amplitudes. In this case the mEPSC or aEPSC distribution provides an accurate estimate of the true qv at each release site. This variance may be due to variable amounts of neurotransmitter release, channel gating fluctuations, or rapid changes in the availability of postsynaptic receptors (Bekkers et al. 1990).

There is evidence that either of these models could apply to central synapses. The intersite model is supported by reports that clear quantal peaks can often be observed in evoked EPSC amplitude histograms, indicating that the intrasite variance is low (CV = 0-0.2; Larkman et al. 1991, 1997; Liao et al. 1992; Kullmann & Nicoll, 1992; Stricker et al. 1996; Jonas et al. 1993; Paulsen & Heggelund, 1994). The intrasite model is supported by theoretical arguments about the variance due to channel gating and fluctuations in the transmitter content of vesicles (Frerking & Wilson, 1996a). It is also supported by experiments on synaptic connections with a single release site, which suggest that intrasite qv is in the range 0.2-0.6 (Gulyás et al. 1993; Silver et al. 1996; Forti et al. 1997; Kondo & Marty, 1998).

We obtained two results with important implications for the debate over the origin of quantal variance. The first was the observation of large amplitude variability of aEPSCs (Table 1). This implies either a high level of intrasite variability, or a high level of intersite variability, or both. We argue below that intrasite variability is the most probable source. The second important observation was an absence of quantal peaks in any of the evoked amplitude histograms. This finding was unexpected because we took great care to optimize the recording conditions and maximize the sample size. The number of evoked events was typically >1000, a larger sample size than obtained in many published quantal analysis studies. The standard deviation of the recording noise was < 1 pA, so quantal peaks separated by 2 pA or more should have been clearly visible. Simulations confirmed that quantal peaks in evoked amplitude histograms would have been detected easily under these conditions. The absence of peaks provides independent confirmation that intersite variability, or intrasite variability, or both, are high for synapses onto dentate granule cells. Thus, quantal analysis of evoked amplitude histograms from this preparation must incorporate a high level of variability (Frerking & Wilson, 1996a).

Intrasite variability provides a plausible explanation of the aEPSC amplitude distribution

In principle, the experimental approach we have adopted cannot distinguish unambiguously between an intersite or an intrasite source for the amplitude variability of aEPSCs. This is because of an unavoidable lack of information about the number of release sites activated by the presynaptic stimulus. Our synaptic connections must have involved more than one functional site, because lowering release probability by lowering the Ca²⁺ and Sr²⁺ concentrations reduced the mean amplitude of synchronous EPSCs, excluding failures (the ‘potency’; Fig. 9A). If there were a single release site the potency would not have changed (Stevens & Wang, 1995; Silver et al. 1996). When many terminals are active, an intersite model and an intrasite model of aEPSC variability make similar predictions about the shape of the aEPSC amplitude distribution (Frerking & Wilson, 1996a). However, these two models diverge when the number of active terminals is low.

We have constructed two models of synaptic function that attribute all of the variability to either an intrasite or an intersite source. The comparison is based on the assumption that the number of active terminals, N, is 50. This is most likely an overestimate of the number of synaptic terminals between a single proximal afferent and a dentate granule cell. It requires a higher level of connectivity than observed in other hippocampal pathways (Amaral et al. 1990) and it requires that the average release probability at a terminal is < 0.02, lower than observed for other synapses (Rosenmund et al. 1993). The predictions of the two models would diverge more sharply if the true value of N was actually smaller, so the selection of N = 50 represents a severe test of our ability to distinguish between these models.

We further suppose that the population aEPSC amplitude distribution can be described using a gamma function (McLachlan, 1978). This was checked for proximal synaptic inputs. Each aEPSC amplitude distribution was optimally fitted with a gamma function, and the χ² statistic was calculated. The gamma function provided an adequate fit in more than half the cases (P > 0.05 for 6/11 cells). Interestingly, the gamma function systematically overestimated the number of aEPSCs smaller than about 3 pA in all cells. This may reflect the fact that the event detection algorithm used to identify aEPSCs systematically underestimates the number of events smaller than 4 times the noise s.d., typically about 3 pA in this system (Clements & Bekkers, 1997). When the fit was restricted to the amplitude range > 4 times the noise s.d., the gamma function provided an adequate fit (P > 0.05) in 10/11 cells. With this restriction, the fitted mean amplitude was 6.8 ± 1.7 pA (±s.d.) and the mean amplitude CV was 0.47 ± 0.07 (±s.d.), similar to the values obtained without restriction from the raw data (Table 1). In summary, a gamma function provided an adequate description of the shapes of the observed aEPSC amplitude distributions.

We used Monte Carlo methods to test whether simulated aEPSC amplitude distributions generated by the intrasite and intersite models could be described by a gamma function. The intrasite model of aEPSC variability requires that the amplitude distribution for synaptic events arising from each terminal follows the same gamma function as the population aEPSC amplitude distribution. Thus, a gamma function should provide an adequate fit to the aEPSC amplitude distribution in almost every case. In contrast, the purely intersite variability model of aEPSC variability requires that the amplitude distribution for synaptic events arising from each of the 50 terminals is a delta function with an amplitude that is sampled from the population aEPSC amplitude distribution. This distribution will differ from cell to cell due to finite sampling. Thus, a gamma function may not provide an adequate fit to the aEPSC amplitude distribution in every case.

We used the intersite model to generate a simulated aEPSC amplitude distribution, as follows. First, the measured noise (s.d. = 0.8 pA) was deconvolved from the aEPSC amplitude distribution recorded from a typical cell (that shown in Fig. 11). A gamma function was fitted to this distribution (mean amplitude 8 pA, amplitude CV 0.4) and 50 amplitudes were drawn randomly from the gamma distribution. Delta functions corresponding to the 50 amplitudes were convolved with a Gaussian representing the measured noise. Next, 1000 random samples were drawn from this distribution, and formed into an amplitude histogram. (Experimental aEPSC amplitude histograms contained 389-1675 entries.) Finally, the sampled distribution was optimally fitted with a gamma function, and the χ² statistic was calculated for the fit. This procedure was repeated 10 times, simulating recordings from 10 separate cells. The gamma function failed to fit the simulated aEPSC distribution in every case (P < 0.001). Results from the first three simulations are shown in Fig. 13A, and reveal clear peaks and inflections due to finite sampling. Such features were not seen in experimental aEPSC amplitude histograms. The entire simulation and fitting procedure was repeated 10 more times, but with the intrasite CV increased from zero to 0.1. It was still possible to reject the gamma function fit in 8/10 cases.

Figure 13.

An intrasite model of aEPSC amplitude variability provides a better description of the observed aEPSC amplitude distributions than an intersite model

A, the intersite model of aEPSC variability was used to simulate aEPSC amplitude distributions. Three typical examples are shown. Continuous lines show the theoretical distribution which represents 50 randomly selected synaptic terminals. The amplitude histograms were sampled from the theoretical distributions. Clear peaks and inflections are evident in both the theoretical and sampled distributions due to finite sampling. None of the sampled distributions could be fitted by a gamma function. (The peaks and inflections were even more obvious when the number of terminals was reduced to 10, perhaps a more plausible number; not illustrated.) In contrast, most of the experimental aEPSC amplitude distributions could be well fitted by a gamma function. B, simulated aEPSC amplitude histograms were also generated using the intrasite variability model. The theoretical distribution is shown as a continuous line, and was the same for every simulation. Amplitude histograms were sampled from this distribution; a typical result is shown. The sampled distribution is relatively free of peaks and inflections. As expected, all of the sampled distributions could be fitted by a gamma function.

When N was reduced to 10 terminals (perhaps a more plausible number) the peaks and inflections in the simulated distributions were even more pronounced than those shown in Fig. 13 (results not illustrated). To ensure that the simulations were working correctly, N was increased to 2000, an unrealistically large number. As expected, peaks and inflections were no longer apparent and all distributions were well fitted by a gamma function (results not shown).

Simulated aEPSC amplitude histograms were also generated using the intrasite variability model. One thousand random samples were drawn from a gamma function with a mean amplitude of 8 pA and a CV of 0.4, that was convolved with a Gaussian (s.d. = 0.8 pA). As expected, the simulated amplitude histograms were well fitted by a gamma function in every case (P > 0.05,n = 10) and a typical result is shown in Fig. 13B.

In summary, our data are consistent with an intrasite model of aEPSC amplitude variability, and we can confidently reject the hypothesis that this variability is due to a primarily intersite source when N≤ 50.

Mean quantal amplitude and the detection of quantal peaks

If most of the quantal variance is intrasite, the mean amplitude of aEPSCs provides an estimate of the mean quantal amplitude (q). Estimates of q given in Table 1 are likely to be underestimates, since fast aEPSCs would be attenuated by both dendritic filtering and electrode series resistance (Jonas et al. 1993; Stricker et al. 1996). (Quantal variance will be much less affected by these errors, being a measure of the variability of q.)Nevertheless, it is useful to compare our value of q with estimates reported elsewhere. A mean q of 6.7 pA (proximal inputs; Table 1) corresponds to a quantal conductance of about 95 pS. By fitting mixtures of Gaussians to evoked EPSC data, estimates of quantal conductance for the Schaffer collateral-CA1 synapse range from 40 to 70 pS (Kullmann & Nicoll, 1992; Liao et al. 1992; Stricker et al. 1996). Our estimate of q is systematically larger than these estimates, which may be due to lower access resistance, activation of more proximal synapses, inherent differences between the two classes of synapses, or invalid assumptions about the identification of q.

It is surprising that, despite our larger q and lower noise (mean s.d. = 0.67 pA, cf. 0.8-2.1 pA for the CA1 studies mentioned above), peaks were often evident in the CA1 experiments but were never apparent in our evoked EPSC amplitude histograms for dentate granule cells. All of these studies used minimal extracellular stimulation in hippocampal slices from young animals and were done at or near room temperature (≤ 30°C). One possible explanation for the discrepancy is that the presence of Sr²⁺ in the bathing solution somehow increases the quantal variance. However, this does not occur at the endplate (Miledi, 1966; Dodge et al. 1969). Another possibility is that excitatory synapses on dentate granule cells have a systematically larger intrasite quantal variance than synapses on CA1 pyramidal cells. This could be tested by using Sr²⁺ and minimal stimulation at CA1 synapses (cf. strong stimulation used by Oliet et al. 1996). If peaks are still apparent, and truly reflect quantal transmission, their shape and spacing should be predictable from the amplitude distribution for aEPSCs arising from the same synapses.

In conclusion, we have shown that Sr²⁺-evoked aEPSCs provide insight into the quantal properties of a certain class of synaptic contact in intact brain tissue. The large variance revealed by this approach confirms some reports but is at odds with others. Future work would need to establish whether this discrepancy arises from methodological differences, or simply reflects the great variety of operation of different classes of synapses in the brain.