Abstract
Focal extracellular recording at visualized boutons of the Drosophila larval neuromuscular junction was used to determine frequency and time course of the spontaneously occurring quantal events. When simultaneous intracellular recordings from the innervated muscle cell were made, more than one class of quantal event occurred at some of the individual boutons. “True” signals (arising at the bouton within the focal macropatch electrode) were often contaminated by additional signals generated outside the lumen of the focal electrode. Inclusion of these contaminating signals gave spuriously low values for relative amplitude, and spuriously high values for spontaneous quantal emission, for the synapses within the focal electrode. The contaminating signals, which appeared to be conducted along the subsynaptic reticulum surrounding the nerve terminals, generally were characterized by relatively small extracellular signals associated with normal intracellular events in the muscle fiber. From plots of simultaneous extracellular and intracellular recordings, the individual data points were classified according to the angles they subtended with the x axis (extracellular signal axis). Statistical procedures were developed to separate the true signals and contaminants with a high level of confidence. Populations of quantal events were found to be well described by Gaussian mixtures of two or three components, one of which could be characterized as the true signal population. Separation of signals from contaminants provides a basis for improving the estimates of quantal size and spontaneous frequency for the synapses sampled by the focal extracellular electrode.
INTRODUCTION
The Drosophila larval neuromuscular junction, originally brought forward for physiological investigation byJan and Jan (1976), has proved in the past few years to be increasingly significant for studies of the basic mechanisms of synaptic transmission. The availability of mutants affecting specific components of the neuromuscular synapse (Broadie et al. 1994; Dudai et al. 1976; Jan and Jan 1978; Ranjan et al. 1998), and the facility with which transgenic flies with altered expression of genes important for synaptic structure and function can be produced and used (Davis et al. 1996) have encouraged physiological analysis of the readily accessible larval neuromuscular junction. The growing significance of the preparation for synaptic studies justifies efforts to improve the procedures used to obtain data from it (Stewart et al. 1994). The present study is based on the observation that quantal events recorded at individual varicosities of the neuromuscular junction with focal extracellular electrodes may consist of more than one population. Procedures for dealing with this situation are described. These may be applied to other neuronal or neuromuscular structures in which similar circumstances arise.
Presynaptic performance is often assessed by measuring quantal release from synapsebearing nerve terminals. For this, an extracellular “macropatch” electrode (Dudel 1981) is placed over a nerve terminal to record spontaneous and nerveevoked signals (extracellular voltages or currents) caused by release of transmitter and its subsequent opening of ligandgated channels in the postsynaptic membrane. An estimate of the relative amplitude and time course of the quantal event can be made by analyzing the spontaneously occurring signals (Fatt and Katz 1952), whereas the number of quantal events appearing in response to nerve impulses is often calculated by taking the ratio of the evoked response to the spontaneously occurring quantal event (Cooper et al. 1995; Katz 1966). The macropatch recording method was introduced for the Drosophila preparation byMallart et al. (1991) and is now being widely used with variation in technique (Davis and Goodman 1998;Davis et al. 1996, 1998; Heckmann et al. 1997). It has also been used extensively for other preparations, including crayfish and frog neuromuscular junctions (Cooper et al. 1996; Parnas et al. 1982;Van der Kloot and Naves 1996;), smooth muscle neuromuscular junctions (Bennett et al. 1993, 1996;Cunnane and Manchanda 1989), and most recently for neurons of the mammalian CNS (e.g., Forti et al. 1997).
While examining spontaneously occurring quantal events in macropatch recordings, we observed that errors in estimating their amplitudes often occur due to contaminating signals arising from sites on the terminal close to but not inside the lumen of the macropatch electrode. The problem is inherent in the relatively low seal resistance of the macropatch electrode. The extraneous signals appear to be conducted along the subsynaptic reticulum (SR) surrounding the nerve terminal (Atwood et al. 1993; Osborne 1967), which can never be effectively sealed at the edge of the recording electrode without damaging the nerve terminal. A similar observation was reported for the frog neuromuscular junction by Van der Kloot and Naves (1996), who found that extracellular signals could be recorded ≤0.8 mm away from the extracellular electrode. In this report, we provide a demonstration of this effect and a statistical method for distinguishing extralumenal contaminating signals from those arising at the recording site (“true” signals). We show that separation of the contaminating signals provides a more accurate estimate of the amplitude and frequency of the spontaneously occurring quantal events at a defined nerve terminal.
METHODS
Physiological procedures
CantonS Drosophila melanogaster wandering third instar larvae reared on cornmeal medium (at 25°C, 60–70% relative humidity) were dissected and prepared for electrophysiological recordings from muscle 6 of segment 3 as previously described (Stewart et al. 1994). Experiments were conducted at room temperature in hemolymphlike physiological solution (HL3) of the following ionic composition (in mM): 70.0 Na^{+}, 5.0 K^{+}, 1.0 Ca^{2+}, 20.0 Mg^{2+}, 10.0 NaHCO_{3}, 5.0 trehalose, 115.0 sucrose, and 5.0 BES (Stewart et al. 1994).
The organ bath containing the preparation was secured onto the stage of an upright microscope (Nikon, Optiphot2) equipped with a Nikon ×40 waterimmersion lens (N. A. 0.55) and Nomarski optics. Live images of the nerve terminals were viewed on a computer (Apple Power Macintosh 7500/100 using the builtin frame grabber) through a lowlightintensity TV camera (Panasonic, WVBP310) mounted onto the microscope, enabling accurate placement of the focal macropatch electrode over the chosen bouton. Narishige hydraulic manipulators mounted on the microscope stage were used to maneuver the recording and stimulating electrodes underneath the water immersion lens.
Electrical recordings
Simultaneous intracellular and extracellular recordings of spontaneously occurring quantal events were made (Fig.1, A and B). Intracellular electrodes (40–60 MΩ), filled with a 2:1 mixture of 3 M potassium acetate to 3 M potassium chloride, were used to record the spontaneous miniature excitatory junctional potential (mEJP). Impalements displaying a resting membrane potential more negative than −70 mV were chosen for analysis. The focal macropatch electrode (tip diameter, 3–5 μm) used to record spontaneous excitatory junction currents extracellularly at selected varicosities was manufactured as previously described (Stewart et al. 1994) and filled with HL3 solution. The tip diameters of these electrodes were made to enclose the selected bouton, minimizing direct pressure on it. After impalement of the muscle fiber by an intracellular electrode, the focal macropatch electrode was placed over the chosen bouton (Kurdyak et al. 1994) (Fig. 1 A).
Signals from the focal macropatch and intracellular recording electrodes were amplified using the Axoclamp2A amplifier (Axon Instruments, Foster City, CA) under bridge mode. The extracellular signal (referred to in this paper as “Ext,” external or extracellular signal, as in Van der Kloot and Naves 1996) was processed further by feeding it into a signal conditioner (Intronix) where it was filtered (lowpass filter: 5.0 kHz; highpass filter: 0.5 Hz) and further amplified (×100) before being fed into the first input channel of the dataacquisition system. The intracellular mEJP signal was fed straight into the second input channel of the dataacquisition system. The MacLab/4 s dataacquisition system (AD Instruments, Sydney, Australia) was used to record the two electrical signals with the same computer used simultaneously for visualization. Data points were sampled at 40 kHz. Sampling was triggered using the software’s voltagethreshold discriminator set to detect extracellular signals exceeding the amplitude of a specific voltage.
In experiments with two focal macropatch electrodes, the signal from each electrode was amplified by a separate Axoclamp2A amplifier and handled as described in the preceding text.
The MacLab data files were converted to Igor Pro files for analysis with subroutines written for the Igor Pro 3 software analysis package (Wavemetrics). The amplitudes of the signals were measured using methods previously described (Bennett et al. 1996;Feeney et al. 1998; Karunanithi et al. 1995; Sayer et al. 1989). We usedttests to assess significance (P < 0.05) between groups. When comparisons are made across nonoverlapping groups (for example, between signals and contaminants), the tests are valid assuming our fitted model is correct. In all other cases,ttest results are used as references.
Statistical procedures
At many recording sites, two or more classes of signal were detected in plots of external signals (Ext) against intracellular signals (mEJP). We wished to estimate the mean Ext generated at a primary recording site. Although Exts of relatively large amplitude and/or brief rise time are more likely to have originated at the recording site, point location is not always known with certainty. Thus the problem becomes one of selecting a portion of the data to be classified as “true” signals (those originating at the recording site). Statistical procedures for this purpose are described here.
The analysis proceeds as follows. For a given data set, the bivariate data were reduced to one dimension by considering only the angles (α) subtended with the extracellular signal axis by the data points (Fig.1 C). The distribution of these angles is assumed to be a mixture of a finite number (m), of Gaussian components. For different values of m, this model is fitted using the maximum likelihood approach. The final value for m is determined using Monte Carlo Likelihood Ratio tests. Finally, each point is classified as a signal or contaminant using Bayes Decision Rule. This above procedure may be applied to the bivariate data although additional constraints on the data may be necessary to adequately fit the model (see Fitting the model).
Data reduction
The data consist of independent observations (Ext_{i}, mEJP_{i}),i = 1, … , N, where N is the number of observations. If the muscle behaves as a passive electrical network, as is known to be the case with small voltage excursions (Jan and Jan 1976), applied currents will evoke a voltage change that increases linearly with current amplitude. Thus the individual signal distributions may be skewed, but true angles should be similar, with some variation due to current duration and other factors. The time course and relative amplitude of the currents at the recording site are represented by the external voltage. However, relationship between Ext and mEJP signals will be different for events generated at different locations with respect to the focal macropatch recording electrode. Thus populations of data points belonging to the true signal category can be distinguished from “contaminating” populations through analysis of their angles, the values of which depend on attenuation of Exts from different sources.
In practice, most data sets exhibit symmetric signal angular distributions that are well fitted by a Gaussian distribution. This justifies the use of a single normal distribution to model the true signal portion of the data. Signals originating from other sources (contaminants) are recorded in attenuated form, but Gaussian mixtures are able to describe the distributions for the angles of these signals.
Normal mixture model
The data consist of angles α_{i}
, i = 1, …, N that are assumed to be independent realizations drawn from a probability density function (finite mixture of normal distributions)
We interpret the first component as the true signal group; points from other sources (contaminants) will usually have smaller currents for a given voltage response, due to greater attenuation of the current (and hence Ext) at the recording site, and therefore larger angles (Fig.1 C, α_{2}).
Fitting the model
We have assumed an mcomponent Gaussian mixture model defined in Eqs. 1
and
2
that depends on the unknown vector θ. To estimate θ, we employ the loglikelihood approach which finds a value θ̂, which maximizes the loglikelihood function
Assuming a bivariate model involves fitting an additional four parameters for each component and several more local maxima may exist. Often it is then necessary to constrain the data to alleviate the above overfitting problem. Some authors constrain the mixture component variances to be equal; this is not consistent with the observed data.Dasgupta and Raftery (1998) examine the situation in which the bivariate components are Gaussian but “linear” (long and narrow ellipsoids); this would work well for clearly bimodal data sets (see Fig. 3). We have chosen to reduce the data in a natural way by modeling the distribution of the univariate angles.
Estimating the number of components (m)
For a given number of components m, the procedure outlined in Fitting the model gives an estimateθ̂_{m}, and the corresponding fitted loglikelihood L(θ̂_{m}). The larger the latter value, the more likely the data arose from a mixture of m components. However, because of the increased number of parameters, the likelihood will increase as m increases. Whether this increase is statistically significant and not due to chance variation may be determined by applying a Monte Carlo loglikelihood ratio test. This test is applied sequentially pairwise (test m = 1 vs. m = 2, then testm = 2 vs. m = 3, and so on). The test proceeds as follows: Consider a test of m =m1 versus m = m2, wherem1 < m2.
Let λ = −2[L(θ̂_{m1}) −L(θ̂_{m2})], where L(θ̂_{m}) denotes the fitted log likelihood under the m component model. Let λ_{obs} denote the observed λ corresponding to the observed data. Then the P value is the probability that λ exceeds λ_{obs} when m =m1. If this value is very small, then it is unlikely that such a large difference λ_{obs} would be observed if the data came from a m1 component model. We then would conclude that m = m2.
Under certain technical conditions, and for a large enough sample sizeN, λ has an approximate χ_{1} ^{2}(χ^{2} with 1 df) distribution whenm = m1, and the P value may be evaluated directly. However, not all these conditions are satisfied in the mixture model setting, so we estimate the P value first by simulating the distribution of λ when m =m1 through Monte Carlo sampling as follows. We randomly generate B samples (each consisting of N angles) from the fitted m1 component model. For each sample, we fit the loglikelihood for each model and compute λ. Our Pvalue is estimated by the proportion of λs that exceed λ_{obs}. We conclude that m =m2 if this value is < 0.1. We take B = 500, which is usually large enough to accurately represent the distribution of λ. Thus for a given data set, we may use the results of these tests to help determine a final estimate of m, giving the final fitted model.
Decision rule
Let P_{j}
(α) denote the (posterior) probability that an observation with angle α belongs to thejth group. In particular, defineP
_{S} = P
_{1}
,the (posterior) probability of belonging to the signal group. Usually, low angles give rise to higher signal probabilities. Using Bayes rule for probabilities (Moore and McCabe 1997)
The usual and most natural way of classifying an observation is to choose the component it is most likely to come from, that is, the group with the largest fitted (posterior) probability [largestP_{j} (α)]. Because we are only concerned with distinguishing two groups, signals and contaminants, we may classify an angle α as a signal precisely whenP _{s}(α) ≥ 0.5. This decision rule is not only intuitive but also minimizes the probability of misclassifying an observation provided the cost of misclassifying a signal as a contaminant is equal to the cost of misclassifying a contaminant as a signal. This is a special case of Bayes Decision Rule (Ripley 1996), which classifies an angle α as a signal when P _{s}(α) ≥ pwhere p is between 0 and 1 and represents the cost of misclassifying a contaminant as a signal relative to the cost of misclassifying a signal as a contaminant (the 2 costs add up to 1).
One also can interpret this rule as only classifying angles as signals if we are ≥100p% sure. It is not immediately clear how to choose p. Because the goal is to estimate the mean Ext, it may seem desirable to choose p large enough to increase the certainty that all classified signals are actually signals. However, such a rule will tend to misclassify some signals as contaminants, which leads to overestimating the mean Ext. Lower values ofp will include more contaminants in the signal group that will underestimate the mean Ext due to low contaminating Ext values. In the absence of information concerning the relative costs of misclassification, we choose p = 0.5. However, one may check the impact of such a rule by estimating the mean Ext for several values of p (see Fig. 3).
RESULTS
Drosophila nerve terminals
The gross structural and ultrastructural features of larvalDrosophila nerve terminals have been described by Jan and Jan (1976), Atwood et al. (1993), Jia et al. (1993), Stewart et al. (1996), andMeinertzhagen et al. (1998). The features considered to be significant for extracellular recording of synaptic events with a macropatch electrode are illustrated in Fig.2. The nerve terminals of the major glutamatergic motor axons generally run longitudinally on the surface of the innervated muscle fibers. They comprise a series of varicosities on which most of the individual small synapses occur, and they are embedded in an extensive network of fine postsynaptic processes, referred to as the subsynaptic reticulum, or SR (Osborne 1967). As shown in Fig. 2, there is considerable extracellular space in the SR, which is continuous along the track of the nerve terminal. Extracellular currents generated at individual synapses must flow through the subsynaptic reticulum. A macropatch electrode placed over a varicosity may possibly form a good seal along the lateral edges of the varicosity (Fig. 2 A), but there is very little likelihood of a good seal being made over the subsynaptic reticulum where it extends longitudinally from the recorded varicosity (Fig.2 B).
The prominent longitudinal muscles (muscles 6 and 7) are conjointly innervated by two motor axons, one of which (motor neuron RP3) has relatively big varicosities (Type Ib) and the other (a common excitor, motor neuron 6/7b), relatively small varicosities (Type Is). Physiological recordings are usually made from Type Ib varicosities, which are easier to see with Nomarski optics, or (in some previous investigations) from both types at once. In the present study, we selected welldefined individual Type Ib varicosities for recording, to avoid complications arising from simultaneous recording from more than one axon terminal.
Localized synaptic signals
The observations of the present study comprised spontaneously occurring synaptic events, most of which represent single quantal units of transmitter release. We recorded simultaneously with intracellular and extracellular electrodes to observe the transmembrane voltage responses generated by each quantal current (Fig. 1, A andB). Because of the highinput resistance of the postsynaptic muscle fiber and its short length (Jan and Jan 1976), it is practically isopotential, and events originating anywhere on its surface can be recorded with high fidelity at a single intracellular recording site.
As illustrated in Fig. 1, A and B, the intracellular voltage response and the extracellular local signal, Ext (measured as a voltage change at the tip of the macropatch electrode) showed a range of amplitudes. There is also some variation in their total duration. In the example illustrated, the amplitudes of Ext and mEJP covary, as would be expected if the muscle cell behaves as a passive electrical network (Jan and Jan 1976;McLachlan and Martin 1981).
We tested the effects of electrode tip opening on Ext. Electrodes were selected to record from only a single bouton. Results using electrodes with tip diameters that enclosed only the bouton, when compared with those from electrodes that also included all of the SR around that bouton, did not show significant differences in amplitude of the recorded currents and their coefficients of variation, CV (bouton only: Ext = 0.29 mV, CV = 0.58; SR + bouton: Ext = 0.31 mV, CV = 0.52. ttest, P < 0.05.n = 7). Thus minor changes in electrode size relative to bouton size did not appear to have much effect on the recorded Ext.
Mixed populations of signals
Plots of the intracellular and extracellular signals recorded simultaneously from several different recording sites showed that whereas some sites produced a quasilinear relationship between the two signals, others showed clear evidence for two or more discrete populations. Figure 3 illustrates a case in which there appeared to be two classes of signal (shown as I and II). One class (I) was well accounted for by a linear regression line, but the second class (II) diverged strikingly, with little or no dependence of intracellular voltage amplitude on Ext amplitude. Variation about the regression line in the first population (I) is most likely due mainly to variation in time course of the current events. Thus two discernable classes of quantal events were reported by the external electrode at this site.
Origin of contaminating signals
Results like those of Fig. 3 (2 populations with different relationships between Ext and mEJP) suggested that the extracellular signals can be generated at more than one location. It seemed likely that some signals originated at locations along the nerve terminal outside the lumen of the macropatch electrode and could be recorded in attenuated form. The SR (Fig. 2) provides a pathway for current flow between adjacent sites, as illustrated diagrammatically in Fig.4 A. Equivalent electrical circuits for this situation have been presented by other authors, e.g.,Bennett et al. (1997). Nearby synapses causing current to flow along the SR could generate a contaminating signal at the external electrode.
A test of this idea was effected by placing two separate macropatch electrodes close together along a nerve terminal for simultaneous recording (Fig. 4, B and C). It was found that signals originating outside the lumen of a macropatch electrode could be recorded within it. On average, they were smaller and often had slower rise times than the signals originating within the lumen of the macropatch electrode (Fig. 4 D).
When the second electrode was placed an equivalent lateral distance from the first, or closer, on the muscle fiber’s surface, no equivalent events were recorded. Thus it is likely that the SR allows contaminating signals to appear at the recording macropatch electrode, but there is little lateral spread of current and little flow through the surface of the muscle fiber.
Statistical separation of signals from different sources
The plot of Fig. 3 shows a clear bimodal structure with the exception of a few observations that fall between the two modes. A histogram of the angles (Fig.5 A) describes the angle density. These data were analyzed by developing theoretical curves for two and three components, as described in methods, assuming a Gaussian mixture. Both two and threecomponent fits (Fig.5 B) clearly show the contaminant peak with a mean angle of 85° and a small standard deviation. However, the threecomponent model displays a more prominent true signal peak, with mean angle of 48°. This model also provides a much smaller standard deviation for the true signal, corresponding to the tight cluster of points about a mean angle. The twocomponent model fits a mean true signal angle of 54.5° with a large standard deviation, arising from intermediate observations. Thus restricting the model to two Gaussian components results in an awkward fit, as the algorithm tries to overcome the skewness (either in the right signal tail or in the left contaminant tail) present in the data. The threecomponent model avoids distortion arising from skewness by further differentiating the noncontaminant data into a smaller signal group and a second midregion contaminant class. Because of the Gaussian assumption, the latter class has a mean angle of 60° and a large standard deviation with tails spread over a large portion of the data range.
Monte Carlo likelihood ratio tests choose the threecomponent model over the twocomponent model (P value = 0.04), whereas a fourcomponent model does not significantly improve the fit (P value > 0.15). Based on p = 0.5 (Fig.3), the twocomponent (m = 2; Fig.6, A–D) model classified most of the intermediate observations as part of the signal group, whereas the threecomponent model (m = 3; Fig. 6,E–H) did the opposite.
Detailed analysis of signals exhibiting a bimodal distribution
FITTING A BIMODAL ESTIMATE TO THE DISTRIBUTION.
The plot of P _{s} (the estimated posterior probability that a point belongs to the signal category) as a function of the angle α is shown in Fig. 6 A and its theoretical prediction in Fig. 6 B. Applied to the data (Fig.3), the probability values show a relatively clear separation of points that belong to either signals or contaminants with a few intermediate points lying in between. The points lying in the intermediate region can be classified into either of the two categories depending on the cutoff chosen for P _{s}. When a cutoff ofp = 0.5 is assigned, the resulting classification of data points produces the distributions for signals (●) and contaminants (○) shown in Fig.7 A. Values derived from the analysis for amplitude and frequency of quantal events are summarized in Table 1 A. The signal group lies at a mean angle of 54.2 ± 1.72° (n = 56), whereas the contaminant group lies at an angle of 84 ± 0.20° (n = 70). Thus segregating the population shows that the signals lie at shallower angles than the contaminants. Exts with amplitudes >0.4 mV (Fig. 6 C) clearly fall into the signal category (P _{s} = 1). Below that value some points fall into the contaminant (P _{s} = 0) group and a few points are intermediate. The amplitudefrequency distributions, the means, and the coefficients of variation (CVs) of Exts belonging to the signal (Fig.7 B) and contaminant (Fig. 7 C) groups are shown for an assigned cutoff of p = 0.5. The mean amplitude of the signal group was 350% larger than that of the contaminant group and 71% larger than that of the entire data set, or unseparated population (0.21 ± 0.02 mV; n = 126). The differences were statistically significant.
The amplitudefrequency distribution, mean, and CV of the mEJPs belonging to the signal category are shown in Fig. 7 D. The mean of the signal group was significantly smaller than those of the contaminant group and the unseparated population (Table 1 A).
The CVs of the Exts belonging to the signal and contaminant groups (Fig. 7, B and C) were considerably smaller than that of the unseparated population (Fig. 7). The CV of the mEJPs of the signal group (Fig. 7 D) was considerably larger than that of the contaminant group and the unseparated population. After separation there is closer agreement (28% difference) between the CVs of the Exts and mEJPs in the signal group than before separation (43% difference). This suggests that as the true signal group becomes better defined, the relationship between Ext and mEJP becomes more linear.
Exts with rise times (t _{r}) > 2.6 ms fall into the contaminant category (Fig. 6 D). When a cutoff of p = 0.5 is assigned, the meant _{r} of the resulting signal group (1.15 ± 0.06 ms) was found to be 38% faster than for the contaminant group (1.86 ± 0.15 ms) and 25% faster than for the unseparated population (1.54 ± 0.09 ms).
The spontaneous frequency of focally recorded spontaneous quantal events before separation was 0.06 s^{−1}. After separation, the spontaneous frequency of the signals was lowered by a factor of 3–0.02 s^{−1} (Table 1 A).
In summary, a bimodal fit to the distribution shows that Exts belonging to the signal group are larger and faster than those belonging to the contaminant group. A possible linear relationship between the amplitude of the Ext and the mEJP is also implicated. The frequency of occurrence of Exts from the site of recording is far lower than would be recorded if the signals and contaminants were not separated.
FITTING A TRIMODAL ESTIMATE TO THE DISTRIBUTION.
This distribution (Fig. 3) also passed the test for fitting a trimodal Gaussianmixture model to the angular density distribution (Fig. 5, m = 3). This estimate further separated the signal group deduced using a bimodal Gaussianmixture model into a new smaller signal group (S, ●) and a second contaminant group (C_{1}, □; Figs. 6 E and 7 E). The pure contaminant group (C_{2}, ○) was still present. The plot of the probability of points belonging to one of the three groups (P _{s},P _{C1}, andP _{C2}) as a function of α is shown in Fig. 6 E and the theoretical distribution of points belonging to S in Fig. 6 F. S was found to lie at a mean angle of 48.9 ± 0.7°, C_{1} at 62.7 ± 3.3°, and C_{2} at 84.9 ± 0.2°. The probability of Ext amplitude being in one of the three groups is shown in Fig.6 G. Amplitudefrequency histograms, mean, and CVs are illustrated for the signal group (Fig. 7 F) and for both contaminant groups (Fig. 7 G: C_{1}, □; C_{2}, ▧). The mean amplitude of S was 90% larger than C_{1}, 450% larger than C_{2}, and 117% larger than the unseparated population. These differences were all statistically significant. When the mean amplitude of S was compared with the mean of the signal group deduced using a bimodal fit, there was no significant difference between the two. The mean of C_{2} was similar to the mean of the contaminant group deduced using a bimodal fit.
The mEJP amplitudefrequency histogram, mean, and CV are presented in Fig. 7 H. The mean for S was not significantly different to that of C_{1} but was significantly smaller than that of C_{2} (Table 1). There were no significant differences between the mean of S and that of the signal group obtained from the bimodal fit nor between the mean of C_{2}and that of the contaminant group ascertained from the bimodal fit. Thus in this example, mean values obtained with the trimodal fit are not significantly different from those obtained with a bimodal fit.
The CVs of the Exts (0.49) and mEJPs (0.48) for S are almost identical from the trimodal fit, whereas there is a 30% difference between the two using the bimodal fit. This implies that the trimodal fit describes a more linear relationship between the mEJP and Ext amplitudes than does the bimodal fit.
The mean t _{r} for S (1.24 ± 0.09 ms) was not significantly different from that for C_{1} (1.08 ± 0.08 ms) but significantly faster than that for C_{2} (1.87 ± 0.16 ms). The t _{r} values from bi and trimodal fits were not significantly different in S or C_{2}groups.
In summary, the trimodal fit does not improve the estimates of mean amplitude, but it does reveal the possible existence of an additional source of contaminating signals (C_{1}), and it describes a more linear relationship between the amplitude of the mEJP and Ext. Because there are fewer members in the new signal group, the frequency of occurrence of spontaneous events is even lower (0.01 s^{−1}) than that estimated using a bimodal fit (Table 1).
Detailed analysis of signals exhibiting a trimodal distribution
FITTING A BIMODAL ESTIMATE TO THE DISTRIBUTION.
At some of the recording sites, the data plots exhibited a trimodal rather than a bimodal distribution (Fig.8 A). The angular density plot for the example in Fig. 8 A showed two large peaks, with a smaller peak between them (Fig. 8 B). To segregate the points into signals and contaminants, we selected a cutoff forP _{s} of 0.5. The points belonging to the signal (●) and contaminant (○) groups then could be distinguished in the data (Fig. 8 A). The data points for the signal group were found to lie at an angle of 44.4 ± 2.0° and those for the contaminants at 80.4 ± 0.5°.
The mean Ext amplitude of the signals is significantly larger than for contaminants (Fig. 8, C and D) and for the unseparated population (Table 1 B). The mean mEJP amplitudes of the signals and contaminants were found to be significantly different (Table 1 B). The CVs of the Exts (0.54) and mEJPs (0.53) in the signal category are almost identical, suggesting a linear relationship.
The frequency of occurrence of Exts belonging to the signal group was lower than for the unseparated population (Table 1 B).
FITTING A TRIMODAL ESTIMATE TO THE DISTRIBUTION.
The observed angular density distribution (Fig. 8 B) was also well fitted with a trimodal Gaussian mixture model. The signal (S) and pure contaminant group (C_{2}) along with a third group (C_{1}) were distinguished (Fig.8 E). Points belonging to S reside at a mean angle of 34.6 ± 1.1°, for C_{1} at 59.5 ± 1.8°, and for C_{2} at 80.4 ± 0.5°.
The mean amplitude of S (Fig. 8 F) is significantly larger than those of C_{1}, C_{2} (Fig.8 G), and the unseparated population (Table 1 B). However, it was not significantly different from the mean of the signal group estimated with bimodal fit (Fig. 8 C). The mean value of C_{2} is close to the mean of the contaminants estimated with bimodal fit (Table 1 B).
Analysis of signals with poorly defined distributions
Figure 9 A illustrates a poorly defined data distribution. When the angular density distribution is plotted (Fig. 9 B), no clear peaks could be discerned, unlike the previous two examples. In such situations, it is initially wise to see whether one can simply separate the population into signals and contaminants by applying a bimodal fit. Points lying at angles <78° are allotted to the signal category. At higher angles, a suitable cutoff has to be selected to separate the remaining points into signals and contaminants. When a cutoff ofP _{s} = 0.5 is chosen, the resulting separation of the points into signals (●) and contaminants (○) is shown in Fig. 9 A. The signal group resides at a mean angle of 74.0 ± 1.21° and the contaminant group at a mean angle of 84.9 ± 0.29°. It is interesting to note that the angles at which the pure contaminants reside fall within the narrow window of 80–85° in all three examples.
The mean amplitude of the signals (Fig. 9 C) was significantly larger than those of the contaminants (Fig.9 D) and the unseparated population (0.17 ± 0.02 mV; Table 1 C). The mEJP amplitude of the signals (Fig.9 E) was significantly smaller than that of the contaminants but not significantly different from that of the unseparated population (0.94 ± 0.05; Table 1 C).
Thus in this poorly defined distribution, the population could be separated into signals and contaminants. After separation, the mean Ext amplitude of the signal group was 33.7% larger than for the unseparated population. Furthermore the close agreement of the CVs of the mEJPs and Exts belonging to the signal group suggests a linear relationship between the two.
DISCUSSION
Use of the focal macropatch recording electrode to define events at individual synaptic foci or clusters is becoming increasingly widespread for the Drosophila neuromuscular junction. Similar recording procedures are used for other preparations, including amphibian neuromuscular junctions, smooth muscle neuromuscular junctions, and mammalian central synapses. Simultaneous whole cell recordings have revealed the lack of correlation between focal and whole cell events at the smooth muscle neuromuscular junction (Cunnane and Manchanda 1989), and evidence for extralumenal events at the frog neuromuscular junction (Van der Kloot and Naves 1996). The present study suggests a mechanism for this type of observation in Drosophila, based on the ultrastructure of the pre and postsynaptic elements, and a procedure for separating the true signals (those arising within the electrode) from contaminants. When this is done, the parameters for true signals are much different than before separation. This will affect measures of synaptic performance, including estimates of relative quantal size and quantal content per synapse, and frequency of spontaneous emission of quanta per synapse.
After the observation that different populations of quantal events can be discerned in the data plots, we examined data from 26 different sites, and found that of these, 3 were clearly unimodal (little evidence of contaminating signals), 9 were bimodal, 5 trimodal, and 9 poorly defined. It is clear that the majority of sites selected for recording produced data that contained a proportion of contaminating signals. Defining the true signals altered the parameters for the recording sites considerably.
Improved estimates of quantal size and frequency at individual boutons
It was surprising that the differences between the mean Ext amplitudes of the true and the unseparated populations are quite large in all three examples (Table 1). In these experiments, efforts were made to record Exts from individual varicosities by looking under Nomarski optics for those well separated from others and also by using macropatch electrodes designed to enclose just one varicosity. Such precautions were still not sufficient to eliminate contaminating currents in our recordings because the SR provides a pathway for current flow, allowing currents generated extralumenally to travel over distances of 10 μm in some cases (Fig. 4). This observation parallels that of Van der Kloot and Naves (1996) at the frog neuromuscular junction, in which extraluminal signals could be detected at an even greater distance (0.8 mm) away from the recording site. Therefore complete electrical insulation from contaminating sources to record just the signal currents may not be possible in this and similar preparations except in a minority of instances. Contaminating signals are likely to contribute significantly in the estimation of quantal size and frequency in the unseparated population. In the three cases analyzed, the quantal amplitude for the Ext increased by 130–210% after separation.
An even larger proportional change occurs for the frequency of spontaneous release at individual boutons. After separation of the data into signal and contaminant populations, the frequency of spontaneous release of the signal group became much lower than that estimated from the unseparated population (Table 1). Relative frequencies of the true signal events were 20–66% of those for the unseparated population. These values are in agreement with studies in which a focal macropatch electrode was used to record release from a few release sites at other neuromuscular junctions (frog: Robitaille and Tremblay 1991, <0.05 s^{−1}; guineapig vas deferens: Brock and Cunnane 1991; and toad:Karunanithi et al. 1992, 0.3–0.05 s^{−1}).
Coefficient of variation as an addition discriminator
Separation of signals was also assessed for its effect on coefficient of variation (CV). For selecting the best estimate for the mean Ext amplitude, the modal fit that gives the smallest difference between the CVs for the Ext and mEJP provides an additional criterion. Modal estimates that give smaller values of CVs for the signal group are preferred. Application of these criteria produce relationships between Exts and mEJPs converging toward linearity, as illustrated (Fig. 10) for the three examples of the present study. A linear relationship between small junctional currents and EJPs has been previously shown at both frog and mouse neuromuscular junctions (McLachlan and Martin 1981). The smaller the differences in the CVs of the Ext and mEJP in the signal group (Fig.10 A), the more the points diverge from the coordinates of points representing the unseparated populations (○) and approach the 45° line (Fig. 10 A, ●, ■, ▴). For the case of the bimodal distribution (BD, ○), the bimodal fit (●) moved the point close to the line, whereas the trimodal fit (■) forced the point to migrate almost onto the line and generated smaller CV values. Thus the best estimate of the mean Ext amplitude of the signal group is given by the trimodal fit (0.45 mV, Table 1). A similar result was obtained for the data showing a trimodal distribution (TD, ○), when bimodal (●) and trimodal (■) fits were applied. The trimodal fit again gave the best estimate of the mean Ext amplitude (0.65 mV). In the case of the poorly defined distribution (PD, ○), the bimodal fit improves the estimate of the mean Ext amplitude (●; 0.22 mV). After separation, the pure contaminants (+) tend to show a greater reduction in CV_{Ext} than CV_{mEJP} (Fig.10 B). Clearcut data from a recent study on mammalian central synapses (Forti et al. 1997) showed equality of CV when plotted in Fig. 10 A (▴), supporting the validity of this approach.
Rise times are less reliable as a separation criterion
For two of the three examples analyzed in the present study, the rise time (t _{r}) was of relatively small value in differentiating the signal and contaminant groups. It is likely determined by several factors, including the concentration and lifetime of the transmitter in the synaptic cleft, the size of the cleft, and the stochastic nature of channel gating (Adelsberger et al. 1997; Heckmann and Dudel 1997;Heckmann et al. 1996). Passive membrane properties of SR may affect the rise time of the contaminating Exts, and the example of Fig. 5 does show a slower rise time for the extraluminal signals. However, in only one of the three examples could a clear differentiation be shown on the basis of rise time (Table 1). This criterion should, however, be tested in larger samples. In the study byForti et al. (1997), spontaneous miniature postsynaptic currents recorded from individual visualized cultured hippocampal synapses using a macropatch electrode had rise times that were highly conserved, although the amplitudes were variable. In their work, it was reported that contaminants arising from boutons outside the electrode were minimized to <1%. For Drosophila, minimization of evoked contaminating signals may be obtained by reducing Ca^{2+} in the bathing solution while keeping it high in the recording electrode.
With regard to quantal size, the true signal populations generally indicate a fivefold range in Ext amplitude, with a corresponding range in mEJP amplitude (e.g., Figs. 8 E and 9 A). This range in quantal size for Drosophila corresponds well with the size ranges reported from other studies, particularly for mammalian central neurons (e.g., Forti et al. 1997;Frerking and Wilson 1996). Various mechanisms have been proposed to explain quantal variability, including variation in synaptic vesicle size and receptor numbers at individual synapses; and although it is known that synapse size varies at theDrosophila neuromuscular junction (Atwood et al. 1993), present information is not sufficient to distinguish critically among available alternatives for this junction.
Acknowledgments
K. Wong and S. Karunanithi contributed equally to this work.
We thank Dr. John Hackett (University of Virginia) and Dr. Martin Wojtowicz (University of Toronto) for reading a draft of the manuscript and offering critical suggestions, and M. HegströmWojtowicz for help in preparing the manuscript.
This work was supported by grants from the National Sciences and Engineering Research Council, Canada, to H. L. Atwood.
Footnotes

Address reprint requests to: H. L. Atwood.

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 Copyright © 1999 The American Physiological Society