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J Neurosci. Author manuscript; available in PMC 2010 July 27.
Published in final edited form as:
PMCID: PMC2825095

Quantal analysis reveals a functional correlation between pre- and postsynaptic efficacy in excitatory connections from rat neocortex


At many central synapses, the presynaptic bouton and post-synaptic density are structurally correlated. However, it is unknown whether this correlation extends to the functional properties of the synapse. To investigate this, we made recordings from synaptically coupled pairs of pyramidal neurons in rat visual cortex. The mean peak amplitude of EPSPs recorded from pairs of L2/3 neurons ranged between 40μV to 2.9mV. 10-90% rise times were consistent with the majority of the synapses being located on basal dendrites; this was confirmed by full anatomical reconstructions of a subset of connected pairs. Almost half of the connections could be described using a quantal model which assumed simple binomial statistics. Release probability (Pr) and quantal size (Q), as measured at the somatic recording site, showed considerable heterogeneity between connections. However, across the population of connections, values of Pr and Q for individual connections were strongly positively correlated with one another. This correlation also held for inputs to layer 5 pyramidal neurons, both from layer 2/3 and neighbouring layer 5 pyramidal neurons, suggesting that during development of cortical connections pre and post synaptic strengths are dependently scaled. For both 2/3 to 2/3 connections and inputs to layer 5, mean EPSP amplitude was correlated with both Q and Pr values but uncorrelated with N, the number of functional release sites mediating the connection. The efficacy of a cortical connection is thus set by co-ordinated pre- and post-synaptic strength.

Keywords: EPSP, Patch Clamp, Postsynaptic, Presynaptic, Pyramidal Cell, Quantal, Release Probability, Synaptic Transmission, Quantal Content, Development


The overall strength of synaptic connections between neurons is determined by multiple factors, some being structural (Walmsley et al., 1998; Rollenhagen and Lubke, 2006). Both the size and the number of boutons (presynaptic elements) mediating a synaptic connection between neurons in the CNS can vary considerably (Walmsley et al., 1998; Rollenhagen and Lubke, 2006). It is now widely accepted that quantal release of transmitter normally occurs at presynaptic active zones (Katz, 1969). In the hippocampus and neocortex, most excitatory synaptic boutons are fairly small and usually have only a single active zone (Peters et al., 1990; Schikorski and Stevens, 1997, 1999). Nevertheless, in boutons with a single active zone, presynaptic strength or release probability (Pr) may be correlated with the area of active zones which can vary considerably (Atwood and Marin, 1983; Schikorski and Stevens, 1997; Murthy et al., 2001).

Another factor which would be expected to influence synaptic efficacy is the postsynaptic location of the synapse on the dendritic tree. Cable theory predicts that more distal synapses should be less efficacious at the soma due to cable attenuation (Rall, 1960; Jack et al., 1981; Jack et al., 1994; Stuart and Spruston, 1998). However it is possible that in some neurons there are compensatory mechanisms to boost the signal of more distal synapses (Andrasfalvy and Magee, 2001; Nicholson et al., 2006). Indeed, studies have shown that, in some neuronal classes, the size of the postsynaptic density (PSD) is larger at increasing distances from the soma (Triller et al., 1990; Alvarez et al., 1997).

There is evidence that the PSD is normally co-extensive with the presynaptic active zone. Quantitative studies have shown strong correlations between co-extensive PSD and active zone areas (Schikorski and Stevens, 1997, 1999) and also between the number of AMPA receptors and the area of the PSD (Nusser et al., 1998; Takumi et al., 1999; Tanaka et al., 2005). At mature synapses, under conditions of postsynaptic saturation (Wall and Usowicz, 1998), the size of the quantal current at the synapse is therefore expected to be related to the area of the PSD, and hence to the area of the active zone (Lim et al., 1999). This leads to the prediction that release probability (pre-synaptic efficacy) is correlated with the synaptic current (post-synaptic efficacy).

The purpose of this study was to explore this prediction in cortex, using paired electrophysiological recordings of synaptically connected pyramidal neurons and subsequent quantal analysis of the recordings (Hardingham et al., 2006; Hardingham et al., 2007). The majority of synaptic contacts in these connections have been shown to be located relatively proximal to the soma on basal or apical oblique dendrites (Koester and Johnston, 2005; Feldmeyer et al., 2006). EPSP amplitudes recorded at the soma of cortical pyramidal neurons have been shown to be relatively insensitive to the location of synapse on the basal dendritic tree (Nevian et al., 2007). The major finding of this study is a strong correlation between release probability and quantal size at excitatory connections in developing rat visual cortex.


Slice preparation and intracellular recording

Recordings were made from brain slices taken from 19-27 day-old Sprague–Dawley rats. Details of slice preparation and intracellular recording are given in (Hardingham et al., 2006). Recordings were made between pairs of layer 2/3 (L2/3) pyramidal neurons, between pairs of layer 5 (L5) to L5 pyramidal neurons and pairs of pyramidal neurons, one in L2/3 and one in L5. A synaptically connected pair of cells was found in 1 in 7 pairs tested for L2/3 neurons and L5-L5 neurons and 1 in 10 pairs of neurons for L2/3 to L5 connections. When testing L2/3 to L5, neurons were selected in the same vertical column of cortex. In some experiments 0.5% biocytin was included in the recording pipette for morphological anatomical reconstructions following recording. Series resistance was estimated by bridge balance and ranged between 20 and 40 MΩ. Both series resistances and pipette capacitances were checked and compensated for during recordings and experiments discontinued if the series resistance changed by over 20% during a recording. The mean resting membrane potentials were −69 ± 6mV (mean ± SD) for L2/3 neurons (n=287) and −67 ± 4mV for L5 neurons (n=62). Post synaptic responses were recorded in the current clamp configuration as EPSPs are less sensitive to changes in the electrode series resistance in this configuration, and suffer less differential attenuation of peak amplitude with electrotonic distance when compared with voltage clamp recording (Major, 1993). Once a synaptic connection had been identified, single action potentials were induced in the pre-synaptic cell at 0.1 Hz by injection of short (5-10 ms) pulses of depolarizing current. Post-synaptic responses were amplified using an AxoProbe 1A amplifier (Axon Instruments), low-pass filtered at 2 KHz, digitized at 5 KHz using a CED (Cambridge Electronic Design) 1401 A/D board and recorded on a PC for analysis off-line. Post-synaptic neurons were held at membrane potentials more negative than −60 mV to ensure that EPSPs were dominated by AMPA receptor mediated currents (holding current was rarely necessary). Recordings were made either at lab temperature (23 to 26°C) or body temperature (36°C). Miniature EPSPs (mEPSPs) were recorded in the presence of tetrodotoxin (TTX, 1μM) and picrotoxin (PTX, 100μM) which were added to the ACSF. mEPSP amplitudes were measured as described in (Hardingham and Larkman, 1998).

Analysis of EPSP data

Only recordings that remained stable (see (Hardingham et al., 2006) for stability criteria) for at least 100 consecutive trials of recording were included in the data set. In all cases we selected the earliest possible stable period of data to avoid analysing data where washout may have caused depression of quantal size or release probability (Larkman et al., 1997). In these stability criteria, both mean EPSP amplitude and SD were required to remain within 15% of their initial values as previous studies have shown significant drifts in quantal size over time with synaptic stimulation, which were sometimes associated with inverse changes in release probability, with no net effect on the mean amplitude but an unstable SD (unpublished observations and (Larkman et al., 1997)). The number of consecutive stable trials per connection ranged from 100 to 1200. For each connection we calculated the mean EPSP amplitude and the failure rate, determined by visual inspection of individual sweeps. The amplitude of each EPSP and associated background noise for the recording was measured off-line according to the methods given in (Hardingham et al., 2006; Hardingham et al., 2007). The mean noise SD (standard deviation) was subtracted from the EPSP SD using the equation:

(EPSPSD)2=(SD of combined EPSP + noise)2(noise SD)2

The coefficient of variation (CV) of the EPSP amplitude was calculated for each connection as being the SD divided by the mean amplitude.

Quantal analysis

Quantal analysis of stable periods of recording was carried out as described in (Hardingham et al., 2006; Hardingham et al., 2007). After fitting the quantal parameters, an array of tests were run to ensure that the fit was considered statistically “adequate”, i.e. the probability that the distribution of EPSP amplitudes could have been produced by the fitted model (Hardingham et al., 2006). Although for most connections we were only able to use relatively small numbers of trials due to stability criteria (mean number of trials were 166 ± 45), in some connections quantal peaks were evident from EPSP amplitude distributions taken from much longer concurrent periods of recording (Sup. Fig. 1). Estimates of Q from these longer numbers of trials were comparable to those derived from the shorter, stable epochs of trials (n=10, all p>0.05, Sup. Fig. 1), although associated with significantly higher values of quantal variance (n=10, p<0.001, Sup. Fig. 1). We included a DC offset parameter in the model optimiser (S) to accommodate a synaptic failures peak offset from zero, which can arise due to extracellular field effects (Stricker et al., 1996). The mean offset value from the models was −13 ± 40 μV for the L2/3 connections (n=50) and 8 ± 63 μV for the L5 inputs (n=12). As an additional check on the measured quantal size for data sets we applied two further tests. The first was to divide the data sets into two halves, in the order in which it was collected. Models were then fitted to each half (constraining N to that found for the data set as a whole) to obtain a value for Q. The values of quantal size for the first and second half (Q1, Q2) of the data set were then compared. If ((Q1-Q2)/Qwhole) exceeded ±15%, the data set was rejected on the grounds of a likely instability of quantal size over the recording, which might lead to an overestimate of quantal variability. We also repeated the 1st half / 2nd half comparison for derived values of quantal content (m, = N * Pr), Pr, and N. All plots had linear regressions close to the diagonal with strong correlations between 1st and 2nd half values (all p<0.001, not shown). The second test used an autocorrelation method (Stratford et al., 1997) to ensure the peaks in the amplitude frequency histogram were statistically robust (eg Sup. Fig. 1), and hence that the peaks in the histogram were not a sampling artefact derived from a smooth underlying distribution. We compared the autocorrelation of the data set with that of simulated Monte Carlo distributions from a smooth unimodal fit to the data set, to obtain a probability that the peaks did not arise from random sampling, with a conventional threshold of 0.05 (see (Stratford et al., 1997)). The average probability of incorrectness (pi) of the L2/3 to L2/3 connections which passed the test was 0.01 ± 0.02 and for the layer 5 inputs it was 0.02 ± 0.01. Just under a half of the L2/3 to L2/3 connections (20/50) had pi values of less than 0.001. Quantal parameters derived from these 20 connections were representative of the overall population of the 50 connections analysed (all comparisons p>0.05). Of the 47 connections that failed the fitting procedure, 28 failed the AC scoring (i.e pi >0.05) and 12 failed the first half / second half consistency in Q.

For 118 of our 180 recordings we were unable to obtain a satisfactory simple binomial model (hereafter called binomial model), a ratio similar to that reported in comparable studies ((Koester and Johnston, 2005; Saez and Friedlander, 2009). Failure to obtain a model for a connection was either as a result of the fitting algorithm being unable to compute an optimal solution, or because the model failed on one or more of the rigorous statistical tests of adequacy. Three of our 180 recordings were rejected on the grounds of having experimental failure rates greatly exceeding that predicted by the model. The incorporation of the probability of conduction (Pcond) as an additional parameter in the model of maximum likelihood fitting yielded adequate fits for these 3 data sets, with conduction probabilities of between 0.69 and 0.92. These three connections were not analysed further.

A small number of the connections (6 from 50 for L2/3 to L2/3 and 3 from 12 for the L5 inputs) were fitted with a quantal model predicting N = 1 (transmission mediated by a single release site). One possibility is that these connections were multi-release site connections with either a small quantal size and/or large quantal variance, combined with significant conduction failures. The mean quantal amplitude of N=1 connections (344 ± 208μV, Fig. 4c, n=6) was not significantly larger (for the L2/3 to L2/3 connections, p>0.05) than connections best fit by N>1 (282 ± 143 μV, Fig. 4c, n=44), arguing against the multi-release site possibility. In addition, EPSPs showing failure rates exceeding that predicted by simple binomial models were rare. However, for N=1 connections, since there is only a single non-failures peak in the histogram, the failure entry may include conduction failures in addition to synaptic failures which would lead to an overestimate of the true synaptic failure rate. With respect to this issue, imaging techniques have been used to study axonal propagation in L2/3 pyramidal cells in brain slices and conduction failures were rarely observed (Koester and Sakmann, 2000).

Figure 4
Quantal analysis of layer 2/3 to layer 2/3 connections

Bootstrap resampling

Bootstrapping was used in order to estimate confidence intervals on fitted quantal parameters (Efron, 1979; Stricker et al., 1994). For each connection, we had n trials of recorded EPSPs. We generated new sets of data referring to sets of EPSP amplitudes for each connection by randomly selecting, with replacement, n EPSPs from the original set. Thus, some of the original EPSPs might appear more than once in the new set, whereas others might not appear at all. In order to avoid having several identical EPSPs in the new sets (which was correctly rejected by our battery of adequacy tests as being essentially impossible), we added a small amount of jitter to these resampled EPSPs. To each resampled EPSP we added a random number drawn from a Gaussian, with a mean of 0 and an SD of one-quarter of the fitted noise SD (or five on the rare occasions where a quarter of the fitted noise SD was less than five). We then rounded the result to the nearest whole number to make all resampled EPSPs into integers, as they were in the original data (expressed as μV). This set of resampled EPSPs was then fitted in exactly the same manner as the original EPSPs were, and the resampled fit was tested for adequacy using the same selection of statistical tests that were applied to the original fit. If the resampled fit passed these tests, it was accepted as a valid resampled fit. The entire procedure was then repeated until 100 valid resampled fits had been acquired for each connection, giving 100 estimates of Q, N and Pr for each connection. 68% confidence intervals derived from these resample (or standard errors) are shown in Fig. 7 for release probability (Pr) and quantal size (Q) and number of release sites (N) for the L2/3 to L2/3 connections and release probability (Pr) and quantal size (Q) for the layer 5 inputs. 95% confidence limits for release probability (Pr), quantal size (Q) for the L2/3 to L2/3 connections are shown in Sup. Fig. 2b. For most connections, these confidence intervals were large, raising the question of whether correlations between these two variables, which both have such large confidence limits can be trusted. To assess this, for each correlation investigated, we used bootstrap resampling to estimate confidence intervals for the correlation r2 and the significance p. Referring to the Pr-Q relationship for the L2/3 to L2/3 connections (n=50 pairs), for each connection we had 100 resampled values for Pr and 100 resampled values for Q. We generated new scatter-plots of Pr vs Q by randomly picking one of these 100 data-points for each of the Nconn connections in the scatter-plot. In this way, potentially 10050 (or 10100) scatter-plots could be generated. We generated a random sub-set of 105 of these 10100 scatter-plots. Four examples are shown in Sup. Fig. 2c. For each resampled scatter-plot, we calculated the correlation between the resampled Pr and Q, and the associated p-value. We thus ended up with 105 resampled values for r2 and p. Distributions are shown in Sup. Fig. 2d. The resampled r2 values were roughly normally distributed, with a mode a little lower than the r2 for the original data set. Thus, many of the resampled data-sets had stronger correlations than that observed in the original data set. The resampled values for the significance p are the most critical in enabling us to assess the reliability of the original correlation. For all but 4 out of 10,000 resampled scatter-plots (i.e. 99.996%), the Pr / Q correlation was significant at the 0.05 level. Thus, despite the large confidence intervals for individual points in the scatter-plot, the overall correlation is extremely statistically robust. We can confidently reject the possibility that the original correlation (r2=0.36) was a chance occurrence between two. The same procedure was also employed to estimate the reliability of other correlations tested in the paper.

Figure 7
A strong correlation between pre- and post-synaptic efficacy exists both for L2/3 to L2/3 connections and inputs to L5

Histological Procedures

Following recording from pairs of neurons, slices were fixed overnight in 4% paraformaldehyde, resectioned at 100μm and reacted to visualize the biocytin as described previously (Trevelyan and Jack, 2002). Only pairs of cells which displayed no obvious truncation of dendritic or axonal profiles, indicative of damage during histological processing, were analysed further. Drawings of labelled pairs of cells were made using a camera lucida and subsequently reconstructed (Trevelyan and Jack, 2002). No correction for shrinkage was performed. Putative synaptic contacts (defined as zones where a synaptic bouton and postsynaptic dendrite came into close apposition in the same focal plane) were identified and photographed using the 100x objective on a Nikon Axio-phot microscope. The majority of contacts were on dendritic spines and not directly on dendritic shafts. For a subset of reconstructed pairs of neurons (n=4), we were able to process the tissue through to electron microscopy to confirm the identity of synaptic contacts (n=8 contacts). The area of contact was serially sectioned at 70nm using a Leica ultramicrotome. The sections were collected on formvar coated grids and photographed using a Jeol 1010 transmission electron microscope. The electron micrograph images allowed serial reconstruction of the boutons; volumes were calculated from the area of the sections and their known thickness.

Modelling data from layer 2/3 and layer 5 pyramids

Simulations of the distribution of synaptic profiles were obtained using anatomically accurate passive cable models of pyramidal cells from previously published studies (L2/3 - (Trevelyan and Jack, 2002); L5 - (Larkman et al., 1992)). In these studies, biophysical parameters were derived by matching the experimentally recorded voltage response to a brief somatic current injection with the behaviour of the model neuron to the same stimulus, yielding values at both room and physiological temperatures (Table 1). The models are available on request.

The synaptic simulations used a branching cable analytical solution with the synaptic current being simulated by the local injection of 0.1pC of charge (Q) over a time course described by the sum of two exponentials (Major et al., 1994) :


with time constants τrise of 0.2ms and τdecay of 2.5ms. This synaptic current was simulated at every 10th dendritic spine, to give a distribution profile for the entire excitatory input to the cell.

Statistical Analysis

All comparisons between distributions of data were carried out using two sample t tests. Regressions of data scatter plots were linear although for amplitude / failure rate scatter plots, hyperbolic fits described the data distributions much more closely (Markram et al., 1997). All population means are given with standard deviations unless stated.


Synaptic strength and reliability of cortical synaptic connections

To investigate the properties of synaptic connections between pyramidal neurons in rat visual cortex we recorded EPSPs from synaptically coupled neurons (Fig 1). Recordings were made between pairs of L2/3 neurons (n=137, Fig.1a&b); between L2/3 and L5 neurons (n=20, Fig.1c&d) and between pairs of layer 5 neurons (n= 23, Fig.1e&f).

Figure 1
Recordings from synaptically connected pyramidal neurons in the cortex

For each connection we calculated the mean EPSP amplitude (Fig.2), the failure rate (a measure of the reliability of the connection, Fig.2), and the trial to trial variance in EPSP amplitude (measured as the coefficient of variation, CV, Sup. Fig.3). The mean EPSP amplitude of L2/3-L2/3 connections ranged from 42 μV to 2.9 mV (mean 433 ± 429 μV, n=137). Mean EPSP amplitudes of L5 to L5 connections were comparable (range 121 μV to 2.1 mV, mean 503 ± 504 μV, n=23) whereas L2/3 to L5 connections were significantly weaker (mean 237 ± 259 μV, range 22 μV to 1.0 mV, Fig.2a, n=20). The mean failure rate of connections between L2/3 neurones and for L2/3 to L5 connections was similar (0.25 ± 0.18 (n=137) and 0.29 ± 0.23 (n=20) respectively). In contrast, L5 to L5 connections were more reliable, with a lower failure rate of 0.12 ± 0.13 (n=23). Connections between different cortical layers have previously been shown to occupy different regions of parameter space in amplitude versus failure plots (Bremaud et al., 2007). Consistent with this, the trial to trial variability in L5 to L5 connections (as measured by the CV) was significantly lower than either the L2/3 to L2/3 or L2/3 to L5 connections (Sup. Fig.3a). For all connections, failure rate was negatively correlated with EPSP amplitude (Fig.2c), demonstrating that strong connections (as determined by mean EPSP amplitude) were also the most reliable. The trial to trial variability in EPSP amplitude (measured as the CV) was also negatively correlated with mean EPSP amplitude for all connections (Sup. Fig.3b). In addition, there was a strong positive correlation between failure rate and CV values for L2/3 to L2/3 connections and inputs onto L5 neurons (Sup. Fig.3c&d).

Figure 2
Amplitude and reliability of EPSPs recorded in layer 2/3 and layer 5 pyramidal neurons

Rise time as an indicator of synapse location

EPSP rise time can be used as an indicator of the location of the synaptic input on the dendritic tree of the post-synaptic neuron (Magee and Cook, 2000). In order to investigate this we measured the 10-90% rise time of the mean EPSP response for each of our connected pairs (Fig.3 and Sup. Fig.3e). Rise times of EPSPs recorded between pairs of L2/3 neurons ranged from 1.4 to 9.8 ms (mean of 3.4 ± 1.3 ms, n=137, Fig.3a, Sup. Figs. 7 and 8).

Figure 3
Rise time as an indicator of dendritic location of EPSP

EPSPs recorded from L5 neurons had on average slower rise times than L2/3 pairs, both for L5 inputs (mean rise time of 4.3 ± 1.0 ms, range 2.5 ms to 6.1 ms, n=23) and particularly for L2/3 inputs (mean rise time of 5.2 ± 2.7 ms, range 1.7 to 11.8 ms, Fig.3b, Sup. Fig.3e, n=20). To investigate the relationship between rise time and dendritic location for both L2/3 and L5 neurons we used a passive cable model of representative L2/3 and L5 pyramidal neurons from previous studies (Larkman et al., 1992; Trevelyan and Jack, 2002). Simulated synaptic currents of identical size were injected at every 10th spine across the entire dendritic tree of each model neuron and the EPSP waveform was calculated for each simulated EPSP when recorded at the soma. The rise time of each simulated EPSP was then plotted as a function of its peak somatic amplitude (Fig.3c&d). For L2/3 neurons, the range of experimental rise times is consistent with anatomical studies, which have shown that the large majority of excitatory inputs onto layer 2/3 neurones are made onto basal or apical oblique dendrites (Larkman, 1991). This also holds for the majority of inputs onto L5 cells, particularly for inputs from other L5 cells (Larkman, 1991)

Both anatomical studies (Feldmeyer et al 2006, Markram et al 1996) and previous quantal studies (Hardingham et al., 2006; Bremaud et al., 2007; Hardingham et al., 2007; Saez and Friedlander, 2009) support the idea that connections made between cortical pyramidal neurons are commonly mediated via more than one functional or anatomical release site. For a given synaptic current, the precise location of the synaptic contact on the dendritic tree determines the peak somatic amplitude it evokes. For L2/3 neurons, the effect of dendritic filtering in basal and proximal oblique dendrites is relatively small (< 30%, Sup. Fig.4) indicating that synaptic efficacy (as recorded at the soma relative to a hypothetical somatic synaptic input) is relatively high. A result of this is that identical synaptic currents distributed over the basal and apical oblique dendritic trees (which represent a large proportion of the excitatory synaptic inputs into these cells) are likely to generate EPSPs of similar amplitude when recorded at the soma. Therefore the effect of inter-site quantal variability brought about by differential dendritic location is likely to be small and this fact may therefore make recordings amenable to quantal analysis.

Extracting quantal parameters for cortical synapses

In order to quantify the cortical synaptic circuitry in more detail, we used quantal analysis techniques on stable periods of recording connections (Larkman et al., 1997; Hardingham et al., 2006; Hardingham et al., 2007). EPSP amplitude distributions for each connection (reflecting the trial to trial fluctuations in EPSP amplitude) were fitted with a simple binomial quantal model of transmitter release (Hardingham and Fox, 2006; Hardingham et al., 2007). In such a model, Q (quantal size) represents the amplitude of the postsynaptic EPSP generated by the release of neurotransmitter at a single release site (as recorded at the soma), N is the number of release sites at which release of neurotransmitter can occur and Pr is the probability that a vesicle of neurotransmitter is released at each site in response to stimulation. EPSP amplitude distributions from 50 connected pairs of L2/3 neurons (from a total of 137) could be described by a simple binomial model (Fig.4a&b). The majority of these connections (44 from 50) were fitted with a model predicting N>1 (ie connections mediated by more than one release site, Fig.4b). However, we found that the mean quantal amplitude of connections best fit by a single release site (N=1, Q = 344 ± 208 μV, n=6, Fig 4c, e.g. in Fig. 4a) was not significantly different (t test, p = 0.48) to the quantal amplitude of connections best fit by more than one release site (N=3.34 ± 1.52, Q = 282 ± 143 μV, n=44, Fig. 4c).

There appeared to be little selection bias evident in connections yielding quantal models compared to the population as a whole with respect to mean amplitude, failure rate, or EPSP 10-90% rise time (Sup. Fig.5b). Estimates of quantal size (Q) for the L2/3 connections that we were able to fit a model to ranged from 104 to 782 μV with a mean of 289 ± 151 μV (n=50, Fig.5a & b). Estimates of quantal size for both L5 to L5 and L2/3 to L5 connections (Fig.5b), were smaller than L2/3 to L2/3 (L5 to L5: 211 ± 65 μV, range 106 to 302 μV, n=7; L2/3 to L5: 170 ± 104 μV, range 82 to 349 μV, n=5). All connections had the statistical reliability of their peaks tested using an autocorrelation technique (see Methods and (Stratford et al., 1997))

Figure 5
Synaptic parameters derived from quantal analysis

In order to obtain an independent estimate of quantal size from the quantal analysis, we recorded miniature EPSPs (mEPSPs) from a separate population of layer L2/3 neurons in the presence of TTX and PTX (which represent EPSPs from single release sites). The distribution of mEPSP amplitudes (mean 275 ± 163μV (n = 2000 amplitude measures, collected from 4 neurons) was similar to that of the quantal amplitudes derived from quantal analysis of paired recordings (Fig.5a, two sample t test, p=0.56). The 10-90% rise time of mEPSPs (mean of 3.50 ± 1.67) was comparable to the 10-90% rise time of the whole population of evoked EPSPs recorded in L2/3 neurons (3.40 ± 1.35, n=137, p>0.05, Sup. Fig. 5b) and the subset of evoked PSPs subjected to a quantal analysis (3.20 ± 1.26, n=50, p>0.05). As well as assigning values for N, Pr and Q, the model incorporated a parameter to account for quantal variance. Quantal variance can result from 2 sources: type 1 or intrasite quantal variance (the trial to trial fluctuation in post synaptic response at a single release site) or type 2 quantal variance (variability in quantal size between release sites) (Wahl et al., 1995). The presence of type 1 quantal variance will be additive, thereby increasing the width of quantal peaks towards the right of the amplitude histogram, leading to the smearing of quantal peaks, especially in connections with a small quantal amplitude or a large number of release sites. In contrast, type 2 quantal variance will tend to sharpen peaks towards the right of the amplitude histogram (Wahl et. al., 1995). To accommodate these 2 possibilities the optimiser was allowed to fit the data either with type 1 quantal variance alone or type 1 in combination with type 2 (implemented as flat or equal quantal variance across all amplitude peaks). Quantal variance was strongly correlated with quantal size for L2/3 to L2/3 connections (r2=0.70, p<0.001, Sup.Fig.5e). For the 2/3 to 2/3 connections, 40% were best fit with type 1 quantal variance and 60% best fit with flat quantal variance, suggesting some degree of inter-site quantal variance was present at the connections, although values of Q, Pr, N and Qsig were not significantly different if models were constrained to either all type 1 or all flat (all p>0.05). Values of Qsig constrained to type 1 variance were also strongly correlated with values of Qsig for the same connection when constrained to flat quantal variance (not shown, r2=0.64, p<0.001). Quantal variance expressed as a coefficient of variance ranged from 0 to 41 %, with a mean of 17 ± 10 % (n=50, 16 ± 10% fitted with just type 1 quantal variance, 18 ± 11 % fitted with just flat quantal variance). The variance was substantially higher than this for connections which failed on one or more of the quantal analysis tests (mean of 43 ± 39%, n=87).

Determining the number of functional release sites per connection (N) and subsequently Pr is more problematic than deriving values for Q (which is visually evident from examining the peak spacing in the amplitude distribution) and statistically validated by our autocorrelation based method). A more reliable measure of synaptic strength is m, the mean quanta released per trial, a measure of total presynaptic strength. The problem of separating out m into Pr and N is especially true for low Pr connections where release sites are rarely all active at the same time (Bekkers and Stevens, 1995)

Estimates for the number of release sites (N) between pairs of L2/3 neurons ranged from 1 to 9 with a mean of 3.1 ± 1.6 (n=50, Fig.5c & 5d). Estimates for N for L5 inputs ranged between 1 and 2 for L2/3 to L5 connections (n=5, mean of 1.6 ± 0.5, Fig. 5d), and between 1 and 7 for L5 to L5 connections (n=7, mean of 3.4 ± 2.2, Fig.5d). With respect to quantal size, we were able to obtain an alternative independent measure by recording mEPSPs. Obtaining an independent estimate for N and Pr is more difficult. However, for a subset of L2/3 to L2/3 connections (n = 13) we were able to make anatomical reconstructions of the recorded neurons after filling with biocytin to allow us to investigate putative ‘anatomical N’ (Fig.6a).

Figure 6
Number of functional release sites for L2/3 to L2/3 connections correlates with number of putative anatomical contacts

Reconstructions of connected pairs of layer 2/3 pyramidal neurons

From light microscope observations, we were able to identify possible sites of contact between presynaptic axon varicosities and postsynaptic dendritic spines (Fig.6a). The mean number of putative contacts per connected pair of neurons (N) was 2.6 ± 0.9 (n=13), with a range of 1 to 4. For 9 of these 13 connections, quantal analysis was able to predict the number of functional release sites that these connections were mediated by, and values of functional N were correlated with the number of putative synaptic contacts identified from anatomical reconstructions (Fig.6b, n=9, r2 =0.48, p<0.05). Five of these 9 connections had the same values for best fit binomial model N and anatomical N while the best fit linear regression was close to the diagonal (Fig. 6b). The majority of contacts (68 %, 23 contacts) were on basal dendrites, 29 % (10 contacts) were on apical oblique dendrites and only 1 contact was found on the proximal apical dendrite (Fig.6c). The majority of the putative synaptic contacts were made on dendritic locations relatively proximal to the cell body of the post-synaptic neuron (mean path length of 62 ± 38 μm, Fig.6d, n = 34). For these connections, quantal size corrected for dendritic location (using EPSP rise time, see legend to Sup. Fig. 6, was positively correlated with the average distance of the synapse to soma (r2=0.62, p<0.01, Fig.6e), although this correlation did not hold for quantal size uncorrected for dendritic location (r2=0.24, p=0.16, not shown). The dendritic locations of the putative synaptic contacts determined anatomically were also consistent with predictions from the modelling data based on the EPSP rise time (Fig. 6f&g). For a small subset of recordings, bouton volume (measured from serial electron microscope (EM) sections) could be calculated and was correlated with somatic Q (or corrected Q, not shown, p<0.05, n=4 connections, 8 boutons).

Additional supporting evidence for goodness of fit for N is provided by a number of L2/3 to L2/3 connections where we were able to fit periods of data recorded at both 23-26 °C and 36 °C (n=5, not shown). For each of these connections, the model returned an identical value for the number of release sites from the 23-26°C and 36°C data, with a similar Q, but a significantly higher Pr (n=5, p<0.05, not shown) (Hardingham and Larkman, 1998).

Relationships between quantal parameters

Estimates for the mean Pr for each connection ranged from 0.12 to 0.91 for L2/3 to L2/3 connections (mean of 0.47 ± 0.20, n=50, Fig.5e). Similar estimates were obtained from L2/3 to L5 and L5 to L5 connections (0.57 ± 0.22 (n=5) and 0.46 ± 0.21 (n=7) respectively, Fig.5f). There was a positive correlation between release probability and quantal size for both the L2/3 to L2/3 connections (Fig.7a, r2 = 0.37, p<0.001) and for both classes of input onto L5 neurons (Fig.7b, r2 = 0.51, p<0.01). Bootstrap resampling was used (as detailed in the methods) to produce standard errors (68% confidence intervals) for our estimates of N, Pr and Q, derived from the fitted binomial model (Efron, 1979; Stricker et al., 1994). 95% confidence intervals for this plot are given in Sup Fig. 2. In order to quantify the effect of the confidence limits on the Pr-Q correlation, quantal parameters for each connection were randomly selected from the resampled data sets and correlations between Pr and Q were recalculated. Virtually all of the resultant resampled correlations were still significant (>99.9% for the L2/3 to L2/3 connections, Sup. Fig. 2) suggesting the correlation is robust and not simply an artefact of sampling. For the L2/3 to L2/3 connections, the number of release sites (N) was also negatively correlated with Pr (Fig.7c, r2 = 0.36, p<0.001). There however was no correlation between quantal size and number of release sites for the L2/3 to L2/3 connections (r2=0.05, p>0.05, not shown).

We were interested to see which of the quantal parameters were responsible for the 70 fold range in mean amplitude observed for individual connections (Fig. 8). For L2/3 to L2/3 connections, mean EPSP amplitude was correlated with both Q (Fig. 8a, r2 = 0.64, p<0.001) and m, the mean number of quanta released per trial (=N*Pr, Fig. 8c, r2=0.51, p<0.001). These correlations also existed for inputs onto L5 cells (Fig.8b, r2=0.37, p<0.05 & Fig. 8d, r2=0.79, p<0.001) suggesting that both pre and postsynaptic factors contribute to synaptic efficacy in L2/3 and L5 cortex. From Fig.8e & f it is clear that Pr and not the number of release sites (N) is the key determinant in the correlation between mean EPSP amplitude and m (compare Fig. 8e, r2 = 0.34 for Pr to Fig. 8f, r2 = 0.01 for N).

Figure 8
Correlation between EPSP amplitude and pre / post-synaptic efficacy

There was no significant correlation between either mean EPSP amplitude and EPSP rise time or quantal amplitude (Q) and EPSP rise time for both L2/3 to L2/3 connections or inputs onto L5 cells (all p>0.05, not shown). From modelling studies it was clear that the dendritic location of synapses can influence both the rise time and the relative attenuation of inputs through dendritic filtering (Stratford, 1989; Trevelyan and Jack, 2002). In order to make some correction for possible attenuation we used EPSP rise time as an indicator of probable dendritic location and applied a correction factor determined via models of the neurons (Sup. Fig. 6). Following correction, both mean EPSP amplitude and quantal amplitude were significantly correlated with rise time, both for 2/3 to 2/3 connections and layer 5 inputs (not shown, all p<0.05). Correction of Q for dendritic attenuation did not significantly improve the Pr / Q correlations (r2 values of 0.37 for the 2/3 connections compared with 0.36 for the uncorrected data, and 0.53 for the layer 5 inputs compared with 0.51 for the uncorrected data (not shown, reference to Fig. 7).


This study sought to investigate the relationship between pre and postsynaptic efficacy in developing cortical synapses, using electrophysiology and quantal analysis. As result of our analysis, which assumed synaptic release could be approximated by a single binomial model, we demonstrate a positive correlation between Pr and Q at excitatory synapses between L2/3 pyramidal neurons, and for excitatory inputs onto L5 pyramids from L2/3 and L5 pyramidal neurons.

Low quantal variance is necessary for successful quantal analysis

We were able to fit an adequate simple binomial model to around a third of our data set. Failure to fit a quantal model is largely due to an inability to discern clear quantal peaks in amplitude frequency histograms, which in the case of connections mediated by more than one release site may arise from quantal amplitudes varying considerably between release sites (type 2 quantal variance). Non-stationarity of quantal size over time (Larkman et al., 1997), poor signal to noise level or large within release site (type 1) quantal variance will also effect the likelihood of generating peaky histograms.

Under conditions of receptor saturation, type 1 quantal variance is largely due to the stochastic nature of channel opening (Faber et al., 1992; Bannister et al., 2002), although can be considerably higher if transmitter fails to saturate postsynaptic receptors, making the quantal amplitude sensitive to peak concentration of glutamate within the synaptic cleft. (McAllister and Stevens, 2000). An observation worth mentioning is that the type I quantal variance correlates with quantal size (Sup. Fig. 5e), implying that there is receptor saturation with small quanta (small number of receptors) and progressively less saturation as the number of postsynaptic receptors increases. This may possibly be an artefact of the physical dimensions of the synapses.

Large quantal variance has been reported in neonatal animals (P5-12 days old, (Hanse and Gustafsson, 2001)) or in cultured slices (Liu et al., 1999)). At the mossy-fiber to granule cell synapse in rat cerebellum, quantal variance falls between P11-15 and P40-57 days (CVs of 34 and 17% respectively, (Wall and Usowicz, 1998), suggesting large quantal variance may be a feature of immature synapses. Given the age of animals that were used in our study (p19-27), it is likely that the synapses activated in our recordings represent some intermediary developmental stage, perhaps closer to a mature than an immature state as our mean CV of quantal variance was also 17%.

Intersite (type 2) quantal variance may result from either differential filtering of release sites located on different parts of the dendritic tree, or from different quantal currents at each release site. The majority of excitatory inputs onto L2/3 and L5 neurons are on basal and apical oblique dendrites, which are electrotonically compact (Larkman et al., 1992; Markram et al., 1997; Trevelyan and Jack, 2002; Feldmeyer et al., 2006). Synaptic currents distributed over these dendritic trees generate EPSPs of similar amplitude at the soma (Nevian et al., 2007). Therefore the effect of intersite quantal variability due to dendritic location is likely to be small. Consistent with this, there was no significant correlation between EPSP rise time and somatic Q (Sup. Fig. 7), nor between somatic Q and mean dendritic distance of the synapse from the soma (Fig. 6 legend), consistent with previous studies in L5 cortical neurons (Markram et al., 1997). Following corrections for likely dendritic filtering, Qcorr showed a significant correlation with EPSP rise time, (see Sup. Fig. 7) suggesting larger synaptic conductances at more distal synapses (Jack et al., 1981; Triller et al., 1990; Andrasfalvy and Magee, 2001; Nicholson et al., 2006).

Quantal amplitude at cortical synapses

The quantal amplitudes we report in this study, measured at the soma, spanned a similar range of amplitudes to previous quantal analysis studies in the cortex (100-800μV, (Torii et al., 1997; Bremaud et al., 2007)). Irrespective of age dependent differences in synaptic efficacy eg (Reyes and Sakmann, 1999), our mean Q (281 ± 21 μV) is smaller than that that reported for the same neurons both in 2-3 week old cortex (Torii et al., 1997) and in adult cortex (Bremaud et al., 2007).

Even though values of quantal amplitude varied considerably between connections, the variability of quantal amplitudes within a connection (type 2 quantal variance) was at least small for the 40% of connections for which we were able to successfully fit quantal models to. This observation is supported by studies performed in the rat hippocampus which showed that the morphologies of non-adjacent dendritic spines innervated by the same presynaptic axon are much more similar than those innervated by different axons (Sorra and Harris, 1993). During development, the quantal properties of synapses experiencing the same pre- and post-synaptic activity may converge to similar values (Larkman et al., 1997). In cortex it has been shown that release probability is similar at the release sites of a given connection (Koester and Johnston, 2005) lending support to this idea. Given that bouton size and PSD area are tightly linked (Schikorski and Stevens, 1997, 1999), this similarity of synaptic properties is therefore likely to extend to quantal size. Many successful quantal analysis studies at a range of central synapses would also suggest this (Stricker et al., 1996; Larkman et al., 1997; Wall and Usowicz, 1998; Hardingham et al., 2006; Bremaud et al., 2007; Hardingham et al., 2007; Saez and Friedlander, 2009).

Our distribution of quantal amplitudes is comparable to the amplitude distribution of mEPSPs we recorded from a separate sample of L2/3 neurons. From analysis of the rise times, the two populations (evoked EPSPs and mEPSPs, Sup. Fig. 8) are likely to be drawn from similar populations of inputs, largely from basal and proximal oblique dendrites (which make up 80% of all the synapses, and are subject only to modest cable attenuation (Larkman et al., 1992)). Comparisons with the distribution of mEPSPs from the model neurons suggests the major difference is the lack of mEPSPs with a rise time greater than ~8ms, arising from the distal apical and the apical tuft synapses, consistent with the observation that distal apical inputs are substantially attenuated at the soma and may be hard to detect (Williams and Stuart, 2002). A similar correlation between putative quantal size (derived from evoked EPSCs) and mEPSC amplitude has been reported in electrically compact granule cells from adult cerebellum (Wall and Usowicz, 1998).

Numbers of release sites and release probability at cortical synapses

For a subset of connections, we were able to identify putative anatomical contacts from histological preparations. These connections showed a positive correlation between the anatomical and functional estimates of N (derived using quantal analysis) Since silent synapses are unlikely to be common at this age (Rumpel et al., 2004), an identified anatomical contact may very well represent one functional release site (Korn et al., 1981; Gulyas et al., 1993; Silver et al., 2003; Biro et al., 2005) as the vast majority of cortical synapses have been shown to consist of a single structural release site (Schikorski and Stevens, 1999), although evidence for multivesicular release under conditions of high release probability exists at some CNS synapses (Wadiche and Jahr, 2001; Oertner et al., 2002; Christie and Jahr, 2006). For a sub-set of connected pairs of neurons we were further able to confirm (using electron microscopy) that these putative contacts were indeed synaptic contacts, but it is possible that some of the contacts identified using light microscopy were erroneous.

Given this caveat, our mean value of N (3.1 ± 0.2) is consistent with that previously reported for anatomical connections between L2/3 cortical cells of similar age (2.8 + 0.7 (Feldmeyer et al., 2006)). Our mean estimate of release probability (Pr) for L2/3 to L2/3 connections (0.47 ± 0.20) is also very close to that derived by optical methods in L2/3 of young rat cortex (0.46 ± 0.26 (Koester and Johnston, 2005)) and also similar to that found from quantal analysis of paired recordings in layer 4 juvenile cortex (0.41 ± 0.13 (Saez and Friedlander, 2009)) and layer 3 adult cortex (0.65 ± 0.18 (Bremaud et al., 2007)). The similarity of mean Pr values from the current study with previous estimations of Pr at cortical synapses also gives confidence in our estimates of N.

Connection strength is set both pre and post-synaptically

We found that the 70-fold range in connection amplitude was due to both differences in pre- (m) and post-synaptic strength (Q) between connections (Fig. 8). The correlation between presynaptic efficacy (m) and mean EPSP amplitude for L2/3 connections is due largely to release probability (Pr) with little correlation between mean amplitude and N. These conclusions are similar to those reached by Markram et. al. for connections between thick tufted L5 neurons (Markram et al., 1997) and Saez et. al. for connections between L4 neurons (Saez and Friedlander, 2009). The connection strength appears to be set in cortex by the strong matching of Pr with Q demonstrated in the present study, which may not be intrinsically fixed but driven by changes in synaptic activity (Thiagarajan et al., 2005; Tokuoka and Goda, 2008).

Supplementary Material

Supplemental Figures


Work Funded by the Wellcome Trust and the M.R.C. We thank Guy Major and Claire Cheetham for helpful comments


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