Download Burst Firing and Modulation of Functional Connectivity in Cat Striate

Burst Firing and Modulation of Functional Connectivity
in Cat Striate Cortex
R. K. SNIDER, J. F. KABARA, B. R. ROIG, AND A. B. BONDS
Department of Electrical and Computer Engineering, Vanderbilt University, Nashville Tennessee 37235
INTRODUCTION
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) 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.
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Another view suggests that discrete structures within the
spike train form a specific code that is relevant to the decision
making processes of postsynaptic neurons. The exact means
by which information is encoded in these sequences (or
even if it is encoded) still are being debated (Shadlen and
Newsome 1994). 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).
The challenge in the study of pattern-based representation
of information lies not only in finding representation
schemes but also in elucidating mechanisms by which these
schemes can be decoded. Even though more information
could be encoded in random patterns that are measured very
precisely, the time constants of pyramidal cortical neurons
(e.g., 7.3 { 2.9 ms for dendrites and 16 { 5.3 ms for the
soma; means { SD) (Kim and Connors 1993) 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.
Most previous studies of neural coding (Abeles and
Gerstein 1988; 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.
Bursts in the visual cortex were first described by Hubel
0022-3077/98 $5.00 Copyright q 1998 The American Physiological Society
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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.
MODULATION OF CONNECTIVITY IN CAT STRIATE CORTEX
METHODS
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 Ç45 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 mgrkg 01rh 01 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 1 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.
For recording, paralysis was induced via intravenous injection of
gallamine triethiodide (Flaxedil, American Cyanamid, Pearl River,
NY; 10 mgrkg 01rh 01 ) through the second cannula. Propofol anesthesia was continued at 0.3 mgrkg 01rh 01 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 37.57C with a servo-controlled heat pad. The
pupils were dilated with 1% atropine sulfate, and the nictitating
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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.
Stimulation
Stimuli were presented on a monochromatic CRT display
(Tektronix 608; mean luminance 30 cd/m 2 , P31 phosphor) with
a 107 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; Wollman and Palmer 1995). Sinewave 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.
The receptive field size of the multiunit groups did not appear
to be much larger than the receptive fields of single neurons that
we have recorded in Area 17. Receptive field dimensions were
approximated by rectangular areas determined by manual plotting.
The centers of the aggregate response fields were all within seven
degrees of area centralis. The areas ranged from a minimum of 3.0
deg 2 to a maximum of 13.0 deg 2 , with an average of 7.1 { 3.21
(SD) deg 2 . This is comparable with the receptive fields of single
cells measured by Hubel and Wiesel (1959) that ranged in size
from 4 to 10 deg 2 .
Data acquisition
Multiunit action potentials were recorded with single tungstenin-glass microelectrodes (Levick 1972) with uninsulated tips
20–30 mm long and 2 mm 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 ú5 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
P(u 0 ks õ X õ u / ks) ¢ 1 0
1
k2
(1)
where u Å mean, s Å standard deviation, X Å random variable,
and k Å 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.
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(1959), 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).
To test the hypothesis that bursts play a significant role
in the transmission of information between cortical cells,
we recorded the activity of several neurons simultaneously.
Neural pairs that showed coupled activity, as determined via
cross-correlation, were analyzed to test the effectiveness of
bursts in causing the driven neuron to fire. We found that
bursts of as few as two spikes were more effective in eliciting
a response in the driven neuron than isolated single spikes
and that this efficiency rose monotonically as burst length
increased. It is the aim of this article to demonstrate that
bursts are an important element in the landscape of neural
codes.
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R. K. SNIDER, J. F. KABARA, B. R. ROIG, AND A. B. BONDS
Classification of action potentials
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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/ mB where mB 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/ mB . 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).
It is possible that, in addition to direct excitation between neurons, common excitation of two neurons can occur as a result of
both responding to a particular stimulus. This response should not
be misinterpreted as indicating direct connectivity between the
neurons. Common excitation usually is synchronized with the stimulus over a period of time that is relatively long compared with
the simultaneous excitation due to connectivity, which is found
over the order of milliseconds. The difference in time scales permits the effects of common excitation to be removed. This usually
is accomplished by subtracting the shift predictor from the original
cross-correlation histogram. Here we corrected for common excitation using the method of Aertsen et al. (1989). We first created a
‘‘raw’’ joint poststimulus time histogram (JPSTH). This is a twodimensional 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) … .
As in the cross-correlation histogram, this JPSTH will contain
contributions from both common stimulation and coincident firing
due to coupling. The contributions that come from stimulus-related
modulation of the joint histogram can be predicted. We begin by
making PSTHs representing responses of individual cells averaged
over K stimulus presentations
» x(t) … Å
1 K
∑ xk (t)
K kÅ1
(2)
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, » 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
Dx ,y (s, t) Å » x(s)y(t) … 0 » x(s) …» y(t) …
(3)
The quantity D(s, t) is the cross-covariance matrix of the spike
trains 1 and y, each collected over all presentations. In terms of
neural responses (Aertsen et al. 1989), 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
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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.
The basic strategy of the classification algorithm was first to
project each waveform as a 120-dimensional vector, each dimension representing the magnitude of one of the samples. These projected vectors then were grouped into many small clusters, where
each point in a cluster represented an action potential. The final
step was to resolve which of these clusters could be combined to
represent the activity of a given neuron.
We started the classification procedure by partitioning the waveform space into many small clusters using the method of binary
tree bisection (Linde et al. 1980). 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 Ç50,000 action potentials.
Cluster consolidation was based on the underlying assumption
that if an action potential changes shape, it does so gradually and
should leave a continuous trail of points as it moves through the
120-dimensional waveform space. Membership of two small clusters in a larger smeared cluster would be indicated if the density
of points falling between these two clusters changes in a linear
fashion from the density of the first cluster to the density of the
second cluster. We first determined local densities by calculating
how many points fall in an area that is one standard deviation away
from the mean of each cluster. The points between the clusters
were assumed to be random variables with probability P of falling
between the clusters and probability q of falling within the clusters.
This is a binomial distribution, which can be approximated by the
standard normal distribution. The z score specifies the area under
the standard normal distribution and thus can be interpreted as a
confidence interval. By using the z score of the standard normal
distribution, we calculated the difference between the actual number of points falling between the two clusters and what we expected
if the clusters are linked. If the number of points on the trajectory
between clusters resulted in a value that is equal to or above a set
threshold (z) value, we then concluded that the two clusters belonged to a single distribution and combined them. By plotting the
number of clusters versus z thresholds, we typically found a plateau
in the number of clusters that spanned a range of threshold values.
In practice this plateau represented a robust threshold representing
reasonably separated clusters even though the clusters could have
arbitrary boundaries.
If more than one action potential peak was detectable within a
4-ms window, each waveform was projected as a separate event,
which permitted independent identification of some events within
the window. A small number of sample windows were not unambiguously classifiable, presumably due to overlap of spike waveforms or excessive noise. These windows typically represented
only 1–3% of the data and were discarded. Discarding overlapping
spikes had minimal effect on our results. We were primarily inter-
ested in action potentials that had a time-delayed coincidence of
3–12 ms and overlapping spikes had a time-delayed coincidence
of Ç0–2 ms.
MODULATION OF CONNECTIVITY IN CAT STRIATE CORTEX
this, Aertsen et al. (1989) propose the use of the normalized PST
histogram
Cx ,y (s, t) Å
Dx ,y (s, t)
q
Dx ,x (s, s)Dy ,y (t, t)
(4)
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 Å 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.
RESULTS
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-tocomplex interactions, and 5 (5.5%) showed complex-to-simple interactions.
Figure 1 shows examples of typical cross-correlations that
we found under different stimulus conditions. The crosscorrelation peak is not restricted to one specific latency, but
rather is spread out between 3 and 12 ms. Miles and Wong
(1986) 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.
Figure 1A shows the responses to presentation of nine
orientations. There is a pronounced peak at both 10 and 207,
but at 40 or 3507 this peak has disappeared even though
there remains some presynaptic activity. The average firing
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rates of the two analyzed neurons are shown in the figures
as X:Y where X is the firing rate of the driving neuron and
Y is the firing rate of the driven neuron. Although the coupling is to some extent dependent on the absolute firing rates
(averaged across the presentation), it should be noted that
these cross-correlation histograms have been normalized
against firing rate (Eq. 4) using the method of Aertsen et al.
(1989) 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.
Figure 1B is another example of the responses to different
orientations though with lower firing rates for both driving
and driven neurons. The coupling between the neurons as a
function of orientation is similar to that seen in Fig. 1A. The
reduction in coupling at nonoptimal orientations is likely
due in part to the reduction of aggregate afferent signals at
nonoptimal orientations. There are other factors that can
influence this coupling, including reduced burst length and
inhibition, that will be investigated later in the paper.
Figure 1C shows the coupling as a function of spatial
frequency. The dependence of coupling on spatial frequency
is typically not as pronounced as the coupling change with
varying orientation. Figure 1D shows how the coupling
changes as a function of contrast that is presented in a
stepped sequence of rising then falling values. This stimulation paradigm is to show the dynamic nature of contrast gain
control (Bonds 1991). 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.
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; Gray
and McCormick 1996). Figure 2 shows an example of this
behavior in three cells. The large peak at Ç3–5 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.
We found that across our entire sample (56 cells,
2,792,593 spikes) an average of 60.5% of the spikes were
contained in bursts. This value is higher than the figure of
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Temporally related spike pairs
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50% of 507 cells having ¢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.
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)
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
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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.
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).
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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.
MODULATION OF CONNECTIVITY IN CAT STRIATE CORTEX
735
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
FIG . 3. Relative effectiveness of single
spikes and bursts, collectively termed
‘‘events.’’ Here the total number of events is
plotted ( j ) 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
rrr separating the single spikes from the
bursts.
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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 Ç20–
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).
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R. K. SNIDER, J. F. KABARA, B. R. ROIG, AND A. B. BONDS
within a burst related to excitation of a postsynaptic spike.
We first identified the bursts associated with at least one
postsynaptic spike and sorted them with respect to burst
length (number of spikes). We then summed the total number of effective presynaptic spikes for each burst length.
Figure 5 shows the fraction of the total effective spikes
represented by each spike in a burst sequence of a given
length. Several of the spikes within a presynaptic burst could
be time related to the same postsynaptic spike because the
time windows (3–12 ms) were longer than the average time
between spikes in a burst ( Ç4 ms). Because shorter bursts
last only 4–8 ms, in many cases, we could not unambiguously resolve whether any particular spike within those
bursts was more effective than the others; this resulted in
equal probability with respect to their contribution toward
inducing a postsynaptic spike. For the longer bursts, the later
spikes in the burst were more likely to result in a postsynaptic
spike. For example, the last spike in a five spike burst is
almost twice as effective (28%) as the second spike (15%).
This most likely reflects temporal summation resulting from
the burst. The increase of effectiveness for later spikes is
consistent for all burst lengths (except for 2-spike bursts).
It is interesting to note that the first spike is more effective
than spike number two or three in the longer bursts. One
interpretation of this result is that if other influences have
prepared the postsynaptic cell to fire, then a single spike has
a good probability of being effective, otherwise a burst will
be necessary to depolarize the cell to threshold.
The increased effectiveness of the later spikes in a burst
is not surprising if one assumes a simple integrate-and-fire
model for pyramidal neurons. Figure 6 shows burst duration
as a function of the number of spikes in the burst. This figure
is averaged over all the bursts in the data set (n Å 588,434).
The data in the figure are very linearly correlated (r Å
0.9999), with a range from 4.3 ms for a 2-spike burst to
36.8 ms for a 10-spike burst. Across all bursts, the average
time between spikes is 4.1 ms, which is well within the
time constants of pyramidal neurons (e.g., 7.3 { 2.9 ms for
dendrites and 16 { 5.3 ms for soma) (Kim and Connors
1993) and thus is suited ideally for burst summation at the
postsynaptic site.
We also looked to see if bursts were not only effective in
eliciting a single post synaptic spike but also caused the
target neuron to burst as well. We built cross-correlation
histograms that treated bursts as single events. No consistent
pattern of bursts begetting bursts was found.
Burst effectiveness for optimal versus nonoptimal
stimulus conditions
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 Å 0.9982).
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The above measurements, showing that bursts enhance
coupling effectiveness, were based on responses to all stimuli. Because Cattaneo et al. (1981a) 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 averag-
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bursts adding another 31%. Bursts of five spikes or less
(including single spikes) comprised 97.7% of the data and
bursts of °10 spikes (including single spikes) account for
nearly all the data (99.7%).
Figure 4 is a direct comparison of the effectiveness of
bursts in transmitting a postsynaptic spike as a function of
burst length. This distribution was calculated from our entire
database, consisting of 588,434 bursts of various lengths
together with 976,424 single spikes. The effectiveness of
single spikes averaged 9.5%. This means that across 91 cell
pairs 9.5% of the presynaptic single spikes from a given cell
contributed to the firing of the particular postsynaptic cell
under study. A burst was considered effective if any of the
spikes in the burst were time related to a spike of the driven
neuron. For bursts of two or more spikes, effectiveness
increased markedly. The relationship is very nearly linear
(r Å 0.9982) from an effectiveness of 15.0% for 2-spike
bursts to 46.6% for 10-spike bursts. This is comparable with
records from hippocampal pyramidal cells, where single
spikes were 5% effective (Miles and Wong 1986) 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, Ç54% of the correlated postsynaptic spikes were
associated temporally with bursts.
One might question whether the increase in effectiveness
found with longer bursts results simply from the fact that
longer bursts have more spikes. This would lead to an increase in the probability of classifying any spike from the
postsynaptic neuron as time related with a presynaptic spike.
If this was the case, then any spike in a burst would have
equal probability of correlating with a postsynaptic spike.
To test this possibility, we examined how the order of spikes
MODULATION OF CONNECTIVITY IN CAT STRIATE CORTEX
737
ing 7.1 deg 2 , 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
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 Å 0.9998) for bursts of °10 spikes.
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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.
Using the preceding definition of optimality, we compared
the effectiveness of bursts at the optimal stimulus condition
to the nonoptimal conditions for orientation, spatial frequency, contrast presented randomly, and contrast presented
sequentially. The nonoptimal response was averaged over
all the nonoptimal stimulus conditions and the optimal response was averaged across all of the optimal stimuli. The
result can be seen in Fig. 8. The effectiveness of bursts in
responses to optimal and nonoptimal stimuli was similar in
that for both effectiveness rose monotonically with burst
length. However, for nonoptimal stimuli, the effectiveness
was lower at all burst lengths by a nearly constant amount
averaging 5.84% (absolute level of effectiveness). This shift
fell outside the 95% confidence level for the standard error
of the mean.
The decrease in effectiveness for nonoptimal stimuli
could simply result from a decrease in overall firing rate.
We consider it highly unlikely that a postsynaptic spike
is the result of one or even several spikes from a single
presynaptic neuron. Rather, it is the consequence of the
aggregate activity of both the presynaptic cells that we
can see ( via recording ) and those we cannot see. A general
decrease in firing rate lowers the statistical expectation
that other cells will be firing in concert with the presynaptic cells that we can observe, which leads to a decrease
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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 Å 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.
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R. K. SNIDER, J. F. KABARA, B. R. ROIG, AND A. B. BONDS
in the overall probability of postsynaptic spikes occurring.
To examine whether the change in effectiveness with different stimuli was related solely to firing rate, we constructed plots of average effectiveness for responses to
optimal versus nonoptimal stimuli across different stimulus classes, including variations in orientation, spatial fre-
FIG . 8. Comparison of burst effectiveness with optimal and nonoptimal
stimulation. Effectiveness was averaged for all presentations of optimal
stimuli ( h ) and all presentations of nonoptimal stimuli ( s ) and is plotted
as a function of burst length. For all burst lengths, effectiveness is Ç5%
higher (absolutely, not relatively) with optimal stimulation. Average effectiveness across all stimuli ( L ) also is shown for comparison.
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quency, contrast presented randomly, and contrast presented in sequential order ( rising, then falling ) to measure
contrast gain control ( Bonds 1991 ) . 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.
When compared with the results from variation of contrast and spatial frequency, the variation of orientation
causes a clearly different impact. Across all nonoptimal
orientations, the firing rate decreased an average of 30.8
spikes / s and the effectiveness dropped by 6.9% ( in absolute effectiveness, not a relative change ) . This is almost
double the average decrease in effectiveness ( a drop of
3.6% ) seen with, e.g., randomized contrast, even though
the decrease in firing rate for lower contrasts, at 36.7
spikes / s, was greater.
These results suggest that the reduction in transmission
efficiency resulting from changing orientation involves
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FIG . 7. Left: examples of orientation tuning of neurons in multiunit groups. Orientations were presented in 107 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.
MODULATION OF CONNECTIVITY IN CAT STRIATE CORTEX
some process beyond that which reduces effectiveness
when contrast is reduced but orientation is optimal. Effectiveness clearly depends on burst length, and burst length
has been shown to be dependent on at least two factors.
Within the range of moderate contrasts, burst length is
more or less proportional to firing rate when contrast is
varied at the optimal orientation. When the firing rate is
varied by driving the cell with nonoptimal orientations,
average burst length is shorter than that found at the same
firing rate ( but lower contrasts ) at the optimal orientation
( Debusk et al. 1997 ) . 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.
To isolate the dependency of effectiveness on burst
length at optimal and nonoptimal orientations, we created
three-dimensional plots for variation of both orientation
and contrast. Orientation was systematically varied across
10 different values centered on the optimal orientation
with 10 presentations at each specific orientation in a random sequence. Thus there were 100 presentations, each 10
s long. For each presentation, we calculated effectiveness,
average firing rate and average burst length. This resulted
in 100 points to plot, each point represented in three dimensions. To clarify the trends in this three-dimensional
space, we fitted a two-dimensional surface representing a
polynomial of order five in both dimensions to these
points. Figure 10, left, shows the surface plots of effectiveness in three neural pairs as a function of both burst length
and firing rate resulting from varying orientation. Plots
from the same cells resulting from randomized variation
of contrast are shown in Fig. 10, right .
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For variation of orientation, the driving neuron is consistently most effective at the greatest firing rate and when
the burst length is the longest. The effectiveness drops
off quite rapidly with a decrease in firing rate, which in
this case is the result of stimulation with orientations to
which the cell responds less robustly. Longer bursts are
generally more effective than shorter bursts irrespective
of firing rate, although at low firing rates all bursts are
ineffective. The increase in effectiveness is much more
pronounced for longer bursts than for shorter bursts as
the firing rate is increased. This is most likely due to the
fact that neighboring neurons are much easier to recruit
( or synchronize ) when they are excited with their preferred orientation, represented by the highest firing rates
and longest bursts.
This characteristic behavior changes dramatically when
the neural pairs are being excited by their preferred orientation but with their firing rate being modified by variation
of contrast. In this case, the driving neuron is much more
effective at low firing rates ( regardless of burst length )
than at these same firing rates when they result from nonoptimal orientation. From a functional standpoint, effectiveness is required at low contrasts because the visual
cortex needs to recruit ( or synchronize ) neighboring cells
to process the visual scene on the basis of sparse information. This requirement would be less desirable with firing
rates that were low due to a nonpreferred orientation because the cortex then would be linking or recruiting cells
that were carrying less relevant visual information. As the
firing rate increases, the effectiveness also increases but
only to a certain point. At moderate contrasts, contrast
gain control ( Bonds 1991; 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.
A more detailed way of showing the difference between
the influences of orientation and contrast on effectiveness is
to compare slices through the two surfaces at similar firing
rates. Taking one of the cells found in Fig. 10 (2nd row),
we chose a nonoptimal orientation that caused the cell to
fire at Ç45 spikes/s. We then found the closest contrast
value that caused the same cell to fire at nearly that same
value (44 spikes/s). At this slice in firing rate, we plotted
the effectiveness as a function of burst length for both orientation and contrast. This was done also for the cell in the
bottom row of Fig. 10 but at a lower firing rate. Results are
shown in Fig. 11, which displays the actual data points instead of the fitted surfaces found in Fig. 10. There is a
general tendency for effectiveness to rise with burst length.
The decrease for long bursts in Fig. 11B is a result of a
low count of bursts for these lengths. In both cases, the
effectiveness of nonoptimal orientations (rrr) is less than
) at all burst lengths even though
that of low contrasts (
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 stimulusrelated variation in the postsynaptic membrane potential that
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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.
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R. K. SNIDER, J. F. KABARA, B. R. ROIG, AND A. B. BONDS
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.
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 ( s ) is lower than that
from variation of orientation ( h ), the effectiveness at the optimal orientation (varied
contrast; s ) is higher at all burst lengths.
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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.
MODULATION OF CONNECTIVITY IN CAT STRIATE CORTEX
Contrast gain control
FIG . 12. Effectiveness and contrast gain control. Here the effectiveness
(
, h ) and firing rate (rrr, *) 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. rrr, 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 Ç14% contrast on the decreasing leg of the curve.
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mechanism underlying this modulation remains unclear, but
tonic hyperpolarization in the postsynaptic cell may be involved (Carandini and Ferster 1997).
DISCUSSION
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), 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 eventbased 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).
We have found that there are at least three factors governing the effectiveness of presynaptic spikes in eliciting a postsynaptic spike. The first two are firing rate and burst length.
Although related, these two are not wholly dependent. Decreasing burst length at a given firing rate, which occurs
with stimuli of nonoptimal orientations, will decrease the
effectiveness. Similarly, decreasing the firing rate with the
burst length remaining constant will decrease the effectiveness. This is presumably due to reduced spatial summation
as a consequence of decreased activity contributed from
other cells. However, even when burst length and firing rate
are accounted for, there is yet another stimulus-dependent
influence on effectiveness, which we attribute to suppression
mediated by network interactions.
Bursting is likely an intrinsic property of the neuron membrane and is mediated via entry of Ca 2/ ions (Pumain et al.
1983; 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
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Bonds (1991) 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 Ç7%
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
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By viewing the coincidence at the burst level, the precise
timing of single spikes, which in any organic environment
would be difficult to attain, becomes relatively unimportant.
More important is whether successive spikes fall within the
time constant of the postsynaptic membrane, thus allowing
temporal integration to occur. The integrate-and-fire model
would be sufficient for the detection of bursts that occur
synchronously and still allow for some random nature of
individual spikes on the order of several milliseconds (Bialek et al. 1991).
The length of the burst itself could play a role in the
modulation of coupling between neurons. The synaptic
strength between two neurons could require a minimal burst
length for successful transmission between them. Another
scenario is learning and memory, where bursts of a certain
length must be simultaneously present to cause a change in
synaptic efficiency. This perspective is related to long-term
potentiation (LTP) where several neurons (cooperativity)
need to be active at the same time (associativity). The spatial
pool of neurons required for LTP could be modulated by
the variation of burst lengths from particular neurons.
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; 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.
The role of bursting is probably not confined within a
particular cortical area. When looking for neural codes, it
would seem reasonable to examine the behavior of neurons
that provide information to the next cortical stage in the
path of visual information processing. Recently Gray and
McCormick (1996) 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 Ç15–50 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.
Decoding of bursts is biologically plausible
Any mechanism for information encoding and decoding
in spike trains must be consistent with the duration required
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is engaged actively in determining the relevance of this information. g-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.
One can postulate that these bursts form the basis of a
combinatorial space-time representation (Wehr and Laurent
1996) 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 corticocortical 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.
Recently, there has been interest in the irregularity of
spike timing (Softky and Koch 1993), 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.
Our view is that a balance of inhibition and excitation is
necessary for the network to control synchronized bursting.
Random and nonspecific cortical activity can be sufficient
to cause the neuron to fire periodically in a Poisson manner.
This changes, however, when the cell has been depolarized
as a result of optimal stimulation. Under this condition, the
increase in burst lengths supports synchronization of the
network with other related neurons. We believe that both
the integrate-and-fire and the coincidence detector models
are correct. We simply view the coincidence as being more
robustly supported by bursts than single spikes.
MODULATION OF CONNECTIVITY IN CAT STRIATE CORTEX
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sensitive anatomic/physiological decoding mechanisms. It
should be noted that the mean of the burst lengths (in time—
up to 5 spikes) are on average õ20 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.
We thank V. Casagrande for thoughtful comments on the manuscript.
This study was supported by National Eye Institute Grant R01EY-0377114 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.
REFERENCES
ABELES, M., BERGMAN, H., MARGALIT, E., AND VAADIA, E. Spatiotemporal
firing patterns in the frontal cortex of behaving monkeys. J. Neurophysiol.
70: 1629–1638, 1993.
ABELES, M. AND GERSTEIN, G. Detecting spatiotemporal firing patterns
among simultaneously recorded single neurons. J. Neurophysiol. 60:
909–924, 1988.
ADRIAN, E. AND ZOTTERMAN, Y. The impulses produced by sensory nerve
endings. J. Physiol. (Lond.) 65: 273–298, 1926.
AERTSEN, A., GERSTEIN, G., HABIB, M., AND PALM, G. Dynamics of neuronal firing correlation: modulation of effective connectivity. J. Neurophysiol. 61: 900–917, 1989.
BAIR, W., KOCH, C., NEWSOME, W., AND BRITTEN, K. Power spectrum
analysis of bursting cells in area MT in the behaving monkey. J. Neurosci.
14: 2870–2892, 1994.
BELL, A., MAINEN, Z., TSODYKS, M., AND SEJNOWSKI, T. ‘‘Balancing’’ of
Conductances May Explain Irregular Cortical Spiking. Institute for Neural Computation, 1995 (Technical Report INC-9502).
BERMAN, N., DOUGLAS, R., MARTIN, K., AND WHITTERIDGE, D. Mechanisms
of inhibition in cat visual cortex. J. Physiol. (Lond.) 440: 697–722, 199.
BIALEK, W. AND RIEKE, F. Reliability and information transmission in spiking neurons. Trends Neurosci. 15: 428–458, 1992.
BIALEK, W., RIEKE, F., DE RUYTER VAN STEVENINCK, R., AND WARLAND,
D. Reading a neural code. Science 252: 1854–1857, 1991.
BONDS, A. Role of inhibition in the specification of orientation selectivity
of cells in the cat striate cortex. Vis. Neurosci. 2: 21–55, 1989.
BONDS, A. Temporal dynamics of contrast gain in single cells of the cat
striate cortex. Vis. Neurosci. 6: 239–255, 1991.
BRAITENBERG, V. Cell assemblies in the cerebral cortex. In: Theoretical
Approaches to Complex Systems, edited by R. Heim and G. Palm. Berlin:
Springer-Verlag, 1978, p. 171–188.
BULLIER, J., MCCOURT, M., AND HENRY, G. Physiological studies on the
feedback connection to the striate cortex from areas 18 and 19 in the cat.
Exp. Brain Res. 70: 90–98, 1988.
BUSH, P. AND SEJNOWSKI, T. Effects of inhibition and dendritic saturation
in simulated neocortical pyramidal cells. J. Neurophysiol. 71: 2183–
2193, 1994.
CATTANEO, B., MAFFEI, L., AND MORRONE, C. Patterns in the discharge of
simple and complex visual cortical cells. Proc. R. Soc. Lond. B Biol. Sci.
212: 279–297, 1981a.
CATTANEO, B., MAFFEI, L., AND MORRONE, C. Two firing patterns in the
discharge of complex cells encoding different attributes of the visual
stimulus. Exp. Brain Res. 43: 115–118, 1981b.
CARANDINI, M. AND FERSTER, D. A tonic hyperpolarization underlying contrast adaptation in cat visual cortex. Science 276: 949–952, 1997.
CELEBRINI, S., THORPE, S., TROTTER, Y., AND IMBERT, M. Dynamics of
07-18-98 12:30:49
neupa
LP-Neurophys
Downloaded from http://jn.physiology.org/ by 10.220.32.247 on May 15, 2017
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). 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.
The minimum number of synaptic stages that visual information must traverse for activation of IT appears to be ¢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 Ç1 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 õ10 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.
This model is particularly troublesome for the coding theory
of Lestienne and Strehler (1988) 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.
How does burst coding fit into this time constraint? If we
looked only at the average firing rate of neurons, which is
typically õ100 spikes/s sustained, this would yield on average
õ1 spike within a 10-ms window. This is hardly enough information on which to base a decision, but bursts can easily
generate three to five spikes in 10 ms. Not only is this very
informative in terms of an instantaneous rate code (similar to
a screaming infant in a room of noisy children), this information can be decoded readily by the postsynaptic neuron using
simple temporal summation as opposed to complicated and
743
744
R. K. SNIDER, J. F. KABARA, B. R. ROIG, AND A. B. BONDS
/ 9k2b$$au38 J-659-7
MACLEOD, K. AND LAURENT, G. Distinct mechanisms for synchronization
and temporal patterning of odor-encoding neural assemblies. Science 274:
976–979, 1996.
MANDL, G. Coding for stimulus velocity by temporal patterning of spike
discharges in visual cells of cat superior colliculus. Vision Res. 33: 1451–
1475, 1993.
MILES, R. AND WONG, R. Excitatory synaptic interactions between ca3
neurones in the guinea-pig hippocampus. J. Physiol. (Lond.) 373: 397–
418, 1986.
MILKMAN, N., SHAPLEY, R., AND SCHICK, G. A microcomputer based visual
stimulator. Behav. Res. Methods Instrum. 10: 539–545, 1978.
MOORE, G., SEGUNDO, J., PERKEL, D., AND LEVITAN, T. Statistical signs of
synaptic interaction in neurons. Biophys. J. 10: 876–900, 1970.
MORRONE, M., BURR, D., AND MAFFEI, L. Functional implications of crossorientation inhibition of cortical visual cells. I. Neurophysiological evidence. Proc. R. Soc. Lond. B Biol. Sci. 216: 335–354, 1982.
OHZAWA, I., SCLAR, G., AND FREEMAN, R. Contrast gain control in the cat’s
visual system. J. Neurophysiol. 54: 651–667, 1985.
PALM, G. Studies of Brain Function: Neural Assemblies. Berlin: SpringerVerlag, 1982, vol. 7.
PAPOULIS, A. Probability, Random Variables, and Stochastic Processes
(2nd ed.). New York: McGraw-Hill, 1984.
PERKEL, D., GERSTEIN, G., AND MOORE, G. Neuronal spike trains and stochastic point processes. I. The single spike train. Biophys. J. 7: 391–
418, 1967a.
PERKEL, D., GERSTEIN, G., AND MOORE, G. Neuronal spike trains and stochastic point processes. II. Simultaneous spike trains. Biophys. J. 7: 419–
440, 1967b.
PERRETT, D., ROLLS, E., AND CAAN, W. Visual neurons responsive to faces
in the monkey temporal cortex. Exp. Brain Res. 47: 329–342, 1982.
PUMAIN, R., KURCEWICZ, L., AND LOUVEL, J. Fast extracellular calcium transients: involvement in epileptic processes. Science 222: 177–179, 1983.
RICHMOND, B. AND OPTICAN, L. Temporal encoding of two-dimensional
patterns by single units in primate inferior temporal cortex. II. Quantification of response waveform. J. Neurophysiol. 57: 147–161, 1987.
RICHMOND, B., OPTICAN, L., AND SPITZER, H. Temporal encoding of twodimensional patterns by single units in primate primary visual cortex. I.
Stimulus-response relations. J. Neurophysiol. 64: 351–369, 1990.
SCHWARTZKROIN, P. AND WYLER, A. Mechanisms underlying epileptiform
burst discharge. Ann. Neurol. 7: 95–107, 1980.
SHADLEN, M. AND NEWSOME, W. Noise, neural codes and cortical organization. Curr. Opin. Neurobiol. 4: 569–579, 1994.
SHANNON, C. A mathematical theory of communication. Bell System Tech.
J. 27(3): 379– 423,623–656, 1948.
SILLITO, A. The contribution of inhibitory mechanisms to the receptive field
properties of neurones in the striate cortex of cat. J. Physiol. (Lond.)
250: 305–329, 1975.
SNIDER, R. The Role of Cortical Burst Firing in the Modulation of Functional Connectivity in Cat Striate Cortex (PhD thesis). Nashville, TN:
Vanderbilt Univ., 1997.
SNIDER, R., KABARA, J., ROIG, B., AND BONDS, A. Synchronous entrainment
of cat striate cortical neurons by display refresh rate (Abstract). Invest.
Ophthalmol. Vis. Sci. 37, Suppl. 3: 2187, 1996.
SOFTKY, W. AND KOCH, C. The highly irregular firing of cortical cells is
inconsistent with temporal integration of random EPSPs. J. Neurosci.
13: 334–350, 1993.
STEIN, R. Some models of neuronal variability. Biophys. J. 7:37–68, 1967.
THORPE, S. AND IMBERT, M. Biological constraints on connectionist modelling. In: Connectionism in Perspective, edited by R. Pfeifer, Z. Schreter,
F. Fogelman-Soulie, and L. Steels. North-Holland: Elsevier Science Publishers B. V., 1989, p. 63–92.
TRAUB, R. AND MILES, R. Neuronal Networks of the Hippocampus. New
York: Press Syndicate of the University of Cambridge, 1991.
VON DER MALSBURG, C. AND BIENENSTOCK, E. Statistical coding and shortterm synaptic plasticity. In: Disordered Systems and Biological Organization, edited by F. Fogelman, F. Weisbuch, and E. Bienenstock. Berlin:
Springer-Verlag, 1986, p. 247–272.
WALPOLE, R. AND MYERS, R. Probability and Statistics for Engineers and
Scientists (3rd ed.). New York: MacMillan Publishing, 1985.
WEHR, M. AND LAURENT, G. Odour encoding by temporal sequences of
firing in oscillating neural assemblies. Nature 384: 162–166, 1996.
WOLLMAN, D. AND PALMER, L. Phase locking of neuronal responses to the
vertical refresh of computer display monitors in cat lateral geniculate
nucleus and striate cortex. J. Neurosci. Methods 60: 107–113, 1995.
07-18-98 12:30:49
neupa
LP-Neurophys
Downloaded from http://jn.physiology.org/ by 10.220.32.247 on May 15, 2017
orientation coding in area v1 of the awake primate. Vis. Neurosci. 10:
811–825, 1993.
CREUTZFELDT, O. AND ITO, M. Functional synaptic organizationof primary
visual cortex neurons in the cat. Exp. Brain Res. 6: 324–352, 1968.
DAYHOFF, J. AND GERSTEIN, G. Favored patterns in spike trains. I. Detection.
J. Neurophysiol. 49: 1334–1348, 1983a.
DAYHOFF, J. AND GERSTEIN, G. Favored patterns in spike trains. II. Application. J. Neurophysiol. 49: 1349–1363, 1983b.
DEBUSK, B., DEBRUYN, E., SNIDER, R., KABARA, J., AND BONDS, A. Stimulus-dependent modulation of spike burst length in cat striate cortical cells.
J. Neurophysiol. 78: 199–213, 1997.
DEL CASTILLO, J. AND KATZ, B. Quantal components of the end-plate potential. J. Physiol. (Lond.) 124: 560–573, 1954.
DOUGLAS, R. AND MARTIN, K. A functional microcircuit for cat visual
cortex. J. Physiol. (Lond.) 440: 735–769, 1991.
DYKES, R., LANDRY, P., METHERATE, R., AND HICKS, T. Functional role of
gaba in cat primary somatosensory cortex: shaping receptive fields of
cortical neurons. J. Neurophysiol. 52: 1066–1093, 1984.
ECKHORN, R., BAUER, R., JORDAN, W., BROSCH, M., KRUSE, W., MUNK,
M., AND REITBOECK, H. Coherent oscillations: a mechanism of feature
linking in the visual cortex? Biol. Cybern. 60: 121–130, 1988.
EGGERMONT, J. AND SMITH, G. Burst-firing sharpens frequency-tuning in
primary auditory cortex. Neuroreport 7: 753–757, 1996.
FROSTIG, R., FROSTIG, Z., AND HARPER, R. Recurring discharge patterns in
multiple spike trains. I. Detection. Biol. Cybern. 62: 487–493, 1990a.
FROSTIG, R., FROSTIG, Z., AND HARPER, R. Recurring discharge patterns in
multiple spike trains. II. Application in forebrain areas related to cardiac
and respiratory control during different sleep-waking states. Biol. Cybern.
62: 495–502, 1990b.
GAWNE, T. J., KJAER, T. W., HERTZ, J. A., AND RICHMOND, B. J. Adjacent
visual cortical complex cells share about 20% of their stimulus-related
information. Cereb. Cortex 6: 482–489, 1996.
GERSTEIN, G., BEDENBAUGH, P., AND AERTSEN, A. M. Neuronal assemblies.
IEEE Trans. Biomed. Eng. 36: 4–14, 1989.
GRAY, C., KONIG, P., ENGEL, A., AND SINGER, W. Oscillatory responses in
cat visual cortex exhibit inter-columnar synchronization which reflects
global stimulus properties. Nature 338: 334–337, 1989.
GRAY, C. AND MCCORMICK, D. Chattering cells: superficial pyramidal neurons contributing to the generation of synchronous oscillations in the
visual cortex. Science 274: 109–113, 1996.
HEBB, D. The Organization of Behavior. New York: Wiley, 1949.
HELLER, J., HERTZ, J. A., KJAER, T. W., AND RICHMOND, B. J. Information
flow and temporal coding in primate pattern vision. J. Computat. Neurosci. 2: 175–193, 1995.
HUBEL, D. Single unit activity in striate cortex of unrestrained cats. J.
Physiol. (Lond.) 147: 226–238, 1959.
HUBEL, D. AND WIESEL, T. Receptive fields of single neurones in the cat’s
striate cortex. J. Physiol. (Lond.) 148: 574–591, 1959.
KIM, H., BEIERLEIN, M., AND CONNORS, B. Inhibitory control of excitable
dendrites in neocortex. J. Neurophysiol. 74: 1810–1814, 1995.
KIM, H. AND CONNORS, B. Apical dendrites of the neocortex: correlation
between sodium- and calcium-dependent spiking and pyramidal cell morphology. J. Neurosci. 13: 5301–5311, 1993.
LESTIENNE, R. AND STREHLER, B. Time structure and stimulus dependence
of precisely replicating patterns present in monkey cortical neuronal spike
trains. Brain Res. 437: 214–238, 1987.
LESTIENNE, R. AND STREHLER, B. Differences between monkey visual cortex
cells in triplet and ghost doublet informational symbols relationships.
Biol. Cybern. 59: 337–352, 1988.
LEVICK, W. Another tungsten microelectrode. Med. Biol. Eng. 10: 510–
515, 1972.
LEVICK, W., CLELAND, B., AND DUBIN, M. Lateral geniculate neurons of cat:
retinal inputs and physiology. Invest. Ophthalmol. 11: 302–311, 1972.
LI, C. AND CREUTZFELDT, O. The representation of contrast and other stimulus parameters by single neurons in area 17 of the cat. Pflügers Arch.
401: 304–314, 1984.
LI, C., ORTIZ-GALVIN, A., CHOU, S., AND HOWARD, S. Cortical intracellular
potentials in response to stimulation of lateral geniculate body. J. Neurophysiol. 23: 592–601, 1960.
LINDE, Y., BUZO, A., AND GRAY, R. An algorithm for vector quantizer
design. IEEE Trans. Commun. 28: 84–95, 1980.
LIVINGSTONE, M. Oscillatory firing and interneuronal connections in squirrel
monkey striate cortex. J. Neurophysiol. 75: 2467–2485, 1996.