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The Journal of Neuroscience, February 1, 1998, 18(3):1161-1170
Variability and Correlated Noise in the Discharge of Neurons in
Motor and Parietal Areas of the Primate Cortex
Daeyeol
Lee1, 2,
Nicholas L.
Port1, 2, 5,
Wolfgang
Kruse1, 2, and
Apostolos P.
Georgopoulos1, 2, 3, 4, 5
1 Brain Sciences Center, Veterans Administration
Medical Center, Minneapolis, Minnesota 55417, Departments of
2 Physiology, 3 Neurology, and
4 Psychiatry, University of Minnesota Medical School,
Minneapolis, Minnesota 55455, and 5 Graduate Program in
Neuroscience, University of Minnesota, Minneapolis, Minnesota 55455
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ABSTRACT |
We analyzed the magnitude and interneuronal correlation of the
variability in the activity of single neurons that were recorded simultaneously using a multielectrode array in the primary motor cortex
and parietal areas 2/5 in rhesus monkeys. The animals were trained to
move their arms in one of eight directions as instructed by a visual
target. The relationship between variability (SD) and mean of the
discharge rate was described by a power function with a similar
exponent (~0.57), regardless of the cortical area or the behavioral
condition. We examined whether the deviation from mean activity between
target onset and the end of the movement was correlated on a
trial-by-trial basis with variability in activity during the hold
period before target onset. In both cortical areas, for about a quarter
of the neurons, the neuronal noise of these two periods was positively
correlated, whereas significant negative correlations were seldom
observed. Overall, neurons with higher signal correlation (i.e.,
similar directional pattern) showed higher noise correlation in both
cortical areas. On the other hand, when the data were divided according
to the distance between the electrode tips from which the neurons were
recorded, a consistent relationship between the signal and noise
correlations was found only for pairs of neurons recorded through the
same electrode. These results suggest that nearby neurons with similar
directional tuning carry primarily redundant messages, whereas neurons
in separate cortical columns perform more independent processing.
Key words:
directional tuning; motor cortex; noise correlation; parietal cortex; synchronized firing; rhesus monkey
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INTRODUCTION |
The activity of single neurons is
quite variable even when tested under the same conditions, and such
"neuronal noise" is thought to limit the capacity of individual
neurons to transmit information (Perkel and Bullock, 1969 ; Johnson,
1980; Tolhurst et al., 1983; Mainen and Sejnowski, 1995). The magnitude
of neuronal noise (SD), taken primarily from the visual cortex, is
comparable with the mean activity (Henry et al., 1973; Tomko and
Crapper, 1974; Rose, 1979; Dean, 1981; Tolhurst et al., 1983; Vogels et al., 1989; Snowden et al., 1992; Britten et al., 1993; Softky and Koch,
1993; Gur et al., 1997). For motor cortical areas, although variability
in neuronal activity during the period of movement preparation has been
linked to changes in response times (Lecas et al., 1986; Riehle and
Requin, 1993), quantitative characterization of neuronal noise has not
been performed.
In most previous studies, the noise of individual neurons was
measured separately, one neuron at a time, and, therefore, one could
not determine whether the noise was correlated among a group of
neurons. However, the correlated noise among multiple neurons can
fundamentally affect the outcome of combining activity in a neuronal
pool (Johnson, 1980; Gawne and Richmond, 1993; Shadlen et al., 1996;
Lee et al., 1998). Although the similarity between the psychometric
function of the animal and the neurometric functions for neurons in the
visual cortex suggests that pooling is limited to a relatively small
number of sensory neurons, the presence of correlated noise may
increase the required size of the neuronal pool (Tolhurst et al., 1983;
Britten et al., 1992; Zohary et al., 1994; Shadlen et al., 1996). In
the motor cortex, the direction of an arm movement in space can be
accurately predicted by a population vector that is the vector sum of
preferred directions of individual neurons weighted according to their
activities (Georgopoulos et al., 1983, 1986, 1988), and the size and
pattern of the correlated noise also play an important role (Lee et
al., 1998). Because it is likely that nearby neurons receive more
common inputs than do those farther apart, it might be expected that
correlated noise decreases with interneuronal distance (Braitenberg and
Schüz, 1991; Zohary et al., 1994; Douglas et al., 1995). On the
other hand, corticocortical connections in the visual cortex
preferentially knit together columns with similar receptive field
properties (Ts'o et al., 1986; Gilbert and Wiesel, 1989). Because
similar focal concentrations of synaptic connections have been found in the motor cortex (DeFelipe et al., 1986; Shinoda and Kakei, 1989), neurons with similar directional tuning may display correlated noise
even in separate cortical columns. In the present study, we
characterized the magnitude and correlation of neuronal noise in the
primary motor cortex and parietal areas 2/5 from neurons recorded in a
wide range of interneuronal distances. The effects of firing patterns
and noise stability on the correlated noise were also examined to
understand the nature and possible roles of neuronal noise.
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MATERIALS AND METHODS |
Animal preparation. Animal care and surgical
procedure have been described previously (Georgopoulos et al., 1982;
Lurito et al., 1991). They conformed to the principles outlined in the
Guide for the Care and Use of Laboratory Animals (National
Institutes of Health publication no. 85-23, revised 1985).
Behavioral paradigms and data collection. Three adult rhesus
monkeys performed reaching movements using a two-dimensional articulated manipulandum (Georgopoulos et al., 1982). Visual stimuli were displayed on a 14 inch computer screen located 57 cm in front of
the animal. The animal controlled the position of a feedback cursor
(circle of 0.3 cm radius) displayed on the screen by moving the
manipulandum. The gain of the feedback cursor was set to one, and the
x-y position of the manipulandum was sampled at
100 Hz with a spatial resolution of 0.125 mm. At the beginning of each trial, the animal was required to maintain the position of the feedback
cursor within the central target (circle of 1 cm radius) for 1-3 sec.
After this variable center hold time (CHT), one of eight peripheral
targets located 8 cm from the central target (every 45°) was
presented, instructing the direction of the required movement. For each
neuron, each direction of movement was repeated four to five times in a
pseudorandom order.
Single cell activity was recorded in the arm area of the motor cortex
(area 4; two hemispheres) and parietal areas 2/5 (two hemispheres),
using an array of seven electrodes the interelectrode spacing of which
ranged from 0.33 to 4 mm (Lurito et al., 1991; Mountcastle et al.,
1991; Lee et al., 1998). Each electrode was connected to a head stage,
low-pass and 60 Hz notch filters, a gain amplifier, an equalizing
bandpass filter, and a dual-amplitude window discriminator (Bak
Electronics, Germantown, MD). The output of the amplifier was connected
to a display oscilloscope (Tektronix 2232) and an audio monitor. Spike
arrival times were stored at 1 µsec resolution. Occasionally, two
neurons were isolated from the same electrode, and the data were
accepted only when separation of the signal was clear as judged by the
shapes of individual spikes. It is possible, however, that some nearly
simultaneous spikes were missed when they produced temporally
overlapping spikes recorded by the same electrode.
Data analysis. For a given neuron, two values were measured
in each trial, namely, the discharge rate during the last second of the
CHT and the discharge rate between the target onset and the end of the
movement [total experimental time (TET)]. These two values are
denoted as Ami,k and
Bmi,k, respectively, where i
refers to a particular neuron, k represents the movement
direction (k = 1, 2, ... , 8 for the movements at
0, 45, ... , 315° counterclockwise, where 0° indicates the
rightward direction), and m indicates the number of trials
within each movement direction (m = 1, 2, ...,
5).
To quantify the variability of discharge rates, we defined the noise as
the deviation from the mean discharge rate during each period. Thus,
noise for the CHT was Ami,k  Ai,k, and that for the TET was
Bmi,k Bi,k,
where Ai,k
(Bi,k) indicates the mean discharge rate
during the CHT (TET) for neuron i and the kth
movement direction. We also calculated SDs for these two measures. For
the CHT:
where Ai is the mean discharge
rate during the CHT for neuron i, and
Nm refers to the number of repetitions for each
movement direction (i.e., Nm = 4 or 5). For the
TET, the SD was calculated separately for each movement direction:
For each neuron, the signal was defined as the mean discharge
rate during the TET for each movement direction, i.e.,
Bi,k. For a given pair of neurons
(i and j), the signal correlation was defined as
the correlation coefficient between the signals of the two neurons:
where:
For each neuron, noise stability was defined as the correlation
coefficient of the noise between the CHT and TET:
For each pair of neurons, the noise correlation was defined as
the correlation coefficient of the noise between the two neurons. For
the CHT:
The noise correlation for the TET was defined similarly:
It should be noted that although each movement direction was
repeated only four or five times, estimates of the noise and signal
correlation were based on the data collected for eight movement
directions, so that the number of trials contributing to these
estimates was at least 32.
For hypothesis testing involving comparison of the above correlation
coefficients, each correlation coefficient (r) was first converted into Fisher's z transform for normalization of
the distribution as follows (Snedecor and Cochran, 1989):
In previous studies of neuronal noise, the coefficient of
variation (CV) has been used frequently to represent the amount of
variability relative to the mean activity. The CV is the ratio between
the SD and the mean (i.e., SD/M) for a given variable. In the present
study, we calculated the CV for the discharge rate (rate CV) and the CV
for the interspike intervals (interval CV) during the CHT. Because CV
is a ratio, it was log-transformed to normalize its distribution for
the purpose of statistical analysis. The SD was also log-transformed
for the same purpose.
To examine the tendency of synchronized firing between a pair of
neurons, we constructed cross-correlation histograms (CCH, or
cross-correlograms) between spike trains during the CHT for all pairs
of neurons that were recorded simultaneously. (Pairs of neurons
recorded through the same electrode were excluded from the analysis
because we could not ensure that synchronous spikes were always
detected properly under these circumstances.) Only pairs of neurons in
which the CCH was based on >200 spikes were considered for reliable
results. A CCH shows the firing frequency of a neuron as a function of
the time elapsed from the occurrence of a spike in another neuron
(Perkel et al., 1967). Synchronized firing was taken as the area under
the CCH between 10 and 10 msec after the average of the CCH between
100 and 100 msec was subtracted as the baseline (Fig.
1). To assess statistical significance, we used a randomization test (Perkel et al., 1967; Manly, 1991) in
which 500 additional CCHs were generated for each pair of neurons after
randomly shuffling the trials from which the spike trains for two
neurons were drawn (Fig. 1, thick solid line). The
frequency with which the amount of synchronized firing in the original
CCH was exceeded in these shuffled CCHs gave the p value for
statistical significance.
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Figure 1.
The CCH or cross-correlogram for a pair of
neurons recorded in the motor cortex (shaded area). The
histogram (thick solid line) represents an example of a
shuffled CCH produced after the trials from which the two neurons were
recorded were randomly shuffled. The degree of synchronized firing was
measured as the area in the CCH between 10 and 10 msec (dotted
vertical lines) after the baseline (thin solid
horizontal line) was subtracted. In this example, none of the
500 shuffled CCHs produced greater synchronization than did the
original CCH (i.e., p < 0.002).
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A method of cell classification developed in our laboratory (Taira and
Georgopoulos, 1993) was applied to classify neurons according to mean
discharge rate, burst characteristics, and proportion of short
interspike intervals. For the burst analysis, the method of
Legéndry and Salcman (1985) and Aldridge and Gilman (1991) was
used. In this method, a series of short interspike intervals is defined
as a burst if it includes at least two successive intervals (three
spikes) less than one-half of the average in the whole spike train and
if the probability of the occurrence of the burst in a random (Poisson)
spike train was <0.001. For each burst, the burst index is calculated
as the square root of the product of the surprise value (the negative
logarithm of the probability of the burst occurrence) and the burst
rate per 1000 spikes. Taira and Georgopoulos (1993) derived the
following classification functions from a discriminant analysis
performed on spike trains of 1925 cortical cells:
where C is the classification function, X
is the mean frequency of the discharge, Y is the percentage
of interspike intervals <20 msec, and Z is the burst index.
A neuron is classified into the group that yields the largest value in
the classification function. These three types correspond to neurons
with a low discharge rate and low bursting (type A), those with a low
discharge rate and high bursting (type B), and those with a high
discharge rate and low bursting (type C).
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RESULTS |
Variability of discharge rates
We recorded the impulse activity of 681 and 492 neurons from
the primary motor cortex and parietal areas 2/5, respectively. We found
that the relationship between the mean and the SD of discharge rates
was fit well by power functions in both motor and parietal cortices for
both CHT and TET (Fig. 2). The power functions that fit the actual data best and the corresponding r2 were:
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In these equations, M represents the mean of discharge rates,
respectively. The coefficients were obtained from a linear regression
after all the variables were log-transformed. To obtain the
relationship between the variance (instead of SD) of discharge rates
and their means, both sides of the above equations can be squared,
resulting in the exponent in these new equations ranging between 1.10 and 1.17. These results indicate that the relationship between the SD
and mean of the discharge rates was quantitatively similar regardless
of the cortical area and the behavioral condition.
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Figure 2.
Relationship between SD of discharge rate
(y-axis) and mean discharge rate
(x-axis) during the CHT (top) and the TET
(bottom). Data are shown separately for the neurons in
the motor cortex (left) and the parietal cortex
(right). The best-fit power functions (see Results) for
the CHT (dotted line) and the TET (solid
line) are shown twice for each cortical area for the sake of
comparison. Because each movement direction is treated separately for
the discharge rates during the TET, but not for the CHT, there are eight times as many data points for the TET than for the CHT. Larger
variability among the data points for the TET is probably attributable
to a smaller number of trials contributing to each data point.
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Because there was no hand movement during the CHT in almost all of the
trials, random hand movements during the CHT were unlikely to be the
cause of neuronal noise during the CHT. Although the activity of
neurons in both motor and parietal areas has been shown to be affected
by hand position, the variability in hand position during the CHT in
the present study was also relatively small (<1 cm), and most neuronal
noise during the CHT was not systematically related to such variability
in hand position. We applied the following multiple linear regression
model to examine the effects of the variability in hand position on the
activity of each neuron during the last second of the CHT:
where b0 ~ b2 are
the regression coefficients, Xmk and
Ymk indicate the average horizontal and
vertical hand positions, respectively, during the last second of the
CHT, and emi,k is an error term. The number
of neurons for which b0,
b1, or b2 differed
from zero in a statistically significant way was small in both the
motor cortex (34 neurons, 5.0%) and the parietal cortex (30 neurons,
6.1%) and was not significantly different from binomial estimates
based on the significance level used (5%).
Stability of neuronal noise
One important piece of information in understanding the nature of
neuronal noise is the stability of neuronal noise over time (a time
course). We measured the noise over two successive time intervals, and
to evaluate stability of the neuronal noise during these two periods
within individual trials, we determined whether trial-by-trial
variability in the activity during the last second of the CHT was
correlated with trial-by-trial variability during the TET. This measure
of noise stability captures relatively slow fluctuations in the
discharge rates within a single neuron over a period of several seconds
and is different from the interneuronal noise correlation (see below).
The distribution of correlation coefficients between these two periods
displayed significant bias toward positive values (Fig.
3). The median correlation coefficients for the motor and parietal cortices were 0.16 and 0.14, respectively. In the motor cortex, neuronal noise between these two periods showed
statistically significant positive correlation in 179 neurons (26.2%)
but showed significant negative correlation in only 3 neurons (0.4%).
In the parietal cortex, 116 neurons (23.6%) and 1 neuron (0.2%)
produced significant positive and negative correlation, respectively.
Thus, these two cortical areas were similar in terms of stability of
neuronal noise. The cumulative probability functions for this
correlation coefficient were not statistically different between these
two areas (Kolmogorov-Smirnov test, D+ = 0.044; p = 0.623). Thus, in both cortical areas, a
substantial portion of the neurons examined displayed relatively
low-frequency fluctuation in their discharge rates across two
behaviorally distinct epochs.
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Figure 3.
Top, Distribution of correlation
coefficients between noise during the CHT and that during the TET, or
noise stability, for the primary motor cortex (left) and
the parietal cortex (right). Filled areas
indicate the neurons with statistically significant correlation
(p < 0.05). Bottom,
Cumulative probability for the same data.
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Cortical neurons display various patterns in their spike trains, and
distinct features in their firing patterns have been used to make
inferences about their anatomical substrates (Steriade, 1978; Taira and
Georgopoulos, 1993). To evaluate the possibility that neurons with
different anatomical features may display different noise patterns, we
classified the neurons examined in the present study according to the
classification scheme developed by Taira and Georgopoulos (1993). One
of these classes (type C), characterized by a relatively high discharge
rate and low bursting, displayed a more stable noise pattern than did
the other two classes (Table 1),
suggesting that the stability of neuronal noise might be different
among groups of neurons with different firing characteristics.
Variability of interspike intervals
Our definition of neuronal noise is based on the rate of discharge
estimated from a period of ~1 sec. We examined whether such neuronal
noise is related to the regularity of interspike intervals. If
successive interspike intervals were statistically independent, the
mean and SD of the discharge rate would be completely determined by the
distribution of interspike intervals. This would not be the case if
there was higher-order statistical structure in the spike trains. To
examine this issue, we used the CV. Larger CVs indicate greater
variability. For variability in discharge rate, we calculated the CV
for the discharge rate during the last second of the CHT (rate CV).
Similarly, the CV for interspike intervals during the same period was
also calculated (interval CV). For this analysis, only neurons that
contributed >20 interspike intervals were considered, because small
numbers of spikes could result in unreliable outcomes. These two CVs
were significantly correlated in both cortical areas. The correlation
coefficients between the log-transformed CVs (see Materials and
Methods) were 0.5840 (n = 598) for the motor cortex and
0.5008 (n = 445) for the parietal cortex (Fig.
4). In both areas, these two variables were more strongly correlated among neurons with relatively small variability in their discharge rates. When the correlation coefficient was recalculated for neurons with rate CVs < 0.5 (Fig. 4,
top, below the dotted line), it increased
to 0.7706 (n = 115) and 0.6410 (n = 126) for the motor and parietal cortices, respectively. In contrast,
when only neurons with rate CVs exceeding this criterion were
considered (Fig. 4, top, above the dotted
line), the corresponding correlation coefficients were
reduced to 0.2491 (n = 483) and 0.1508 (n = 319), respectively. These results indicate that
the amount of regularity in the interspike intervals is more strongly related to the variability of the discharge rate when the variability in the discharge rate is relatively small.
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Figure 4.
Top, Relationship between the rate
CV and the interval CV during the same period for the primary motor
cortex (left) and the parietal cortex
(right). Bottom, Relationship between
noise stability (correlation of noise between the CHT and the TET) and
the interval CV.
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For a random spike train (Poisson process), in which the variance of
discharge rate is identical to its mean, the value of interval CV is
one (Softky and Koch, 1993), and a value of interval CV larger than one
is an indication of a multistate neuron (Wilbur and Rinzel, 1983). For
neurons with a rate CV < 0.5, the percentages of neurons with an
interval CV larger than one were 35 and 56% for the motor and parietal
cortices, respectively, whereas for those with a rate CV > 0.5, the corresponding values were 84 and 87%. These results suggest that
relatively large values of rate CV are the result of switching between
multiple states with different mean discharge rates.
Next, we examined whether noise stability is affected by the relative
amount of variability in the discharge rates or the regularity of
interspike intervals. The rate CV during the CHT did not have
significant effects on noise stability. The correlation coefficient
between the log-transform of the rate CV and the z transform
of noise stability was 0.0411 and 0.0540 for the motor and parietal
cortices, respectively. On the other hand, the log-transform of the
interval CV showed a small but significant negative correlation with
noise stability in the parietal cortex (r = 0.1359;
p < 0.05), whereas a weak positive correlation in the
motor cortex was not statistically significant (r = 0.0389; Fig. 4, bottom). These results suggest that the
noise stability is not influenced in any major way by either the
variability in the discharge rates or the regularity in the interspike
intervals.
Relationship between signal correlation and noise correlation
Our analysis of the correlated noise was based on 1416 and
1087 pairs of neurons that were recorded simultaneously in the primary
motor cortex and parietal areas 2/5, respectively. The value of noise
correlation varied widely, and there was a slight bias toward positive
correlation in the distribution of noise correlation in both areas. The
mean values for the z transforms of the noise correlation
were statistically different from zero in both areas for both the CHT
and the TET (t test, p < 0.05; Table
2). In addition, there was a weak but
statistically significant correlation between signal correlation and
noise correlation. The correlation coefficient between the z
transforms of signal correlation and noise correlation is shown in
Table 3 for different cortical areas and
behavioral conditions (CHT and TET). We subdivided these data according
to the distance between electrode tips from which pairs of neurons were
recorded to examine whether spatial proximity between two neurons
affects the relationship between the signal correlation and the noise
correlation. The numbers of pairs that were recorded through the same
electrode were 60 and 46 for the two areas, respectively, and they
formed a separate group in this analysis. For both cortical areas, the
highest correlation between the signal correlation and the noise
correlation was found for neurons that were recorded through the same
electrodes (Figs. 5-7),
and there was a tendency for such correlation to decrease gradually as
the distance between the electrodes increased (Fig. 7). This was true
whether the noise correlation was obtained from the CHT or TET.
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Table 3.
Correlation coefficient between z transforms of
the signal correlation and the noise correlation during the CHT (TET)
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Figure 5.
Relationship between the signal correlation and
the noise correlation in the motor cortex during the CHT
(top) and the TET (bottom). Pairs of
neurons were divided into seven groups according to the distance
between the electrode tips from which they were recorded. The
solid line in each panel was determined
by a linear regression. The correlation coefficients for these data are
shown in Figure 7.
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Figure 6.
Relationship between the signal correlation and
the noise correlation in parietal areas 2/5. The same conventions
described in Figure 5 apply.
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Figure 7.
Effects of the distance between the electrode tips
(x-axis) on the correlation coefficient between the
signal correlation and the noise correlation during the CHT
(top) and the TET (bottom) for the
primary motor cortex (right) and the parietal cortex
(left). The y-axis shows Fisher's
z transform ± SE for the correlation coefficient
between the noise correlation and the signal correlation as shown in
Figures 5 and 6. The asterisks indicate the correlation coefficients that were significantly different from zero
(p < 0.05).
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We examined the relationship between the signal correlation and the
noise correlation separately for pairs of neurons of the same or
different classes (Taira and Georgopoulos, 1993). Type C neurons were
not included in this analysis because of the small sample size (Table
1). In both cortical areas, the noise correlation was more closely
correlated with the signal correlation during the CHT if both neurons
in the pair were of type A, a type that was characterized by a low
discharge rate and low bursting, but this was not the case during the
TET (Table 4). These results suggest that
if two neurons are both of type A, similarity in their directional
signal is more likely because of either common inputs or reciprocal
connections between them.
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Table 4.
Effects of cell types on the correlation coefficient
between the z transforms of the signal correlation and the
noise correlation during the CHT (TET)
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Effects of noise stability on correlated noise
Neurons differed substantially in their amount of
noise stability (Fig. 3), and we therefore considered the possibility
that the amount of noise correlation is related to noise stability in
the neurons in a given pair. To test this possibility, we screened pairs of neurons in which both neurons displayed statistically significant noise stability, i.e., significant correlation in neuronal
noise between the CHT and TET. Mean values of the z
transforms of the noise correlation for these neurons were not
statistically different from the corresponding values of the entire
sample (Table 2). These results suggest that the amount of correlated
noise is independent of stability of neuronal noise. We also calculated the correlation coefficient between the z transforms of the
signal correlation and the noise correlation for those pairs of neurons that displayed significant noise stability (Fig.
8). There was significant correlation
between the signal correlation and the noise correlation in the
parietal cortex only for the CHT (Table 3).
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Figure 8.
Effects of the signal correlation on the noise
correlation during the CHT (top) or the TET
(bottom) for the neurons with significant noise
stability in the primary motor cortex (left) or the
parietal cortex (right).
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Effects of synchronized firing on the signal and
noise correlation
To examine whether pairs of neurons with a tendency to fire
synchronously show more similar directional tuning or higher noise correlation, we selected pairs of neurons that displayed statistically significant positive peaks at approximately zero time lag in the CCH
(see Materials and Methods). The percentage of neuronal pairs with
significant positive peaks was similar in the two cortical areas, 18.7 and 17.2% for the motor and parietal cortices, respectively (Table 2).
The distribution of interelectrode distances for pairs of neurons with
such functional connectivity did not differ significantly from the
distribution of entire samples for either cortical area (Kolmogorov-Smirnov test; D+ = 0.0923 and
p = 0.2037 for the motor cortex; D+ = 0.0728 and p = 0.6318 for the parietal cortex).
Finally, we examined whether neurons are more likely to show positive
peaks in their CCHs if they belong to the same or specific classes, according to the scheme of Taira and Georgopoulos (1993), but we did
not find any significant differences.
In both cortical areas, there were statistically significant
differences between the distributions of signal correlation of all
possible pairs and those with significant synchronized firing (Kolmogorov-Smirnov test, p < 0.05). These
differences were caused by the fact that there were more pairs of
neurons with relatively high signal correlation among those with
synchronized firing than would be expected from the entire population
(Fig. 9). Similarly, those pairs of
neurons with synchronized firing in both areas displayed higher noise
correlation during both the CHT and TET (Kolmogorov-Smirnov test,
p < 0.01; Table 2).
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Figure 9.
Top, Distribution of the signal
correlation between pairs of neurons with significant synchronized
firing in the primary motor cortex (left) and the
parietal cortex (right) is shown. These neurons were
selected according to the criteria described in Materials and Methods
(see also Fig. 1). Bottom, Thick lines
show the cumulative probability for the same data, and thin
lines show the cumulative probability for the signal
correlation between neurons without significant synchronized
firing.
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On the other hand, the relationship between the signal and the noise
correlations for neurons with significant synchronized firing was
similar to that for neurons without a tendency for synchronized firing,
except for noise during the CHT in motor cortex (Fig.
10, Table 3). For noise during the CHT
in motor cortex, the correlation coefficient between the z
transforms of the signal correlation and the noise correlation for
those neurons with synchronized firing (r = 0.3326;
n = 147) was significantly higher than that for those
without synchronized firing (r = 0.0001;
n = 640). Even when a pair of neurons that showed
extremely high correlation in both signal and noise was excluded from
the analysis (Fig. 10, CHT, motor cortex,
one data point in the top right corner), the
correlation coefficient for neurons with synchronized firing (r = 0.1766; n = 146) was significantly
different from those without synchronized firing at the 10% level
(p = 0.055). Thus, although the degree of
synchronized firing had minor effects on the relationship between the
signal and the noise correlations in most cases, it may play a role in
the motor cortex during the CHT.
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Figure 10.
Effects of the signal correlation on the
noise correlation during the CHT (top) or the TET
(bottom) for neurons with significant synchronized
firing in the primary motor cortex (left) and the parietal cortex (right).
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|
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DISCUSSION |
Sources of variability in activity of cortical neurons
To separate neuronal noise from the signal, it is necessary to
control all variables that have systematic influences on the activity
of neurons under consideration. Otherwise, one might obtain an
overestimation or artifactual correlation of neuronal noise. Gur et al.
(1997), for example, showed that small eye movements during fixation
are responsible for a substantial portion of the response variability
of neurons in the primary visual cortex. In the present study, because
the hand was stationary during the CHT, the neuronal noise was not
caused by random movements during the CHT. Alternatively, the neuronal
noise might have been caused by the intertrial variability in the hand
position (Evarts, 1969; Thach, 1978; Georgopoulos et al., 1984a; Ashe
and Georgopoulos, 1994), but we showed with a multiple linear
regression model that the variability in the hand position was not a
significant factor in the neuronal noise during the CHT.
Activity in motor cortex during the TET is related to more than one
movement parameter, including direction and amplitude (Fu et al., 1993;
see also Georgopoulos, 1994). In the present study, neuronal noise
during TET was calculated separately for each movement direction, thus
eliminating from the noise the intertrial variability in neuronal
activity related to movement direction. We did not attempt to relate
the remaining variability in neural activity to other movement
parameters, because the number of trials was too small for such
analysis. However, the following observations suggest that a large
proportion of the neuronal noise during the CHT and the TET shares a
common origin. First, functions describing the relationship between SD
and mean activity were similar in these two periods (Fig. 2). Second,
variability in these two periods was often significantly correlated
(Fig. 3). This is consistent with a recent optical imaging study that
showed that the evoked response in the visual cortex is correlated with
the preceding ongoing activity (Arieli et al., 1996). Finally, the
effects of signal correlation and spatial proximity on noise
correlation were similar (Figs. 5-7). The noise correlation was higher
for neurons with similar directional tuning primarily when they were
recorded through the same electrodes. To the extent that neuronal noise during TET is related to variability in the movement parameters, the
relationship between signal correlation and noise correlation would
have been similar regardless of the spatial proximity of the two
neurons involved. These results suggest that the properties of neuronal
noise remain relatively constant under these two different behavioral
conditions.
Comparison across different areas
The two cortical areas examined in the present study, i.e.,
the primary motor cortex and parietal areas 2/5, were similar with
respect to the relationship between variability and mean activity (Fig.
2), noise stability (Fig. 3), and noise correlation (Figs. 5-7). Most
previous studies on neuronal noise have been performed on the visual
structures, and to our knowledge, no previous studies have provided
quantitative characterization of neuronal noise in the cortical areas
dealt with in the present study. Nevertheless, a power function with
similar exponents seems to be a good descriptor of the variability
across different structures (Werner and Mountcastle, 1965; Dean, 1981;
Tolhurst et al., 1983; Vogels et al., 1989; Snowden et al., 1992;
Hartveit and Heggelund, 1994; Gur et al., 1997). These results suggest
that a common mechanism is responsible for the neuronal noise in these
cortical areas. The issues on correlated noise can be addressed only
with simultaneous recording of multiple neurons, and such data have
been available only from a small number of studies (e.g., Gawne and
Richmond, 1993; Zohary et al., 1994). Those other studies were
performed using a single electrode, and therefore effects of spatial
proximity on noise correlation could not be examined. In the middle
temporal visual area (MT), Zohary et al. (1994) showed that neurons
with similar preferred directions tend to have higher noise
correlation. Our results suggest that such a linkage is manifested only
for neurons in close proximity and not for neurons farther apart.
Effects of cell type
Using the procedure developed by Taira and Georgopoulos (1993), we
classified neurons into three classes. It has been suggested that type
A neurons correspond to pyramidal cells, whereas types B and C comprise
both interneurons and pyramidal cells (Steriade, 1978; Taira and
Georgopoulos, 1993). The issue of whether different classes of neurons
display different patterns of noise has not been addressed in the past.
In the present study, type C neurons (high discharge rates, low
bursting) displayed more stable neuronal noise, suggesting that stable
noise is related to the regulatory functions of inhibitory local
circuits (Berman et al., 1992; Shadlen and Newsome, 1994). In addition,
pairs of type A neurons (low discharge rates, low bursting) showed
stronger effects of signal correlation on noise correlation during the
hold period (CHT). These results were consistent regardless of the
cortical area examined.
Effects of synchronized firing
The percentages of neuronal pairs that displayed statistically
significant positive peaks in their CCH were similar in the two
cortical areas examined in our study. In addition, in both areas, such
neurons were more likely to have similar directional tuning as well as
higher noise correlation, although the size of these effects was
modest. Previous results from our laboratory have shown that neurons
with similar preferred directions tend to have more synchronized firing
in the motor cortex, based both on the waiting time probability density
function (Georgopoulos et al., 1993) and on the CCH (Georgopoulos et
al., 1994). The database used for the current study was different from
that used in these earlier reports and therefore provides additional,
and independent, evidence that similarity in directional tuning is an
important factor determining functional neuronal connectivity.
In the inferior temporal areas (IT), it was shown that signal
correlation was not significantly affected by the presence or absence
of functional connectivity as revealed by the CCHs, although this
conclusion was based on a relatively small sample size (Gawne and
Richmond, 1993). These investigators did not report whether noise
correlation was affected by functional connectivity. In the primary
visual cortex, horizontal corticocortical connections preferentially
connect the columns with similar receptive field properties (Gilbert
and Wiesel, 1989), and the neurons in these columns are more likely to
display positive peaks in their CCHs (Ts'o et al., 1986). Similarly,
in the motor cortex, both pyramidal cells and thalamic inputs give rise
to long-range collateralization with focal concentration of synaptic
connections (DeFelipe et al., 1986; Shinoda and Kakei, 1989), and
therefore either could provide the mechanisms for the functional
connectivity revealed in the CCHs.
Functional significance of correlated noise
We showed that the noise correlation was increased when two
neurons were recorded through the same electrode and had similar directional tuning (i.e., high signal correlation). Because it is
difficult to assign all the spikes unequivocally to their proper sources when two neurons produce temporally overlapping spikes recorded
by the same electrode, it is conceivable that neurons with similar
directional tuning gave rise to artificially high noise correlation
during the TET because of some uncertainty in spike sorting. However,
such random misassignment of spikes would lower the noise correlation
among these neurons. In addition, such idiosyncratic interaction of
directional tuning and correlated noise is difficult to explain in the
case of the noise during the CHT, and therefore we think it unlikely
that these results are caused by technical problems in spike
identification.
The effect of signal averaging in reducing noise depends on several
factors, including the correlated noise and the way inputs are averaged
(Johnson, 1980; Shadlen et al., 1996). If one assumes that the
averaging occurs only within groups of neurons that share similar
directional tuning, then the magnitude of the correlated noise sets an
upper limit for the benefit of signal averaging (Britten et al., 1992;
Zohary et al., 1994; Shadlen et al., 1996). On the other hand, if the
averaging occurs among neurons with opposite preferred directions,
correlated noise would be factored out by signal averaging (Johnson,
1980; Lee et al., 1998). Recently, we showed that accuracy in the
estimation of directional signal in a pool of simultaneously recorded
neurons was not affected by a manipulation that eliminated any
correlated noise among these neurons (Lee et al., 1998). This is hardly
surprising because on average the interneuronal correlation coefficient
for neuronal noise was close to zero (Table 2).
Correlated noise must be a reflection of common or reciprocal inputs
and cannot be attributed to the noise intrinsic to individual neurons.
A question arises concerning the potential benefits for these neurons
to carry messages redundant not only in their signals but also in their
noise. One possible reason for several neurons to carry redundant
messages may be to enhance the temporal resolution in coding a dynamic
variable that can change rapidly (Stein, 1970; Knight, 1972).
Introduction of time-varying signals may also affect some properties of
neuronal noise, such as the relationship between the mean and variance
of discharge rates (de Ruyter van Steveninck et al., 1997). Our results
also indicate that neurons with similar directional tuning display
primarily uncorrelated noise if they are not very close together, i.e.,
if they belong to separate cortical columns (Georgopoulos et al.,
1984b; Amirikian and Georgopoulos, 1997). Although a common directional
signal may still be responsible for similarity in directional tuning
between the two neurons in different columns, the absence of correlated
noise among these neurons with similar directional tuning suggests that
local cortical circuitry performs independent processing unique to
different cortical columns.
| |
FOOTNOTES |
Received June 13, 1997; revised Nov. 10, 1997; accepted Nov. 12, 1997.
This study was supported by United States Public Health Service Grant
1-PSMH48185, the United States Department of Veterans Affairs, and the
American Legion Chair in Brain Sciences.
Correspondence should be addressed to Dr. Apostolos P. Georgopoulos,
Brain Sciences Center (11B), Veterans Administration Medical Center,
One Veterans Drive, Minneapolis, MN 55417.
Dr. Lee's present address: Department of Neurobiology and Anatomy,
Wake Forest University School of Medicine, Medical Center Boulevard,
Winston-Salem, NC 27157-1010.
Dr. Kruse's present address: Department of Zoology and Neurobiology,
Ruhr University Bochum, D-44780 Bochum, Germany.
| |
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Top
Abstract
Introduction
![z=0.5[<UP>ln</UP>(1+r)−<UP>ln</UP>(1−r)].](/content/vol18/issue3/fulltext/1161/img008.gif)
