1Sloan Center for Theoretical Neuroscience, California Institute of Technology, Pasadena, California 91125; 2Department of Neurobiology, State University of New York at Stony Brook, Stony Brook, New York 11794; and 3Computation and Neural Systems Program, California Institute of Technology 139-74, Pasadena, California 91125
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ABSTRACT |
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Reinagel, Pamela, Dwayne Godwin, S. Murray Sherman, and Christof Koch. Encoding of visual information by LGN bursts. Thalamic relay cells respond to visual stimuli either in burst mode, as a result of activation of a low-threshold Ca2+ conductance, or in tonic mode, when this conductance is inactive. We investigated the role of these two response modes for the encoding of the time course of dynamic visual stimuli, based on extracellular recordings of 35 relay cells from the lateral geniculate nucleus of anesthetized cats. We presented a spatially optimized visual stimulus whose contrast fluctuated randomly in time with frequencies of up to 32 Hz. We estimated the visual information in the neural responses using a linear stimulus reconstruction method. Both burst and tonic spikes carried information about stimulus contrast, exceeding one bit per action potential for the highest variance stimuli. The "meaning" of an action potential, i.e., the optimal estimate of the stimulus at times preceding a spike, was similar for burst and tonic spikes. In within-trial comparisons, tonic spikes carried about twice as much information per action potential as bursts, but bursts as unitary events encoded about three times more information per event than tonic spikes. The coding efficiency of a neuron for a particular stimulus is defined as the fraction of the neural coding capacity that carries stimulus information. Based on a lower bound estimate of coding efficiency, bursts had ~1.5-fold higher efficiency than tonic spikes, or 3-fold if bursts were considered unitary events. Our main conclusion is that both bursts and tonic spikes encode stimulus information efficiently, which rules out the hypothesis that bursts are nonvisual responses.
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INTRODUCTION |
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The dorsal lateral geniculate nucleus of the
thalamus (LGN) is the primary relay by which visual information from
the retina reaches the cortex. Retinal ganglion cells are connected to
LGN relay cells with relatively little divergence or convergence, so
the spatial receptive-field organization that the LGN inherits from the
retina is largely preserved. Rather than extracting new spatial
features in the visual input, the function of the LGN may be to
selectively transmit or "gate" visual information as a function of
time. Transmission could be facilitated, inhibited, or filtered by the
many nonretinal inputs to the LGN relay cell, for example, from the
brain stem, thalamic reticular nucleus, or cortex (reviewed in
Sherman and Guillery 1996; Sherman and Koch
1986
; Singer 1977
; see also Crick
1984
).
One mechanism by which the thalamus might gate visual information is
through controlled activation of It. The inward
current It is attributed to a low-threshold
calcium conductance (Guido and Lu 1995; McCormick
1992
; McCormick and Feeser 1990
; Steriade and Llinás 1988
), which is voltage dependent
(Coulter et al. 1989
). When this conductance is
inactive, at relatively depolarized membrane potentials, a brief
depolarizing pulse (such as might be generated by a presynaptic retinal
action potential) will cause an LGN relay cell to fire one or a few
unitary action potentials. If the cell experiences a prolonged
hyperpolarization (
100 ms), It becomes primed
or "deinactivated" (Jahnsen and Llinás
1984a
,b
). Once this has occurred, the cell will respond to a
depolarizing pulse with a characteristic burst of action potentials
riding the crest of a slower calcium spike (Scharfman et al.
1990
).
Thus each individual cell can be described as having a response mode
(burst or tonic) at each point in time, depending on the instantaneous
degree of It inactivation. To a first
approximation, the mode can be regarded as binary (Coulter et
al. 1989). When a cell is in tonic mode, it is poised to fire
one or more individual action potentials in response to an input, if it
fires at all; when a cell is in burst mode, its next response will be a
stereotyped burst. The bursts associated with It
can be distinguished reliably from tonic spikes on the basis of its
interspike interval (ISI) pattern (Lu et al. 1992
).
Therefore, on the basis of extracellular recordings, one can infer the
underlying response mode of a cell at the time of each observed response.
Under some conditions, such as low arousal or sleep, LGN cells become
uncoupled from retinal input (Coenen and Vendrik 1972; Fourment et al. 1984
; Livingstone and Hubel
1981
). In this physiological state the LGN relay cells are
relatively hyperpolarized, such that It is in a
primed state much of the time, i.e., the cells are predominantly in
burst mode. LGN cells then burst rhythmically and synchronously, due to
the biophysical properties of the current in conjunction with other
intrinsic membrane properties and local circuit properties (Bal
and McCormick 1997
; McCormick and Feeser 1990
;
Steriade and Llinas 1988
; von Krosigk et al.
1993
). These observations suggest the hypothesis that whenever
an LGN cell enters burst mode, the cell becomes uncoupled from visual
input. This hypothesis predicts that when bursts occur during visual stimulation, individual bursts will not be related systematically to
stimulus events.
In lightly anesthetized or awake animals, a mixture of tonic spikes and
arrhythmic bursts is found, with the ratio of responses occurring in
the two modes falling on a continuum (Guido et al. 1992,
1995
; Guido and Weyand 1995
;
Mukherjee and Kaplan 1995
). Under these conditions, when
bursting was varied pharmacologically, bursts were found to correlate
with enhanced detectability of near-threshold visual stimuli. The
improvement, due in part to the reduction in spontaneous activity, was
at the expense of response linearity that may be important for stimulus
discrimination (Godwin et al. 1996b
; Guido et al.
1995
). The correlation between detectability and burst fraction
suggests the hypothesis that the bursts directly encode visual
information. This hypothesis predicts that individual bursts can be
systematically related to individual stimulus events.
In the present study, we set out to determine whether these differences
between burst and tonic firing response modes correspond to differences
in visual information transmission properties. The "information" in
a neural response is defined as the extent to which observing the
response would reduce a receiver's uncertainty about the particular
visual stimulus, compared with not observing the response and relying
only on the average statistics of that stimulus (Rieke et al.
1997; Shannon and Weaver 1963
). We estimated the
information using a stimulus reconstruction method (Bialek et
al. 1991
; Rieke et al. 1997
). We found that both
burst and tonic firing modes relay roughly equivalent amounts of
stimulus-related information to visual cortex. Preliminary results of
this study have been reported in abstract form (Reinagel et al.
1997
).
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METHODS |
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Physiological methods
PREPARATION. We performed experiments on cats that we initially anesthetized with 3.5% halothane and then maintained after surgery on 0.5-1.5% halothane in a 70/30 mixture of N2O/O2. Cats were paralyzed with gallamine triethiodide (5.0 mg) and were artificially respired through a tracheal cannula. Paralysis was maintained with gallamine triethiodide (3.6 mg/h) and tubocurarine (0.7 mg/h). We treated wound margins and pressure points with a topical anesthetic. Cats were placed in a stereotaxic apparatus for recordings. Rectal temperature, heart rate, and end-tidal CO2 were continuously monitored and maintained within normal physiological limits.
Access to the LGN was obtained through a craniotomy (5.0 mm diam) centered at A 5.0, L 9.0. We recorded from single neurons in the LGN A-laminae with a tungsten-in-glass recording electrode [impedances 8-14 MCLASSIFICATION OF CELLS. We initially determined neuronal receptive-field position, center sign, size, and ocularity by plotting neuronal activity in response to small spots of light projected onto the tangent screen. We then replaced the tangent screen with a Tektronix 608 oscilloscope monitor for the presentation of test stimuli. We classified all neurons as X or Y using a battery of tests, including latency to electrical stimulation from optic chiasm, linearity of spatial summation, center size, and the response of the surround to a large, rapidly moving stimulus of opposite sign to the receptive-field center.
VISUAL STIMULATION. We presented a time-varying contrast signal to the cells on a Tektronix 608 monitor, with a space average luminance L0 = 60 cd/m2. Monitor contrast was controlled by a computer via a 12-bit A/D converter using the Picasso stimulus generation system (Innisfree).
The spatial form of the stimulus was a stationary sinusoidal grating presented through a fixed circular aperture (Fig. 1A). This particular spatial structure is not relevant to the analysis except that LGN relay cells respond well to its temporal modulation. We define contrast as (Lmax
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Numerical methods
All calculations were carried out in Matlab 5.0 (MathWorks).
BURST IDENTIFICATION.
We classified burst responses from extracellularly recorded spike
arrival times using previously published criteria (Godwin et al.
1996b; Guido et al. 1995
; Lu et al.
1992
). Our operational definition of a "burst" is a group
of action potentials each of which is <4 ms apart, with the first
spike in a burst preceded by a period of >100 ms devoid of spiking
activity. Previous intracellular recordings in this preparation
(Lu et al. 1992
) demonstrated that this ISI pattern is a
stringent criterion for identifying the bursts that are associated with
the low-threshold calcium conductance that results from
It. As additional evidence that these burst events in our data reflected It activity, in a
subset of experiments we also showed that these events were sensitive
to application of the metabotropic agonist ACPD (data not shown), which
slightly depolarizes LGN relay cells and thereby inactivates
It (Godwin et al. 1996b
).
ESTIMATION OF SPIKE TRAIN CODING CAPACITY.
Given an observed set of neural responses to a specific set of stimuli,
the information the responses could convey about the stimuli is limited
by the total variability of the response, i.e., the diversity of
different spike trains the cell uses across the entire range of
stimuli. In our analysis we represented neural responses, or components
of these responses (tonic or burst), as "spike trains," in which
the value in each time bin reflects the number of action potentials in
that interval. The variability of these spike trains may be quantified
in an information theoretical framework by an entropy rate, which has
units of bits per second. The entropy rate of a spike train is
analogous to the "baud rate" of a computer modem: a spike train
from an ensemble with a higher entropy rate has greater capacity for
carrying encoded information, although this capacity may or may not be
fully utilized. We call this entropy rate the "coding capacity" of
the response. Note that this is different from the "channel
capacity" of the neuron (Shannon and Weaver 1963),
which is the maximum coding capacity the cell could have to
any set of stimuli, using any code, based only on
its physical limitations.
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(1) |
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(2) |
ESTIMATION OF TRANSMITTED INFORMATION.
The information transmitted by an LGN response about the stimulus
contrast, Htrans, was estimated by computing the
optimal linear reconstruction of the stimulus from the spike train
(reviewed in detail in Rieke et al. 1997). Thus our
perspective is to ask how well a hypothetical recipient of the neural
response would be able to infer the stimulus. The stimulus property we
reconstructed was its contrast, but we note that reconstructing any
linear transform of the contrast by this method would have produced
identical results. For example, the temporal derivative of the contrast
is linearly related to the contrast; in our stimulus, the luminance at
the receptive field center is also linearly related to contrast.
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(3) |
OPTIMAL LINEAR FILTER.
The optimal filter (Fig. 2D), expressed as a function of
frequency, is uniquely given by h( f ) = SAB( f )/SAA( f ),
where SAB( f ) is the Fourier transform of the
cross-correlation between the spike train (A) and the
stimulus (B), and SAA( f ) is the Fourier transform of the autocorrelation of the spike train
(Wiener 1949). If spikes were always farther apart than
the extent of the filter in time, the optimal filter would be simply
the average stimulus preceding a spike (sometimes called the "reverse
correlation" or "spike-triggered average"). However, because
spikes are often close enough together that filters overlap in time in
the reconstruction, a correction is needed for the autocorrelation of
the spike train. For a spike train completely unrelated to the
stimulus, this filter is flat and equal to the mean of the stimulus.
ESTIMATION OF CODING EFFICIENCY.
The coding efficiency is the fraction of coding capacity used to
transmit visual information. We estimate the efficiency by
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(4) |
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RESULTS |
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We recorded a total of 35 cells from 6 cats in response to random temporal visual stimuli. We concentrate below on the quantitative analysis of data from 25 cells from 4 cats, for which we used stimuli with the properties described in METHODS (Fig. 1). This population consisted of nine ON-center X cells, eight ON-center Y cells, four OFF-center X cells, and four OFF-center Y cells. The remaining data showed qualitatively similar trends, but could not be analyzed by the same quantitative methods because of differences in the stimulus design.
Bursts are distinctive firing events
A representative short segment of the voltage trace from an
LGN relay cell in response to the randomly fluctuating visual stimulus
(Fig. 1) is shown in Fig. 3A.
The events identified as bursts by our criteria are marked with stars.
In all the cells we studied, we found that the responses contained
bursts intermingled with tonic spikes, as has been described previously
(Guido et al. 1992, 1995
; Lu et
al. 1992
; Mukherjee and Kaplan 1995
). We define
the "burst fraction" as the fraction of action potentials in a
trial that were found in bursts according to our ISI criterion (see
METHODS). The X cells we recorded had a lower burst
fraction (0.2 ± 0.2, mean ± SD) than the Y cells (0.6 ± 0.3).
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Under our recording conditions, LGN cells did not exhibit sustained
periods of burst (or tonic) mode, in the sense of extended stretches of
time during which exclusively burst (or tonic) activity occurred. Nor
was the occurrence of bursts oscillatory. We did not find any
consistent relationship of the burst fraction with the stimulus
parameters we varied. However, greater depth of anesthesia appeared to
increase the burst fraction (data not shown) (see also Guido and
Weyand 1995).
The distribution of successive pairs of ISIs could be analyzed in some very long trials, one of which is shown in Fig. 3B. For each action potential, a single point is plotted based on the preceding ISI (abscissa) versus the subsequent ISI (ordinate). The observed pattern is not that expected from a highly regular spike train, for which the points would fall on the diagonal. A conspicuous firing pattern observed in our data, evident as a clear cluster in this ISI plot, is the event identified by our burst criterion.
The shaded area at the bottom right of Fig. 3B
defines the criterion for the first spike of a burst: a preceding
interval of 100 ms, and a subsequent interval of
4 ms. All
subsequent spikes in bursts must by definition lie within the shaded
area on the left (preceding interval
4 ms). Those falling
within the box at the bottom left are spikes within a burst
(because the next interval is
4 ms, these are not the last spikes of
bursts). The cluster near the closed arrow represents the final spikes in bursts that were followed by a short interval; the cluster near the
open arrow represents the last spikes in bursts that were followed by a
long interval. Some but not all of the latter spikes are followed by
another burst. In this trial, 73% of the spikes were in bursts, with
an average of 2.9 spikes per burst. In other words, about half of the
independent firing events were bursts containing an average of about
three spikes.
To further explore the degree to which bursts were stereotyped events,
we measured the variability of the number of spikes in a burst within
individual trials. Figure 3C shows, for the data shown in
Fig. 3B, the distribution of the number of spikes in the
bursts. All bursts by definition have at least two spikes, but the
number of spikes per burst in this single trial varied from two to as
many as five. This variability in burst size can be quantified by the
coefficient of variation (CV), defined as the standard deviation
divided by the mean. The CV of number of spikes in a burst in this
trial was 0.26. This is less variability than would be found if the
number of spikes had been determined by a Poisson process for a fixed
duration, in which case the expected CV would be 1.0 (Gabbiani
and Koch 1998; Papoulis 1984
). Similar results
were found for all cells in this study: the mean number of spikes per
burst was 3.0 ± 1.4 (X cells) or 2.7 ± 0.5 (Y cells), and
the CV of burst size within individual trials was 0.25 ± 0.11 (X
cells) or 0.23 ± 0.05 (Y cells).
The timing of spikes within a burst was also stereotyped. The ISIs within a burst increased in length systematically. In the trial shown, the mean lengths for the first three intervals in a burst were 2.5, 3.0, and 3.4 ms, respectively; the mean length of the first postburst interval was much longer (360.3 ms; Fig. 3D). The sharp shoulder at 4 ms in the distribution of lengths for the later intervals in the bursts implies that some spikes that belong to a burst have not been classified as such due to the stringent 4-ms cutoff we impose on the ISI. The width of the distributions for within-burst intervals (SD is 0.4 for each of the 1st 3 intervals) indicates that the variability in the timing of spikes within burst was small. This variability was similar for all X and Y cells studied (not shown).
Taken together, the results presented in Fig. 3 confirm that in the responses to this novel dynamic stimulus, the burst criteria identify a frequent and stereotyped class of firing events having properties consistent with the bursts associated with the low-threshold calcium conductance.
Within-trial comparison of bursts to tonic spikes
We show the response of an LGN relay cell at the top of Fig. 4A. The cell was responsive to the stimulus, in that its firing rate varied with time as more and less excitatory stimulus sequences occurred in the random pattern. For example, with the use of a sliding 100-ms window to compute a time-varying firing rate, the LGN response in this trial was <10 Hz 85% of the time, but exceeded 40 Hz 2% of the time, and reached 90 Hz at its peak.
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The first step of our analysis was to identify the bursts in the LGN response and represent the burst and tonic spikes as separate "spike trains" for analysis (also shown in Fig. 4A). The "Tonic" channel contained all spikes not identified as parts of bursts. We either used all the spikes in each burst ("Bursts"), or represented each burst by a single event ("Burst Events"), as described in METHODS. The difference is that Burst Events lacked information about the number of spikes in the event. Neither representation was sensitive to the differences between bursts in the timing of spikes, because these differences were small (Fig. 3D) compared with our time bins (4.96 ms). We use the term spike train generically to refer to any kind of event train, including Tonic, Burst, or Burst Event response components.
Information transmission
The stimulus reconstruction we obtained from each component spike train (as described in METHODS1) is shown in Fig. 4A. Based on these reconstructions, we estimated the amount of visual information each spike train contained, at each temporal frequency present in the stimulus. The results for this trial are shown in Fig. 4C. The similarity in the shapes of these curves (inset) indicates that all the temporal frequencies present in this stimulus were encoded equally well by either tonic or burst responses. When stimuli contained higher frequencies, we sometimes observed qualitative differences in the shapes of these curves. However, longer recordings would have been necessary to determine the rolloff frequency from these high CF stimuli, because the estimation of the SNR at each frequency is noisier for broader band stimuli.
The overall transmission of visual information by each spike train (Htrans, Fig. 4F) is given by the area under each curve in Fig. 4C. The LGN response as a whole transmitted 3.4 bits/s of visual information about this stimulus. The tonic response transmitted 2.6 bits/s, and the bursts transmitted 2.4 bits/s, or 2.5 bits/s when they were treated as unitary events. To take into account differences in the number of events of each type (Fig. 4D), we expressed the information rate in units of bits per spike or event (Fig. 4G). We found that in this trial, the tonic spikes carried more information per action potential (0.9 bits/spike) than the bursts (0.4 bits/spike), but bursts regarded as unitary events encoded more information per event (1.4 bits/event).
The coding capacity of a spike train depends on both the number of spikes and the regularity of the spike train. We estimated the information coding capacity of each of the spike trains of Fig. 4A, based on the entropy of their ISI histograms (not shown). This estimate, Hcapacity (Fig. 4E), is the maximum information coding capacity for a spike train (binned at this resolution) that is consistent with the statistical regularity we observed (see METHODS). Although the burst response had many more spikes than the tonic response in this trial (Fig. 4D), the tonic spikes were more variable, such that both channels had about the same coding capacity (Fig. 4E).
The coding efficiency is defined as the fraction of the coding capacity used to carry information about this stimulus. On the basis of the maximum capacity (set by Hcapacity) and the minimum visual information (set by Htrans), we could determine the minimum efficiency, E (Fig. 4H). In this trial, tonic spikes and spikes in bursts had about the same coding efficiency (14 and 13%, respectively), whereas bursts regarded as events were somewhat more efficient (19%).
Interpreting the optimal filters
To obtain the linear reconstructions discussed above, we computed
the optimal linear filter for each spike type, based on the data from
this trial (see ESTIMATION OF TRANSMITTED INFORMATION in
METHODS). These optimal filters are shown in Fig.
4B. The filters for tonic and burst responses have similar
shapes, as revealed by scaling them all to the same peak
(inset). The small amplitude oscillations in the filter
reflect the temporal correlations in the visual stimulus, and depend on
the temporal cutoff frequency CF (not shown). The large positive lobe
between zero and 100 ms reflects that this ON-center Y
cell fired preferentially when the stimulus in the previous 100 ms was
brighter than average in the receptive field center (and thus, darker
than average in the immediate surround). The negative lobe between
100 and
200 ms indicates that the cell was also more likely to fire
if this interval was preceded by a stimulus that was dark in the
receptive field center (and thus, bright in the surround). In other
words, the cell integrated over ~200 ms, and responded best to
increases in luminance in the center or decreases
in luminance in the surround.
The similarity of the filter shapes can be measured by the correlation
coefficient between them, which can range from zero (no correlation) to
+1 (perfect correlation) or 1 (perfect anticorrelation). This measure
is insensitive to linear scaling of the filters. In the example of Fig.
4B, the burst and tonic filters have a correlation
coefficient of 0.92. We measured the correlation coefficient between
the burst and tonic filter, for every trial in which both burst and
tonic responses had at least 50 spikes encoding at least 0.1 bits per
spike. We found that burst and tonic filter shapes were always similar
(correlation coefficient 0.83 ± 0.11, n = 74 trials). We conclude that the two types of response always encoded
qualitatively similar messages about the visual stimulus.
The complete analysis shown in Fig. 4 was performed for every individual trial, to compare the coding properties of bursts to tonic spikes within trials. The key results we obtained from each trial were the information rates (expressed in bits per spike or per event), and the coding efficiencies (expressed as a fraction of coding capacity) of each response type.
Effect of on spike trains and visual coding
We varied the stimulus effectiveness by varying , the standard
deviation of the contrast modulation. Figure
5 shows results from a single cell as the
amplitude of the contrast modulation was increased from 0.01 to 0.20 in
different trials. This covers the range from stimuli that are well
below response threshold to ones that are well above it.
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As the contrast modulations were made stronger, firing rates increased
on average over the entire trial (not shown). The increase in firing
rate with was variable and relatively modest, possibly due to
adaptation to the amplitude of fluctuations in spatial contrast
(Smirnakis et al. 1997b
).
The spike train coding capacity (Hcapacity) increased with firing rate, but according to a different relationship for bursts and tonic spikes, as shown in Fig. 5A. Over the range of firing rates observed, the coding capacity (Hcapacity) of the tonic spike trains was close to the maximum possible, given our chosen temporal resolution of 4.96 ms. The coding capacity of bursts was much lower than this maximum at any given firing rate. This reflects the greater regularity in burst firing patterns. When this regularity is taken into account, by treating bursts as unitary events, bursts then had close to maximal entropy. These results emphasize the importance of measuring the entropy of the spike trains, rather than using firing rate as an indirect measure of coding capacity.
The rate of transmission of visual information
(Htrans) increased with the amplitude of
stimulus modulation. There was a baseline firing rate in the absence of
stimulation, approximated by = 0.01, for which no visual
information was encoded. Therefore, as
and therefore
Htrans increased, more information was encoded per spike (Fig. 5B), and the coding efficiency
(E) increased (Fig. 5C). In other words, the
timing of spikes became increasingly determined by the stimulus.
We performed an equivalent analysis of each cell in our study. The amplitude of stimulus modulation determined the absolute coding properties of both burst and tonic responses, but we did not find any evidence that this affected their relative coding properties. Therefore we include trials from all stimuli in our population summary below.
Population results
Whether measured in bits per event or in fractional coding efficiency, on a trial-by-trial basis the information encoded by the two response modes was similar. This is illustrated in Fig. 6 by the fact that all the points fall roughly along the diagonal. The approximate equivalence of burst and tonic spikes for coding this stimulus was supported by fact that ACPD reduced bursting (see METHODS), yet had little effect on visual coding. For 13 trials with a high burst fraction (0.45 ± 0.14), application of ACPD reduced the burst fraction by at least half (to 0.03 ± 0.03) in the cell's response to a stimulus with the same parameters. Despite the change in burst fraction, there was no statistically significant change in the average firing rate, coding capacity, information rate, or coding efficiency (not shown).
|
Although burst and tonic modes were essentially similar, several small differences were statistically significant in the within-trial comparisons. In most trials, the amount of visual information encoded per burst was greater than per tonic spike (see closed symbols in Fig. 6A). Information per burst was on average 2.7 times greater than per tonic spike (P < 0.001 by a binomial test, see legend). However, tonic spikes consistently encoded more information than bursts per action potential (1.8-fold more on avarage, P = 0.006, see open symbols in Fig. 6A). The coding efficiency (E) was higher for bursts than for tonic spikes (Fig. 6B), regardless of whether all the spikes in the burst are considered (1.5-fold, P = 0.011) or only the burst as an event (2.8-fold, P < 0.001).
The Y cells in our population encoded more information about this
visual stimulus than the X cells (i.e., circles, representing X cells,
are below and to the left of squares, representing Y cells, in Fig. 6,
A and B). However, the relative coding properties of bursts and tonic spikes were the same in both populations. The
coding efficiency (E = Htrans/Hcapacity) of
bursts was higher when bursts were treated as unitary events (closed
symbols are above open symbols in Fig. 6B). We attribute
this to two distinct reasons: the entropy rate
(Hcapacity) was lower, and the visual information (Htrans) was also higher (not
shown). Thus the additional variability contained within bursts,
considered at the temporal resolution of 4.96 ms, carried more noise
than linearly decodable visual information (but see McCormick
and Feeser 1990).
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DISCUSSION |
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Bursts encode visual information
We have shown that burst responses of LGN relay cells carry
information about the time-varying contrast of randomly changing visual
stimuli with temporal frequencies of up to 32 Hz. The coding efficiency
of tonic and burst responses was roughly similar within individual
trials, over a wide range of absolute coding efficiencies (Fig. 6). We
found that both bursts and tonic spikes can have information rates
exceeding 1 bit/spike. We observed examples of coding efficiency as
high as 60% for tonic spikes and 63% for bursts treated as single
events. In previous experiments using random stimuli and similar
analysis methods, typical estimates of information rates in other
sensory neurons were 1-3 bits per spike, and estimates of the average
coding efficiency in other sensory neurons ranged from 11 to 60%
(Bialek et al. 1991; Buracas et al. 1998
;
Rieke et al. 1993
; 1995
,
1997
; Warland et al. 1997
; Wessel
et al. 1996
).
These findings challenge the view that burst firing in the LGN is
exclusively a feature of the sleeping or pathological brain (McCormick and Feeser 1990; Steriade
1992
; Steriade and Llinás 1988
;
Steriade and McCarley 1990
; Steriade et al.
1993
). The fact that bursts participate in thalamic
oscillations in normal sleep or in pathological conditions does not
preclude the possibility that the same biophysical machinery could, in
other circumstances, transmit useful data. Indeed, visually driven
bursts have also been observed in the responses of LGN relay cells of
awake, visually behaving cats (Guido and Weyand 1995
)
and monkeys (Ramcharan et al. 1998
; P. Reinagel,
unpublished analysis of data from McClurkin et al.
1991
).
Our analysis was designed to be conservative with respect to assigning
visual function to bursts. For this reason, we used a stringent
criterion for identifying bursts. We also report only strict lower
bounds on visual information content and coding efficiency, so that the
information content and coding efficiency must be at least
what we report. We estimated the information content of each response
by an optimal first-order linear reconstruction. The result may be an
underestimate, for three reasons: 1) additional information
might be encoded in the spike trains in a form that could only be
reconstructed using higher order (nonlinear) terms; 2)
additional visual information might be encoded by spike time information at higher temporal resolution than the 4.96 ms time bins
used; and 3) the use of the power spectra to estimate the information in the reconstruction entails a worst-case assumption that
the errors are Gaussian. Moreover, our stimulus is unlikely to be
optimal for the cell, and natural stimuli in particular may be much
more efficiently encoded (Rieke et al. 1995). Therefore, future studies may well reveal additional visual information, and
higher coding efficiencies, in both the burst and tonic responses of
LGN relay cells.
Bursts are efficient
We did not find any evidence that bursts encode a special feature
of the visual stimulus. However, we found that a relay cell in burst
mode can transmit slightly more information in an event than the same
cell in tonic mode (Fig. 6A), and does so with slightly less
stimulus-unrelated response variability (Fig. 6B). These findings are consistent with prior indications that LGN bursts have
selective advantages in the detection of periodic visual stimuli with
comparable temporal frequencies (Guido et al. 1995).
There is precedent in other systems for the observation that bursts
carry qualitatively the same information as isolated spikes, but with
higher reliability (reviewed in Lisman 1997). In
pyramidal cells of the electrosensory organ of the fish
Eigenmannia, bursts and isolated spikes appear to detect
similar stimulus features, but the burst response appeared to be a more
reliable detector of the feature (Gabbiani et al. 1996
).
Similarly, ganglion cells of the salamander retina were found to fire
discrete bursts (Smirnakis et al. 1996
), and these
bursts were preceded by a narrower distribution of possible stimuli
than were single spikes (Smirnakis et al. 1997a
).
Temporal filtering by bursts
Previous experiments in vitro showed that LGN bursts follow
high-frequency stimulation poorly (McCormick and Feeser
1990), and in vivo experiments have suggested a role for bursts
in filtering out high frequencies in visual stimuli (Mukherjee
and Kaplan 1995
). When we averaged SNR curves over trials and
cells, we found that the average tonic SNR rolled off at somewhat
higher frequencies than the average burst SNR, in both X and Y cell
populations (not shown). From these population results, we cannot
distinguish whether there is a direct causal connection between
bursting and temporal filtering, or whether both filtering and bursting
both result from some common cause, such as hyperpolarization. To
explore this question further, it will be important to devise
experiments that allow for within-trial comparisons, so that visual
information in each frequency range may be attributed specifically to
the burst events and tonic events within the responses of one cell under a single physiological condition.
Control of burst mode
We have shown that switching the response mode of the LGN cell has
only minor consequences for the visual information content of the
cell's response. Our experiments do not address what mechanisms normally determine the response mode during visual processing (but see
Godwin et al. 1996b; Lu et al. 1993
).
Because burst mode reflects the activation of a voltage-dependent
conductance, it could in principle be influenced by any of the cell's
synaptic inputs, including cortical feedback (Sherman and
Guillery 1996
). Nonretinal inputs constitute the majority
(90-95%) of the synapses onto LGN relay cells (Erisir et al.
1997
), yet their function for vision is poorly understood. One
possible function could be to modulate the response mode of an LGN
cell, perhaps feeding back results of higher level visual processing or
implementing an automatic bottom-up form of attention. Our data neither
support nor exclude this possibility. If burst mode is controlled by
such mechanisms, we conclude that the consequences for vision would probably not be found at the level of the information
encoded by the LGN; the consequences of bursting might
instead be found at the level of its decoding.
Synaptic mechanisms
The temporal pattern of action potentials could have important
consequences for transmission of visual information across the
thalamocortical synapses (reviewed in Castro-Alamancos and Connors 1997b; Lisman 1997
; see also
Maass and Zador 1997
). Based on our results, to maximize
the recovery of visual information from the LGN, a synapse should
transmit both bursts and single spikes reliably, and transmit bursts as
unitary events. Indeed, layer 4 thalamocortical synapses with high
transmission probability and paired-pulse depression
(Castro-Alamancos and Connors 1996
, 1997a
; Stratford et al. 1996
) might have
these properties.
If other thalamocortical synapses are more like other cortical
synapses, with low transmission probability and paired-pulse facilitation, these could transmit a distinct, burst-only information stream. For example, the layer 6 targets of LGN relay cells might have
distinct information requirements. These cortical cells send axons back
to the LGN to modulate relay cell responses (Godwin et al.
1996a,b
; Sillito et al. 1994
), and also project
to the LGN cell targets in layer 4 to modulate the efficacy of the
primary feed-forward projection (Ferster and Lindstrom
1985a
,b
; Katz 1987
; Usrey and Fitzpatrick
1996
; Wiser and Callaway 1996
).
A direct test of these hypotheses will require measuring the postsynaptic potentials of cortical cells in response to a thalamic input spike train containing the pattern of ISIs of It bursts, as well as the ISI patterns characteristic of tonic LGN responses.
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ACKNOWLEDGMENTS |
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Computer programs used to generate stimulus sequences and for preliminary data analysis were generously shared by F. Gabbiani. We are indebted to B. Vaughan for adapting stimulus display software for the experiment.
P. Reinagel and C. Koch were supported by the Sloan Foundation Center for Theoretical Neuroscience as well as by the National Institute of Mental Health and National Science Founadation. D. Godwin and S. M. Sherman were supported by the National Institutes of Health.
Present address of D. Godwin: Dept. of Neurobiology and Anatomy, The Wake Forest University School of Medicine, Medical Center Blvd., Winston-Salem, NC 27157-1010.
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FOOTNOTES |
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Present address and address for reprint requests: P. Reinagel, Dept. of Neurobiology, Harvard Medical School, 220 Longwood Ave., Boston, MA 02115.
1 Figures 2 and 4-6 are related to one another hierarchically. In Fig. 2 (METHODS) we used a single spike train to illustrate the method by which we measure the transmission of visual information. In Fig. 4 we present the detailed results of such an analysis, for all the spike trains obtained from a single trial. We then demonstrate how the spike trains and their coding properties vary across trials for a single cell when the stimulus amplitude is varied in Fig. 5. Finally, we show the distribution of the key results over the entire population of cells in our study (Fig. 6).
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 25 August 1998; accepted in final form 15 December 1998.
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REFERENCES |
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