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Previous Article | Next Article
The Journal of Neuroscience, March 1, 2000, 20(5):1964-1974
Interspike Intervals, Receptive Fields, and Information Encoding in Primary Visual Cortex
Daniel S. Reich1, 2, Ferenc Mechler2, Keith P. Purpura2, and Jonathan D. Victor2 1 Laboratory of Biophysics, The Rockefeller University, New York, New York 10021, and 2 Department of Neurology and Neuroscience, Weill Medical College of Cornell University, New York, New York 10021
ABSTRACT
TOP
ABSTRACT
INTRODUCTION
In the primate primary visual cortex (V1), the significance of individual action potentials has been difficult to determine, particularly in light of the considerable trial-to-trial variability of responses to visual stimuli. We show here that the information conveyed by an action potential depends on the duration of the immediately preceding interspike interval (ISI). The interspike intervals can be grouped into several different classes on the basis of reproducible features in the interspike interval histograms. Spikes in different classes bear different relationships to the visual stimulus, both qualitatively (in terms of the average stimulus preceding each spike) and quantitatively (in terms of the amount of information encoded per spike and per second). Spikes preceded by very short intervals (3 msec or less) convey information most efficiently and contribute disproportionately to the overall receptive-field properties of the neuron. Overall, V1 neurons can transmit between 5 and 30 bits of information per second in response to rapidly varying, pseudorandom stimuli, with an efficiency of ~25%. Although some (but not all) of our results would be expected from neurons that use a firing-rate code to transmit information, the evidence suggests that visual neurons are well equipped to decode stimulus-related information on the basis of relative spike timing and ISI duration.
Key words: spike train; primary visual cortex; V1; information theory; white noise; receptive field; synaptic depression; synaptic facilitation; temporal coding; m-sequence; interspike interval
INTRODUCTION
Cortical sensory neurons have high intrinsic temporal precision (Mainen and Sejnowski, 1995
; Nowak et al., 1997
as and Albright, 1999
Here, we answer the first two questions experimentally by measuring the responses of neurons in the primary visual cortex (V1) of macaque monkeys to rapidly varying, pseudorandom ("m-sequence") stimuli. The interspike intervals (ISIs) of spike trains fired by these neurons fall into three subsets, distinguished on the basis of ISI duration, in a stereotyped manner across neurons. We use a reverse-correlation procedure to generate receptive field (RF) maps from the full responses as well as from response subsets that only contain spikes that follow ISIs of particular durations. Finally, we use information theory to quantify the rate and efficiency with which full responses and response subsets convey messages about the visual stimulus.
Our results indicate that spikes in different ISI subsets are fired in response to different visual stimuli. In particular, spikes preceded by ISIs <3 msec, which occur during periods of very high firing rate, tend to be evoked by stimuli that have several subregions of opposite contrast covering the neuron's receptive field. Each of these spikes also tends to convey more stimulus-related information than the average spike. On the other hand, spikes preceded by ISIs >38 msec are often fired in response to spatially uniform stimuli that reverse contrast over time.
The third question, concerning the ways in which these different messages are decoded, is not addressed directly by our experiments. We note at the outset that this question is conceptually independent from another much-debated question in cortical physiology: whether cortical neurons encode information through a rate code or a temporal code. In fact, both types of code can generate receptive-field maps and information rates similar to what is described here. However, the existence of stereotyped ISI durations in V1 (described in this paper), together with recently described synaptic and dendritic machinery (such as depression, facilitation, and coincidence detection) that can selectively increase or decrease the importance of particular spikes in shaping a postsynaptic response, suggests that real-time decoding of neuronal signals may rely on known biophysical mechanisms specifically sensitive to ISI duration.
MATERIALS AND METHODS
Recording and stimuli. We recorded the responses of single V1 neurons in opiate-anesthetized macaque monkeys (Reich et al., 1998
Our stimuli look to human observers like random and rapidly flickering checkerboards. In fact, however, the stimuli are highly structured. They consist of a grid in which the temporal sequence of the luminance levels (0 or 300 cd/m2) in each of 249 pixels (typically 16 × 16 arc-min) is determined by a pseudorandom, binary m-sequence (Sutter, 1992
Receptive field maps. Cross-correlation of an evoked spike train with the m-sequence stimulus
a process also known as "spike-triggered averaging"
To the degree that the neuron is a linear system, the derived RF map can also be considered to depict its "spatiotemporal impulse response"
Information. To measure the information contained in m-sequence responses, we use a method modified from Strong and colleagues (de Ruyter van Steveninck et al., 1997
To measure the full information in a spike train, we would need to use a limitless sample of infinitely long words containing infinitesimally short letters. This is clearly impossible, so we choose our word and letter lengths according to physiological criteria, taking into account factors such as integration time and temporal precision, and also according to the amount of available data, which limits the accuracy with which the word probabilities can be estimated. We use 14.8 msec words [the stimulus frame time, but also similar to the time constant of cortical neurons (Ogawa et al., 1981
The information that the neuron transmits about a particular stimulus is defined as the signal entropy, or variability, minus the noise entropy. The signal entropy is derived from the total set of words spoken by the neuron during the course of its response. The noise entropy is derived from the set of the words spoken at each particular time in the response, and it is averaged across the entire response duration. The signal entropy is calculated by constructing a probability table of all words in the response and applying Shannon's formula, Hs =
pjlog2pj (Cover and Thomas, 1991
1)/2N ln(2), in bits, where k is the number of possible words and N is the total number of words observed (Carlton, 1969
It is more difficult to obtain an accurate estimate of the noise entropy because we have access to only 16 trials, at most, for each neuron. However, we can obtain an upper bound on the noise entropy, and a lower bound on the transmitted information, by assuming that the letters in a word are independent of one another, and then adding the noise entropies letter by letter (Cover and Thomas, 1991
RESULTS
Interspike intervals
We report on the responses of 99 V1 neurons in anesthetized macaque monkeys to multiple repeats of pseudorandom (m-sequence) stimuli. These stimuli contain a wide variety of spatial and temporal patterns, none of which dominates the stimulus but some of which are typically effective stimuli for these neurons. The stimuli are therefore well suited to probe a neuron's ability to convert spatial information into spike trains.
Figure 1 shows interspike interval histograms (ISIHs) constructed from the response of a simple cell to both the m-sequence stimulus (solid line) and a uniform field of the same mean luminance (shaded gray region). The top panel is the standard ISIH, in which ISIs are collected into equal bins of 1 msec width. For both the m-sequence and uniform-field responses, the standard ISIH features a prominent peak at very short ISIs, which decays rapidly. The peak is higher for the m-sequence response than for the uniform-field response, but it has approximately the same width. After the initial peak and rapid decay, the m-sequence ISIH shows a secondary, slower decay that lasts from ~5 msec until 20 msec; this secondary decay is almost entirely absent from the uniform-field response. Finally, both responses begin a very slow decline, the "long tail" (Gerstein and Mandelbrot, 1964
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Figure 1. Construction of the log-interspike interval histogram (log-ISIH). Each panel shows the ISIHs of the m-sequence response (solid line) and the response to a uniform field at the same mean luminance (shaded) of a simple cell (44/9t) that fired 21.0 spikes/sec, 35,581 ISIs total. Top, Standard ISIH (1 msec bins); middle, standard ISIH plotted on a logarithmic time axis; bottom, log-ISIH consisting of 300 bins spaced logarithmically between 1 msec and 10 sec, which bracketed the distribution of ISIHs found in the data. Each bin is 3.1% larger than the previous one. We obtain a relatively smooth histogram by applying a uniformly distributed, random timing jitter to each ISI, the magnitude of which is at most half the data collection resolution of 0.1 msec. The log-ISIH allows us to easily distinguish three separate ISI peaks, which are not readily visible in the standard ISIH.
To more prominently display the short-ISI features, we plot the same standard ISIH on a logarithmic time scale (Fig. 1, middle panel). The similar shape of the initial peak and the differential secondary decay are clearly evident in this plot, as well. However, because the binning is relatively coarse at short ISIs and relatively fine at high ISIs, which obscures detail on both time scales, we present the data in yet another way. In the bottom panel, the histogram is constructed with logarithmic time bins so that the duration of each successive bin is a fixed multiple of the previous one. This "log-ISIH," a new way of looking at such data, highlights features such as prominent peaks or shoulders that are at best barely visible in the standard ISIH. The log-ISIH of the m-sequence response has three distinct peaks (corresponding, in the standard ISIH to the initial rapid peak, the secondary decay, and the long tail), whereas the log-ISIH of the uniform-field response has only two peaks (the initial rapid peak and the long tail). The differences between the log-ISIHs of the m-sequence response and the uniform-field response indicate that not all of the log-ISIH features are attributable to m-sequence stimulation. The similarity of the prominent short-ISI peak suggests that this feature, in particular, is largely intrinsic to the neuron.
In Figure 2, we replot the log-ISIH of the m-sequence response from Figure 1 (top panel), and we add log-ISIHs from three additional neurons. Each log-ISIH is subdivided, by eye, into its component peaks; the number of peaks varies from neuron to neuron. Thus, the top neuron has three peaks, the next two have two peaks (which differ in position), and the fourth neuron has only a single peak. Peaks are gray scale-coded according to the relative position of the maximum: black for short, light gray for medium, and dark gray for long ISIs. The bottom panel is a log-histogram of the estimated boundary between ISI peaks; it summarizes data from 66 neurons and includes 19 short/medium boundary points and 32 medium/long boundary points. Across all 99 neurons, 34 had a single peak, 46 had evidence of two distinct peaks, and 19 had three peaks. We found no significant difference between simple and complex cells in terms of the number of log-ISIH peaks (
2 test).
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Figure 2. Division of log-ISIHs into component peaks. The top four panels are the responses of different neurons to the m-sequence stimulus. Log-ISIHs consist of 200 bins spaced logarithmically between 0.1 msec and 2 sec, so that each bin is 5.1% larger than the previous one. Each log-ISIH is divided, by eye, into its component peaks, which are then color-coded according to the position of the maximum (black for <3 msec, light gray for 3-38 msec, and dark gray for >38 msec). Top, Same simple cell as in Figure 1; three peaks. Second panel, Simple cell (38/6), 5.9 spikes/sec, 11,343 ISIs; two peaks (short and long). Third panel, Simple cell (34/12t), 5.2 spikes/sec, 9,997 ISIs; two peaks (medium and long). Fourth panel, complex cell, 29.9 spikes/sec, 57,943 ISIs; one peak (medium). The boundary positions across 66 neurons are collected into a log-ISIH (bottom panel), which reveals a tightly clustered, bimodal distribution.
Two very surprising results emerge from this analysis. First, the summary histogram is bimodal. This reflects the fact that there are at most three log-ISIH peaks in any neuron's response. Moreover, neurons with only two log-ISIH peaks (the majority) have boundary points that match either the short/medium or medium/long boundary of the three-peak neurons, rather than some intermediate value. The medians of the two boundary points are 3.0 msec (90% range: 1.8-3.7 msec) and 38.1 msec (90% range: 20.3-64.8 msec). The second surprising feature of the summary histogram is that the two modes are quite sharp, which indicates that log-ISIH peaks are remarkably consistent across neurons. Because the boundary points do not correspond to temporal features of the stimulus, which occur in multiples of 14.8 msec, or to the frame time of the visual display, which was 3.7 msec, we suspect that they reflect some aspect of the intrinsic biophysical hardware of cortical neurons and/or their connections.
The consistency of the boundary points across neurons also raises the possibility that the subsets delimited by those boundaries play distinct roles in information encoding. To address this possibility, we divided the ISIs in each neuron's response into three subsets, applying the median boundary points across neurons regardless of the number of peaks in the particular neuron's log-ISIH. We considered ISIs <3 msec to be part of the short-ISI subset, ISIs between 3 and 38 msec to be part of the medium-ISI subset, and ISIs >38 msec to be part of the long-ISI subset. Averaged across neurons, we found that 10% of spikes fell into the short-ISI subset, 45% into the medium, and 45% into the long. Box plots showing the distributions across neurons of the percentage of spikes in each subset are drawn in Figure 5 (top).
The first step in demonstrating that the individual subsets play important roles in information encoding is to show that they are not epiphenomena of the firing rate modulation. To do this, we performed an "exchange resampling" procedure (Victor and Purpura, 1996
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Figure 3. Real versus exchange-resampled log-ISIHs. We compare the log-ISIHs (same parameters as in Fig. 2) of real spike trains (shaded) with those obtained from a resampling procedure that preserves the firing rate modulation and distribution of spikes per trial from the original data (solid lines). If the original data were consistent with a modulated Poisson process, then the original and resampled log-ISIHs in all panels would superimpose. Top row, left panel (asterisk), Complex cell (33/1), 31.7 spikes/sec, 61,556 ISIs. Top row, right panel (plus sign), Simple cell (39/9), 34.7 spikes/sec, 67,269 ISIs. Middle row, left panel, Simple cell (35/1), 10.0 spikes/sec, 19,283 ISIs. The other three log-ISIHs are from Figure 2.
Receptive field maps
For each neuron, we calculated RF maps or spike-triggered average stimuli (see Materials and Methods) from the full response and from response subsets, where the spikes in each subset were preceded by ISIs from a single ISI subset (short, medium, or long). Figure 4 shows example RF maps from two neurons, depicting representative examples of the changes that we saw across ISI subsets. RF maps are shown as a series of interpolated contour plots, each averaged over 14.8 msec of the response, at different time lags; taken together, they depict the dynamics of the RF. Red signifies on-subregions of the RF, in which bright stimuli were associated with a higher firing rate than dark stimuli, and blue signifies off-subregions. The ratio of the RF map scales of two subsets is equal to the ratio of the numbers of spikes in the two subsets.
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Figure 4. Receptive-field maps. A, Complex cell (33/1), average firing rate 31.7 spikes/sec, spatial extent 1°22' × 1°22', information rate 25.2 bits/sec or 0.79 bits/spike, efficiency 17.8%, log-ISIH in Figure 3 (asterisk). Calibration:
In general, we found that RF maps derived from spike subsets differed from RF maps derived from the full responses, and from each other, in both shape and amplitude. Figure 4A shows the RF map of a complex cell that primarily displayed both shape and amplitude changes. This cell fired an average of 31.7 spikes/sec in response to our stimulus, and its log-ISIH is shown in Figure 3 (asterisk). The RF map derived from all spikes (top row) is dominated by the off-subregion, although there is evidence of a weaker on-subregion. When only short-ISI spikes are considered (second row), however, the on-subregion is selectively enhanced in two ways: (1) its duration, measured with a resolution finer than what is shown in Figure 4A, is 42 msec instead of 19 msec; and (2) its peak amplitude, after correcting for the different numbers of spikes, is 2.9 times greater than the corresponding amplitude in the all-spikes RF map. The relative amplitude of the off-subregion is also enhanced in the short-ISI RF map, but only by a factor of 1.8 and not at all time lags. The shape of the short-ISI RF map suggests that these spikes may selectively encode stimuli that are characterized by strong spatial opponency.
A second prominent RF map change in Figure 4A occurs in the long-ISI subset (bottom row). For this subset, the single RF subregion has a biphasic time course, changing from off to on at ~89 msec, even while the RF maps of other subsets are still dominated by an off-subregion. The time course of the long-ISI RF map, and the fact that it is for the most part spatially uniform at each time lag, suggests that these spikes may primarily encode temporal features in the stimulus and that they typically follow, by at least 89 msec, a period during which the neuron was inhibited by the stimulus. Ignoring the ISI structure and treating all spikes equally obscures the effect of this inhibition.
Figure 4B is the RF map of a simple cell that fired an average of 34.7 spikes/sec in response to the m-sequence stimulus; the log-ISIH of its response is shown in Figure 3 (plus sign). The short- and medium-ISI RF maps show evidence of large amplitude changes but less evidence of large shape changes. In other words, scaling these subset RF maps by some factor (which we call the "efficacy"; see below) would make them look very similar to the all-spikes RF map. The long-ISI RF map, however, primarily exhibits a shape change: the off-subregion is relatively diminished between 30 and 59 msec, and the on-subregion is relatively enhanced between 59 and 74 msec.
Two related indices can be used to quantify these shape and amplitude changes. To obtain these indices, we treat the RF maps as vectors in space and time, with dimension equal to the product of the number of stimulus pixels and the number of time bins. We define the similarity index (DeAngelis et al., 1999
where f is the vectorized RF map of the full spike train, s is the vectorized RF map of the subset spike train, <... ,... > denotes the inner product, and
(1) ...
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Figure 5. Across-neuron distributions of RF map indices. Data from 66 neurons. Box plot whiskers show the 5th and 95th percentiles, and box boundaries show the 25th and 75th percentiles. The horizontal line divides each box at the median, and the square represents the mean. Top, Percentage of spikes with preceding ISIs <3 msec (short), 3-38 msec (medium), and >38 msec (long). Middle, Similarity index (or correlation coefficient) between the subset and full-response RF maps; values can be between
To measure amplitude changes, we calculate the efficacy, the factor by which the amplitude of the subset RF map must be scaled to best match the full RF map in a least-squares sense, after correcting for differences in the number of spikes. Mathematically:
(2) where nf is the number of spikes in the full spike train, ns is the number of spikes in the subset spike train, and other variables are as in Equation 1. An efficacy >1 signifies that subset spikes play a larger role in the generation of the all-spikes RF map than expected given the number of spikes in that subset, whereas an efficacy <1 signifies the opposite. An efficacy <0 would indicate that the RF map polarity must be flipped and then scaled to obtain the best match. The short-ISI RF map of Figure 4B has a particularly high efficacy of 1.77, signifying a large contribution from those spikes to the overall RF properties of that neuron. On the other hand, the medium-ISI RF map of Figure 4A has an efficacy of 1.02, indicating that those spikes contribute the expected amount to the overall RF map.
Across all neurons, similarity indices are in the range 0.5-1 (Fig. 5, middle), meaning that shape changes, although present, are only moderate. On the other hand, the efficacy distributions of the three subsets are distinct and largely nonoverlapping (Fig. 5, bottom), which indicates that short-ISI spikes make the largest contribution to the all-spikes RF maps, long-ISI spikes make the smallest contribution, and medium-ISI spikes contribute about as much as expected given their frequency.
Rate versus temporal encoding
To test whether our findings about shape and amplitude changes of RF maps are consistent with a rate code model of neuronal firing, we compared real data with the results of an exchange-resampling procedure. Exchange resampling exactly preserves the firing-rate modulation inherent in the original data, as described above. In fact, this procedure yields the only ensemble of spike trains that match the time-varying firing rate of real data and are rigorously consistent with a firing-rate model. We exchange-resampled each spike train 200 times, and we calculated the similarity indices and efficacies of the subset RF maps of those resampled spike trains. We used the same ISI subset definitions for resampled spike trains as we had for the real spike trains, despite the fact that the log-ISIHs were different (Fig. 3). We then compared the similarity indices and efficacies of the real responses with the means and distributions obtained from exchange-resampled responses.
Figure 6 shows a series of scatter plots that describe the relationship between similarity indices (left column) and efficacies (right column) for real and resampled responses. Each point represents a different neuron. The similarity index or efficacy of that neuron's real RF map is plotted along the horizontal axis, and the corresponding mean value from 200 exchange resamplings is plotted along the vertical axis. Results from different subsets are in different rows. In nearly all panels, the cloud of points lies near the line of equality, where real and resampled RF maps have the same similarity indices or efficacies. The major exception is the top right panel, which shows that the short-ISI efficacies tend to be higher for resampled RF maps than for real RF maps, indicating that short-ISI spikes play an even larger role in generating the RF properties of rate-code-generated spike trains than of real spike trains.
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Figure 6. RF map changes: real versus exchange-resampled. In each panel, we plot the similarity index (left column) and efficacy (right column) for real data on the horizontal axis, and the mean value of the same parameter derived from 200 exchange resamplings of the real data on the vertical axis. Data are from 66 neurons, and each point represents a different neuron. The exchange-resampling procedure tests the hypothesis that the observed RF map changes could have been generated by a neuron that fires spikes according to a rate code with exactly the same firing rate modulation as the original response. Filled squares represent subsets for which the real data were significantly different from the resampled data, that is, points that fell significantly (p < 0.05, two-tailed direct comparison) off the diagonal in each panel.
On a neuron-by-neuron basis, the similarity indices and efficacies of the real spike trains tended to fall in the tails of the distributions of similarity indices and efficacies of resampled spike trains. In Figure 6, solid points represent cases in which the real data fell within either 2.5% tail of the distribution of resampled data. However, the behavior of the two indices was qualitatively, and for the most part quantitatively, similar for real and resampled RF maps, suggesting that the rate code model does a reasonable job of explaining the indices (although not the ISI statistics).
Information
In addition to comparing RF maps, we calculated the stimulus-related information carried by spikes in the full spike train and in each ISI subset (see Materials and Methods) (de Ruyter van Steveninck et al., 1997
The results of the information calculation are shown in Figure 7. Not surprisingly, the full spike train conveys the most stimulus-related information on an absolute scale of bits per second (top), more than is carried by any subset of that spike train. Short-ISI spikes, which are rarest, convey the least information. On a neuron-by-neuron basis, the sum of the transmitted information across the three ISI subsets is larger than the information carried by the full spike train. This is perplexing, because the full spike train must contain as much information as the sum of its subsets. However, there are at least two explanations for this finding. First, because we calculated the information transmitted via a code consisting of 14.8 msec words and 3.7 msec letters, and because our method was designed to give us a lower bound on information in the first place, it is possible that we systematically underestimate the information in the full spike train to a greater extent than in the subset spike trains. Second, the three subset spike trains may contain redundant information. This is likely because the process of selecting a particular ISI subset necessarily places constraints on the other, nonoverlapping subsets. These constraints and redundancies are not taken into account in the word/letter code.
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Figure 7. Across-neuron distributions of transmitted information values. Data are from 98 neurons. As in Figure 5, box plot whiskers show the 5th and 95th percentiles, and box boundaries show the 25th and 75th percentiles. The horizontal line divides each box at the median, and the square represents the mean. The full response (leftmost distribution in each panel) is compared with each of the three ISI subset responses. Top, Transmitted information, measured in units of bits per second (bits/s). Middle, Transmitted information, bits per spike (bits/spike). Bottom, Efficiency, or percentage of the total signal entropy (see Materials and Methods) that is used to transmit stimulus-related information.
On a bits per spike scale (Fig. 7, middle), the short-ISI spikes, which convey the least information per second, are actually most informative: on average, each short-ISI spike conveys 4.6 bits of information about the stimulus, corresponding to the high efficacy of these spikes. Medium- and long-ISI subset spikes convey substantially less information, not much more than what is conveyed by each spike in the full spike train. This is also reflected in our measure of efficiency (de Ruyter van Steveninck et al., 1997
Finally, Figure 8 shows the neuron-by-neuron comparison between real and exchange-resampled information values, for the full spike train and for the three ISI subsets. The results are qualitatively similar to the results for the similarity index and efficacy, which are shown in Figure 6. In general, whether measured on a bits per second or bits per spike scale, and regardless of the particular ISI subset, the information in a real spike train is similar to the information in its exchange-resampled counterparts: most points lie along the line of equality. This means that the qualitative differences among subsets would be expected from neurons that use a rate code. On the other hand, nearly all points fall significantly off the line of equality (p < 0.05, two-tailed direct comparison,
vs
), indicating that on a neuron-by-neuron basis, the results are quantitatively inconsistent with the predictions of a rate code.
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Figure 8. Information: real versus exchange-resampled. In each panel, we plot the information in bits per second (bits/s) (left column) and bits per spike (bits/spike) (right column) for real data on the horizontal axis, and the mean value of the same parameter derived from 40 exchange resamplings of the real data on the vertical axis. Data are from 98 neurons, and each point represents a different neuron. The exchange resampling procedure tests the hypothesis that the observed RF map changes could have been generated by a neuron that fires spikes according to a rate code with exactly the same firing rate modulation as the original response. Filled symbols represent subsets for which the real data were significantly different from the resampled data, that is, points that fell significantly (p < 0.05, two-tailed direct comparison) off the diagonal in each panel.
DISCUSSION
Our results provide new evidence that different spikes within a single response can convey messages about different stimulus features, a finding that is consistent with earlier reports (McClurkin et al., 1991
In a pioneering study of the H1 neuron of the blowfly (de Ruyter van Steveninck and Bialek, 1988
Bursts
Our results suggest that short-ISI spikes are especially important for the transmission of visual information. These short-ISI spikes likely correspond to the class of spikes known as "bursts" (Connors and Gutnick, 1990
In the visual cortex, where the mechanisms of burst production are less well understood, several lines of evidence suggest that short-ISI spikes are particularly important for information transmission. Compared with other spikes, short-ISI spikes are differently tuned to certain stimulus attributes (Cattaneo et al., 1981
Information
We found that most V1 neurons convey between 5 and 30 bits/sec, or between 1 and 3 bits/spike. This range is consistent with information rates calculated from responses to similar stimuli in other systems, ranging from fly to primate (Bura
Another reason that the information rates are so different for the two kinds of stimuli is methodological: the "direct method" of calculating information used here makes no assumptions about the stimuli, but rather compares the response variability over time with the response variability across trials. Methods that typically yield lower information rates, on the other hand, evaluate a neuron's ability to discriminate between N particular stimuli, which limits the total amount of information that can be encoded to log2N. In this regard, it is important to realize that our stimuli are not optimized to drive V1 neurons to convey information at a rate close to their channel capacity.
Encoding and decoding
The processes of encoding and decoding information are logically distinct. It is possible, for example, that V1 neurons encode information into their rapidly modulated firing rates by means of a Poisson spike generator, consistent with a rate-coding model, even while they decode information by measuring presynaptic ISI durations. In this paper, we compare real responses with exchange-resampled responses, which we consider to be rate-coded because the spike times are determined only from the firing rate. Because exchange-resampling exactly preserves spike times, the firing rate fluctuations occur at the same rate as they do in real data.
According to one definition (Borst and Théunissen, 1999
In our view, the consistent presence of distinct ISI subsets across neurons, and the different types of visual information that can be extracted by examining spikes from the various subsets in isolation, suggest that ISI decoding may be an important feature of V1 neurons, just as it has been shown to be in much simpler systems such as the visceral ganglia of Aplysia (Segundo et al., 1963
Although our results provide support for the hypothesis that ISI decoding plays a role in information transfer in the visual cortex, they are also consistent with other types of decoding schemes that do not make use of ISIs. Such a scheme includes, for example, the estimation of firing rates through averaging across many neurons that convey similar information (Shadlen and Newsome, 1998
Real synapses may accomplish ISI decoding by means of processes such as short-term, real-time synaptic modification, including synaptic depression and facilitation (Gerstner et al., 1997
FOOTNOTES Received Sept. 27, 1999; revised Dec. 9, 1999; accepted Dec. 17, 1999.
This work was supported by National Institutes of Health Grants GM07739 and EY07138 (D.S.R.), NS36699 (K.P.), and EY9314 (J.D.V.). We thank Bruce Knight, David Reich, Jason Eisner, Steve Kalik, and Anne-Marie Canel.
Correspondence should be addressed to Daniel Reich, The Rockefeller University, 1230 York Avenue, Box 200, New York, NY 10021. E-mail: reichd{at}rockefeller.edu.
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