Department of Electrical and Computer Engineering, Vanderbilt University, Nashville Tennessee 37235
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ABSTRACT |
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Snider, R. K., J. F. Kabara, B. R. Roig, and A. B. Bonds. Burst firing and modulation of functional connectivity in cat striate cortex. J. Neurophysiol. 80: 730-744, 1998. We studied the influences of the temporal firing patterns of presynaptic cat visual cortical cells on spike generation by postsynaptic cells. Multiunit recordings were dissected into the activity of individual neurons within the recorded group. Cross-correlation analysis was then used to identify directly coupled neuron pairs. The 22 multiunit groups recorded typically showed activity from two to six neurons, each containing between 1 and 15 neuron pairs. From a total of 241 neuron pairs, 91 (38%) had a shifted cross-correlation peak, which indicated a possible direct connection. Only two multiunit groups contained no shifted peaks. Burst activity, defined by groups of two or more spikes with intervals of 8 ms from any single neuron, was analyzed in terms of its effectiveness in eliciting a spike from a second, driven neuron. We defined effectiveness as the percentage of spikes from the driving neuron that are time related to spikes of the driven neuron. The effectiveness of bursts (of any length) in eliciting a time-related response spike averaged 18.53% across all measurements as compared with the effectiveness of single spikes, which averaged 9.53%. Longer bursts were more effective than shorter ones. Effectiveness was reduced with spatially nonoptimal, as opposed to optimal, stimuli. The effectiveness of both bursts and single spikes decreased by the same amount across measurements with nonoptimal orientations, spatial frequencies and contrasts. At similar firing rates and burst lengths, the decrease was more pronounced for nonoptimal orientations than for lower contrasts, suggesting the existence of a mechanism that reduces effectiveness at nonoptimal orientations. These results support the hypothesis that neural information can be emphasized via instantaneous rate coding that is not preserved over long intervals or over trials. This is consistent with the integrate and fire model, where bursts participate in temporal integration.
Current concepts of the receptive field organization and behavior of visual cortical cells have been developed almost entirely from single-unit recordings. In general, these recordings have been interpreted on the basis of average firing rate as the primary response indicator. The historical roots of this approach lie in the demonstration by Adrian and Zotterman (1926) Preparation
Six adult cats (2.5-4.0 kg) were prepared for electrophysiological studies following guidelines established by the American Physiological Society and Vanderbilt University's Animal Care and Use Committee. Each cat was injected intramuscularly with 0.5 ml acepromazine maleate (TechAmerica, Elwood, KS) and 0.5 ml atropine sulfate (Elkins-Sinn, Cherry Hill, NJ). After ~45 min, the cats were anesthetized with 5% halothane (Fluothane, Ayerst, Philadelphia, PA) in O2. After cannulating two forelimb veins, the halothane was discontinued and anesthesia was maintained with intravenous injection of 0.4 mg·kg Stimulation
Stimuli were presented on a monochromatic CRT display (Tektronix 608; mean luminance 30 cd/m2, P31 phosphor) with a 10° circular field and 256-Hz frame rate. Initially in these experiments a Video Monitors 20 inch gray-scale monitor with a 60-Hz frame rate was used, but this was discontinued because the 60-Hz frame rate had the undesirable effect of introducing periodic peaks in the cross-correlation histograms. The periodic peaks resulted from synchronous entrainment of cortical neurons by the screen refresh rate (Snider et al. 1996 Data acquisition
Multiunit action potentials were recorded with single tungsten-in-glass microelectrodes (Levick 1972
INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References
that the amplitude of a sensory signal is well represented by the firing frequency (rate code) of the neuron. This viewpoint has had considerable influence on the interpretation of neural responses and has provided the philosophical framework for the wide acceptance of averaged poststimulus time (PST) histograms as indicators of neural responsiveness. However, the sequential averaging of histograms eliminates any information about the temporal relationships of individual spikes.
). Information theory predicts that the more random a signal, the more information it contains, provided the proper decoding mechanism exists (Shannon 1948
). Thus the more random the intervals between the spikes and the more precisely these intervals can be detected, the more information a neuron could convey to other neurons. This general principle has stimulated research into the representation of information by specific temporal patterns within spike trains (e.g., Dayhoff and Gerstein 1983a
; Lestienne and Strehler 1987
; Richmond et al. 1990
).
) tend to constrain interval-based coding schemes involving very short or extremely long intervals, at least in single neurons. Although longer time constants have been measured, the number of synapse traversals required for cognitive processing tasks (Thorpe and Imbert 1989
) puts a practical limit on the integration time allowable at each stage (see DISCUSSION). The fact that transmitter release is a probabilistic function (del Castillo and Katz 1954
) adds to the uncertainty that a highly precise mechanism can be used in decoding.
; Abeles et al. 1993
; Dayhoff and Gerstein 1983a
,b
; Frostig et al. 1990a
,b
; Lestienne and Strehler 1987
, 1988
; Stein 1967
) have been based on an empiric search for patterns in the output of single neurons, the spike train. A second method for analyzing the neural code is to start at the other end and examine what information a target neuron could reasonably be expected to extract from a single spike train (Bialek and Rieke 1992
; Bialek et al. 1991
). We have taken this approach to shed some light on the operational transfer of information between two cortical cells. In earlier work (Debusk et al. 1997
), we have described how the generation of bursts can be affected by the form of the visual stimulus. Here we demonstrate that burst structures play a significant role in mediating the effectiveness of neural coupling in the visual cortex.
, who remarked on the irregularity of single unit spike trains in awake, behaving cats. Cattaneo et al. (1981a)
subsequently found a relationship between clustered spikes (bursts) and stimulus orientation. They showed that with stimuli at optimal orientations, proportionally more spikes were contained in bursts than were found with stimuli at nonoptimal orientations. Debusk et al. (1997)
confirmed and extended these results. The reduction of spikes in bursts with nonoptimal stimuli arises from a decrease in average burst length, even after correction for dependence on firing rate. If bursts are important to the transmission of information in the cortex, this result would imply that nonoptimal stimuli result in a less efficient neural code, thereby enhancing the filter characteristics of cortical cells. This has been shown to be the case in the primary auditory cortex, where bursts act to sharpen frequency tuning (Eggermont and Smith 1996
).
METHODS
Abstract
Introduction
Methods
Results
Discussion
References
1·h
1 of Propofol (Stuart Pharmaceuticals, Wilmington, DE) through one of the cannulae. The trachea then was cannulated, and the head was mounted in a stereotaxic device. A small craniotomy (3 × 5 mm) was performed over the area centralis representation in Area 17 (H-C coordinates P4-L2). The dura was incised, and after positioning the electrode over an area free of surface vessels, the hole was covered with agar mixed in mammalian Ringer solution. Melted Tackiwax (Cenco, Chicago, IL) then was poured over the agar to provide an effective hydraulic seal.
1·h
1) through the second cannula. Propofol anesthesia was continued at 0.3 mg·kg
1·h
1 while the cat was respirated at 30 breaths/min with a mixture of N2O:O2:CO2 (70:28.5:1.5%), and pCO2 was held at 3.9%. The heart rate and brain activity were monitored, via electrocardiograms and electroencephalograms, respectively, to ensure anesthetic stability. Accelerated heart rate or lack of occasional sleep spindles were treated with bolus intravenous injections of Propofol. Rectal temperature was maintained at 37.5°C with a servo-controlled heat pad. The pupils were dilated with 1% atropine sulfate, and the nictitating membranes were retracted with 10% phenylephrine hydrochloride. Contact lenses with 4-mm artificial pupils were fitted to the nearest 0.25 mm base curve radius, and auxiliary lenses were added as dictated by direct ophthalmoscopy to render the retina conjugate with the viewing screen 57 cm distant. Retinal landmarks (optic disk and area centralis) were projected onto the plotting screen with a reversible ophthalmoscope.
; Wollman and Palmer 1995
). Sine-wave gratings were generated with a microprocessor-based pattern generator similar in concept to that described by Milkman et al. (1978)
. Spatial frequency, contrast, orientation, and drift rate were systematically varied to characterize the spatial filter properties of groups of neurons. Quantitative curves of group activity were based on amplitude threshold triggering. This characterization was aimed at finding stimulus conditions that maximized the firing rate of a group of neurons as opposed to a single isolated neuron.
that ranged in size from 4 to 10 deg2.
) with uninsulated tips 20-30 µm long and 2 µm wide at the base. The neural signal coming from the microelectrode was amplified by 1,000, bandlimited between 100 and 10,000 Hz, and sampled at 30 kHz by a digital signal processing (DSP) board (AT&T DSP32C). The DSP board continuously monitored the incoming signal and when a sampled voltage exceeded >5 SD above (or below) the mean noise level, the sample was presumed to represent an action potential and was time marked for storage. Chebyshev's Theorem (Walpole and Myers 1985
) defines the probability that any random variable X will assume a value within k standard deviations of the mean as
where u = mean, s = standard deviation, X = random variable, and k = number of standard deviations from mean. This holds for any distribution of observations and is a lower bound only. By using a criterion of 5 SD for acceptance, the stored sample had no more than a 4% chance of being noise. On this basis, we feel that all action potentials were recorded in addition to a small amount of noise. To capture the action potential, we saved the waveform from one msec before the trigger point to 3 ms after the trigger point. The sample window thus totalled 4 ms and contained a total of 120 sampled points. The trigger was not reset until the sampled values no longer exceeded 5 SD from the mean.
(1)
Classification of action potentials
The data associated with each stored sample window represented the action potential of one of several neurons that were firing during the recording. To analyze the interaction between the neurons contributing to the group activity, the waveform contained within each window was assigned to a specific class, which was associated with the activity of a specific neuron. We used a spike sorting method (Snider and Bonds, unpublished data) to classify the recorded waveforms. The activity of up to six neurons could be recorded simultaneously and subsequently classified but most groups discussed here consisted of from two to four neurons.
). We defined an initial mean vector (the average of all vectors in a cluster) based on all of the waveform vectors. A second mean then was created by adding small random values to the first mean. The vectors were grouped to the closest mean and the two means were updated as the average of the grouped vectors. This process was repeated until convergence. These means then were split into two and the process was continued. Once a given waveform vector was assigned to a particular mean, it stayed with that particular mean's descendants. In practice we typically split the data six times for a total of 64 cluster means representing ~50,000 action potentials.
Cross-correlation
We used the cross-correlation histogram (Perkel et al. 1967a,b
) to determine putative connectivity between spike train pairs. The cross-correlation histogram was constructed by selecting each spike from neuron A and making a histogram of the intervals to all spikes (within, say, ±100 ms) from neuron B. If the spike trains from neurons A and B are independent, then the resulting histogram should equal the constant value of 1/µB where µB is the mean interval between spikes from neuron B. Peaks (valleys) in the cross-correlation histogram indicate temporal relationships that are more (less) probable than independent behavior indicated by a flat value of 1/µB. If both neurons are excited from a common source, a peak occurs centered at a time lag of zero. If neuron A directly excites neuron B, then a shifted peak occurs and the shift corresponds to the time it takes for neuron A to affect B (Moore et al. 1970
).
. We first created a "raw" joint poststimulus time histogram (JPSTH). This is a two-dimensional histogram in which each bin represents a delayed coincidence of the two spike trains averaged over all stimulus presentations, and is represented by
x(s)y(t)
.
where xk(t) denotes the response of neuron x at bin t of sweep k and K represents the set of all sweeps. The only restriction is on the binwidth, which is chosen such that in each trial we collect at most one spike per bin. The JPSTH predictor is created by taking the cross product matrix of the individual PSTHs representing the responses from two cells,
(2)
x(s)
y(t)
, and represents the null hypothesis of no interaction between the neurons. To compare the difference between the raw JPSTH and the JPSTH predictor, we just subtract the two
The quantity D(s, t) is the cross-covariance matrix of the spike trains × and y, each collected over all presentations. In terms of neural responses (Aertsen et al. 1989
(3)
), the first term on the right represents the joint PST histogram that was developed directly from the data and the second term represents the JPSTH that would be predicted if neurons x and y were firing independently even though responding to a common source. The values of D cannot, however, be a good indication of the connectivity of the neurons x and y because they depend on the firing rate. To compensate for this, Aertsen et al. (1989)
propose the use of the normalized PST histogram
The denominator can be shown to be the standard deviation of the predicted PSTH. If the normalized cross-covariance matrix now is integrated along the principal diagonal (s = t), the result is the normalized cross-correlation histogram, which is the measure of correlated firing that we used in this study. This approach of constructing the cross-correlation histogram is equivalent to using the standard shift predictor histogram which has been averaged over the set of all possible shift predictors, i.e., all different orders of shift including zero, which gives a more robust statistical result than when using the ordinary shift predictor.
(4)
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RESULTS |
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Temporally related spike pairs
We examined the corrected cross-correlation histograms for peaks that were shifted from time lag zero. This shifted peak strongly indicated a direct causal relationship between two neurons, i.e., excitation from one cell contributing to the action potential from a second cell. There were 241 neuron pairs in the 22 multiunit groups recorded. These groups yielded collectively 56 individual neurons. A multiunit group typically showed activity from two to six neurons and thus contained between 1 and 15 neuron pairs. Of the 241 neuron pairs, 91 of these pairs (38%) had a shifted cross-correlation peak, which indicated a possible direct causal connection. Only two multiunit groups contained no shifted cross-correlation peaks. Of the 91 pairs that showed a causal connection, 82 (90.1%) showed complex-to-complex interactions, where a complex cell participated in the firing of a complex cell, 2 (2.2%) showed simple-to-simple interactions, 2 (2.2%) showed simple-to-complex interactions, and 5 (5.5%) showed complex-to-simple interactions.
Burst analysis
Analysis of spike intervals from visual cortical cells does not yield a uniform or even Poisson distribution of the interval values. Most cells produce a bimodal distribution with a prominent peak at short intervals and a lower, broader peak or plateau at longer intervals (Debusk et al. 1997
Neural coupling
The delayed peak found in the cross-correlograms of 91 neuron pairs suggested strongly that spikes from the first neuron contributed to the decision to fire by the second neuron. These pairs were analyzed further to see how bursts in the spike train affected the transmission of a spike from one neuron to the next. To quantify the strength of the coupling between a pair of related cells, Levick et al. (1972) Effectiveness of bursts
Figure 3 diagrams the populations of bursts of varying length as well as their effectiveness. In our sample, the number of single spikes approached one million (1st column). The dark gray bars represent the number of bursts of a particular length and the superimposed light gray bars represent the number of those bursts that were effective in eliciting a spike from the driven neuron. The effectiveness of each burst length is represented by the percentage above the dark gray bars. The longer bursts are much more likely to cause a spike in a postsynaptic cell than shorter bursts, but their overall impact is much less because there are fewer long bursts. In general, bursts were short. Figure 3, inset, plots the cumulative probability of events, where an event is either a single spike or a burst, as a function of event length. About 62% of the total events were single spikes with two-spike bursts adding another 31%. Bursts of five spikes or less (including single spikes) comprised 97.7% of the data and bursts of
Burst effectiveness for optimal versus nonoptimal stimulus conditions
The above measurements, showing that bursts enhance coupling effectiveness, were based on responses to all stimuli. Because Cattaneo et al. (1981a)
Contrast gain control
Bonds (1991)
Modulation of effective coupling
We have shown that the more spikes a burst contains, the more effective this burst is in eliciting a time-related spike from a driven neuron. Since the effectiveness of a multispike burst is slightly less than the summed probability of effectiveness of the individual component spikes taken in isolation, one might question whether bursts actually provide any real advantage in the propagation of information. The key issue is timing. When looking at neural coding from the perspective of the target neuron (Bialek et al. 1991 Impact of bursting across the cortex
Some studies describe an oscillation in cortical cells in the region of 30-60 Hz. Recordings of local field potentials and multiunit activity show that this oscillation can lead to synchronization of firing across long distances both within and between cortical areas (e.g., Eckhorn et al. 1988 Decoding of bursts is biologically plausible
Any mechanism for information encoding and decoding in spike trains must be consistent with the duration required to complete a visual task. An example of a severe constraint for temporal codes is the 100-150 ms it takes to excite inferotemporal cortex (IT) neurons, which are selective for facial features (Perrett et al. 1982 We thank V. Casagrande for thoughtful comments on the manuscript.
This study was supported by National Eye Institute Grant R01EY-03771-14 and Core Grant R30EY-08126. J. F. Kabara was supported by National Institutes of Health Training Grant T32-07135.
Address for reprint requests: A. B. Bonds, Dept. of Electrical and Computer Engineering, Box 1824 Sta. B, Vanderbilt University, Nashville, TN 37235. Received 11 August 1997; accepted in final form 28 April 1998.
found a latency to peak of excitatory postsynaptic potentials (EPSPs) of 7-12 ms. Their measurement was done in slices from guinea pig hippocampus, where activation stemmed from a single presynaptic neuron or antidromic activation that activated only part of the CA3 population. We believe that our latency range encompasses shorter values because spikes were presumably generated not only by temporal summation but also by synchronous spatial summation. With an intact preparation and optimal stimulation conditions, the postsynaptic cell receives input from many active neurons in addition to the one we identified as presynaptic. Activity from these other cells also contributes to the depolarization of the postsynaptic cell, thus increasing the probability that the rising phase of a single EPSP will trigger a spike.
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FIG. 1.
Cross-correlations as a function of parametric variations of the stimulus. In all cases, the magnitude of the cross-correlation function is normalized to the number of spikes and is therefore independent of firing rate. Total measurement duration for each stimulus condition was 100 s (10 10-s sweeps). Average firing rate of the pre- and postsynaptic cells is shown (at left of each histogram) for each example by pre:post. Degree of correlation is more sensitive to stimulus change when orientation is varied (A and B) than when spatial frequency (C) or contrast (D) is varied.
to enable direct comparisons of synaptic efficiency independent of firing rate. The decrease in coupling is thus not just due to a decrease in the number of spikes available for analysis, rather the effectiveness of the driving neuron in causing the driven neuron to fire also has decreased. Local dependence of coupling on changes of firing rate within a given response period was possible, but it is likely that any such changes were not organized. Most recorded cells were complex, and the response was simply a generalized elevation of firing rate, with no temporal features associated with stimulation.
). Here again, the degree of coupling seems less dependent on firing rate than was found with variation of orientation. The relationship between particular kinds of stimulation and coupling will be considered in more detail later.
; Gray and McCormick 1996
). Figure 2 shows an example of this behavior in three cells. The large peak at ~3-5 ms drops off steeply, and frequently there is a noticeable dip in the region of 10-12 ms that precedes the broader peak at 15-30 ms. As proposed by Cattaneo et al. (1981a
,b
) we define bursts to be any group of two or more spikes that have intervals of
8 ms, corresponding to spikes contained in the peaks near the origin. This criterion is consistent with the falloff seen in the histograms and also has been used by Mandl (1993)
in cat superior colliculus and by Bair et al. (1994)
in monkey medio-temporal (MT) cortex.
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FIG. 2.
Three examples of interspike interval distributions of neurons that burst. Typical behavior shows a prominent peak at 1-3 ms and a steep decrease between 5 and 10 ms. This often is accompanied by a minimum at 10 ms and a secondary peak at ~20-30 ms (e.g., A and B). We believe that these latter features represent a burst refractory period and intrinsic network-mediated excitation, respectively (Debusk et al. 1997 ).
42% of their spikes in bursts found by Debusk et al. (1997)
. However, the multiunit activity in the experiment reported here was recorded mainly from the supragranular layers. Gray and McCormick (1996)
reported a tendency for bursting cells to be located in the upper laminae. The lower figure cited by Debusk et al. (1997)
is probably the result of averaging activity over all layers. Similar levels of burst activity also are found in other cortical areas. Eggermont and Smith (1996)
, defining bursting as spikes that could not be predicted by a modulated Poisson process, found that in the auditory cortex 54 ± 11% of spikes were contained in bursts.
defined effectiveness (or efficacy) (Aertsen et al. 1989
), which is the percentage of spikes from the presynaptic neuron (of all of its spikes) that are time related with spikes of the postsynaptic neuron. It is important to note that this definition is based purely on the statistics of the linkages between two cells and does not directly address the actual mechanisms involved in spike transmission. Levick et al. (1972)
defined effectiveness for spikes that were related by a precise time delay. In most cases, generation of a spike in pyramidal cells requires integration of a number of input events over several milliseconds (Miles and Wong 1986
). We therefore modified the previous definition of effectiveness. Instead of a precise time delay, we used a time-delayed window, where the width of the window was determined from the width of the peak in the cross-correlation histogram. For example, if the peak in the cross-correlation histogram started at 5 ms and ended at 8 ms, then any spike from the second neuron that had a time lag of 5-8 ms after the first neuron's spike was considered to be time related to the first neuron's spike. The criterion for correlation in the 91 pairs judged to be coupled required a positive peak that remained above the noise floor for at least four 1-ms bins.
10 spikes (including single spikes) account for nearly all the data (99.7%).
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FIG. 3.
Relative effectiveness of single spikes and bursts, collectively termed "events." Here the total number of events is plotted ( ) as a function of event (burst) length.
, effectiveness of events of each length, also noted as percentages at the top of each bar. Inset: cumulative probability of events as a function of event length, with ··· separating the single spikes from the bursts.
) and presynaptic bursts ranged in effectiveness from 30 to 50% (Traub and Miles 1991
). We found that the average effectiveness of all bursts was 18.5%, about twice the effectiveness of single spikes. This is less than the effectiveness averaged between 2- and 10-spike bursts because of the far greater numbers of bursts with lower spike counts. Altogether, ~54% of the correlated postsynaptic spikes were associated temporally with bursts.
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FIG. 4.
Postsynaptic effectiveness of events as a function of event length, averaged across a total of 1,564,858 presynaptic events and 201,620 postsynaptic events. Relationship is highly correlated (r = 0.9982).
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FIG. 5.
Distribution of effectiveness within bursts. This figure describes the likelihood that a particular spike in a burst will result in a postsynaptic spike in comparison with other spikes in the same burst (total probability = 1). Duration of 2-spike bursts is so short that either spike could be related causally with a postsynaptic spike, so probabilities are equal. As the duration of bursts grow, it becomes apparent that the later spikes in a burst are more effective in eliciting a postsynaptic spike, presumably due to temporal summation.
) and thus is suited ideally for burst summation at the postsynaptic site.
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FIG. 6.
Burst duration as a function of the number of spikes in a burst. Average interval within a burst is 4.08 ms, and the relationship is highly correlated (r = 0.9998) for bursts of 10 spikes.
showed that more spikes were contained in bursts for optimal stimulus conditions than for nonoptimal conditions, we expected to see a dependence between coupling effectiveness and the stimulus configuration. We examined this question by first driving neurons with optimal (or nearly so) stimuli with optimality being defined by stimuli that yielded the greatest firing rate within the ensemble. We were recording from groups of cells with receptive fields that were concentrated within an area averaging 7.1 deg2, and independent stimulus optimization for each cell was not possible. Although spatial selectivity within a given group differed in detail, most of the cells detected at a single recording site tended to have similar spatial tuning properties (Gawne et al. 1996
). This presumably occurred because we were recording group activity from a single microelectrode with a region of sensitivity that did not spread significantly beyond a given organizational column. Figure 7A shows the orientation tuning curves for three multiunit groups each consisting of two or three cells. The neurons in each group show peak firing rates at about the same orientation, although these firing rates are different. Figure 7B shows the spatial frequency tuning curves for three multiunit groups. Within each group of from two to four cells, the peak firing rates for each cell within the group result from spatial frequencies within 0.1 cycle/deg of one another.
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FIG. 7.
Left: examples of orientation tuning of neurons in multiunit groups. Orientations were presented in 10° increments. Groups shown here are representative in that preferred orientations are similar across a group within the resolution of the measurement. Right: spatial frequency selectivity of neurons in multiunit groups. As with orientation tuning, the favored spatial frequency of neurons in a local group tended to be quite similar within the limits of the measurement resolution.
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FIG. 8.
Comparison of burst effectiveness with optimal and nonoptimal stimulation. Effectiveness was averaged for all presentations of optimal stimuli ( ) and all presentations of nonoptimal stimuli (
) and is plotted as a function of burst length. For all burst lengths, effectiveness is ~5% higher (absolutely, not relatively) with optimal stimulation. Average effectiveness across all stimuli (
) also is shown for comparison.
). The comparison across different stimulus modalities was made so that we could differentiate the changes in effectiveness resulting from modulation of firing rate via different mechanisms. Figure 9 shows the change in effectiveness (in absolute percent) as a function of the change in firing rate of the presynaptic cell, averaged across optimal and nonoptimal stimulating conditions, for each stimulus class. The points representing both sequenced and randomized contrast presentations show moderate absolute losses in effectiveness across a broad range of response reduction. We believe that the greater response reduction seen with randomized contrast (across the same set of contrasts used for sequential contrast presentations) results from cells undergoing less contrast adaptation on average for sequentially presented stimuli than for randomly presented stimuli, especially at lower contrasts. Nonoptimal spatial frequencies yield slightly greater losses of effectiveness than low contrasts, but the difference is not significant.
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FIG. 9.
Change in effectiveness vs. change in firing rate of the presynaptic cell resulting from variation of different stimulus parameters. Each point represents the average reduction of both firing rate and effectiveness for stimulation with nonoptimal orientations, spatial frequencies and contrasts (both randomized and sequenced presentations), as labeled. Dependence of effectiveness on firing rate can vary markedly depending on which stimulus property is varied.
). We thus would expect to see effectiveness reduced more at nonoptimal orientations as a result of shorter average burst lengths. It is also possible that reduced effectiveness at nonoptimal orientations could result from a systematic modification of the response waveform, which could disproportionately reduce transmission efficiency without changes in overall mean firing rate.
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FIG. 10.
Effectiveness as a function of burst length and firing rate of the presynpatic neuron. Left: firing rate is varied by varying stimulus orientation and contrast is held constant. Right: firing rate is varied by varying contrast and the orientation is optimal and constant. Meshes are 5th-order polynomials fit to the actual data to clarify general trends. In general, low firing rates resulting from nonoptimal orientations are much less effective than those same rates resulting from low contrasts.
; Ohzawa et al. 1985
) is activated and drives down the overall effectiveness, presumably to prevent overdriving the postsynaptic neuron. This gain suppression is seen in the contrast plots as a clear dip beyond the peak found at moderate firing rates. This peak is not evident in the plots parametric on orientation; the plots were measured at a fixed contrast.
) at all burst lengths even though the curves for orientation were taken at a greater firing rate than for the contrast curves. The reduction of effectiveness for nonoptimal orientations most likely reflects a stimulus-related variation in the postsynaptic membrane potential that is in addition to dependences on presynaptic firing rate and burst length but the actual mechanism remains unknown. We suggest that this additional mechanism is likely to involve inhibition (Berman et al. 1991; Bonds 1989
; Bush and Sejnowski 1994
; Douglas and Martin 1991
; Li et al. 1960
; Morrone et al. 1982
; Sillito 1975
). If there was not some type of inhibitory mechanisms controlling the difference between contrast and orientation, then the curves based on variation of orientation, measured at greater firing rates, should show greater effectiveness not less.
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FIG. 11.
Detail of effectiveness as a function of burst length with variation of orientation and contrast. These 2 examples represent slices taken from the 3-D plots of Fig. 10, 2nd (A) and 3rd (B) rows. Even though for each example the firing rate from variation of contrast ( ) is lower than that from variation of orientation (
), the effectiveness at the optimal orientation (varied contrast;
) is higher at all burst lengths.
demonstrated the dynamic nature of contrast gain control in cortical neurons of cats by presenting contrast values sequentially in first increasing then decreasing logarithmic steps. All cortical cells show response hysteresis, where the response to a given contrast is lower when it is preceded by a higher contrast than when it is preceded by a lower contrast. The adaptive effects of higher contrasts are seen nearly instantaneously but take several seconds to subside. The active gain control mechanism observed in Fig. 10, right, can be more clearly seen in Fig. 12 where the responses and effectiveness found with sequentially varying contrast are superimposed. Each contrast was presented for 10 s, and these curves have been normalized to facilitate comparison. The response plot peaks at 40% contrast and drops slightly at 56%, indicating some supersaturation (Li and Creutzfeldt 1984
). Presentation of 40% contrast immediately thereafter results in a response amplitude that is only 64.7% of the peak value, and responses to successive presentations are also attenuated down to 3% contrast. On the other hand, effectiveness peaks at only 20% contrast, falling to 79.5% of its peak value at the response peak at 40% contrast, and is only 68.3% of its peak at the highest contrast of 56%. One should note that the peak effectiveness is seen where the slope of the response versus contrast curve is highest, and the deceleration of this curve is reflected by a decrease in effectiveness. As the state of adaptation recovers on presentation of lower contrast levels, effectiveness also recovers, with some restoration of both response and effectiveness at 14% contrast, and preadaptation levels appearing at ~7% contrast. We thus conclude that contrast adaptation in cortical cells is dependent on modulation of the effectiveness with which presynaptic spikes evoke postsynaptic spikes, although this may not be the only factor. The physiological mechanism underlying this modulation remains unclear, but tonic hyperpolarization in the postsynaptic cell may be involved (Carandini and Ferster 1997
).
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FIG. 12.
Effectiveness and contrast gain control. Here the effectiveness ( ,
) and firing rate (···, *) are normalized and plotted for sequential presentation of contrasts from 3 to 56% and back. Top of each curve represents rising contrasts, and the lower edge falling contrasts. ···, reponse hysteresis typical of all cortical cells (Bonds 1991
). Fall in effectiveness parallels the saturation in the response curve, and recovery of effectiveness is evident at ~14% contrast on the decreasing leg of the curve.
DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References
), bursts can be viewed as "packets" of information that are instantaneously more meaningful than isolated spikes. Our results show that bursts are about twice as effective as single spikes. Longer bursts, although fewer in number, can support event-based transfer ratios approaching 0.5. With this mechanism, a single neuron can markedly amplify the probability of its immediate influence on postsynaptic cells. This is done in a deterministic fashion that is not equivalent to summation of the probability of propagation of individual spikes over some arbitrary time interval because the message is specific not general. One consequence is an effective enhancement of orientation tuning. Stimulation with optimal orientations yields a higher proportion of spikes contained in bursts, as well as longer bursts (even at low firing rates) (Debusk et al. 1997
), compared with stimulation at nonoptimal orientations. At optimal orientations, intercellular linkage thus is amplified, leading to an increase of orientation selectivity (Cattaneo et al. 1982) across a wide range of contrasts. Bursts similarly have been found to sharpen the tuning of neurons in auditory cortex (Eggermont and Smith 1996
).
; Schwartzkroin and Wyler 1980
). It can be modulated by the surrounding circuitry, which synchronizes, suppresses, or possibly terminates the bursts (Bush and Sejnowski 1996; Gray and McCormick 1996
). We believe that bursting reflects a natural tendency of cortical cells that is necessary to overcome the high threshold of the postsynaptic cortical cell (Creutzfeldt and Ito 1968
). The transfer of information then is tempered by a network "moderator" that is engaged actively in determining the relevance of this information.
-Aminobutyric acid-A (GABAA)-mediated inhibition is a possible basis for this mechanism because it has been shown to shorten bursts (Debusk et al. 1997
; Dykes et al. 1984
) and is likely to reduce firing of other cells that contribute to spatial summation. It is thus difficult to disengage network interactions from bursting.
) of information in cell assemblies (Braitenberg 1978
; Gerstein et al. 1989
; Hebb 1949
; Palm 1982
). An important function of the network would be to synchronize these bursts. Synchronization would allow the next cortical stage to bind together cortical neurons that are temporally dependent. One consequence of functional linkage is a support for learning by grouping neurons that usually become active together to cause a postsynaptic neuron to fire (Hebb 1949
). MacLeod and Laurent (1996)
have shown that fast GABA-mediated inhibition underlies neuronal synchronization in the olfactory system. Kim et al. (1995)
also have shown that it is possible to phase lag and lead EPSPs in the dendritic branches by inhibitory control. It is therefore reasonable to expect that the network can adjust and synchronize bursts. The effects of such synchronized bursting would be profound. Braitenberg (1978)
proposes the existence of an "amplification" with respect to the number of active synapses needed to raise a neuron above its threshold. He notes that an epileptic focus on one side of the brain may excite the contralateral cortex producing epileptic activity. Because the callosal fibers are only a few percent of the total cortico-cortical fibers, he concludes that synchronous activation of only a few percent of the synapses is sufficient for exceeding threshold. Thus with synchronous bursts, not only does temporal summation occur, but spatial summation as well, a symbiotic interaction reinforcing the activity of the target neuron.
), which has heightened interest in the issues of neural coding (Shadlen and Newsome 1994
). One of the reasons proposed for this irregularity is the balance between excitation and inhibition in order for the neuron to avoid saturation and yet be near the firing threshold (Bell et al. 1995). Shadlen and Newsome (1994)
raise the question of whether neurons should be viewed as coincidence detectors or integrate-and-fire devices and that an irregularity caused by balancing excitation and inhibition is problematic for the coincidence detector viewpoint. This is because the timing of postsynaptic activity would be random, no longer reflecting the timing of presynaptic events. Thus the precise patterns of spikes would fail to propagate.
).
; Gray et al. 1989
; Livingstone 1996
). Although bursting in individual cells is difficult to resolve in the multiunit recordings, in at least one report (Livingstone 1996
) the term "bursting" is used synonymously with oscillation, implying a tendency to find bursts during periods of oscillation. If this is the case, the resulting synchronization would be consistent with the instantaneous enhancement of cellular coupling resulting from bursts.
described a class of cells they termed chattering cells, which represent a subset of our definition of neurons that burst. They describe these cells as having bursts of two to five spikes, having intraburst firing rates as high as 800 spikes/s, and having burst repetition at intervals of ~15-50 ms. The interspike interval (ISI) histograms of these cells are similar to those described here as well as in Debusk et al. (1997)
and in Mandl (1993)
. Gray and McCormick (1996)
have identified the chattering or bursting cells as layer 2/3 pyramidal neurons. These neurons have axon collaterals which project into layers 2/3 and 5, and the axon itself projects into white matter and to higher cortical areas. Because layer 2/3 pyramidal cells are the major output cells of the striate cortex, bursting might play a significant role in conveying information to, and perhaps synchronizing, the higher cortical centers.
). A more detailed argument is presented in Thorpe and Imbert (1989)
, but the main points will be given here to argue that burst coding is consistent with these constraints whereas other proposed schemes for temporal coding challenge these constraints.
10. One synaptic stage is between the photoreceptors and bipolar cells, one between the bipolar cells and ganglion cells, one between ganglion cells and cells in the lateral geniculate nucleus (LGN), one between LGN cells and layer 4 cells in V1, one between layer 4 and layer 2/3 cells in V1, two in V2, two in V4, and one in IT. Because neurons in the temporal lobe have visual response latencies on the order of 100-150 ms and there are
10 synapses to negotiate, this yields a limit on average of 10-15 ms per synapse in which to process visual information. About 10 ms total would be required to account for delay through all of the 10 synapses. Given a conduction speed of intracortical axons of ~1 m/s (Bullier et al. 1988
), one can estimate
70 ms for spike transit from retina to V1 to IT. With these adjustments, the average processing time per synapse is reduced to <10 ms. This figure is reasonably consistent even if we ignore the processing before V1. The latency to V1 is 50-70 ms (Celebrini et al. 1993
), leaving 50-80 ms to go from V1 through five synaptic stages to neurons in the temporal lobe.
because their proposed symbols (spike triplets) are spread in time
100 ms. It would take 100 ms for single recipient neurons to decode these symbols, yet this is the time actually required for visual information to go through 10 synapses. A similar problem exists for Richmond and Optican (1987)
who propose methods of information transfer requiring integration over periods of
100 ms, although a more recent examination of their data (Heller et al. 1995
) suggests that most of the information is contained within the first 75 ms. The model of Von der Malsburg and Bienenstock (1986)
proposes that information is carried in the degree of correlation between neurons and that 100 ms is likewise needed for the determination of this correlation. For all of these models, if each neuron has to wait 100 or even 75 ms to determine the presence of relevant information, the time to receive and decode visual information in an area such as IT could take upwards of 1 s, which is clearly not the case. One could argue that the particular temporal structures of a given model are preserved through several stages of processing and are not decoded at every synapse, but there is thus far no clear evidence that this degree of coherence is maintained from one cell to the next.
up to 5 spikes) are on average <20 ms, which is well within the practical summation capabilities of pyramidal neurons. We would note that because we have not explored the temporal relationship between stimulus onset and burst genesis, we cannot be assured that bursting plays a role in rapid identification tasks. Moreover by no means does our argument rule out the existence of coding schemes that require longer integration times for some visual purposes. We do suggest that by their very nature such schemes are less useful for visual judgments that must be made rapidly.
ACKNOWLEDGEMENTS
FOOTNOTES
REFERENCES
Abstract
Introduction
Methods
Results
Discussion
References
0022-3077/98 $5.00 Copyright ©1998 The American Physiological Society