Journal of Neuroscience Methods 105 (2001) 15 – 24
www.elsevier.com/locate/jneumeth
A pattern grouping algorithm for analysis of spatiotemporal
patterns in neuronal spike trains. 2. Application to simultaneous
single unit recordings
Igor V. Tetko a,b, Alessandro E.P. Villa a,*
a
Laboratoire de Neuro-heuristique, Institut de Physiologie, Uni6ersité de Lausanne, Rue du Bugnon 7, CH-1005 Lausanne, Switzerland
b
Department of Physiology of Brain, Bogomoletz Institute of Physiology and Department of Biomedical Applications, IBPC,
National Ukrainian Academy of Sciences, Kyi6, Ukraine
Received 14 July 2000; received in revised form 27 September 2000; accepted 29 September 2000
Abstract
This study demonstrates the practical application of the pattern grouping algorithm (PGA), presented in the companion paper
(Tetko IV, Villa AEP. A pattern grouping algorithm for analysis of spatiotemporal patterns in neuronal spike trains. 1. Detection
of repeated patterns. J. Neurosci. Methods 2000; accompanying article), to data sets including up to 30 simultaneously recorded
spike trains. The analysis of a large network of simulated neurons shows that the incidence of patterns cannot be simply related
to an increase in firing rates obtained after Hebbian learning. Patterns that disappeared and reappeared in the thalamus of
anesthetized rats when the cerebral cortex was reversibly inactivated suggest that widespread cell assemblies contribute to the
generation and propagation of precisely timed activity. In an another experiment multiple spike trains were recorded from the
temporal cortex of freely moving rats performing a complex two-choice discrimination task. The presence or absence of particular
patterns in the period preceding the cue was associated with changes in reaction time. In conclusion, neuronal network
interactions may generate spatiotemporal firing patterns detectable by PGA. We provide evidence of such patterned activity
associated with specific animal’s behavior, thus suggesting the existence of complex temporal coding schemes in the higher nervous
centers of the brain. © 2001 Elsevier Science B.V. All rights reserved.
Keywords: Multiple single unit recordings; Temporal firing patterns; Spike train analysis; Neural code; Temporal cortex; Thalamus; Synchronization; Synfire chain
1. Introduction
Early electrophysiological studies led to recognize
that neurons convey a temporal code and that spike
trains were related with meaningful physiological variables (Bullock, 1961; Segundo et al., 1963, 1966; Perkel
and Bullock, 1965; Nafe, 1968). Subsequent work confirmed the presence of precise temporal patterning in
spike train data in different experimental circumstances
and animal species, proposing worthwhile quantification procedures and providing new insights (Perkel et
al., 1967a,b; Segundo and Perkel, 1969; Legendy, 1975;
Eckhorn et al., 1976; Abeles, 1982; Tsukada et al.,
* Corresponding author. Tel.: +41-21-6925534; fax: + 41-216925505.
E-mail address: avilla@lnh.unil.ch (A.E.P. Villa).
1982; Sherry and Klemm, 1984; Rosenberg et al., 1989;
Bialek et al., 1991; Rapp et al., 1994). While these
original studies demonstrated the presence of temporally organized neural activity, the neuronal mechanisms supporting temporal coding remain unclear.
Abeles’ synfire chain theory suggests that generation
and propagation of precise timing of neuronal discharges in the brain may be achieved by means of
feed-forward chains of convergent/divergent links and
re-entry loops between interacting neurons forming an
assembly (Abeles, 1982). In cell assemblies interconnected in this way, some ordered sequences of intervals
will recur within spike trains of individual neurons, and
across spike trains from neurons located at different
places in the network. Such ordered and precise repetitions (in the order of few ms jitter) of interspike interval
relationships are referred to as ‘spatiotemporal pat-
0165-0270/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 5 - 0 2 7 0 ( 0 0 ) 0 0 3 3 7 - X
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I.V. Tetko, A.E.P. Villa / Journal of Neuroscience Methods 105 (2001) 15–24
terns’ of discharges. A fundamental prediction of such
a model is that simultaneous recording of activity of
cells belonging to the same assembly involved repeatedly in the same process should be able to reveal
repeated occurrences of such spatiotemporal firing patterns. This term encompasses both their precision in
time and the fact that they can occur across different
neurons, even recorded from separate electrodes.
Experimental evidence exists that correlated firing
between single neurons recorded simultaneously in the
primate frontal cortex may evolve within tens of milliseconds in systematic relation to behavioral events
without modulation of the firing rates (Vaadia et al.,
1995). Precise firing sequences have been described in
relation to particular temporal relationships to stimuli
(Villa and Abeles, 1990), or movement (Abeles et al.,
1993), or differentially during the delay period of a
delayed response task (Villa and Fuster, 1992; Prut et
al., 1998). Moreover, exact spike synchronization has
been reported in relation to purely internal events
(Riehle et al., 1997). Synfire chains formed by sparsely
connected neural networks have been investigated for
their stability (Hertz, 1999) and for their properties of
associative memories for encoding afferent stimuli
(Hertz and Prugel-Bennett, 1996; Lauritzen, 1998). The
new theoretical developments of the spike-based Hebbian learning rule (Kempter et al., 1999) can provide
adequate mechanism for neural network learning by
synfire chains. However, the existence of causal relations between the occurrence of precise temporal patterns and behavioral output has not yet been
established unambiguously due to the limitations of
currently available methods of analysis (Fetz, 1997;
deCharms, 1998).
The companion article (Tetko and Villa, 2000)
demonstrates the performance of a new algorithm (pattern grouping algorithm, PGA) for the detection of
significant patterns of spikes with variable jitters in
simulated data where other algorithms alone failed. The
aim of the present work is to demonstrate practical
applications of this newly developed algorithm in multiple spike trains recorded simultaneously in three different experimental settings of increasing complexity. In
the first case study we investigated whether patterned
activity can be detected in randomly sampled elements
from realistic artificial neural networks. Synfire chain
theory predicts that strongly interconnected brain regions should be involved in organized activity that will
generate temporally patterned spike trains. In the second case study we tested this prediction in the corticothalamic system, by recording from the medial
geniculate body during reversible cortical deactivation.
A further prediction of the theory is that if the network
operations giving rise to detected patterned activity are
of biological significance, then the patterns should be
correlated in some way with behavioral output. In the
third case study multiple spike trains were recorded
from the auditory cortex of freely-moving rats performing an auditory conditioned task, and the trial-by-trial
occurrence of detected patterns correlated with behavioral measures.
2. Methods
2.1. Artificial neural network data
We have applied PGA to two records from a large
scale simulated network described elsewhere (Amit and
Brunel, 1997) with settings w=500 ms and J= 7 ms
(i.e. 9 3 ms plus 1 ms due to data accuracy). The
network was composed of 15 000 integrate-and-fire
cells, from which 12 000 were excitatory and 3000 were
inhibitory. Each cell in the network had a probability
0.15 of a direct contact with other cells and received, on
average, 1800 excitatory and 450 inhibitory synapses
from neurons belonging to the network and 1800 excitatory synapses from outside the network. In the first
record, referred to as ‘random’, the strength of neuronal connections was initially set by random (Amit
and Brunel, 1997) and was not modified. Thirty units
were selected by chance and their corresponding spike
trains were recorded during 180 s with an accuracy of 1
ms. In the second record, referred to as ‘Hebbian’, the
weights of specific populations of synapses were
modified according to a Hebbian learning rule described in detail elsewhere (Amit and Brunel, 1997).
2.2. Experimental data
All animal experiments were conducted in young
adult Long–Evans hooded rats in compliance with
Swiss guidelines for the care and use of laboratory
animals and after receiving governmental veterinary
approval.
2.2.1. Thalamic recordings with cooling deacti6ation of
the ipsilateral auditory cortex
Twelve spike trains were recorded simultaneously (in
a single session) in the auditory thalamus of the anesthetized rat during cooling deactivation of the ipsilateral auditory cortex. Details on the experimental
procedure can be found elsewhere (Villa et al., 1999b).
Briefly, under anesthesia by a mixture of ketamine (57
mg/kg) and xylazine hydrochloride (8 mg/kg) the animals were mounted in a stereotaxic apparatus and
openings for the thalamic microelectrodes and for the
cortical cooling probe were drilled through the skull.
Extracellular single unit recordings in the auditory thalamus were made with glass-coated platinum-plated
tungsten microelectrodes having an impedance in the
range 0.5–2 MV measured at a frequency of 1 kHz
I.V. Tetko, A.E.P. Villa / Journal of Neuroscience Methods 105 (2001) 15–24
17
(Frederick Haer & Co., Brunswick, Maine). Cortical
cooling was achieved by circulation of a cooling fluid.
The steady state was reached in 15 – 20 min. During
cooling the temperature of the probe was near 5°C and
the temperature of the deep cortical layers in the range
16 – 22°C, low enough to inactivate cortical synapses.
The temperature of the probe-end proximal to the
cerebral cortex was monitored continuously by a thermocouple and the degree of reversible inactivation of
cortical activity was assessed by means of microelectrodes monitoring the auditory evoked responses in the
cortex. The spike trains were recorded during 300 –1000
s in a steady-state condition without external stimulus,
referred to as ‘spontaneous’ activity, before, during,
and after cortical deactivation.
a Go choice (either correct or incorrect) the animal
moves towards the feeder area and the response period
is ended by crossing an infrared beam located by the
feeder. In case of a NoGo choice (either correct or
incorrect) the rat remains still in the rest area and the
response period is ended after a delay of 4 s (this delay
corresponds to the maximum allowed time for a Go
response). In case of a Go choice a ‘post-movement’
period is defined by the interval between the entrance
into the feeder, immediately followed by eating the
reward seed for correct choices, and the return back to
the rest area. In case of a NoGo choice no post-movement period is defined and a wait period follows immediately a post-stimulus period, unless the rat leaves the
rest area and roams freely in other sectors of the cage.
2.2.2. Cortical recordings in auditory two-choice
(Go/NoGo) reaction-time task
Fifteen single units were simultaneously recorded
from the auditory cortex of rats performing an auditory, two-choice (Go/NoGo), reaction-time task (Villa
et al., 1998, 1999a). In brief, the rats were trained in
daily sessions of 30 – 90 min to respond to a 500 ms
auditory stimulus which contained two types of information: pitch (high, 12 kHz or low, 3 kHz), and
location (left or right). During the first phase of training, the location was kept constant and subjects had to
discriminate between tones of high and low pitch, with
one signaling Go and the other NoGo. Reinforcement
(automated delivery of a sunflower seed) was done only
after correct Go trials. In the second phase, pairs of
tones were delivered (one tone from each location),
with four possible tone-position combinations. Two of
these tone-pairs were conflictual with respect to the
initial training in that tones of both Go and NoGo
pitch were delivered. This conflict could however be
resolved if the animal learnt to associate both pitch and
location with reward. We have shown (Villa et al.,
1999a) that despite the lack of reward for correct NoGo
performance, and the lack of painful punishment for
incorrect trials, all rats could learn the task at least to
a level of 70% and some animals with overtraining
could reach 90% correct performance. The data reported here were recorded from rats that were chronically implanted with electrodes in the temporal cortex
after the second phase of training.
For each trial several periods can be distinguished in
the behavioral task studied here (Villa et al., 1999a). At
the beginning, the rat must remain at the back of the
cage for a certain time without crossing an infraredbeam delimiting the ‘rest’ area. This period corresponds
to the ‘wait’ period and is ended by the stimulus onset.
The wait time was equal to 10 s for the data analyzed
here. After the stimulus is delivered the rat decides
whether to go or not to go towards the feeder area. The
stimulus onset triggers the ‘response’ period. In case of
2.3. Analysis of patterns using the pattern grouping
algorithm
The details of this analytical method are given in the
companion paper (Tetko and Villa, 2000). Briefly, this
algorithm can search and cluster together into a single
group individual patterns which differ from each other
by a small jitter in spike timing of the order of few ms.
The general form of a pattern of complexity c can be
noted as Ži1,…, ij,…, ic ; t1 9 (D1/2),…, tj 9 (Dj /2),…,
tc − 1 9 (Dc − 1/2)\ where ij are labels of the recorded
neurons, t1,…, tj,…, tc − 1 are the time delays between
the first i1 and the ij spike forming the pattern and Dj
are the corresponding time jitters.
The estimation of significance of the detected patterns is done according to three different tests. The first
test is an extension of the pattern detection algorithm,
PDA (Abeles and Gerstein, 1988) and estimates the
significance of a pattern complexity c that repeated r
times by:
(r)
Á pPDA = pr{1,N (r)
c = 1− exp(−N c )}
Ã
(r)
(r)
N c = Q(a, c, V) · N0 c
Í
Ã
V!
ÄQ(a, c, V)= F(c− a, a) · (V− a)!a!
(1)
where N0 (r)
c estimates the expected number of patterns
formed solely by the spikes of the neurons in the
analyzed pattern. The factor Q accounts for the chance
effects due to an increase of the number V of simultaneously recorded neurons and the number a counts
how many different cells participate to the analyzed
pattern. The Fibonacci (or Figurate series) number F(i,
j ) corresponds to the number of different combinations
formed by i out of j neurons, including repetitions of
the same neuron (Hogben, 1950).
The significance of each group was also estimated
according to the modified versions of Favored Pattern
Detection, FPD (Dayhoff and Gerstein, 1983), and
Joint Triplet Histogram, JTH (Prut et al., 1998) as
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I.V. Tetko, A.E.P. Villa / Journal of Neuroscience Methods 105 (2001) 15–24
indicated in Tetko and Villa (2000). The significance
levels calculated by these methods were designated as
pFPD and pJTH, respectively.
The three adjustable parameters in PGA include the
maximal duration of the pattern measured as a delay
between the first and the last spike in the sequence of
spikes (i.e. the window duration, w), the level of significance to be used for detection of significant groups and
the upper bound of allowed jitter applied to all the
groups, designated as J.
The Fano Factor c6 was also calculated for all data.
It is defined as c6 = sDt /D( t, where D( t is the mean value
of the interspike intervals and sDt the standard deviation of that mean. This factor may be used to characterize the variability of the spike train and it is equal to
1 for the data generated according to Poisson processes
(Softky and Koch, 1993).
events formed a significant subpattern at a higher precision. The detected pattern was significant at level
pPDA = 3×10 − 3, pJTH = 3× 10 − 8 and pFPD B0.01.
This pattern contained a significant subpattern of complexity 4 Ž17, 17, 17, 17; 16693.5, 1869 3.5, 2319
1.5 that repeated 24 times with pPDA = 2×10 − 3,
pJTH = 7×10 − 7, pFPD B 0.01 and a subpattern of complexity 3 Ž17, 17, 17; 1689 1.5, 1879 2.5 that repeated 48 times with pPDA = 3× 10 − 3, pJTH = 4×10 − 4,
pFPD B 0.01.
3.2. Corticofugal modulation of spatiotemporal firing
patterns
PGA was applied to the recordings performed during
3. Results
3.1. Recurrent spatiotemporal firing patterns in randomly
connected networks
During the ‘random’ recording the activity of the
thirty sampled units from the artificial neural network
corresponded to sustained spontaneous rates, in the
range 0.1–11.7 spikes/s (mean=4.0 spikes/s and median= 3.1 spikes/s). The activity of the same set of
units recorded following a Hebbian learning was characterized by increased discharge rates of cells (mean=
6.5 spikes/s, median= 4.2 spikes/s).
No patterns were detected by PGA in the ‘random’
record, whereas most cells (20/30 of our sample)
formed patterns in the ‘Hebbian’ record. All detected
patterns were formed by one cell. The firing rates
(mean =7.1 spikes/s, median= 5.3 spikes/s) of cells
participating to significant patterns were higher than
the rates (mean= 5.3 spikes/s, median=3.9 spikes/s) of
cells that never formed a temporal pattern. Most of the
autocorrelograms were almost flat and indicated that
the spike trains deviated only slightly from process a
Poisson renewal point (Fig. 1a).
In our sample, cell no. 16 was characterized by a
firing rate of 17.6 spikes/s but no significant temporal
pattern was observed. Cell no. 17 fired at a similar rate,
17.2 spikes/s, and its autocorrelogram was similar to
that of cell no. 16 (Fig. 1a), but 238 patterns of
complexity 3–5 were detected. Neither the firing rates
nor the shapes of the autocorrelograms were predictive
of the presence of patterns. Fig. 1b illustrates a significant pattern formed by five events in this unit repeating
ten times, i.e. Ž17, 17, 17, 17, 17; 31 92.0, 168 91.5,
1869 3.5, 23192.0. In this example the event at delay
186 ms from the pattern onset was detected only at the
maximum allowed variability, whereas the other four
Fig. 1. A high complexity pattern elicited by an attractor mode of
activity in ‘cells’ in a randomly connected artificial neuronal network
following ‘Hebbian’ learning. (a) Autocorrelograms of three cells
recorded simultaneously. The abscissa is lag (in ms) and the ordinate
is scaled in rate units (spikes/s). The curves are smoothed with a 10
ms Gaussian shaped bin; the dashed lines indicate the 99% confidence
level assuming a Poisson distribution. Note that the shapes of the
curves are similar for the three cells, but cell c16 produced no
significant patterns. (b) Ten repetitions of a pattern of complexity five
formed by repeated events of cell c 17 are displayed as rasters
aligned on pattern start. Note that the fourth event, at a delay of 186
ms, was detected on the limit of the maximum allowed accuracy
(J = 7 ms). The average firing rates of cells c16, c17 and c 18
were 17.6, 17.2 and 8.4 spikes/s and the values of the Fano Factor
were 0.7, 0.7 and 1.8, respectively. Cell c16 tended to be inhibited
after the discharges of cell c 17, thus explaining the lower activity of
cell cshown in the above raster plot.
I.V. Tetko, A.E.P. Villa / Journal of Neuroscience Methods 105 (2001) 15–24
the control condition, grouped together with recordings
during cortical cooling and after the cortical temperature returned back to normal with window duration
w =500 ms and jitter J =7 ms. The rationale is that
patterns associated to a specific state of cortical activation would appear almost exclusively during that condition, but should be searched in the whole data set in
order to avoid a circular argument in the searching
strategy. We found ten significant patterns of complexity 3 repeating at least seven times in the combined set.
Four patterns were characterized by their occurrences
only during one recording condition, either before,
during or after cortical deactivation. The remaining six
patterns were characterized by their occurrences being
equally distributed before and after cooling of the
auditory cortex. The total number of repetitions per
pattern varied between nine and 20 but only one occurrence, if any, was observed during cortical deactivation.
These data show that cortical deactivation can disrupt
precisely timed activity within the thalamus in a reversible way.
Fig. 2 illustrates the pattern Ž1, 2, 2; 263 9 4.5,
3079 3.5 formed by two cells. The significant pattern
was observed nine times in 400 s (i.e. 1.4 pattern
occurrences/min) of spontaneous activity recorded during the control condition. Only one pattern was observed in 300 s of recording time during cooling (0.2
patterns/min) but the same pattern was observed again
six times in 300 s (1.2 patterns/min) during the recovery
period. Note that between the first and the last occurrence of the pattern 90 min had passed. The autoand the cross-correlogram of neurons 1 and 2 were
almost flat (Fig. 2a). This indicated an absence of
bursting activity and significant cross-correlation between these neurons. The firing rate of these neurons
was slightly affected by cortical cooling. It was 3.8, 3.9
and 4.6 spikes/s for neuron c1 and 3.1, 2.2 and 3.1
spikes/s for neuron c2 before, during and after the
cortical cooling respectively. Thus, the main parameter
that was dramatically affected for this pair of neurons
during cortical cooling was the disappearance of the
spatiotemporal pattern. The level of significance of this
pattern was pPDA =9 × 10 – 4 and pJTH =7 × 10 – 6. This
pattern was significant at level p0 B0.05 if data sets
recorded before or after cortical cooling were considered separately. The low level of significance can be
attributed to a small number of repetitions of this
pattern within each dataset separately. With an extended jitter of 11 ms this pattern was repeated 12 times
at a level of significance pPDA =6 ×10 – 3 and pJTH =
6× 10 – 5.
3.3. Beha6ioral correlates of spatiotemporal patterns
The PGA analysis was done on 10 s periods preced-
19
Fig. 2. A spatiotemporal firing pattern of real neurons in the thalamus that is reversibly disrupted by cortical deactivation. (a) Autocorrelograms and crosscorrelograms of the participating cells recorded
before, during and after cooling of the auditory cortex in the rat
medial geniculate body. (b) Sixteen occurrences of the pattern Ž1, 2,
2; 14594.5, 225 9 2.5 are displayed as a special raster aligned on
pattern start. The labels on the left indicate the patterns detected
before and after inactivation of cortex by reversible cooling, respectively. Only one occurrence of the pattern was detected during the
cortical cooling. The value of the Fano Factor was equal to 1.1 for
both cells c1 and c 2.
ing stimulus onsets in the wait periods. Each record
included the sets of trials performed by an animal in
one day was analyzed using window duration of w=
1000 ms. The significance level p= 0.01 and maximum
jitter of J=7 ms were used. The pattern groups were
reanalyzed using J=11 ms jitter to collect additional
occurrences, if any. We identified the records that contained a sequence of intervals found to be significant. It
is important to emphasize that the rat could not know
in advance which randomly chosen stimulus would
occur. The patterns occurred prior to the auditory cue
that prompted the rat whether to go or not to go, and
as expected, were distributed independently of the na-
20
I.V. Tetko, A.E.P. Villa / Journal of Neuroscience Methods 105 (2001) 15–24
ture of the randomly selected cueing stimulus. The
number of significant patterns detected per session was
in the range from zero up to 35 patterns. Certain
patterns were specific for one of the two possible behavioral responses — Go or NoGo — irrespective of
whether or not the response was correct.
For example, in a record we found one pattern that
repeated in five trials, exclusively in the wait period
before a Go response was produced (Fig. 3). This
particular pattern was of complexity four Ž5, 3, 3, 3;
2389 2.5, 580 91.5, 726 92.0 with significance
pPDA =1× 10 − 3 and pJTH =3 ×10 − 9 (the JTH method
was extended to patterns of four spikes as indicated in
Tetko and Villa (2000)). Moreover, the triplet Ž3, 3, 3;
34292.5, 48892.5 corresponding to one of the four
possible subpatterns also repeated significantly during
the periods preceding the Go responses (five times in
addition to those occurrences forming the quadruplet).
The other triplets representing the remaining subpat-
Fig. 4. A spatiotemporal firing pattern related to behavioral output.
The pattern Ž5, 6, 5; 224 92.0, 412 94.0 repeated 14 times during
the experimental session and is displayed as a special raster aligned
on pattern start. Note that 12/14 repetitions, once per trial, occurred
before the rat decided to go to the feeder area after onset of the
response stimulus. The reaction time measured for these 12 trials was
on average 174 ms faster than for the Go-responses that were not
preceded by this pattern occurrence. The average firing rates of cells
c5 and c6 were 2.9 and 2.3 spikes/s and the values of the Fano
Factor were 1.1 and 1.0, respectively.
Fig. 3. A spatiotemporal firing patterns from two neurons recorded
from the same electrode in the temporal cortex of a behaving rat. (a)
Autocorrelograms and crosscorrelogram of both cells recorded during
810 s corresponding to the 10 s waiting periods in 81 Go trials. (b)
Five repetitions of the quadruplet Ž5, 3, 3, 3; 2389 2.5, 5809 1.5,
7269 2.0 are displayed as a special raster aligned on pattern start.
Out of the four possible subpatterns formed by three neurons only
the pattern Ž3, 3, 3; 3429 2.5, 488 92.5 was significant and repeated also five times. In the display this triplet is aligned on the
second event of the quadruplet. Altogether the remaining three
subpatterns, starting with cell 5, repeated ten times and were aligned
on the start event of the quadruplet. The average firing rates of cells
c3 and c 5 were 3.6 and 4.0 spikes/s and the values of the Fano
Factor were 1.1 and 1.3, respectively.
terns of the original quadruplet, formed by sequences
of intervals leaded by a spike of cell no. 5 followed by
two spikes of cell no. 3, repeated ten times altogether,
but none was individually significant. Fig. 3 shows all
20 occurrences of the quadruplet and its related subpatterns observed in 25% (20/81) of trials followed by a Go
response. It is important to note that in this session the
rat performed 124 NoGo responses. In these trials there
were 16 occurrences (13% of all NoGo trials) of the
triplets forming the subpatterns but in none of these
triplets was the level of occurrence significant.
In order to obtain a more specific measure of the
extent to which these patterns were predictive of behavior we performed an analysis of the association of
patterns with changes in reaction time. In this analysis
every occurrence of the pattern was taken into account.
The reaction time was measured as the delay between
stimulus onset and crossing of the infrared beam delimiting the standing area of the subject waiting for the
stimulus (Villa et al., 1999a). We found that the occurrence of some patterns was indeed related to the speed
of the reaction. An example of such pattern is shown in
Fig. 4. On the day of this recording the rat performed
116 Go and 114 NoGo responses. The pattern Ž5, 6, 5;
I.V. Tetko, A.E.P. Villa / Journal of Neuroscience Methods 105 (2001) 15–24
22492.0, 41294.0 repeated 14 times during the experimental session, 12 of which were in wait periods
preceding the Go responses. The reaction time of those
trials characterized by the presence of the pattern was
875969 ms (average and S.E.M.), which was significantly faster (PB 0.05, t-test) than the reaction time
measured for trials without that pattern, (10499 38
ms). The level of significance of this pattern was
pPDA =3× 10 – 3 and pJTH =8 ×10 – 6.
Interestingly, during the same day cell no. 5 participated in another significant pattern Ž5, 11, 5; 32093.5,
6629 1.0 that was detected 17 times, 13 of which were
before Go responses. This pattern had the same relation to the behavior of the animal, i.e. the reaction time
of Go responses in trials with the pattern (8749103
ms) was significantly faster (P B 0.05, t-test) than for
Go responses without the pattern (1049937 ms). The
presence of both patterns during the same day was not
correlated and in only one trial both patterns were
detected simultaneously. This would be consistent with
the idea that similar behavior can be produced by
different cell assemblies.
The average firing rates of neurons c5, c 6 and
c11 were equal to 3.2, 2.4 and 3.3 spikes/s for all
trials, respectively, and equal to 3.5, 2.5 and 3.3 spikes/s
during the trials that contained the patterns. No significant change in the firing rates was observed, thus
suggesting that the observed phenomena could not be a
by-product of increased excitability of the neurons.
4. Discussion
We have presented evidence that the PGA described
in the companion paper (Tetko and Villa, 2000) can be
used to reliably detect spatiotemporal firing patterns in
realistic large scale artificial neural networks, and in
both anesthetized and behaving animals. This method
enables the detection of and significance estimation for
individual spatiotemporal patterns with variable, optimized jitter in spike timing. We investigated the network and behavioral associations of individual patterns
formed by spikes occurring in spike trains of different
simultaneously recorded neurons. We have shown that
the occurrence of individual patterns can be modified
by alternations in network dynamics, and also in association with specific aspects of behavioral output. This
is particularly important if one considers that state-ofthe-art technique allows several laboratories to record
tens of cells simultaneously in behaving rats (Skaggs
and McNaughton, 1996; Nicolelis et al., 1997).
The method presented here does not assume a Poisson process for the spike trains, but it actually counts
the number of patterns that occur in a given piece of
data and can provide reliable estimations even for data
generated with non-stationary renewal Poisson point
21
processes (Abeles and Gerstein, 1988; Tetko and Villa,
1997c). The assumption that spike intervals are distributed according to a Poisson process does not correspond to data characterized by bursting activity. These
data show a significant peak near time zero in the
autocorrelogram. Similar peaks are produced by simulated spike train data generated by non-stationary Poisson processes used to verify the PGA (see Fig. 3 of
Tetko and Villa, 2000). However, most experimental
spike train data reported here were characterized by
almost flat autocorrelograms and satisfied the Kolmogorov-Smirnov test (Press et al., 1994) at level p0 =
0.05 that the distribution of interspike interval was
consistent with Poisson renewal process for all neurons
but two.
The parameters that affect the result of PGA are the
level of significance, the jitter and the window duration.
Significance levels in the range 0.01–0.001 are usually
used in biological studies and the same levels can be
recommended for application of PGA. The maximum
value of jitter is not critical for applying PGA because
the algorithm optimizes the jitters according to the
actual distribution of spikes in the pattern. Provided a
sufficiently large value of jitter, PGA detects the same
patterns at the same significance level, but the use of
large jitters significantly decreases the speed of calculation. Previous studies (Lestienne, 1996; Prut et al.,
1998) reported maximum jitters in the range 91 – 93
ms (i.e. J= 3–7) and indicated that jitters up to 910
ms resulted only in a small increase of significant
patterns. Window duration comparable to the duration
of one record necessarily tends to bias the results of
PGA in favor of shorter patterns. In practice, we
observed that the distribution of duration of patterns
was uniform, thus suggesting the absence of a bias to
detect patterns with short duration. As a rule of the
thumb, window duration should be set at least one
order of magnitude smaller than the record length.
Further restrictions for the use of windows larger than
1000 ms were simply due to limitations for speed and
physical memory (2 GB) of the available computers.
A recent study suggests that precise patterns of spikes
during neural responses to visual stimuli can be explained by a simple spike count-matched model (Oram
et al., 1999). This model accounted for the refractory
period of cells (using inter-spike-interval histogram)
and for variation in cell firing (measured by peristimulus time histogram) during the response to the stimulus.
The results of this study are not directly applicable to
our data. Firstly, the experimental data presented in
our study were recorded during spontaneous activity
and no significant bursting activity was observed as it
was in the data reported by Oram et al. (1999). Secondly, the authors focused their attention on patterns
with short duration, i.e. less than 25 ms long, while our
study explicitly disregarded such data by analyzing
22
I.V. Tetko, A.E.P. Villa / Journal of Neuroscience Methods 105 (2001) 15–24
patterns lasting more than 20 ms. Thirdly, the experimental data reported in our study were characterized
by smaller values of Fano Factor, in the range 1.0–1.3
compared with 1.4– 2.9 reported by Oram et al. (1999).
It should be noted that for spike trains with values of
Fano Factor near 2, used in simulation studies (Tetko
and Villa, 2000), the performance of PGA was good
and no significant patterns were detected in those spike
trains.
An additional test to evaluate the probability to find
a pattern by chance consisted in a random shift of all
spikes (Hertz, 1999) in data by910 ms and application
of PGA with the same setting used to analyze the
experimental data. This procedure completely eliminated all patterns reported in this study and no spurious patterns were detected by PGA.
Simulation of large-scale neuronal networks formed
by integrate-and-fire model neurons are also becoming
popular to test hypotheses on the significance of temporal information processing in the brain (Amit and
Brunel, 1997; Hill and Villa, 1997; Lumer et al., 1997).
The possibility to insert virtual electrodes in such networks and to record from hundreds or even from
thousands virtual neurons will certainly become a routine analysis in the forthcoming years. Then, the possibility to detect and estimate carefully the significance of
high complexity spatiotemporal patterns of spikes appears as a crucial step for the evaluation of coding
schemes.
The ability to record large numbers of simultaneously recorded neurons has two contradictory effects
on the detection of patterns. On the one hand, by
increasing the number of recorded neurons one increases the probability of detecting spatiotemporal patterns that are generated only by a small fraction of cell
assemblies (Abeles and Gerstein, 1988; Tetko and Villa,
1997c). On the other hand, an increase of simultaneously recorded spike trains increases the number of
combinations Q(a, c, V) (see Eq. (1)) and therefore
decreases the probability that repetitions of the same
pattern will reach significance in the analyzed data. For
the analysis of patterns formed by one cell, the number
of possible combinations Q(1, c, V) is equal to the
number of simultaneously recorded neurons V. For
triplets and quadruplets formed by different neurons
the number Q increases approximately by ten and
twenty times, respectively, when the number of simultaneously recorded neurons is doubled. The statistical
significance of firing patterns detected in data sets of
tens of spike trains recorded simultaneously tends to
become underestimated with the increase of number Q.
This is partly due to the fact that we assume a ‘blind’
application of the algorithm. In practice, it is possible
to use preliminary information to decrease the number
of neurons for analysis with PGA. The application of
the burst filtering procedure to each spike train should
be used to determine the proportion of discarded spikes
and, consequently, to discard those neurons characterized by irregular firing (e.g. say with more than 10% of
discarded spikes by the filtering procedure). Furthermore, the cells characterized by a very low firing rate
are unlikely to participate in sequences of intervals
repeating a significant number of times. Then, at the
very first step of the PGA it is possible to determine
which cells participate to patterns with very few repetitions, if any. A threshold corresponding to the minimum repetition rate of an exact firing pattern could be
implemented to screen the participation of all neurons
to precisely timed activity and reduce the number of the
final set of spike trains analyzed by PGA.
In simulation studies a very large number of spike
trains can be collected by virtual electrodes and PGA
could be applied in two steps. The neurons that participate to lower complexity patterns, e.g. triplets, could
be determined at first, then only these spike trains
would be analyzed for higher complexity patterns. Additional methods to reduce the number of analyzed
spike trains could be based on the relations between
deterministic dynamics of the spike train and detection
of significant firing patterns (Tetko and Villa, 1997a).
The existence of an excess of significant patterns of
spikes in the cat’s thalamus has previously been demonstrated using PDA (Villa and Abeles, 1990). In the
experiment analyzed here we provide further evidence
that precisely timed activity within the thalamus critically depends on the input from the cortex. Reversible
cooling deactivation (Villa et al., 1999b) provoked the
temporary disruption of spatiotemporal firing patterns
across several neurons recorded simultaneously from
different electrodes in adjacent subdivisions of the rat
medial geniculate body. This finding is in agreement
with the hypothesis that time-structured neural assemblies may be sustained by the cortico-thalamo-cortical
loops (Miller, 1996). This circuit provides a high-security link and could be a good candidate to support
sustained activity of synfire chains. Moreover, the corticofugal effect on patterned activity within the thalamus
may provide additional support to the hypothesis that
the auditory cortex exerts a dynamic control over the
functional segregation of signals transmitted through
the thalamus (Villa et al., 1991, 1999b; Tetko and Villa,
1997b).
We have presented evidence that in behaving rats
patterned activity occurs reliably under particular behavioral conditions. The present study has analyzed
new data by PGA and confirmed previous results of
association of specific spatiotemporal patterns occurring during the wait period with the subsequent reaction time obtained using an extension of PDA (Tetko
and Villa, 1997c). Accurate application of complex
pattern detection methods enables correlation between
discrete brain states and measures of behavioral perfor-
I.V. Tetko, A.E.P. Villa / Journal of Neuroscience Methods 105 (2001) 15–24
mance on a trial-by-trial basis. The fact that the timing
of pattern occurrence could relate to reaction time
indicates that the network phenomena underlying them
reflect some state of the animal that is able to influence
behavioral output. Changes in cortical network activity
during the wait period may therefore be related to the
concepts of ‘attention’ and ‘set’, with emphasis on
processes related to motor output in the former (Wise
and Kurata, 1989) and to sensory processing in the
latter (Shinba et al., 1995). It is interesting to note that
in the behavioral experiments reported here we found
relatively few significant patterns, in the order of few
hundreds, for tens of hours of analyzed recording time
(Villa et al., 1998, 1999c). The analysis of cell activity is
done over short periods (10 s) per trial but one behavioral experiment could last several hours and we cannot
discard that the single unit detection might be unstable
over such a prolonged time.
In summary, in this study we have provided new data
from electrophysiological results that demonstrated the
presence of precisely timed neural activity. In the analysis of artificial neural networks, we showed that significant patterns of spikes can not be detected in the
randomly connected network, but they can be detected
following the Hebbian learning. In the reversible cortical inactivation study we have shown that there are
firing patterns distributed spatially within the thalamus
under the control of cortical activity. In a psychophysiological study with freely moving rats we have provided
additional evidence that precisely timed neural activity
occur reliably under particular behavioral conditions.
We want to emphasize that we do not rule out the
possibility that rate codes and synchronization codes
can coexist in the same network. One prediction is that
rate coding might prevail at levels of processing that are
close to sensory input and motor output, whereas complex computations (e.g. involving ‘binding’, crossmodal associations, memory retrieval, planning, etc.)
might involve network activities, such as synfire chains,
that will be reflected in precise patterns of specific
inter-neuronal spike timing.
Acknowledgements
We acknowledge the participation of B. Hyland, A.
Kuhn, and A. Najem to some experimental sessions.
We thank D. Amit and N. Brunel for providing us with
simulated data and B. Hyland for his helpful comments. A part of calculations was performed at the
Swiss Center for Scientific Computing. This study was
partially supported by HFSPO STF-421/95, Swiss NSF
2053-055753.98/1 and INTAS-OPEN 97-0168 and 970173 grants.
23
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