Download Spike synchronization and firing rate in a population of motor cortical

Biol. Cybern. 88, 360–373 (2003)
DOI 10.1007/s00422-002-0385-3
Ó Springer-Verlag 2003
Spike synchronization and firing rate in a population of motor cortical
neurons in relation to movement direction and reaction time
F. Grammont , A. Riehle
Center for Research in Cognitive Neuroscience, CRNC – CNRS, Marseille, France
Received: 16 January 2002 / Accepted in revised form: 26 November 2002 / Published online: 7 April 2003
Abstract. We studied the dynamics of precise spike
synchronization and rate modulation in a population of
neurons recorded in monkey motor cortex during
performance of a delayed multidirectional pointing task
and determined their relation to behavior. We showed
that at the population level neurons coherently synchronized their activity at various moments during the trial
in relation to relevant task events. The comparison of
the time course of the modulation of synchronous
activity with that of the firing rate of the same neurons
revealed a considerable difference. Indeed, when synchronous activity was highest, at the end of the
preparatory period, firing rate was low, and, conversely,
when the firing rate was highest, at movement onset,
synchronous activity was almost absent. There was a
clear tendency for synchrony to precede firing rate,
suggesting that the coherent activation of cell assemblies
may trigger the increase in firing rate in large groups of
neurons, although it appeared that there was no simple
parallel shifting in time of these two activity measures.
Interestingly, there was a systematic relationship between the amount of significant synchronous activity
within the population of neurons and movement direction at the end of the preparatory period. Furthermore,
about 400 ms later, at movement onset, the mean firing
rate of the same population was also significantly tuned
to movement direction, having roughly the same preferred direction as synchronous activity. Finally, reaction time measurements revealed a directional preference
of the monkey with, once again, the same preferred
direction as synchronous activity and firing rate. These
results lead us to speculate that synchronous activity and
firing rate are cooperative neuronal processes and that
the directional matching of our three measures – firing
rate, synchronicity, and reaction times – might be an
effect of behaviorally induced network cooperativity
acquired during learning.
Correspondence to: A. Riehle
(e-mail: ariehle@lnf.cnrs-mrs.fr,
Tel.: +33-491-164329, Fax: +33-491-774969)
Present address: Istituto di Fisiologia Umana, Università di
Parma, Via Volturno 39, 43100 Parma, Italy
1 Introduction
Reduction of uncertainty is one of the basic principles
for understanding the mechanisms underlying preparation for action (Requin et al. 1991). In this context,
(un)certainty is equivalent to information about the
required motor response. Movement preparation can be
studied best by manipulating information about various
aspects of the movement. For that purpose two signals
are presented successively during each trial and separated by an instructed delay, the preparatory period. The
first, or preparatory, signal provides prior information
about (aspects of) the movement, which must be
executed after the occurrence of the second, or response,
signal. Two main categories of information may be
manipulated. On the one hand, providing prior information about spatial and/or kinematic parameters of the
movement, e.g., direction, extent, force, etc., reduces
uncertainty such that it leads to a significant reduction in
reaction time (Rosenbaum 1980; Bonnet et al. 1982;
Lépine et al. 1989; Riehle and Requin 1989, 1995; Riehle
et al. 1994). On the other hand, manipulating temporal
aspects of the task by systematically varying the
duration of the preparatory period has been shown to
efficiently alter the preparatory state of the subject
(Bertelson and Boons 1960; Bertelson 1967). When
presenting a finite number of durations of the preparatory period at random, but with equal probability,
reaction time decreases with increasing duration (for a
review see Requin et al. 1991). Indeed, as time goes on
during the trial and the response signal is not presented
at the first possible moment, the probability for its
occurrence increases with each subsequent possible
moment (Riehle et al. 1997).
It is commonly accepted that behavioral and cognitive processes are reflected in the (mean) discharge rate
of neurons (Barlow 1972; Shadlen and Newsome 1994).
In the framework of movement preparation, it has been
shown that motor cortical neurons selectively change
their activity long before movement execution in relation to prior information about various parameters such
as direction (Weinrich and Wise 1982; Weinrich et al.
1984; Riehle and Requin 1989; Bastian et al. 1998),
361
force (Riehle et al. 1994; Riehle and Requin 1995), or
movement extent (Riehle and Requin 1989; Kurata
1993; Riehle et al. 1994). In parallel, another concept
emerged claiming that computational processes in neocortical areas could also rely on the relative timing
correlation of spiking discharges among neurons within
functional groups (Abeles 1982, 1991; Gerstein et al.
1989; Singer 1999), commonly called cell assemblies
(Hebb 1949; for a review see Fujii et al. 1996). Experimental evidence for such precise temporal relations
among spiking activities of multiple neurons was provided essentially in sensory areas (visual: reviewed in
Singer and Gray 1995; auditory: Ahissar et al. 1992;
DeCharms and Merzenich 1996; somatosensory: Nicolelis et al. 1995; frontal: Aertsen et al. 1991; Vaadia
et al. 1995). Recently it has been shown that in motor
cortical areas spike synchronization can also occur in
relation to signal expectancy (Riehle et al. 1997, 2000).
Furthermore, spike synchronization was observed during sensorimotor transformation between neurons that
were classified, on the basis of their changes in firing
rate, as being functionally involved in different processes, e.g., preparation- or execution-related (Grammont and Riehle 1999). Finally, it has been shown that
spike synchronization of motor cortical neurons, along
with their discharge rate, carried about 10% more information about movement direction than discharge
rate alone (Hatsopoulos et al. 1998).
Studies on neuronal coding has stimulated an important discussion in recent years among experimentalists (Abeles et al. 1993; Shadlen and Newsome 1994;
Softky 1995; Singer and Gray 1995; Roskies 1999) and
theoreticians (Von der Malsburg 1981, 1995; Abeles
1982, 1991; Aertsen et al. 1994, 1995; Diesmann et al.
1999). Of particular interest here are debates currently in
progress for determining the implication of a temporal
code in cognitive processes (for reviews see Fujii et al.
1996; Roskies 1999). As two modes of neural coding,
i.e., rate code and temporal code, may in fact be considered to be related to cognitive processes at various
levels, our integrative approach tends to explore their
complementary involvement in one of the same processes – here preparation for action.
To that end we simultaneously recorded the activity
of up to seven single neurons in the primary motor
cortex of a monkey in the context of a delayed multidirectional pointing task. Both prior information about
movement direction and the duration of the instructed
delay were systematically manipulated. We used the
modified version of the unitary event analysis for detecting synchronized spiking activities in pairs of neurons (Grün 1996; Grün et al. 1999, 2002a,b). Basically
this technique allows one to determine epochs containing spike coincidences that violate the assumption of
independence of the participating neurons. The interdependence is then interpreted as a signature of a
functional cell assembly (Aertsen et al. 1991). The statistical null-hypothesis is formulated on the basis of the
individual firing probabilities and allows one to calculate
the number of expected coincidences. The statistical
significance of the measured number of coincidences is
evaluated by comparing it with the expected number. By
using this analysis in sliding windows, we can deal with
nonstationarities of firing rates and determine epochs of
significant synchronized activity along the trials. The
temporal precision of spike synchronization is obtained
by additionally varying the allowed coincidence width in
the analysis between 1 to 20 ms (Grün et al. 1999). If cell
assemblies are involved in cortical information processing, they should be activated in systematic relation to the
behavioral task (Riehle et al. 1997, 2000; Grammont and
Riehle 1999). Thus, in order to clarify the contribution
of cell assemblies to cognitive motor processes, we
quantified data from many pairs of neurons by calculating the probability of significant synchronization
(Grammont 2001). This provides a measure describing
the evolution both in time and temporal precision of
synchronous spiking activity at the level of an entire
population of single neurons. We then compared the
dynamics of synchronized activity of this population of
neurons with its mean firing rate, according to movement direction and reaction time. Preliminary results
have been presented in abstract form (Grammont and
Riehle 2000).
2 Material and methods
2.1 Behavioral procedure
A male Rhesus monkey (Macaca mulatta) was trained to
perform a delayed multidirectional pointing task (Riehle
et al. 2000). It was cared for in the manner described in
the Guiding Principles in the Care and Use of Animals of
the American Physiological Society and in French
government regulations. The animal sat in a primate
chair in front of a vertical panel on which seven touchsensitive, light emitting diodes (LEDs) were mounted,
one in the center and six placed equidistantly on a circle
around it (Fig. 2, inset). The monkey had to initiate a
trial by touching with the left hand the central target
when it was lit in yellow (start trial, ST, Fig. 1a). After a
fixed delay of 500 ms during which the monkey had to
continue pressing the target, two signals were presented
successively, separated by a variable time interval. The
first, the preparatory signal (PS), consisted of the
illumination of one of the peripheral targets in green.
It indicated the target for the upcoming movement.
After a delay of either 600 or 1200 ms, presented at
random with equal probability, during which the animal
had to continue to press the central target, the illuminated peripheral target turned red, serving as response
signal (RS) and target to be pointed. During the first
600 ms of the preparatory period of each trial, the
probability for the response signal to occur at 600 ms
was 0.5 (RS1). Once this moment passed without signal
occurrence, conditional probability changed to 1 (RS2).
The monkey was rewarded by a drop of juice at the end
of each correct trial. It completed 300 trials during one
session including 12 trial types, 6 movement directions in
combination with 2 durations of the preparatory period.
Reaction time was defined as the delay between the
362
electrodes, outer diameter 80 lm, impedance: 2–5 MX
at 1000 Hz). The electrodes were arranged in a circle,
one electrode in the middle and six around it, equally
spaced 330 lm apart. From each electrode, electrical
signals were amplified and band-pass filtered from
300 Hz to 10 kHz. Using a window discriminator,
spikes from only one single neuron per electrode were
then isolated. Neuronal data along with behavioral
events (e.g., occurrences of signals and performance of
the animal) were stored on a PC for offline analysis with
a time resolution of 1 kHz.
Electromyographic (EMG) activity was recorded
from nine selected muscles of the active arm and
shoulder as well as the trunk during representative
sessions by using surface electrodes on the skin. Prior
to recordings hairs on the skin were carefully removed
to provide electrical contact. The muscles were the
deltoidius, trapezius, triceps, biceps, carpi radialis,
carpi ulnaris, policis longus, bracchio radialis, and
pectoralis.
A
–500
ST
B
0
600
PS
RS1 or ES
1200 ms
RS2
reaction time (ms)
150
140
130
120
110
4
5
6
1
directions
2
C
3
D
5
6
5
6
2.3 Data analysis
4
1
3
2
4
1
3
2
Fig. 1. Experimental design of the task. a Schematic representation of
a trial. For details see Sect. 2.1. ST: start trial; PS: preparatory signal;
ES: expected (response) signal; RS: response signal, RS1 after a short
trial and RS2 after a long one. b Mean reaction times (ms standard
errors, solid curve) as a function of movement direction in long delay
trials. The cosine fit (dash-dotted) revealed a systematic, statistically
significant tuning to movement direction (r ¼ 0:79, p < 0:05). The
behavioral preferred direction (PD), corresponding to the shortest
reaction time determined by the cosine fit, was between target 6 and 7
(PD ¼ 6:7). Directional modulation index I ¼ 0:11. c and d Distributions of preferred directions of the significantly tuned neurons in
the selected data set (24/33 neurons, c) and the entire population (301/
396 neurons, d)
occurrence of the response signal and the release of the
central target.
2.2 Surgical procedures and recording technique
After training, the animal was prepared for multiple
single-neuron recordings. A cylindrical stainless steel
recording chamber (inner diameter: 15 mm) was implanted over the contralateral (right) primary motor
cortex under aseptic conditions and general halothane
anesthesia (< 2:5% in air). A stainless steel T-bar was
cemented to the skull to fixate the animal’s head during
recording sessions. Before and after surgery antibiotics
and analgesics were administered. In order to record
extracellular single-neuron activity, a multielectrode
microdrive (Reitböck system, Thomas Recording, Giessen, Germany; Mountcastle et al. 1991) was used to
transdurally insert independently from each other seven
microelectrodes (quartz-insulated platinum-tungsten
2.3.1 Unitary event analysis. Dynamic changes in the
temporal relations between the occurrences of spikes in
sets of simultaneously recorded pairs of neurons were
analyzed offline on a UNIX workstation with Matlab
(The MathWorks, Inc.) by using an extension of the
unitary event method (Grün 1996), the multiple shift
method (Grün et al. 1999). It treats the data in their
(original) high time resolution (1 ms). Such a procedure
allows one to search for coincidences with various
coincidence widths. Technically, coincident spikes are
detected in pairs of neurons by shifting the spike trains
against each other over the range of allowed coincidence
widths (ranging from 1 to 20 ms) and integrating the
number of exact coincidences (on the time resolution of
the data) over all shifts. In order to evaluate the
significance of the detected coincidences (measured
coincidences), the outcomes are compared to the expectation. Under the null-hypothesis that neurons fire
independently from each other, the expected number
of occurrences (expected coincidences) and its probability distribution can be estimated on the basis of the
single-neuron firing probability. Expectation is calculated as the product of the marginal probability of firing
and then summed for all possible shifts. The statistical
significance of a positive or negative difference between
measured and expected coincidences can be assessed
from a Poisson distribution (with the mean set to the
expected coincidence value) as the cumulative probability P of observing a larger or smaller number of
coincidences than expected by chance (Fig. 2 in Grün
et al. 2002a). The larger the number of excessive
coincidences, the closer P is to 0. Conversely, the larger
the number of lacking coincidences, the closer its
complement, 1 P , is to 0, while P approaches 1. Those
occurrences of coincident spikes that exceed the significance level of 5% were called unitary events. For a
better visualization (Fig. 3c), we use a logarithmic
363
events at each instant in time along the trials over the
various pairs of neurons and movement directions
(Riehle et al. 2000; Grammont 2001). Technically, for
each pair of neurons we constructed each movement
direction and each coincidence width (from 1 to 20 ms) a
binary vector that indicates by ‘‘1’’ a significant sliding
window of unitary events and by ‘‘0’’ a nonsignificant
one. In Fig. 3d, an example of such a binary vector is
provided for one pair of neurons during movement
direction 6 by selecting a coincidence width of 2 ms. By
averaging all binary vectors determined for a given
coincidence width and behavioral condition, we calculated the probability of significant synchronization as a
function of time and coincidence width. For brevity, in
what follows we call this measure synchronicity.
2.3.3 Directional selectivity. In order to test directional
selectivity, mean data of synchronicity, firing rate, and
behavioral reaction times were fitted to a model by using
an adapted method originally proposed by Georgopoulos et al. (1982). A first-degree periodic (sinusoidal)
regression to be fitted is
Fig. 2. Electromyographic (EMG) activity was recorded from nine
muscles of arm, shoulder, and trunk of the active side during
representative sessions with surface electrodes on the skin. The
muscles were the 1: deltoidius, 2: trapezius, 3: triceps, 4: biceps, 5:
carpi radialis, 6: carpi ulnaris, 7: policis longus, 8: bracchio radialis,
and 9: pectoralis. PS: preparatory signal, ES: expected (response)
signal, RS: (actual) response signal, Mvt: movement onset. The inset
shows the spatial configuration and numbering of the targets
(movement directions). Movements were to be started from the
center circle
function of the two: log10 ½ð1 P ÞP (surprise measure,
Palm et al. 1988).
To deal with nonstationarities through time in the
firing rate of the neurons, temporal relations among
spikes were analyzed in time segments by using a sliding
boxcar window of 100 ms, which was shifted in steps of
5 ms along the data. This sliding window procedure was
applied to each trial and the data of corresponding
segments in all trials were then analyzed as one stationary data set.
Only neurons were selected for analysis that reached
the following criteria: (1) a lowest firing rate of more
than seven impulses/second (Roy et al. 2000), (2) stationarity of rate changes across trials (Grün et al. 2002b;
this issue), (3) a minimum of about 20 trials per condition, and (4) of course at least two neurons had to fulfill
these criteria in the same recording session in order to
constitute a pair. All these criteria were applied to each
movement direction. As a consequence, for one single
pair of neurons not all movement directions were necessarily selected for further analysis so that the sample
size is smaller than the number of selected pairs times the
number of movement directions.
2.3.2 Quantification of synchronized spiking activity. In
order to quantify synchronous activity at the population
level, we calculated the probability of observing unitary
y ¼ b0 þ b1 sin h þ b2 cos h
ð1Þ
where b0 , b1 and b2 are regression coefficients. The least
square unbiased estimators of these coefficients for six
movement directions are
b0 ¼ ðy1 þ y2 þ y3 þ y4 þ y5 þ y6 Þ=6
ð2Þ
where y1 . . . y6 are the mean data for each of the six
movement directions.
b1 ¼
1 pffiffiffi
3ðy2 y3 þ y5 þ y6 Þ
2
1
1
1
1
1
y1 þ y2 y3 y4 y5 þ y6
b2 ¼
3
2
2
2
2
ð3Þ
ð4Þ
Statistical significance of the tuning is determined by
calculating a linear correlation coefficient r between the
empirical data and the cosine fit. The preferred direction, PD, is calculated using the circular mean of the
fitted sine wave and expressed in fractions of target
numbers. Finally, a directional modulation index, I, is
determined by calculating a proportional increase of the
studied data sample at the preferred direction over its
overall mean b0 (Georgopoulos et al. 1982)
b0
I ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
b21 þ b22
ð5Þ
3 Results
3.1 Behavioral results and EMG data
Mean reaction times were calculated for each of the 12
trial types on the basis of correct trials in all recording
sessions. The sample size (n ¼ 118, see below) for each
364
coinc/sec
B
spikes/sec
Spike Rates, neuron 1 (solid), neuron 4 (dashed)
A
50
0
Coincidence Rates: measured (solid), expected (dashed)
20
10
C
J–surprise
0
Significance Level
2
0
–2
Binary Vector (zero
one)
D
sig (1)
n–sig (0)
PS
300
ES
900
RS
yo049–14– 6
Fig. 3. Dynamic changes in synchronous spiking activity of a pair of
neurons during the execution of one type of trials (long preparatory
period, direction 6). For calculation, a sliding boxcar window of
100 ms was shifted along the spike trains in 5-ms steps. The allowed
coincidence width was 2 ms. Since data were aligned trial by trial to
movement onset (vertical line in all plots), the occurences of the signals
(gray bars) were plotted with respect to the mean reaction time, the
width of the bars corresponding to its standard deviation
(RT ¼ 89 47 ms). PS: preparatory signal, ES: expected (response)
signal, RS: response signal. Time is running along the x-axis and
indicated in milliseconds. a Firing rate of the two neurons in spikes/
second. b Measured (solid) and expected (dashed) coincidence rates are
shown in coincidences/second. c For each sliding window the statistical
significance (joint-surprise value) was calculated for the difference
between measured and expected coincidence rates. The result of each
window was placed in its center. Whenever the significance value
exceeded the threshold (upper dashed line, p ¼ 0:05), this defined an
epoch in which significantly more coincidences occurred than expected
by chance. Occasionally, this value dropped below the lower dashed
line, thus indicating epochs in which significantly (p < 0:05) fewer
coincidences occurred than expected by chance. d A binary vector is
plotted on which ‘‘1’’ indicates a significant sliding window of unitary
events and ‘‘0’’ a nonsignificant one. The ‘‘1’’ and ‘‘0’’ entries were
plotted in the center of each corresponding sliding window of 100 ms.
The binary vectors were subsequently used for the quantification
analysis presented in Fig. 4. Synchronous activity was at chance level
during the first 600 ms of the preparatory period and then started to
increase. It modulated for the remaining period with increasing
amplitude to reach a maximum just before the presentation of the
response signal. During movement onset neuronal activity was
considered to be antisynchronized, i.e., there were significantly fewer
coincidences than expected
delay duration corresponds to the number of selected
pairs times the number of movement directions after
removal of individual data sets that did not reach the
criteria defined in Sect. 2.3.1. Since two different durations of the preparatory period were presented at
random with equal probability, the response signal
could occur either 600 or 1200 ms after the preparatory
signal. Mean reaction times in relation to the duration of
the preparatory period are shown in Table 1. Reaction
times were significantly shorter when they were produced after a long preparatory period [RT(2)], i.e., when
the probability for the response signal to occur was 1,
than after a short one [RT(1)], i.e., when the probability
of signal occurrence was 0.5. The difference of 130 ms
between short and long trial reaction times over all
movement directions is highly statistically significant
(t-test of Student: t ¼ 31:59, df ¼ 234, p 0:0001). The
same is true for the difference in reaction time between
right-sided and left-sided movements after long delays
(t ¼ 2:82, df ¼ 116, p < 0:01) and short delays (t ¼ 7,
df ¼ 116, p << 0:001). Individual reaction times during
each movement direction and delay duration are indicated in Table 1. In Fig. 1c, a cosine function was fitted
(dash-dotted line) to the reaction time data for each
movement direction in long delay trials, revealing
statistical significance of the fit (r ¼ 0:79, p < 0:05).
Furthermore, the cosine fit allows one to determine the
behavioral preferred direction, i.e., the movement direction in which reaction time was shortest (PD ¼ 6:7).
However, although reaction times were significantly
tuned to movement direction, the directional selectivity
index was rather low (I ¼ 0:11).
We recorded electromyographic (EMG) activity from
task-related muscles of the active arm and shoulder.
Figure 2 shows a typical example of the activity of nine
muscles during long trial performance in each movement
365
Table 1. Mean reaction times (RT ) and standard deviations (SD),
in milliseconds, were calculated for each movement direction and
each duration of the preparatory period (PP ) from the means in
each recording session per neuron pair
Direction
Short PP RT(1)
Long PP RT(2)
All directions
Right movements
(directions 6-1-2)
Left movements
(directions 3-4-5)
Direction 1
Direction 2
Direction 3
Direction 4
Direction 5
Direction 6
254 ± 29
238 ± 19
124 ± 36
115 ± 27
269 ± 29
132 ± 41
241
238
271
284
252
236
111
113
145
131
121
121
±
±
±
±
±
±
22
18
26
29
24
18
±
±
±
±
±
±
23
23
41
44
36
35
direction. It can clearly be seen that during the preparatory period, and particularly at the moment when a
response signal was expected (ES), no overt change in
activity could be detected in any muscle.
3.2 Neuronal results
3.2.1 Data set. Among 396 neurons recorded in the
primary motor cortex, only 33 were selected from 14
recording sessions by severely applying the criteria
described in Sect. 2.3.1 for constituting 22 pairs. A
single neuron could participate in several pairs. The
main reason for the small number of selected neurons is
that most of the neurons phasically changed their
activity in relation to signal occurrence and/or signal
expectancy, while returning to almost zero spikes/second
between bursts, thereby making the unitary event
analysis impossible (see Sect. 2.3.1). Furthermore, all
selected neurons changed their activity in close temporal
relationship to movement performance. In order to
preserve stationarity across trials, spiking activities were
therefore aligned, trial-by-trial, to movement onset
(Fig. 8 in Grün et al. 2002b). To qualify the discharge
patterns of the neurons, their spiking activities were
tested for directional selectivity by fitting a cosine to the
mean firing rates determined during movement execution, defined as the period between the occurrence of the
response signal and touching the requested target. In 24
neurons (73%), directional selectivity was statistically
significant (p < 0:05). The distribution of preferred
directions of these neurons is shown in Fig 1c. The
difference, however, between preferred directions of
directionally selective neurons within a pair extended
over the whole possible range of movement directions
from 6 to 168 . By comparison, directional selectivity
was statistically significant during movement execution
in 76% of the neurons of the entire population (301/
396). The distribution of the preferred directions of the
significantly tuned neurons of the whole population is
represented in Fig. 1d. Both distributions proved to be
homogeneously distributed over the whole range of
movement directions by calculating the circular variance
(selected sample: S24 ¼ 0:93, whole population: S301 ¼
0:97, Mardia 1972).
For each pair of neurons and in each behavioral
condition, significant synchronous spiking activities
were calculated individually for each coincidence width
between 1 and 20 ms, as described in Sect. 2.3.2. Only
data obtained during the long preparatory period were
taken into account for the analysis at the population
level, because there is no a priori difference between the
short preparatory period and the first half of the long
one; during this part of the trial the animal did not know
whether or not a response signal would occur at 600 ms.
Figure 3 shows a typical example of the distinct modulation of synchronous activity during the trial.
3.2.2 Modulation of synchronicity as a function of time
and coincidence width at the population level. In order to
test whether statistically significant synchronous activity
during particular epochs of the trial was reproducible
over the entire population of neurons, we quantified
individual data (see Sect. 2.3.2). The probability for
obtaining significant synchronization calculated among
all pairs of neurons and all movement directions, thus
obtaining a sample size of n=118, is shown in Fig. 4a.
Probability was calculated as a function of both time
and coincidence width. If neuronal synchronization
plays a role in information processing, it should
modulate systematically through time and coincidence
widths rather than being homogeneous. Indeed, distinct
increases in synchronicity could be observed at three
specific epochs of the task: (1) around the preparatory
signal, (2) precisely after the moment when the response
signal was first expected but did not occur, and (3) about
300 ms before the actual occurrence of the response
signal. By comparing the first with the second half of the
preparatory period, synchronicity appeared to be much
higher during the second than the first half, i.e., when
the probability for the response signal to occur passed
from 0.5 to 1. However, synchronicity dropped down to
almost zero during movement execution. Remember
that the higher synchronicity, i.e., the higher the
probability of being significantly synchronized, the more
pairs of neurons synchronized significantly their activity.
Note that the precision of synchronous activity, i.e., the
range of coincidence widths, also varied over time.
3.2.3 Modulation of firing rate at the population level.
The mean firing rate was calculated for the same
population of neurons and averaged over all movement
directions (Fig. 4b). There was a slight tonic increase in
activity during the first part of the preparatory period
followed by two successive phasic modulations during
its second part. Indeed, activity peaked first about
150 ms after the first response signal was expected but
did not occur, reaching a first maximum of about 27
spikes/second. Firing rate then peaked a second time at
movement onset and reached its absolute maximum of
44 spikes/second, showing the typical motor activity for
primary motor cortical neurons.
Interestingly, when synchronicity was highest
(Fig. 4a), about 300 ms before the occurrence of the
366
coincidence width (ms)
A
Probability of Significant Synchronization
20
15
10
5
0
0
300
0.04
spikes / s
B
0.06
600
900
Probability (max=0.19)
0.08
0.1
0.12
1200
0.14
MVT
0.16
0.18
Mean Firing Rate
45
35
25
15
PS
300
ES
900
response signal, firing rate was low (Fig. 4b), and, conversely, when the discharge was highest at movement
onset, synchronicity was lowest. In fact, the increase of
synchronicity tended to precede the increase in firing
rate, although not in a systematic temporal relationship.
3.2.4 Comparison between synchronicity and mean firing
rate as a function of movement direction. In Fig. 5, the
same data as in Fig. 4a are presented separately for each
movement direction. It is clear that the modulation of
the probability of significant synchronization was not
homogeneously distributed over movement directions.
For instance, during the second part of the preparatory
period the probability of significant synchronization was
highest for direction 6 but very low for the opposite
direction 3. Synchronicity varied between these two
extremes in an apparent systematic manner. In fact, a
further analysis realized during the second part of the
preparatory period demonstrates that these variabilities
observed in terms of both synchronicity and firing rate
RS
MVT
Fig. 4. Quantification of correlated activity of all pairs of
selected neurons pooled over all
six movement directions
(n ¼ 118). a For each pair of
neurons and each movement
direction a matrix was calculated
containing entries of 0s and 1s
(binary vectors, Fig. 3d) based
on the statistical significance for
spike synchronization (parameters: sliding window of 100 ms,
shift offset 5 ms, coincidence
widths ranging from 1 to 20 ms).
All obtained matrices were then
pooled to calculate the probability matrix. It contains per
entry position the probability for
being significantly synchronized
across behavioral conditions
(from dark blue to dark red
probabilities ranging from 0.02
to 0.19, see color bar). b The
averaged mean firing rate from
the same neuronal population
(also calculated within sliding
windows of 100 ms width, which
were shifted in 5-ms steps along
the trial). PS: preparatory signal,
ES: expected (response) signal,
RS: (actual) response signal,
MVT: movement onset. Since all
data are aligned, trial by trial, to
movement onset, signal occurrences varied from trial to trial
as a function of reaction time.
The width of the gray bars
indicating the signals corresponds to the standard deviation
of reaction times
followed a systematic law (Fig. 6). We calculated the
tuning curves of the two types of neuronal activity at
two distinct moments, corresponding, first, to the peak
of mean synchronicity (dotted line at 300 ms before the
response signal) and, second, to the peak of the mean
firing rate (dash-dotted line shortly after movement
onset). Both the probabilities of significant synchronization and the mean firing rates were tuned, but at two
different moments. Indeed, synchronicity was significantly tuned during the preparatory period (Fig. 6c;
cosine fit: r ¼ 0:92, p < 0:01), whereas firing rate showed
no tuning at the same moment (Fig. 6e). In contrast,
firing rate was significantly tuned in relation to movement onset (Fig. 6f; cosine fit: r ¼ 0:93, p < 0:01),
whereas synchronicity was very low and did not
modulate with movement direction at this time
(Fig. 6d). In both cases, when synchronicity and firing
rate were significantly tuned, the preferred direction
(PD) was roughly the same, i.e., less than a target
distance apart, that is, 6.8 for synchronicity long before
367
Direction 5 (max=0.3)
Direction 6 (max=0.37)
20
20
15
15
10
10
5
5
0
0
coincidence width (ms)
Direction 4 (max=0.23)
Direction 1 (max=0.32)
20
20
15
15
10
10
5
5
0
0
Direction 3 (max=0.24)
Direction 2 (max=0.3)
20
20
15
15
10
10
5
5
0
PS
0
ES
0.1
RS MVT
0.2
0.3
0
0
300
0
600
0.1
900
0.2
1200ms
0.3
Probability of Significant Synchronization
Fig. 5. Probability of significant synchronization for each movement
direction during long delay trials. The same type of analysis as in
Fig. 4a was applied to the same population data for each movement
direction separately. The location of each matrix in the figure
corresponds to the location of the respective targets (Fig. 2, inset).
Note, however, that the probability for being significantly synchronized was much higher (color bar ranging from 0 to 0.3 is valuable for
all six matrices) in individual data, reaching a maximal probability of
0.37 (direction 6). For the analysis, all data were aligned, trial by trial,
to movement onset (MVT, black vertical lines). The red vertical lines
correspond to the preparatory signal (PS), the expected (response)
signal (ES), and the actual response signal (RS). Since for each
movement direction mean reaction times were different (Table 1),
signal occurrences are indicated accordingly
movement onset (Fig. 6c) and 6 for the firing rate during
movement onset (Fig. 6f). As an individual example and
for compatibility with Fig. 7, the synchronicity tuning
was also calculated for a single coincidence width of
6 ms. This analysis revealed virtually the same results as
above, namely, a significant tuning during the
preparatory period (PD ¼ 6:9, r ¼ 0:95, p < 0:001,
I ¼ 1:1) and no tuning during movement onset
(r ¼ 0:67).
By fitting any function to the data, only the mean
values determined for each movement direction are
tested for their statistical significance in relation to the
368
Probability of Significant Synchronization
A
probability
0.3
0.2
0.1
0
Mean Firing Rate per Movement Direction
B
50
Dir 6
Dir 1
Dir 2
Dir 3
Dir 4
Dir 5
spikes / s
40
30
20
10
ES
–450
–300
During Preparatory Period
C
0.1
MVT
0.3
probability
0.2
RS
During Movement Onset
D
0.3
probability
–150
r=0.49 non–sel
0.2
0.1
PD=6.8 r=0.93 p<0.01) I=0.69
0
E
4
5
6
1
2
F
30
r=0.65
non–sel
25
20
5
6
1
directions
2
3
5
6
1
2
3
45
40
4
4
50
spikes / s
spikes / s
0
3
PD=6 r=0.93
4
chosen model as, for instance, a cosine function. However, this does not indicate whether or not data samples,
which are at the origin of the means, are significantly
different from each other. In the next analysis we
therefore tested if there was a statistically significant
difference between neuronal activities during right-sided
and left-sided movements (Fig. 7). In order to apply a
v2 -test to the individual data from all neuron pairs, we
have chosen for testing the difference in synchronicity a
typical coincidence width of 6 ms (Fig. 4a and the individual calculation performed for the data presented in
Fig. 6). In each sliding window of 100 ms, the proportions of ‘‘1’’ entries with respect to the sample size,
corresponding to the number of significant data sets at
5
p<0.01 I=0.11
6
1
directions
2
3
Fig. 6. Comparison between
synchronicity and firing rate in
the same population of neurons
as in Figs. 4 and 5 during the
second part of long delay trials.
a Probability of significant synchronization, averaged over all
coincidence widths, for each
movement direction separately.
b Mean firing rate for the same
data as in a. ES: expected (response) signal, RS: (actual) response signal, MVT: movement
onset. Since all data were
aligned, trial by trial, to movement onset, signal occurrences
varied from trial to trial as a
function of reaction time. The
width of the gray bars indicating
the signals corresponds to the
standard deviation of reaction
times. c–f Tuning curves (solid)
as a function of movement direction and the corresponding
cosine fits (dash-dotted) are
shown. The tuning was calculated from the mean values of
the probability of significant
synchronization (c and d) and
the corresponding firing rate (e
and f) at two distinct moments
during the trial indicated by the
two vertical lines in a and b.
Tuning curves at the moment
indicated by the dashed lines are
shown in c and e, whereas those
indicated by the dash-dotted lines
are shown in d and f. In each
subfigure, the correlation coefficient r of the linear regression
between the tuning curve and the
cosine fit and its statistical significance is indicated. Furthermore, in subfigures in which the
tuning is statistically significant
(c and f), the preferred direction
(PD) is indicated in fractions of
target numbers as well as the
directional modulation index I
this epoch (Sect. 2.3.2), were compared for right-sided
and left-sided movements, and their statistical significances were calculated. Only the data inside the marked
boxes were significantly different (p < 0:05), two adjacent windows at about the moment when a response
signal was expected, but did not occur, and ten adjacent
windows at about 300 ms before its actual occurrence.
In other words, within the entire population significantly
more neurons synchronized significantly their activity
during preparation for right-sided movements than
during preparation for left-sided movements (Fig. 7a).
In Fig. 7b, the mean firing rates were compared for
the same right-sided and left-sided movements by applying, sliding window by sliding window, a t-test of
369
Probability of Significant Synchronization
A
Right movements
Left movments
probability
0.25
0.2
0.15
0.1
0.05
0
300
600
900
1200ms
Mean Firing Rate
B
spikes / s
40
30
20
PS
300
ES
900
RS MVT
Fig. 7. Comparison between synchronicity and firing rate in the same
population of neurons as in Figs. 4 to 6 during the long delay trials in
relation to right-sided (solid, n ¼ 58) and left-sided (dash-dotted,
n ¼ 60) movements. a Probability of significant synchronization at a
coincidence width of 6 ms. The difference in synchronicity between
right-sided and left-sided movements was statistically significant inside
the two boxes, i.e., when the response signal was expected and about
300 ms before its actual occurrence (chi square-test, v2 ranging
between 5.05 and 11.25, df ¼ 1, p 0:05). b Mean firing rate in the
same conditions as in a. The application of a t-test of Student for
comparing individual data during right-sided and left-sided movements in each sliding window did not reveal any statistical significance
Student to the samples of mean activities of all individual data sets. Although the mean firing rate was
higher during preparation and execution of right-sided
movements than left-sided movements, no statistical
significance could be detected so far.
4 Discussion
4.1 Time course of synchrony and firing rate
In this paper, we compare the time course of the
modulation of precise spike synchronization with that of
the mean firing rate in a population of motor cortical
neurons in the behaving monkey during the performance
of delayed multidirectional pointing movements. In
general, significant synchronous activity reveals, at the
population level, a clear structure (Fig. 4a). This suggests that motor cortical neurons systematically synchronized their activity in relation to relevant task
events. Interestingly, the temporal pattern of synchronous activity is by no means predictable by inspecting
the mean firing rate of the same neuronal population.
The task was designed such that the animal could
anticipate signal occurrences, including preparatory and
response signals. As a matter of fact, a first peak in
synchronicity preceded the occurrence of the preparatory signal, although with low temporal precision. A
second one followed precisely at the moment when the
first possible response signal was expected, but did not
occur, preceding the first peak in firing rate. Finally,
synchronicity reached a maximum at the end of the instructed delay, about 300 ms before the occurrence of
the actual response signal, whereas the mean firing rate
did so much later, at movement onset, an epoch where
synchronous activity was almost absent.
Although the task was temporally organized in periods of 600 ms, the dynamics of synchronicity did not
follow a rhythmic temporal structure. Indeed, an increase in synchronous activity sometimes preceded a
task event, sometimes followed it, depending on the
underlying cognitive processes. Furthermore, the temporal precision of synchronous activity varied systematically during the task, from very low precision around
the preparatory signal to highest temporal precision (2
to 3 ms) at the end of the preparatory period. Note that
in individual pairs of neurons the precision of synchrony
may reach values of 1 ms (Riehle et al. 2000; 2 ms in
Fig. 3).
Such a timing suggests that synchronous neuronal
activity in motor cortex may be preferentially involved
in early preparatory and motor cognitive processes, including signal expectancy (cf Riehle et al 1997), whereas
the modulation in firing rate may control rather movement initiation and execution. In particular, the fact that
during movement onset firing rate was highest and
synchrony almost absent indicates that processes underlying movement initiation relate almost exclusively to
changes in firing rate. An additional argument in favor
of this hypothesis is the fact that EMG activity (Fig. 2)
did not reveal any modulation during the preparatory
period, indicating that neuronal activity was not involved in executive processes at this moment, i.e., cortical preparatory processes did not reach periphery.
Furthermore, by comparing the time courses of synchronicity and mean firing rate in an entire population
of neurons, it appeared that there was no simple parallel
shifting in time of these two measures, as already described for individual pairs of neurons (Riehle et al.
2000). This makes it unlikely that the two coding
schemes are tightly coupled by any kind of stereotyped
transformation; they seem to obey rather different dynamics. There is, however, a clear tendency for synchrony to precede firing rate, suggesting that the
coherent activation of cell assemblies may trigger the
increase in firing rate in large groups of neurons.
4.2 Movement initiation
In contrast to the data described by Hatsopoulos et al.
(1998), we detected virtually no significant synchronization during movement onset, although firing rate was
highest. This is true for both long (Fig. 4a) and short
trials (not shown). The increase in firing rate in relation
to movement onset suggests that the type of neurons in
both studies was similar and rather movement related.
In our data, however, peak synchrony occurred in long
trials long before movement onset, about 300 ms before
presentation of the response signal. This difference may
be due to the experimental design. Hatsopoulos and
colleagues (1998) employed a random 1-s to 1.5-s
370
instructed delay, whereas in our task the temporal
constraints were precisely defined by presenting only two
fixed durations at random. This means that the monkey
could estimate the time of signal occurrences, although
with different probabilities. During the second part of
the preparatory period, the probability for the response
signal to occur at a precise moment was 1. The first peak
in synchronicity appeared right after the moment when
the first response signal was expected but did not occur.
This increase in the number of neurons synchronizing
their activity is thus related to a purely internal –
cognitive – event, the moment when the animal realized
that the expected signal did not occur. The second and
highest peak of synchronicity, which was also internally
triggered, occurred about 300 ms before the actual
response signal. In both tasks, directional information
could already be processed during the waiting period,
inciting the animal to prepare the movement in advance.
However, movement initiation could be anticipated
precisely in our task but not in that of Hatsopoulos
et al. (1998). The fact that reaction time was significantly
longer after a short delay – a situation in which the
probability for the occurrence of the response signal
and, thus, the probability to execute the requested
movement was much lower (p ¼ 0:5) than after a long
delay (p ¼ 1) – suggests that the monkey indeed
prepared the movement in advance. In the context of
the preparation paradigm, the preparatory coherent
activation of cell assemblies, by way of synchrony, might
trigger the increase in firing rate in large neuronal
networks, which in turn communicate with the periphery
for initiating the movement.
4.3 Movement direction
We first analyzed the discharge patterns of individual
neurons during each movement direction. The percentage of significant directional selectivity, defined by fitting
a cosine function (73% of the selected data sample and
76% of the entire data set), corresponds to data
described in the literature (e.g., Georgopoulos et al.
1982; Hatsopoulos et al. 1998). Although in the majority
of pairs (14/22, 64%) the activities of both neurons were
significantly tuned during movement execution, there
was no systematic relationship between preferred directions of the two neurons forming the pair. Such an
example was already shown by Grammont and Riehle
(1999) for three simultaneously recorded neurons in a
similar task during which the duration of the preparatory period was kept constant. Even though the firing
rates of all three neurons were differently tuned to
movement direction (see inset in Fig. 2 of Grammont
and Riehle 1999), they synchronized significantly their
activity in each possible combination of two or even
three neurons during short periods of the task. However,
no systematic relationship could be detected in relation
to movement direction. Hatsopoulos et al. (1998) described in a similar way, by calculating crosscorrelation
functions for individual pairs of motor cortical neurons,
that synchronous activity did indeed convey directional
information, mostly during movement onset. The authors classified, however, a pair of neurons as directionally tuned if synchrony was statistically significant in at
least one direction. No systematic relation to movement
direction was required as, for instance, determining the
preferred direction by fitting a cosine function to the
degree of synchronous activity in each movement
direction, as directional tuning is most often defined
for firing rate (Georgopoulos et al. 1982). In the same
way as in Hatsopoulos et al. (1998), no relationship
could be detected in our data between the preferred
direction determined for the firing rate of each of the
neurons in a pair and the highest amount of synchrony,
although all pairs of neurons did significantly synchronize their activity during at least one movement
direction, most often during more than one.
Here we show for the first time, at the population
level, a clear systematic relationship between synchronicity and movement direction. Our time-resolved
analysis technique revealed directionally tuned synchronicity only during movement preparation at a distinct moment in time toward the end of the preparatory
period. The cosine fit of the amount of synchronous
activity was statistically significant (Fig. 6c), its directional selectivity index revealed a strong modulation
(I ¼ 0:71) and the means of the probabilities for being
significantly synchronized for right-sided and left-sided
movements were significantly different (Fig. 7a). Although the mean firing rate of the same population of
neurons was also significantly tuned to movement direction about 400 ms later (Fig. 6f), during movement
onset, its directional selectivity index was rather low
(I ¼ 0:11), and the means of individual firing rates
during right-sided and left-sided movements were never
significantly different during the whole task (Fig. 7b).
Interestingly, however, preferred directions of both
synchronicity and mean firing rate appeared to be at
almost the same movement direction (6.8 vs. 6, Figs. 6c
vs. 6f).
Recently, Oram et al. (2001) argued that synchronous
spikes do not provide more directional information than
firing rates. They recorded motor cortical activity during
the same task as that presented by Hatsopoulos et al.
(1998) but used different analytical procedures. The
main differences between Oram et al. (2001) and the
present report is that, first, we utilized time-resolved
statistics in order to determine and compare the dynamics of both synchrony and firing rate, and, second,
our calculations are based on an entire population of
neurons and not on individual pairs. The significant
directional selectivity of synchrony in our data is based
on the number of neurons that significantly synchronized their activity during a given movement direction at
a distinct moment in time. We have shown, at the
population level, not only that both measures – the
mean firing rate and synchronicity – modulated significantly with movement direction, but particularly that
modulation strength varied in time and peak values
occurred at different epochs during the trial, synchrony
largely preceding firing rate. Furthermore, the modulation of both types of activity occurred systematically
371
within an entire population of neurons. Finally, directional modulation appeared to be, at the population
level, much larger for synchrony than for firing rate.
4.4 Reaction time
Behavioral data revealed that reaction time varied with
movement direction in a systematic way, that is, mean
reaction times obtained in each movement direction
fitted significantly a cosine function (Fig. 1b). The
animal’s behavioral preferred direction was close to the
most right-sided target, target 1 (PD ¼ 6:7, Fig. 1b).
This corresponded almost perfectly to the preferred
direction of synchrony at about 300 ms before the
occurrence of the response signal (PD ¼ 6:8, Fig. 6c).
The question arises whether synchronous neuronal
activity is involved in processing the direction of the
movement or rather in speeding up its initiation. There is
much evidence from the literature that the increase of
motor cortical activity during the preparatory period is
strongly involved in the reduction of reaction time. It
has been shown that not only global EEG activity
recorded over human motor cortical areas at the end of
a preparatory period (Coles 1989) but also the firing rate
of single motor cortical neurons (Kubota and Hamada
1979; Lecas et al. 1986; Riehle and Requin 1989, 1993)
were significantly correlated with reaction time. However, as far as we know a correlation between synchronous spiking activity and reaction time has never been
described in the literature.
In this context, two hypotheses must be discussed:
does the increase of synchronicity at the population level
represent movement direction per se or does it reflect the
behavioral preference of the animal expressed by reaction times? If synchronous spiking activity were involved
only in processing movement direction, similar changes
in synchronicity in relation to the different movement
directions should be observed as in Fig. 5, even when the
same reaction times were produced in each of them. In
view of the fact that systematically in each behavioral
session reaction time varied in relation to movement
direction, this hypothesis could not be tested reliably in
our data.
On the contrary, synchronous activity may increase
during trials in specific directions only because of inducing short reaction times and not because of its involvement in processing movement direction. If this
hypothesis were true, we should be able to observe
similar differences in synchrony in relation to reaction
times by dividing each data set (i.e., for each pair of
neurons and each selected movement direction) into two
equal subsamples of short and long reaction time trials.
Unfortunately, the limited number of trials within each
data set did not allow for the application of correct
statistics for calculating significant synchronization in
such subdivisions (see Sect. 2).
One argument, however, in favor of the reaction-time
hypothesis is that the probability of significant synchronization undeniably depended on reaction time
when data were averaged over all movement directions
(Fig. 4a) and thus no longer depended on individual
movement directions. Indeed, synchronous activity was
much lower during the first half of the preparatory period than during the second half. Recall that reaction
times after short trials were much longer than after long
ones, the highly significant difference of 130 ms (Table 1) being explained by the probability of signal occurrence (p ¼ 0:5 vs. p ¼ 1).
The fact that synchronicity, firing rate, and reaction
times were tuned to roughly the same movement direction is far from being trivial. First, the directional selectivity of the population firing rate cannot be explained
by a directional bias due to the small sample size because
the distribution of preferred directions of the selected
neurons appeared to be statistically homogeneous
(Fig. 1c). Furthermore, it is important to note that the
population tuning was calculated by determining the
mean activity of all neurons in each time step and each
movement direction, irrespective of the preferred directions of the neurons. Since we did not normalize neuronal activity, neurons exhibiting a higher mean firing
rate contribute more than neurons with low firing rates.
Second, our data and those of others (Hatsopoulos et al.
1998; Grammont and Riehle 1999) did not show any
systematic relationship between the directional tuning of
the firing rate and significant synchronization. These
results lead us to speculate that synchronous activity and
firing rate are cooperative neuronal processes and that
the directional matching of our three measures – firing
rate, synchronicity, and reaction times – might be an
effect of behaviorally induced network cooperativity
acquired during learning. In other words, the monkey
developed during training its behavioral right-sided
preference, which shaped the dynamical interplay in a
large group of neurons without changing their individual
tuning properties.
Acknowledgements. We wish to thank Sonja Grün, Markus
Diesmann, and Bill MacKay for many helpful and exciting discussions and one anonymous referee for her/his helpful comments. Special thanks go to Annette Bastian for her help in data
collection, Michèle Coulmance for writing data acquisition and
parts of data analysis software, and Marc Martin for animal
welfare. This research was supported in part by the CNRS, GIS
(Sciences de la Cognition), and ACI Cognitique (Invariants and
Variability). FG was supported by the French government
(MENRT).
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