Correlated Neuronal Response: 
Time Scales and Mechanisms 
Wyeth Bair 
Howard Hughes Medical Inst. 
NYU Center for Neural Science 
4 Washington Pl., Room 809 
New York, NY 10003 
Ehud Zohary 
Dept. of Neurobiology 
Institute of Life Sciences 
The Hebrew University, Givat Ram 
Jerusalem, 91904 ISRAEL 
Christof Koch 
Computation and Neural Systems 
Caltech, 139-74 
Pasadena, CA 91125 
Abstract 
We have analyzed the relationship between correlated spike count 
and the peak in the cross-correlation of spike trains for pairs of si- 
multaneously recorded neurons from a previous study of area MT 
in the macaque monkey (Zohary et al., 1994). We conclude that 
common input, responsible for creating peaks on the order of ten 
milliseconds wide in the spike train cross-correlograms (CCGs), 
is also responsible for creating the correlation in spike count ob- 
served at the two second time scale of the trial. We argue that 
both common excitation and inhibition may play significant roles 
in establishing this correlation. 
1 INTRODUCTION 
In a previous study of pairs of MT neurons recorded using a single extracellular 
electrode, it was found that the spike count during two seconds of visual motion 
stimulation had an average correlation coefficient of r = 0.12 and that this cor- 
relation could significantly limit the usefulness of pooling across increasingly large 
populations of neurons (Zohary et al., 1994). However, correlated spike count be- 
tween two neurons could in principle occur at several time-scales. Correlated drifts 
Correlated Neuronal Response: Time Scales and Mechanisms 69 
in the excitability of the cells, for example due to normal biological changes or 
electrode induced changes, could cause correlation at a time scale of many min- 
utes. Alternatively, attentional or priming effects from higher areas could change 
the responsivity of the cells at the time scale of an experimental trial. Or, as sug- 
gested here, common input that changes on the order of milliseconds could cause 
correlation in spike count. The first section determines the time scale at which the 
neurons are correlated by analyzing the relationship between the peak in the spike 
train cross-correlograms (CCGs) and the correlation between the spike counts using 
a construct we call the trial CCG. The second section examines temporal structure 
that is indicative of correlated suppression of firing, perhaps due to inhibition, which 
may also contribute to the spike count correlation. 
2 THE TIME SCALE OF CORRELATION 
At the time scale of the single trial, the correlation, rsc, of spike counts x and y from 
two neurons recorded during nominally identical two second stimuli was computed 
using Pearson's correlation coefficient, 
E[xy] - ExEy 
ro: , (1) 
O' x O'y 
where E is expected value and a 2 is variance. If spike counts are converted to 
z-scores, i.e., zero mean and unity variance, then rc - E[xy], and rsc may be 
interpreted as the zero-lag value of the cross-correlation of the z-scored spike counts. 
The trial CCGs resulting from this procedure are shown for two pairs of neurons in 
Fig. 1. 
To distinguish between cases like the two shown in Fig. 1, the correlation was broken 
into a long-term component, rtt, the average value (computed using a Gaussian 
window of standard deviation 4 trials) surrounding the zero-lag value, and a short- 
term component, rt, the difference between the zero-lag value and rtt. Across 92 
pairs of neurons from three monkeys, the average rst was 0.10 (s.d. 0.17) while rtt 
was not significantly different from zero (mean 0.01, s.d. 0.11). The mean of rst 
was similar to the overall correlation of 0.12 reported by Zohary et al. (1994). 
Under certain assumptions, including that the time scale of correlation is less than 
the trial duration, rst can be estimated from the area under the spike train CCG 
and the areas under the autocorrelations (derivation omitted). Under the additional 
assumption that the spike trains are individually Poisson and have no peak in the 
autocorrelation except that which occurs by definition at lag zero, the correlation 
coefficient for spike count can be estimated by 
'peak  Area, (2) 
where AA and As are the mean firing rates of neurons A and B, and Area is the area 
under the spike train CCG peak, like that shown in Fig. 2 for one pair of neurons. 
Taking Area to be the area under the CCG between :t:32 msec gives a good estimate 
of short-term rt, as shown in Fig. 3. In addition to the strong correlation (r - 0.71) 
between rpeak and rt, rpeak is a less noisy measure, having standard deviation (not 
shown) on average one fourth as large as those of rst. 
We conclude that the common input that causes the peaks in the spike train CCGs is 
also responsible for the correlation in spike count that has been previously reported. 
70 W. BAIR, E. ZOHARY, C. KOCH 
4_ Neuron 1 
-4 
  . , Neuron 2 
'.".", 
0 80 160 240 320 
Trial Number 
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400 800 1200 
Trial Number 
0.3 
0.2 
0.1 
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mu080 l ll 
Lag (Trials) 
Lag (Trials) 
Figure 1: Normalized responses for two pairs of neurons and their trial cross- 
correlograms (CCGs). The upper traces show the z-scored spike counts for all 
trials in the order they occurred. Spikes were counted during the 2 sec stimulus, 
but trials occurred on average 5 sec apart, so 100 trials represents about 2.5 min- 
utes. The lower traces show the trial CCGs. For the pair of cells in the left panel, 
responsivity drifts during the experiment. The CCG (lower left) shows that the drift 
is correlated between the two neurons over nearly 100 trials. For the pair of cells 
in the right panel, the trial CCG shows a strong correlation only for simultaneous 
trials. Thus, the measured correlation coefficient (trial CCG at zero lag) seems to 
occur at a long time scale on the left but a short time scale (less than or equal to one 
trial) on the right. The zero-lag value can be broken into two components, rst and 
rtt (short term and long term, respectively, see text). The short-term component, 
rst, is the value at zero lag minus the weighted average value at surrounding lag 
times. On the left, rst  O, while on the right, rtt  O. 
Correlated Neuronal Response: Time Scales and Mechanisms 71 
5 
4 
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8 16 
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Width at HH (msec) 
0 emu064P 
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Figure 2: A spike train CCG with central peak. The frequency histogram of widths 
at half-height is shown (inset) for 92 cell pairs from three monkeys. The area of the 
central peak measured between 4-32 msec is used to predict the correlation coeffi- 
cients, rpe,k, plotted in Fig. 3. The/i-axis indicates the probability of a coincidence 
relative to that expected for Poisson processes at the measured firing rates. 
.6   
  
   
 0.4    
/ ee ee  
   /  
   
-0.2 *  " , , , , 
-0.2 0 0.2 0.4 0.6 0.8 
r (Short Term) 
Figure 3: The area of the peak of the spike train CCG yields a prediction, r (see 
Eqn. 2), that is strongly correlated (r = 0.71, p < 0.00001), with the short-term 
spike count correlation coefficiem, rst. The absence of points in the lower right 
corner of the plot indicates that there are no cases of a pair of cells being strongly 
correlated without having a peak in the spike train CCG. 
0.8 
72 W. BAIR, E. ZOHARY, C. KOCH 
In Fig. 3, there are no pairs of neurons that have a short-term correlation and yet 
do not have a peak in the 32 msec range of the spike train CCG. 
3 CORRELATED SUPPRESSION 
There is little doubt that common excitatory input causes peaks like the one shown 
in Fig. 2 and therefore results in the correlated spike count at the time scale of the 
trial. However, we have also observed correlated periods of suppressed firing that 
may point to inhibition as another contribution to the CCG peaks and consequently 
to the correlated spike count. 
Fig. 4 A and B show the response of one neuron to coherent preferred and null 
direction motion, respectively. Excessively long inter-spike intervals (ISis), or gaps, 
appear in the response to preferred motion, while bursts appear in the response 
to null motion. Across a database of 84 single neurons from a previous study 
(Britten et al., 1992), the occurrence of the gaps and bursts has a symmetrical 
time course both are most prominent on average from 600-900 msec post-stimulus 
onset, although there are substantial variations from cell to cell (Bair, 1995). The 
gaps, roughly 100 msec long, are not consistent with the slow, steady adaptation 
(presumably due to potassium currents) which is observed under current injection 
in neocortical pyramidal neurons, e.g., the RS and RS2 neurons of Agmon and 
Connors (1992). 
Fig. 4 C shows spike trains from two simultaneously recorded neurons stimulated 
with preferred direction motion. The longest gaps appear to occur at about the 
same time. To assess the correlation with a cross-correlogram, we first transform 
the spike trains to interval trains, shown in Fig. 4 D for the spike trains in C. 
This emphasizes the presence of long ISis and removes some of the information 
regarding the precise occurrence times of action potentials. The interval cross- 
correlation (ICC) between each pair of interval trains is computed and averaged 
over all trials, and the average shift predictor is subtracted. Fig. 4 E and F show 
ICCs (thick lines) for two different pairs of neurons. In 17 of 31 pairs (55%), there 
were peaks in the raw ICC that were at least 4 standard errors above the level of the 
shift predictor. The peaks were on average centered (mean 4.3 msec, SD 54 msec) 
and had mean width at half-height of 139 msec (SD 59 msec). 
To isolate the cause of the peaks, the long intervals in the trains were set to the 
mean of the short intervals. Long intervals were defined as those that accounted 
for 30% of the duration of the data and were longer than all short intervals. Note 
that this is only a small fraction of the number of ISis in the spike train (typically 
less than about 10%), since a few long intervals consume the same amount of time 
as many short intervals. Data from 300-1950 msec was processed, avoiding the 
on-transient and the lack of final interval. With the longest intervals neutralized, 
the peaks were pushed down to the level of the noise in the ICC (thin lines, Fig. 4 
E, F). Thus, 90% of the action potentials may serve to set a mean rate, while a few 
periods of long ISis dominate the ICC peaks. 
The correlated gaps are consistent with common inhibition to neurons in a local 
region of cortex, and this inhibition adds area to the spike train CCG peaks in 
the form of a broader base (not shown). The data analyzed here is from behav- 
ing animals, so the gaps may be related to small saccades (within the 0.5 degree 
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Figure 4: (A) The brisk response to coherent preferred direction motion is in- 
terrupted by occasional excessively long inter-spike intervals, i.e., gaps. (B) The 
suppressed response to null direction motion is interrupted by bursts of spikes. (C) 
Simultaneous spike trains from two neurons show correlated gaps in the preferred 
direction response. (D) The interval representation for the spike trains in C. (IS,F) 
Interval cross-correlograms have peaks indicating that the gaps are correlated (see 
text). 
74 W. BAIR, E. ZOHARY, C. KOCH 
fixation window) or eyelid blink. It has been hypothesized that blink suppression 
and saccadic visual suppression may operate through the same pathways and are 
of neuronal origin (Ridder and Tomlinson, 1993). An alternative hypothesis is that 
the gaps and bursts arise in cortex from intrinsic circuitry arranged in an opponent 
fashion. 
4 CONCLUSION 
Common input that causes central peaks on the order of tens of milliseconds wide in 
spike train CCGs is also responsible for causing the correlation in spike count at the 
time scale of two second long trials. Long-term correlation due to drifts in respon- 
sivity exists but is zero on average across all cell pairs and may represent a source of 
noise which complicates the accurate measurement of cell-to-cell correlation. The 
area of the peak of the spike train CCG within a window of +32 msec is the basis of 
a good prediction of the spike count correlation coefficient and provides a less noisy 
measure of correlation between neurons. Correlated gaps observed in the response 
to coherent preferred direction motion is consistent with common inhibition and 
contributes to the area of the spike train CCG peak, and thus to the correlation 
between spike count. Correlation in spike count is an important factor that can 
limit the useful pool-size of neuronal ensembles (Zohary et al., 1994; Gawne and 
Richmond, 1993). 
Acknowledgements 
We thank William T. Newsome, Kenneth H. Britten, Michael N. Shadlen, and J. 
Anthony Movshon for kindly providing data that was recorded in previous studies 
and for helpful discussion. This work was funded by the Office of Naval Research 
and the Air Force Office of Scientific Research. W. B. was supported by the L. A. 
Hanson Foundation and the Howard Hughes Medical Institute. 
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