The Journal of Neuroscience, July 30, 2003, 23(17):6798-6809
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Coherent Oscillations in Neuronal Activity of the Supplementary Motor Area during a Visuomotor Task
Daeyeol Lee
Department of Brain and Cognitive Sciences, Center for Visual Science,
University of Rochester, Rochester, New York 14627
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Abstract
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Neural activity recorded in behaving animals is nonstationary, making it
difficult to determine factors influencing its temporal patterns. In the
present study, rhesus monkeys were trained to produce a series of visually
guided hand movements according to the changes in target locations, and
multichannel single-neuron activity was recorded from the caudal supplementary
motor area. Coherent oscillations in neural activity were analyzed using the
wavelet cross-spectrum, and its statistical significance was evaluated using
various methods based on surrogate spike trains and trial shuffling. A
population-averaged wavelet cross-spectrum displayed a strong tendency for
oscillatory activity in the 
frequency range (30
50 Hz) to
synchronize immediately before and after the onset of movement target. The
duration of synchronized oscillations in the frequency range increased
when the onset of the next target was delayed. In addition, analysis of
individual neuron pairs revealed that many neuron pairs also displayed
coherent oscillations in the 
frequency range (15-30 Hz). Coherent
frequency oscillations were less likely to be synchronized than
frequency oscillations, consistent with the fact that coherent
frequency oscillations were not clearly seen in the population-averaged
cross-spectrum. For a given neuron pair, the time course and phase of coherent
oscillations were often similar across different movements. These results are
consistent with the proposal that synchronized oscillations in the
frequency range might be related to the anticipation of behaviorally relevant
events and the contextual control of cortical information flow.
Key words: neuron assemblies; monkey; SMA; spike synchrony; wavelet cross-spectrum; sequence learning
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Introduction
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Cortical information processing relies on a massive number of connections
within a large population of neurons. The number of neurons contributing
synaptic inputs to a given cortical neuron is large, and many such inputs
arise locally or from neighboring cortical columns with similar functional
properties (Breitenberg and Schüz,
1998
). In addition, long-distance corticocortical projections are
mostly reciprocal, providing additional opportunities for nearby cortical
neurons to receive correlated inputs. Consistent with these anatomical
patterns, cortical neurons often display correlation in their spike trains.
For example, spike synchrony has been observed in many different cortical
areas (Gray, 1999), and
synchronous activity of individual neurons often displays oscillations at
various frequencies (Eckhorn et al.,
1988; Gray et al.,
1989). However, the role of correlated activity in cortical
information processing is not well understood. On the one hand, correlated
activity might be merely a consequence of anatomical and biophysical means to
achieve reliable information transmission
(Shadlen and Newsome, 1998).
On the other hand, correlated activity might play a more active role in
cortical information processing. For example, effects of synaptic inputs on
the activity of a given neuron can be influenced by the pattern of correlation
in the inputs (Murthy and Fetz,
1994; Salinas and Sejnowski,
2000; Svirskis and Rinzel,
2000). In addition, the relationship between correlated activity
and the information-coding capacity of a neuronal ensemble depends on how
different variables are coded in neural activity
(Oram et al., 1998;
Panzeri et al., 1999).
Finally, it has been proposed that synchronization of oscillatory activity
across different neuronal populations enhances transmission of information
among them (Roelfsema et al.,
1997; Llinás et al.,
1998; Rodriguez et al.,
1999; von Stein et al.,
2000; Engel et al.,
2001; Varela et al.,
2001).
Flow of information through a population of neurons is reflected in
temporal changes in their activity. If coherent oscillations play an important
role in the control of cortical information flow, they must also display
dynamic patterns systematically related to the requirements of behavioral
tasks. However, nonstationarity in the spike trains often makes it difficult
to evaluate the statistical significance of coherent oscillations. In the
present study, coherent oscillations in the activity of neurons in the
supplementary motor area proper (SMA) were analyzed using the wavelet
cross-spectrum (Lee, 2002).
Although oscillatory activity has been found in other motor cortical areas
(Murthy and Fetz,
1996a,b;
MacKay, 1997; Crone et al.,
1998a,b;
Donoghue et al., 1998;
Aoki et al., 1999;
Lebedev and Wise, 2000;
Baker et al., 2001), coherent
oscillations in activity of individual SMA neurons had not been examined. It
was found in the present study that SMA neurons displayed coherent
oscillations in the (15-30 Hz) and (30-50 Hz) frequency bands.
In addition, coherent oscillations in the frequency range became
strongly synchronized during the hold period, suggesting that synchronized
frequency oscillations might play a role in anticipation or
preparation of upcoming movements.
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Materials and Methods
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Animal preparation and neural recording
Two male adult rhesus monkeys (Macaca mulatta; body weight, 6-8
kg) were used. Four titanium posts were attached to the skull, and an eye coil
was placed around the orbit of one eye by sterile surgery. In a second
surgery, a titanium chamber (inner diameter, 18 mm) was implanted above the
supplementary motor area for the purpose of neurophysiological recording.
Neuronal activity was recorded using an Eckhorn 16-channel mictroelectrode
manipulator (Thomas Recording, Giessen, Germany) and a Plexon (Dallas, TX)
multichannel acquisition processor. Electrodes were arranged in a four-by-four
grid, and the distance between neighboring electrodes was 350 µm. A
detailed description of the methods used to collect behavioral and single-unit
data has been published (Lee and Quessy,
2003). All the procedures used in the current study were approved
by the University of Rochester Committee on Animal Research and conformed to
the principles outlined in the Guide for the Care and Use of Laboratory
Animals (National Institutes of Health publication 85-23, revised
1985).
Behavioral task
The animal was seated in a primate chair and faced a 17-inch computer
monitor on which visual stimuli were presented. The monitor was located
57 inches from the animal's eyes and subtended 30 and 22° visual
angles horizontally and vertically, respectively. The neural data described in
this report were collected from two different behavioral paradigms. In both
cases, the animal was required to capture a series of targets (red disk)
presented on the monitor by moving its right hand on a touch screen, which was
installed horizontally in front of the animal at its waist level. The location
of the touch was indicated to the animal by a feedback cursor (white disk;
radius, 0.5°) on the computer screen. The touch screen was calibrated so
that a 1 cm displacement on the touch screen corresponded to the same distance
(1° visual angle) on the computer monitor. In each trial, the animal was
required to acquire 10 successive targets to receive a drop of apple
juice.
In the first paradigm, targets were presented in a four-by-four grid. The
center-to-center distance between the neighboring target locations was
4.2°, and the radius of the target was 1.4°. The interval between the
acquisition of a target and the onset of the next target [response-stimulus
interval (RSI)] was always 250 msec. Within a block of eight trials, target
locations were determined randomly in one pseudorandomly selected trial,
whereas for the remaining trials, they followed three different deterministic
sequences. These sequences were generated with five locations that were
selected randomly for each daily session. Denoting them A-E, the sequence
ABC-ABC-ABC-A was used in five trials selected randomly in each block (primary
trials). For the remaining two trials in each block, the sequences were
DEC-DEC-DEC-D (secondary trials) and DEC-DEC-ABC-A (switch trials),
respectively. This particular combination of target sequences was designed to
evaluate the nature of changes in neural activity related to the learning of
visuomotor sequences (Lee and Quessy,
2003). In the present report, only the data from the primary
trials were used because they provided a large amount of data with a
consistent pattern of visual stimuli and behavioral responses.
In the second paradigm, two different values of the RSI (250 and 650 msec)
were used to determine how the time course of coherent oscillations in the
activity of SMA neurons was affected by the temporal parameters of the task.
Targets were presented in a three-by-three grid, and the center-to-center
distance between the neighboring target locations was 5.6°. The radius of
the target was the same as in the first paradigm. Within a block of 10 trials,
target locations were determined randomly in two trials. In one of these two
trials, the long and short RSIs were selected randomly for each target,
whereas for the other trial, they alternated. For the remaining eight trials,
the target locations followed a predetermined sequence of nine targets, which
was selected pseudorandomly for each recording session, but the pattern of RSI
varied across different trial types. For six of these (referred to as primary
trials), either the even- or odd-numbered (determined randomly for each
sequence) targets in the sequence were associated with the short RSI, whereas
the long RSI was used for the remaining targets. For another trial, this
RSI-target mapping was reversed. For the remaining one trial in a block, the
RSI was selected randomly for each target. The order of these different trial
types was randomized for each block. These different types of trials were
designed to examine the interaction between the temporal and spatial
dimensions of sequence learning (Lee,
2000). In the present study, only the data from the primary trials
with consistent mapping between the targets and the RSI were analyzed.
Data analysis
Time-resolved cross-correlation function. For the quantitative
analyses of single-unit activity, the spike train from a neuron j was
represented as:
where t indicates time from target onset; n is the index for
the analysis window for each target (n = 1, 2,..., N); and
t = 1 msec. For most analyses in the present study, the
analysis window covered the period beginning 200 msec before and ending 500
msec after target onset. Because 10 targets were presented in a given trial,
each successful trial provided 10 analysis windows. The first window in each
trial was excluded from the analysis because the initial hand position was not
controlled for the first target. Although temporal correlation in spike trains
has been commonly analyzed with cross-correlation function (CCF;
Perkel et al., 1967), the
utility of CCF is primarily limited to stationary processes. Spike trains are
nonstationary, however, when they are influenced by sensory stimuli or
behavioral responses. In such cases, the joint perievent time histogram (JPTH)
can be used (Aertsen et al.,
1989). This is defined as:
where t1 and t2 denote time for spikes
in neurons 1 and 2, respectively. For visualization of synchronous spikes, it
is convenient to use the time-resolved cross-correlation function (TrCCF;
Baker et al., 2001), which is
related to the JPTH according to the following equation:
where t denotes time from target onset, and 
is the time lag.
For neuron pairs with independent, rate-modulated spike trains, the expected
TrCCF can be estimated as the product of spike density functions of individual
neurons (Aertsen et al., 1989;
Baker et al., 2001;
Lee, 2002). Denoting the spike
density function for neuron j in trial n as
Fjn(t), the expected TrCCF can be
defined as:
In the present analysis, the spike density function was calculated with a
Gaussian kernel (
= 40 msec).
Wavelet cross-spectrum. Whereas the TrCCH provides a tool to
examine temporal changes in the amount of synchronous spikes, analyses in the
frequency domain can provide more concise descriptions for temporal
correlation in the oscillatory patterns of spike trains. However, the need to
examine time-dependent changes in the frequency characteristics of neural
activity faces a problem known as the uncertainty principle because there is a
tradeoff between temporal and spectral resolutions. In the wavelet analysis,
this problem is resolved by adjusting the width of the kernel as a function of
frequency (Torrence and Compo,
1998; Lee, 2002).
The wavelet transform of a spike train from neuron j in the
nth analysis window can be defined as:
where 
[] denotes a wavelet function, and * is the complex
conjugate. The variables t and s indicate the time and scale
of the wavelet function, and T is the duration of the analysis
window. In practice, this was calculated using the fast Fourier transform
implemented in MATLAB (The MathWorks, Natick, MA). To avoid edge effects, the
original spike trains during the additional 150 msec intervals surrounding the
analysis window were included before the Fourier transform and removed after
the inverse Fourier transform. The mean spike rate of each analysis window was
subtracted from the spike train. In the present study, the Morlet wavelet
function was used (Fig. 1
B), which is defined as:
where
is the nondimensional time parameter; and 
0 is taken
to be 6 to make this function localized in both time and frequency space
(Torrence and Compo, 1998).
The frequency of the Morlet wavelet function is approximately the inverse of
the scale parameter. In the present study, the frequency range between 10 and
82.5 Hz was examined at a 2.5 Hz resolution. The wavelet cross-spectrum for
the two spike trains from neurons j and k in the
nth analysis window can be defined as
Wjn(t,
s)Wkn*(t, s)
(Fig. 1 D). To
determine whether a pair of neurons displays any consistent phase relationship
in their oscillatory activity, the cross-spectrum was averaged across all
trials to compute the average wavelet cross-spectrum (AWCS) according to the
following:
The summation in the above equation is performed in the complex plane, and as
a result, the amplitude of the resulting cross-spectrum would be relatively
small if there were no consistent phase relationship
(Fig. 1 E).
Accordingly, a significantly large amplitude in the average wavelet
cross-spectrum is referred to as coherent (i.e., phase-locked) oscillation.
Coherent oscillations with a small phase difference (e.g., <90°) are
referred to as synchronized or synchronous coherent oscillations. In the
present study, cross-spectrum was used instead of coherence because the latter
could not be computed for many neuron pairs when the spike rates became close
to zero.
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Figure 1. The wavelet cross-spectrum can detect coherent oscillations in
simultaneously recorded spike trains. A, Examples of two separate
simulated spike trains. Spikes in Neuron 1 were generated at the constant
frequency of 40 Hz, whereas the frequency of spikes in Neuron 2 changed from
20 Hz during the first 150 msec (black bar at top), to 40 Hz during the next
400 msec (white, gray bars), and back to 20 Hz during the last 150 msec (black
bar). During the period indicated by the white bar, the spikes of the two
neurons were synchronized, whereas the gray bar indicates the period in which
the spikes of the two neurons were counterphased. The exact timing of spikes
was jittered according to a normal distribution with the SD of 1 msec.
B, Example of the Morlet wavelet function with the frequency of 20 Hz
(scale, 50 msec) centered at 0 msec. Real and imaginary components are
indicated by solid and dotted lines, respectively. C, Wavelet spectra
calculated for the spike trains of Neurons 1 (top) and 2 (bottom). D,
Amplitude (top) and relative phase (bottom) of the wavelet cross-spectrum
computed for the same spike trains. E, Amplitude (top) and relative
phase (bottom) of the average wavelet cross-spectrum. This was calculated over
10 different pairs of simulated spike trains like those in A. The
spikes during the interval indicated by the white bar were always
synchronized, whereas the relative phase of the spikes during the interval
indicated by the gray bar was randomly varied.
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Phase-locking index. The average wavelet cross-spectra of
individual neuron pairs were averaged across the entire population of
simultaneously recorded neuron pairs to yield the population average wavelet
cross-spectrum. To quantify the extent to which the oscillatory activity of
neuron pairs in the SMA display consistent phase locking across the
population, the phase-locking index (PLI) was defined as the following:
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where the summation was performed for all neuron pairs recorded
simultaneously, and || indicates the amplitude of the cross-spectrum. The
value of PLI would be 1 if the AWCS for all neuron pairs displayed the same
phase difference, whereas it would be close to zero if the phase difference is
randomly distributed.
Statistical significance of the wavelet cross-spectrum. Although a
large amplitude in the cross-spectrum could indicate a consistent phase
relationship for a given pair of neurons, the possibility that this might be
the result of random variations in spike trains must be evaluated. In
practice, however, this task is not trivial because the statistical
significance of any observation can be evaluated only relative to a specific
null hypothesis. In the present study, the statistical significance of
coherent oscillations in each neuron pair was evaluated using three different
methods.
The first method was based on a set of surrogate spike trains
(Oram et al., 1999). In this
method, the spike density function was calculated for each analysis window
with a Gaussian kernel ( = 40 msec). Next, the amplitude of the average
wavelet cross-spectrum was recalculated from the Poisson surrogate spike
trains generated according to the same spike density functions on a
trial-by-trial basis. This process was repeated 10 times to estimate the mean
and SD for the amplitude of the surrogate average cross-spectrum. A p
value for the amplitude of the original average cross-spectrum was then
calculated for each combination of time and frequency, according to a normal
distribution with the mean and SD of the surrogate average cross-spectrum
amplitude after square root transformation
(Lee, 2002). The result is a
map of p values indicating for each point in the cross-spectrum how
likely it would be for the amplitude value of the original average
cross-spectrum to have occurred by chance in surrogate spike trains. For the
Gaussian kernel used in the present study with the SD of 40 msec, simulations
showed that this method effectively randomized the phase for high-frequency
components of >10 Hz (Fig.
2). The phase of lower-frequency components was still preserved
because the surrogate spike trains shared the same spike density functions
with the original spike trains. Accordingly, this procedure tested the null
hypothesis that the observed level of coherent oscillation resulted by chance
from two spike trains in which spike rates were modulated by the same spike
density functions and the phase difference for frequency components of >10
Hz was random. Because the surrogate spike trains included the same number of
spikes in each data window as the original spike trains, the results obtained
with this method would not be biased by correlated changes in spike counts
(Lee et al., 1998;
Brody, 1999). However, a
potential problem with the use of Poisson surrogate spike trains is that it
destroys all of the temporal structures in the original spike trains. This
would increase the variance of the wavelet cross-spectrum, raising the
possibility that the estimates obtained with this method might be too
conservative. For example, the Poisson process is not an ideal model for real
spike trains, which display a refractor period. Therefore, a separate analysis
was performed with surrogate spike trains. In this analysis, a
relative refractory period was introduced to the surrogate spike trains by
initially generating a Poisson spike train with twice as many spikes as in the
original spike train and then decimating every other spike. This procedure
produces the distribution of an interspike interval histogram that follows the
distribution with the shape parameter of 2
(Baker and Lemon, 2000).
The second method used the shift predictor
(Perkel et al., 1967). This
method tests the null hypothesis that the spike trains of different trials are
independent and drawn from the same distributions. Accordingly, the
significance of coherent oscillations could be potentially inflated when there
are correlated changes in spike counts or the latency of neural activity
(Brody, 1999). This method,
however, has the advantage that it preserves all the temporal structures
within the spike trains of individual neurons (e.g., autocorrelation
function). For comparison with the methods based on surrogate spike trains,
the statistical significance of coherent oscillation for each neuron pair was
also evaluated using the resampled wavelet cross-spectrum calculated after
shuffling the order of trials (Lee,
2002). Similar to the method based on surrogate spike trains, the
p value was evaluated for each combination of time and frequency by
fitting a normal distribution to a set of 10 resampled average wavelet
cross-spectra.
As shown in Results, the proportion of neuron pairs with significant
coherent oscillations differed for the above two methods, especially for
coherent oscillations in the frequency range. To understand the cause
of this discrepancy better, statistical significance of coherent oscillations
was also tested with surrogate spike trains generated after trial shuffling.
This method was identical to the methods based on surrogate spike trains,
except that the spike density functions were calculated after randomizing the
order of trials for one of the neurons in the pair. This analysis was
performed for Poisson and surrogate spike trains separately.
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Results
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Neuronal database
A total of 191 neurons were recorded in the left SMA proper of two animals
during 33 daily recording sessions. Of these, 60 neurons were excluded from
the analysis either because they were recorded individually, or because they
were lost without sufficient amount of data (120 trials in the primary
condition, or 1080 movements). The remaining 131 neurons provided 270 neuron
pairs analyzed in the present study. Among them, 217 pairs were examined with
a single RSI (250 msec), and 53 pairs were examined with two different RSIs
(250 and 650 msec). The mean numbers of trials ± SD for neuron pairs
examined with these two paradigms were 263.7 ± 69.0 and 269.2 ±
61.7, respectively. These values corresponded to 2373 and 2422 movements.
Among the neuron pairs tested with a 250 msec RSI, 10 were isolated from the
same electrode.
Coherent oscillations in individual SMA neuron pairs
Individual neuron pairs in the SMA displayed substantial variability in
their phase-locked (coherent) oscillatory activity in terms of the frequency
and phase of oscillations and their time course. For example, the neuron pair
shown in Figure 3 displayed
coherent oscillations in both the and frequency ranges. One of
the neurons in this pair displayed substantial modulation in its activity
throughout the task period according to the changes in target locations
(Fig. 3A), whereas the
modulation in the second neuron was similar across different targets
(Fig. 3B). There was a
robust tendency for these two neurons to display phase-locked oscillatory
activity during a period of several hundred milliseconds around the time of
target onset. This can be seen from the time-resolved cross-correlation
function (Fig. 3C,D),
but the wavelet cross-spectrum revealed more clearly how the frequency of this
coherent oscillation and its phase changed over time. In the wavelet
cross-spectrum averaged across three different target positions used in the
primary trials, the peak amplitude was found precisely at the time of target
onset at the frequency of 30 Hz (Fig.
3E). The corresponding phase difference was 74.7°
(Fig. 3F), which is
equivalent to the time lag of 6.9 msec at 30 Hz. This coherent oscillation in
the frequency range was highly significant statistically. For the
phase-locked oscillations around the time of target onset in the frequencies
ranging from 27.5 to 35 Hz, the p values calculated on the basis of
Poisson surrogate spike trains (see Materials and Methods) were
<10-16 (Fig
3H), and the results were similar for shuffled wavelet
cross-spectra. The maximum power in the wavelet cross-spectrum computed from
the Poisson surrogate spike trains was only 41.2% compared with the original
cross-spectrum (Fig.
3G). For this particular neuron pair, the frequency of
coherent oscillation decreased to the range within the first 100 msec
period after target onset (Fig.
3E). The power in the wavelet cross-spectrum at <20 Hz
peaked 100 msec from target onset at 17.5 Hz and the corresponding phase
difference was 148.8°, equivalent to the time lag of 23.6 msec. This
coherent oscillation in the frequency range was also highly significant
regardless of the methods used to evaluate the statistical significance
(p < 10-16;
Fig 3H).
For many neuron pairs in the SMA, the pattern of coherent oscillation was
consistent across individual target locations. For example, in the neuron pair
illustrated in Figure 3, the
strong coherent oscillations at the frequency range at the time of
target onset and the -frequency oscillation after target onset were
consistently observed in all of the three different movements examined in the
primary trials (Fig. 4). The
peak amplitude at 30 Hz occurred 6 and 2 msec after target onset for the first
and third movements (Fig.
4A,G), respectively, and 49 msec before target onset for
the second movement (Fig.
4D). The corresponding phase differences were 82.7, 62.9,
and 72.8°, respectively. The peak amplitudes at 17.5 Hz occurred 159, 89,
and 95 msec from target onset, and again displayed similar phase differences
(135.4, 153.9, and 163.7°).
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Figure 4. Amplitude (A, D, G), relative phase (B, E, H), and the
map of p values (C, F, I) of the average wavelet
cross-spectra of the same neuron pair illustrated in
Figure 3, computed separately
for three different movements directed toward the triplet of targets used in
the primary trials. The average spike density functions for these three
different movements are indicated by different colors in
Figure 3,A and
B (A-C, red; D-F, green; G-I,
blue).
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In some neuron pairs, coherent oscillations were predominantly observed in
the frequency band. For example, in the neuron pair illustrated in
Figure 5, the peak amplitude in
the average wavelet cross-spectrum collapsed across different targets was
found 15 msec after target onset at the frequency of 15 Hz, and the phase
difference for this peak was 142°, which corresponds to 26.3 msec.
Therefore, although the oscillatory activity was phase-locked for these two
neurons, there was a relatively large difference in their phases. For this
neuron pair, the time course of coherent oscillation in the frequency
varied somewhat across different target locations, although robust
oscillations with similar phase differences were found in all cases
(Fig. 5C-K).
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Figure 5. Coherent oscillation in the frequency range found in a pair of SMA
neurons. A, B, Spike density functions of individual neurons, same
format as in Figure 3.
C-K, Amplitude (C, F, I), relative phase (D, G, J),
and the map of p values (E, H, K) of the average wavelet
cross-spectra calculated separately for the movements directed to three
different targets, same format as in Figure
4.
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Population analysis of coherent oscillation in the SMA
To determine whether there was any systematic pattern in the frequency and
relative phase of coherent oscillations across SMA neurons, the average
wavelet cross-spectra obtained for individual neuron pairs were averaged in
the complex plane across all the neuron pairs examined in this study. In this
averaging process, coherent oscillations in different neuron pairs would be
canceled if their phase differences were opposite. The resulting
population-averaged wavelet cross-spectrum would therefore emphasize coherent
oscillations with consistent phase differences, particularly those with small
phase differences. This population-averaged cross-spectrum displayed a salient
peak in the frequency range, and its amplitude reached the maximum
value 33 msec before target onset at the frequency of 32.5 Hz
(Fig. 6A). The phase
difference for this peak amplitude was 21.5°, which corresponds to 1.8
msec (Fig. 6B).
Therefore, there was a tendency for frequency oscillations in the SMA
neurons to become synchronized shortly before target onset. In addition,
relatively large power in the frequency range was clearly seen
throughout the 200 msec period before target onset. During this period, the
frequency of oscillation decreased somewhat from 37.5 to 32.5 Hz before target
onset and increased to 50 Hz during the following 200 msec interval after
target onset. Beginning 200 msec from target onset, the amplitude of the
averaged cross-spectrum decreased substantially. The average reaction time for
this task was 242 msec (Lee and Quessy,
2003); therefore, this decrease in the cross-spectrum amplitude
began on average 40 msec before movement onset.
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Figure 6. Coherent oscillations in the population of SMA neurons. A, B,
Amplitude (A) and phase (B) of the population AWCS.
C, Phase-locking index for the population AWCS (see Materials and
Methods). D-F, Percentage of neuron pairs (N = 217 neuron
pairs x 3 movements = 651) with coherent oscillations that were judged
to be statistically significant (p < 0.05), according to the
methods based on Poisson surrogate spike trains (D), trial shuffling
(E), and their combination (F).
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The phase in this population-averaged cross-spectrum was relatively close
to zero when its amplitude was large (Fig.
6B), and this is expected because oscillations in any
neuron pair with nonzero phase lags are likely to be canceled by similar
oscillations in another neuron pair with opposite phase differences. However,
the population-averaged cross-spectrum provides little information regarding
the extent to which the phase difference varies across the population. To
examine this issue, a phase-locking index (see Materials Methods) was
calculated for the entire population of simultaneously recorded neuron pairs
(Fig. 6C).
Essentially, the phase-locking index reflects the amount of coherent
oscillations that display consistent phase differences across the entire
population, normalized by the total amount of coherent oscillations found for
individual neuron pairs regardless of their phase differences. This index
displayed a pattern similar to that of the population-averaged wavelet
cross-spectrum amplitude, suggesting that the latter reflected mostly the
result of phase locking that takes place consistently across a large number of
neurons. Similar to the amplitude of the population-averaged cross-spectrum,
the phase locking index reached its peak 33 msec before target onset at the
frequency of 30 Hz. This maximum value was 0.39, suggesting that a substantial
number of neuron pairs tended to display similar phase differences. Combined
with the observation that the population-averaged cross-spectrum displayed
phase differences close to zero at the frequency range during the
target hold period, these results indicate that there was a robust tendency
for synchronous oscillations in the frequency range.
Phase difference in coherent oscillations
To determine how often neuron pairs in the SMA displayed coherent
oscillations with relatively large phase differences, the percentage of cases
with statistically significant powers in the average cross-spectra for
individual neuron pairs was calculated for each combination of frequency and
time. A total of 651 cases were examined in this analysis because each of 217
neuron pairs contributed three different average wavelet cross-spectra,
corresponding to the three movements included in the primary trials. As
described in Materials and Methods, statistical significance was evaluated
using three different methods. Overall, the method based on surrogate spike
trains generated consistently lower percentages of neuron pairs with
significant coherent oscillations compared with the method based on trial
shuffling for the entire range of time and frequency range examined (Figs.
6D,E,
7). The difference was most
pronounced in the frequency range but was also found in the
frequency range after movement onset.
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Figure 7. A, Average percentage of neuron pairs with statistically
significant coherent oscillations collapsed across the entire duration of the
analysis window shown in Figure
6. The results obtained with the method of Poisson surrogate spike
trains (solid line), trial shuffling (dotted line), and their combination
(dashed line) are shown separately. B, Average percentage of neuron
pairs with significant coherent oscillations estimated using the same methods
as in A during the 200 msec interval before target onset. C,
D, Same as in A and B, except that surrogate spike
trains were generated as a process with a shape parameter of 2 to
incorporate a refractory period.
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As described in Materials and Methods, these two methods are somewhat
complementary because they test different null hypotheses. As a result, each
method has a weakness. The results obtained with the method of trial shuffling
might have been inflated by correlated changes in spike counts and spike
density functions, whereas those with the Poisson surrogate spike trains could
have underestimated the amount of coherent oscillations attributable to the
increased variance in the cross-spectrum. To resolve these issues, statistical
significance of coherent oscillations was also evaluated with
surrogate spike trains that incorporated a relative refractor period (see
Materials and Methods). If the discrepancy between the methods based on
Poisson surrogate spike trains and trial shuffling were at least in part
attributable to the increased variance in the Poisson spike trains, one would
expect that the inclusion of refractory periods in surrogate spike
trains would increase the estimate of neuron pairs with coherent oscillations
in the frequency. The results were consistent with this prediction
(Fig. 7C,D). In
addition, a method that combined trial shuffling and Poisson surrogate spike
trains was also tested. If the trial-to-trial variation in the spike counts
and spike density function inflated the estimates obtained with the method of
trial shuffling, the results obtained by this combined approach should be
similar to those of trial shuffling because both of these methods used the
same spike counts and spike density functions. In contrast, if the destruction
of temporal structures in the original spike trains was responsible for the
difference between the method based on surrogate spike trains and that of
trial shuffling, the results from this third approach should be similar to
those of surrogate spike trains. The results from this third method were
intermediate between the other two methods (Figs.
6F,
7), indicating that at least a
part of the discrepancy was attributable to the increased variance of the
cross-spectrum in the surrogate spike trains.
Despite these differences related to the statistical methods, however, the
percentage of neuron pairs with significant coherent oscillations revealed two
additional features (Fig.
6D-F) not obvious in the population-averaged
cross-spectrum (Fig.
6A) or phase-locking index
(Fig. 6C). First,
coherent oscillations in the frequency range were found in a
significant number of neuron pairs. According to the method based on Poisson
surrogate spike trains, the percentage of significant coherent oscillations
averaged across the entire duration of the 700 msec analysis window was 6.8%
for the frequency of 15 Hz, and this was significantly higher than the used
criterion (p < 0.05) of statistical significance (binomial test,
p = 0.019). During the last 200 msec of the hold period, this
percentage was 8.7% (binomial test, p < 0.001). The corresponding
percentages for the method of trial shuffling were 20.0 and 21.4%,
respectively, and they were 8.6 and 10.3% when Poisson surrogate spike trains
with shuffled spike density functions were used. When processes were
used to generate surrogate spike trains, the percentage of neuron pairs with
significant coherent oscillations in the frequency range increased
somewhat. The averages for the entire analysis window and the last 200 msec of
the hold period were 10.1 and 12.6%, respectively
(Fig. 7). Second, the method
based on Poisson surrogate spike trains showed a modest increase in the
percentage of neuron pairs with significant coherent oscillations in the
frequency range after movement onset
(Fig. 6D,F), whereas
the method based on shuffling produced much higher estimates throughout the
analysis window (Fig.
6E). A large reduction in the amount of coherent
oscillations before movement onset was found for both the original Poisson
surrogate spike trains and those combined with trial shuffling. Therefore,
this discrepancy is probably related to the intertrial variability in the
movement-related activity in the SMA.
These results raise the possibility that some neuron pairs displayed
coherent oscillations with large phase differences, although they were
canceled out in the population-averaged cross-spectrum. To examine this
further, the percentages of neuron pairs with significant coherent
oscillations were calculated separately for neuron pairs with small
(<90°, in-phase) and large (>90°, out-of-phase) phase
differences. As expected, the percentage of neuron pairs with significant
coherent oscillation in the frequency range was substantially higher
for in-phase oscillations than for out-of-phase oscillations until 100
msec after target onset, regardless of the methods used to evaluate
statistical significance (Fig.
8). In contrast, coherent oscillations in the frequency
displayed a much weaker tendency for synchronization
(Fig. 8). The method of trial
shuffling revealed some bias for synchronization in the frequency
range, but this was still much weaker than in the frequency
oscillations. The methods based on Poisson surrogate spike trains did not
reveal any bias for synchronization in the frequency range. Overall,
these results are consistent with the observation that the population-averaged
cross-spectrum and phase-locking index did not reveal clear signs of coherent
oscillations in the frequency range.
View larger version (92K):
[in this window]
[in a new window]
|
Figure 8. Percentage of neuron pairs that displayed significant coherent oscillations
with small (<90°; A, D, G) and large ( 90°; B, E,
H) phase differences among neuron pairs in which the average activity was
5 spikes/sec for both neurons (N = 335). C, F, I,
Percentage of neuron pairs with significant coherent oscillations with small
(light) and large (dark) phase differences calculated for the two frequency
values selected at the peaks of and frequency bands (green, 15
Hz; red, 32.5 Hz) as indicated by the dotted lines in the other panels. Given
the level of statistical significance used for testing individual neuron pairs
(5%), the expected percentage of neuron pairs with significant coherent
oscillations for each of the in-phase and out-of-phase groups is 2.5%, as
indicated by the border between the dark and intermediate levels of gray.
Light gray and white backgrounds correspond to p < 0.05 and 0.01,
respectively. The results obtained with the method of Poisson surrogate spike
trains (A-C), trial shuffling (D-F), and their combination
(G-I) are shown separately.
|
|
Time course of synchronous oscillations
To determine whether synchronization of oscillatory activity was more
closely related to the offset of the preceding movement or the onset of the
next target, the interval between these two events was systematically varied
in 53 neuron pairs (see Materials and Methods). As shown for an example neuron
pair (Fig. 9A,B) and
for the population average (Fig.
9C,D), synchronous oscillations in the frequency
range were prolonged as the RSI was increased from 250 to 650 msec, suggesting
that such oscillatory activity might reflect the anticipation of upcoming
targets. The results in the -frequency range were not clear, presumably
because of the small size of samples examined with this paradigm. This is not
surprising because the tendency for synchronous oscillatory activity before
target onset was weaker for frequency oscillations
(Fig. 8).
View larger version (99K):
[in this window]
[in a new window]
|
Figure 9. Effect of the RSI on coherent oscillations in the SMA. A, B,
Amplitude of the average wavelet cross-spectrum in an example pair of SMA
neurons during a short (250 msec; A) and long (650 msec; B)
RSI. C, D, Amplitude of population-averaged wavelet cross-spectrum.
RSI is indicated by the gray bar at the top.
|
|
|
Discussion
|
|---|
Coherent oscillations in the SMA
A tendency for individual neurons to synchronize their spikes has been
demonstrated in a large number of cortical areas, including the primary
sensory cortical areas in visual (Eckhorn
et al., 1988; Gray et al.,
1989), auditory (Barth and
MacDonald, 1996), and somatosensory
(Nicolelis et al., 1995;
Steinmetz et al., 2000)
modalities. Similar findings were also obtained for the posterior parietal
cortex and frontal cortex (Vaadia et al.,
1995; Murthy and Fetz,
1996a,b;
Riehle et al., 1997;
Lee et al., 1998;
Funahashi and Inoue, 2000;
Baker et al., 2001;
Constantinidis et al., 2001).
Nevertheless, it is not yet clear what role, if any, synchronous spikes play.
Theoretical studies showed that synchronous spikes can be more effective in
driving a postsynaptic neuron compared with when they are randomly distributed
in time (Murthy and Fetz,
1994; Salinas and Sejnowski,
2000; Svirskis and Rinzel,
2000). In addition, recent in vitro physiological studies
have uncovered many cellular and network properties necessary for individual
cortical neurons to act as coincidence detectors
(Larkum et al., 1999;
Galarreta and Hestrin, 2001;
Pouille and Scaziani, 2001).
These findings are consistent with the proposal that cortical neurons
synchronize their spikes as a means to combine (or "bind")
different types of information they carry. However, it remains difficult to
demonstrate that synchronization or coherent oscillation in the activity of
cortical neurons in behaving animals plays a special role in the integration
of locally processed information. One common methodological problem stems from
the fact that spike trains recorded in behaving animal are not stationary.
Previous studies have demonstrated that the presence of synchronous spikes or
oscillatory activity may last only for brief periods related to various
behavioral events (Murthy and Fetz,
1996a; Riehle et al.,
1997), suggesting that spike synchronization is a dynamic process.
Similarly, many SMA neurons examined in the present study displayed coherent
oscillations in their activity, but they were relatively brief. This was
analyzed with the wavelet cross-spectrum, because traditional methods, such as
cross-correlation functions or the Fourier spectrum, are not adequate for the
analysis of nonstationary spike trains. The results showed that coherent
oscillations occurred throughout the task mostly in the and
frequency bands. Interestingly, the pattern of phase difference in coherent
oscillation changed during the task. For both and frequency
oscillations, there was a tendency for oscillatory activity to be synchronized
during the hold period before target onset. This tendency was stronger for the
frequency band. The duration of synchronized oscillations in the
frequency range increased when the duration of the hold period was
lengthened. For the frequency band, a weak tendency for synchronization
was found only with the method of trial shuffling. For both frequency bands,
the proportion of neuron pairs with synchronized oscillation decreased after
target onset.
Functions of coherent oscillations in the motor cortex
Although a large number of studies have reported synchronous spikes in many
different brain regions, coherent oscillations have been found less
consistently in the recordings of single-neuron activity. This discrepancy
might be related to the fact that coherent oscillations tend to occur briefly
and that their frequencies might change over time, as demonstrated in the
present study. In addition, a large number of trials may be required to detect
a statistically significant level of coherent oscillation for neurons with low
levels of activity. Recordings of local field potentials (LFP) or
electroencephalographic (EEG) activities have commonly revealed oscillatory
activity (Niedermeyer and Lopes da Silva,
1999). This is likely the result of the averaging process
intrinsic to the recording of field potentials because many neuron pairs
examined in the present study show little or no sign of coherent oscillations.
However, averaging is also a weakness in field potential recording studies
because coherent oscillations in single-neuron activity with large phase
differences may not be detected. For example, many neuron pairs examined in
the present study displayed coherent oscillations in the frequency
range with phase differences of 90°. In some neuron pairs,
oscillations with such large phase differences were also found in the
frequency range. These oscillations with large phase differences were
cancelled in the population-averaged wavelet cross-spectrum, as would happen
in the recordings of field potentials.
With these caveats, the fact that synchronous oscillations in the
frequency range dominated the pattern in the population-averaged
cross-spectrum is consistent with the results from previous EEG and
electrocorticographic (ECoG) recording studies in human subjects. For example,
the power of the EEG activity recorded over the SMA in human subjects
decreased (referred to as event-related desynchronization) for the 
frequency range but increased (event-related synchronization) for the
frequency range during an interval of several seconds before movement onset
(Andrew and Pfurtscheller,
1996). Similar results have been observed in ECoG activity (Ohara
et al., 2000,
2001). Although EEG or ECoG
activity in the human SMA has been examined only in a small number of studies,
the results from these studies are also similar to the patterns found in the
regions around the primary motor and somatosensory cortex
(Pfurtscheller et al., 1993;
Andrew and Pfurtscheller, 1996;
Crone et al.,
1998a,b;
Aoki et al., 1999;
Pfurtscheller and Lopes da Silva,
1999; Ohara et al.,
2001). LFP recordings obtained from the primary motor cortex also
display an increase in the frequency oscillation in association with
preparation of upcoming movements
(Donoghue et al., 1998).
There are also some differences between the results from the present study
and previous EEG and ECoG recording studies. Most noticeably, previous studies
have commonly observed opposite changes in the and frequency
bands (Crone et al.,
1998a,b;
Aoki et al., 1999;
Ohara et al., 2001), whereas
in the present study, the increase in the percentages of neuron pairs with
synchronous oscillatory activity in the frequency range was found
without the corresponding decrease in the frequency band. For the
method of trial shuffling, synchronized oscillation in the and
frequency bands displayed a similar time course. This discrepancy might be
related to the differences in recording methods, but it is also possible that
the discrepancy was attributable to the differences in behavioral tasks. For
the majority of the neuron pairs examined in the present study, a target for
the next movement was presented only 250 msec after the completion of the
previous movement. It is possible that desynchronization in the
frequency range might develop more slowly.
Despite the large number of studies demonstrating oscillatory activity in
distinct frequency bands, functions of these rhythmic brain activities are not
yet completely understood. A few studies have provided evidence that
synchronous spikes or an oscillatory pattern in spike trains might carry
behaviorally relevant information independent of other measures of neural
activity such as spike rates (Vaadia et
al., 1995; Riehle et al.,
1997). Other studies found that synchronization of oscillatory
activity might occur more frequently during the periods in which the animal
anticipates the delivery of a stimulus and prepares for required behavioral
responses (Cardoso de Oliveira et al.,
1997; Donoghue et al.,
1998). In addition, it has been shown that synchronous spikes and
synchronization of oscillatory activity in the frequency band occur
more frequently for neurons activated by attended stimuli
(Steinmetz et al., 2000;
Fries et al., 2001). These
results have been interpreted according to the proposal that coherent
oscillation in the activity of cortical neurons contributes to the
establishment of the behavioral context or task set
(Llinás et al., 1998;
Engel et al., 2001).
Many studies have also shown that field potential recordings from multiple
brain regions display task-dependent changes in their coherence
(Bressler et al., 1993;
Sarnthein et al., 1998;
Rodriguez et al., 1999;
Srinivasan et al., 1999;
von Stein et al., 1999;
Fries et al., 2001). Activity
throughout the cortical network involved in the preparation of movements might
be integrated through the same mechanism. For example, the oscillatory field
potentials recorded in the SMA and the primary motor cortex become
synchronized before movement onset (Ohara
et al., 2001). Coherent oscillations in the activity of individual
SMA neurons might provide a substrate for such interareal synchronization of
oscillatory activity. In future studies, this possibility needs to be tested
directly with simultaneous single-unit recordings in multiple cortical
regions.
|
Footnotes
|
|---|
Received Apr. 9, 2003;
revised May. 28, 2003;
accepted May. 29, 2003.
This work was supported by National Institutes of Health Grants R01-MH59216
and P30-EY01319. I am grateful to Rita Farrell, Ryan Murray, and Stephan
Quessy for help with the experiment and Bruno Averbeck, Michelle Conroy, and
Jeong-woo Sohn for comments on this manuscript.
Correspondence should be addressed to Dr. Daeyeol Lee at the above address.
E-mail:
dlee{at}cvs.rochester.edu.
Copyright © 2003 Society for Neuroscience
0270-6474/03/236798-12$15.00/0
|
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Abstract
Introduction
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