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The Journal of Neuroscience, August 15, 2002, 22(16):6837-6841
BRIEF COMMUNICATION
Precise Firing Events Are Conserved across Neurons
Pamela
Reinagel and
R. Clay
Reid
Department of Neurobiology, Harvard Medical School, Boston,
Massachusetts 02115
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ABSTRACT |
Sensory neurons can respond to dynamic stimuli with temporally
precise firing events. In the lateral geniculate nucleus (LGN) of the
thalamus, we found previously that when a flickering visual stimulus
was repeated, individual cells fired action potentials at the same time
in every trial to within 1 msec. We now show that these precise firing
events are also reproducible across cells of the same class. Therefore,
the mechanisms for producing precise timing must be conserved within a
cell class. Our results further suggest that cortical neurons would
require only a few generic processing mechanisms to extract the fine
temporal information available in their LGN inputs.
Key words:
reliability; precision; synchrony; timing; coding; thalamus; LGN; vision
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INTRODUCTION |
Lateral geniculate nucleus (LGN)
relay cells can be remarkably deterministic, with reliable and
temporally precise responses controlled primarily by the visual
stimulus and altered very little by noise (Reinagel and Reid, 2000 ).
Similar results have been found for many other visual neurons (Bair et
al., 1994; Berry et al., 1997; de Ruyter van Steveninck et al., 1997;
Bura as et al., 1998). Yet the reliability of each LGN neuron
does not imply similarity of different neurons. Reliable, precise
firing events could be determined by the idiosyncrasies of each LGN
cell and the retinal circuit providing its input (such as connectivity, synaptic strengths, dendritic branching, and balance of conductances). Indeed, heterogeneity of precise firing events might be expected because LGN neurons within a class, and their retinal inputs, vary
significantly in other temporal properties, such as the average time
courses of visual responses (Victor, 1987, 1988; Cai et al., 1997;
Wolfe and Palmer, 1998).
Precise temporal patterns of firing in the LGN carry rich information
about time-varying visual stimuli, such as a strong diffuse flicker;
however, whether this information is transmitted to the cortex depends
on the nature of the cortical responses to the LGN input. If cortical
cells discriminated LGN spike times to a precision of only 8 msec, they
could use <50% of the available information; but with 1 msec
precision, they could use >90% of the available information (Reinagel
and Reid, 2000). Moreover, if cortical targets could distinguish
different sequences of spikes, up to ~20% more information could be
extracted from some LGN cells (Reinagel and Reid, 2000). This raises
the question of whether cortical cells are sensitive to either precise
spike timing or spike interval patterns.
The synapse between LGN neurons and their targets in layer 4 of the
primary visual cortex can transmit LGN spikes with a temporal precision
of ~1 msec in vivo (Tanaka, 1983; Reid and Alonso, 1995). In addition, this thalamocortical transmission is sensitive to temporal
patterns: the efficacy of an LGN spike in driving a cortical target to
fire depends on the time since the previous spike, and even on the time
of the spike before that (Usrey et al., 2000). More generally, cortical
synapses are modulated in a complex but consistent manner by the
temporal pattern of input spikes (Markram and Tsodyks, 1996; Tsodyks
and Markram, 1997; Varela et al., 1997; Nelson and Abbott, 2001), and
cortical neurons produce spikes reproducibly when injected with large
time-varying currents (Mainen and Sejnowski, 1995). What was not known,
however, was whether the precise timing of visual responses in the LGN
was a reproducible phenomenon or an arbitrary property of each cell.
Therefore, we compared the responses of different LGN neurons to
determine whether precise firing events were conserved across cells of
a class, specifically ON and OFF X cells.
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MATERIALS AND METHODS |
Experimental procedures
Physiology. Individual neurons were recorded in the
LGN of cats anesthetized with sodium pentothal according to standard
methods, as described by Reinagel and Reid (2000). Cells were
classified by conventional physiological tests, including
spatiotemporal receptive field mapping (Reid et al., 1997) and a
modified null test to differentiate X and Y cells (Hochstein and
Shapley, 1976). Experimental data were recorded only for X cells in
this study. We included in our analysis all 12 well isolated cells from
which we recorded responses to 128 repeats of this visual stimulus: seven ON X cells and five OFF X cells recorded in four different experimental animals.
Visual stimuli. The visual stimulus was a spatially
uniform wide-field illumination that was modulated in time (diffuse
flicker). The time course of modulation was a random sequence of
luminance values drawn from the distribution measured in a natural
stimulus (Reinagel and Reid, 2000). The stimulus was displayed on a
computer monitor with photopic mean luminance (>10
cd/m2; eyes dilated) and a refresh rate of
128 Hz. Because the luminance value was chosen independently for each
time frame, the power spectrum of the stimulus was flat between 0 and
64 Hz (white noise).
Analysis
Identification of firing events. We presented the
same dynamic stimulus repeatedly for 128 trials and accumulated a
peristimulus time histogram (PSTH), which represents the probability of
firing as a function of time. We divided this PSTH into discrete firing events using the method of Berry et al. (1997). Briefly, the PSTH was
smoothed by a Gaussian filter whose width was determined by the
trial-to-trial jitter of spike timing, as computed from the autocorrelation between two trials. In this smoothed PSTH, minima that
were deep compared with adjacent maxima were taken as boundaries between distinct events. These boundaries were then used to divide the
original, unsmoothed PSTH into discrete firing events, such that all
spikes were assigned to one and only one event. We excluded from
additional analysis any event that was represented by <10 spikes over
all of the trials. We defined the time of the event as the mean of the
best-fit Gaussian to the peak in the unsmoothed PSTH and the precision
of the event as the width (2 ) of this Gaussian.
Alignment of events between cells. To compare event
timing across cells, we created an event train for each cell by
representing every peak as a single event, as defined above. We matched
corresponding events of different cells by a method originally
developed to compare the spike trains of a single cell in different
trials (Victor and Purpura, 1997). This elegant and efficient algorithm is based on a method used for aligning homologous genetic sequences. The optimal alignment of two event trains is defined in terms of the
shortest path to convert one into the other by means of three
elementary operations: deleting a spike, adding a spike, or shifting a
spike in time. The optimal alignment depends on one free parameter, the
"cost" of shifting a spike. This parameter defines how far we may
shift an event to align it with an event of the other cell. We chose
this cost parameter such that events separated by more than four times
the average width of events were considered distinct events. Many cell
pairs had a small systematic latency difference that affected all
events. We corrected for latency before aligning the events of the two
cells, based on time of the peak in the cross-correlation between the
PSTHs of the two cells. This latency correction ensured that the mean
difference in event time was 0 in all cases. The mean latency
correction was 2.9 msec (range, 0.3-6.2).
Normalized time difference. For each aligned peak, we
defined the normalized time difference as the difference in peak times between the two cells divided by the average width of the two peaks. Thus, if the Gaussian fits to the aligned PSTH peaks of two
cells are defined by
(µ1,1) and
(µ2,2) and the width
of each peak is defined as 2, then the normalized time difference of
the paired firing event is given by: (µ1  µ2)/1 + 2).
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RESULTS |
Precise firing events happen at the same times for
different cells
Our finding can be readily observed by direct inspection of the
data. When the same dynamic visual stimulus was presented repeatedly,
individual neurons responded with action potentials at the same precise
times in every trial (Fig.
1A). When the identical stimulus was used to study different cells, even in different animals,
the precise spike times were remarkably similar from cell to cell (Fig.
1, compare A and B). This similarity was found to
a greater or lesser degree for all cells of the same class (Fig.
1D). The remainder of our discussion quantifies this
observation for a small sample data set.
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Figure 1.
Precise firing events happen at the same times in
different cells. A, Responses of an LGN neuron
(ON-center X cell) to 128 repeats of the same dynamic visual stimulus.
Each row represents a single trial, with each action
potential represented by a single point; the
horizontal axis represents time (the first 500 msec of an 8 sec trial is shown; the time axis is shared with
B and C). B, Responses of
another ON-center X cell to the same stimulus, recorded in a different
animal. C, Luminance time course of the visual stimulus
(Stim) for the responses shown in A and
B. Spike events typically occurred between three and
four frames after a dark-to-light transition in the stimulus (frame
duration, 7.8 msec). D, Responses of all ON-center X
cells for which we recorded at least 128 trials with this stimulus (7 cells from 4 different animals). For each cell, 128 repeats are shown
for the first 2500 msec of the 8 sec trial. The spike times are aligned
relative to the stimulus onset, without correction for latency
differences among the cells. The mean firing rate of each cell for the
entire trial is indicated at the right. Cells 6 and 4 are expanded in A and B,
respectively.
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Precision of firing events of individual cells
The first step in quantifying the similarity of responses across
cells was to identify the times and precisions of the firing events in
each cell. Each peak in the PSTH was fitted by a Gaussian curve whose
width (2) we take as a measure of the trial-to-trial variability of
the event time (Fig.
2A). In the cell shown,
the peak widths ranged from 0.7 to 4.0 msec, with an average width of
2 = 2.1 msec (Fig. 2B). The distribution of
peak widths was similar for all cells (Fig. 2C), despite a
>10-fold range of the overall firing rate. The average width ranged
from 1 to 4 msec, and all cells had peaks of width of <1 msec. This
result is consistent with our previous finding that the temporal
precision required to extract all of the information in individual
spike trains is 1-2 msec for all cells, regardless of the firing rate
(Reinagel and Reid, 2000).
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Figure 2.
Precision of firing events across trials for
individual cells. A, PSTH for the cell shown in Figure
1A (average number of spikes in each 1 msec bin;
500 msec of the 8 sec trial is shown). The width of each peak (2, in
milliseconds) is indicated above. Peaks with <10 spikes were not
analyzed. B, Distribution of peak widths for the cell
shown in A. The mean and SD are indicated by the
point and line above the histogram
(2.1 ± 0.9 msec; n = 179 peaks).
C, Mean peak width for each cell recorded with this
stimulus: the seven ON-center X cells shown in Figure
1D (white bars) and five
OFF-center X cells (black bars). Error
bars indicate the SD over peaks (n = 85-329 peaks). Cell 6 is shown in A and
B.
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Peak timing differs by less than peak widths
The peaks in the firing rates of two cells are often aligned to
within a fraction of the widths of the peaks (Fig.
3A, PSTH). To formalize this observation, we used Victor and Purpura's (1997) method to identify the corresponding peaks of two cells. We allowed for
corresponding peaks to be separated up to four times the average peak
width for the two cells (for a maximum distance of ~8 msec). In the
example shown, 159 of 176 (90%) peaks in one cell were aligned to 1 of
the 179 peaks in the other cell. These peaks were aligned much more
precisely than required by our cutoff criterion (Fig. 3B,
black bars vs dashed lines). Most (94%) were
displaced by less than the average peak width of the two cells (1.8 msec). The magnitudes of peaks tended to scale with the average firing rate of the cell, but not always in a simple way (for example, the
second event from the right in Fig. 3A).
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Figure 3.
Peak timing differs by less than peak widths.
A, PSTHs for cells 6 (black) and 4 (red). A small systematic difference in latency
(1.6 msec) was removed before this analysis. The mean times of the
analyzed peaks for both cells are indicated by the tick
marks above. Numbers above the paired events
indicate the normalized time difference between the two cells, in units
of peak widths. B, Histogram of absolute time
differences for all paired events for these two cells (black
bars; n = 159). Because of the latency
correction, the mean time difference was 0 by construction.
Dashed lines indicate the minimum and maximum time
difference we allowed (4 times the average peak width, or 7.4 msec for
this cell pair). The blue curve shows the average
distribution obtained from time-shifted controls (averaged over 31 different time shifts with an average of n = 52 peaks matched by chance). C, Distribution of normalized
time differences for all paired events of this cell pair. The
blue curve shows the distribution of normalized time
differences for randomly matched events in time-shifted controls. The
SD of each distribution is given at the right; this is a
measure of the overall alignment precision for a pair of responses. As
a control for the uncertainty in our estimate of event times, we did
the same calculation for a single cell, comparing one-half of the data
set to the other half. This yielded a much narrower distribution of
normalized time differences (SD = 0.09). D, The SD
of the normalized time difference for all 21 possible pairings of the
seven ON cells (white bars; gray bar is
for pair shown in A-C) and all 10 pairings of the five
OFF cells (black bars). Results for time-shifted
controls are shown as blue points.
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To measure alignment on a peak-by-peak basis, we normalized the time
difference between cells by the average width of the two matched peaks.
A value of <1 indicates that the average spike time was more
precise from cell to cell than the timing of individual spikes from
trial to trial within each cell. For the cell pair shown, the
normalized time difference was 0.02 ± 0.51 peak widths (Fig.
3C) (Norm'd  t of example peaks shown in
Fig. 3A). In other words, 68% of peaks were aligned within
0.51 peak width, and 95% were aligned within 1.02 peak widths. The
SD of the normalized time difference is a measure of how well
any of the peaks of any two cells were aligned (summarized for the
population in Fig. 3D).
All pairs of cells of the same class had a substantial number of peaks
in common. In any pair, the cell with the lower firing rate had fewer
peaks, but those peaks tended to be aligned with peaks of the other
cell. For ON cell pairs, 80-100% of the peaks (of the cell with fewer
peaks) were aligned; 44-85% were aligned for OFF cell pairs. When we
measured the quality of the alignment, 16 of 21 ON cell pairs (Fig.
3D, white bars) and 5 of 10 OFF cell pairs
(black bars) had an SD of  1 for the normalized time
difference. Thus, for these cell pairs, most events were aligned even
more precisely than the trial-to-trial precision of either cell.
As a control, for each cell pair we compared the responses of the two
cells to different segments of the visual stimulus. In these
time-shifted controls, considerably fewer peaks were aligned by chance,
and these were equally likely to be shifted by any amount of time
within the range allowed (Fig. 3B, blue curve).
Therefore, the normalized time difference (our measure of the precision
of alignment) also had a broad distribution (Fig. 3C,
blue curve). For all cell pairs, the true alignment of peaks (Fig. 3D, bars) was much more precise than for
the time-shifted controls (Fig. 3D, blue
dots).
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DISCUSSION |
Cells in the LGN can respond with precise firing events whose
widths are on the order of milliseconds. Here we have shown that the
timing of these events is conserved among cells of a given class, even
in different animals. LGN cells of a class differed in firing rate,
absolute latency, the number of peaks, and the heights of peaks,
without altering the relative timing or temporal precision of these
firing events. The striking invariance of event timing suggests that
this may be a functionally important feature of LGN responses.
Origins of conserved patterns
It is likely that event times are at least as well conserved in
retinal ganglion cells, which provide the feedforward input to the LGN
neurons we studied. To the extent that intrinsic properties or circuit
connectivity vary in the retina and LGN, those physiological parameters
are apparently not important in determining the precise timing of
firing events. In the retina, simultaneously recorded cells of the same
class were found to transmit redundant information about a full-field
visual stimulus (Warland et al., 1997). Keat et al. (2001) presented a
20 parameter model that can predict the precise firing events of
individual retinal ganglion cells or LGN neurons. In some cases, two or
more cells of the same class were analyzed, and the parameters that fit
the cells were similar. These results are consistent with our findings.
Generality of results
In this study, we found that precisely timed firing events were
conserved within broad classes of cells (ON and OFF center X cells). We
have shown the analysis of responses to a spatially uniform random
flicker (white noise) with a natural distribution of luminance values.
We found qualitatively similar results for other spatially uniform
stimuli: a binary black-white random flicker (Reid et al., 1997) (Fig.
4A) and a temporally
nonwhite stimulus whose luminance time course was taken from a recorded
natural scene (van Hateren, 1997) (Fig. 4B). It
remains to be seen whether a similar conservation of firing events is
found within other cell types in the LGN and whether this result is
restricted to spatially uniform stimuli.
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Figure 4.
Examples of conserved firing events for other
stimuli. A, Responses of two OFF X cells recorded in two
different animals. The visual stimulus (Stim) was a
wide-field binary flicker with the luminance time course shown beneath.
B, Responses of another two OFF X cells (cells 8 and 9 of Fig. 2C), recorded sequentially in the same animal.
The stimulus was a spatially uniform field modulated with a luminance
time course recorded from nature, shown beneath. In both
A and B, spike times are shown relative
to the stimulus time, with no correction for differences in absolute
latency. For each cell, spike times are shown for 128 repeats of the
stimulus for 1 sec in the middle of an 8 sec trial.
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Another example of conserved firing patterns has been reported recently
for the motion-sensitive neuron H1 of the fly. In that study, an
information-theoretic measure was used to quantify the similarity
between H1 neurons in different flies. The visual information was
measured from the responses of each H1 cell separately (such that each
cell could have a unique neural code) and compared with the information
in the pooled responses of several H1 cells (such that all cells were
constrained to use a common code). In the case of H1, 70% of the
information was found to be universal for the cell class; that is, it
did not depend on knowing which H1 neuron produced a given
response (Schneidman et al., 2001). We performed the same analysis
and found that most of the visual information in our LGN responses was
universal for a given class (75% of information was universal for ON X
cells, 78% was universal for OFF X cells; data not shown).
Consequences for downstream neurons
Our stimuli subtended 5-10 receptive field diameters, not the
entire visual field. This might resemble the situation in which an
identical visual stimulus abruptly covers a local neighborhood of
receptive fields, such as when an object moves across part of the
visual field or when the animal makes a saccade across an edge between
uniform regions of an image. Our result suggests that in this
situation, the local population of LGN neurons could signal this event
with a temporally precise and nearly synchronous response, regardless
of whether they share common retinal ganglion cell inputs. A
convergence of several synchronous spikes would be a highly effective
input to cortical targets (Alonso et al., 1996; Usrey et al.,
2000).
Apart from of the issue of synchrony, there is the question of whether
reproducible temporal patterns in the LGN are important to downstream
neurons. It was known that single neurons produce reliable patterns of
spikes (Bair et al., 1994; Berry et al., 1997; de Ruyter van Steveninck
et al., 1997; Buraas et al., 1998; Reinagel and Reid, 2000) and
that dynamic synapses respond to a given pattern of spikes in a
reproducible way (Markram and Tsodyks, 1996; Abbott et al., 1997;
Dobrunz et al., 1997; Tsodyks and Markram, 1997; Varela et al., 1997;
Dobrunz and Stevens, 1999). The fact that spiking patterns are
reproducible across the LGN cell class now raises the question of
whether the dynamics of thalamocortical synapses are also stereotyped
for the presynaptic and postsynaptic cell class, as is the case among
cortical interneurons (Gupta et al., 2000). If so, cortical targets of
a given class could also have consistent temporal responses to
equivalent visual stimuli and precisely synchronized responses to
simultaneous large-field stimuli.
In conclusion, we have argued previously that precise temporal patterns
of firing in the LGN are visually driven and that they could provide a
rich source of visual information to the cortex. Our finding that this
complexity can be reduced to just a few types of temporal patterns
lends much greater plausibility to the hypothesis that the patterns
might be decoded in the cortex and might play an important role in vision.
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FOOTNOTES |
Received Dec. 18, 2001; revised April 12, 2002; accepted May 1, 2002.
This work was supported by National Eye Institute Grants R01 EY10115,
R01 EY12815, and P30 EY12196. We thank Christine Couture for expert
technical assistance and Sergey Yurgenson for software support.
Correspondence should be addressed to Dr. R. Clay Reid, Department of
Neurobiology, Harvard Medical School, 220 Longwood Avenue, Boston, MA
02115. E-mail clay_reid{at}hms.harvard.edu.
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R. D. Kumbhani, M. J. Nolt, and L. A. Palmer
Precision, Reliability, and Information-Theoretic Analysis of Visual Thalamocortical Neurons
J Neurophysiol,
November 1, 2007;
98(5):
2647 - 2663.
[Abstract]
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B. Tripp and C. Eliasmith
Neural Populations Can Induce Reliable Postsynaptic Currents without Observable Spike Rate Changes or Precise Spike Timing
Cereb Cortex,
August 1, 2007;
17(8):
1830 - 1840.
[Abstract]
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K. S. Gaudry and P. Reinagel
Benefits of Contrast Normalization Demonstrated in Neurons and Model Cells
J. Neurosci.,
July 25, 2007;
27(30):
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[Abstract]
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S. Augustinaite and P. Heggelund
Changes in firing pattern of lateral geniculate neurons caused by membrane potential dependent modulation of retinal input through NMDA receptors
J. Physiol.,
July 1, 2007;
582(1):
297 - 315.
[Abstract]
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X. Hu, H. Jiang, C. Gu, C. Li, and D. L. Sparks
Reliability of oculomotor command signals carried by individual neurons
PNAS,
May 8, 2007;
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[Abstract]
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A.-M. M. Oswald, B. Doiron, and L. Maler
Interval Coding. I. Burst Interspike Intervals as Indicators of Stimulus Intensity
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April 1, 2007;
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J. D. Victor, E. M. Blessing, J. D. Forte, P. Buzas, and P. R. Martin
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B. N. Lundstrom and A. L. Fairhall
Decoding stimulus variance from a distributional neural code of interspike intervals.
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C. P. Billimoria, R. A. DiCaprio, J. T. Birmingham, L. F. Abbott, and E. Marder
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R. Schaette, T. Gollisch, and A. V. M. Herz
Spike-Train Variability of Auditory Neurons In Vivo: Dynamic Responses Follow Predictions From Constant Stimuli
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A. Vogel, R. M. Hennig, and B. Ronacher
Increase of Neuronal Response Variability at Higher Processing Levels as Revealed by Simultaneous Recordings
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R. Balu, P. Larimer, and B. W. Strowbridge
Phasic Stimuli Evoke Precisely Timed Spikes in Intermittently Discharging Mitral Cells
J Neurophysiol,
August 1, 2004;
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[Abstract]
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V. J. Uzzell and E. J. Chichilnisky
Precision of Spike Trains in Primate Retinal Ganglion Cells
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R. Jolivet, T. J. Lewis, and W. Gerstner
Generalized Integrate-and-Fire Models of Neuronal Activity Approximate Spike Trains of a Detailed Model to a High Degree of Accuracy
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August 1, 2004;
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J.-M. Fellous, P. H. E. Tiesinga, P. J. Thomas, and T. J. Sejnowski
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March 24, 2004;
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S. Schreiber, J.-M. Fellous, P. Tiesinga, and T. J. Sejnowski
Influence of Ionic Conductances on Spike Timing Reliability of Cortical Neurons for Suprathreshold Rhythmic Inputs
J Neurophysiol,
January 1, 2004;
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[Abstract]
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D. M. Blitz and W. G. Regehr
Retinogeniculate Synaptic Properties Controlling Spike Number and Timing in Relay Neurons
J Neurophysiol,
October 1, 2003;
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[Abstract]
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E. J. Chichilnisky and R. S. Kalmar
Temporal Resolution of Ensemble Visual Motion Signals in Primate Retina
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TOP
ABSTRACT
INTRODUCTION
