Departments of 1Pharmacology and 2Neurology, State University of New York, Health Science Center at Brooklyn, Brooklyn, New York 11203
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ABSTRACT |
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Ling, Douglas S. F. and Larry S. Benardo. Restrictions on Inhibitory Circuits Contribute to Limited Recruitment of Fast Inhibition in Rat Neocortical Pyramidal Cells. J. Neurophysiol. 82: 1793-1807, 1999. To further define the operational boundaries on fast inhibition in neocortex, whole cell recordings were made from layer V pyramidal neurons in neocortical slices to evaluate evoked inhibitory postsynaptic currents (IPSCs) and spontaneous miniature IPSCs (mIPSCs). Stimulating electrodes were placed in layers VI and I/II to determine whether simultaneous stimulation of deep and superficial laminae could extend the magnitude of maximal IPSCs evoked by deep-layer stimulation alone. The addition of superficial-layer stimulation did not increase maximal IPSC amplitude, confirming the strict limit on fast inhibition. Spontaneous miniature IPSCs were recorded in the presence of tetrodotoxin. The frequency of spontaneous mIPSCs ranged from 10.0 to 33.1 Hz. mIPSC amplitude varied considerably, with a range of 5.0-128.2 pA and a mean value of 20.7 ± 4.1 pA (n = 12 cells). The decay phase of miniature IPSCs was best fit by a single exponential, similar to evoked IPSCs. The mean time constant of decay was 6.4 ± 0.6 ms, with a range of 0.2-20.1 ms. The mean 10-90% rise time was 1.9 ± 0.2 ms, ranging from 0.2 to 6.3 ms. Evaluation of mIPSC kinetics revealed no evidence of dendritic filtering. Amplitude histograms of mIPSCs exhibited skewed distributions with several discernable peaks that, when fit with Gaussian curves, appeared to be spaced equidistantly, suggesting that mIPSC amplitudes varied quantally. The mean separation of Gaussian peaks ranged from 6.1 to 7.8 pA. The quantal distributions did not appear to be artifacts of noise. Exposure to saline containing low Ca2+ and high Mg2+ concentrations reduced the number of histogram peaks, but did not affect the quantal size. Mean mIPSC amplitude and quantal size varied with cell holding potential in a near-linear manner. Statistical evaluation of amplitude histograms verified the multimodality of mIPSC amplitude distributions and corroborated the equidistant spacing of peaks. Comparison of mIPSC values with published data from single GABA channel recordings suggests that the mean mIPSC conductance corresponds to the activation of 10-20 GABAA receptor channels, and that the release of a single inhibitory quantum opens 3-6 channels. Further comparison of mIPSCs with evoked inhibitory events suggests that a single interneuron may form, on average, 4-12 functional synapses with a pyramidal cell, and that 10-12 individual interneurons are engaged during recruitment of maximal population IPSCs. This suggests that inhibitory circuits are much more restricted in both the size of the unit events and effective number of connections when compared with excitatory inputs.
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INTRODUCTION |
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In CNS neurons, fast inhibitory postsynaptic
currents (IPSCs) arise from the activation of the
Cl conductance associated with the
GABAA receptor/channel complex (for review see
Mody et al. 1994
; Nicoll et al. 1990
). In
the neocortex this form of inhibition is mediated by inhibitory
interneurons, which are ubiquitous (Huntley et al. 1994
;
Kawaguchi and Kubota 1993
). These cells perform the
important task of gating and shaping extrinsic and intrinsic excitatory
inputs. Our prior work on inhibition focused on characterizing
population inhibitory events evoked by extracellular stimulation. We
found that inhibitory neurons were maximally recruited at relatively
low stimulus levels, but that there was a fixed limitation on the
magnitude of evoked fast IPSCs (Ling and Benardo 1995a
).
What underlies the limit on fast inhibition?
Although much recent work has been directed at investigating cortical
fast inhibition (Benardo 1994; Chagnac-Amitai and
Connors 1989
; Deuchars et al. 1995
;
Deuchars and Thomson 1995
; Kawaguchi 1995
; Kubota and Kawaguchi 1994
; Salin
and Prince 1996a
), there is still insufficient information
available about cortical local circuitry to understand the precise
functional processes mediating the limit on fast inhibition. Several
very elegant studies in cortical slices combining paired recordings
from synaptically coupled neurons with electron microscopic analysis
have provided some physiological and anatomic data on the connectivity
of discrete sets of interneuron-pyramidal cell pairs (Buhl et
al. 1994
; Tamás et al. 1997
;
Thomson et al. 1996
). However, because obtaining paired
recordings from the entire ensemble of interneurons connected to given
pyramidal cells would be an impossible undertaking, the details
regarding interneuron-to-pyramidal cell transmission and the
distribution of inhibitory synapses on principal cells for entire
inhibitory networks still remain to be quantified. Basic information
such as this is needed to better define the finite nature of fast
cortical inhibition. A fundamental approach to investigating this issue
is to undertake an analysis of miniature fast inhibitory events as a
means to obtain a first approximation of the number of inhibitory
synapses involved in the mediation of maximal evoked IPSCs.
Miniature synaptic events are thought to arise from the spontaneous
release of a single packet, or quantum, of transmitter at individual
synaptic terminals. Previously, quantal analyses of miniature events
have utilized complex mathematical methods, such as deconvolution, to
extract peaks in amplitude distributions (Bekkers 1994;
Korn and Faber 1991
; Redman 1990
). This
was necessitated by the large variance in inhibitory postsynaptic
potential (IPSP)/IPSC amplitudes imposed by the high noise of
traditional intracellular recording methods. As such, previous
estimates of IPSC quantal size and variability were premised, at least
in part, on assumptions regarding release statistics, deconvolution
analysis, and anatomically based models of transmitter release
(Korn and Faber 1991
; Redman 1990
).
However, Edwards et al. (1990) showed that whole cell
patch techniques can be used to obtain high resolution, low-noise
recordings of spontaneous synaptic currents in situ. Thus direct
measurement of miniature IPSC (mIPSC) amplitudes can be made with
sufficient precision for detailed analyses of amplitude distributions.
This has allowed for improved detection of peaks within amplitude
histograms of miniature synaptic currents, bypassing the need for more
complex methods of signal extraction. However, peaks in amplitude
distributions may nonetheless arise from other artifactual sources,
such as statistical variations due to finite sampling, and this has
prompted the development of rigorous statistical tests to evaluate the reliability of histogram peaks (Stratford et al. 1997
).
In this study, we utilized whole cell recording techniques in slice
preparations of rat somatosensory cortex to further examine limits on
evoked IPSCs and to evaluate mIPSCs in layer V pyramidal neurons. We
have described the kinetics of miniature inhibitory events in
neocortical pyramidal cells and the quantal nature of their amplitude
distributions. Similar to other investigations of inhibitory events
(Edwards et al. 1990; Ropert et al.
1990
), we report skewed distributions of mIPSC amplitudes
exhibiting multiple peaks that are unlike the unimodal, skewed
distributions often observed with miniature excitatory events
(Mody et al. 1994
; Redman 1990
). The
reliability of the peaks observed in these histograms was tested using
both
2 and autocorrelation scoring methods
(Stratford et al. 1997
). Comparisons of these data to
measurements made on evoked IPSCs were used to derive practical
estimates of the functional properties and limits of cortical fast
inhibitory circuits.
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METHODS |
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Preparation and maintenance of slices
Cortical slices were prepared from Sprague-Dawley rats aged
postnatal day 18 to 30 (P18-P30),
using methods previously described (Benardo 1993;
Edwards et al. 1989
). Rats were deeply anesthetized by
either inhalation of halothane or by intramuscular injection of
ketamine (87 mg/kg) and xylazine (13 mg/kg) and killed by decapitation. Their brains were quickly removed and placed in chilled (0-5°C) physiological saline. Coronal slices (300-400 µm), which included somatosensory cortex and dorsal hippocampus, were prepared using one of
two methods, depending on the recording technique used (i.e.,
"blind" or visualized whole cell patch). For blind patch recordings, slices were cut using a McIlwain tissue chopper and then
placed in a warm (35.5 ± 1°C) recording chamber where they rested on a nylon net at the interface between physiological saline and
a stream of humidified gas (95% O2-5%
CO2).
For slices used in visualized patch recording, the somatosensory cortical region was blocked off, dissected, and attached to a dissection block with cyanoacrylate glue. The tissue block was then transferred to the ice-chilled bath of a Vibratome tissue slicer (Oxford) that contained oxygenated saline. This saline contained low calcium (0.5 mM) and elevated magnesium (8 mM) to reversibly block synaptic activity. Coronal slices were cut and then transferred to an antechamber where they rested submerged in warm (35.5 ± 1°C), oxygenated (95% O2-5% CO2) physiological saline. Slices were allowed to incubate for at least 1 h before recording. Following incubation, a single slice was transferred to a recording chamber placed on the stage of an upright microscope (Zeiss Axioskop, Carl Zeiss, Thornton, NY), and perfused with warm (34-35°C) oxygenated saline at ~5 ml/min. Cells were visualized and accessed using infrared differential interference contrast (IR-DIC) optics with a ×40 water immersion objective.
Normal, external physiological saline contained (in mM) 124 NaCl, 5 KCl, 26 NaHCO3, 1.6 MgCl2, 2 CaCl2, and 10 glucose and was continuously bubbled with a mixture of 95% O2-5% CO2 (pH between 7.35 and 7.4). All drugs were delivered through the perfusate.
Whole cell recordings and analysis
Whole cell recordings were obtained from layer V pyramidal cells
in slices using both the blind (Blanton et al. 1989;
Ling and Benardo 1995a
) and visualized (Edwards
et al. 1989
) patch techniques. Patch electrodes were pulled to
tip resistances of 2-5 M
and filled with a solution composed of (in
mM) 130 Cs-gluconate, 2 MgCl2, 2 CaCl2, 10 EGTA, 10 HEPES, 2 Na-ATP, and 10 QX-314, pH 7.25, adjusted with CsOH. QX-314 was included to block
voltage-dependent sodium currents and thus reduce cell spiking.
Currents were recorded under voltage clamp with a Warner PC-501A
patch-clamp amplifier (Warner Instrument, Hamden, CT). Criteria for
cell acceptability were the same as previously detailed (Ling
and Benardo 1995a
), and all cells meeting these criteria were
included in the results presented, without further bias. Briefly, cells
accepted for study had resting input resistances of
100 M
(typically
150 M
) and access resistances
20 M
(typically <15
M
). Cells were discarded if access resistance increased
significantly (>20%) during the experiment. Cell membrane
characteristics (input resistance, resting membrane potential) were the
same with both whole cell recording methods. Signals were digitized at
47 kHz via a 14-bit PCM interface (VR-10B Digital Data Recorder,
Instrutech, Elmont, NY) and stored on VHS videotape for post hoc
analysis. Recorded data were filtered off-line at 1-5 kHz (
3 dB,
4-pole Bessel) and digitally sampled at 10-20 kHz with pCLAMP 6.0 software (Axon Instruments, Foster City, CA) running on a
PC/AT-compatible Pentium-166 MHz microcomputer.
Synaptic events were evoked by extracellular stimulation with coated,
monopolar, tungsten electrodes placed in layer VI lateral to the
recording electrode (proximal location). A second electrode was placed
in layer I/II (distal location) for simultaneous stimulation of
superficial laminae within the same vertical column as the first
electrode. Cathodal shocks (2-10 V; 200 µs duration) were delivered
through a digitally controlled stimulus isolation unit (World Precision
Instruments) at a low frequency (0.1 Hz) that does not induce
depression of fast IPSC amplitude (Deisz and Prince 1989).
Spontaneous mIPSCs were detected and measured using Mini Analysis 4.0 software (Synaptosoft, Leonia, NJ), which identifies spontaneous currents on the basis of several criteria, including threshold amplitude and the area under each event. As a routine check, we visually inspected all mIPSCs detected by the software and rejected any events that did not exhibit the general shape expected for synaptic events. Background noise was measured from quiescent sections of records (i.e., devoid of spontaneous events) or, in cases in which picrotoxin was applied, from records acquired during picrotoxin blockade of mIPSCs. The peak-to-peak noise level in our recordings ranged from 2 to 5 pA.
Kinetic analysis of synaptic currents was performed according to
methods previously described (Ling and Benardo 1994).
Exponential curves were fit to the decaying phase of current traces by
an iterative least-squares method of regression based on the Simplex algorithm (Nelder and Mead 1965
), yielding values for
time constants.
Histograms of the distribution of peak IPSC amplitudes were constructed
from mIPSC measurements (amplitude vs. number of observations). Amplitude distributions were first assessed by eye to determine whether
histogram peaks were readily apparent. This was possible due to the
high resolution (high signal-to-noise ratio) of current recordings made
with whole cell patch techniques. In all cases, peaks in amplitude
histograms were detectable by eye. Peak values thus determined were
then used as initial estimates for fitting of distributions with
Gaussian curves. IPSC histograms were analyzed using the PSTAT analysis
program (pCLAMP, Axon Instruments), which determines the best fit for a
sum of Gaussian distributions using a least-squares method based on the
Simplex algorithm (Nelder and Mead 1965).
All data throughout this report are expressed as means ± SE, unless indicated otherwise.
Statistical evaluation of mIPSC amplitude distributions
The reliability of the peaks observed in the amplitude
histograms was evaluated using both the standard
2 test and the recently developed
autocorrelation (AC) scoring method of Stratford et al.
(1997)
. Specifically, these tests were used to check whether
multimodal distributions could have arisen from parent unimodal
distributions. Multimodal and unimodal distributions were fit to
amplitude histograms by an iterative least-squares method of regression
based on the Simplex algorithm (Nelder and Mead 1965
;
Press et al. 1992
). Histogram fits using sums of
multiple Gaussians (i.e., multimodal) were compared with fits obtained with Weibull functions (i.e., unimodal).
Skewed unimodal fits were obtained with the Weibull function
(Stratford et al. 1997; Zanakis 1979
)
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2 TEST.
Fits of amplitude distributions were compared using
2 goodness-of-fit tests (Guttman et al.
1971
; Press et al. 1992
). The best multimodal
fits of the amplitude data using sums of Gaussians were compared with
the best unimodal fits obtained with the Weibull function. Bins with
values <5 were pooled to avoid errors with small expected values
(Guttman et al. 1971
).
AUTOCORRELATION SCORING.
Histogram fits were also evaluated using the AC scoring method as
described by Stratford et al. (1997). This test involves a multistep procedure whereby the raw amplitude histogram is first smoothed using filtering algorithms derived from Fourier techniques traditionally used to filter time-varying signals. The filter strength
was set to eliminate all peaks and valleys in the amplitude histogram.
The smoothed plot was then subtracted from the raw histogram to obtain
a plot of the difference (or residuals) between the smoothed and
original data plots. The difference plot was then lightly smoothed and
its autocorrelation calculated (Press et al. 1992
) and
plotted. The AC score of the amplitude distribution was taken from the
autocorrelation plot, which has a characteristic damped-sinusoidal
profile, as the difference in magnitude between the first peak (i.e.,
zero-lag) and the preceding trough.
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Materials
All chemicals were purchased from Sigma Chemical (St. Louis, MO) except for N-(2,6-dimethylphenylcarbamoylmethyl)triethylammonium bromide (QX-314, Research Biochemicals International, Natick, MA).
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RESULTS |
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Evoked IPSCs
One possible explanation for the previously reported limit on the
recruitment of fast inhibition (Ling and Benardo 1995a) is a restricted capacity of deep-layer stimulation to engage the entire
inhibitory network. Simultaneous stimulation of regionally separate
sites might activate additional inhibitory cells and, in turn, evoke
maximal IPSCs of greater amplitude than those recruited with deep-layer
stimulation alone. To test this possibility directly, electrical
stimulation was applied in both superficial (layer I/II) and deep
(layer VI) cortical laminae (Fig.
1A, left) to evoke
fast IPSCs in layer V pyramidal cells. IPSCs were selectively recorded
by holding target cells at the empirically determined reversal
potential (~0 mV) for excitatory postsynaptic currents (EPSCs; Fig.
1A, right). The results showed that the addition of superficial-layer stimulation did not alter the peak amplitude of
maximal IPSCs evoked with deep-layer stimuli. The reason for this can
be deduced from a comparison of the respective input-output relationships for layer VI and layer I/II stimulation (Fig.
1B). When stimuli were applied in layer VI, the threshold
intensity values were
3.0 V, and maximal IPSCs were evoked at
intensities 2.0-2.5 V above threshold, similar to our previously
reported findings (Ling and Benardo 1995a
). When stimuli
were delivered solely in superficial cortical layers, the threshold was
significantly higher (~2-fold), and the slope of the input-output
curve was less steep. The plot of the input-output functions revealed
that layer VI stimulation evoked maximal IPSCs at intensities that were
approximately equal to the threshold values for layer I/II stimulation.
Thus electrical stimulation delivered in deep cortical layers proximal
to the recording site is apparently sufficient to recruit all available
inhibitory neurons in the inhibitory network. The results also show
that superficial stimuli likewise engage this inhibitory system, albeit
at higher intensities.
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Spontaneous mIPSCs
We examined spontaneous synaptic activity from whole cell recordings obtained from 12 cells (10 slices) that satisfied our criteria for inclusion in our analyses. Tetrodotoxin (TTX, 1-10 µM) was used to block spontaneous IPSCs arising from action potential-dependent release of GABA from presynaptic inhibitory cells, leaving mIPSCs resulting from the spontaneous release of GABA (Fig. 2A). mIPSCs were selectively recorded at the EPSC reversal potential (~0 mV). Application of 50 µM picrotoxin (PTX) completely blocked spontaneous mIPSCs, confirming that they were mediated by GABAA receptors (Fig. 2A).
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The frequency of mIPSCs within single neurons ranged from 10.0 to 33.1 Hz, with a mean value of 19.5 ± 0.6 Hz (mean ± SE, n = 12). The amplitude of mIPSCs varied considerably,
with a range of 5.0-128.2 pA and a mean value of 20.7 ± 4.1 pA
(determined by pooling 18,456 events from 12 cells). Given an IPSC
reversal potential of 74.1 mV in these cells (Ling and Benardo
1995a
), the mean mIPSC conductance, as given by Ohm's Law, is
~0.3 nS (range ~0.1-1.8 nS).
The average mIPSC amplitude overlaps with the lower range of values we
found for fast IPSCs evoked by minimal strength extracellular stimuli,
which varied from 28 to 300 pA (mean, 168 ± 84 pA) (Ling and Benardo 1995b). The source of this wide range of magnitudes for minimally evoked IPSCs is unclear. Interestingly, when we restricted our examination to minimally evoked events with peak amplitudes <60 pA, the mean threshold value for evoked IPSCs was 28.7 ± 1.6 pA (n = 25 cells), close to the
amplitude of mIPSCs.
Kinetic properties of mIPSCs
The decay phase of miniature IPSCs was best fit by a single
exponential (Fig. 2B), similar to evoked IPSCs (Fig.
2C, same cell) as previously reported (Ling and
Benardo 1995b). As shown in Fig. 2B, the decay
kinetics did not appear to vary with mIPSC amplitude. The mean time
constant of decay (
d) was 6.4 ± 0.6 ms
(n = 12 cells), with a range of 0.2-20.1 ms. The
10-90% rise time of mIPSCs ranged from 0.2 to 6.3 ms, with a mean
value of 1.9 ± 0.2 ms (n = 12).
Amplitude distributions of spontaneous miniature IPSCs
The distribution of mIPSC amplitudes displayed an overall skewing toward the lowest values (Fig. 3). However, multiple peaks could be visually detected in mIPSC histograms for all cells, and multipeak Gaussian curves could be fit to the amplitude distribution histograms (Fig. 3, A and B). Table 1 summarizes the results of fitting Gaussian distributions to the amplitude histograms generated for each cell. The mean separation of Gaussian peaks ranged from 6.2 to 7.8 pA. The standard deviations of the fitted Gaussians remained fairly constant within individual data sets, ranging from 1.0 to 3.4 pA and were consistently larger than the standard deviations of the background noise, which varied between 0.6 and 1.7 pA. The regularity of the spacing between peaks suggests that these represent a quantal distribution of IPSC amplitude, with the smallest amplitude mIPSC representing the response to a single quantum of GABA. This is supported by the observation that the peak separation for all cells was close to the value of the first Gaussian. The similarity of mean peak separation values between cells suggests a consistency of quantal GABA release within this cortical region.
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Effects of altering extracellular Ca2+ and Mg2+ on mIPSCs
In four cells, the extracellular solution was changed from normal
TTX-containing saline to a solution containing (in addition to TTX) a
lower calcium (0.5 mM) and higher magnesium (8 mM) concentration to
block calcium-mediated events. Perfusion of slices with low Ca2+/high Mg2+ saline
resulted in a decrease in mIPSC mean amplitude (19.7 ± 5.6%) and
frequency (41.5 ± 6.7%). The reduction in mIPSC magnitude was
reflected in the amplitude histograms, which exhibited a decrease in
the proportion of larger amplitude events and a reduction in the number
of histogram peaks. In three cells, only one clear histogram peak
remained after Ca2+ and
Mg2+ concentrations were altered, whereas in the
fourth cell two peaks remained. Figure
4A shows the amplitude
distribution measured in one cell during bath perfusion of
TTX-containing saline with the normal concentration of 2 mM
Ca2+ and 1.6 mM Mg2+. The
histogram was best fit by the sum of three Gaussians with a mean peak
separation of 7.2 pA. After exposure to low
Ca2+/high Mg2+ saline, only
one peak remained, which was best fit by a single Gaussian with a mean
of 7.4 pA. In the second example (Fig. 4B), the amplitude
histogram of mIPSCs recorded in TTX exhibited three peaks with a mean
peak separation of 6.9. Perfusion with low
Ca2+/high Mg2+ saline
eliminated the third peak, leaving two peaks with a mean separation of
7.1. Overall, these results are consistent with previous reports that
alterations in calcium-magnesium concentration ratios affect the
probability of divalent cation-dependent transmitter release, but not
quantal size (Bekkers and Stevens 1994; Del
Castillo and Katz 1954
).
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Effect of altering cell holding potential on mIPSC amplitude
In two cells, cell holding potential was increased from 0 to +40
mV, which translates to an ~50% increase in the driving force of the
chloride-mediated fast IPSC (ECl = 74.1 mV). The change in holding potential led to a 51.2% increase in
mean mIPSC amplitude, from 16.6 ± 0.4 pA to 25.1 ± 0.6 pA
(Fig. 5A). The amplitude
distributions measured at both holding potentials were similarly best
fit by the sums of several Gaussians (Fig. 5, B and
C), but the peak separation was greater at the higher
potential. At 0 mV, the mean separation between peaks was 6.3 pA
(cell 9, Table 1), whereas at +40 mV, the peak separation
was 10.5 pA, representing a 66.7% increase in quantal size. Thus mIPSC
amplitudes increased in a near-linear fashion with respect to membrane
potential. The observed increase in mIPSC amplitude and quantal size
could not be attributed to increased background noise, which was
0.1 ± 1.4 pA at 0 mV and
0.1 ± 1.7 pA at +40 mV.
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Contribution of histogram bin size
Because peaks in amplitude histograms can erroneously arise from
sources such as data binning, variations in data subsets, and finite
sampling from large populations, it was essential to subject the
amplitude data to various tests to evaluate the reliability of the
multipeak fits. One potential source of error with the least-squares
method of fitting Gaussian distributions is the dependency of this
algorithm on bin size (Edwards et al. 1990). Figure
6 shows the effect of varying bin size on
data distributions. Bin width size had no significant effect on the fit
of Gaussian curves to amplitude histograms, causing very little change
in the overall amplitude distributions and positions of peaks.
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Consistency of distributions within a data set
Another possible source of error might lie in variations in the
sample populations taken. One check against this is to compare subsets
of data taken within the same data set (Edwards et al. 1990). If the quantal nature of the distributions is an
artifact of either small sample size or the sampling procedure, then
different subsets of the data would be expected to exhibit different
peaks. Figure 7 shows the effect of
displaying sequential subsets of data taken from the same data set. The
peaks fall in the same locations, thereby ruling out the possibility of
a sampling artifact or systematic change in mIPSC amplitude with time.
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Statistical analysis of histogram distributions
The results of these initial tests supported the reliability of
the multipeak fits. The data were then subjected to more rigorous, statistical tests to check whether histogram peaks could have arisen
from errors in sampling from unimodal distributions. Both the
2 test and autocorrelation scoring method were
employed to assess this possibility.
We first evaluated amplitude distributions using the
2 method. Here, the best fits of mIPSC
amplitude histograms obtained with the unimodal (Weibull) function were
compared against the fits obtained with a sum of Gaussians. The
2 test was used to assess whether the
amplitude distributions were significantly different from either
multimodal or unimodal fits, i.e., if multimodal fits yielded
significantly better fits than unimodal fits (Fig.
8). In all cases, multipeak fits obtained with the sum of Gaussians produced better fits than unimodal Weibull functions (P < 0.05), with Weibull fits failing in
most cases to meet
2 goodness-of-fit criteria.
In no case did single Gaussians provide adequate fits to amplitude
distributions.
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However, there is evidence that suggests that the
2 test (in addition to other conventional
tests) may not be the most sensitive means of distinguishing histogram
modality or "peakiness" (Stratford et al. 1997
).
Consequently, amplitude data were also analyzed with the AC scoring
method, which has been shown to be superior to the
2 and Kolmogorov-Smirnov tests for this
application (Stratford et al. 1997
). First, amplitude
histograms were smoothed using Fourier filtering techniques until all
peaks were eliminated (Fig. 9A). The smoothed curve was
then subtracted from the data histogram, yielding a plot of the
difference (Fig. 9B). The difference plot was lightly
smoothed, and the autocorrelation of the smoothed difference plot was
calculated and graphed (Fig. 9C). The AC score was taken
from the autocorrelation plot as the peak-to-peak difference in
magnitude between the first peak (i.e., nonzero lag) and the preceding
trough, which in the case of the data depicted in Fig. 6 was 2,314. Notably, the first peak in the AC plot occurred at 7 pA, with
subsequent peaks occurring approximately every 6-7 pA. This is in
close agreement with the separation values between peaks of the
multiple Gaussians fitted previously.
|
The next step was to determine whether unimodal distributions fit to the amplitude histograms could generate data sets that appear to be multimodal, i.e., yield AC scores equal to or higher than the original data. If so, this would suggest that the peaks in the amplitude histogram may have erroneously arisen from sampling artifacts. For each real data set, a unimodal curve was fit to the amplitude histogram, which in all cases was best-fit by a Weibull function. The Weibull distribution was then used in Monte Carlo simulations to generate at least 100 sets of amplitude data, each consisting of the same number of samples as the original data set. Each simulated data set was smoothed with the same strength filter employed for the real amplitude distribution, and its AC score determined. The AC scores were then compared against the real data, and the number of scores exceeding the AC value of the real amplitude histogram noted. If <5 in 100 simulated data sets exhibited AC scores higher than the original data, this would suggest that the probability that histogram peaks resulted from sampling errors is <5% (i.e., P < 0.05). In no case did more than 2% of the simulation trials exceed the AC score for the real amplitude data, suggesting that the amplitude histogram peaks were not the result of sampling artifact.
Dendritic filtering of mIPSCs
Synaptic signals generated at distant dendritic locations, but
recorded somatically, would be expected to be distorted (Burgard and Hablitz 1993; Rall 1969
). However, past
experiments have indicated that neocortical pyramidal cells are
electrotonically compact (Larkman et al. 1992
;
Stafstrom et al. 1984
), and previous studies have found
little or no correlation between decay time constants and rise times,
suggesting that miniature synaptic events are generated within a
restricted region of the dendritic tree (Burgard and Hablitz
1993
). Electrotonic filtering is usually signaled by a negative
correlation between rise time and amplitude. Events that are generated
more distally from the recording site would be both attenuated and
delayed due to the cable properties of dendrites (Rall
1969
).
We examined mIPSCs for evidence of dendritic filtering and found no
negative linear correlation between mIPSC rise time and amplitude (Fig.
10A), suggesting that most
mIPSCs were generated within a confined location of the dendritic tree.
However, other investigators have raised valid concerns regarding the
limitations of this type of analysis (Soltesz et al.
1995), arguing that the lack of a negative correlation may not
definitively exclude electrotonic filtering. Therefore to further
assess cable filtering effects, the population of mIPSCs was
arbitrarily separated into two nonoverlapping subclasses of events with
fast (
1.0 ms) and slow (
1.5 ms) rise times to determine whether
either class was more restricted in amplitude. The expectation is that
if filtering is present, slower events should be generally smaller in
amplitude than fast events (Soltesz et al. 1995
). To the
contrary, our findings showed that fast and slow mIPSCs encompass
broad, overlapping ranges of amplitudes (Fig. 10B). Although
mIPSCs may be generated within a confined region on an individual cell,
we have no information on the relative distribution of individual
synapses within this restricted locus. In fact, small positive
correlations were observed between rise time and
d (Fig. 10C,
r = 0.39) and between rise time and half-width duration
(Fig. 7D, r = 0.52), suggesting that mIPSCs
may be generated from diffusely distributed sites within a confined
region on individual cells (Fig. 10C). Some small degree of
local dendritic filtering could account for the correlated changes in
the rising and decaying phases of mIPSCs. The extent to which the
anatomy of the neuronal circuit or space-clamp limitations contribute
to this finding is presently not known. Prior examinations of miniature
excitatory events in hippocampal CA3 pyramidal cells showed that mEPSC
rise time was correlated to
d but not to
amplitude, suggesting that, although mEPSC shape was partly determined
by electrotonic filtering, variations in mEPSC amplitude were not
(McBain and Dingledine 1993
). Similarly, the locus of
inhibitory synaptic terminals on layer V pyramidal cells may be too
confined for passive cable properties to affect mIPSC amplitude, but
may likewise contribute to shaping mIPSCs.
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As a final check for evidence of electrotonic filtering, amplitude
histograms were constructed using mIPSCs with only fast rise times
(1.5 ms) and then compared with the amplitude distribution of the
parent data set (Fig. 11). If dendritic
filtering influences mIPSC amplitude in a systematic way, then it could
lead to a quantal-like distribution. Analyzing only those events with
fast rise times, and hence minimal filtering, would obviate this
potential problem. We found that histogram peaks were consistent across
both data sets, further suggesting that dendritic filtering does not
play a prominent role in determining the amplitude of mIPSCs recorded in these cells.
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DISCUSSION |
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IPSCs evoked with simultaneous stimulation in deep and superficial layers
Previous studies in cortex (Nicoll et al. 1996;
Salin and Prince 1996b
) have shown that stimulation of
superficial layers can evoke inhibitory responses in layer V pyramidal
neurons. This raised the question whether synchronous stimulation of
both proximal and distal inhibitory neurons could extend the magnitude
of maximal IPSCs evoked by deep-layer stimulation alone. Our findings
confirmed that superficial-layer stimulation can evoke inhibitory
responses in layer V target cells, albeit at higher threshold
intensities. A comparison of input-output plots revealed that
deep-layer stimulation evoked maximal amplitude IPSCs at intensities
where superficially evoked responses were still relatively small.
Stimuli delivered simultaneously to both layers I/II and VI did not
evoke maximal IPSCs of greater amplitude than those obtained with layer
VI stimulation alone, confirming the strict limit on recruitment of
fast inhibition. Thus deep-layer stimulation ultimately engages all
inhibitory elements presynaptic to layer V pyramidal cells. This
interpretation is supported by previous work examining the relationship
between stimulus placement and peak IPSC amplitude (Salin and
Prince 1996b
) that showed that stimuli applied <350 µM from
the pyramidal cell soma produced the strongest inhibitory responses and
by studies in our laboratory (Yang and Benardo 1997
)
that demonstrated that maximal inhibitory postsynaptic potentials
recruited with deep-layer stimuli are reduced in magnitude (by ~25%)
when superficial circuit activity is pharmacologically eliminated.
Amplitude distributions of mIPSCs
It appears from our analyses that mIPSCs exhibit multimodal
amplitude distributions. Similar work in other central neurons showed
that mIPSCs display a skewed, unimodal amplitude distribution, with the
peak corresponding to the first peak of amplitude distributions of
evoked, unitary IPSCs (Bekkers 1994; Korn and
Faber 1991
). The mIPSCs recorded in our study also displayed
gross skewing of the overall distribution toward the lowest amplitude
values. However, closer inspection revealed that mIPSC amplitude
histograms were multimodal and well fit by sums of Gaussian curves.
mIPSC amplitudes appeared to be quantally distributed, similar to the findings of previous studies of mIPSCs (Edwards et al.
1990
; Korn et al. 1993
; Ropert et al.
1990
). The amplitude distributions did not appear to an
artifact of instrument (e.g., noise) or statistical variation. In low
Ca2+/high Mg2+, the
majority of amplitude histograms fell to a single peak corresponding to
the first Gaussian, which is consistent with decreased probability of
quantal GABA release. Increasing the cell holding potential revealed a
near-linear dependence of mIPSC mean amplitude and histogram peak
separation (quantal size) on chloride-current driving force, suggesting
that the amplitude distributions were not the result of instrument
artifact. It also confirmed that the mIPSCs recorded were
GABAA-mediated events and that the majority were apparently under adequate voltage-clamp control. Statistical evaluation of mIPSC amplitude histograms supported the reliability of the multipeak Gaussian fits, suggesting that the observed peaks in the
amplitude distributions are not artifacts of sampling or statistical errors. Moreover, the estimates of the spacing between peaks given by
the autocorrelation method were in close agreement to the peak separation values between fitted Gaussians.
Between cells, the peak separations of mIPSCs were remarkably similar,
suggesting a consistency within this inhibitory network for the
determinants of quantal size such as
GABAA-receptor channel conductance, synaptic
connectivity, number of release sites, postsynaptic receptor
distributions, and the number and size of quanta (vesicle content)
released (Mody et al. 1994). Whether this is related to
homogeneity of the population of cells examined is unknown, but sample
variation would be expected to decline even further with increased
sample size.
The variance of the fitted Gaussians was larger than the variance of
the background noise recorded, which is consistent with quantal
variability. The variance in fitted Gaussian curves did not
consistently increase over successive peaks as would be expected for
superposition of independent quantal events, although in one neuron,
the variance was generally larger for higher order peaks. Several
mechanisms are believed to underlie variations in quantal size (for
review see Frerking and Wilson 1996), which can be
generally categorized between presynaptic and postsynaptic origins.
In the context of the "all-or-nothing" scheme (Redman
1990), variations in quantal size have been attributed to
variations in the transmitter content in vesicles (Bekkers and
Stevens 1995
; Frerking et al. 1995
), suggesting
that the amplitude of synaptic events is determined by the amount of
transmitter released. Alternatively, it has been proposed that quantal
variation is determined by the number of postsynaptic receptors at each
synapse, which assumes saturation of all postsynaptic receptors by the
contents of a single vesicle. There is also increasing evidence that
the variations in the amplitude of miniature synaptic events may derive
from differences intrinsic to each synaptic contact (Bekkers et
al. 1990
; Liu and Tsien 1995
).
Assuming that a single synaptic contact comprises several independent
release sites, equidistant peaks in amplitude distributions could
result from synchronous vesicle release at multiple independent sites
or activation of receptor aggregates by individual quanta (Behrends and Ten Bruggencate 1998; Edwards et
al. 1990
). Our observation that low
Ca2+/high Mg2+ saline
eliminated multiquantal events is consistent with coincidental summation of events arising from synchronized multivesicular release of
GABA, either within a single release site or between neighboring sites
(Lewis and Faber 1996
; Poisbeau et al.
1996
). The former assumes that not all receptors at a given
site are saturated by a single quantum of transmitter, which is in line
with previous studies showing that the likelihood of receptor
saturation may vary between synapses for a single cell (Frerking
et al. 1995
; Frerking and Wilson 1996
;
Nusser et al. 1997
). Findings in cerebellar granule
cells (Nusser et al. 1997
) suggest that receptor
occupancy at these synapses is heterogeneous and depends on the number
of postsynaptic receptors present at each synapse.
However, in the present study, the variance of fitted Gaussian curves
did not consistently increase over successive peaks, as would be
expected for superposition of independent events that should lead to
summation of the individual variances. This, however, may not
necessarily preclude multivesicular release. A constancy of variance
has been reported for evoked IPSCs in dentate granule cells
(Edwards et al. 1990) and in goldfish Mauthner cells
(Korn et al. 1987
), and several explanations for this
have been proposed. Edwards et al. (1990)
showed that
relatively small sample sizes could give rise to apparent invariant
standard deviations. However, in this study, the lack of increase in
variance was also observed with data sets comprised of considerably
larger samples (n > 1,000). The constancy of variance
may also indicate that larger amplitude, multiquantal mIPSCs result
from the synchronous activation of multiple
GABAA-receptor aggregates at individual synaptic
terminals by a single packet of transmitter (Edwards et al.
1990
). This might explain the amplitude distribution data in
which two histogram peaks remained in low
Ca2+/high Mg2+ saline (Fig.
4B). In either case, the consistency of the quantal size
suggests that the response of individual GABAA
receptors in these circuits are very similar.
Characteristics of mIPSCs
The general characteristics of mIPSCs presented in this study are
in agreement with those reported for miniature inhibitory events
recorded with similar techniques in both neocortex and hippocampus
(De Koninck and Mody 1994; Edwards et al.
1990
; Otis and Mody 1992
; Ropert et al.
1990
; Salin and Prince 1996a
). The mean mIPSC
amplitude and conductance were in accord with values found in other
cortical regions, and the average frequency of mIPSCs overlaps with
that reported by Salin and Prince (1996a)
for neocortex.
As in those previous studies, mIPSCs were found to decay exponentially
with a single time constant, and the values for rise times and decay
time constants were similar to those reported for pyramidal cells in
neocortex and dentate gyrus. The kinetics were faster than those found
by Ropert et al. (1990)
in hippocampal CA1 region, but
in that study cooler temperatures were used, which could account for
the slower kinetics reported.
Comparison of mIPSCs with GABA-mediated currents
A primary objective of this study was to increase our understanding of the properties of local cortical inhibitory circuits that underlie limited fast inhibition. The aim was to obtain estimates of the number of interneurons involved in generating maximal, ensemble inhibitory events. Because of the prohibitive difficulty in obtaining paired recordings from all interneurons connected to a single pyramidal cell, we elected to examine spontaneous miniature events as a means to estimate the number of interneurons in the circuit through comparisons with published data on evoked IPSCs and GABA-mediated currents.
We found that the mean mIPSC conductance was ~0.3 nS, which is close
to values previously reported for cortex (0.42-0.48 nS) (Salin
and Prince 1996a) and hippocampus (0.2-0.4 nS) (Otis
and Mody 1992
). Studies examining GABAA
receptor-activated conductances in excised membrane patches (De
Koninck and Mody 1994
; Edwards et al. 1990
) and
cultured neurons (Segal and Barker 1984
) have reported
single-channel conductance values in the range of 18-30 pS. Thus the
mean mIPSC conductance would correspond to the activation of 10-20
GABAA receptor channels. The quantal inhibitory
current of ~7 pA (at 0 mV holding potential) is equivalent to a
conductance of ~0.1 nS. Given this, the number of channels underlying
a quantal event would range from three to six. These low numbers are in accord with previous estimates suggesting that mIPSCs and quantal GABA
events in mammalian cortex involve the activation of only a small
number of channels (De Koninck and Mody 1994
;
Edwards et al. 1990
; Ropert et al. 1990
;
Salin and Prince 1996a
).
Comparison of mIPSCs with evoked IPSCs
Previously, we found that the conductance of IPSCs evoked with
minimal stimulation ranged widely, from 0.4 to 9.3 nS, with an average
value of 2.4 ± 1.2 nS (Ling and Benardo 1995b).
This would suggest that for a given target cell, 4-90 quanta of
transmitter are released in response to the minimal extracellular
stimulus needed to evoke an IPSC. These minimally evoked IPSCs likely
represent unitary IPSCs resulting from the activation of a single
interneuron (Edwards et al. 1990
; Jonas et al.
1993
; Redman 1990
). Assessing the lowest range
of values, these events appear to be the result of release of a few
quanta of GABA. Assuming no transmission failures or silent release
sites, this suggests that a single interneuron forms at least a few
(i.e., probably >4) synapses (or release sites) onto the postsynaptic
target cell (cf. Buhl et al. 1994
; Tamás et
al. 1997
; Thomson et al. 1996
). Extending this
analysis further, we can develop estimates, or a range of estimates,
for the number of quanta released, synapses activated, and interneurons engaged for a maximally evoked population IPSC recorded in a single pyramidal neuron.
Although the values for miniature, unitary, and maximal IPSCs vary
considerably, comparisons of mIPSC values with those of evoked IPSCs
should yield preliminary, quantitative estimates to describe the
functional properties of these local inhibitory circuits. Previously,
we found that the mean peak conductance of the maximal IPSC evoked with
extracellular stimulation was 25.9 ± 4.2 nS (range 10.5-41.2 nS)
(Ling and Benardo 1995a,b
). If the average minimal
evoked IPSC conductance (2.4 ± 1.2 nS) is taken as a measure of
the unitary inhibitory conductance (i.e., event associated with the
activation of a single, presynaptic, inhibitory interneuron), then on
average 10-12 individual interneurons are engaged during generation of
maximal population IPSCs, very close to estimates in neocortex
(Benardo 1994
) and hippocampus (Miles and Wong
1984
) made using current-clamp recordings. If we assume that
all neurons connected to an individual pyramidal cell can be activated
during the maximal evoked population IPSC (i.e., no "silent
cells"), then this number would also correspond to the total number
of interneurons that synapse onto a given principal cell in the slice
preparation. Of course, this likely underestimates the neuronal
connectivity in neocortex in vivo. Nonetheless, to extrapolate further,
if the mIPSC is representative of transmitter release from a single
synapse, we could estimate, given a mean mIPSC conductance of ~0.3
nS, that a single interneuron may form, on average, ~4-12 synapses
with an individual pyramidal cell. This estimate is in line with
findings from combined electrophysiological and anatomic studies of
mammalian cortex that show that individual cells belonging to certain
classes of inhibitory interneurons may form up to a dozen or more
synapses with a single principal cell (Buhl et al. 1994
,
1995
; Tamás et al. 1997
;
Thomson et al. 1996
). Thus the functional connectivity
scheme for inhibition is low as compared with excitatory circuits
(Thomson and Deuchars 1994
), consistent with a
high-fidelity throughput system in which the activation of only a small
number of inhibitory cells is sufficient to exert a substantial
regulatory influence on principal cell excitation (Miles
1990
; Miles and Wong 1984
).
Dendritic filtering of mIPSCs
There were no indications that dendritic filtering contributed to
variations in mIPSC amplitude in our experiments. As stated above,
investigations examining synaptic events in neocortex using standard
intracellular techniques indicated that neocortical pyramidal cells are
electrotonically compact (Larkman et al. 1992;
Stafstrom et al. 1984
). Furthermore, studies examining
laminar differences in neocortical circuitry (Salin and Prince
1996b
) suggest that the majority of inhibitory input to layer V
pyramidal neurons may originate from presynaptic elements proximal to
the principal cell soma. Thus the majority of fast IPSCs may be
generated within an electrotonically restricted locus relative to the
soma, which would explain the apparent lack of dendritic filtering in
our recordings. However, this does not preclude the existence of distal inhibitory GABAergic synapses, because previous studies have provided evidence for distal sites of IPSC generation in cortical pyramidal cells (Benardo 1997
; Salin and Prince
1996b
). In the present study, access to these distal sites may
be impeded on technical grounds owing to possible space-clamp
limitations (Salin and Prince 1996a
,b
). However, the
variations observed in mIPSCs rise times and decay time constants
suggest that some cable filtering was present, which might contribute
to determining the shape of mIPSCs. The importance of distally
generated IPSCs in gating excitatory drive in layer V cells provides a
further impetus to our attempts to better define fast inhibition in
this cortical region.
In conclusion, our analysis provides electrophysiologically based estimates on the connectivity scheme of inhibitory cortical circuits. Although this purely electrophysiological analysis cannot provide complete, definitive information on the cell-to-cell connection patterns, it does reveal some important empiric parameters describing the functional properties of inhibitory connections and, in turn, the physiological limits of fast inhibition, and thus provides a functional correlate to anatomic data. As such, our findings help to further define the operational boundaries of cortical inhibition.
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ACKNOWLEDGMENTS |
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The authors thank Dr. Stephen H. Lockhart and D. Teager for helpful comments on curve fitting and Fourier smoothing, respectively.
This work was supported by National Institute of Mental Health Grants MH-51677 and MH-01431 to L. S. Benardo and a grant to D.S.F. Ling from the New York City Council Speaker's Fund for Biomedical Research: Towards the Science of Patient Care.
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FOOTNOTES |
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Address for reprint requests: D.S.F. Ling, Dept. of Pharmacology, State University of New York, Health Science Center at Brooklyn, 450 Clarkson Ave., Brooklyn, NY 11203.
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 4 September 1998; accepted in final form 21 June 1999.
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REFERENCES |
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