Cross-correlations DO NOT imply synchrony

[Carlos Brody]

Cross-correlations DO NOT imply synchrony: announcing 3 papers
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Suppose that you record from two stimulus-driven cells simultaneously,
over many trials. Interested in whether they are synchronized, you
compute the average cross-correlogram of their spike trains. (For the
initiated, you compute their shuffle-corrected cross-correlogram, so
as to get rid of direct stimulus influences.) You find, in the
resulting correlogram, that there is a narrow peak, centered at zero,
with a width of say 15 ms. "Ah! The cells are synchronized on a 15-ms
timescale!" you conclude.

In concluding this you will be doing what most people do, and what
most papers in the literature do.

THIS CONCLUSION DOES NOT NECESSARILY FOLLOW.

How and why? If the PSTHs of the cells have narrow peaks, by which I
mean as narrow as the peak in the xcorrelogram itself, then even if
the mechanism synchronizing the cells has a very very slow timescale
(e.g. tens of seconds), the xcorrelogram will have a narrow peak.

Such a peak would NOT be an artifact. It arises ONLY if there *IS* an
interaction -- synchrony, if you will -- between the two cells. What
is wrong is the conclusion regarding the timescale of the interaction.
A narrow peak (tens of ms) does NOT necessarily mean a fast
interaction or a fast timescale of synchronization. Wrong
interpretations of this sort can make nonsense of the arguments one is
making with respect to the data. An example in point is Sillito et
al. "Feature-linked synchroni`zation of thalamic relay cell firing
induced by feedback from the visual cortex", Nature 369: 479-482
(1994). A paper recently published in J. Neurophysiol (see pointer
below) uses a simple biophysical model to go through that example in
detail. It shows how one can get exactly the same xcorrelograms
Sillito et al. got, but without any binding-related (i.e. fast)
synchrony at all. Instead, in the model the only interaction between
the cells is that their resting potential slowly covaries over the
trials of the experiment. That slow (tens of seconds) covariation
reproduces Sillito et al.'s data in remarkable detail.

Two other papers, in press in Neural Computation, go through these
kind of issues in a more abstract manner. The first describes the
problem, and tries to provide rules of thumb for being alert to when
interpretation problems may arise. The second paper suggests a couple
of methods to try to disambiguate interpretations.

Comments welcome.

Carlos Brody
carlos at sonnebend.ifisiol.unam.mx       http://www.cns.caltech.edu/~carlos



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SLOW COVARIATIONS IN NEURONAL RESTING POTENTIALS CAN LEAD TO
ARTEFACTUALLY FAST CROSS-CORRELATIONS IN THEIR SPIKE TRAINS.

by C.D. Brody

J. Neurophysiol., 80: 3345-3351 (Dec 1998)

Reprint also at 
http://www.cns.caltech.edu/~carlos/papers/slowcovs.pdf


A model of two lateral geniculate nucleus (LGN) cells, that interact
only through slow (tens of seconds) covariations in their resting
membrane potentials, is used here to investigate the effect of such
slow covariations on cross-correlograms taken during stimulus-driven
conditions. Despite the slow time-scale of the interactions, the model
generates cross-correlograms with peak widths in the range of 25 --
200 milliseconds. These bear a striking resemblance to those reported
in studies of LGN cells by \cite{Sillito94}, which were taken at the
time as evidence of a fast spike timing synchronization interaction;
the model highlights the possibility that those correlogram peaks may
have been caused by a mechanism other than spike synchronization. Slow
resting potential covariations are suggested instead as the dominant
generating mechanism. How can a slow interaction generate covariogram
peaks with a width 100 to 1000 times thinner than its timescale?
Broad peaks caused by slow interactions are modulated by the cells'
PSTHs. When the PSTHs have thin peaks (e.g., tens of milliseconds),
the cross-correlogram peaks generated by slow interactions will also
be thin; such peaks are easily misinterpretable as being caused by
fast interactions. Though this point is explored here in the context
of LGN recordings, it is a general point and applies elsewhere. When
cross-correlogram peak widths are of the same order of magnitude as
PSTH peak widths, experiments designed to reveal short-timescale
interactions must be interpreted with the issue of possible
contributions from slower interactions in mind.


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http://www.cns.caltech.edu/~carlos/papers/nosynch.ps.Z
                                          nosynch.pdf


CORRELATIONS WITHOUT SYNCHRONY

by C.D. Brody

In press, Neural Computation

Peaks in spike train correlograms are usually taken as indicative of
spike timing synchronization between neurons. Strictly speaking,
however, a peak merely indicates that the two spike trains were not
independent.  Two biologically-plausible ways of departing from
independence which are capable of generating peaks very similar to
spike timing peaks are described here: covariations over trials in
response {\em latency} and covariations over trials in neuronal {\em
excitability}. Since peaks due to these interactions can be similar to
spike timing peaks, interpreting a correlogram may be a problem with
ambiguous solutions. What peak shapes do latency or excitability
interactions generate? When are they similar to spike timing peaks?
When can they be ruled out from having caused an observed correlogram
peak?  These are the questions addressed here. A companion paper
\citep{Brody98b} proposes quantitative methods to tell cases apart
when latency or excitability covariations cannot be ruled out.


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http://www.cns.caltech.edu/~carlos/papers/disambiguating.ps.Z
                                          disambiguating.pdf


DISAMBIGUATING DIFFERENT COVARIATION TYPES

by C.D. Brody

In press, Neural Computation

Covariations in neuronal {\em latency} or {\em excitability} can lead
to peaks in spike train covariograms which may be very similar to
those caused by spike timing synchronization \citep{Brody98a}. Two
quantitative methods are described here: (1) A method to estimate the
excitability component of a covariogram, based on trial-by-trial
estimates of excitability. Once estimated, this component may be
subtracted from the covariogram, leaving only other types of
contributions. (2) A method to determine whether the covariogram
could potentially have been caused by latency covariations.


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