1Department of Statistics and 2Department of Physiology, University of Toronto, Toronto, Ontario M5S 1A8, Canada
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ABSTRACT |
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Wong, K., S. Karunanithi, and H. L. Atwood. Quantal Unit Populations at the Drosophila Larval Neuromuscular Junction. J. Neurophysiol. 82: 1497-1511, 1999. 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.
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INTRODUCTION |
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The Drosophila larval neuromuscular
junction, originally brought forward for physiological investigation by
Jan 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 synapse-bearing nerve terminals. For this, an extracellular
"macropatch" electrode (Dudel 1981) is placed over a
nerve terminal to record spontaneous and nerve-evoked signals (extracellular voltages or currents) caused by release of transmitter and its subsequent opening of ligand-gated 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 by
Mallart 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.
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METHODS |
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Physiological procedures
Canton-S 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 hemolymph-like physiological solution (HL3) of the
following ionic composition (in mM): 70.0 Na+,
5.0 K+, 1.0 Ca2+, 20.0 Mg2+, 10.0 NaHCO3, 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, Optiphot-2) equipped with a Nikon ×40 water-immersion 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 built-in frame grabber) through a low-light-intensity TV camera (Panasonic, WV-BP310) 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 M), 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. 1A).
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Signals from the focal macropatch and intracellular recording
electrodes were amplified using the Axoclamp-2A 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 (low-pass filter: 5.0 kHz;
high-pass filter: 0.5 Hz) and further amplified (×100) before being
fed into the first input channel of the data-acquisition system. The
intracellular mEJP signal was fed straight into the second input
channel of the data-acquisition system. The MacLab/4 s data-acquisition
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 voltage-threshold 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 Axoclamp-2A 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 used t-tests 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,
t-test 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 ()
subtended with the extracellular signal axis by the data points (Fig.
1C). 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
(Exti, mEJPi),
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
i, i = 1, ..., N that are assumed to be independent realizations
drawn from a probability density function (finite mixture of normal
distributions)
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(1) |
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(2) |
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.
1C, 2).
Fitting the model
We have assumed an m-component Gaussian mixture model
defined in Eqs. 1 and 2 that depends on the
unknown vector . To estimate
, we employ the log-likelihood
approach which finds a value
, which maximizes the
log-likelihood function
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(3) |
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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
over-fitting 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 estimate
m, and the corresponding fitted
log-likelihood L(
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
log-likelihood ratio test. This test is applied sequentially pairwise
(test m = 1 vs. m = 2, then test m = 2 vs. m = 3, and so on). The test
proceeds as follows: Consider a test of m = m1 versus m = m2, where
m1 < m2.
Let =
2[L(
m1)
L(
m2)], where
L(
m) denotes the fitted log likelihood
under the m component model. Let
obs denote the observed
corresponding to
the observed data. Then the P value is the probability that
exceeds
obs when m = m1. If this value is very small, then it is unlikely that
such a large difference
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 size
N, has an approximate
12
(
2 with 1 df) distribution when
m = 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
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 log-likelihood for each model and compute
. Our P value is estimated by the proportion of
s that exceed
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
. 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 Pj() denote the (posterior)
probability that an observation with angle
belongs to the
jth group. In particular, define PS = P1,
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
)
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(4) |
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 [largest
Pj()]. Because we are only concerned
with distinguishing two groups, signals and contaminants, we may
classify an angle
as a signal precisely when
Ps(
)
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
as a signal
when Ps(
)
p where 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 of
p 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).
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RESULTS |
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Drosophila nerve terminals
The gross structural and ultrastructural features of larval
Drosophila nerve terminals have been described by Jan
and Jan (1976), Atwood et al. (1993)
, Jia
et al. (1993)
, Stewart et al. (1996)
, and
Meinertzhagen 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. 2A), 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.
2B).
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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 well-defined 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 and
B). Because of the high-input 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. t-test, 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.
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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.
4A. 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.
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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. 4D).
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. 5A) 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 three-component fits (Fig. 5B) clearly show the contaminant peak with a mean angle of 85° and a small standard deviation. However, the three-component 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 two-component 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 three-component 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.
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Monte Carlo likelihood ratio tests choose the three-component model over the two-component model (P value = 0.04), whereas a four-component model does not significantly improve the fit (P value > 0.15). Based on p = 0.5 (Fig. 3), the two-component (m = 2; Fig. 6, A-D) model classified most of the intermediate observations as part of the signal group, whereas the three-component model (m = 3; Fig. 6, E-H) did the opposite.
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Detailed analysis of signals exhibiting a bimodal distribution
FITTING A BIMODAL ESTIMATE TO THE DISTRIBUTION.
The plot of Ps (the estimated
posterior probability that a point belongs to the signal category) as a
function of the angle is shown in Fig. 6A and its
theoretical prediction in Fig. 6B. 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 Ps. When a cutoff of
p = 0.5 is assigned, the resulting classification of
data points produces the distributions for signals (
) and
contaminants (
) shown in Fig.
7A. Values derived from the
analysis for amplitude and frequency of quantal events are summarized
in Table 1A. 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. 6C) clearly fall into the signal
category (Ps = 1). Below that value
some points fall into the contaminant
(Ps = 0) group and a few points are
intermediate. The amplitude-frequency distributions, the means, and the
coefficients of variation (CVs) of Exts belonging to the signal (Fig.
7B) and contaminant (Fig. 7C) 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.
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FITTING A TRIMODAL ESTIMATE TO THE DISTRIBUTION.
This distribution (Fig. 3) also passed the test for fitting a
trimodal Gaussian-mixture model to the angular density distribution (Fig. 5, m = 3). This estimate further separated the
signal group deduced using a bimodal Gaussian-mixture model into a new
smaller signal group (S, ) and a second contaminant group
(C1,
; Figs. 6E and 7E).
The pure contaminant group (C2,
) was still
present. The plot of the probability of points belonging to one of the three groups (Ps,
PC1, and
PC2) as a function of
is shown in Fig. 6E and the theoretical distribution of points belonging
to S in Fig. 6F. S was found to lie at a mean angle of
48.9 ± 0.7°, C1 at 62.7 ± 3.3°,
and C2 at 84.9 ± 0.2°. The probability of
Ext amplitude being in one of the three groups is shown in Fig.
6G. Amplitude-frequency histograms, mean, and CVs are
illustrated for the signal group (Fig. 7F) and for both
contaminant groups (Fig. 7G: C1,
;
C2,
). The mean amplitude of S was 90% larger than C1, 450% larger than
C2, 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 C2 was similar to
the mean of the contaminant group deduced using a bimodal fit.
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.
8A). The angular density plot
for the example in Fig. 8A showed two large peaks, with a
smaller peak between them (Fig. 8B). To segregate the points into signals and contaminants, we selected a cutoff for
Ps of 0.5. The points belonging to the
signal () and contaminant (
) groups then could be distinguished
in the data (Fig. 8A). 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°.
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FITTING A TRIMODAL ESTIMATE TO THE DISTRIBUTION. The observed angular density distribution (Fig. 8B) was also well fitted with a trimodal Gaussian mixture model. The signal (S) and pure contaminant group (C2) along with a third group (C1) were distinguished (Fig. 8E). Points belonging to S reside at a mean angle of 34.6 ± 1.1°, for C1 at 59.5 ± 1.8°, and for C2 at 80.4 ± 0.5°.
The mean amplitude of S (Fig. 8F) is significantly larger than those of C1, C2 (Fig. 8G), and the unseparated population (Table 1B). However, it was not significantly different from the mean of the signal group estimated with bimodal fit (Fig. 8C). The mean value of C2 is close to the mean of the contaminants estimated with bimodal fit (Table 1B).Analysis of signals with poorly defined distributions
Figure 9A illustrates a
poorly defined data distribution. When the angular density distribution
is plotted (Fig. 9B), 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 of
Ps = 0.5 is chosen, the resulting
separation of the points into signals () and contaminants (
) is
shown in Fig. 9A. 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.
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The mean amplitude of the signals (Fig. 9C) was significantly larger than those of the contaminants (Fig. 9D) and the unseparated population (0.17 ± 0.02 mV; Table 1C). The mEJP amplitude of the signals (Fig. 9E) was significantly smaller than that of the contaminants but not significantly different from that of the unseparated population (0.94 ± 0.05; Table 1C).
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.
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DISCUSSION |
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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; guinea-pig 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.
10A), the more the points diverge from the coordinates of points representing the unseparated populations (
) and approach the
45° line (Fig. 10A,
,
,
). 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
CVExt than CVmEJP (Fig.
10B). Clear-cut data from a recent study on mammalian
central synapses (Forti et al. 1997
) showed equality of
CV when plotted in Fig. 10A (
), 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 (tr) 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 by
Forti 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
Ca2+ 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. 8E and 9A). 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 the
Drosophila neuromuscular junction (Atwood et al.
1993
), present information is not sufficient to distinguish critically among available alternatives for this junction.
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ACKNOWLEDGMENTS |
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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. Hegström-Wojtowicz 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.
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FOOTNOTES |
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Address reprint requests to: H. L. Atwood.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 21 September 1998; accepted in final form 28 April 1999.
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REFERENCES |
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