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The Journal of Neuroscience, June 15, 1999, 19(12):5074-5084
Spatial Summation in the Receptive Fields of MT Neurons
Kenneth H.
Britten1, 2 and
Hilary W.
Heuer1
1 Center for Neuroscience and 2 Section of
Neurobiology, Physiology, and Behavior, University of California
Davis, Davis, California 95616
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ABSTRACT |
Receptive fields (RFs) of cells in the middle temporal area (MT or
V5) of monkeys will often encompass multiple objects under normal image
viewing. We therefore have studied how multiple moving stimuli interact
when presented within and near the RF of single MT cells. We used
moving Gabor function stimuli, <1° in spatial extent and ~100 msec
in duration, presented on a grid of possible locations over the RF of
the cell. Responses to these stimuli were typically robust, and their
small spatial and temporal extent allowed detailed mapping of RFs and
of interactions between stimuli. The responses to pairs of such stimuli
were compared against the responses to the same stimuli presented
singly. The responses were substantially less than the sum of the
responses to the component stimuli and were well described by a
power-law summation model with divisive inhibition. Such divisive
inhibition is a key component of recently proposed "normalization"
models of cortical physiology and is presumed to arise from lateral
interconnections within a region. One open question is whether the
normalization occurs only once in primary visual cortex or multiple
times in different cortical areas. We addressed this question by
exploring the spatial extent over which one stimulus would divide the
response to another and found effective normalization from stimuli
quite far removed from the RF center. This supports models under which
normalization occurs both in MT and in earlier stages.
Key words:
normalization; divisive inhibition; visual motion; dorsal
pathway; directional selectivity; motion models; reverse correlation; hierarchy
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INTRODUCTION |
Extrastriate cortex of monkeys
contains a series of linked areas, often termed the "motion
system," which are highly specialized for the analysis of visual
motion. The middle temporal area (MT, or V5) appears to take an
intermediate position in this hierarchically organized series of areas.
One correlate of the hierarchy in this pathway is progressively
increasing receptive field (RF) size. Thus, the RFs of MT cells are
larger than those of their inputs by as much as a factor of 10 and
smaller than those of its targets by a similar ratio (Maunsell and Van
Essen, 1983b ; Tanaka et al., 1986; Raiguel et al., 1995, 1997; Movshon
and Newsome, 1996). Spatial summation is therefore prevalent in
extrastriate cortex and is probably important in the function of the
motion system. Despite this, few quantitative measurements of summation
have been made outside of striate cortex. In this paper, we used small, transient motion stimuli to densely map spatial interactions in MT cell
RFs. These were presented individually or pair-wise over the RFs of MT
cells. The rapid stimulus sequence allowed us to explore a very large
number of combinations of different locations and thus to obtain new
and detailed information on the spatial structure of MT cell spatial
interactions. This stimulation method might be generally useful for
other studies that require the exploration of many stimulus conditions.
In our default conditions, we used 300 distinct stimulus conditions for
each cell and could gather adequate data in a practical span of time.
Two classes of experiment have described summation in MT, but neither
has explored the current question of interactions within and near the
RF center. Several experiments have addressed the interaction between
the classical RF center and the antagonistic surround (Allman et al.,
1985; Born and Tootell, 1992; Raiguel et al., 1995). The surround may
overlap with the RF center, but to evaluate this question, we need to
know how stimuli interact in the RF center and its immediate neighborhood.
Other studies have measured responses to multiple stimuli moving
through the RF of MT cells. The stimuli have either been pairs of dots
traversing the RF (Ferrera and Lisberger, 1997; Recanzone et al., 1997)
or moving dot fields (Britten and Newsome, 1990; Snowden et al., 1991).
The general result from these studies is that MT cells
average multiple inputs. In other words, the evoked response
when presented with two stimuli together will be intermediate between
the responses to each presented alone. This result indicates that
linear summation is an inadequate explanation; an additional step is
required. A candidate for this extra step is provided by a recent model
(Simoncelli and Heeger, 1998) of MT that employs recursive, divisive
inhibition to scale the responses of MT cells by an amount proportional
to total activity in some region. However, no experiment has addressed
the spatial extent of the mutually inhibitory interactions in MT. Our
experiment provides the first direct test of the spatial extent of such
inhibitory interactions.
These results have previously appeared in abstract form (Britten,
1995).
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MATERIALS AND METHODS |
Preparation. Two adult female rhesus macaques
(Macaca mulatta) were used in this study. Before recording,
each had been trained to fixate stationary targets in the presence of
visual stimuli. Each was implanted with a scleral search coil (Judge et
al., 1980) and was equipped with a stainless steel head restraint post
and recording cylinder located over occipital cortex. A plastic grid secured inside this cylinder provided a coordinate system of guide tube
support holes at 1 mm intervals (Crist et al., 1988). Animal procedures
complied with the Institute for Laboratory Animal Research Guide
for the Care and Use of Laboratory Animals and were approved by the
University of California Davis Animal Care and Use Committee. On
recording days, guide tubes were inserted transdurally through these
holes, and Parylene-insulated tungsten microelectrodes were inserted
through the guide tubes. To localize area MT, we used both anatomical
and physiological landmarks. Anatomical landmarks included recording
depth and the transitions between active gray matter and "silent"
areas marking white matter or sulci. Physiological landmarks included
brisk, directional responses, retinotopy, receptive field size, and
columnar organization for preferred direction.
Once MT was localized, we would record and isolate activity using
standard extracellular methods. Electrode signals were amplified and
filtered, and single spikes were converted to digital pulses, whose
time of arrival would be recorded with 1 msec resolution using the
public domain software package REX (Hays et al., 1982). Search stimuli
were chosen to match local multiunit preferences and could be moving
bars, dot fields, or Gabor motion impulse stimuli. Once a cell was
isolated, its RF location was crudely mapped using hand-held moving bar
stimuli, and quantitative testing commenced.
Stimuli. All stimuli were presented on the face of a cathode
ray terminal monitor, subtending 60° horizontally by 48° vertically (1280 × 1024 pixels), operating at a vertical refresh rate of 72 Hz. Stimuli were generated by custom software running on a dedicated
display computer. For early experiments, we used an SGI (Mountain View,
CA) Indigo2, and in later experiments, we used a Pentium personal
computer hosting an ATI Technologies (Thornhill, Ontario, Canada) Mach
64 video card, running in 8 bit mode. Screen luminance was measured as
a function of gray scale value using a Tektronix (Wilsonville, OR)
photometer, fit with a cubic polynomial, and this was inverted to
establish a linearized gray scale lookup table. Average screen
luminance was set to 30 cd/M2, and maximum
achievable contrast was effectively 100% (background luminance was 0.1 cd/M2).
The stimuli for these experiments were moving, two-dimensional oriented
"motion impulses," whose spatial luminance function was a Gabor
function, or the product of a sine wave and a Gaussian function. These
are members of the family that Watson refers to as "generalized
Gabors" (Watson and Turano, 1995), which have the property that both
carrier (the sine wave) and the Gaussian contrast envelope are free to
move. In our case, carrier and envelope moved together in the preferred
direction of the cell under study. One such stimulus is illustrated in
Figure 1A. The
space-time luminance was described by the function:
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(1)
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where (µx,µy) is the instantaneous location
of the center of the impulse, and ( x,y) describe
its dimensions. The coordinate system is rotated so that the positive
x-axis is in the preferred direction of the cell under
study. The constant  establishes the spatial frequency of the
carrier. The x coordinate of the center of the impulse moved
linearly in time, and the spatial offset per frame was usually set to
one-fourth of the cycle of the carrier. The contrast function C(t) was a trapezoid spanning seven frames (98 msec) illustrated in Figure 1B. The default values for these
parameters were 1.07 cycles/deg carrier spatial frequency, 18 Hz
temporal frequency, x = 0.56°, and y = 1.12. It
is worth noting that the small dimensions of the contrast envelope
relative to the underlying carrier frequency made these stimuli
spatially rather broad-band, compared with "typical" Gabor stimuli;
this was a necessary consequence of their small spatial dimensions. These were adjusted only if the cell responded poorly or if the stimulus grid was so small that adjacent stimulus locations would overlap. We did not attempt to exhaustively search for optimal parameters but inspected on-line raster displays for responses clearly
above baseline and listened for stimulus-related modulation on the
audio monitor.
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Figure 1.
Single Gabor motion impulse depicted as a function
of space and time. A, Two-dimensional representation of
typical stimulus. This portrays the default values for spatial
parameters used in these experiments, which were only varied if these
proved ineffective in driving the cell. Aspect ratio was always 2:1,
but the ratio of carrier period to Gaussian envelope was more variable.
The numbered points indicate the successive locations of
an arbitrary spatial reference point in seven successive frames of the
stimulus; the white numbers are only for graphic
clarity. B, Contrast as a function of time. Each
point represents a single frame, corresponding to the
locations indicated in A. In a sequence of continuously
presented stimuli, the next stimulus frame 0 would immediately follow
frame 8, producing an overall interval of 125 msec between successive
stimuli.
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These stimuli were presented in a rapid sequence, with only two frames
intervening between sequentially presented impulses (Fig.
1B), and the location of the next impulse(s) was
selected pseudorandomly. Single trials consisted of periods ~3 sec in
duration during which the monkey was required to hold fixation during
stimulus presentation, and the monkey was rewarded for correctly
maintaining fixation. The final individual stimulus period in trials in
which fixation was broken was discarded from subsequent analysis.
Locations of the Gabors were chosen from a 5 × 5 grid of possible
locations, covering the RF of the cell, illustrated in Figure 2. The circle schematically
illustrates the RF of the neuron under study, showing that the intended
configuration placed the corners of the grid off the RF, in largely
unresponsive locations. However, there was substantial random variation
in the exact relationship between RF size and grid dimensions, because
the hand-mapping stimulus often provided a different estimate of the RF
boundary than did the Gabors.
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Figure 2.
Spatial arrangement of Gabor impulses,
schematically illustrated over an MT cell RF (circle).
Stimuli could either be presented individually or else in pairs
(illustrated). The direction of the stimuli (arrows) was
adjusted to match the preference of the cell, and the dimensions were
adjusted so the corner stimuli gave approximately equal, very small
responses.
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Two different types of blocks of trials were presented, in which the
stimuli were presented singly or in pairs. Each individual stimulus and
pair-wise combination (in the paired-stimulus blocks) was presented an
equal number of times. Typically, the single-stimulus block was
presented first, and inspection of on-line peristimulus time histogram
(PSTH) displays would reveal if adjustment of the grid size or location
was required. Usually, 50 presentations of each stimulus location were
given in the single-stimulus blocks, and for the double-stimulus block,
trials were run for as long as the cell could be held. For the data
presented in this paper, the number of presentations of each
combination of locations ranged from 4 to 151, with a median of 21.
Data analysis. Spike times were extracted from the raw data
files, corrected for the vertical location of the stimulus on the
screen (the raster was measured to take 12 msec to traverse the
vertical extent of the screen), and compiled into standard PSTHs. For
calculating spike rates, identical windows of 25-150 msec after
stimulus were used for both the single-stimulus and paired-stimulus trials.
For collapsing data across cells, individual cell RF profiles were fit
with two-dimensional, oriented Gaussian functions, allowing
standardization of different RF profiles to a single "standard" RF.
The Gaussian functions to which the single-stimulus data were fit were
of the form:
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(2)
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where (x',y') are rotated from screen
coordinates by an angle  , A is an amplitude parameter,
and C is the maintained activity.
Histology. One of the monkeys used in this study has been
killed, and histological confirmation of the recordings was
obtained. Before killing, two fluorescent tracer injections were made
through the guide tube support grid in known locations. The monkey was killed with an overdose of barbiturates and perfused transcardially with 0.9% saline followed by fixative (4% paraformaldehyde in 0.1 M phosphate buffer), followed by fixative with 10%
sucrose. The brain was removed, allowed to sink in 30% sucrose
solution, and then blocked and parasagitally sectioned at 50 µm
thickness on a freezing microtome. Alternate series were stained for
myelin (Gallyas, 1979) and for Nissl substance and mounted for
fluorescence imaging. The location of the injection sites was charted
on the superior temporal sulcus and used to confirm that the recording sites were in the heavily myelinated region corresponding to area MT.
The other monkey is alive and being used in other experiments.
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RESULTS |
We recorded from 89 cells in two hemispheres of two adult female
macaques. In 72 of these, we held the cells long enough to measure
responses to stimuli presented in pairs. In this section, we first
document the responsiveness of the neurons to these stimuli presented
singly and then turn to the interactions between pairs.
Single-stimulus responses
These responses came from the blocks of trials in which stimuli
were presented singly. Before we consider how these responses vary
across the RF, we need to look at the temporal dynamics of the
responses. This will allow us to establish appropriate time windows for
measuring responses. Figure 3 shows the
"grand average" PSTH for all cells and all stimulus conditions.
Each individual response (cell and location) was independently
normalized, so this shows the average temporal dynamics of the sample
as a whole, independent of response amplitude. The figure shows a clear
response transient starting ~30 msec after stimulus onset, rising to
peak at 50 msec, and then falling without reaching a clear plateau, as
one would expect for longer-duration stimuli. We chose to select one
time window for all spike rate analysis, to avoid problems with
selection of individual cell response windows, which can be unreliable
or subjective. In this figure, the vertical lines show the
boundaries of the time window chosen for subsequent analysis.
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Figure 3.
Grand average temporal envelope of MT response to
single motion impulses. The responses of each cell were individually
normalized and then averaged to produce the histogram shown. The
vertical dashed lines indicate the boundaries of the
temporal window used to calculate the rates used as the principal
response metric in this paper. The bold horizontal line
above the histogram denotes the stimulus period. The histogram peaks to
which these responses were normalized averaged 102 impulses/sec across
our sample of cells, and the average integrated response above
baseline, in the center of each RF, was 61 impulses/sec.
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We next sought to estimate the dependence of response on location for
each cell. Results from two example cells are illustrated in Figure
4. For each cell, PSTHs from each of the
25 stimulus locations are shown. These examples are chosen to represent
both the range of grid dimensions used, relative to the size of the RF,
and the range of cell response magnitudes to these stimuli. Most
importantly, in nearly all cases, the range of stimulus locations used
in the grid provoked wide response differences from location to
location; we thus have sampled the spatial dynamic range of each cell.
Although we did not reach the edge of the RF for every cell in the
sample, in all we covered enough of the RF to well estimate its
shape.
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Figure 4.
Responses of two representative MT cells, shown as
PSTHs. Each small axis shows the response to the stimuli
presented in the corresponding spatial location. Each is only 150 msec
in duration; the responses of each cell were individually normalized,
and the vertical calibration is indicated in the bottom
left PSTH. The locations of each stimulus grid are indicated in
degrees relative to the center of gaze. The vertical calibration bars
express firing rate in impulses/sec. The ratios of the size of the
sampling grid to the derived RF size (see Fig. 5) were 1.84 for the
cell in A and 0.84 for the cell in B. The
geometric mean of this ratio was 1.33 for our sample of cells.
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Average spike rates were calculated for each of the locations over the
time window illustrated by the dashed lines in Figure 3. A
two-dimensional, oriented Gaussian surface was fit to the responses
using maximum likelihood fitting. Because this is a novel mapping
method, it is important to test whether the RF dimensions estimated in
this way correspond to those estimated using other methods. To test
this, we plotted the relationship between RF size and eccentricity,
which is shown in Figure 5. The
diagonal line is the line fit using linear regression,
assuming equal experimental error on both axes (Press et al., 1988).
This fit yields an intercept of  5.12 and a slope of 1.35. This
relationship appears similar to previous work (Maunsell and Van Essen,
1983b; Raiguel et al., 1995), although the slope is a bit higher. The
negative intercept is not realistic and probably indicates that the
slope is also modestly overestimated. However, if we apply simple
linear regression, which assumes no error in the independent variable
(eccentricity), the estimated slope drops to 0.85. This value, like
previous estimates from the literature, is probably a modest
underestimate, because experimental error on the independent variable
causes slope underestimates in simple regression (Sokal and Rohlf,
1969). However, this method is directly comparable to other estimates
(which all lie near 0.7-0.8) and is only slightly larger. Thus, our
mapping method appears quite comparable to other means of quantifying
RF dimensions, although our diameters are slightly larger than other
estimates. Whether this modest difference lies in the stimuli or in the
analysis remains to be determined.
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Figure 5.
RF size to eccentricity relationship estimated
from the single motion impulses. Eccentricity was the center point of
the best-fit two-dimensional Gaussian function fit to the spike rate
data. Size was the sum of the x and y parameters,
or average diameter.
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Paired-stimulus responses
The primary goal of these experiments was to compare the results
of stimuli presented in pairs with the responses to the same stimuli
presented individually. In separate blocks of trials, the same stimuli
were presented simultaneously at two locations on the grid shown in
Figure 2. Pair-wise combinations were chosen pseudorandomly from a
table of all possible pairs (300 pairs for the default 5 × 5 grid; the combination of a location with itself was physically
impossible at 100% contrast). This list was completed, scrambled, and
repeated for as long as isolation could be maintained. Two cells,
representative of the range of observations, are shown in Figure
6. In each panel, we plot the observed
responses to simultaneously presented pairs against the separately
observed responses to the individual components of each pair (responses 1 and 2, the x- and y-axes). The mesh surface and
contours are derived from the best-fitting summation model (see below).
These cells display two main features characteristic of our data.
First, the observed response is less than the expected response given by unscaled, linear summation (note the z-axis scale is
approximately the same as the x- and y-axis
scales; it would have to be twice as large to accommodate linear
summation). Second, the observed responses rise
approximately in a plane from the origin to the far corner
containing maximal response. This suggests that summation is linear to
a first approximation, but the sum is scaled by an approximately
constant amount, reducing the slope of the plane below the expectation
of simple linear summation.
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Figure 6.
Responses of 2 MT cells to pairs of Gabor motion
stimuli. The x- and y-axes show the
responses to each component stimulus presented individually
(arbitrarily assigned to x or y), and the
vertical axis shows the observed response to the pair
presented simultaneously. Dots connected to the
x-y plane show observed data points, whereas the
surfaces and associated contour lines show the best-fit model (Eq. 3).
A, Cell for which linear summation provided good account
of the data. B, Different cell, which shows summation
closer to winner take all.
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The cell in Figure 6B also reveals another
characteristic that was frequently observed in our data. In this cell,
the summation surface is clearly curved away from the plane of linear
summation, such that the response to pairs tends to follow the response
to the more effective stimulus of the pair and is less influenced by
the less effective stimulus. This particular example is chosen to
illustrate this characteristic clearly; most cells in the sample showed
far less curvature than this cell.
However, the population as a whole does show the same trend toward
slightly "concave" summation, as can be seen in Figure 7. This shows the average, normalized
response as a function of the effectiveness of the component stimuli.
We normalized the responses according to the height of the best-fit
Gaussian derived from the single-stimulus data. Responses to pairs of
stimuli were binned, and the geometric mean was taken in each bin.
Thus, each cell contributes equally to this portrayal, no matter its
level of overall responsiveness. From the clearly concave nature of this surface, one can see that the population uses a slightly nonlinear
summation mechanism.
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Figure 7.
Sample average summation. Each response (including
the z-axis, or gray scale value) is normalized to the
same value: the height of the two-dimensional Gaussian fit to the
single-stimulus data. Each individual paired-stimulus condition was
binned according to the observed response to the components of the
pair, and then the bins were averaged. The surface was mirror-reflected
across the diagonal for graphical clarity.
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To describe these data, we have considered a family of related models,
some of which are illustrated in Figure
8. In Figure 8A, we
show the predictions of scaled linear summation. Under this rule, the
summation surface rises as an inclined plane, whose slope is given by a
scale factor (0.5 in this case, corresponding to averaging). In Figure
8B, we show the prediction of a winner-take-all model, in which the more effective stimulus controls the response completely. These models are in fact parametrically distinct versions of a generalized nonlinear summation model:
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(3)
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In this expression, r1 and
r2 represent the responses to the single Gabors
in a pair, corrected for maintained activity, presented individually.
R is the response to the pair, similarly corrected. The
intercept, b, is included to correct for errors in the
estimate of maintained activity, which are indirect and not completely
reliable. The two parameters of greatest interest in this model are the
scale factor, a, and the exponent, n. These control the slope and the curvature of the summation surface, respectively. For the hypothetical example model in Figure
8A, the scale parameter is 0.5, and the exponent is 1. For
the winner-take-all summation shown in Figure 8B, the scale
factor assumes a value of 1, and the exponent is large (125).
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Figure 8.
Comparison of predictions of three models for this
experiment. A, Linear model: a = 0.5; n = 1. B, Winner-take-all
model: a = 1; n = 100. C, Summation followed by squaring: a = 0.0025; n = 0.5. For comparison, the fit values
for the two cells portrayed in Figure 6 were Figure
6A: a = 0.72;
n = 1.36; Figure 6B:
a = 0.93; n = 6.68.
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The model illustrated in Figure 8C is a reduced version of
the model developed by Simoncelli and Heeger (1998), which is also a
member of this family of models. In their model, MT cells sum their
inputs linearly and then use a "half-squaring" (quadratic) nonlinearity after summation. This corresponds to an exponent of 0.5 in
Equation 3. (The square root operation applied to each term in the sum
recovers the "underlying linear response," and the summed quantity
is then squared.) The divisive normalization factor in their model
depends on total contrast, which is constant in our experiment. Thus
the scale constant, a, is equivalent in our model and will
be less than unity for divisive normalization.
We have fit various versions of this model to the data resulting from
our experiments, and Table 1 summarizes
the quality of their account of out data. All models performed
acceptably, because all generally agreed with the dominant trend in the
data, rising from the left front corner in a portrayal like those in Figure 6, up toward the back right corner. However, some models clearly
performed better than others. Both winner-take-all (deep concavity in
the surface) and the model of Simoncelli and Heeger (1998) (modest
convexity) provided poor accounts of the data. Simple linear averaging
fit somewhat better, but allowing the slope to vary noticeably improved
the fit, accounting for an additional 4% of response variance on
average. This improvement was significant in 61 of 70 cells (nested
log-likelihood test, p < 0.05). By comparison, if the
exponent is allowed to vary, but the slope is forced to unity, the fits
are on average somewhat worse than simple averaging. Unsurprisingly,
the best account of the data is provided by the model that allows both
scale factor and exponent to vary, and this captures 75% of the
observed variance in response, on average. This is an additional 7% of
the variance over the scaled linear model on average, and this
improvement was significant for 63 of 70 cells.
Figure 9 shows a more detailed comparison
among three of these models: scaled linear, Simoncelli and Heeger
(1998), and scaled power-law summation. In Figure 9A, we see
that the fits for the Simoncelli-Heeger model are systematically worse
than the linear model, although both incorporate a free scale factor
("normalization constant"). In Figure 9B, we see that
allowing the exponent to vary consistently improves the fits, as one
would expect from the performance comparisons described above. Thus,
the individual cells in the sample are quite consistent with regard to
which summation model best describes these data.
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Figure 9.
Comparison of variance accounted for by three
models. Variance accounted for was calculated as 100 * (1 var(obs pred)/var(obs)). A, Linear model
compared against the model of Simoncelli and Heeger (1998).
B, Linear model compared against the generalized
power-law summation model. Note that all three models provided fair
accounts of the data but also that the generalized model provided the
consistently lowest errors.
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Finally, we examined the sample distributions for the best-fit
parameters to the model that provided the best account of the data: the
scaled power-law summation model. The sample distributions of the scale
factor and exponent terms (a and n in Equation 3) are shown in Figure 10. This shows that
on average, the responses to pairs of stimuli are less than expected
from unscaled, linear summation by a substantial amount. In our
experiment, this scale factor was almost exactly halfway between
averaging (0.5) and summation (1.0). Second, Figure
10B shows that the summation is on average modestly
nonlinear, characterized by an exponent of 2.72. There is, however,
substantial diversity of summation behavior. Cells near the left end of
the distribution in Figure 10B are essentially linear, whereas the group that goes off scale to the right can be
considered to use a winner-take-all rule. This diversity of summation behavior was not correlated across the sample of 70 cells
with any independent measure, including responsiveness, maintained
activity, RF size, or location. Furthermore, there was no significant
relationship between the scale parameter, a, and the
exponent, n (all r values < 0.23).
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Figure 10.
Sample histograms for the two key parameters of
the generalized power-law summation model. See Results for
details.
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Spatial effects
All the preceding analysis was based on the assumption that the
summation rule was invariant across space, and the response to two
stimuli could be predicted from only the response amplitudes to each
component stimulus. We have investigated the spatial dependence of
summation in two ways. First, we will describe the average sample
summation as a function of the spatial location of each stimulus, which
is model-free and descriptive. Then we will explore the residuals to
the model fits as a function of stimulus location. The latter analysis
investigates whether spatial dependence is also necessary, in addition
to the amplitude terms included in our summation model.
For both of these analyses, we expressed the location of each component
stimulus in terms of , derived from the two-dimensional Gaussian
fits to the single-stimulus data. The Gaussian fits (derived from Eq. 2) provided two different values if the RF was elliptical, and in
such cases, a single was derived for each stimulus location from
its position with respect to the principal axes of the ellipse. Thus,
each stimulus location is expressed in terms of its radial location in
a standard RF. Figure
11A shows the average
normalized response (analogous to the portrayal in Fig. 7) as a
function of the stimulus locations. On this response surface, the
contour lines depict lines of constant average response. One can see
that these contours remain parallel to the axes for most of their
lengths. In these areas, moving one stimulus has relatively little
effect on the response. This is especially true once one or the other stimulus is beyond ~1 in radial position. Thus, moving the second stimulus away from the RF does not allow the response to rise very
much. In other words, the scaling influence of a stimulus on MT cell
responses is still very much in effect with one or the other stimulus
well away from the RF (note the height of the highest contours near
each axis).
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Figure 11.
Responses and model residuals as a function of
spatial location of the component stimuli. A, Average
responses normalized as in Figure 7. B, Residuals from
the best-fit generalized power-law summation model, also normalized to
the same value, the amplitude of the Gaussian function fit to the
single stimulus data.
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We have also analyzed the residuals to our best-fitting power-law
summation model as a function of stimulus location, and the results of
this analysis are shown in Figure 11B. The surface clearly systematically deflects upward along the x- and
y-axes, indicating that the nonlinear summation model
systematically underestimated the responses when one or the other (but
not both) stimuli departed the RF. However, this underestimation was
modest in magnitude: only ~5% at a distance of 2-3 RF radii from
the RF center. This is at a location where the first-order response of
the cell to the stimulus is effectively zero. Thus, stimuli that are
largely ineffective at driving the cell because they lie outside the
classical excitatory RF center are still effective at normalizing the
responses to stimuli within the RF, and summation and normalization are effectively constant across a region substantially larger than the RF
of the cell. The distance over which normalization operates is large:
the average RF diameter in our data set was ~9°. Therefore, it
appears that stimuli divisively interact in MT over distances of at
least 20°.
Temporal effects
We know that the responses to many different kinds of stimuli
adapt rapidly to repeated or continuous presentation, owing to synaptic
depression (Abbott et al., 1997) or spike rate adaptation (Connors and
Gutnick, 1990). Interaction between such adaptation and the divisive
interactions would be of considerable interest, because this would
suggest the two processes share biophysical mechanisms. Our rapid,
high-contrast stimuli provoked substantial adaptation during the 3 sec
trials, which declined during the 2 sec intertrial interval. We may
thus relate the time course of neuronal adaptation to the time course
of the interaction between stimuli. To do this, we measured the
responses of our neurons as a function of order within a trial for both
the single and paired stimuli. Figure
12 shows the results of this analysis.
Figure 12A shows the decline in response during a
trial for stimuli presented individually. To derive the average
Z scores, two steps were needed. First, cumulative means and
SDs were calculated for each stimulus location in the grid. Then, for
each stimulus within a trial, the Z score was calculated by
reference to the statistics for that spatial location. These
Z scores standardize all stimuli so that they can be
averaged. One can see that the average response drops substantially
across the first three stimuli in a trial (375 msec) and somewhat more
slowly for the next several hundred msec. Thus, the expected response
is clearly dependent on time.
View larger version (18K):
[in this window]
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|
Figure 12.
Effects of time on responses to paired stimuli.
A, Responses to single-motion impulses, shown as a
function of time within a trial. Z scores were
calculated relative to the entire distribution of responses to each
stimulus location, independent of time, and then averaged for each time
position, across stimulus location. Responses clearly decline rapidly
in the first 500 msec of each trial (four stimuli). B,
Responses to pairs of stimuli, compared against the expected response
for that location and time position. Because the
stimulus sequence was random, many stimulus location-time position
combinations were not represented in any given experiment, but all that
were presented contribute to this average. For both A
and B, the error bars denote the SEM across cells.
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|
Knowing that the predicted response should vary within a trial, we can
now ask whether the summation behavior also varies. To do this, we
again looked at the residuals from the power-law summation model, but
now as a function of time within a trial. For each stimulus pair, we
first select the single-stimulus presentations for the same point in
time to make the model prediction and then calculate the residual from
those predictions. In Figure 12B, we show the average
residuals to the model fits. We know from Figure 11A
that response falls with time; this asks whether normalization is
additionally affected by time. Figure 12B shows that
there is a modest effect of time: the residuals are positive for the
first 625 msec before declining to near zero values. Although it is possible that this dependence is simply an amplitude-summation nonlinearity not captured by our model, rather than a true effect of
time, we think this is unlikely, because in that case the residuals would be expected to fall with the rate change seen in Figure 12A. At the very least, one would expect the first
stimulus presentation, which has the largest rate, to show the greatest
effect, and it does not. Thus, there appears to be a true time
dependence of the divisive interactions in MT, which evolves over a few
hundred msec, but which is modest in amplitude, because the residuals were never large. Most of the inhibitory interactions are clearly in
effect in the first stimulus period (125 msec), so the process appears
quite rapid.
| |
DISCUSSION |
In this paper we have explored the manner in which brief,
localized stimuli interact within the RFs of MT cells. We found that
the response to pairs of local motion impulses fell well short of the
response expected from summation of the individual component responses.
Although responses were well predicted by scaled, linear summation of
the inputs, the prediction was markedly improved by using power-law
summation. The divisive scaling is not highly dependent on the exact
spatial location of the stimuli, but is consistent across a wide
region, extending well beyond the classical RF center. We have also
studied the interaction as a function of time within a trial, because
our stimuli were presented in a rapid sequence, allowing fairly fine
sampling of the temporal dimension. The responses dropped rapidly at
the onset of the trial, in the first 500 msec, but the interaction
between stimuli changed little in this same period. This suggests that divisive normalization is at least partially a separate process from
response adaptation.
Technical issues
The single- and double-stimulus pairs were presented in separate
blocks lasting at least 10-15 min. If the normalization process were
very slow and took seconds or minutes to change states, then both main
results of this paper would be called into question. We have considered
this issue, and there are two principal arguments against such slow
mechanisms. First, the normalization is nearly identical if the single-
and double-stimulus conditions are interleaved, as is shown in related
work from our laboratory. For the comparable cases as presented in this
paper, the median slope relating observed and predicted responses is
0.745, a value nearly identical to the value of 0.745 reported in this
paper (H. W. Heuer and K. H. Britten, unpublished observations).
These results, which are beyond the scope of the present paper, also
help resolve a potential ambiguity in the present work. Because firing
rate is monotonically related to both spatial location in the RF and to
the temporal order of stimuli, it is in principle difficult to
distinguish amplitude summation effects from spatial or temporal
effects. In our more recent experiments (Heuer and Britten, unpublished
observations), contrast was varied as well as spatial location,
allowing the disambiguation of firing rate and location. In preliminary
analysis of these results, the spatial pattern of residuals appears
very similar to that seen in Figure 11. Therefore, we are confident in
our estimates of the spatial extent of the divisive normalization.
Relationship to previous work
Several studies have addressed the responses of MT cells to
multiple moving stimuli in their RFs. Studies using plaid grating stimuli have tended to focus on directional tuning, rather than amplitude of the responses (Movshon et al., 1985; Rodman and Albright, 1989; Stoner and Albright, 1992). Because we do not vary direction, we
cannot compare our results with these. Several studies have, however,
quantitatively analyzed the amplitude of responses to multiple stimuli,
but none have yet addressed the spatial location of the stimuli.
Snowden et al. (1991) measured responses to transparently presented dot
fields, whereas Recanzone et al. (1997) and Ferrera and Lisberger
(1997) have used pairs of dots traversing the RFs of MT cells. The
consensus finding from these studies is that MT cells average multiple
inputs using some form of divisive operation. The present work extends
these observations by exploring their dependence on spatial location,
and we find that the normalization extends well beyond the classical RF
center. In the present data, we find somewhat less normalization than
previous studies in which the effects of space were not explored. The
divisive scale factor we found was 0.75, whereas Recanzone et al.
(1997) reported that averaging (0.5) slightly overestimates
the response. Snowden et al. (1991) used a slightly different metric
and reported an average value indicating near perfect averaging. On the
other hand, Ferrera and Lisberger (1997) explored the influence of a
second moving stimulus near but outside the RF of MT cells. Although it
is difficult to know how far their "distractor" stimuli were from
the RF, from what they present, they consistently observe no effect of
the second stimulus on the response of the MT cells to a preferred stimulus (a = 1.0 in our notation). Although it is
possible that differences in the stimuli or the fact that they recorded
from cells with more central RFs might explain the difference in
results, a more parsimonious explanation is that their distractor
stimuli were farther from the RF, and that the divisive inhibition had declined by this distance.
The comparison with the results of Ferrera and Lisberger (1997) also
helps with respect to any potential involvement of antagonistic surround mechanisms (Allman et al., 1985; Born and Tootell, 1992; Raiguel et al., 1995). The smallest stimuli that have been used to
measure surround effects are dot fields subtending a substantial fraction of the RF width (Raiguel et al., 1995). The much smaller stimuli of Ferrera and Lisberger (1997) probably do not trigger surround modulation. Although we cannot rule out activation of surround
mechanisms in the present experiments, we suspect that our small,
transient stimuli more resemble the moving dots of the experiments of
Ferrera and Lisberger and probably do not much influence the surround.
Detailed examination of the relationship between divisive interactions
in the center and surround mechanisms (which are often considered
subtractive) is clearly an important direction for future work.
One feature of the present work, not previously reported, is the
nonlinear summation captured by the value of the exponent in our
power-law summation model. Because space and response strength covary
in our measurements, this term must be viewed with some caution. We
have argued in Results against such an interpretation, but it remains
open. No other work on MT has explicitly considered nonlinear
summation, but in work on simple cells in V1 by Carandini et al.
(1997), a related nonlinearity helps describe the summation of pairs of
superimposed grating stimuli varying in contrast. Interestingly,
although their biophysically motivated model differs from ours in many
ways, the average value of their exponent is very close to ours
(2.34-2.61 vs 2.72). It is also very interesting that in the
"selection model" of Nowlan and Sejnowski (1995), normalized,
nonlinear summation is used.
Mechanism
The measurements in the present work allow further constraint on
possible mechanisms of divisive normalization. Specifically, these
interactions can be seen to occur across wide regions of space. In many
of our experiments, stimuli were 10-20° apart. Normalization was
still effective at these distances, probably beyond the extent of
lateral connections in V1. Although these observations do not exclude
normalization in V1 as one component, they suggest that an additional
step at MT is also necessary. Because normalization is effective even
for stimuli well outside the RF, which evoke little response by
themselves, it also seems necessary to invoke lateral connections from
neurons that are activated by these stimuli. Otherwise, if some
homosynaptic or recurrent gain control were operating, its
effectiveness would be expected to fall with the main excitatory effect
of the stimulus. This is clearly not supported by the data.
Two types of mechanism appear to satisfy the constraints imposed by the
present data. One is lateral inhibitory networks within MT. These would
presumably connect in a mutually inhibitory manner cells with largely,
partially, or barely overlapping RFs. Decline in the density of such
connections would then explain the declining effectiveness of
normalization at distances of 2-3 RF radii. Another possibility
involves feedback from higher areas, such as MST. Recent observations
suggest that feedback from MT is important in center-surround
interactions in V1 (Hupe et al., 1998); an analogous operation might
allow MST feedback to modulate divisive interactions in MT. Two
observations argue against this possibility, in our view. First, the
rapid kinetics of the divisive interactions we observe seem to render
it less likely: the inhibition appears to be in effect in the first 125 msec. Second, the connections between MT and MST are topographically
imprecise (Maunsell and Van Essen, 1983a; Boussaoud et al., 1990).
Thus, feedback-dependent inhibition might be expected to be even less
dependent on spatial location than what we observe in the present
study. However, either mechanism remains possible at present.
We have termed the divisive interactions normalization, consistent with
one recent model of MT cell responses. The main function of this
mechanism is to keep the representation of direction (or anything else
that is represented) approximately invariant in the face of changing
stimulus contrast. This is because animals rarely care about the
contrast of an object; it is more important to determine object
attributes such as direction of motion. To fully test the relationship
between the phenomenon we have described and contrast normalization, we
will need to measure the contrast dependence of these divisive
interactions. Work addressing this question is presently under way in
our laboratory.
| |
FOOTNOTES |
Received Sept. 14, 1998; revised March 1, 1999; accepted March 24, 1999.
This work was supported by National Institutes of Health Grant EY10562
to K.H.B. We thank E. A. Disbrow, R. E. Tarbet, and J. L. Moore for excellent technical assistance and Arthur Jones for
writing the stimulus generation software. We thank L. A. Krubitzer, M. Sum, and H. Tran for helping with histological
reconstruction. We also thank S. D. Elfar, K. J. Huffman,
K. L. Nace, G. H. Recanzone, M. L. Sutter, and R.J.A.
van Wezel for thoughtful discussion and comments on earlier versions of
this manuscript.
Correspondence should be addressed to Kenneth H. Britten, Center for
Neuroscience, University of California Davis, 1544 Newton Court, Davis,
CA 95616.
| |
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TOP
ABSTRACT
INTRODUCTION
