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1Departments of Neurobiology and Psychology, Jules Stein Eye Institute, Brain Research Institute, University of California, Los Angeles, California 90095; and 2Center for Neural Science, New York University, New York City, New York 10003
Submitted 11 November 2002; accepted in final form 11 February 2003
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ABSTRACT |
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 TOP ABSTRACT METHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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The temporal development of neural selectivity to stimulus attributes can
provide important clues about the underlying circuitry
(Bredfeldt and Ringach 2002
;
Pei et al. 1994;
Ringach et al. 1997b;
Volgushev et al. 1995).
Cortical excitation and inhibition onto a neuron are expected to be delayed
with respect to the monosynaptic input from the lateral geniculate nucleus
(LGN). Suppose one measures responses of a cortical neuron at different delay
times with respect to stimulus onset. The early response would be dominated by
excitation from the LGN input, whereas the late response would correspond to a
combination of both LGN input and intracortical interactions. For
orientation-tuning dynamics, some groups report dynamical changes in the shape
of the tuning curves (Pei et al.
1994; Ringach et al.
1997b; Volgushev et al.
1995) while others observe a scaling of its magnitude and no
significant changes in its shape (Celebrini
et al. 1993; Gillespie et al.
2001; Mazer et al.
2002; Muller et al.
2001; Sharon and Grinvald
2002).
In our earlier study (Ringach et al.
1997b) on the timing of the development of orientation tuning, we
found that there were, in many cells, significant dynamical changes in shape
of the orientation tuning curves. In particular, we suggested that the
development of Mexican-hat tuning curves in the response could be accounted
for by the presence of a tuned suppressive component centered on the preferred
orientation of the cell. In more recent studies, we have concluded that in
addition to a tuned suppressive component, there is a global suppressive
component involved in the tuning for orientation and spatial frequency
(Bredfeldt and Ringach 2002;
Ringach et al. 2002a).
However, up until now, we only reported results about these global components
at a fixed delay time (the peak) in the time evolution of the response. In
this paper, we bring together these concepts to study both the time evolution
of the global components in the dynamical response and the relationship of the
global to the tuned components. This brings new insights into the cortical
processes that are responsible for the generation of orientation tuning.
Here we re-examine the dynamics of orientation tuning in macaque V1 using
an improved version of the reverse-correlation method where in addition to
oriented patterns, "blank" frames of uniform luminance appear
within the stimulation sequence (Ringach
et al. 1997a). The blanks provide a baseline that allows direct
detection of response enhancement and suppression by an oriented pattern. This
modified reverse-correlation technique allowed us for the first time to
measure enhancement and suppression components that are un-tuned for
orientation. Previous techniques used by us and others
(Mazer et al. 2002) do not
allow the measurement of such global effects of oriented dynamical stimuli.
These new measurements reveal important new phenomena, as shown in detail in
RESULTS. One new phenomenon is global response enhancement early in
the response of most neurons. The second new phenomenon is global suppression,
also observed in most neurons. What is remarkable is the rapid time course of
global suppression and its strength. In many neurons, we also observed the
phenomenon of orientation-tuned suppression that was evident in our earlier
data (Ringach et al. 1997b).
Because of the overlap in time of enhancement and suppression, we attempted to
gauge the strength of the global and the tuned suppression relative to that of
enhancement through analysis with a descriptive model.
The dynamics data were analyzed in the context of a model in which, at each time, the tuning curve is obtained as a linear combination of two fixed, tuned components (enhancement and suppression) and one global (untuned) component. Data analysis with this model suggests that early global enhancement causes the cell to respond to all orientations. Then global and tuned suppression develop rapidly and are comparable in magnitude to the tuned enhancement the cells receive. The suppressive components appear responsible for increasing the "modulation depth" of the tuning curve, for the dynamical narrowing of orientation bandwidth, for the generation of Mexican-hat tuning profiles, and for producing small shifts in the preferred orientation over the time course of the response. This leads to the conclusion that global and tuned suppression are important factors that determine the selectivity and dynamics of V1 responses to orientation.
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METHODS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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Acute experiments were performed on adult Old-World monkeys (Macaca
fascicularis) in compliance with National Institutes of Health and New
York University/UCLA guidelines. Animal preparation and recording were done as
described in Ringach et al.
(2002a,b).
Each cell was stimulated monocularly through the dominant eye and
characterized by measuring its steady-state response to high contrast drifting
gratings (the non-dominant eye was occluded). Using this method, we recorded
basic attributes of the cell, including spatial and temporal frequency tuning,
orientation tuning, and contrast and color sensitivity as well as area
summation curves. Receptive fields were located at eccentricities between 1
and 6°. The mean luminance of the screen was 50 cd/m2, the
viewing distance 90–120 cm, and the refresh rate was 60 Hz or 100
Hz.
Reverse correlation in the orientation domain
A modified version of reverse correlation in the orientation domain was used to measure the time evolution of orientation tuning. For each cell, a set S of sinusoidal gratings of a fixed spatial frequency (optimal for the cell) and contrast (in the range 80–99%) but different orientations and spatial phases was generated and stored in the computer's memory. The orientation domain was sampled in equal steps ranging from 3 to 12°. For most cells, the angular step was fixed at 10°. For each orientation, sinusoidal gratings at eight equally spaced spatial phases, spanning the entire 360° range, were included in the set. Eight "blank" (uniform) images, of the same luminance as the mean of the gratings' luminance, were included in the set as well. In a typical experiment the total number of images in S was 152 (18 orientations times 8 spatial phases plus 8 blanks).
The stimulus was generated by randomly selecting, at each video refresh
frame, a new image from S with replacement. The stimulus was
presented in 30-s-long trials with 
1- to 2-s inter-stimulus intervals. A
total of 30 trials was presented to each cell, making the total experimental
time 15 min. The specific image sequence was saved by the computer, and action
potentials were recorded and time-stamped by the data acquisition system. The
radius of the stimulus was two to four times the radius of classical receptive
field (RF) defined by the peak or saturation point of an area summation curve
(Sceniak et al. 1999). Thus
both the classical RF of the cell and its surround were stimulated. We
reasoned that under these conditions both feed-forward and intracortical
mechanisms of orientation tuning may be engaged, while stimuli restricted to
the classical receptive field may bias the results to the direct contribution
of the LGN inputs. In addition, natural images are spatially extended and
contours tend to have long-range structure. Large stimuli covering both the
receptive field and the surround approximate the natural situation closer than
a stimulus restricted to the classical receptive field of the neuron.
The time course of orientation tuning was determined according to the
following algorithm. First, an array of counters corresponding each to the
orientations present in the stimulus, and one separate counter representing
the blanks, were zeroed. A fixed value of a time-delay parameter 
was
selected. For each nerve impulse, we went back ms and determined the
frame that was last present in the image sequence. If the stimulus was a
grating, the counter corresponding to its orientation was incremented by one.
If the stimulus was a blank, the counter corresponding to the blanks was
incremented by one. Gratings of different spatial phases but the same
orientation contributed to the same counter. Thus this procedure averages
across spatial phase at each orientation. At the end of this procedure, all
the spikes recorded end up being distributed in the counters. Thus the sum of
all the counts in the counters equal the total number of spikes collected.
This is the case irrespective of the time delay chosen. The resulting
counts were normalized by the actual number of times each orientation (or
blank) appeared in the sequence. This provides an estimate of the probability
that the cell will fire in a window (, + T) ms after a
stimulus is shown (where T is the duration of 1 frame). This function
is identical, up to a scaling factor, to the probability that a stimulus
preceded a spike by ms. In previous work, we described our results in
terms of the probability of a stimulus preceding a spike; but in
recent years, we realized that our colleagues find it more intuitive to think
about the "forward" interpretation, which we now adopt. These two
interpretations are equivalent if the "forward" cross-correlation
is smoothed in time with a T-ms box window. Once the probability of
firing in response to an oriented pattern, p(
, ), and the
blank, p(blank, ), were estimated we calculated
R(, ) = log10[p(,
)/p(blank, )], which we refer to as the tuning curve at a
time lag . Oriented patterns that generate responses identical to the
"blank" are mapped to R(, ) = 0, stimuli that
enhance cell's response are mapped to R(, ) > 0, while
stimuli that suppress the cell's response are mapped to R(,
) < 0. A statistical justification for the log transform in the
definition of R(, ) was provided in Ringach et al.
(2002a). Furthermore, one can
view this transformation as providing an estimation of a log-linear model of
p(, ) based on the stimuli assuming that the weight of
the "blank" stimulus is zero. A log-linear model for the
probability of firing is more appropriate than simply linear regression as the
latter can generate predictions outside the [0, 1] range.
Nonparametric analysis of orientation dynamics
Consider a hypothetical tuning curve at a fixed time lag
(Fig. 1). Using nonparametric
methods, we estimate a number of features of the curve. These include the
orientation angle of the peak response, max, and its
magnitude Rmax; the orientation angle and magnitude of the
minimum response, min and Rmin; the
angle orthogonal to max, denoted here by
orth, and the magnitude attained by the tuning curve there,
Rorth; the "modulation depth" of the tuning
curve, defined by A = Rmax –
Rmin; and the dynamic half-bandwidth
Bd defined by half the width of the tuning curve at a
criterion level of Rorth + (Rmax
– Rorth)/2.
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Parametric analysis
The parametric analysis was performed by fitting R(, )
= 
()E() + 
()S() +
() to the data, where
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) normalized
between zero and one. The von Mises distribution has been shown to provide
very good fits to empirical data (Swindale
1998). The parameter e determines the center of
the component and 
e its width. Similarly, the suppressive
component was parameterized by
 |
, ) was done by a fixed-point algorithm defined by the
repeated interaction of two steps. In the first step, we assumed the
parameters of E() and S() were known (and
fixed) and found the best fitting coefficients at each time delay
independently (under the constraints , > 0). In the second
step, we found the best fitting values of (e,
e, s, s) using the
coefficients from the first step. The process was repeated until there was
<0.1% change in the parameters from one interaction to the next. Although
we do not have a proof that this algorithm is guaranteed to converge in all
situations, it worked remarkably well in nearly every single instance we
tried. Confidence intervals
Confidence intervals for the estimated parameters were determined by
bootstrap simulation as follows (Efron and
Tibshirani 1993). For each time delay, the algorithm provides a
distribution of N spikes into M bins. These multinomial data
were resampled to generate different tuning curves, and the parameters
estimated from the resampled data. A total of 500 simulations was performed at
dev and dec to determine 95% confidence
intervals for each parameter and their differences. For each data set,
nonparametric estimates were obtained after linearly interpolating the raw
data with 0.1° resolution and smoothing the tuning curve with a von Mises
distribution with a parameter = 14, which corresponds to a
half-bandwidth at half-height of 10°.
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RESULTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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The behavior of A(), Rmin(), and
Rorth() for four representative neurons is depicted
in Fig. 2, left. The
modulation depth, A(), normally increases to reach a peak and
then declines back to baseline. We used the time course of the modulation
depth to define three time lags at which the orientation tuning curves were
subsequently analyzed (Fig. 2,
middle and right). These correspond to the points at which
the modulation depth achieved its maximum value (pk), and the
points at which it achieved half its maximum value during the development
(dev) and decay (dec) phases of the response
(vertical dashed lines in Fig.
2, left). The distribution of dec –
dev over the V1 population had a mean of 22.3 ± 6.6 ms
(1 SD) and the dynamical changes described in the following text occur over
this time scale.
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Figure 2, middle
and right, depicts orientation-tuning curves for these four
representative neurons at dev (red, middle),
dec (blue, middle), and pk
(right). The changes with time in the height of these curves compared
to the baseline, and the changes in their shapes, show that orientation
selectivity varies dynamically in most V1 neurons in a very clear way.
The dynamic behavior of Rmin() shows a number of
important features. In all four examples,
Rmin(dev) > 0, as the red curves in
Fig. 2, middle, are
above zero for all four neurons. This means that during the development of the
response all orientations induced the cell to fire more than to a
blank stimulus. In contrast, Rmin(dec)
< 0, indicated by the blue curves in
Fig. 2, middle, being
below zero. Thus during the decay phase of the response, some orientations
suppressed spike firing. In some V1 neurons, this effect appears to be
mediated by global suppression (Fig. 2,
A and B, middle and right). In
other cells, however, there is also evidence of tuned suppression developing
over the time course of the response, which causes the shape of the tuning
curve to develop into a Mexican-hat profile during the decay phase
(Fig. 2,C and
D). For the cells in
Fig. 2, C and
D, Rmin() and
Rorth() begin to diverge around the time of the peak
response, implying that after pk the minimum response occurs
at a location other than the orthogonal—the signature of a Mexican-hat
profile.
Average dynamics in V1
The average dynamics of A, Rmin, and
Rorth in our population of n = 178 V1 cells are
shown in Fig. 3. An important
feature of the data is the sharp downward change in time course of
Rmin() and Rorth()
before pk. This suggests that the mechanism of
suppression is rapid and contributes to the modulation depth at the peak time.
Another important feature is the positive sign of Rmin and
Rorth early in the response, indicating that, on average,
V1 cells tend to respond to all orientations at this time.
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Population analysis
The dynamics of Rmin across the population are analyzed
in Fig. 4. There is an initial
tendency for cells to respond to all orientations during the development phase
of the tuning curve—the sample mean of
Rmin(dev) is significantly greater than
zero (t-test, P < 3 x
10–6; Fig.
4A, bottom). However, most cells tend to be
suppressed at some orientations during response decay because the sample mean
of Rmin(dec) is significantly less than
zero (t-test, P < 1 x
10–10; Fig.
4, left). Thus Rmin decreases from
the development to the decay phases of the response as illustrated by the
difference histogram along the diagonal
(Fig. 4A). The average
difference Rmin(dev) –
Rmin(dec) is significantly greater than
zero (t-test, P < 1 x
10–10). These results on the dynamics of
Rmin() depend on being able to have a baseline
against which to measure the early enhancement and later suppression. They
indicate a major qualitative change in orientation-tuning curves with time
across the V1 population of the kind seen in the representative neurons in
Fig. 2.
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It is possible to establish a correlation between orientation selectivity
and suppression by examining the natural variability across the V1 population.
There is a correlation between the maximum modulation depth
A(pk) and
Rmin(dec)
(Fig. 4B). The larger
the suppression observed during response decay, the larger the modulation
depth of the tuning curves at their peak. This result indicates that cortical
suppression may be needed for high orientation selectivity in V1.
The shape of the tuning curves changes over the response period in many neurons (Fig. 5). A common pattern we observe is the transition from a Gaussian-like tuning curve to a Mexican-hat shaped one (Fig. 2,C and D). To quantify this effect, we compared the minimum response to the response at the orthogonal orientation. Figure 5A shows a scatter-plot for Rorth – Rmin at the development and decay times. When the minimum response in the tuning curve occurs at the orthogonal orientation, Rorth – Rmin = 0. For a Mexican-hat shaped tuning curve, this difference will be positive, as the minimum occurs at an orientation other than the orthogonal. The population data in Fig. 5A show that most cells have a minimum response near the orthogonal orientation both during the development and the decay of the response but that during the decay phase, a significant number of cells have Rorth > Rmin, implying a Mexican-hat shape for the tuning curve of these neurons.
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The location of the minimum response relative to the peak orientation correlates with the bandwidth of the cell (Fig. 5B). Cells that are broadly tuned tend to have their minimum response at locations near the orthogonal orientation, whereas cells that are more sharply tuned tend to have a minimal response at flanking orientations (<90° away). The graph in Fig. 5B illustrates the point that whenever the bandwidth during the decay phase was small (indicating the cell was sharply tuned), flank suppression was invariably observed.
The bandwidth can change dynamically over time
(Fig. 6). A scatter-plot of
Bd(dev) versus
Bd(dec) shows that the bandwidths of some
cells narrow (points below the unit line) and others broaden (points above the
unit line; Fig. 6A).
Figure 6B depicts the
percent decrease in bandwidth versus the bandwidth of the tuning curve at
dev. A summary of the data is provided in the form of two
histograms showing the percent decrease in bandwidth for cells that achieve a
small bandwidth [Bd(dev) < 30°] and
those that do not [Bd(dev) 
30°;
Fig. 6C]. Sharply
tuned cells sharpen over time (Fig.
6C, top, t-test, P <
10–10) while there is a tendency for cells that
are initially moderately or broadly tuned to broaden over time
(Fig. 6C, bottom,
t-test, P < 0.015).
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To investigate if the changes in bandwidth occur preferentially during the
rising or decay phase of the response, we plotted the relative change in
bandwidth, as a function of the initial bandwidth, in the time periods
(dev, pk) and (pk,
dec) (Fig. 7). The scatter plots have the same overall structure as the one in
Fig. 6B. Sharply tuned
cells (with bandwidths <30°) tend to show a decrease in bandwidth in
both periods, with a slighter larger decrease during the decay phase (mean of
4.6% decrease in the rising phase and 6.3% in the falling phase). The
situation appears to be more complex for broadly tuned cells, which also show
a decrease in bandwidth during the rising phase but appear to broaden during
the decay. The net effect is a slight broadening
(Fig. 6, A and
B).
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The preferred orientation of neurons usually remained relatively constant
within the (dev, dec) window, but significant
changes in the order of 5–15° were observed in some neurons
(Fig. 8). We note that the
present analysis of orientation shifts was restricted to the time window
defined by dev and dec. As reported by us
previously, if we were to look at times larger than dec, many
of the tuning curves that develop into Mexican-hat profiles at
dec will evolve into a tuning curve that appears
"inverted" at a later time and where the maximum is at the
orthogonal orientation (Ringach et al.
1997b). We define a response to be inseparable in orientation and
time if either the bandwidth or the peak orientation showed significant
changes between dev and dec. With this
criterion, 123 of 178 cells (69%) showed inseparable responses.
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Model-based interpretation of orientation dynamics
The empirical results presented in Figs.
2 and
3 indicate that there are at
least three different kinds of processes leading to orientation selectivity
and that they overlap in time in the dynamical responses. To explore the
mechanisms of suppression, we fitted a three-component model to the data. One
component was tuned enhancement; one was tuned suppression; and the third
component was untuned (or global) enhancement or suppression (depending on the
sign of the global term). The three-component model is described by
R(, ) = ()E() +
()S() + (). Here E()
> 0 and S() < 0 represent tuned enhancement and
suppression components, and their shapes are parameterized by (normalized) von
Mises functions with different centers and widths (see METHODS). At
each point in time, the response R(, ) is approximated as
a linear combination of these two tuned components plus the flat (global)
component. The coefficients (), (), and ()
represent the coefficients for tuned enhancement, tuned suppression, and the
global component, respectively. While () and () were
constrained to be positive, () was free to be either positive or
negative. The model provided very good fits to the data (in 90% of the neurons
the residual variance was <10%). Figure
9A shows an example of how dynamics data in
Fig. 2D (open circles)
were fit by the model (solid curves) at dev and
dec by linear combination of the fixed components shown
right.
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Global and local suppression develop during the time course of the response
(Fig. 9B). We define
the "strength" of each component by the area under it.
Specifically, the area bounded between the orientation axis and
()E() is denoted by (), the area
bounded by ()S() is denoted by (), and
the area bounded by the constant component (). To compare the
relative weight of each component, we define '() =
()/(() + () +
|()|), '() =
()/(() + () +
|()|) and '() =
()/(() + () +
|()|). Notice that ' and '
are always positive but that ' can be either positive or
negative. Because ' + ' +
|'| = 1, we can visualize the points
(', ', ') in barycentric coordinates
(Fig. 9B). The
coordinates of each point are graphed as distance from the sides of two
abutting equilateral triangles. Distance from the right hand side of each
triangle is the relative weight of tuned enhancement, '. Distance
from the left hand side is the relative weight of tuned suppression,
'. Distance above and below the common base of the triangles is
the signed weight of the global component, ' (if '
is positive the point is plotted in the upper triangle, if it is negative in
the lower triangle).
Figure 9B,
left, shows that the responses at dev are mainly
located in the upper triangle near the left-hand side. This implies that
average relative weight of tuned enhancement,
'(dev), was much greater than the weight of tuned
suppression, '(dev), and the global component was
net positive— meaning global enhancement was fairly strong in most cells
at dev. Relative to the distribution of points at
dev, the distribution of the relative component weights later
in the response, at dec, is shifted down and to the right
(Fig. 9B,
right). The shift downward implies that, during the decay phase, the
global component's sign '(dec) shifts from
positive to negative; the shift rightward implies that a tuned suppressive
component must be included to fit the tuning curves at dec.
Early in the response, the tuned suppressive component is weaker than the
enhancement component (points clustered to the left of the diagram). But
later, tuned suppression and enhancement are more nearly equal (points near
the vertical axis of the diamond).
The modeling also reveals that global suppression grows stronger with time,
and for many neurons is also comparable in strength to tuned
enhancement—as seen by the cluster of neurons that lie near the middle
of the lower triangle in the right-hand barycentric plot of
Fig. 9B. Furthermore
the results show that the relative strengths of tuned enhancement, tuned
suppression, and global enhancement and suppression vary dynamically. Within
this model, the changes in bandwidth, the development of Mexican-hat profiles,
and changes in preferred orientation are explained by the development of the
tuned suppressive component over time. Although in some cases the suppression
may appear smaller than the enhancement in the plots of R(),
this does not mean necessarily that the neural mechanisms of suppression are
weak. Overlap in time and orientation of enhancement and suppression can mask
the true strength of the suppressive signals. The results of the descriptive
model presented in Fig. 9
support this reasoning.
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DISCUSSION |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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, )
(Ringach et al. 1997b). The
present technique makes global and tuned suppression evident by the inclusion
of "blank" images in the sequence. Both global and tuned
suppression contribute to the development of orientation selectivity by
enhancing the overall "modulation depth" of the tuning curve. In
addition, tuned suppression is responsible for dynamic decreases in
orientation bandwidth and for the generation of Mexican-hat-shaped tuning
profiles, especially in cells that are very well tuned. These results are in
general agreement with two recent reports from our group that showed the
association of suppression and tuning selectivity using a different kind of
dynamical stimuli (Ringach et al.
2002a) and the diversity of steady-state orientation selectivity
and the association of high selectivity with suppression below spontaneous
firing at off-peak locations (Ringach et
al. 2002b). All of these recent results, together with previous
work (Benevento et al. 1972;
Blakemore and Tobin 1972;
Bonds 1989; Crook et al.
1997,
1998;
Monier et al. 2000;
Nelson 1991;
Nelson and Frost 1978;
Pei et al. 1994;
Sato et al. 1986;
Sillito et al. 1980), point to
the important role of suppression in generating high selectivity for
orientation angle.
The results of these experiments indicate that orientation tuning in V1 is
a dynamic process driven by rapid excitation and sculpted by almost equally
rapid inhibitory processes. The early broad excitation that could be caused by
LGN input is expected on theoretical grounds to show a response at all
orientations (McLaughlin et al.
2000; Troyer et al.
1998,
2002;
Wielaard et al. 2001). Our
experimental data are consistent with this theoretical prediction as evident
in the presence of early enhancement at all orientations. A number of
investigators have proposed that this global excitation from the LGN must be
cancelled, later in time, by intra-cortical inhibition to obtain sharp tuning
(McLaughlin et al. 2000;
Shelley et al. 2002; Troyer et
al. 1998,
2002;
Wielaard et al. 2001). Our
results also support the notion of such a "canceling" process.
However, detailed cortical network models have so far only accounted for
global inhibition that would suppress the responses at all angles including
the orthogonal. Tuned suppression, of the kind we have observed causes
narrowing of bandwidth in the most highly tuned cells, has not been accounted
for in these models yet but has been incorporated in more abstract "ring
models" (Ben-Yishai et al.
1995; Carandini and Ringach
1997; Pugh et al.
2000; Somers et al.
1995). Future theoretical research has as a challenge to explain
how tuned suppression arises in a model based on a realistic cortical
architecture.
Comparison with results of previous studies
Gillespie et al. (2001)
studied the dynamics of orientation tuning of the membrane potential in 20
cells of cat area 17. The behavior of their offset parameter [which is
analogous to our global component ()] showed an early
depolarization and a late hyperpolarization that is consistent with the global
effects that we find (Fig. 9).
Thus global excitation and inhibition are evident in their intracellular data.
However Gillespie et al.
(2001) did not observe the
dynamic changes in bandwidth and preferred orientation that we observed. One
major methodological difference that could explain the differences in results
is that their stimuli were flashed at a relatively low temporal frequency (10
Hz); this means that the orientation of the pattern in their stimuli change
every 100 ms. Because the orientation is constant throughout the integration
time of the neurons, the response of the cell will represent an integrated
response— or "step response"—to the constant presence
of the stimulus. In contrast, if the orientations change on a faster time
scale than the integration time of the cell, the result of the experiment will
represent the "impulse response" of the cell to a briefly flashed
orientation. We believe most of the features we observe at late times in our
impulse response data are likely to be blurred by time averaging, which is
what effectively is done by calculating a step response. Another important
methodological difference is stimulus size. Gillespie et al.
(2001) used small stimuli
restricted to the "classical RF" of the cell, while we used
stimuli that were two to four times the size of the RF. It is possible that
some of the suppressive effects we observe originate in the surround; this
means they would have not been present when stimulating with small
stimuli.
Mazer et al. (2002)
measured the dynamics of orientation and spatial frequency tuning of single
neurons in awake, fixating monkeys using methods similar to those in our 1997
paper (see also, Bredfeldt and Ringach
2002; Ringach et al.
1997c). Their stimuli did not include blanks within the sequence
and, therefore, Mazer et al. could not have measured the dynamically changing
global effects (early global enhancement and later global suppression) we
describe in the present paper. To address the issue of dynamic changes in the
shape of the tuning curve, Mazer et al.
(2002) applied a singular
value decomposition (SVD) of p(, ) and calculated the
amount of variance accounted for by the first component. Their data were
described as being largely separable in orientation/time and
spatial-frequency/time because a single component could account for a large
percentage (90%) of the overall variance. Separability in
orientation/time means that there are no dynamical changes in the shape of the
tuning curve. A possible reason for this discrepancy is that an SVD analysis
will be mainly dominated by the large values of p(, ) and
any possible changes in the small probabilities at off-optimal orientations
will be largely ignored. We performed a SVD analysis of p(,
) in some of the cells that showed large and statistically significant
changes in our population. We assume that the minimum response across all
orientations was subtracted for each time slice before the SVD calculation was
performed. Even when changes were obvious, such as the cell in
Fig. 2D, the amount of
variance accounted for by a single component was large (93% in this case).
Thus we think that because the variance of the signal in p(,
) is dominated strongly by the central peak, the SVD analysis might not
be sensitive enough to detect clear geometric changes in the shape of the
tuning curve that, nevertheless, contribute moderately to the overall energy
of the signal. Our analysis, instead, is based on the logarithm of the
probability, which will tend to emphasize the structure of the tuning curve at
off-peak locations. Therefore the differences between our results and those of
Mazer et al. are likely due to the combination of insensitivity of their
analysis method and a low signal to noise in their data.
Mazer et al. (2002) also
criticized our previous work stating that the dynamical features we observed
could have been caused by temporal smoothing of noise because of the temporal
autocorrelation of the frames, that artifacts can arise when calculating
cross-correlations at 1-ms time scales, that the statistical significance of
the smoothed data cannot be assessed, and that our normalization of the
distribution of spikes counts across bins is inappropriate. We answer these
criticisms as follows. First, the stimulus is not a constant frame that
changes instantaneously from one pattern to the next in the sequence. In a
typical situation, the entire computer screen, at a viewing distance of 114
cm, spans 15° of visual angle in both vertical and horizontal axes.
The size of a typical receptive field in parafoveal V1 is 1° in
diameter. Thus it takes the raster <2 ms to stimulate the area
corresponding to the RF. From the point of view of the cell, the stimulus
resembles a sequence of short pulses with no stimulation in between. The
autocorrelation of the input is then a very sharp peak 3 ms wide and can
be considered effectively white—there are no long temporal
autocorrelations in the stimulus as Mazer et al.
(2002) suggest. Nevertheless,
our data are indeed smoothed in time with a box window of width T.
This is a consequence of the algorithm used, which assigns a spike to the
orientation that was presented last when looking back ms into the
stimulus. This smoothing was done to increase the signal to noise of the
measurements at the expense of losing some temporal resolution. Smoothing will
only blur any features present in the data and cannot create new ones. Clearly
a Mexican-hat profile cannot be generated by smoothing a family of
Gaussian-shaped tuning curves. Mazer et al.
(2002) also suggested that a
smooth change in the preferred orientation may result simply from temporal
smoothing of a noisy signal. This is indeed correct and can happen if the
total number of spikes to be distributed in the orientation bins is small.
However, the statistical significance of such a shift can be assessed in the
way we propose here using bootstrapping methods and our data show
statistically significant shifts in many cells. Finally, we do not think there
is any difference in the normalization procedure used by us versus that used
by Mazer et al. Each time slice in our data gets normalized by the same
number, which also corresponds to a simple scaling operation as in Mazer et
al. (2002) (see
METHODS). We also point out that scaling of the data is irrelevant
for the analysis in the present study that is based on the ratio between the
tuning curve at one orientation and a blank. Scaling, as long as it is
identical at each time frame, will not change any of the results reported
here.
In another recent study, Sharon and Grinvald measured the average dynamics
of orientation tuning in cat area 17 using optical imaging with
voltage-sensitive dyes (Sharon and
Grinvald 2002). Similar to the findings of Gillespie et al.
(2001), these authors report
the "step response" of the optical signal and found no major
changes in its bandwidth during the time course of the response. They
interpreted their results as implying that the bandwidth of orientation tuned
neurons in V1 was constant with time. However, given the data presented here
and the preceding considerations about step-response measurements, it is
likely that Sharon and Grinvald could not have resolved the sharpening in
bandwidth we observed. Also, it is important to realize that narrowing of the
orientation bandwidth does not occur in every cell but tends to be most
prominent in sharply tuned neurons (Fig.
6C), which are a minority of the population. Second,
broadening (of the tuning curves of more broadly tuned neurons) is also seen
in our data (Fig. 6C).
This suggests that the optical signal, which represents an average of the
population, might have missed the effects seen when recording individual
neurons.
Two other groups have measured the step response of macaque V1 neurons to a
flashed bar or grating at different orientations and built dynamical
orientation tuning curves by temporal slicing of these data
(Celebrini et al. 1993;
Muller et al. 2001). In
examples shown by Celebrini et al.
(1993), there is evidence of
fast suppression at off-optimal orientation, which is consistent with our
results. We think the failure of both groups to observe dynamic changes in
bandwidth could be due to the coarser time resolution of their measurements
(10 and 50 ms, respectively) and the fact that they are analyzing step
responses and not impulse responses. Furthermore, in some cells, threshold
effects (flashing gratings when the spontaneous firing rate of the cell is
near or at 0) probably prevented the measurement of subthreshold orientation
tuning dynamics. Celebrini et al.
(1993) interpreted the fast
emergence of a well-tuned response as evidence for a feed-forward theory of
orientation selectivity. However, this interpretation was based on the
assumption that intracortical inhibition is a slow process, taking hundreds of
milliseconds, contrary to the evidence we supply here and to their own
published examples. In addition, recent theoretical work
(Jin and Seung 2002) shows
that in the context of a cortical network model with rapid inhibition, one
should actually expect the fast emergence of a tuned response.
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ACKNOWLEDGMENTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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FOOTNOTES |
|---|
Address for reprint requests: D. L. Ringach, Dept. of Psychology, Franz Hall, University of California, Los Angeles, CA 90095-1563 (E-mail: dario{at}ucla.edu).
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REFERENCES |
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, points for which
Rmin(
30° vs. a set of broadly
tuned cells Bd(
, statistically significant
changes; 
, statistically insignificant changes.