1School of Psychology, University of St. Andrews, Fife KY16 9JU, United Kingdom; 2Department of Neuroscience, Brown University, Providence, Rhode Island 02912; and 3National Institute of Mental Health/National Institutes of Health, Bethesda, Maryland 20892
![]() |
ABSTRACT |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Oram, Mike W., Nicholas G. Hatsopoulos, Barry J. Richmond, and John P. Donoghue. Excess Synchrony in Motor Cortical Neurons Provides Redundant Direction Information With That From Coarse Temporal Measures. J. Neurophysiol. 86: 1700-1716, 2001. Previous studies have shown that measures of fine temporal correlation, such as synchronous spikes, across responses of motor cortical neurons carries more directional information than that predicted from statistically independent neurons. It is also known, however, that the coarse temporal measures of responses, such as spike count, are not independent. We therefore examined whether the information carried by coincident firing was related to that of coarsely defined spike counts and their correlation. Synchronous spikes were counted in the responses from 94 pairs of simultaneously recorded neurons in primary motor cortex (MI) while monkeys performed arm movement tasks. Direct measurement of the movement-related information indicated that the coincident spikes (1- to 5-ms precision) carry ~10% of the information carried by a code of the two spike counts. Inclusion of the numbers of synchronous spikes did not add information to that available from the spike counts and their coarse temporal correlation. To assess the significance of the numbers of coincident spikes, we extended the stochastic spike count matched (SCM) model to include correlations between spike counts of the individual neural responses and slow temporal dependencies within neural responses (~30 Hz bandwidth). The extended SCM model underestimated the numbers of synchronous spikes. Therefore as with previous studies, we found that there were more synchronous spikes in the neural data than could be accounted for by this stochastic model. However, the SCM model accounts for most (R2 = 0.93 ± 0.05, mean ± SE) of the differences in the observed number of synchronous spikes to different directions of arm movement, indicating that synchronous spiking is directly related to spike counts and their broad correlation. Further, this model supports the information theoretic analysis that the synchronous spikes do not provide directional information beyond that available from the firing rates of the same pool of directionally tuned MI neurons. These results show that detection of precisely timed spike patterns above chance levels does not imply that those spike patterns carry information unavailable from coarser population codes but leaves open the possibility that excess synchrony carries other forms of information or serves other roles in cortical information processing not studied here.
![]() |
INTRODUCTION |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
The study of neural
responses has concentrated, in general, on how the number of spikes
varies with input stimulus, motor output, or the conjunction of both
signals. More recently, precise spike timing has been proposed as a
mechanism to represent information not available from coarse temporal
response measures (Abeles 1991; Rieke et al.
1996
; Singer and Gray 1995
). The idea that
the nervous system could use the precise times as well as the number of
spikes is compelling. Neural spike trains have the potential to carry substantially more information than that available from spike count if
timing (approximately millisecond accuracy) between neurons is
considered (Abeles 1991
; Buracas and Albright
1999
; Rieke et al. 1996
). Temporal correlation
at fine scales could underlie aspects of higher cognitive process such
as binding, motor coordination, and even consciousness because they
could signal relationships among neurons carrying separate codes in
their coarse temporal response measures (Abeles 1991
;
Engel et al. 1992
; von der Malsburg 1995
;
von der Malsburg and Schneider 1986
).
Studies of precisely timed spike patterns from cortical areas related
to motor function have shown that the number of precisely timed spike
patterns, including synchronous spikes, carries information about the
occurrence, initiation, and direction of limb movement unavailable from
chance, under the assumption of statistical independence of each of the
engaged neurons (Hatsopoulos et al. 1998b; Riehle et al. 1997
; Vaadia et al. 1995
). Further study
showed that the correlation between the spike counts of cells assessed
over extended intervals (100's of milliseconds) also carries
information unavailable from consideration of independent spike counts
(Maynard et al. 1999
). Given that correlation of coarse
temporal response measures almost always increases the information
carried by spike count (Abbott and Dayan 1999
;
Deneve et al. 1999
; Maynard et al. 1999
; Oram et al. 1998
; Snippe and Koenderink
1992
), we examined whether the information carried by
synchronous spikes between responses of motor cortical neurons is
completely explained by the information carried by the number of spikes
in the neuron pair and their coarse temporal correlation (>20-ms time scale).
We find that, when the coarse temporal statistics within and between motor cortical responses are included, both information theoretic and modeling methods indicate that synchronous spikes do not carry information unavailable from the spike count pairs. Despite the observation that they carry no unique directional information, the synchronous spikes occur at a rate higher than expected from two independent stochastic processes, leaving open the possibility that synchrony may have other roles. The difference between observed and predicted numbers of synchronous spikes may be explained by postulating a common input or some other form of functional connectivity.
![]() |
METHODS |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Task
Two monkeys (macacca fascicularis) were operantly
trained to move a cursor on a computer monitor whose position was
controlled by a handle connected to a two-joint mechanical arm. Each
monkey was required to move the cursor from a center target to one of eight possible targets positioned radially from the center. Each trial
was composed of four different epochs: 1) a 500-ms hold period beginning with the start of trial event during which the monkey
had to keep the cursor over the center target, 2) a variable 1-1.5 s instructed delay period beginning with the appearance of one
of the eight radially positioned targets (instruction trigger), 3) the reaction time period beginning with the go signal
(which was indicated by the blinking of the radially positioned
target), and 4) a movement period beginning with the onset
of movement defined as the moment at which the cursor left the center
target. Because each radially positioned target could appear with equal probability, this task was fully specified by three bits of information (see Hatsopoulos et al. 1998a,b for more details
regarding this task). One of two monkeys was also trained on a second
task that involved generating a two-segment sequential movement.
Because there were two sequences that were possible under two
conditions (either preplanned or not), the conditions were specified by
two bits (N. G. Hatsopoulos, L. Paninski, and J. P. Donoghue,
unpublished observations).
Recordings
An array of 100 microelectrodes was implanted in the MI arm
representation, as described in earlier publications (Maynard et
al. 1999). Of the total array, only 22 and 11 were connected in
the 2 animals, respectively, and thus available for recording, The
microelectrode arrays (Bionic Technologies, Salt Lake City, UT)
consisted of 100, 1.5-mm-long platinized tip, silicon probes arranged
in a square grid (400 µm on center). All surgical procedures conducted for this study were in accordance with Brown University IACUC-approved protocols and the Guide for the Care and Use of Laboratory Animals (National Institute of Health publication no. 85-23, revised 1985).
Assessment of coarse temporal response measures (>20-ms resolution)
The number of spikes were counted in ±50-, 100-, 200-, 500-, and 1,000-ms sample periods centered on each of the four event triggers
(as the monkey's behavior is not controlled for before the start of
trial trigger, we only examined data after the start of trial trigger).
The mean and variance of firing rate were calculated and the fano
factor (variance/mean) evaluated from data in the ±1,000-ms sample
period using sliding windows of 20, 50, 100, 200, and 500 ms. To
evaluate the independence of the responses over time, correlation of
spike counts between these sliding windows was also assessed for each
arm movement direction for individual cells. Statistical comparison of
the correlation for each cell in each sliding window against
independence (r = 0) was performed using the Fisher
transform of the correlation coefficient (Snedecor and Cochran
1980) from each arm movement direction to ensure normality of
the distributions.
Coarse temporal correlation between the responses of different neurons
was calculated for each direction of arm movement using the spike
counts from the sample periods ±50, 100, 200, 500, and 1,000 ms
centered on the triggers. The correlation across all directions was
calculated by transforming each set of responses to each direction
d, rd, into its
z-score rz = (rd
d, where
d is the standard deviation of the responses
to direction d. The overall correlation is therefore the
correlation of the normalized response variability and does not reflect
correlation of the signal, nor is it biased toward those directions
with greater absolute response variability.
Assessment of synchronous spikes
The spike times were binned (i.e., rounded) to a temporal accuracy of 1 ms. "Synchrony" was defined at three different temporal resolutions: 1, 3, and 5 ms counted for each trial. That is, spikes in one neuron were considered synchronous if they occurred at 0, ±1, or ±2 ms, relative to spikes in the second neuron, respectively. We used the number of synchronous spikes to form our measure of a precise temporal code for the information theoretic analysis in the different sample windows. Results based on 3- and 5-ms temporal resolutions were qualitatively similar to those observed at a 1-ms resolution and for conciseness are not included.
Measuring the information content of neural codes
Transmitted information is a statistical measure quantifying, in
the present situation, how well different directions of arm movement
can be distinguished from each other using the responses of the
neurons. The amount of information carried by a neuron's response
depends on the code used to interpret the response (e.g., spike count).
If precisely timed spikes play a special role by encoding unique
information (Abeles 1991; Engel et al.
1992
; Lestienne and Strehler 1987
; Vaadia
et al. 1995
; von der Malsburg and Schneider 1986
), then some of the information they carry should be
unavailable from considering the pair of spike counts alone. We were
therefore interested in how much information was carried by the number
of synchronous spikes and second whether the synchronous spikes
together with the paired spike count carried more information than that carried by the paired spike count code alone.
Details of information theory can be found elsewhere (Cover and
Thomas 1991; Golomb et al. 1997
; Shannon
1948
) In brief, we asked how well the responses of single or
populations of neurons could, in principle, tell us which direction of
arm movement was performed. Mutual information is defined
as
![]() |
(1) |
While p(d) is determined exactly from the
experiment, p(r) and
p(d|r) must be estimated from the
neuronal data. Because of limited sample size
p(r) and especially
p(d|r) are subject to misestimation
(Kjaer et al. 1994; Optican et al. 1991
).
Several methods have been developed to correct for limited sample size (e.g., Kjaer et al. 1994
; Victor and Purpura
1996
; for review see Golomb et al. 1997
). We
chose the method of Kjaer et al. (1994)
because it does
not require us to make assumptions (e.g., Gaussian) to incorporate the
distributions of the response measures and their possibly nonlinear covariation.
The method of Kjaer et al. (1994) uses a
back-propagation neural network that performs nonlinear regression of
the selected neural code on the direction of arm movement. The response
measures were used as inputs to the neural network, and the directions of arm movement were used as target outputs (Kjaer et al.
1994
). After training, the outputs represent
p(d|r). The network was trained on
three-quarters of the data and tested on the remaining quarter,
preventing over-fitting that leads to the overestimates of the
information (Kjaer et al. 1994
). We used the spike
count, the number of synchronous spikes, or the conjoint code of spike count and number of synchronous spikes as response measures for input
to the network of Kjaer et al. (1994)
. This method
provides a good estimate of
I(D;R) (Golomb et
al. 1997
; Heller et al. 1995
; Kjaer et
al. 1994
). Statistical analysis of the information measures was
performed after transforming to ensure homogeneity of variance.
Assessment of the statistical significance of the numbers of synchronous spikes
We were also interested in estimating the number of synchronous
spikes expected by chance. Any synchronous spikes above chance levels,
even if they do not carry information, would indicate that there was
some level of functional connectivity between the neurons. Such
connectivity between neurons has been examined using the precise
temporal structure of responses in visually responsive cortical areas
(e.g., Gochin et al. 1991). The spike density function captures coarse (<30-Hz bandwidth, >20-ms time scale) temporal structure in the responses and is known to influence expected numbers
of precise response structures (Abeles and Gerstein
1988
; Aertsen et al. 1989
; Dayhoff and
Gerstein 1983a
,b
; Lestienne and Strehler 1987
;
Lestienne and Tuckwell 1998
; Victor and Purpura 1996
). We therefore calculated the spike density function (SDF) for each cell to each stimulus by convolution of individual responses with a Gaussian (SD = 5 ms) (Richmond et al. 1987
).
We extended the spike count matched model (Oram et al.
1999) to examine the number of precisely timed spikes expected
from an underlying stochastic mechanism. Briefly, for each cell in the
pair, the SDF is transformed into a cumulative spike density function
(CSDF) for each stimulus at each time point t
t) in which a spike occurs,
tspike, is such that tspike satisfies
CSPF(k)
R[0..1] < CSPF(k + 1), the time of the kth bin being
k
t
(k + 1)
t.
Each pair of spike count distributions and their correlation are preserved by stepping through the experimental data trial by trial and forcing each simulated trial to have the same number of spikes as the corresponding experimental trial. The extended SCM model therefore incorporates the slow variation in firing rate and the distribution of spike counts generated by individual neurons as well as the coarse temporal correlation of the spike counts and the correlation between the SDFs (i.e., correlation between the slow variation in firing rate of the individual neurons over time: the possible tendency for the spike density functions of different neurons to rise and fall together). The numbers of synchronous spikes were counted and compared with the experimental data using standard regression and ANOVA methods.
![]() |
RESULTS |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
For the present study it was critical to have well-isolated single
neurons. To avoid potential distortion of the spike numbers and times
from interference between spikes, we only accepted data from the
activity of the optimal single neuron on an electrode. This also means
that our analysis always compared pairs of cells recorded at least 400 µm apart. The analysis required sufficient data for each experimental
condition to perform the information theoretic analysis (see
Golomb et al. 1997). We therefore required each
direction of arm movement to be repeated at least 15 times (typically
~30-50, range 17-156, mean 58.7; total numbers of spikes: range
538-36,482, mean 5,753.9). The data from 28 motor cortical neurons
were examined from 2 monkeys (see also Hatsopoulos et al.
1998b
; Maynard et al. 1999
). The cells were
simultaneously recorded in groups of 4, 6, 8, and 10 cells, giving 94 pairs in total (6, 15, 28, and 45 pairs from the respective recording
session). For the pairs, the mean number of trials was 252.6 (range
188-337), and the mean number of spikes was 24,729.5 (range
4,905-69,169).
We are primarily interested in the potential for spike trains to convey
two independent messages: one message in the coarse temporal response
properties and one using fine temporal response properties. Most
previous studies have estimated the number of precisely timed spike
patterns using models that assume a spike count distribution based on a
Poisson process. As any deviation from a Poisson distribution of spike
count will necessarily influence the number of precisely timed spike
patterns expected by chance (Oram et al. 1999), we begin
with a detailed examination of the coarse temporal response statistics
of single motor cortical neurons (Figs.
1-6). We then examine the occurrence of
precisely timed patterns of pairs of spikes between neurons and show
that synchronous spikes occur at a rate higher than expected by chance
(Figs. 7-9). However, an information theoretic analysis indicates that
information obtained from synchronous spikes is redundant with the
information from the spike counts (Fig. 10). Examination of the
relationship between the coarse and fine temporal response
characteristics using a statistical model (Figs. 11-13) suggests the
most parsimonious explanation of the excess synchrony is that of fixed,
common input related to the firing rates of both neurons in the pair.
|
Coarse temporal response statistics of single motor cortical neurons
Given the strong relationship between the coarse temporal response
statistics of single neurons and the expected fine temporal structure
both within and between neurons (Aertsen and Gerstein 1985; Dayhoff and Gerstein 1983a
;
Lestienne and Tuckwell 1998
; Oram et al.
1999
), it is essential to incorporate the relevant statistics
in any assessment of the possible functional significance of precisely
timed spike patterns. While the non-Poisson nature of the responses can
be known from the interspike interval (ISI) histograms, the effect of
changes in response variability is more influential on the numbers of
precisely timed spike patterns than is deviation of the ISI from that
expected from a Poisson process (Oram et al. 1999
). We
therefore begin by examining the variability of the responses of motor
cortical neurons.
The fano factor
Figure 1 shows the fano factor (variance/mean) assessed using a
short (20 ms, Fig. 1, top) and long (500 ms, Fig. 1,
bottom) sliding window of the data from one cell over the
±1,000-ms sample period. The fano factor using the small time window
is <1 and becomes larger than one when longer time windows are used
(compare Fig. 1, top and bottom). The result of a
fano factor different from 1 demonstrates that the responses of this
cell are not consistent with a Poisson firing process. Figure
2 shows the average fano factor for the
motor cortical cells assessed using different sample windows starting
at each of the four triggers. For the 20- and 50-ms sample windows, the
variance is less than the mean firing rate taken around all triggers
(P < 0.001 each comparison), indicating that at short
sample windows there is less variability between neural responses to
single directions of movement than would be expected from a Poisson
process. For the 100-ms sample window, the fano factor is less than one
taken from the instruction trigger (P < 0.001). The
variance is, on average, numerically larger than the mean when windows
longer than 100 ms are considered for the start of trial, go and start
of arm movement triggers and for the 500-ms window for the instruction
trigger (P < 0.0005 each comparison), indicating that
at long sample windows there is greater variability between neural
responses than would be expected from a Poisson process. In summary,
the fano factor is significantly smaller than 1 with short sample
windows and significantly greater than 1 with longer windows. Thus the
responses of motor cortical neurons are not consistent with random
samples from a Poisson process (see also Baker and Lemon
2000; Lee et al. 1998
).
|
Sequential correlation within responses
A second method of assessing whether the neural response can be
characterized as a Poisson process is to examine temporal correlation
within the responses of a single neuron. Correlation between time
points within single responses indicates a non-Poisson process and is
another influence on the expected numbers and types of precisely timed
spike patterns. While a certain amount of correlation is implied by
deviation of the response variability from that expected from a Poisson
process, other sources of correlation are also possible. Note that the
correlation between time periods of the response measures the
deviations about the mean response at those time periods and is not
therefore related to the time course (spike density function) of the
response. Figure 3, top, shows
the correlation of spike count between successive 20-ms time windows of
one cell over the ±1,000-ms sample period. There is some evidence of
negative correlation before the start of arm movement with a short time
window for the responses of this cell, but little sign of correlation
of spike count after the start of arm movement (Fig. 3,
top). The bottom section of Fig. 3 shows the
correlation of successive 500-ms windows of the responses from the same
cell, showing positive correlation for most of the sample windows.
Figure 4 illustrates the mean ± SE
strength of mean correlation across neurons between successive time
windows centered about each of the four triggers for each of the sample windows (20, 50, 100, 200, and 500 ms). Overall, it can be seen that as
the window size increases the correlation between successive windows
increases, changing from r 0 at the shortest window (20 ms) to positive correlation of spike count between 50 ms or longer
windows. The correlation is significantly different from 0 for all
triggers at all sample windows >20 ms (P < 0.005 each comparison) and for the instruction trigger at 20-ms window
(P < 0.0005). These results also demonstrate that the
responses of motor cortical cells cannot be adequately described as
Poisson processes.
|
|
ISI distribution
Finally, a third potentially independent influence on the expected
number of precisely timed spike pattern is the distribution of the
ISIs. In a Poisson process the occurrences of events (spikes) are
statistically independent. This implies an exponential distribution of
ISIs for a constant-rate process. Even with variable firing rate, the
ISI distribution would be a sum of exponentials showing a monotonic
decline. The top panel of Fig.
5 shows the ISI distribution for the cell
in Fig. 1. The bottom panel of Fig. 5 shows the ISI distributions of a second cell recorded simultaneously with the cell in
the top panel. The ISI distribution does not have the exponential shape expected of a Poisson process (Kolmogorov-Smirnov test, P < 0.05; exponential estimated by least-squares
fit) in either of these examples, nor in any of the 28 recorded
neurons. There is no reason to believe these are cells that are
damaged. First, it is well established that certain cortical neurons
exhibit bursts of spikes with short ISIs. These so-called intrinsic
bursting cortical neurons bursters are usually pyramidal neurons and
have somata that lie in layers IV and V, which is likely from where we
are recording (Connors and Gutnick 1990).
Second, the recorded cells exhibit normal movement-related modulation
that begins several hundred milliseconds before movement onset typical
of cells in primary motor cortex.
|
Coarse temporal correlation between responses of neuron pairs
When the spike counts between different neurons were compared in ±500-ms sample period around the start of arm movement, many cell pairs showed significant correlation (Fig. 6). Note that the correlation could be either negative (Fig. 6, top) or positive (Fig. 6, bottom). Thirteen percent (1,061/8,080) of the pairs of responses over all of the individual movement directions at all sample windows and all triggers showed significant (P < 0.05) correlation. Forty-five percent (850/1,880) of the cell pairs showed significant correlation between responses (P < 0.05, after Bonferroni correction for multiple comparisons) for at least one of the individual movement directions assessed over all time windows and all triggers. A significant proportion (average over triggers 37%, Table 1) of pairs showed correlation of response variability either of the combined responses (see METHODS) or for one of the movement directions in sample periods as short as ±50 ms. The majority (~60%, Table 1) of the recorded pairs of cells showed at least one significant correlation value at longer sample periods (±500 and ±1,000 ms).
|
|
Number and distribution of synchronous spikes
Figure 7 shows the cross-correlogram
of one pair of the motor cortical neurons. Each point indicates the
correlation coefficient for the offset delay between the pair of
neurons. This value is the number of times that spikes were observed to
occur in the responses of both cells at each delay scaled to account
for the firing rates. We examined the cross-correlograms for patterns ranging from 100- to 100-ms delay. A single pair showed a clear peak
indicative of a monosynaptic connection between the two neurons: all
other significant peaks were at or centered near the zero delay bin
(synchrony). The existence of sharp synchrony exhibited in Fig. 7 has
been observed before: Hatsopoulos et al. (1998b)
estimated that 36% of all cell pairs that exhibited significant synchrony showed cross-correlation peaks with widths at half height of
1-3 ms. The majority of cell pairs (64%) showed broader peaks with
widths ranging from 10 to 15 ms at half height. The cross-correlogram illustrates two points. First, the correlation is low, peaking at 0.02, indicating that at best, knowledge of a spike at one time point
accounts for only 0.0004 of the variability in whether a spike is going
to occur at a given offset in the response of the second cell. The
correlation gives an indication of the potential power of the signal
carried by synchronous spikes; if a high correlation was observed it
would imply many synchronous spikes above chance levels and hence the
possibility of a strong signal that was unavailable from spike count.
However, the low observed correlation suggests that the potential
information carried by synchronous spikes unavailable from spike count
is limited. If synchronous spikes were to carry direction information
unavailable from spike count, the cross-correlation at 0 ms delay would
be high relative to the other delays for some but not all directions of
arm movement. Indeed, the correlation at the fine temporal scale varies
with direction of arm movement, suggesting that it may act as a neural
code independent of the spike counts. The low correlation values
suggest that the code would, however, be relatively weak.
|
The peak in the cross-correlogram at a delay of 0 ms is clearest when
all trials for a pair of cells are considered, regardless of the
particular direction of arm movement (Fig. 7, middle panel, calculated from pooling all trials across all directions of arm movement). Thus the result suggests the amount of synchrony varies continuously with direction. This was further examined by ranking the
cross-correlation over delays 55 to +55 ms for each direction and
each cell pair. The R2 of the
correlation of the ranks between directions at the 0-ms delay
(synchronous spikes) was 0.19, compared with 0.02-0.09 (mean = 0.05) for delays between 5 and 55 ms. This indicates that knowledge of
the cross-correlation at 0-ms delay of one direction of arm movement
allows some prediction of the cross-correlation at 0-ms delay (but not
other delays) to the other directions of arm movement. This confirms
that if a peak at 0-ms delay is present in one direction, then a peak
is likely for other directions, and if a pair does not show a peak in
the cross-correlogram for one direction, peaks will tend not be found
in other directions. Note that this does not indicate whether the
information about direction carried by synchronous spikes is
independent of spike count. If the distribution of synchronous spikes
changes across direction in a way that can be related to the coarse
temporal response measures, then the information they carry will be
redundant with the information carried by those coarse temporal
response measures.
The number of synchronous spikes for a pair of neurons varies from trial to trial, even when the spike counts are comparable across trials. Figure 8 shows the number of synchronous spikes observed for one pair of neural responses. The middle panel shows the summed distributions. The numbers of synchronous spikes to each direction of arm movement varies considerably, and the distributions show appreciable overlap. This also suggests that when considering pairs of neurons the numbers of synchronous spikes will carry relatively little information related to direction of arm movement.
|
The relationship between the number of spikes and the number of
synchronous spikes was investigated because a nonlinear relationship implies that the exact rather than assumed distribution of spike counts
needs to be incorporated into models used to estimate the expected
numbers of precisely timed spikes (Oram et al. 1999). The numbers of synchronous spikes from all cell pairs and all directions of arm movement have been combined and plotted as a function
of the pair of spike counts in Fig. 9,
top. The nonlinearity is illustrated in the bottom
section of Fig. 9, where the observed number of synchronous spikes
along the diagonal of the top section is plotted as a
function of the response strength (number of spikes, responses of both
neurons having the same number of spikes). The regression curves show
that the nonlinear (quadratic) function fits the data more closely than
a simple linear function. The nonlinearity was confirmed across all
spike count pairs using regression of a linear plane on the data and
comparing it with the regression of a surface defined by the sum of the
individual spike counts and their product. For all sample periods, the
increase in R2 when including the
product of the two spike counts in the regression was significant
(P < 0.05; see Table 2).
|
|
Information carried by synchronous spikes is redundant with that carried by spike count
The observation of precisely timed synchrony between the firing of two neurons does not in and of itself indicate that the synchrony is separable from the coarse temporal characteristics of the responses. We use information theoretic analysis to directly assess whether the synchrony can form a separable code from the coarse temporal characteristics. Although the analyses were performed using all four trigger points, we present data from all cell pairs primarily for the analyses around the go signal and start of arm movement because these are the only time periods where significant information related to direction of arm movement was found. The three response measures used in the calculation of the information were 1) the dual spike counts (1 spike count from each neuron), 2) the number of synchronous spikes, and 3) the conjoint code of the dual spike counts and the number of synchronous spikes (see METHODS for further details).
The information from synchronous spikes obtained from single pairs of cells is much less than that available from considering the spike count code of that same pair (Fig. 10, top, and Table 3). Synchronous spikes carry an average 7.9 ± 1.06% of the information carried by spike count (0.029 ± 0.001 bits vs. 0.325 ± 0.006 bits). However, the information per synchronous spike pair is larger than the information per individual spike (overall average 0.0115 ± 0.001 vs. 0.0010 ± 0.0007 bits per event). Adding the number of synchronous spikes to the spike count code adds no further information to that already available from knowing the two spike counts (compared for all pairs in Fig. 10, bottom), demonstrating that no additional information about movement direction is added by synchronous events (P > 0.05). Note that the lack of additional information about movement direction provided by synchronous events holds for all 96 pairs (Fig. 10, bottom), including those pairs with the greatest absolute numbers of synchronous spikes and those pairs with the greatest excess of synchronous spikes above chance levels. This result was found at all window periods.
|
|
To investigate further whether the synchronous spikes carried information unavailable from spike counts and the coarse correlation, an ANOVA was performed using code and cell as factors. Information values were log transformed to ensure homogeneity of variance. This analysis also revealed no effect of code (dual spike count 0.3247 ± 0.006 bits, addition of synchronous spikes 0.3252 ± 0.006 bits, F[1,93] = 0.184, P > 0.5). The power of the analysis was such that changes of a few 100th of bits (±0.02 bits) would have been deemed significant, so the result is not due to lack of sensitivity of the test. The addition of synchronous spikes did not interact with neural pair (F[93,5408] = 0.78, P > 0.5), indicating that synchronous spikes did not add information above that carried by spike counts for any of the 94 pairs (see also Fig. 10, bottom). Note again that this includes those pairs with the greatest absolute numbers of synchronous spikes and those pairs with the greatest excess of synchronous spikes above chance levels. This effect did not vary with trigger point (F[1,93] = 3.7, P > 0.05). The lack of extra information carried by synchronous spikes was robust across the sizes of sample windows (F[4,372] = 0.73, P > 0.5), for all pairs at all sample periods (F[372,5408] = 0.48, P > 0.5) and for all pairs at both trigger points (F[93,5408] = 0.303, P > 0.5). In summary, despite extensive examination, there was no evidence that the synchronous spikes between the responses of cell pairs carried information beyond that available from a code that includes spike counts and their coarse temporal correlations.
Scaling the SCM model to predict the numbers of synchronous spikes
The information theoretic analyses showed that a relationship
exists between the coarse temporal response characteristics and the
precisely timed synchrony. Excess synchrony would be expected to carry
information redundant with the coarse temporal characteristics if
simple (e.g., linear) relationships exist between the predicted and
observed numbers of synchronous spikes. For example, local network
properties can give rise to synchronous firing (Bush and Sejnowski 1996; Engel et al. 1991a
,b
;
Hansel 1996
; White et al. 1998
). The
simplest source of excess synchrony is to postulate a direct common
input from either a single neuron or a small population of neurons. The
source of excess synchrony could be independent of the particular arm
direction: this would give rise to excess synchrony that was equal
across all directions of arm movement. Alternatively the common input
could form part of the driving inputs, predicting excess synchrony that
rose in proportion to the chance numbers of synchronous spikes.
Figure 11 shows the regressions of the number of synchronous spikes predicted by the SCM model against the number of synchronous spikes found in six pairs from the motor cortical data. The R2 values indicate the proportion of the variance in the number of synchronous spikes seen in the neural data that can be accounted for by a linear transformation of the SCM estimate. The range of R2 values is generally high. However, when the range of observed numbers of synchronous spikes is low (<1, pair 1 and 4), the R2 value becomes low for some pairs. The regression slopes are <1, demonstrating that there is an excess of synchronous spikes for these cell pairs. Thus the SCM model does not predict the absolute number of synchronous spikes. For those cases with high R2, a simple scaling of the numbers of synchronous spikes from the model would produce nearly perfect predictions. For those cases where the R2 is low, there are two possibilities. Either the synchronous spikes observed in the neural data are not predictable from the spike counts and the coarse temporal correlation, or the low R2 values are simply due to a small range in the mean number of synchronous spikes and the high variability in the individual distributions of the synchronous spikes (Fig. 8). We tested which of these possibilities is more likely by examining the relationship between the results from the regressions and the range of the mean number of synchronous spikes found for the different directions of arm movement.
|
The top section of Fig. 12 shows the distribution of the R2 for all 94 pairs of motor cortical neurons from all the 5 different sample periods (±50, 100, 200, 500, and 1,000 ms). When the range of the observed number of synchronous spikes is small, the R2 value is evenly distributed across the entire range (0-1). This is to be expected. With small ranges, different samples from a single distribution would give rise to small differences in the mean number of synchronous spikes. Under these circumstances, the observed variability in the numbers of synchronous spikes would be due to sample bias and not a systematic variation. Thus the observed variability in the number of synchronous spikes simply reflects the statistics of small sample sizes, so no additional explanation for this variability is necessary. As the range of the mean numbers of synchronous spikes to different movement directions increases, only high values of R2 values are seen. This shows that when significant variation is observed in the range of the number of synchronous spikes, the SCM model explains a high proportion of the variance (>80%). The bottom section of Fig. 12 shows the slope of the regressions between the numbers of synchronous spikes predicted by the SCM model and the number observed in the neural data. As all intercepts of the regressions were at or near to zero, a slope of 1 corresponds to equality between the SCM model and the motor cortical data. The slopes were variable when the range of the numbers of synchronous spikes was small. When the range of synchronous spikes was higher, the slopes showed more consistent values, clustering in the range 0.75-0.85. However, it is noteworthy that the slopes varied across cell pairs, so that a different constant had to be added to the model for each cell pair to account for the fit between the predicted number of synchronous spikes and the number obtained from the data. This individuality means that excess synchrony cannot be reduced to a simple global feature of rate modulation for all pairs, but the excess can, nevertheless, be related to rate modulation on a pair by pair basis.
|
The correlation coefficient associated with each
R2 can be transformed to account for
its limits (1 and 1) and the average taken (see METHODS)
(Snedecor and Cochran 1980
). Taking all data values,
including those with the expected R2 = 0.0 (i.e., little variation in the neural data), the reverse transform
of the mean suggests the average r = 0.874 giving an R2 of 0.76 ± 0.03 (mean ± SE). Thus a scaled version of the SCM model accounts for approximately
three-quarters of the variance in the observed number of synchronous
spikes even when including pairs of neurons where there is no
meaningful variation in the number of synchronous spikes between
directions. The top section of Fig.
13 shows the average
R2 calculated for each of the time
windows from those window/pair combinations that had a range of at
least 0.5 synchronous spikes/trial or more over different movement
directions. As there was no significant difference between the time
windows (F[4,176] = 0.93, P > 0.4) the estimates were combined. When the values
are taken from all sample window/neural pair combinations that showed a difference of 0.5 synchronous spikes/trial or more between different arm movements, R2 was 0.93 ± 0.05 (mean ± SE). This suggests that when there is true variation
in the neural data (rather than sample error), the SCM model typically
accounts for >90% of the variance in the number of synchronous
spikes.
|
While the SCM model accurately predicts the variability in the number of synchronous spikes, the model consistently underestimates the absolute numbers. The high R2 values indicate that applying a scaling factor to the numbers of synchronous spikes obtained from the SCM model would bring those numbers into line with those observed in the neural data. The appropriate scale factor for each pair is given by 1/slope of the regression. Across all pairs and sample windows the average slope was 0.65 ± 0.051 (mean ± SE). When the estimates of the slope were taken from those neural pairs that showed a difference of 0.5 synchronous spikes/trial or more between different arm movements, the average slope was to 0.78 ± 0.015 (Fig. 13, bottom), giving a mean scale factor of 1.41 ± 0.05.
![]() |
DISCUSSION |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Correlation between the spike counts of motor cortical neurons has
been shown to exist (Lee et al. 1998; Maynard et
al. 1999
), and incorporating them into models improves the
discrimination of movement direction (Maynard et al.
1999
). Broad temporal correlation therefore needs to be
considered when measuring information carried by populations of spike
counts (Abbott and Dayan 1999
; Oram et al.
1998
). It is also essential to consider broad correlations to
provide an accurate estimate of the information carried by synchronous
spikes. The ability to obtain simultaneous recording of many MI neurons
now makes it possible to examine directly whether or not synchronous
spikes added to the information available from the spike counts plus
their broad correlations across different cells. As with previous
studies, we found ~10-20% of cell pairs showed levels of synchrony
that were significantly (P < 0.05) above chance
(Baker et al. 2001
; Hatsopoulos et al.
1998b
). Unlike most previous studies, we could extend the
examination of cell pair characteristics beyond those recorded on the
same electrode to neurons that were separated by 400 µm or more in
the cortex. Thus our study is novel in that we provide an analysis of a
simultaneously acting neuron populations acting over several square
millimeters of cortex.
Our results show that there is an excess of synchronous spikes in
MI neuron pairs. However, this excess provides no additional information about movement direction beyond that provided by the spike
count and broad covariance of the same cell pair. Others have examined
the responses of motor cortical responses for more complex patterns of
precisely timed spikes (Baker and Lemon 2000). The
existence of an excess number of synchronous spikes (see
RESULTS) (Baker et al. 2001
;
Hatsopoulos et al. 1998b
) indicates greater than
expected numbers of any complex patterns of spikes that
incorporates synchronous spikes. While the numbers of repeating
triplets of spikes within a single neuron (Oram et al.
1999
) are predicted almost exactly by the SCM model
(unpublished observation), the excess synchrony is spread across all
the complex spike patterns involving synchrony and does not therefore
appear to be above chance levels for any particular complex spike
pattern. Thus the analysis we performed was aimed to examine the excess
synchrony (delay 0 ms): delays up to ±100 ms were not found to be
significant, and, with the proviso given above, we found no evidence
for more complex spike patterns to be above chance levels (see also
Baker and Lemon 2000
). Of course, this analysis is
restricted to spike patterns across pairs of neurons and does not
address other possible patterns involving more than two neurons.
Response statistics of single motor cortical neurons and fine temporal structure
The responses of single MI neurons cannot be characterized by a
Poisson process because 1) the variance/mean of the
responses is less than that expected from a Poisson process (1.0) at
short intervals and >1.0 at long sample periods (Figs. 1 and 2) (see also Lee et al. 1998), and 2) significant
sequential correlation was found (Figs. 3 and 4). (Note that the
sequential correlation is over and above the correlation between
successive points of the average response profile.) As any deviation of
the spike count distribution of responses from Poisson indicates that
correlations must exist within the responses of the cells (Oram
et al. 1999
), it was necessary to include the observed spike
count distribution when assessing the expected number of synchronous spikes.
The ISI distribution deviates significantly from a monotonic
distribution for the first 15-ms intervals or so (Fig. 5). Studies of
the responses of retinal ganglion cells have shown that the ISIs also
have an influence on the expected fine temporal structure of responses
(Berry and Meister 1998). The ISI distribution of responses from LGN and striate cortical neurons require adjustment to
the first and second intervals to match that seen in the data (Oram et al. 1999
). It was therefore necessary to
include the observed ISI distributions as well as the observed
distributions of the spike counts to properly assess the statistical
significance of synchrony.
Coarse temporal correlation in spike count between neurons and synchrony
The responses between pairs of MI neurons are significantly
correlated at coarse temporal scales (Fig. 6 and Table 1). Previous studies have shown similar correlation between the spike counts of
motor cortical neurons (Lee et al. 1998; Maynard
et al. 1999
). Moreover, these broad correlations add additional
information about movement direction (Maynard et al.
1999
). Such correlation needs to be included when calculating
numbers of synchronous spikes occurring by chance on a fine time scale
(Brody 1999a
,b
), because these factors markedly effect
their numbers.
The observed positive correlation of spike counts between neuron pairs
means there will be more instances with both counts being high or both
being low than if the responses were independent. The nonlinear
relationship between the pair of spike counts and the number of
synchronous spikes (Fig. 9 and Table 2) implies that a decrease in
synchronous spikes in low spike count trials is more than offset by an
increase in synchronous spikes in high spike count trials. Thus the
expected number of synchronous spikes is sensitive to the coarse
temporal correlation of spike count (Brody 1999a-c
). A
misestimate of the distribution or failure to account accurately for
any coarse temporal correlation will therefore necessarily lead to a
misestimate of the expected number of synchronous spikes.
Information carried by spike counts and synchronous spikes
We incorporated the observed spike count distributions and the
coarse temporal correlation when examining the information carried by
synchronous spikes using the method of Kjaer (Kjaer et al.
1994). The amount of information provided by a single
synchronous spike pair was ~12-fold larger than that from a single
spike, but the total information available in time windows from ±50 to ±1,000 ms was only ~1/12 of that available from the number of spikes. Further, the information carried by the synchronous spikes was
redundant with that carried by the spike counts (Fig. 10), so that the
synchronous firing of a pair of cells provided no new information about
the direction of arm movement. Within a given time window the reverse
is not true: spike counts provide information about direction that is
not available from synchronous spikes. Previous analysis demonstrated
that the synchronous spike carried directional information above that
available from coincidences from statistically independent responses
(Hatsopoulos et al. 1998b
). The present analysis shows
that this directional information is the same as or part of the
information carried by the correlation of the coarse response measures.
Thus under the present experimental conditions, synchronous spikes do
not code directional information that is separate from that coded by
the spike counts and their coarse temporal statistics. Our experimental
paradigm, however, does not allow us to determine whether the observed
synchronous spikes between neurons (or indeed spike counts) of the
individual neurons are actually being used by the nervous system. Both
these signals contain directional information, and they may be used in
separate ways to "tag" movement direction for subsequent or ongoing
processing. It is clear that the postsynaptic impact of synchronously
arriving events is considerably more powerful than spikes that are
temporally dispersed. The synchrony we observed may be more significant
physiologically in directional coding than the firing rates of
individual neurons. Therefore one cannot equate the redundancy in the
abstract information sense with physiological relevance. Indeed, it is
possible that synchrony we observed is created to increase the
functional impact of the elevated firing rates. The synchrony (as
measured by the number of spikes within ±0, 1, 2, or 5 ms) does not,
however, add information that is unavailable from the firing rates (the
spike counts from each of the neurons in the pair) assessed from
windows ranging from 50 to 1,000 ms.
Modeling synchronous spikes between motor cortical responses
We predicted numbers of synchronous spikes using the coarse
temporal statistics within and between individual MI neurons. To do
this we extended the spike count matched model (Oram et al.
1999) to include the responses of a pair of neurons. The
extended SCM model incorporates the observed spike count distribution
of the individual cells and thereby includes the within response correlation induced by deviation from a Poisson process (see
Oram et al. 1999
for discussion). By matching the spike
counts of each recorded pair of responses on a trial-by-trial basis,
the extended SCM model implicitly includes both linear and nonlinear
coarse temporal correlation between the spike counts of the individual neurons. While we could have calculated the standard co-variance measure and assumed a multidimensional Gaussian distribution of spike
count, the method adopted makes fewer assumptions about the coarse
temporal statistics and was therefore more appropriate for assessing
relationships between observed coarse and fine response statistics. It
is also known that the numbers of synchronous spikes depends on the
"shape" or profile of responses (Aertsen and Gerstein 1985
; Lestienne and Tuckwell 1998
; Oram
et al. 1999
). The SCM model incorporates the response profiles
of each neuron by using the SDF (Oram et al. 1999
), and
the extended SCM model used here incorporates not only each SDF but
also any co-variation between the two SDFs.
With inclusion of a linear adjustment, the SCM model generally predicted the mean number of synchronous spikes for all directions. The variability in the synchronous spikes is large compared with the range (Fig. 8), and therefore the differences in mean spike counts over different directions when the range is small is likely due to noise. Thus those cases where the model did not predict the mean number of synchronous spikes can be attributed to the effects of the high variability in the trial-by-trial numbers of synchronous spikes (Fig. 12). Thus a parsimonious explanation of these data are that the synchronous spikes above chance levels are directly related to the spike counts and their correlation. The model does, however, require a different scaling factor for each cell pair. The variability in the number of synchronous spikes with direction of arm movement (Figs. 7 and 8) indicates the presence of a "tuning curve" for the synchronous spikes with direction. In predicting the variability in the number of synchronous spikes, the SCM model generates the correctly shaped tuning curve: all that is missing is the amplitude of the tuning curve. The SCM model therefore can be thought of as providing a normalized tuning curve. Thus while the absolute numbers of synchronous spikes are not accounted for by the model, the variation in the numbers of synchronous spikes between different directions are directly related to the firing rates and their correlation. As the variation in numbers of synchronous spikes with direction is predictable from the coarse temporal characteristics of the responses, the number of synchronous spikes cannot carry any information about the direction that is not present in the coarse temporal characteristics of the responses. While the excess of synchrony could be used to provide a code giving information about aspects of behavior not studied here, it will be essential to incorporate concurrent changes in the coarse temporal characteristics of the responses for these conditions.
Excess synchronous spikes and information
Despite incorporating the coarse temporal correlation between and within the responses, the extended spike count matched model consistently underestimated the number of synchronous spikes found in the neural data (Fig. 11). Closer examination revealed that the SCM model underestimated the observed number of synchronous spikes by a scale factor that was constant across directions of movement (Fig. 13). Had we examined data from just two directions, we would have noted that the excess synchronous spikes depended on the particular direction but could not have observed that the excess was in proportion to the expected number. The scaling factor suggested that the numbers of synchronous spikes in the neural data were approximately 1.4 times the number expected by chance for all directions of arm movement.
The observed excess of synchronous spikes does not, by itself, support the hypothesis that synchronous spikes have a special role in directional coding. When a constant scaling factor for each neural pair is incorporated, the extended SCM model accounted for >90% of the variability on average (R2 = 0.93 ± 0.05, mean ± SE) in the absolute numbers of synchronous spikes to different arm movement directions (Fig. 13). Thus there is a small amount of total variability (<10%) in the number of synchronous spikes that is not explained by the differences in spike counts between directions of arm movement. It is only this residual variability that could carry directional information unavailable from spike count. Hence it is not surprising that the information theoretical analysis indicated that the directional information carried by synchronous spikes was redundant with the information carried by spike count (Fig. 10). The lack of additional information about movement direction added by synchronous events was found for all pairs and therefore holds for those pairs with both small and large numbers of synchronous spikes, both in terms of absolute numbers of synchronous spikes and in terms of the excess of synchronous spikes above chance levels. This, combined with the sensitivity of the measure (a change of 0.02 bits being deemed significant) leads us to conclude that our findings are not a "false-negative" but reflect a genuine lack of a unique role for most or all synchronously occurring spikes in coding directional information.
Excess synchronous spikes and functional connectivity
It is natural to consider possible structural or anatomical explanations for this mismatch between the observed synchrony and that predicted by the statistical SCM model. In general, the mechanism driving the excess of synchronous spikes seen in the neural data increases its effectiveness with increasing expected numbers of synchronous spikes (Fig. 11). [In those cases where the model does not predict the variability in the numbers of synchronous spikes, there is little variation present and the low R2 value can likely be attributed to sampling error (Fig. 12).] As the number of synchronous spikes increases with the spike count (Fig. 9 and Table 2), the mechanism driving the excess of synchronous spikes rises with the spike counts. In other words, for most of the cell pairs it is not possible to distinguish between the inputs driving the neural activity and the mechanism that gives rise to the synchronous spikes above the number expected by chance. We note that the presence of a single scaling factor from the SCM model for each neural pair shows that a variable amount of excess in the numbers of synchronous spikes with direction does not necessarily imply changes in the relationships between the neurons. We have shown here that data from several conditions is needed before being able to conclude that an excess of synchronous spikes, or indeed any precisely timed spike pattern, reflects dynamic changes in the relationships between neurons.
One possible explanation for the observed excess in synchrony may be
that it is a natural consequence of a network of mutually interconnected neurons. There is anatomical evidence that neurons in
motor cortex are highly interconnected via horizontal connections (Donoghue et al. 1996; Huntley and Jones
1991
). Moreover, functional studies have shown that motor
cortex, unlike primary sensory cortices, exhibit distributed patterns
of activation with very little somatotopy (Sanes et al.
1995
; Schieber and Hibbard 1993
), consistent
with the anatomically demonstrated extensive interconnectivity
(Huntley and Jones 1991
). A number of neural modeling
studies have shown that neurons with mutual interconnections can engage
in synchronous firing, particularly if one or more of the component
cells are oscillatory (Bush and Sejnowski 1996
;
Engel et al. 1991a
,b
; Hansel 1996
;
White et al. 1998
). However, such networks engage in
synchronous firing patterns in ways that do not necessarily predict a
linear increase in the excess synchrony with the background firing rate.
Another possible explanation for the excess of synchronous spikes is common driving input from a cell or population of cells. Consider a pair of neurons, each with their own set of inputs, and a further neuron (or population) that is connected directly to each of the pair. Assuming this input represents the entire source of synchronous spikes above chance levels and that the synaptic strength of this input is constant within the experimental period, it follows that the excess of synchronous spikes above chance levels will be determined solely by the activity of this input. The more active this input neuron is, the greater the excess of synchronous spikes. This would give rise to the excess over chance levels rising with the number of observed synchronous spikes and is precisely what was observed (Figs. 11-13). This argument explains our data only if the postulated common input mechanism co-varied with the other inputs to the cells. It is possible to imagine two cells with common preferred directions (say 90°) and common input being greatest for another direction of arm movement (say 270°). The largest number of synchronous spikes could then occur at 90° because of the high activity of both cells, but the greatest number of unexpected synchronous spikes would be at 270°. This was not seen in our data. Hence the argument based on common input with fixed functional connectivity that co-varies with the other inputs is consistent with the data. A puzzling aspect of the "common input" hypothesis, however, is that pairs of cells at a distance from each other almost always show a zero lag correlation. That is, there is little evidence of cross-correlations between distant cortical cells with short lags indicative of monosynaptic driving of one cell onto another.
Recent computational studies provide further insight into how a fixed
functional connectivity between neurons and neural populations could
give rise to the results we observed. Chawla and colleagues (Chawla et al. 1999) have shown, using both integrate
and fire models and models based on Hodgkin-Huxley equations, that
changes 1) in the strength or number of inhibitory
connections, 2) the strength or numbers of excitatory
connections, or 3) changes in the time course of the
synaptic connections can all influence the relationship between the
numbers of synchronous spikes and firing rate. Changes or variation in
these parameters with experimental condition would therefore allow
information unavailable from the spike count to be carried by the
synchronous spikes. For constant values relating to 1-3
above, they found their models indicated that the number of synchronous
spikes above chance levels increased with increasing firing rates of
the interconnected populations, but the synchronous spikes could not
carry information beyond that available from the spike count and coarse
temporal correlation (Chawla et al. 1999
). The analysis
of our motor cortical data also shows that the number of synchronous
spikes above chance levels typically increased with increasing firing
rates and that the synchronous spikes did not carry information beyond
that available from the spike count and coarse temporal correlation.
Thus our data are consistent with a network that, under the
experimental variations used (see METHODS), showed
1) no change in in the strength or number of inhibitory
connections, 2) no change in the strength or numbers of
excitatory connections, or 3) no change in the dynamics of
the synaptic connections.
Summary
In summary, because the responses of individual motor cortical neurons are not well described by a Poisson process, they must contain temporal structure (correlation). Furthermore, the responses between different neurons assessed at coarse time scale are correlated. Even though we included these sources of correlation in our calculations, there was a clear excess of synchronous spikes seen in our data. However, we found no evidence that the synchronous spikes carried information related to direction of arm movement above that available from the spike counts and their correlation. These issues highlight the difficulties in interpretation of cross-correlograms from nonstationary data. It is important to note that current methods make it practical only to examine synchrony among cell pairs. There is no reason to believe that there is particular significance of our randomly selected cell pairs; the cortex may operate using very large numbers of cooperating elements. These may create synchrony occurring across various collections of cells that we have inadequately sampled. Our experiments do not rule out the possibility that larger groups of cells provide considerable information about direction or other aspects of movement, beyond that found in rate alone. Despite these caveats, our results show conclusively that detection of an excess of synchronous spikes above chance levels does not imply that the synchronous spikes carry information unavailable from spike count. It remains to be seen whether synchrony or any other relational code among motor cortical neurons carries information about other aspects of movement planning and execution.
![]() |
FOOTNOTES |
---|
Address for reprint requests: N. G. Hatsopoulos (E-mail: nichoh{at}brown.edu).
Received 18 August 2000; accepted in final form 18 June 2001.
![]() |
REFERENCES |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|