| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
Received 11 December 1997; accepted after revision 8 April 1998.
 |
ABSTRACT |
|---|
 TopAbstract IntroductionMethodsResultsDiscussionReferences |
|---|
r) was unusually high (0·90 ± 0·03 at 0·033 Hz, n = 5), but as the frequency of stimulation was increased,
|
INTRODUCTION |
|---|
|
TopAbstractIntroductionMethodsResultsDiscussionReferences |
|---|
Quantal analysis is a classical approach to the investigation of mechanisms underlying synaptic transmission, in which key parameters - the number of functional release sites (N), the quantal size (q) and the release probability - are extracted from fluctuations in synaptic responses using statistical models. Unlike the situation at the neuromuscular junction (NMJ), application of quantal analysis to central synapses has proved difficult because some of the necessary simplifying assumptions are often not valid. For example, at synapses where release probability is non-uniform, a compound binomial (Jack, Redman & Wong, 1981; Walmsley, Edwards & Tracey, 1988; Stricker, Field & Redman, 1996) rather than a simple binomial statistical model is required, increasing the number of parameters to be estimated from the data set. Variations in quantal size at individual release sites, and between release sites, makes it difficult to identify peaks in distributions of synaptic response amplitude and complicates their interpretation (Walmsley, 1995). Furthermore, the difficulty in testing the accuracy of these methods directly has led, for example, to controversy in attributing long-term changes in synaptic efficacy to a pre- or postsynaptic locus. Recently, several alternative strategies have been developed to examine the quantal properties of transmitter release. These include the use of a non-competitive antagonist to estimate release probability (Rosenmund, Clements & Westbrook, 1993), the use of capacitance measurement to monitor vesicle release (Heidelberger, Heinemann, Neher & Matthews, 1994), and the use of the fluorescent dye FM1-43 to examine vesicle cycling and transmitter release (Ryan, Reuter, Wendland, Schweizer, Tsien & Smith, 1993; Issacson & Hille, 1997; Murthy, Sejnowski & Stevens, 1997). However, these techniques provide only part of the quantal description of the synapse, and there are difficulties in applying them to slice preparations in which synaptic architecture is preserved.
In order to overcome these problems, we have developed a new approach which extends previous quantal analysis methods (del Castillo & Katz, 1954a; Miyamoto, 1975; Clamann, Mathis & Lüscher, 1989; Malinow & Tsien, 1990; Bekkers & Stevens, 1990). With this approach, which we term 'multiple-probability fluctuation analysis' (MPF analysis), quantal parameters are estimated from synaptic current fluctuations measured over a wide range of experimentally imposed release probabilities at the same input. This method, which is also related to non-stationary fluctuation analysis of ion channels (Sigworth, 1980; Traynelis, Silver & Cull-Candy, 1993; Silver, Cull-Candy & Takahashi, 1996) and to a method recently suggested by Frerking & Wilson (1996), provides estimates for the underlying quantal parameters with minimal assumptions. Furthermore, it can provide estimates of N, q and the mean release probability when both the quantal size and release probability are non-uniform.
At synaptic connections, the underlying quantal parameters are not static, but change with time as a result of short-term facilitation and depression (Zucker, 1989) or long-term changes in synaptic efficacy. Understanding this dynamic behaviour is central to understanding transmission, since synaptic efficacy, at any given time, is dependent on the recent history of the input. Furthermore, modelling studies have shown that the temporal behaviour of synaptic efficacy (the tendency to exhibit short-term facilitation or depression) is important in determining the pattern of frequency-coded information that is transmitted to the postsynaptic cell (Sen, Jorge-Rivera, Marder & Abbott, 1996; Tsodyks & Markram, 1997). Since the early work of del Castillo & Katz (1954b) at the NMJ, synaptic depression is generally assumed to have a presynaptic locus. However, at central glutamate synapses the situation appears less clear. While several studies have demonstrated presynaptic depression (Larkman, Stratford & Jack, 1991; Borst & Sakmann, 1996; von Gersdorff, Schneggenburger, Wies & Neher, 1997), non-NMDA receptors desensitize when exposed to low concentrations of glutamate, so postsynaptic desensitization may persist long after the synaptic current has decayed. Indeed, recent studies have shown that postsynaptic desensitization plays an important role in synaptic depression at some central excitatory synapses (Trussell, Zhang & Raman, 1993; Zhang & Trussell, 1994).
In this study, we have investigated transmission at the climbing fibre-Purkinje cell synaptic connection, which in paired-pulse experiments exhibits substantial EPSC depression (Konnerth, Llano & Armstrong, 1990; Perkel, Hestrin, Sah & Nicoll, 1990). This synaptic connection, as part of the olivocerebellar pathway, is thought to play an important role in the timing of motor tasks (Welsh, Lang, Sugihara & Llinas, 1995) and in motor learning (Ito, 1984). Each Purkinje cell is innervated by a single climbing fibre (CF) which forms a distributed synaptic connection with numerous contacts on the extensive dendritic tree. CF stimulation generates a large glutamate-mediated EPSC, which, under physiological conditions, causes Purkinje cells to fire complex spikes (Eccles, Llinas & Sasaki, 1966). We have investigated the locus of frequency-dependent depression by examining the underlying quantal parameters with MPF analysis. Our results show that this input has unusual quantal parameters for a central synaptic connection. Furthermore, we demonstrate with MPF analysis that the frequency-dependent depression at the CF synapse has a purely presynaptic origin over a physiological range of frequencies. Our results suggest that the temporal dynamics of release probability at this synapse are specialized to ensure highly reliable low-frequency transmission. Some of these findings have been published in this journal in a preliminary form (Silver, Momiyama & Cull-Candy, 1997).
|
METHODS |
|---|
|
TopAbstractIntroductionMethodsResultsDiscussionReferences |
|---|
Experimental preparation and data acquisition
Following decapitation, in accordance with The Animals (Scientific Procedures) Act 1986, the brains from 12- to 14-day-old Sprague-Dawley rats were removed and cooled in ice-cold saline. Parasagittal slices of cerebellum, 200 µm thick, were prepared and incubated at 31°C for 1 h (see Silver et al. 1996). The saline solution used for slicing and incubation contained (mM): 125 NaCl, 2·5 KCl, 1 CaCl2, 5 MgCl2, 1·25 NaH2PO4, 26 NaHCO3 and 25 glucose (pH 7·3 when bubbled with 95 % O2 and 5 % CO2). Slices were then transferred to the recording chamber and perfused with solutions containing (mM): 125 NaCl, 2·5 KCl, 0-4 CaCl2, 1-5 MgCl2, 1·25 NaH2PO4, 26 NaHCO3 and 25 glucose (pH 7·3 when bubbled with 95 % O2 and 5 % CO2). Climbing fibre EPSCs were recorded at room temperature (21-25°C) with 20 µM 7-chlorokynurenic acid (and occasionally 20 µM D-amino-5-phosphonopentanoic acid, d-AP5), 20 µM bicuculline methiodide, 25 µM picrotoxin and 0·5 µM strychnine added to the perfusate to block NMDA, 
-aminobutyric acid and glycine receptors, respectively. The following agents were also added to the external solution in specific experiments: 1 µM 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX), 10-30 µM CdCl2, 5 mM SrCl2, 500 µM (RS)-
-methyl-4-carboxyphenylglycine (MCPG), 200 µM (RS)--methyl-4-tetrazolylphenylglycine (MTPG), 250 µM (RS)--methyl-4-phosphonophenylglycine (MPPG), and 50 µM L-2-amino-4-phosphonobutyric acid (L-AP4). Drugs were obtained from Tocris Cookson (Bristol, UK) or Sigma.
Patch pipettes were made from thin-wall borosilicate glass (Clark Electromedical). The pipette solution contained (mM): 110 CsF, 30 CsCl, 2 NaCl, 0 or 0·5 CaCl2, 10 Hepes, 5 or 10 EGTA and 2 Mg-ATP (adjusted to pH 7·3 with CsOH). CF inputs were stimulated at 0·033-10 Hz (5-30 V; duration, 0·02-0·2 ms) with a second patch electrode filled with 1 M NaCl placed in or on the surface of the granule cell layer. We restricted analysis to frequencies of 10 Hz and below because this covered the physiological range, and EPSC stimulation became unreliable above this frequency. EPSCs were recorded with an Axopatch 200A (Axon Instruments) and, in dual recording experiments, voltage measurements were made with an L/M-EPC-7 amplifier (List Electronic). Series resistance was estimated from the settings of the Axopatch 200A, and series resistance compensation was used with capacitance compensation and prediction switched off. Signals were recorded on DAT (DTR 1204, Biologic, France) after filtering at 10 kHz. EPSCs recorded on tape were subsequently filtered to 1-5 kHz (Bessel filter) and digitized at 20-25 kHz using AxoTape 2 and a Digidata 1200 interface (Axon Instruments).
Identification of single climbing fibre inputs and optimization of synaptic current recordings
Climbing fibre EPSCs were distinguished from parallel fibre EPSCs (which exhibit paired-pulse facilitation) by their large size and characteristic paired-pulse depression (Fig. 1A). We ensured that no small-amplitude parallel fibre EPSCs contaminated the CF EPSC by examining current records that were just below the CF threshold (Fig. 1B). In neonatal rats (postnatal days (P)0-P12), Purkinje cells are innervated by multiple climbing fibres, but after this time only a single climbing fibre remains (Mariani & Changeux, 1981). We ensured that only a single CF was activated in our preparation by examining whether EPSCs showed an all-or-none response to a stimulus of graded intensity (Fig. 1C).
The large size of the CF EPSCs and the extensive dendritic arbor of the Purkinje cell make voltage clamp of these currents technically difficult. We adopted several strategies to optimize the quality of voltage clamp and to minimize the errors involved. Firstly, 12- to 14-day-old animals (mainly P13) were used, as at this age the Purkinje cell dendritic arbor is less extensive than in the adult, and CF innervation is located on the soma and proximal dendrites (Altman, 1972). Secondly, the electrode resistance was minimized by using large electrodes (2-3 M
) combined with series resistance compensation (70-85 %; mean series resistance after compensation, 0·94 ± 0·04 M; n = 29). Thirdly, recordings were made at depolarized voltages (-30 mV; with the exception of the Sr2+ and Cd2+ experiments) so that the amplitudes of synaptic currents were reduced and voltage-gated currents inactivated. The effectiveness of this approach is illustrated in Fig. 1D; depolarization from -60 mV activated large voltage-gated currents, but at a holding potential of -30 mV these currents were completely inactivated.
Climbing fibre EPSCS recorded under these conditions were still distorted by an escape voltage which arose due to the large size of the CF current. This is likely to have two components; voltage drop down the dendrite (see 'Consideration of remaining voltage-clamp errors', below) and voltage drop across the recording pipette (somatic voltage escape). To estimate the latter component, we made recordings from Purkinje cells that were patched with two electrodes, one measuring voltage and the other current (Fig. 1E). During the large CF synaptic current the voltage in the cell soma deviated from the command voltage (upper dashed line). This voltage drop was due to current flowing through the current recording electrode and could therefore be calculated from the compensated electrode resistance and the current. This calculation relies on the fact that the EPSC current-voltage relationship was linear (data not shown) and that the change in EPSC kinetics over the range of escape was negligible (change in half-decay time (t½), 5·3 ± 0·9 % between -30 and -15 mV; n = 4). Figure 1F shows that the correction using the measured voltage and the correction using the voltage calculated from the compensated electrode resistance agree closely. We further tested the adequacy of our escape-voltage correction by comparing the corrected waveforms of control EPSCs (with typical escape voltages) with corrected EPSCs where the synaptic conductance had been substantially reduced with a sub-maximal concentration of the non-NMDA receptor antagonist CNQX (Fig. 6A), so that there was little voltage escape. No change in the half-decay time of the EPSC was observed following reduction of the EPSC to 14 ± 1 % of control with CNQX (n = 5; P = 0·26, Student's t test), indicating that our correction procedure restored EPSC waveforms distorted by the voltage escape across the patch electrode. We have therefore used this approach to calculate the somatic voltage escape for each EPSC in this study and have corrected the EPSC waveform to that expected if there were no voltage escape (with the exception of the experiments involving Sr2+, where voltage escape was negligible).
 |
View larger version [in this window] [in a new window] |
|
|
A, CF EPSCs identified on the basis of paired-pulse depression. Part of the stimulus artifact was omitted for clarity. B, EPSC and failure evoked at just above and just below the stimulation threshold and recorded at high gain to check that no parallel fibre responses were present. C, stimulus-response relationship for climbing fibre EPSCs recorded at 0·2 Hz (excluding failures). The slight relaxation just above threshold is due to the effect of failures around the stimulation threshold and frequency-dependent depression of the synaptic current. Error bars were smaller than symbol size and therefore omitted. D, leak-subtracted voltage-activated currents in a Purkinje cell held at -30 and -60 mV. Depolarizations indicated at the top were incremented by 5 mV. E, simultaneous current and voltage recording at the Purkinje cell soma during CF activation. F, correction of EPSC for escape voltage across the electrode. Correction 1 was done using recorded voltage from E, and correction 2 was done using the voltage escape calculated from compensated electrode resistance. Dashed lines in E and F show baseline level before CF activation. | ||
Consideration of remaining voltage-clamp errors
The time course of the EPSC will be affected by low-pass filtering by the cell circuit. Simulations using a multicompartment model Purkinje cell from a P14 animal with 100 synaptic contacts extending along the primary and secondary dendrites suggests that EPSCs recorded at the soma will yield an underestimate of the synaptic conductance (
65 % of the true value; A. Roth & M. Häusser, personal communication). Since the peak variance will also be reduced, quantal size measured directly and that estimated from MPF analysis will be attenuated by cell filtering to a similar degree. However, this distortion of the synaptic current will have relatively little effect on estimates of release probability because attenuation of the EPSC and attenuation of quantal size (and therefore the maximal response) will be similar.
Correction for voltage escape at the soma by compensating for the voltage drop across the recording electrode does not correct for any voltage drop that occurs due to current flow across the spine neck or down the proximal dendrites. Simulations indicate that at high release probabilities, when the synaptic conductance change is maximal, the drop in driving force down the dendrite could be substantial. However, three experimental observations argue against this being a major problem. Firstly, there was no difference between the quantal size estimated at low release probabilities when the voltage drop was minimal, and the quantal size estimated at high release probabilities when the voltage drop was maximal (see Fig. 5B). Secondly, there was a positive correlation between the synaptic conductance and estimated quantal size (P = 0·01, Spearman rank test). Thirdly, quantal size estimated with MPF analysis was similar to that measured directly with Sr2+ and Cd2+. The simplest explanation of these results is that the drop in the driving force down the dendrite was lower in our recordings than suggested by simulations, possibly due to the synapses being located more proximally than assumed in the simulation. However, we cannot rule out the possibility that the quantal conductance increased with release probability, as a result of spillover of glutamate from neighbouring sites, compensating for the drop in driving force.
Analysis of EPSCs
EPSCs were recorded in solutions containing different [Ca2+] and [Mg2+] that gave a range of different release probabilities for MPF analysis. CFs were stimulated for sufficient time for EPSCs to be recorded at steady state for a particular probability condition. Series resistance and reversal potential were measured at the beginning and end of each epoch and series resistance stability was monitored throughout, from the current response to a voltage step prior to each EPSC. EPSCs were then corrected using these parameters and the command potential. Corrected EPSCs were averaged by aligning on the stimulus artifact (unless there was a frequency-dependent change in latency), and the time of the peak amplitude determined. The amplitude of individual EPSCs was then calculated from the difference between two 0·2 ms windows, one placed just prior to the artifact and the other at the time of the peak of the mean current. Current fluctuations in the background were estimated in the same manner with the two measurement windows shifted into the pre-event baseline. EPSC conductance, variance and CV were calculated from the largest number of contiguous EPSCs whose amplitude showed no temporal correlation (Spearman rank test implemented in MathCad, MathSoft International, UK). MPF analysis data were plotted as CV or variance against mean synaptic conductance (Fig. 2B and C).
Data analysis was carried out using Clampfit (Axon Instruments), Origin 4.10 (Microcal, Northhampton, MA, USA) and Statistica (StatSoft, Tulsa, OK, USA). EPSC decays were fitted with exponential functions using a Simplex routine implemented in 'N' (Stephen Traynelis, Emory University, Atlanta, GA, USA). Plots of CV against mean synaptic conductance, variance against mean synaptic conductance, and EPSC amplitude recovery were fitted using a Levenberg-Marquardt algorithm implemented in Mathematica (Wolfram Research, UK) and SigmaPlot (Jandel, Germany). Each data set was fitted several times with a range of different initial parameters to ensure that the fitted equation converged on one solution. In some fits of CV and variance against mean synaptic conductance plots, the quantal parameters N and q were constrained to be > 0. In most cases fits converged on single finite solutions. However, when local minima occurred these were located and the solution was chosen with the lowest sum of squares of the residuals. Each fit was checked 'by eye' to ensure the equation fitted well to the data. All data reported are expressed as means ±
Estimation of quantal parameters with binomial and multinomial models
We have used two classes of statistical model to estimate quantal parameters from CV-conductance and variance-conductance plots (MPF analysis plots). Simple binomial and multinomial models, which assume that transmitter release probability is uniform, and compound binomial and multinomial models, which incorporate non-uniform release probability.
Uniform release probability models
We first used the simple binomial model to estimate quantal parameters from MPF analysis plots, which assumes that release probability and quantal size are uniform. This can be expressed in terms of CV and conductance, G, (for the CV-conductance plots) where qb (subscript b denotes binomial model) is equal to the quantal size, q, and Nb is equal to the number of functional release sites, N, when there is no quantal variability:
(1)
Alternatively, the same binomial model can be expressed in terms of variance (
It should be noted that if the quantal size is not uniform, qb will not be the true arithmetic mean but weighted towards the larger quantal amplitudes.
In the second model we included intersite quantal variability (this could result from different quantal conductances or imperfect voltage clamp), which was measured directly from asynchronous EPSCs evoked in the presence of Sr2+ (Fig. 3A and B). We took an approach similar to that used by Markram, Lübke, Frotscher, Roth & Sakmann (1997) to derive a simplified multinomial equation that included intersite quantal variability as measured at the soma by assuming that the release probability was uniform and that intrasite variance was negligible (though this can be included in the model if known; see eqn (8)). With these simplifications the multinomial model can be expressed in terms of the CV, quantal size (qm), number of release sites (Nm)
(subscript m denotes multinomial model), and the coefficient of variation of the intersite quantal amplitude, CVqII:
(3)
Alternatively, this multinomial model can be expressed in terms of variance and conductance:
(4)
These simple multinomial and simple binomial functions have an identical shape, and when CVqII = 0 the simple multinomial model reduces to the simple binomial. CVqII cannot be determined from the fit and must be measured independently. In both models the release probability was calculated from the ratio of the synaptic conductance and the maximal synaptic response (the product of N and q).
Effect of non-uniform release probability on the variance-conductance relationship
The simple binomial and simple multinomial models assume a uniform release probability. Since we were unable to measure the release probability at each release site (Pr), we do not know the shape of the Pr distribution, or how this would change as a function of mean release proba{fontsize bility (
f(Pr) = (1/B(
where B(
CVPr = [(1 -
This gave a CVPr as a function of
(6)
Expressing this relationship in terms of synaptic conductance, G:
The EPSC variance expected for non-uniform Pr is less than that for the uniform binomial with the same
The presence of non-uniform Pr may not always result in a variance-mean release probability plot that is skewed towards larger values, since Pr distributions are possible which are not described by our model. If the CVPr is large as
Non-uniform release probability models
We have developed compound binomial and compound multinomial models that incorporate non-uniform release probability because this property appears widespread at central synaptic connections (Jack et al. 1981; Walmsley et al. 1988; Stricker et al. 1996; Issacson & Hille, 1997; Murthy et al. 1997). The theoretical relationship for a synaptic connection with non-uniform Pr and non-uniform q but with no correlation between these two parameters is shown in eqn (8) (see Frerking &Wilson 1996):
(8)
where CVqI is the coefficient of variation of intrasite quantal variation. This general equation has too many free parameters to be useful for extracting quantal parameters. However, it can be simplified by assuming that the dispersion in Pr as a function of
(9)
If CVqII is unknown, the (1 + CVqII2) term can be dropped giving a compound binomial expression.
These models have several advantages. Firstly, the level of non-uniformity in Pr is not assumed. The
(10)
If variance-conductance plots are skewed towards smaller values, eqns (9) and (10) are not appropriate. In such cases, where the CVPr becomes large as
(11)
This equation gives variance-conductance relationships that are mirror images of those for eqn (9) when
Effect of correlations between release probability and quantal size on the variance-conductance relationship
A correlation between quantal size and release probability is theoretically possible at synapses where both release probability and quantal size are non-uniform. Although a recent study (Nusser, Cull-Candy & Farrant, 1997) suggested that no such correlation existed for inhibitory synapses on cerebellar stellate cells, another study suggests a positive correlation between these parameters at excitatory hippocampal synapses (Murthy et al. 1997). We have therefore used simulations to examine how correlations between quantal size and release probability would affect estimated quantal parameters. The release probability was calculated at 100 independent release sites from a cumulative beta distribution (using the InverseBetaRegularized function in Mathematica). This provided a list of 100 ranked Pr values for each mean release probability,
Two quantal distributions were used. In the first model, ranked quantal size was calculated by making the quantal amplitude at each site a linear function of site number. A slope of 1/101 gave a mean q = 0·5, CVqII = 0·57 and a range of q values of 1/101 to 100/101. In the second, biologically more accurate simulation, CF quantal events were used (measured in Sr2+, Fig. 3B). A normalized cumulative distribution was made from 1438 quantal current amplitudes pooled from four cells. A list of 100 ranked quantal sizes was generated from these data by interpolating the cumulative probability verses quantal amplitude plot. Figure 4D shows an example of a negative correlation between q at each site and Pr for a simulation in which measured quantal events were used. The four different plots show the relationship between q and Pr at different mean release probabilities.
Since fits to the correlated variance-conductance relationships gave qualitatively similar results for the two simulations, we only show results from simulations using measured quanta in Sr2+ (Table 1 and Fig. 4). Plots from positive correlations between q and Pr were skewed in a manner similar to those for non-uniform Pr when q was uniform but with an initial slope that was steeper than the weighted mean quantal size (Fig. 4E,
Table 1. Effect of correlations between quantal size and release probability on estimated quantal parameters for simulation with measured quanta in Sr2+
Remaining assumptions
Application of these statistical models assumes (1) a constant number of independent release sites, (2) the quantal size does not vary with time, and (3) linear summation of quanta. Several pieces of evidence indicate that these are appropriate at the CF synaptic connection. The very low EPSC variance observed at high release probabilities (CV = 0·0103 at 0·033 Hz in 4 mM Ca2+, 0·5 mM Mg2+) suggests that any temporal fluctuations in N and release probability must be small. It also argues against any co-ordinated temporal modulation in quantal size at this input. The fact that direct measurement of quantal events recorded in the presence of Sr2+ (Fig. 3A and B; and those in Cd2+) have amplitudes similar to the quantal size estimated from MPF analysis is consistent with release sites being independent and summating linearly. If transmitter released from neighbouring sites overlaps, summation of quantal events might deviate from linear if synaptic receptors were not saturated by a quantum of transmitter. Consistent with transmitter spillover in the CF cleft, the half-decay time of the EPSCs was longer (in 5 out of 6 cells) at high release probabilities (0·96; t½ = 3·7 ± 0·4 ms) than at low release probabilities (0·06; t½ = 2·5 ± 0·1 ms, n = 6; P < 0·05, Student's t test). However, these observations would also be consistent with changes in the release process itself giving different transmitter concentration profiles at different release probabilities.
Quantal parameters underlying transmission at the climbing fibre-Purkinje cell synaptic connection
Synaptic transmission at CF inputs was investigated with patch-clamp recording from visually identified Purkinje cells in cerebellar slices from young rats. We used several strategies to optimize the quality of voltage clamp and we corrected for deviations from the command voltage at the soma (see Methods). The average waveform of CF EPSCs following such correction had a 10-90 % rise time of 0·83 ± 0·03 ms and a peak conductance of 200 ± 23 nS (n = 16; as measured at the soma) when evoked at 0·2 Hz. Since the fit to one exponential function was inadequate, the sum of two exponential functions was used to describe the EPSC decay. The mean time constants were 3·2 ± 0·2 and 10 ± 1 ms (n = 15), with the fast component constituting 82 ± 2 % at the peak.
We investigated the quantal parameters underlying transmission at this synaptic connection with multiple probability fluctuation (MPF) analysis - illustrated in Fig. 2. This figure shows CF EPSCs evoked at 0·2 Hz in solutions with different [Ca2+]/[Mg2+] ratios which gave different probabilities of release. In the presence of high [Ca2+], low [Mg2+], when the release probability was maximal, the EPSC was large. Furthermore, the EPSC amplitude variability, as indicated by the coefficient of variation (CV, standard deviation/mean), was small. As the EPSC amplitude was reduced by lowering [Ca2+] and raising [Mg2+], the CV increased (Fig. 2A). No failures occurred even at the lowest calcium concentration used, ruling out the possibility of contaminating variance arising from failure to stimulate the presynaptic axon. Figure 2B shows the relationship between CV and EPSC (expressed as conductance) for this cell. The data points, recorded at different release probabilities, were well fitted by a simple binomial model (eqn (1), Methods) indicated by the continuous line. Figure 2C shows a plot of variance verses conductance for data from the same cell, fitted with eqn (2) (Methods). This type of plot has been used previously by Clamann et al. (1989) to investigate quantal parameters during post-tetanic potentiation of synaptic currents, and is similar to the convention used for non-stationary noise analysis of ion channels (Sigworth, 1980). It is particularly useful for quantifying q and mean release probability (
By fitting the variance-conductance data with a simple binomial model (eqn (2), Methods) it was possible to estimate the underlying quantal parameters. This approach gave a mean of 510 ± 70 (range, 285-740; n = 6) for the number of functional release sites (Nb; subscript indicates the estimate of N is from the binomial model), and a mean of 0·50 ± 0·04 nS (range, 0·34-0·61 nS) for the quantal size (qb). As the underlying non-NMDA channels are relatively impermeable to calcium (Häusser & Roth, 1997), our estimates of qb and Nb are unlikely to be affected by the changes in Ca2+ that we have used to alter
A, superimposed EPSCs (6 shown) recorded at 0·2 Hz stimulation in different [Ca2+]/[Mg2+] solutions. Holding voltage, -30 mV. B, relationship between CV and mean synaptic conductance at the peak of the EPSC for the cell in A.
Extension of the simple binomial model to include variability in quantal size
Variations in quantal size can occur at an individual release site (the so-called intrasite, type I or temporal quantal variance) or as a result of different quantal sizes at different release sites (intersite, type II or spatial quantal variance). These two types of quantal variance affect the relationship between variance (or CV) and synaptic conductance in different ways (Wahl, Stratford, Larkman & Jack, 1995; Frerking & Wilson 1996; see also Sigworth, 1980, for equivalent situation with ion channel subconductance levels), and can complicate the interpretation of quantal parameters estimated with the binomial model. At high release probabilities (
The total quantal variance (intra- and intersite) can, in principle, be estimated from the distribution of miniature EPSCs. However, except during early development, Purkinje cells are innervated by both parallel and climbing fibre inputs, so it is not possible to measure CF miniature currents in isolation. We have overcome this problem by evoking CF EPSCs in the presence of Sr2+ (which causes desynchronized transmitter release from activated terminals; Abdul-Ghani, Valiante & Pennefather, 1996). This gave a frequency of CF quanta approximately 10-fold higher than the background frequency in the absence of CF stimulation. Figure 3A shows a cell in which CF EPSCs were evoked in 5 mM Sr2+ and 1 mM Mg2+ at 0·2 Hz. We analysed synaptic events in a 520 ms window starting 200 ms after the evoked event, in which there was no correlation of quantal amplitude with time (P > 0·05, Spearman rank test), indicating that the level of postsynaptic receptor desensitization was constant. The distribution of quantal amplitudes was skewed (see Fig. 3B,
If the simple binomial model is used under conditions where q is non-uniform across sites, the estimate of qb will be weighted towards the larger events, and Nb may be underestimated. Under such conditions, a simple multinomial model is required to estimate the true mean quantal size. However, this can be reduced to a simple binomial expression multiplied by a constant that includes the intersite variability (Markram et al. 1997; see Methods). A simple multinomial model (eqn (4)), with a fixed intersite quantal variability of CVqII = 0·37, gave an estimate of 580 ± 80 (n = 6) for the number of functional release sites (Nm; subscript denotes multinomial model), 13·7 % greater than that estimated from the simple binomial (Nb). The mean quantal size (qm) was 0·44 ± 0·03 nS, 88 % of that estimated from the simple binomial (qb). However, since the product of these two parameters was unchanged, estimates of the maximal response and release probability are similar for both models. Both the binomial and multinomial models assume intrasite quantal variance is negligible. If this is not the case, and the CF intrasite quantal variability is close to our estimate of its the upper limit,
A, evoked EPSCs recorded at 0·2 Hz in 5 mM Sr2+, 1 mM Mg2+ at -70 mV. The peak of the EPSC was cropped to illustrate asynchronous quantal events in the tail. Inset shows later EPSCs with initial part of current omitted. Bar indicates analysis window. B, amplitude histogram of 401 asynchronous quantal events from the cell shown in A, yielding a mean quantal size, q, of 0·56 nS and a CV of 0·39.
Non-uniform release probability
A potential problem with the application of simple binomial and simple multinomial models to central synapses is that they assume that the Pr is uniform across release sites. Non-uniformity in Pr has been observed at several central synapses (Walmsley et al. 1988; Rosenmund et al. 1993; Stricker et al. 1996; Isaacson & Hille, 1997; Murthy et al. 1997) and would complicate our analysis because the EPSC variance will be less than for the uniform Pr case and, thus, estimates of quantal parameters will be incorrect (Quastel, 1997). Since we were unable to measure Pr at each release site, we investigated the effects of non-uniformity in Pr on MPF analysis with simulations. We have modelled spatial non-uniformity in Pr by using sets of beta distributions to describe both the Pr distribution (Fig. 4A) and how it changes as a function of
A, examples of beta distributions used to model the distribution of Pr. Continuous lines show three representative examples of distributions with
A, measured variance-mean synaptic conductance plot from a CF input that showed non-uniformity in Pr.
A model that incorporates both non-uniform quantal size and non-uniform release probability
Since the level of spatial non-uniformity in Pr is likely to vary from cell to cell, we developed a multinomial model that includes both non-uniform quantal size and non-uniform release probability (eqn (9)). This compound multinomial model incorporates spatial non-uniformity in Pr, yet remains relatively simple, by assuming that the dispersion in Pr as a function of mean release probability can be approximated by a family of beta distributions with a particular
Testing the method of multiple-probability fluctuation analysis
We have tested our method by comparing results from MPF analysis with several independent measures. One quantal parameter that could be measured directly was the quantal size. As illustrated in Fig. 3B, direct measurement of the quantal size in Sr2+ gave a peak conductance of 0·55 ± 0·01 nS (n = 4), similar to qm estimated from the MPF analysis using the compound multinomial model (P = 0·26; Student's t test). We also estimated the quantal size in the presence of 2 mM Ca2+. This was done by using Cd2+ (a non-specific blocker of calcium channels) to reduce the release probability to very low levels such that it was possible to resolve quantal events (Issacson & Walmsley, 1995; data not shown). The signal-to-noise ratio was relatively low in these Cd2+ recordings, so we estimated the quantal size from the ratio of the variance and mean current (simplification of eqn (2) at low
In a second independent test we reduced the postsynaptic responsiveness to 14 ± 1 % of control (n = 5) with a submaximal concentration (1 µM) of the non-NMDA receptor antagonist CNQX. Figure 6A shows the averaged EPSCs, while Fig. 6B shows the effect of CNQX on the CV-conductance plot. Estimates for Nm were unaffected by CNQX (P = 0·94, Student's t test) but, as expected, the quantal size was substantially reduced (to 13 ± 2 %). Indeed, the ratio of the control quantal size to that in CNQX, estimated from the fit, was not different from the ratio of the EPSC amplitudes (P = 0·09, Student's t test). This demonstrates that the MPF analysis method is capable of correctly assigning a postsynaptic locus to the actions of CNQX. These control experiments confirmed that MPF analysis, when used with an appropriate statistical model, gave quantitative information of quantal parameters at this synaptic connection.
A, averaged EPSCs recorded in control solution (2 mM Ca2+, 1 mM Mg2+ at 0·2 Hz) and in the presence of 1 µM CNQX. Stimulus artifact omitted for clarity. B, relationship between CV and synaptic conductance measured from EPSCs recorded at different frequencies (0·033-10 Hz) in control solution (
Table 2. Estimated quantal parameters at the climbing fibre synapse
Quantal parameters measured during frequency-dependent depression
One of the most striking features of the CF input is the frequency dependence of the EPSC amplitude during sustained stimulation. This is illustrated in Fig. 7A, which shows averaged CF EPSCs obtained at different stimulation frequencies (0·033-10 Hz) under steady-state conditions. The relationship between EPSC peak amplitude and stimulus frequency is shown in Fig. 7B. At 10 Hz stimulation the mean peak current was only 2 ± 1 % (n = 4) of that at 0·033 Hz. In general, such depression could arise presynaptically, as has been long established at the NMJ (del Castillo & Katz, 1954b). But, at central synapses the situation is more controversial since both presynaptic (Larkman et al. 1991; Mennerick & Zorumski, 1995; Borst & Sakmann, 1996; von Gersdorff et al. 1997) and postsynaptic (Trussell et al. 1993; Zhang & Trussell, 1994) mechanisms have been proposed. We have investigated the locus of depression at the climbing fibre-Purkinje cell connection by establishing how the underlying quantal parameters were affected by stimulation frequency.
A, averaged EPSCs from the same input recorded at different simulation frequencies. Inset shows the same 5 and 10 Hz data at a higher gain. Mean currents were collected once EPSC amplitude had reached steady state. Part of the stimulus artifact was omitted for clarity. B, frequency dependence of EPSC peak amplitude. EPSC amplitude was normalized to the peak amplitude at 0·033 Hz. For all points, n = 5 (except 10 Hz, n = 4).
In the MPF analysis described above (Fig. 2), EPSCs were recorded at a fixed low frequency of stimulation, and different release probabilities were set by varying the [Ca2+]/[Mg2+] ratio of the external solution. We repeated this protocol at a higher stimulation frequency to examine which of the quantal parameters changed during the depression of the synaptic conductance. Figure 8A shows that changing the stimulation frequency from 0·2 to 3 Hz resulted in a significant depression in the EPSC amplitude in 2 mM Ca2+ and 1 mM Mg2+, as expected. The plots in Fig. 8B and C show the CV-conductance and variance-conductance relationships recorded at 3 Hz stimulation. In both cases the data collected at 3 Hz fall on the same theoretical relationships estimated from the low-frequency data illustrated in Fig. 2 (continuous lines) but are shifted to smaller amplitudes, indicating that N and q remain the same for these two stimulation frequencies. When the variance-conductance plots obtained at 3 Hz were fitted (with
A, mean EPSC waveforms recorded at 0·2 and 3 Hz in 2 mM Ca2+, 1 mM Mg2+ at -30 mV. B, relationship between CV and mean synaptic conductance for 3 Hz stimulation. C, relationship between variance and mean synaptic conductance for 3 Hz stimulation. Data in A, B and C are from the same cell as shown in Fig. 2. In B and C, each data point shows a measurement made at a different release probability set with a particular [Ca2+]/[Mg2+] solution, and the continuous lines are the binomial relationships derived from data in Fig. 2 (a compound multinomial fit to these data gave a relationship with a similar shape,
We next examined whether depression of the EPSC was still presynaptic at frequencies up to 10 Hz. However, instead of changing the [Ca2+]/[Mg2+] ratio and stimulating at a single frequency, we recorded synaptic currents at several different frequencies in the same external solution. As shown in Fig. 9, simply changing the stimulation frequency over the range 0·033-10 Hz gave a full variance-conductance relationship where each data point corresponds to a single frequency of stimulation. Fitting the compound multinomial model to variance-synaptic conductance plots gave values of 420 ± 50 for Nm and 0·76 ± 0·1 nS for qm (n = 5). Two factors complicate comparison of these estimates with those where the [Ca2+]/[Mg2+] ratio was altered. There was a significant positive correlation between qm and G (recorded in 2 mM Ca2+ at 0·2 Hz; r = 0·7363, P = 0·01, Spearman rank test, slope = 1·49 × 10-3) and a difference in the synaptic conductance between the two groups of cells (group mean at 0·2 Hz; 271 and 199 nS). When these factors were taken into account by normalizing to a synaptic conductance of 200 nS there was no difference between the two qm values (P = 0·148; see Table 2 for values). The
A, relationship between variance and synaptic conductance at the peak of the EPSC recorded at different frequencies in 2 mM Ca2+, 1 mM Mg2+. Continuous line shows the compound multinomial fit. The large
Testing for the presence of presynaptic metabotropic receptors
We investigated whether metabotropic glutamate receptors (mGluRs) mediate frequency-dependent depression at the CF terminal by applying antagonists to group I, II and III mGluRs at different stimulation frequencies. EPSC amplitude remained unchanged in the presence of 500 µM MCPG, 200 µM MTPG or 250 µM MPPG at both low (0·2 Hz) and high (3 or 5 Hz) stimulation frequencies (n = 3). Furthermore, the mGluR agonist L-AP4 (50 µM), had no effect on the climbing fibre EPSC at 0·2 or 3 Hz (n = 4, P > 0·05, Student's t test). These results indicate that frequency-dependent depression at the CF is not mediated by activation of mGluRs.
Temporal characteristics of transmitter release probability
To understand the temporal characteristics of presynaptic depression in more detail, we used two experimental approaches to gather information about release probability kinetics. First, we used paired-pulse stimulation repeated at low frequency (0·033 Hz), which induced presynaptic depression.
Interpreting EPSC recovery from depression in terms of release probability assumes that the depression is presynaptic, as we have shown for sustained stimulation up to 10 Hz. However, in the paired-pulse experiments, depression of a second EPSC after a 100 ms interval is not directly comparable with the depression by sustained stimulation at 10 Hz because
Figure 10B shows several superimposed paired-pulse trials; as the interval between the two EPSCs was increased from 100 ms, the amplitude of the second EPSC recovered. In five out of six cells, a single exponential function gave a poor fit to the recovery data. In these cells a fit to the sum of two exponential functions gave time constants of 350 ± 90 ms (37 ± 7 %) and 3·2 ± 0·4 s (n = 5) as illustrated in Fig. 10C. Since
A, relationship between release probability and stimulation frequency calculated from the relationship in Fig. 7B. B, seven superimposed trials from a paired-pulse experiment with stimulus artifacts removed for clarity. The intertrial period was 30 s, so the first EPSC of the pair (EPSC1) had a high release probability (
In order to establish whether processes with similar kinetics were involved during sustained stimulation, we used a second approach, illustrated in Fig. 11A. This shows an example of the onset time course of EPSC depression during a 180 s train at 2·8 Hz stimulation. The amplitude of the second EPSC in the conditioning train dropped to 57 ± 4 % (n = 5) of the first EPSC. The subsequent depression in EPSC amplitude (small circles) could not adequately be described by a single exponential function in three out of five cells, so a dual exponential function was used. In the remaining two cells the onset was well fitted with a single exponential, and this had a the time constant similar to the slow component of the dual exponential fit in the other cells (
A, onset and recovery of EPSC amplitude with sustained stimulation. Filled bar indicates duration of stimulation at 2·8 Hz; open bar indicates variable interpulse interval. Small open circles indicate onset time course of depression after first EPSC (mean of 4 trials); large open circles show EPSC1 and last EPSC (each point a single trial; EPSCrecovery). Each trial was separated by an interval of 200 s to ensure full recovery of
In this paper we describe a new quantal analysis method which is applicable when quantal size and release probability are both non-uniform. We have used this method to investigate transmission at the cerebellar climbing fibre-Purkinje cell synaptic connection. We show that this distributed synaptic input has a large number of functional release sites and that the mean release probability across all sites is high at low stimulation frequencies. As the frequency of stimulation increases, the release probability falls off dramatically due to a slow recovery of release probability at each site. These properties appear specialized to act as a low-pass filter, promoting reliable transmission at low frequencies but inhibiting transmission at sustained high frequencies.
Multiple-probability fluctuation analysis
The major experimental difference between MPF analysis and previous quantal analysis methods (del Castillo & Katz, 1954a; Clamann et al. 1989; Malinow & Tsien, 1990; Bekkers & Stevens, 1990; Frerking & Wilson, 1996) is that quantal parameters are estimated from multiple measurements made over a wide range of experimentally imposed release probabilities at a single input (but see Miyamoto, 1975). This approach has several advantages. Estimating q and N from a number of measurements made under different probability conditions is likely to provide more reliable quantal estimates than if only a single experimental condition is analysed. Unlike methods that involve fitting amplitude histograms, MPF analysis allows quantitative estimates of N and q at synaptic connections where quantal size is non-uniform. This property may be widespread in the CNS neurons, as many miniature distributions are highly skewed. This could result from intra- or intersite non-uniformity in q or from spatial non-uniformity in q arising from electrotonic attenuation of signals from more distal synapses. If it is not possible to estimate quantal variability independently from the mini distribution, application of the binomial model will give a weighted mean quantal size that deviates from the true mean by a factor of 1 + CVq2.
The other main advantage of MPF analysis is that the shape of the relationship between variance and mean synaptic conductance contains information about the dispersion in Pr. This allows application of models that do not assume that release probability is uniform or that dispersion in Pr occurs at any fixed level across cells. Recent direct measurements of CVPr at hippocampal synapses (0·3-0·7; Isaacson & Hille 1997; Murthy et al. 1997), and the substantial effect of non-uniform Pr on uniform statistical models (see Methods), highlight the importance of methods that incorporate non-uniform release probability (Jack et al. 1981; Walmsley et al. 1988; Stricker et al. 1996). It should be noted, however, that although our method incorporates dispersion in Pr, it is possible that errors in estimating q and N could arise if q and Pr were strongly correlated (see Methods for extreme case). Since errors in estimated N and q occur in opposite directions and therefore cancel when multiplied together, estimates of mean release probability are relatively insensitive to these complicating synaptic characteristics. At the CF synapse such correlations, if present, must be weak given the similarity between the quantal size estimated from MPF analysis and that measured independently.
MPF analysis is applicable to other types of synaptic connections, even those where peaks in amplitude histograms cannot be resolved. It may therefore be useful in identifying the quantal parameters that change during other forms of synaptic plasticity such as long-term potentiation and long-term depression. To extract the full quantal description of the synapse with MPF analysis, it is necessary to manipulate 
2) and conductance (for the variance-conductance plots):
2 = qbG - (G2/Nb). (2)
r). We have therefore used simulations to examine the effect of non-uniform Pr on the shape of the EPSC variance-conductance relationship. The effect of non-uniform Pr was modelled with beta distributions implemented in Mathematica. Beta distributions such as those illustrated in Fig. 4A were generated with the density function:
,
))Pr-1(1 - Pr)-1,
,) is the beta function. Since the mean of a beta distribution is simply /( + ), a particular distribution can be defined in terms of its mean and . Each simulated Pr distribution could therefore be defined in terms of and mean release probability r, by substituting for where = /r - . This approach allowed a large set of different beta distributions to be generated for a particular value by varying r from 0 to 1. A wide variety of distribution shapes was covered by using a range of values (0·1, 0·5, 0·9, 1, 2 and 5) to generate the sets of distributions (i.e. compare = 1 and = 5 in Fig. 4A). It is therefore likely that some of these simulated distributions will approximate the true distribution of Pr. This approach is strengthened by the fact that the measured Pr distribution for hippocampal synapses in culture (Murthy et al. 1997) is described by a gamma distribution, which is closely related to the beta distribution. Having constructed a set of distributions for each value that covers the full range of r, the coefficient of variation of release probability (CVPr) was then calculated for each distribution from eqn (5):
r)/(r + )]½. (5)
r, illustrated in Fig. 4B for = 0·1, = 1, and = 5. The relationship between the expected EPSC variance and mean release probability was then calculated using eqn (6):
2 = qbG - (G2 / Nb)(1 + CVPr2). (7)
r by an amount equal to Nbqb2 times the variance of Pr (Pr2 ). Distortion of the variance-r relationship (Fig. 4C) and the variance-conductance relationship from the parabolic uniform Pr case therefore depends on the degree of dispersion of Pr. Because dispersion of Pr at the CF synaptic connection and its dependence on r are unknown, it is not possible to calculate the precise errors involved. However, because the effect of non-uniform Pr becomes minimal as r becomes small (see eqn (6)), the initial slope of the variancer (or conductance) relationship was similar to the uniform Pr case (Fig. 4C) even when non-uniformity in Pr was relatively large (Fig. 4B) and the relationship markedly skewed towards larger values (i.e. less variance in higher r regions). In such cases estimates of q from low r regions are less affected by dispersion in Pr. Reliable estimates of N can therefore be obtained with a uniform model when Pr is non-uniform by combining such estimates of q with estimates of Gmax = Nq from high r measurements.
r 
0 and decays more rapidly as a function of r than the examples in Fig. 4B, the second term in eqn (6) can become significant at low r values. Under these conditions the variance-conductance relationship may be skewed towards smaller values with the initial slope significantly lower than the uniform case, giving an underestimate of q. In such cases the steeper slope at high r values will provide a more accurate estimate of q. This situation can be modelled with beta distributions where is varied as a function r and is kept constant (see below). We have not used this model (derived below) at the CF synapse as variance-conductance plots that were not symmetrical were skewed towards larger values. It is also possible that the variance-conductance relationship could be parabolic when CVPr > 0 if it is constant over the full Pr range (see eqn (7)). However, this could only occur if synapses were present with Pr = 0. Since we define N as the number of functional release sites, the variation in release probability due to 'silent' synapes (i.e. release sites where Pr remains at 0) can be disregarded. If such sites are excluded, CVPr must become lower when the mean release probability approaches 1 because 0 < Pr 
1. Thus, any non-uniformity in Pr must be associated with a CVPr that depends on r. A symmetrical variance-conductance plot could only occur with non-uniform Pr if the CVPr-r relationship was such that it compensated for the reduced effect of CVPr at low r values. This situation seems unlikely.
r (CVPr in the relationship) can be approximated by a family of beta distributions with a particular value. By substituting CVPr in eqn (8) for eqn (5), a compound multinomial relationship can be derived. When CVqII is known from the mini distribution and intrasite variance is negligible, qm, Nm and are the only free parameters:
value (and therefore the CVPr ) is determined by the shape of the variance-conductance data. This approach will therefore be applicable to cases where each cell in the population has a different Pr distribution. Secondly, the full MPF analysis plot can be fitted even when the variance-conductance relationship is highly skewed, allowing more accurate estimates of the underlying quantal parameters than from initial slope estimates. Thirdly, these models include the simple multinomial model (or the simple binomial model) as one of the solutions ( r, which can be calculated from and eqn (5). However, it should be noted that the estimated value indicates the family of beta distributions that can generate the fitted relationship. It does not necessarily imply that the Pr distributions underlying the EPSCs are beta distributions. Even if the underlying Pr distributions are not well approximated by a beta distribution, eqn (9) is likely to provide a better estimate of the initial slope of the relationship, and thus qm and Nm, than the uniform Pr model. If finding a solution to eqn (9) is problematic, initial guesses for the fit can be determined from the variance-conductance plot normalized by the maximal conductance (Gmax 
Nmqm)by applying a simplified version of eqn (9) where only qm and are free parameters and where Gn is G/Gmax:
r 0 and the relationship decays rapidly with r, the steeper slope of high r region will give a more accurate estimate of q. Quantal parameters can be estimated under these conditions with a related model, again based on the beta distribution, but where is varied instead of . As r becomes small, becomes small and thus CVPr becomes very large. The equation for this model can be derived from the mean and variance of a beta distribution (in a similar way to eqn (9)) but by substituting for ( = r /(1 - r) instead of , giving eqn (11):
and have the same value in the two equations. The large range of solutions to eqns (9) and (11) make these models applicable to synapses with a wide range of underlying Pr distributions.
r. Simulations with different levels of non-uniformity in Pr were generated by using a range of values (5, 1, 0·5 and 0·1). A positive correlation between Pr and quantal size was produced by ranking quantal amplitudes as a function of site number. A negative correlation was generated by simply reversing the ranking order of q. The mean synaptic conductance and variance were calculated by summing qPr and mean square conductance-mean conductance squared over the 100 release sites. Quantal parameters were estimated from variance-conductance plots by fitting the compound multinomial model (eqn (9)).
). With negative correlations, variance-mean release probability relationships exhibited rather symmetrical shapes (Fig. 4E, 
). This presumably resulted from two effects that distort the relationship in opposite ways: a skew towards larger values from non-uniform Pr (see Fig. 4C) and a skew towards smaller values from low Pr sites with large quantal size which will generate substantial variance at high r values. The variance was lower than for the uncorrelated case (Fig. 4E, continuous line; eqn (8)) and resulted in underestimates of qm and over estimates of Nm. However, it should be noted that for both simulations the correlation is the strongest possible for the quantal amplitude distribution and the beta distribution of release probabilities. Thus, distortions in the estimates of qm and Nm (Table 1) probably represent an extreme case. Furthermore, both positive and negative correlations gave reliable estimates of r.
Correlation between q and Pr qm = 0·653 nS Nm = 100 Nmqm = 65·3 nS valuePositive correlation = 50·75 86 64·4 1·19 = 10·92 69 63·1 0·40 = 0·51·05 60 63·1 0·22 = 0·11·73 35 60·5 0·05 Negative correlation = 50·51 133 67·2 54304 = 10·33 207 67·5 404 = 0·50·29 237 69·5 1·31 = 0·10·16 423 67·6 0·32
RESULTS
Top
Abstract
Introduction
Methods
Results
Discussion
References
r), and showing changes in the latter. The relationship was parabolic with variance minima occurring at both low and high probabilities of release and maximal variance at an intermediate r.
r.
View larger version
[in this window]
[in a new window]
Figure 2. Estimating quantal parameters with MPF analysis
, measurements made at different release probabilities, set by the [Ca2+]/[Mg2+] ratio at 0·2 Hz. , measurement recorded at 0·033 Hz. The continuous line is a simple binomial fit to the data (eqn (1)). C, relationship between variance and mean synaptic conductance at the peak of the EPSC (same cell as A and B). Continuous line shows the fit with a binomial relationship (eqn (2)), which gave Nb = 285 and qb = 0·61 nS for this cell.
r 1), only variance arising from intrasite quantal variation remains. An upper limit can therefore be estimated for intrasite quantal variability from the CV of the EPSC (0·0103 ± 0·0009, n = 6, in 4 mM Ca2+/0·5 mM Mg2+), the quantal size (recorded independently, see below) and the number of release sites.
This gave an upper limit of CV = 0·19 indicating that quantal variability at an individual site is relatively low.
) and had a CV of 0·37 ± 0·01 (background noise corrected; n = 4). Since the intrasite variability was relatively small, this measure of total quantal variability can be used as an estimate for intersite quantal variability. It is possible that this could still be an underestimate of intersite variability for MPF analysis because any voltage drop down the dendrite during CF-evoked currents would increase variability seen at the soma (see Methods).
r could be underestimated by 4 %.
View larger version
[in this window]
[in a new window]
Figure 3. Variation in quantal size
, background noise.
r (Fig. 4B). These models indicate that large dispersions in Pr can result in substantial distortion of the EPSC variance-conductance relationship (Fig. 4C). However, they also show that estimates of q made from low r regions are likely to be little affected by dispersion in Pr when the variance-conductance relationship is skewed towards larger values. Although the pooled variance-conductance data (normalized to the maximum conductance from each cell) had a symmetrical parabolic shape (Fig. 5B), indicating that there was little systematic dispersion in release probability, some plots from individual cells (Fig. 5A) were skewed towards larger values, consistent with dispersion in Pr at some climbing fibre connections (see below).
View larger version
[in this window]
[in a new window]
Figure 4. Effect of non-uniform release probability on MPF analysis
= 1 and r as specified on the graph (in parentheses). Dashed line shows a single example of a beta distribution from the set generated with = 5. B, relationship between the coefficient of variation of Pr (CVPr) and r for sets of beta distributions with = 0·1, = 1 and = 5. Each curve was generated by calculating CVPr (eqn (5)) for 100 beta distributions where was constant and r = /( + ). , values for the three = 1 distributions and one = 5 distribution shown as examples in A. C, relationship between predicted EPSC variance and r, for uniform and non-uniform Pr cases. All plots were calculated assuming N = 600 and q = 0·44 nS using eqn (6). Dotted line indicates the case for uniform Pr (where CVPr = 0). Continuous lines show the non-uniform Pr cases where CVPr was calculated as a function of r using eqn (6) with = 0·1, = 1 and = 5 (as shown in B). D, simulated negative correlations between quantal size and release probability at each site. Examples of relationships between Pr and q for a simulated synapse with 100 release sites at four different mean release probabilities values (shown in parentheses). The Pr was calculated from cumulative beta distributions ( = 1) and q was derived from measured quantal amplitudes recorded in Sr2+ (see Methods). The mean and CV of q were 0·653 nS and 0·426, respectively. The negative correlation was generated by positively ranking Pr and negatively ranking q with site number. E, normalized variance-mean release probability relationships for simulated synapses with correlations between Pr and q. , negative correlation between Pr and q for the same simulation as D. , corresponding positive correlation between Pr and q. Continuous line shows theoretical relationship for the same case when Pr and q are not correlated. Dotted line shows the theoretical relationship for the same non-uniform q when Pr is uniform. Results of fits of the compound multinomial model to correlated data are shown in Table 1.
View larger version
[in this window]
[in a new window]
Figure 5. Individual and pooled variance-conductance plots
, recorded at 0·2 Hz; , recorded at 0·033 Hz. The continuous line shows the fit to the compound multinomial model (eqn (9)) with qm = 0·40 and Nm = 639. If the underlying Pr distribution approximates a family of beta distributions, CVPr can be calculated from using eqn (5) (see Methods). B, pooled variance-conductance relationship normalized by peak conductance. , pooled data from six cells where data from each cell were normalized by the maximal conductance (Gmax), so the abscissa is approximately equal to r. The dotted line shows the fit using eqn (10) (qm = 0·47). The continuous lines show a fit for the simple multinomial model over the low r range (r = 0-0·3, qm = 0·46) and the high r range (r = 0·7-1·0, qm = 0·44). The similarity in the quantal estimates from the different r regions, and the high value obtained with the compound multinomial fit, indicates that there was no systematic distortion of the variance-conductance relationship by non-uniform Pr at the CF synaptic connection.
value (see Methods). Application of the compound multinomial model gave estimates of qm = 0·50 ± 0·03 nS, with a range of 0·40-0·58 nS, and Nm = 510 ± 50, with a range of 313-652 (n = 6). The dispersion in Pr, as indicated from the value, ranged from 1·2 to 5·1 × 104 for the six cells. In half of the cells < 10, indicating significant dispersion in Pr (Fig. 5A; this can be calculated from using eqn (5) - but see Methods for interpretation). However, when the compound multinomial model was fitted to the pooled data (Fig. 5B), the large value obtained (104) confirmed that there was no systematic distortion of the variance-conductance relationships by dispersion in Pr at the CF synapse.
r), as this did not rely on separating events from failures. The quantal size was 0·64 ± 0·09 nS (n = 5), not significantly different from qb estimated from MPF analysis using the compound binomial model (P = 0·47; see Table 2 for comparison of quantal size obtained with different methods).
View larger version
[in this window]
[in a new window]
Figure 6. Testing the MPF analysis method
) and in the presence of 1 µM CNQX (). The dotted lines indicate measurements made at the same frequency. In the presence of CNQX the synaptic conductance was reduced but the CV remained similar. The continuous lines show the compound multinomial fit to the two data sets. The quantal size, estimated from the fit, was substantially reduced in CNQX, but the number of release sites was similar to control.
Method Quantal size (nS) Number of release sites Number of cells [Ca2+]/[Mg2+] change at 0·2 Hz Simple binomial model 0·50 ± 0·04 510 ± 70 6 Simple multinomial model 0·44 ± 0·03 580 ± 80 6 Compound multinomial model 0·50 ± 0·03 510 ± 50 6 (corrected for synaptic conductance) 
(0·50 ± 0·04) [Ca2+]/[Mg2+] change at 3 Hz Compound multinomial model * 0·50 ± 0·04 810 ± 220 ² 6 Frequency change (0·033-10 Hz) Compound multinomial model 0·76 ± 0·1 420 ± 50 5 (corrected for synaptic conductance) (0·63 ± 0·07) Frequency change in CNQX Compound multinomial model (0·033-5 Hz) * 0·100 ± 0·004 480 ± 170 5 Direct measurement Sr2+ 0·55 ± 0·01 - 4 Cd2+ 0·64 ± 0·09 - 5 qm corrected for positive correlation between qm and G (recorded at 0·2 Hz), value expected for G of 200 nS. * Compound multinomial model with constrained to control value as only part of r range present or too few points to estimate accurately. ² Poorly constrained as estimated from the linear, low r region of the relationship.
View larger version
[in this window]
[in a new window]
Figure 7. Frequency-dependent depression of the CF EPSC
values constrained to the 0·2 Hz control value) they gave a value of qm that was not different (qm = 0·50 ± 0·04 nS; P = 0·86, Student's t test) from that obtained at 0·2 Hz. This demonstrates that the EPSC depression at 3 Hz stimulation is caused by a reduction in release probability rather than by a change in the postsynaptic responsiveness.
View larger version
[in this window]
[in a new window]
Figure 8. Quantal parameters during frequency-dependent depression
= 10·7). The fact that the 3 Hz data fall on the same binomial relationship indicates that the EPSC depression was caused by a reduction in release probability rather than a change in N or q.
values (mean = 4·4; range, 0·5-18; and synaptic conductance were not correlated, P = 0·4) obtained from variance-conductance plots where frequency was varied indicate that dispersion in Pr became greater at higher stimulation frequencies. If a beta distribution is a good approximation to underlying Pr distribution, the values we observe at the CF correspond to a range of coefficient of variation of release probabilities that overlap with those estimated directly at hippocampal synapses (Issacson & Hille, 1997; Murthy et al. 1997). These results strongly suggest that frequency-dependent synaptic depression at this connection is entirely presynaptic over the range 0·033-10 Hz. Calculation of r for the frequency range over which depression was presynaptic showed that there was a 50-fold reduction in release probability between the lowest and highest stimulation frequencies (see Fig. 10A). The mean release probability ranged from 0·90 ± 0·03 (n = 5) during stimulation at 0·033 Hz to 0·02 ± 0·01 at 10 Hz (n = 4; recorded in 2 mM Ca2+, 1 mM Mg2+).
View larger version
[in this window]
[in a new window]
Figure 9. Variance-conductance plots generated by changing stimulation frequency
value indicates that Pr is relatively uniform at this synapse. B, a variance-conductance plot from a cell that showed significant dispersion in Pr. Note the skewed shape of the plot and the low value of the fitted compound multinomial function (eqn (9)). C, pooled normalized variance-conductance relationship obtained at different stimulation frequencies. Symbols show data from five CF inputs where data from each cell were normalized by the maximal conductance (Gmax), so the abscissa is approximately equal to r. The continuous line shows the compound multinomial fit using eqn (10) (qm = 0·71). The value of the fit to this pooled data indicates a relatively small systematic distortion by non-uniform Pr.
r for the first EPSC in the pair (EPSC1, Fig. 10B) was close to one. We tested whether a paired-pulse depression at a 100 ms interval was presynaptic by estimating the quantal size from variance-conductance relationships constructed from the first and second EPSCs in the pair. The mean quantal size estimated from a simple multinomial fit was 0·39 ± 0·05 nS (n = 5) in these experiments, not significantly different from the quantal size estimated from MPF analysis (0·44 nS; P = 0·46, Student's t test). However, we cannot rule out the possibility that a small contribution of desensitization remains but is not detectable with our method.
r for EPSC1 was close to one, this biphasic recovery represents the time course of recovery of r following transmitter release at practically all release sites.
View larger version
[in this window]
[in a new window]
Figure 10. Recovery of
r following transmitter releaser, ~0·90). The dashed line indicates the full recovery amplitude. C, EPSC recovery plot for the same cell as shown in B. This was constructed by plotting the ratio of the paired EPSC amplitudes against the paired-pulse interval. Each data point indicates the results from an individual paired-pulse trial, except the 30 s point, which was normalized to one. The continuous line shows the fit to the sum of two exponentials. Since the depression is presynaptic, this represents the time course of recovery of r following release at almost all sites.
1 = 0·9 ± 0·4 s, 32 ± 5 %, n = 3; 2 = 34 ± 3 s, n = 5). Each conditioning train was followed by a single EPSC of variable latency (EPSCrecovery, large circles in Fig. 11A), and trials were separated by an interval of 200 s to allow full recovery of r. The pooled recovery time course data (n = 5), shown in Fig. 11B, were fitted with the sum of two exponentials with time constants of 1·7 s (amplitude, 61 %) and 24 s. These results indicate that following release the recovery of r is slow at the CF synapses and that the kinetics of recovery of the presynaptic terminal depends on the stimulation protocol and therefore on the history of the synapse.
View larger version
[in this window]
[in a new window]
Figure 11. Onset of and recovery from depression of
r with sustained transmitter releaser. Dashed line shows amplitude of EPSC1 and thus the full recovery amplitude. B, recovery time course data for five cells. Time course was constructed by plotting the ratio of EPSCrecovery and EPSC1 against the interval between the last EPSC in the 2·8 Hz train and EPSCrecovery. The continuous line shows the fit to the sum of two exponential functions. Since the depression is presynaptic at this frequency, the time course represents the recovery of r following sustained release.
DISCUSSION
Top
Abstract
Introduction
Methods
Results
Discussion
References
r over a wide range, as the shape of the relationship is necessary for models that incorporate non-uniform Pr. Fortunately, synapses with a low r in control conditions often exhibit presynaptic facilitation, so inducing such facilitation, or increasing calcium, could be used to raise r to levels suitable for MPF analysis. If varianc
