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71:347-374, 1994. ;J Neurophysiol
G. C. DeAngelis, R. D. Freeman and I. Ohzawa
primary visual cortex
Length and width tuning of neurons in the cat's
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JOURNALOF NEUROPHYSIOLOGY
Vol. 71, No. 1, January 1994. Printed in U.S.A.
Length and Width Tuning of Neurons in the Cat’s Primary
Visual Cortex
GREGORY C. DEANGELIS, RALPH D. FREEMAN, AND IZUMI OHZAWA
Groups in Bioengineering and Neurobiology, and School of Optometry, University of California,
Berkeley, California 94 720
SUMMARY AND CONCLUSIONS
I. The classically defined receptive field of a visual neuron is
the area of visual space over which the cell responds to visual
stimuli. It is well established, however, that the discharge pro-
duced by an optimal stimulus can be modulated by the presence of
additional stimuli that by themselves do not produce any re-
sponse. This study examines inhibitory influences that originate
from areas located outside of the classical (i.e., excitatory) recep-
tive field. Previous work has shown that for some cells the re-
sponse to a properly oriented bar of light becomes attenuated
when the bar extends beyond the receptive field, a phenomenon
known as end-inhibition (or length tuning). Analogously, it has
been shown that increasing the number of cycles of a drifting
grating stimulus may also inhibit the firing of some cells, an effect
known as side-inhibition (or width tuning). Very little informa-
tion is available, however, about the relationship between end- ~
and side-inhibition. We have examined the spatial organization
and tuning characteristics of these inhibitory effects by recording
extracellularly from single neurons in the cat’s striate cortex
(Area 17).
2. For each cortical neuron, length and width tuning curves
were obtained with the use of rectangular patches of drifting sinu-
soidal gratings that have variable length and width. Results from
82 cells show that the strengths of end- and side-inhibition tend to
be correlated. Most cells that exhibit clear end-inhibition also
show a similar degree of side-inhibition. For these cells, the excit-
atory receptive field is surrounded on all sides by inhibitory zones.
Some cells exhibit only end- or side-inhibition, but not both. Data
for 28 binocular cells show that length and width tuning curves for
the dominant and nondominant eyes tend to be closely matched.
3. We also measured tuning characteristics of end- and side-in-
hibition. To obtain these data, the excitatory receptive field was
stimulated with a grating patch having optimal orientation, spatial
frequency, and size, whereas the end- or side-inhibitory regions
were stimulated with patches of gratings that had a variable param-
eter (such as orientation). Results show that end- and side-inhibi-
tion tend to be strongest at the orientation and spatial frequency
that yield maximal excitation. However, orientation and spatial
frequency tuning curves for inhibition are considerably broader
than those for excitation, suggesting that inhibition is mediated by
a pool of neurons. This conclusion is further supported by the
finding that the strength of end- and side-inhibition does not de-
pend on the relative spatial phase between excitatory and inhibi-
tory grating stimuli.
4. Laminar analysis reveals that end- and side-inhibited neu-
rons are found in all layers of the cortex. The only laminar special-
ization observed involves a distinct population of neurons, located
predominantly in Layer 6, that have very long receptive fields and
exhibit pronounced side-inhibition.
5. To determine where end- and side-inhibition are generated
in the visual pathway, we obtained dichoptic measurements of
length and width tuning. For this purpose, an optimal patch of
grating was confined within the excitatory receptive field of one
eye, whereas the inhibitory regions of the other eye were stimu-
lated with grating patches of variable length or width. Results from
13 cells show that end- and side-inhibition are mediated dichopti-
tally. For three cells, inhibitory orientation and spatial frequency
tuning curves were obtained dichoptically; these exhibit selectivity
similar to that seen in monoptic tests. The strength of inhibition is
not found to depend on the binocular (phase) disparity between
inhibitory stimuli presented to the left and right eyes. Overall,
these dichoptic results suggest that end- and side-inhibition are
generated through intracortical inhibitory interactions between
binocular neurons.
INTRODUCTION
Most studies of visual cortical neurons have made use of
small spots or thin bars of light to characterize the structure
of receptive fields. On the basis of this approach, the recep-
tive field of a visual neuron is typically defined as the area of
visual space in which an appropriate stimulus excites the
cell (e.g., Barlow et al. 1967; Hubel and Wiesel 1959, 1962;
Kuffler 1953; Maffei and Fiorentini 1976). It is well
known, however, that the response of many neurons to an
optimal stimulus can be modulated (i.e., inhibited) by the
presence of additional stimuli. Several researchers have
studied the inhibitory effects produced when two stimuli of
different orientations (Bonds 1989; DeAngelis et al. 1992;
Morrone et al. 1982; Petrov et al. 1980) or spatial frequen-
cies (Bauman and Bonds 199 1; DeValois and Tootell
1983 ) are superimposed. Recently we have shown that the
suppressive effect obtained by superimposing two stimuli of
different orientations (cross-orientation inhibition) origi-
nates from within the excitatory receptive field of most cor-
tical cells ( DeAngelis et al. 1992 ) . Moreover, the strength of
this localized suppression is generally not dependent on the
orientation of the inhibitory stimulus. In this paper we ex-
amine the organization of inhibitory effects produced by
stimuli located outside of the excitatory receptive field.
Numerous investigators (e.g., Albus and Fries 1980;
Blakemore and Tobin 1972; Bolz and Gilbert 1986; Born
and Tootell 199 1; DeValois et al. 1985; Dreher 1972; Fries
et al. 1977; Hubel and Wiesel 1965; Kato et al. 1978; Maffei
and Fiorentini 1976; Nelson and Frost 1978; Orban et al.
1979a,b; Rose 1977; Sillito 1977; Sillito and Versiani 1977;
Tanaka et al. 1987; von der Heydt et al. 1992; Yamane et al.
1985) have studied inhibitory effects produced by stimuli
that extend beyond the classical excitatory receptive fields
of cortical cells. Hubel and Wiesel ( 1965) first observed
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347
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348
G. C. DEANGELIS, R. D. FREEMAN, AND I. OHZAWA
that some cells in Areas 18 and 19 of the cat are tuned for
the length of an optimally oriented bar stimulus. For these
cells, response increases with stimulus length up to some
optimum value, after which further increasing the length of
the stimulus produces an attenuation of the response. Hu-
be1 and Wiesel ( 1965 ) referred to cells exhibiting this prop-
erty as hypercomplex. Subsequent studies (e.g., Dreher
1972; Gilbert 1977; Kato et al. 1978; Rose 1977) have
shown that many neurons in Area 17, including both sim-
ple and complex cells, exhibit length tuning. This property
is now commonly referred to as end-inhibition, and is
thought to originate from inhibitory “end-zones” (cf. Or-
ban et al. 1979a,b) that lie beyond the excitatory receptive
field along the axis of a cell’s preferred orientation. The
neural mechanisms that underlie the generation of end-in-
hibition are not completely understood, and several differ-
ent models have been proposed. Some of the models posit
that intracortical connections mediate end-inhibition (e.g.,
Bolz and Gilbert 1986; Dobbins et al. 1987, 1989; Hubel
and Wiesel 1965)) whereas others (Cleland et al. 1983;
Rose 1979) postulate that end-inhibition derives from the
length tuning properties of neurons in the lateral geniculate
nucleus (LGN). Other studies (Murphy and Sillito 1987;
Sillito et al. 1993) suggest that length tuning originates in
the LGN and is enhanced by corticofugal feedback from
Layer 6 of the striate cortex.
An effect analogous to end-inhibition may be observed if
the width (or number of cycles) of a grating stimulus is
varied. Maffei and Fiorentini ( 1976) were the first to report
that as the number of cycles of a grating is increased some
cells show response attenuation when the grating extends
into inhibitory regions located along the sides of the recep-
tive field. Other investigators (Born and Tootell 199 1; De-
Valois et al. 1985; Foster et al. 1985; von der Heydt et al.
1992) have also studied this phenomenon, which is com-
monly referred to as width tuning or side-inhibition. The
neural mechanisms underlying side-inhibition are largely
unknown.
It is natural to ask whether end- and side-inhibition are
related to one another, given the similarities in their phe-
nomenology. On the basis of recordings obtained from the
visual cortex of cats and monkeys, DeValois et al. ( 1985 )
note that cells exhibiting pronounced side-inhibition also
tend to show end-inhibition. On the other hand, Born and
Tootell ( 199 1) report that there is no relationship between
the presence of end- and side-inhibition for cells in the su-
pragranular layers of macaque striate cortex. It should be
noted, however, that end-inhibition was not measured
quantitatively in either of these two studies. Thus the rela-
tionship between length and width tuning has not been sol-
idly established.
Another unresolved issue concerns the stimulus selectiv-
ity of end- and side-inhibition. Some studies (Fries et al.
1977; Maffei and Fiorentini 1976) report that inhibition
may be nonspecific, or very broadly tuned, for orientation.
Other studies (e.g., Born and Tootell 199 1; Hubel and Wie-
se1 1965; Orban et al. 1979b) report that the strength of
inhibition is typically greatest at the optimal orientation for
excitation and vanishes at orientations nearly orthogonal to
the excitatory optimum. Some of these differences between
studies may result from insufficient methods for determin-
ing the extent of the classical (excitatory) receptive field
(see DeAngelis et al. 1992).
The overall goal of the study we report here is to provide a
comprehensive analysis of the length and width tuning
properties of neurons recorded from the striate cortex of the
cat. This paper focuses mainly on three specific questions.
1) What is the relationship between the strengths of end-
and side-inhibition? 2) How do end- and side-inhibition
depend on stimulus parameters such as orientation, spatial
frequency, spatial phase, and contrast? 3) At what level of
the visual pathway is end-inhibition (or side-inhibition)
generated? This latter question is addressed by determining
whether end- and side-inhibition are mediated dichopti-
tally.
The findings reported here show that most cells ( -2 / 3 )
exhibit very similar degrees of end- and side-inhibition. The
remaining cells generally show either end-inhibition or
side-inhibition, but not both. The tuning characteristics of
end- and side-inhibition, for parameters such as orientation
and spatial frequency, are generally quite similar. End- and
side-inhibition tend to be strongest at orientations and spa-
tial frequencies that are close to the optimal values for pro-
ducing excitation. However, both the orientation and spa-
tial frequency bandwidths of inhibition are much larger
than those for excitation, suggesting that inhibition is me-
diated by a pool of neurons. The strength of inhibition gen-
erally does not depend on the relative phase between a stim-
ulus confined within the excitatory receptive field and a
stimulus confined to the end- or side-inhibitory regions
Results from binocular neurons show that length and width
tuning curves are generally well-matched for the two eyes.
Last, end- and side-inhibition are shown to be mediated
dichoptically, suggesting that intracortical inhibitory cir-
cuits are primarily responsible for generating these phenom-
ena. Overall, these findings constrain models for the genera-
tion of end- and side-inhibition and help to elucidate the
neuronal circuitry that underlies these phenomena.
METHODS
All experiments were performed with adult cats reared in a nor-
mal environment. Detailed descriptions of the experimental appa-
ratus and procedures have been given in recent reports ( DeAngelis
et al. 1992, 1993a; Freeman and Ohzawa 1992; Ghose and Free-
man 1992 ) . Therefore only a brief description of the relevant de-
tails is given below.
Surgical procedures
After initial preanesthetic doses of acepromazine and atropine
( 1 .O and 0.2 mg
l
kg-’ SC, respectively), each cat was anesthetized
with halothane (2.53% in 0,) for the remainder of the surgical
preparation. A rectal temperature probe was inserted, electrocar-
diographic (ECG) electrodes were secured, and a femoral vein was
catheterized. Subsequently a tracheostomy was performed and a
tracheal tube inserted. The animal was then secured in a stereo-
taxic apparatus using ear bars. Electroencephalographic (EEG)
screw electrodes were placed over the frontal sinus and a section of
skull and dura ( - 5 mm diam, centered on Horsley-Clarke coordi-
nates P4.0, L2.0) was removed to allow insertion of a pair of
tungsten-in-glass microelectrodes (Levick 1972). After we low-
ered the electrodes to the cortical surface, we used agar at 38°C to
seal the hole and applied melted wax over the agar to create a
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LENGTH AND WIDTH TUNING IN STRIATE CORTEX
349
sealed chamber. The cat was then paralyzed with gallamine trieth-
iodide (Flaxedil), which was continuously infused at a rate of 10
mg . kg-’
l
hr-” ) along with 1 mg 0 kg-’ . hr-’ of sodium thiamylal
(Surital) as a supplementary anesthetic. Artificial ventilation was
carried out with a gas mixture of 70% N,O-29% Q2- 1% C02. The
respirator was set at 25 strokes per minute and stroke volume was
adjusted to maintain a constant end-tidal CO2 of -4.5%. Temper-
ature, heart rate, EEG, ECG, and intratracheal pressure were
monitored continuously and additional doses of Surital were
given, if necessary, to maintain an appropriate level of anesthesia.
Pupils were dilated with atropine ( 1% ), nictitating membranes
were retracted with Neo-synephrine ( 10%)) and corrective ( +2D)
contact lenses with 4-mm artificial pupils were positioned on each
cornea.
Experiments typically lasted 4 days. At the end of an experi-
ment the animal was administered an overdose of Nembutal.
After perfusion and fixation (with a buffered 0.9% saline solution
followed by 10% Formalin) the cortex was frozen and sectioned
into 40-pm-thick slices. Tissue was stained with thionin, electrode
tracks were reconstructed, and laminae were identified. Histologi-
cal analysis confirmed that all cells were recorded from Area 17
and that cells were sampled from all laminae.
Visual stimulation and data collection
The receptive field of each cortical neuron was initially located
using a bar of light that was optically back-projected onto a tan-
gent screen in front of the cat. Subsequently all visual stimulation
was provided by computer-generated patterns displayed on either
or both of two video displays, one for each eye, that the cat viewed
through half-reflecting mirrors. The video displays (Mitsubishi
Electronics; mean luminance 45 cd/m2; screen size 28 x 22 cm)
had a resolution of 1,024 X 804 pixels and were refreshed (synchro-
nously) at 76 Hz. Visual stimuli were generated on these displays
by a dedicated computer that employs two high-resolution graph-
ics boards (Imagraph). This visual stimulator is capable of gener-
ating multiple patches of sinusoidal grating stimuli having arbi-
trary size, spatial frequency, orientation, velocity, and contrast.
The action potentials of cortical neurons were detected by tung-
sten-in-glass microelectrodes, amplified, and recorded as binary
events with I-ms resolution. A computer controlled the presenta-
tion of stimulus sequences while simultaneously displaying peris-
timulus time histograms ( PSTHs) of the cells’ responses, as shown
in Fig. 1, A and B. During quantitative tests, grating stimuli were
presented for 4 s each in blocks of randomly interleaved trials.
Each stimulus was typically presented four to eight times, and
successive stimuli were separated by a period of 2-3 s during
which the animal viewed blank screens of the same mean lumi-
nance as the gratings. After presentation of a complete set of stim-
uli, the magnitude of the accumulated response to each different
stimulus was computed by Fourier analysis. Response amplitude
was taken as the mean firing rate or as the mean amplitude of the
first harmonic of the response, depending on which was greater.
We classified cells as simple if the first harmonic of the firing rate
was larger than the mean rate for spatial frequencies higher than
the optimum ( DeValois et al. 1982; Skottun et al. 199 1). The
remainder of the cells were classified as complex.
Preliminary procedure
Once the action potential of a single cell was isolated, the recep-
tive field was initially explored with a bar of light that was moved
manually. The location of the receptive field (relative to the posi-
tions of the optic disks) was marked on plotting paper by means of
a large beam splitter behind the rear projection screen. Ocular
dominance was also estimated at this time.
Before starting quantitative measurements, an interactive
“search” program (see DeAngelis et al. 1993a) was used to make
preliminary observations of the stimulus selectivity of each cell. In
this procedure the cell was stimulated using round grating patches
whose orientation, spatial frequency, position, and size were man-
ually controlled using a pointing device. Once the optimal orienta-
tion and spatial frequency were estimated, a small ( 1-2O ) patch of
grating was positioned carefully to give the largest response from
the neuron. This position was taken as the location of the center of
the receptive field, and all stimuli used subsequently were centered
on this point. Before conducting quantitative tests, the size of a
grating patch was varied manually to determine whether or not
the cell exhibited end- or side-inhibition. If so, then the size of the
grating patch was adjusted to give the largest response from the
cell. This search procedure was performed for both the dominant
and nondominant eyes of binocular cells.
After completing the search procedure described above, quanti-
tative measurements of the length and width tuning of each cell
were performed as described below. Between successive runs, the
stimulus was often recentered on the receptive field as a precau-
tion against eye movements. These repeat estimates of the recep-
tive field center location are generally very reliable and repeatable
(to within a few tenths of a degree).
RESULTS
For this study, data have been obtained from 88 neurons
in the striate cortex of 15 cats. Of these neurons, 56 were
simple cells and 32 were complex cells. All cells studied had
receptive fields located within t 15’ of the area centralis.
We first measured monoptically for each eye the orienta-
tion and spatial frequency selectivity of each cell (see Figs. 5
and 7 for examples of tuning curves). These measurements
were obtained using patches of drifting sinusoidal gratings.
The size of the grating patch was adjusted to be approxi-
mately optimal for each cell, as determined in the prelimi-
nary procedure
(see METHODS).
After determining the opti-
mal orientation and spatial frequency, tests were conducted
to characterize the length and width tuning properties of
each cell. Whenever possible, these measurements were ob-
tained for both the dominant and nondominant eyes by
interleaved stimulation of the two eyes (see Fig. 12). How-
ever, in most (60/ 88 ) cases, length and width tuning mea-
surements were restricted to the dominant eye.
Comparison oflength and width tuning
To characterize length and width tuning, response was
measured as a function of the length and width of a rectan-
gular patch of drifting sinusoidal grating centered on the
receptive field of the cell being studied. Length, L, is de-
fined as the dimension of the stimulus parallel to the bars of
the grating (i.e., parallel to the cell’s preferred orientation),
whereas width, IV, is the dimension orthogonal to the bars
(see Fig. 1, top). It should be emphasized that u/ refers to
the width of the stimulus patch (i.e., the rectangular win-
dow), not to the width of the bars in the grating. Thus
increasing u/ is tantamount to increasing the number of
cycles of grating in the stimulus while keeping the spatial
frequency of the sinusoid constant. In Fig. 1, representative
measurements of length and width tuning are shown for a
simple cell. Figure 1 A shows PSTHs of the responses of this
simple cell to grating patches that vary in width from 0.2 to
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350
G. C. DEANGELIS, R. D. FREEMAN, AND I. OHZAWA
s 6.0
g 4.0
3 1.0
0.5
0.2
Null
819-21
B
15.0
10.0
8.0
E 6.0
a> 4.0
5 3.0
hlbw -0- - .-. -.---
Null
D
20
T
t
2 -0
I t t
Wick, W (Z&)
15 0
Lensgth, L ;doeg)
15
FIG.
1. Measurement of length and width tuning curves for a simple cell
(Cell 819-21) . A : peristimulus time histograms (PSTHs) are shown as
obtained in response to grating patches of different widths. Each PSTH
spans 2 s. The stimulus configuration is shown schematically above the
PSTHs. Thick square: cell’s classical excitatory receptive field. Line
through square: axis of the cell’s preferred orientation. The length of the
grating patch (defined as the dimension parallel to the bars of the grating)
is fixed at the optimal value, L, = 2.5 O, estimated during preliminary
observations
(see METHODS).
The width of the grating (defined as the
dimension orthogonal to the bars) is varied from 0.2 to 15”. Note that the
responses shown in the PSTHs are modulated at the temporal frequency (2
Hz) of the stimulus, and that the largest responses are obtained for widths
of 1 S-2”. The histogram marked as “Null” shows the cell’s spontaneous
discharge during interleaved control conditions in which no stimulus is
presented. The optimal grating for this cell was oriented 20” from horizon-
tal and had a spatial frequency of 0.6 1 cycles per degree. Stimulus contrast
was 50% and gratings drifted at 2 Hz in the cell’s preferred direction. B:
PSTHs of responses of the same simple cell to grating patches of variable
length. In this case, the width of the grating patch is fixed at the optimal
value, W, = 2”, determined from the responses shown in A, and the length,
L, is varied from 0.2 to 15”. The largest responses occur for lengths of
1.5-2”. C: width tuning curve obtained from the responses to gratings
shown in A. Filled triangles: 1 st harmonic of the cell’s firing rate plotted as
a function of width. Response reaches a maximum at a width of 2” and
decreases sharply for larger widths, an effect known as side-inhibition. D:
length tuning curve for the same cell obtained by analyzing the responses
shown in B. Response is strongly attenuated for lengths >2O, an effect
known as end-inhibition.
15 O. Note that the discharge of the cell is modulated at the
temporal frequency (2 Hz) of the grating, as is typical of
simple cells (e.g., DeValois et al. 1978, 1982; MaKei and
Fiorentini 1973; Movshon et al. 1978). Note also that re-
sponse strength increases with the width of the stimulus up
to -2’ and that the magnitude of the response is strongly
attenuated for widths >3”. Thus this simple cell is sharply
tuned for the width of the grating stimulus. This can be seen
clearly in Fig. 1 C, where the amplitude of the first harmonic
of the cell’s response is plotted as a function of stimulus
width. The reduction in response rate for large widths will
be henceforth referred to as side-inhibition, or width tuning.
Figure 1 B shows PSTHs of the responses of the same
simple cell to grating patches of variable length. Again the
cell is sharply tuned for the length of the stimulus, with
gratings >3” producing little or no response. Average re-
sponse amplitude ( 1st harmonic) is plotted as a function of
stimulus length in Fig. 1
D.
The response attenuation exhib-
ited for long stimuli will be referred to throughout this
paper as end-inhibition, or length tuning.
Unlike the cell shown in Fig. 1, many cells in the striate
cortex do not exhibit any side- or end-inhibition in re-
sponse to stimuli of variable dimensions. In these cases,
response amplitude simply increases with the length and
width of the grating stimulus up to some plateau level.
Other cells exhibit varying degrees of end- and side-inhibi-
tion. Figure 2 shows the effect of varying the length and
width of a grating stimulus on the responses of three repre-
sentative neurons: two simple cells (Fig. 2, A,
B,
E, and F)
and a complex cell (Fig. 2, C and
0).
In Fig. 2, and
throughout this paper, the amplitude of the first harmonic
of the response is plotted for simple cells (A), whereas the
average firing rate (i.e., DC response) is plotted for complex
cells (
l
) . Figure 2, A and
B,
shows the width and length
tuning curves, respectively, of a simple cell that exhibits
both side-inhibition and end-inhibition. These data are sim-
ilar to those shown in Fig. 1, C and
D,
except that the inhibi-
tory effects are somewhat weaker. In Fig. 2, A and
B,
the
cell’s response for large widths and lengths is approximately
half of the peak response value, whereas the response of the
neuron shown in Fig. 1 is completely suppressed for large
widths and lengths. For cells that exhibit both end- and
side-inhibition (such as those in Figs. 1 and 2, A and
B),
the
receptive field can be represented schematically as shown to
the right of Fig.
2B.
The excitatory receptive field (indi-
cated by a thick square) is surrounded in all directions by
inhibitory regions. Those located at the ends of the recep-
tive field (i.e., along the axis of the preferred orientation,
shown by the thick line) may be termed end-inhibitory re-
gions (cross-hatched), and those located along the sides of
the receptive field may be called side-inhibitory regions
(checkered).
Many of the neurons studied here, like that of Fig. 2, A
and
B,
exhibit both end-inhibition and side-inhibition.
However, this is not always the case. Figure 2, C and
D,
shows data from a complex cell that exhibits pronounced
end-inhibition, but no side-inhibition. As illustrated to the
right of Fig. 2
D,
the excitatory receptive field of this cell is
flanked by inhibitory regions only along the axis of the pre-
ferred orientation. There are no inhibitory regions along
the sides of the receptive field. The opposite situation is
illustrated in Fig. 2,
E
and F, which shows response ampli-
tude as a function of width and length for a simple cell
recorded from Layer 6 of the striate cortex. In this case the
neuron exhibits strong side-inhibition but no end-inhibi-
tion. Note that the response of this cell increases as a func-
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LENGTH AND WIDTH TI NING IN STRIATE CORTEX
30
T
452-01
t? 0 5 10 15 0 5 10 15
a>
cc
E F
157 496-l 9 15-
Width (deg)
Length (deg)
351
Excitatory End-Inhibitory
Side-Inhibitory
ReceptiveField Region
Region
FIG.
2. Length and width tuning curves are shown for 3 cells: 2 simple cells (A, B, E, and F) and a complex cell ( Cand 0).
For the simple cells response is plotted as the mean amplitude of the 1 st harmonic of the firing rate (A ) . For the complex cell,
average firing rate is plotted (
l
). A and B: this simple cell ( Cell 452-M) shows side-inhibition in its width tuning curve and
end-inhibition in its length tuning curve. A schematic illustration of the excitatory receptive field and the associated inhibi-
tory regions is shown to the right of B. Thick square: excitatory receptive field. Thick line: cell’s preferred orientation.
Inhibitory regions are present along the sides of the receptive field (shown checkered) and at the ends of the receptive field
( shown cross-hatched). The spatial frequency and contrast of the stimulus were 0.3 1 cycles per degree and 40%, respectively,
and the orientation was 2 1 O from vertical. C and D: this complex cell ( Cell 181-26) shows pronounced end-inhibition in its
length tuning curve (D) but no side-inhibition in its width tuning curve (C). Thus there are inhibitory regions at the ends of
the receptive field but not along the sides (see depiction to the right of D). The optimal grating for this cell was oriented 20°
from horizontal and had a spatial frequency of 0.73 cycles per degree. Contrast was 20%. E and F: width and length tuning
curves are shown for a simple cell
(Cell
496-19) that exhibits strong side-inhibition but no end-inhibition. This cell has a
very long excitatory receptive field (see illustration to the right of F) with inhibitory regions along the sides. The optimal
orientation for this cell was 42” from horizontal and the optimal spatial frequency was 0.5 1 cycles per degree. The contrast of
the stimulus was 50%.
tion of length up to 20’ (F). Thus the cell has a very long
excitatory receptive field that is flanked by inhibitory re-
gions only along the sides (see the schematic illustration to
the right of Fig. 2F). This neuron produces vigorous re-
sponses to long, thin bar stimuli, but no response at all to
large-field sinusoidal gratings. Only when the width of a
grating stimulus is restricted to ~3” does the cell produce
any substantial response. It is important to emphasize that
the side-inhibitory regions depicted in Fig. 2 F are not sim-
ply
ON
or OFF subregions of a simple cell receptive field.
Stimulation of these side-inhibitory regions with either
bright or dark bars produces no response from the neuron.
Moreover, it is clear that the excitatory receptive field itself
contains both
ON
and OFF subregions, because a stimulus of
optimal width ( 2’ ) contains one full grating cycle at the
cell’s preferred spatial frequency (0.5 1 cycles per -degree).
It should be noted that length and width tuning curves
are obtained by symmetrically expanding a grating stimu-
lus about the center of the excitatory receptive field. Thus
our stimuli simultaneously probe inhibitory regions on
both ends or sides of the classical receptive field. This study
does not explore the relative strengths of inhibitory regions
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352 G. C. DEANGELIS, R. D. FREEMAN, AND I. OHZAWA
695-l 1
B
c
25
T Wo,t (optimal width)
Width, W (deg)
Lopt (optimal length)
1::::::::::::::::::: I
0 5 IO
15 20
Length, L (deg)
FIG.
3. Fitting procedures used to extract parameters from length and width tuning curves. A : filled circles: response as a
function of width for a side-inhibited complex cell (Cell 695-l 1). Solid curve: best fit of Eq. 2 to these data. The optimal
width, Wept , is defined as the width at which the curve reaches its peak value. Percent side-inhibition (%SI) is defined as the
difference between the peak response amplitude and the response at large widths divided by the peak response. For this cell,
w opt
= 2.5” and %SI = 52%. B: length tuning data (
l
) are shown for the same complex cell as in A. There is no end-inhibi-
tion. The best fit of Eq. I to these data is shown by the solid curve. The optimal length, Lopt , is given by a in Eq. 1 (see text).
This cell preferred a grating oriented 10” from vertical with a spatial frequency of 0.44 cycles per degree.
on opposite ends or sides of the receptive field. Previous
work has shown that virtually all cells have inhibitory re-
gions at both ends of the receptive field and that regions at
opposite ends of the receptive field differ in strength by an
average of 26% (Orban et al. 1979a). It should also be noted
that our stimuli do not probe regions of the surround that
are offset diagonally from the receptive field. Thus, for cells
like that shown in Fig. 2, A and
B,
we cannot be sure that
inhibitory regions form a continuous moat around the excit-
atory receptive field.
To quantify the strength of end- and side-inhibition, the
fitting procedure shown in Fig. 3 has been applied to the
width and length data of all cells. Figure 3 shows responses
(0) from a Layer 6 complex cell that exhibits side-inhibi-
tion (Fig. 3A) but no end-inhibition (Fig. 3
B)
. The length
tuning curve for this cell
(B)
can be used to illustrate how
the data are fit in cases where there is no inhibition. The
solid curve shown in
B
is the best-fitting function of the
form
s
72
R(s) = k
,-(2Y/a)2 dy + R,
(1)
y=
-72
where
k, a,
and
R,
are free parameters. The variable s can
represent either length or width, as appropriate. This func-
tion, the integral of a Gaussian, is chosen because the recep-
tive field envelopes of cortical cells are approximately
Gaussian-shaped (Baker and Cynader 1986; Field and Tol-
hurst 1986; Jones and Palmer 1987a,b).
Equation 1
is fit to
length or width data only when there is no indication of
end- or side-inhibition, respectively. To gauge the length or
width of the receptive field, the size constant,
a,
of
Eq. 1
is
used. Thus, for the cell of Fig. 3
B,
an estimate of the “opti-
mal” length, ’ Lopt, is given by
a = 7.9”.
’ For cells that do not exhibit end- or side-inhibition there is actually no
optimal length or width, in the sense that one particular length or width
gives the largest response. In these cases, the values of Lopt or W,,, give an
estimate of the length or width, respectively, at which the response of the
cell saturates.
When the length or width data exhibit end- or side-inhi-
bition, respectively, the formulation of
Eq. 1
is no longer
appropriate. Instead, we use a modified formulation that
adds pairs of inhibitory zones at the sides or ends of the
excitatory receptive field. These inhibitory regions are also
assumed to have Gaussian weighting functions. Specifi-
cally, the data are fit with a function of the form
R(s) = k,
s
72
e-(2Yla)2
&
y=
-72
72
-
k
i
s
@(Y
- oi)lW2 dy + R,
(2)
y=
-72
where
k,, a,
and
R,
are free parameters describing the excit-
atory discharge region and
ki
, 6, and Oi are parameters re-
lated to the inhibitory zones (their strength, size, and offset
from the center of the receptive field). As illustrated by Fig.
3A,
Eq.
2 provides an acceptable fit to width (or length)
data for cells that exhibit side-inhibition (or end-inhibi-
tion). From this fit (Fig. 3A, solid curve) two parameters
are extracted. The optimal width, Wept, is the value of wat
which the curve reaches its peak value. Percent side-inhibi-
tion, %SI, is defined as the amount of attenuation observed
at large widths, as a percentage of the peak response ampli-
tude. For the cell shown in Fig. 3A, W.,, = 2.5” and %SI =
52%. For cells exhibiting end-inhibition, the optimal
length, Lopt 9
and percent end-inhibition, %EI, are defined
analogously. In a few cases, the formulation of
Eq.
2 did not
provide an acceptable fit to the length or width data; these
data have been fit by hand and the same parameters have
been extracted.
Having performed the fitting procedure shown in Fig. 3,
the width and length tuning of each cell may be character-
ized by four parameters: %SI, %EI, Wept, and L,,, . Figure
4A summarizes the relationship between %EI and %SI for
82 cells. Each datum represents one neuron, with triangles
denoting simple cells and circles denoting complex cells.
Values of %EI or %SI near 0% indicate a lack of end- or
side-inhibition; values near 100% indicate complete re-
sponse suppression for large stimuli (e.g., Fig. 1). If there
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LENGTH AND WIDTH TUNING IN STRIATE CORTEX
353
were no correlation between the incidence of end-inhibi-
tion and the incidence of side-inhibition, then the data
points would be scattered randomly throughout the do-
main shown in Fig. 4A. Clearly this is not the case. A major-
ity of the data points ( 52/ 82) lie within the shaded region,
indicating a difference of ~20% between the strengths of
end- and side-inhibition, and several of the remaining
points lie just above the shaded area. However, there are
two groups of cells for which the strengths of end- and side-
inhibition are not correlated. One group of cells, indicated
by points lying along the vertical axis (open symbols), ex-
hibits end-inhibition but no side-inhibition. Another group
of cells, indicated by points falling along the horizontal axis
(half-filled symbols), shows side-inhibition but no end-in-
hibition.
The question arises as to whether cells that exhibit only
end-inhibition or only side-inhibition can somehow be dis-
tinguished, anatomically or functionally, from those that
exhibit both. It appears that the group of cells exhibiting
only side-inhibition is, indeed, functionally distinct. This
can be seen by examining Fig.
4B,
which shows the rela-
tionship between Lopt and Wept for the same population of
cells shown in Fig. 4A. The 11 cells that exhibit only side-
inhibition are represented by half-filled symbols in both
panels of Fig. 4. It is clear from Fig. 4
B
that these cells tend
to have very long receptive fields, because virtually all of the
half-filled symbols lie in the
top
I& corner of this domain.
Moreover, 8 of 11 of these cells have been shown histologi-
cally to reside in Layer 6, which is known to possess many
cells with long receptive fields (Gilbert 1977; Grieve and
Sillito 199 la). Two of these 11 cells were recorded from
Layer 3 and the laminar location of the remaining cell
could not be determined. Thus there appears to be a distinct
subpopulation of neurons in Layer 6 that possess long re-
ceptive fields and exhibit only side-inhibition. These cells
generally respond well to long, narrow stimuli; they do not
respond well to round grating patches of any size or spatial
frequency. This type of behavior has been reported previ-
ously (e.g., Schiller et al. 1976b; von der Heydt et al. 1992)
but it has not been directly linked to the presence of side-in-
hibitory regions.
It is natural to ask whether the group of cells that exhibit
only end-inhibition (open symbols lying along the vertical
axis in Fig. 4A ) is also functionally or anatomically distinct.
Although this possibility cannot be ruled out, we have not
observed any distinguishing characteristic of these neurons.
As shown in Fig.
4B
(open symbols), these cells do not
exhibit any unusual pattern of optimal lengths and widths,
nor do they show any tendency to be localized within a
particular lamina. This group of cells also does not stand
out with respect to any of the other stimulus parameters
that we have examined (see below). Nevertheless it is possi-
ble that these cells might be distinguishable on the basis of
some response parameter or anatomic feature that we have
not measured.
Before leaving Fig. 4, it should be noted again that many
cells do not exhibit any end- or side-inhibition. A group of
such cells is represented by the cluster of points near the
origin of Fig. 4A. The population of neurons that do not
show any inhibition is actually much larger than indicated
bv Fig. 4A. because cells that failed to show anv end- or
A
100
80
n
8
5
60
I-
z
.-
1
L
40
e
W
20
0
B
N=82
I I I
I
I I . I I
20 40 60 80 100
Side-Inhibition (%)
t, i 4 6 6 lb i2
Optimal Width, Wept (deg)
FIG.
4. Comparison of length and width tuning parameters for 82 neu-
rons ( 52 simple cells and 30 complex cells). A : summary of the relation-
ship between percent end-inhibition (%EI) and %SI is shown as a scatter
plot. Each datum represents 1 neuron. Triangles: simple cells. Circles:
complex cells. Filled symbols: cells that exhibit both end- and side-inhibi-
tion. Diagonal line indicates perfect correspondence between %EI and
%SI. Shaded region contains points for which the 2 values differ by ~20%.
Most points ( 52/ 82) are contained within the shaded region, meaning that
the strengths of end-inhibition and side-inhibition are very similar for
these cells. Several data points (open symbols) fall along the vertical axis;
these cells exhibit end-inhibition but no side-inhibition. Similarly, several
points are located on the horizontal axis, denoting cells that have side-inhi-
bition but no end-inhibition. Eleven cells that exhibit only side-inhibition
are denoted by half-filled symbols. Eight of these 11 cells were recorded
from Layer 6.
B:
relationship between Lopt and Wept is summarized here
for the same population of cells shown in A. Open symbols: cells that
exhibit end-inhibition but no side-inhibition. Half-filled symbols: cells that
exhibit only side-inhibition. For many cells, the values of Lop1 and Wept are
similar (i.e., points that cluster around the diagonal). However, there is a
group of side-inhibited cells, denoted by half-filled symbols, that have very
long, narrow receptive fields.
side-inhibition during the preliminary
examination
(see
METHODS)
were often not studied quantitatively with re-
spect to end- or side-inh ibition. In stead, m .any of these neu-
rons were used as Dart of other studies.
Thus we ca nnot
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354
G. C. DEANGELIS, R. D. FREEMAN, AND I. OHZAWA
accurately estimate the proportion of cells that show nei-
ther end- nor side-inhibition.
Tuning characteristics ofend- and side-inhibition
To better understand the neuronal mechanisms that un-
derlie end- and side-inhibition it is helpful to consider how
the strength of the inhibition depends on various stimulus
parameters, such as spatial frequency, orientation, spatial
phase, and contrast.
SPATIAL FREQUENCY SELECTIVITY.
Figure 5 shows a compar-
ison between the spatial frequency tuning of inhibition and
w
i
0.1 1 3
the spatial frequency tuning of excitation. A and C show
data for a complex cell that exhibits side-inhibition;
B
and
D
show data for a simple cell that exhibits end-inhibition.
Let us first consider the side-inhibited complex cell. Figure
5A shows a standard spatial frequency tuning curve for this
neuron. The stimulus is a grating patch of optimal orienta-
tion that is approximately the same size as the cell’s excit-
atory receptive field (see Fig. L4, inset). The spatial fre-
quency of this grating patch is varied in blocks of randomly
interleaved trials (see
METHODS),
and the average discharge
rate is plotted as a function of spatial frequency (filled cir-
B
5oT 321-35
a
__--
---
D
._--
,
-d--l
, __--
__--
27 --
--------------------------
Spatial Frequency (cycles/deg)
FIG.
5. Measurements of spatial frequency tuning for excitation and inhibition. Data are shown for 2 cells: a side-inhibited
complex cell (A and C) and an end-inhibited simple cell (B and D). A : spatial frequency tuning of excitation for the complex
cell ( Cell 186-23). Filled circles: mean firing rate in response to grating patches of variable spatial frequency. The grating
patches are oriented 43 O from vertical and are approximately the same size as the excitatory receptive field ( 3 X 3 O ) . Contrast
is 50%. Solid curve: best fit of Eg. 3 to the data. B: excitatory spatial frequency tuning curve for the end-inhibited simple cell
(Cell 321-3.5). In this case, the stimulus is a patch of grating, oriented 15” from horizontal, that is 4 X 4” in size and has a
contrast of 50%. Solid curve: best-fitting Gaussian (Eq. 3). C: spatial frequency tuning of side-inhibition for the same
complex cell whose excitatory response is shown in A. The stimulus configuration is illustrated directly above the graph. The
cell is excited by a square (3 X 3O ) patch of grating that is confined within the excitatory receptive field (thick square;
dimensions of the excitatory receptive field were determined from quantitative length and width tuning runs). This excit-
atory stimulus has a spatial frequency of 0.5 cycles per degree and a contrast of 50%, and is oriented 43” from vertical. Two
patches of grating extend outward from the receptive field into the side-inhibitory regions. These inhibitory stimuli each have
a length of 3’ and a width of 5.5 O. They have the same orientation as the excitatory stimulus and a contrast of 30%. There is a
small gap (0.5O ) between the excitatory stimulus and the inhibitory stimuli on each side of the receptive field. The spatial
frequency of the inhibitory grating patches is varied from 0.14 to 3 cycles per degree. Dashed line: cell’s response during
control conditions in which only the central excitatory stimulus is presented. Solid curve: best-fitting (inverted) Gaussian,
given by ,!Q. 3. D: spatial frequency tuning of end-inhibition for the simple cell whose excitatory tuning curve is shown in B.
In this case, the cell is excited by an optimally sized ( 3 x 3.5 O ) patch of grating having the optimal orientation ( 15 O from
horizontal) and spatial frequency (0.4 cycles per degree). Inhibitory grating patches (of 50% contrast) extend outward from
the receptive field into end-inhibitory regions. Filled triangles: 1 st harmonic of the cell’s response when the inhibitory stimuli
are 3’ in width and 8.5” in length. Open squares: response of the cell to inhibitory stimuli that are 8” wide and 8.5 O long (see
dotted lines above D). Dashed line: response to the excitatory stimulus presented alone. Solid curve: best fit of Eq. 3 to the
data indicated by filled triangles. Clearly the spatial frequency tuning of inhibition is much broader than that of excitation
(compare B and D).
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LENGTH AND WIDTH TUNING IN STRIATE CORTEX
355
cles) . The solid curve in Fig. 5A is the best-fitting Gaussian
of the form
R@f) = k&f -sF,,Jd2 + R
0
(3)
where k, SFopt,
a, and R, are free parameters and sfdenotes
spatial frequency.
Figure 5C shows the spatial frequency tuning of side-in-
hibition for the same complex cell as in Fig. 5A. The stimu-
lus configuration is depicted schematically above C. The
cell is excited by a grating patch of optimal orientation,
spatial frequency, length, and width. The optimal length
and width are determined from quantitative measure-
ments, as described above. Side-inhibitory regions are stim-
ulated by two grating patches, each of optimal orientation
and length, that extend outward along the sides of the re-
ceptive field. By varying the spatial frequency of these inhib-
itory stimuli we constructed a spatial frequency tuning
curve for side-inhibition, as shown in Fig. 5C (filled cir-
cles). The solid curve is the (inverted) Gaussian, given by
Eq. 3, that best fits the data points. The dashed line in Fig.
5C shows the response level of the cell during interleaved
control conditions in which only the excitatory grating
patch (i.e., the center portion of the stimulus) is displayed.
It is clear that side-inhibition is effective for all spatial fre-
quencies below - 1.5 cycles per degree. Comparison of Fig.
SC with Fig. 5A shows that the spatial frequency tuning of
side-inhibition is considerably broader than the spatial fre-
quency tuning of excitation for this complex cell.
Figure 5, B and D, shows that a similar conclusion can be
reached concerning the spatial frequency tuning of end-in-
hibition. Figure 5 B shows the standard excitatory spatial
frequency tuning curve for a simple cell, obtained using a
grating patch of optimal orientation, length, and width. Fig-
ure 5 D shows the spatial frequency tuning of end-inhibi-
tion for this same simple cell. The stimulus configuration is
similar to that of Fig. 5C, except that the inhibitory grating
patches now extend outward along the axis of the cell’s pre-
ferred orientation (i.e., into the end-inhibitory regions).
Clearly the spatial frequency tuning of end-inhibition (Fig.
5 D, filled triangles) is much broader than the spatial fre-
quency tuning of excitation (Fig. 5 B, filled triangles). In
fact, end-inhibition is effective at all spatial frequencies up
to -4 cycles per degree, a range that is nearly as broad as
the cat’s entire contrast sensitivity function (see Bisti and
Maffei 1974; Blake et al. 1974; Pasternak and Merigan
198 1). In other words, for this cell, end-inhibition is effec-
tive over approximately the entire range of spatial frequen-
cies to which the cat’s visual system is sensitive!
It is important to note that the temporal frequency of the
inhibitory stimulus is fixed (at 2 Hz), whereas the spatial
frequency is varied. This means that the velocity of the in-
hibitory stimulus varies inversely with spatial frequency. As
a result, when the excitatory and inhibitory gratings have
different spatial frequencies their relative positions (or
phases) change as the stimuli are drifted. This would pre-
sent a problem if the strength of inhibition were dependent
on the relative phases of the two stimulus components.
However, as shown below (Fig. 9), end- and side-inhibition
are generally independent of the relative spatial phase be-
tween excitatory and inhibitory stimuli.
Another potential problem is that the inhibitory grating
patches in Fig. 5 D are fairly narrow ( 3O in width). Thus
when the spatial frequency of the inhibitory stimulus is low
its amplitude spectrum becomes broader. It could be ar-
gued that the spatial frequency tuning of end-inhibition
shown in Fig. 5 D is artificially broadened by the use of
narrow inhibitory stimuli. To control for this possibility we
adjusted the inhibitory grating patches to a width of 8O (see
dotted lines in the schematic above Fig. 5 D) and the experi-
ment was repeated. The data from this repeat trial are
shown in Fig. 5 D as squares and the result is very similar to
that obtained using narrow patches (filled triangles). More-
over, the inhibitory tuning curves shown in Fig. 5 D are
broader than the excitatory curve at both low and high spa-
tial frequencies. The effectiveness of inhibition at high spa-
tial frequencies cannot be due to spatial truncation of the
stimulus. It should be noted that the excitatory spatial fre-
quency tuning curve (Fig. 5 B) is also obtained with the use
of a narrow grating patch. Thus any broadening at low spa-
tial frequencies would apply to both excitation and inhibi-
tion. We conclude, therefore, that the broad spatial fre-
quency tuning of end-inhibition reflects neural connecti-
vity rather than some stimulus artifact.
Figure 6 summarizes the relationship between the spatial
frequency tuning of excitation and the spatial frequency
tuning of end- and side-inhibition. These data are obtained
from the best-fitting Gaussian curves, as illustrated in Fig.
5. For each excitatory or inhibitory tuning curve, two spa-
tial frequency parameters are extracted: the optimal spatial
frequency, SF,,, (see Eq. 3) and the spatial frequency
bandwidth at half-maximal height, SF,,. SF,, is defined as
1.65cu, where a is the parameter in Eq. 3 that determines the
spread of the Gaussian. Figure 6A shows the optimal inhibi-
tory spatial frequency plotted against the optimal excitatory
spatial frequency for a population of 32 cells. Filled and
open triangles denote end-inhibited and side-inhibited sim-
ple cells, respectively; filled and open circles denote end-
and side-inhibited complex cells. There is a reasonably
strong correlation (r = 0.79, P < 0.00 1) between the opti-
mal inhibitory spatial frequency and the optimal excitatory
spatial frequency for this population of cells, as evidenced
by clustering of the data points around the diagonal line. In
some cases, however, optimal inhibitory and excitatory
spatial frequencies differ substantially. Figure 6 B shows a
scatter diagram of inhibitory and excitatory spatial fre-
quency bandwidths. It is clear that the spatial frequency
tuning of inhibition is generally much broader than the tun-
ing of excitation, because nearly all of the data points in Fig.
6 B lie well above the diagonal. This applies to both end-in-
hibition (filled symbols) and side-inhibition (open sym-
bols). For several cells, the spatial frequency tuning of inhi-
bition is 4 to 8 times broader than the excitatory tuning
curve. This result suggests that end- and side-inhibition are
mediated by a pool of cortical cells, members of which ex-
hibit a fairly broad range of optimal spatial frequencies.
Very similar findings concerning the spatial frequency selec-
tivity of end-inhibition have been reported by Tanaka et al.
( 1987) for neurons in Area 19 of the cat (see their Fig. 9).
ORIENTATION SELECTIVITY.
The orientation selectivity of
end- and side-inhibition can be measured using a procedure
that is analogous to that described above for spatial
fre-
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356
G. C. DEANGELIS, R. D. FREEMAN, AND I. OI-IZAWA
N=32 A
0.0 0.5
1.0
1.5
Excitatory SFopt (cycles/deg)
”
I
I I I I I
I I I I I I
0 1
2 3
Excitatory SF bw (cyclesideg)
FIG. 6. The relationship between the spatial frequency tuning of excita-
tion and inhibition is summarized here. A : optimal inhibitory spatial fre-
quency is plotted against the optimal excitatory spatial frequency for a
population of 32 cells. In this scatter diagram, each datum represents 1
neuron, with triangles denoting simple cells and circles denoting complex
cells. Filled and open symbols represent cells for which end-inhibition and
side-inhibition, respectively, have been studied. Most points cluster
around the diagonal, indicating that the optimal spatial frequencies for
excitation and inhibition are usually similar.
B:
relationship between the
spatial frequency bandwidths of inhibition and excitation for the same
population of cells shown in A. Bandwidth is measured as the full width of
the tuning curves at half-maximal height (see text). Virtually all of the
points in this scatter plot lie above the diagonal, meaning that the spatial
frequency tuning of inhibition is much broader than the spatial frequency
tuning of excitation. Average values of spatial frequency bandwidth at
half-maximal height,
SF,,, ,
are 0.59 cycles per degree for excitation, 1.15
cycles per degree for side-inhibition (open symbols), and 1.23 cycles per
degree for end-inhibition (filled symbols).
quency tuning. Figure 7 shows orientation tuning curves
for excitation and inhibition; these data were obtained from
the same two cells for which spatial frequency tuning data
are shown in Fig. 5. Figure 7A shows the standard orienta-
tion tuning function for a side-inhibited complex cell. The
stimulus is a grating patch of optimal spatial frequency and
approximately optimal length and width (as determined
from preliminary observations). The orientation of the
grating is varied in small steps around each of two opposite
directions of motion (shown 180’ apart in Fig. 7A). This
cell is clearly direction selective, because the peak response
in one direction (orientation N 230’ ) is more than twice as
large as the peak response in the opposite direction (orienta-
tion N 50° ) . The solid curves in Fig. 7A are Gaussians,
formulated in a manner analogous to that described by Ey.
3, that best fit the orientation tuning data. From the Gauss-
ian fit to responses in the preferred direction of motion, two
orientation tuning parameters are extracted: the optimal
orientation, ORopt, and the orientation bandwidth (full
width at half-maximal height), OR,, . For this cell OR,,, =
228O and OR,, = 42’.
Figure 7C shows the orientation selectivity of side-inhibi-
tion for the same complex cell as in Fig. 7A. The stimulus
configuration (shown above Fig. 7C) is similar to that
shown in Fig. SC, except that the orientation of the inhibi-
tory grating patches is now varied. Filled circles in Fig. 7C
show the cell’s response as a function of the orientation of
gratings that extend into the side-inhibitory regions. The
dashed line represents the response to the excitatory grating
patch when presented alone. Two troughs of inhibition are
clearly seen in Fig. 7C and these troughs are centered
around the optimal orientations for excitation in each of
the two opposite directions. Thus side-inhibition is most
pronounced when the orientation of the inhibitory stimu-
lus matches the orientation of the excitatory stimulus, as
previously reported by Born and Tootell ( 199 1). When the
inhibitory gratings are oriented orthogonally to the cell’s
preferred orientation, inhibition vanishes. The smooth
curve in Fig. 7C shows the inverted Gaussian that best fits
the data corresponding to the preferred direction of motion.
From this fit the optimal inhibitory orientation ( ORopt =
235O ) and the OR,, ( 149” ) are determined. Although the
optimal orientation for inhibition matches that for excita-
tion, the orientation tuning of side-inhibition is consider-
ably broader than that for excitation.
Similar orientation tuning results are shown in Fig. 7, II
and D, for an end-inhibited simple cell. Figure 7 B shows
the orientation selectivity of excitation for this neuron. The
optimal excitatory orientation is 185 O and the cell is quite
direction selective (the response in the preferred direction
being -4 times larger than the response in the nonpre-
ferred direction). An orientation tuning curve for end-inhi-
bition is shown in Fig. 7 D. These data are obtained by vary-
ing the orientation of grating patches that extend outward
from the excitatory receptive field into end-inhibitory re-
gions (see illustration above Fig. 7 D). Again, two troughs
of inhibition can be seen in the orientation tuning function,
and these troughs are centered around the peak excitatory
orientations for the preferred and nonpreferred directions.
These data confirm earlier reports ( Hubel and Wiesel 1965;
Nelson and Frost 1978; Orban et al. 1979b) that end-inhi-
bition has maximal strength at approximately the same ori-
entation that produces peak excitation. The smooth curve
in Fig. 70 shows the inverted Gaussian that best fits the
portion of the inhibitory tuning curve corresponding to the
preferred direction of motion. The optimal inhibitory orien-
tation is 197O and the orientation bandwidth of end-inhibi-
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LENGTH AND WIDTH TUNING IN STRIATE CORTEX
357
A B
'ST
186-23 5oT 321-35
-30 60 150
240 330 -90 0 90 180 270
I : :
: : : : : I
-30 60 150 240 330
D
25
20
15
IO
5
0
t : : : : : : : I
-90 0 90 180
270
Orientation (deg)
FIG.
7. Comparison of orientation tuning curves for excitation and inhibition. Responses are shown for the same 2 cells
for which spatial frequency tuning data are exhibited in Fig. 5. The convention used here is that 0” (or 180” ) represents
horizontal and 90” (or 270° ) represents vertical. A : bidirectional orientation tuning function (0) is shown for a side-inhi-
bited complex cell ( Cell 186-23). The stimulus is a single patch of grating ( 3
X
3 O ) that has a spatial frequency of 0.5 cycles
per degree and a contrast of 50%. Seven different orientations, 12” apart, are tested around each of 2 opposite directions of
motion ( 180” apart). Solid curves show the best-fitting Gaussians (formulated in a manner analogous to that described by
Eq. 3) to each of the 2 sets of data, corresponding to the preferred and opposite directions of motion. B: bidirectional
orientation tuning curve (A ) is shown for an end-inhibited simple cell (Cell 321-3.5). In this case, the patch of grating
measures 4
X
4” and has a spatial frequency of 0.40 cycles per degree, and a contrast of 50%. C: orientation tuning of
side-inhibition for the complex cell shown in A. The stimulus configuration (shown above C) is identical to that described in
Fig. 5C, except that the orientation of the inhibitory grating patches is varied and their spatial frequency is fixed at 0.5 cycles
per degree. Dashed line: response to the central excitatory stimulus when presented alone. Thick curve: inverted Gaussian
that best fits the portion of the data corresponding to the preferred direction of motion. Data points centered around the
nonpreferred direction of motion are connected by a thin line. Note that the orientation tuning of inhibition is considerably
broader than that for excitation. It should be noted here that the inhibitory grating is rotated within a fixed rectangular
window. The orientation of the fixed window is 227 O. D : orientation selectivity of end-inhibition for the simple cell shown in
B.
The stimulus configuration is the same as described in Fig. 5 D, except that the spatial frequency of the inhibitory grating
patches is fixed at 0.35 cycles per degree and the orientation is varied. Thick curve: Gaussian that best fits the portion of the
data corresponding to motion in the cell’s preferred direction. In this case, the orientation of the rectangular stimulus
window, in which the inhibitory gratings are rotated, is 15”.
tion is 115 O. As for side-inhibition, the orientation tuning
of end-inhibition is broader than the tuning for excitation.
Inspection of the stimulus configurations shown above
Fig. 7, C and
D,
reveals that the bars of the inhibitory grat-
ing stimuli change length as these gratings are rotated
within their rectangular borders. In Fig. 7C, the bars of the
inhibitory gratings are shortest when these stimuli are ori-
ented parallel to the cell’s preferred orientation. It could be
argued that the orientation tuning of side-inhibition in Fig.
7C is artificially broadened because of the spatial limita-
tions of the inhibitory stimulus. However, the excitatory
orientation tuning curve (Fig. 74 is obtained with a grat-
ing patch of the same length; thus the excitatory and inhibi-
tory tuning curves should be affected similarly.
An interesting feature of the data shown in Fig. 7, C and
D,
is that the strength of inhibition is approximately equal
for opposite directions of motion (i.e., orientations sepa-
rated by 180’ ). Thus, although excitation is direction selec-
tive (Fig. 7, A and B), inhibition is not. One possible impli-
cation of this result is that inhibition is mediated by cells
that are not direction selective. Alternatively, inhibition
may be mediated by a pool of neurons having varied direc-
tional preferences, such that their net effect is non-direction
specific. This latter possibility seems more consistent with
our findings that inhibition is phase insensitive (Fig. 9) and
broadly tuned for spatial frequency (Figs. 5 and 6).
Figure 8 summarizes the relationship between the orien-
tation selectivity of excitation and the orientation selectiv-
ity of end- and side-inhibition. In Fig. 8A the optimal inhibi-
tory orientation is plotted against the optimal excitatory
orientation for a population of 25 cells. Filled and open
triangles denote end- and side-inhibited simple cells, respec-
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358
G. C. DEANGELIS, R. D. FREEMAN, AND I. OHZAWA
A
360
5s
+
270
c
E
cr”
0
180
2
0
.- z
c 90
s
-
0
B
200
s
$ 150
-i
cr”
0 100
2
2
3
5 50
-
0
N=25
sb IS0 2jo 360
Excitatory ORopt (deg)
N=23
I
I
I I
I I I I
0 50 100 150 200
Excitatory ORbw (deg)
FIG.
8. Comparison of the orientation tuning of inhibition with that of
excitation. The format of this figure is similar to that of Fig. 6. A : scatter
diagram showing the optimal inhibitory orientation plotted against the
optimal excitatory orientation for 25 cells. There is a strong correlation
(Y = 0.99) between the 2 parameters, as most points cluster tightly around
the diagonal.
B:
relationship between orientation bandwidths for excita-
tion and inhibition is summarized. Almost all points lie well above the
diagonal, indicating that the orientation tuning of end- and side-inhibition
(filled and open symbols, respectively) is broader than the orientation
tuning of excitation. The average values of orientation bandwidth (full
width at half-maximal height),
ORbw
, are 46.6 O for excitation, 104” for
side-inhibition, and 89” for end-inhibition.
tively. Filled and open circles indicate end- and side-inhib-
ited complex cells. There is a very strong correlation (r =
0.99, P < 0.00 1) between the optimal excitatory and inhibi-
tory orientations. It should be noted that the values of ORopt
plotted on the horizontal axis in Fig. 84 refer to the optimal
excitatory orientation in the preferred direction of motion.
Similarly, values of the optimal inhibitory orientation are
for motion in the preferred direction of each cell. Figure 8 B
shows the relationship between the orientation tuning
bandwidths of inhibition and excitation. In general, the ori-
entation tuning of inhibition is broader than the tuning of
excitation, as evidenced by the fact that almost all of the
data points lie above the diagonal in Fig. 8 B. This result is
similar to that shown in Fig. 6 B for spatial frequency band-
widths, and it suggests that end- and side-inhibition are me-
diated by a pool of neurons (see
DISCUSSION).
SPATIAL PHASE TUNING.
Another useful parameter to con-
sider is the relative spatial phase between the excitatory and
inhibitory grating stimuli. On the basis of findings of Bolz
and Gilbert (1986), Dobbins et al. (1987, 1989) have for-
mulated a model for end-inhibition in which a simple cell
with a long receptive field inhibits another simple cell with
a short receptive field, thus endowing the latter cell with
end-inhibition (see
DISCUSSION).
This model predicts that
the strength of end-inhibition should be markedly depen-
dent on the relative spatial phase between a grating con-
fined to the excitatory receptive field and a grating confined
to the inhibitory end-zones. Similar considerations would
apply to side-inhibition if an analogous model is assumed.
Figure 9, A and B, shows the spatial phase tuning of side-
and end-inhibition, respectively, for the same two cells for
which data are shown in Figs. 5 and 7. In each case, the cell
is excited by a patch of grating, having optimal orientation
and spatial frequency, that is confined within the excitatory
receptive field. For the complex cell of Fig. 9A, inhibitory
grating patches are placed in the side-inhibitory regions; for
the simple cell of Fig. 9B, inhibitory grating patches are
located in the end-inhibitory regions. By varying the rela-
tive spatial phase between the excitatory grating and the
inhibitory gratings, the spatial phase tuning of inhibition
can be evaluated. Filled circles in Fig. 9A show the spatial
phase tuning of side-inhibition for the complex cell. The
dashed line indicates the response level during interleaved
control conditions in which only the excitatory grating
patch is presented. Note that the response of this complex
cell is suppressed almost uniformly at all spatial phases. A
similar result is shown in Fig. 9 B for the end-inhibited sim-
ple cell. Phase independence of end-inhibition has also
been found for neurons in Area 19 of the cat (Tanaka et al.
1987).
To quantify the spatial phase tuning of end- and side-in-
hibition, the data of Fig. 9, A and B, have been fit with a
sinusoid of the form
R(@) = A sin ((a - 4) + R,,,
(4)
where A, #, and R,,,, are free parameters and ip denotes
relative spatial phase. This function is chosen because it
provides a good empirical description of the data: in cases
where there is some dependence of the strength of inhibi-
tion on phase, this modulation appears to be sinusoidal.
The solid curves in Fig. 9, A and B, show the sinusoids that
best fit the experimental data. In both cases, the amplitude
of the best-fitting sinusoid is small because response is sup-
pressed almost uniformly at all phases. The spatial phase
tuning of inhibition can be parameterized by computing a
phase sensitivity index, which is defined as
Phase Sensitivity Index = R
A
_ R
control mean
(5)
In this equation, A and R,,,, represent the amplitude and
mean value of the best-fitting sinusoid, respectively (see Eq.
4 >
l
Rcontrol
is the response level produced by the excitatory
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LENGTH AND WIDTH TUNING IN STRIATE CORTEX
359
FIG.
9. Measurement of the spatial phase sensiti vity of end- and side-inhibition. A : data are shown for the same side-inhi-
bited complex cell ( Cell 186-23) described in Figs. Kand 7C. The stimulus configuration (shown above A ) is similar to that
described in Fig. 5C. The excitatory (center) stimulus has a spatial frequency of 0.5 cycles per degree and a contrast of 50%
and is oriented 43” from vertical. The patches of grating that surround the receptive field on 2 sides have the same orientation
and spatial frequency as the center patch but a contrast of 20%. Filled circles: response of the cell as the relative spatial phase
between the center and surround stimuli is varied over 360’. Solid curve: best fit of
Eq.
4 to the data. Dashed line: response
elicited by presentation of the center patch only. Note that the cell’s response is suppressed at all spatial phases by the
presence of the surrounding stimuli. B: spatial phase tuning of end-inhibition ( A ) for the same simple cell shown in Figs. 5 D
and 7 D. In this case both the excitatory and inhibitory gratings have a spatial frequency of 0.35 cycles per degree and a
contrast of 50% and are oriented 15” from horizontal. Note that the strength of end-inhibition is roughly independent of the
relative spatial phase. C: distribution of the phase sensitivity index, as computed by
Eq.
5, for a population of 20 cells. Black
and white bars: groups of cells for which end- and side-inhibition, respectively, were studied. Hatched portions of bars: data
obtained from complex cells. Unhatched portions: simple cells. Values of the phase sensitivity index near 0.0 indicate that the
strength of inhibition is independent of the relative phase between the excitatory and inhibitory stimuli.
n
tj
20
321-35
I
--------------------------
15
u 0 90 180 270 360 0 90 180 270 360
Relative Spatial Phase (deg)
0.0 0.2 0.4 0.6 0.8
1.0
Phase Sensitivity Index
grating patch when presented alone (Fig. 9, A and
B,
dashed
lines). If the strength of inhibition is independent of rela-
tive spatial phase, the phase sensitivity index will have a
value close to 0. If inhibition depends strongly on spatial
phase, the phase sensitivity index will have a value close to
1. For the cells shown in Fig. 9, A and
B,
values of the phase
sensitivity index are 0.07 and 0.09, respectively, indicating
that inhibition is roughly independent of phase.
Figure 9C shows the distribution of the phase sensitivity
index for 20 cells. White bars denote side-inhibited cells
and black bars denote end-inhibited cells. Hatched and un-
hatched portions of the bars distinguish between complex
and simple cells, respectively. For 12 of these 20 neurons,
the phase sensitivity index has a value ~0.2. Only three cells
show a phase sensitivity index >0.4. Median values of the
phase sensitivity index are 0.12 for end-inhibition and 0.18
for side-inhibition, but this difference is not significant (2 =
0.84, P = 0.40). Differences between distributions of the
phase sensitivity index for simple and complex cells are also
not significant, neither for end-inhibition (white bars: 2 =
1.04, P = 0.29) nor side-inhibition (black bars: 2 = 0.14,
P = 0.89). Some of the cells in this sample exhibited only
end-inhibition ( 5 / 11) or only side-inhibition ( 5 / 9 ) ,
whereas others exhibited both; however, the phase sensitiv-
ity index does not appear to depend on the relative
strengths of end- and side-inhibition. Overall, these data
show that the strength of inhibition is generally indepen-
dent of the relative phase between the excitatory and inhibi-
tory stimuli. This result is at odds with the model for end-
inhibition proposed by Dobbins et al. ( 1987, 1989) (see
DISCUSSION
for more on this point). Also, it is important to
note that this relative phase insensitivity allows us to con-
duct measurements of the orientation and spatial frequency
tuning of inhibition (described above) without having to
worry about possible.phase effects (see also Tanaka et al.
1987).
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360
G. C. DEANGELIS, R. D. FREEMAN, AND I. OHZAWA
I
I , IIIIIII I I
I I I IIIlll
I I
1
10
40
Surround Contrast (%)
3 IO
30 40
Center Contrast (%)
,,~~flyy~---
.
I : ::::::
I I
I
I
3
10
30 40
Center Contrast (%)
D
I 4
0 3 6 9 12
Surround Contrast
0
(0
0
FIG.
10. Effect of inhibition on contrast-response functions. Data are shown for an end-inhibited complex cell (Cell
181-26). A :
l
: dependence of the strength of end-inhibition on contrast. The stimulus ( shown above A ) consists of a central
grating patch, 3O wide by 2” long, that is surrounded on 2 ends by inhibitory grating patches, each of which is 3” wide by 8.5”
long. Both the center and surround stimuli have a spatial frequency of 0.75 cycles per degree and are oriented 15 O from
horizontal. The center patch has a contrast of 20%, whereas the contrast of the surround is variable. As usual, the dashed line
shows the level of response when the surround is absent (i.e., when surround contrast is 0%). Note that response strength (0)
decreases monotonically with increasing surround contrast. B: effect of surround inhibition on the excitatory contrast-re-
sponse function. The stimulus configuration is identical to that described in A, except that the contrast of the surround is
fixed [at 1 of 4 different values: 0% (o ) ,5% (
l
) ,9% ( •I ), or 12% (
n
)] and the contrast of the center stimulus is varied from 3%
to 40%. C: data of panel B, replotted here along with the best-fitting curves given by Eg. 6 ( see text for details). D: saturation
level, Rn,, 7
of the best-fitting hyperbolic ratio function (Eq. 6) is plotted against surround contrast. The unit of measure for
R,,, is spikes per second. E: exponent, n, of the best-fitting hyperbolic ratio function is plotted against surround contrast. F:
semisaturation coefficient, c 50, is plotted as a function of surround contrast. The unit of measure for csO is percent contrast.
CONTRAST RESPONSE.
Another way to assess the mecha-
nisms underlying end- and side-inhibition is to examine
how these inhibitory influences affect a cell’s contrast-re-
sponse function. For example, studies of cross-orientation
inhibition (Bonds 1989; Morrone et al. 1982) have shown
that the presence of an inhibitory stimulus causes a shift in
the excitatory contrast-response function. This shift is con-
sistent with a divisive mechanism for cross-orientation inhi-
bition (Heeger 1992). There are two salient questions re-
garding the contrast dependence of end- and side-inhibi-
tion. First, how does the strength of inhibition vary with the
contrast of the inhibitory stimulus? Second, how does the
presence of an inhibitory stimulus affect the excitatory con-
trast-response function?
Figure 10A addresses the first of these two questions.
Data are shown here for a complex cell that exhibits end-in-
hibition. The cell is excited by a grating patch (of optimal
orientation, spatial frequency, and size) that has a contrast
of 20%. End-inhibitory regions are stimulated by patches of
gratings that have variable contrast (see the illustration
above Fig. 10A). Filled circles in Fig. 10 A show the cell’s
response as a function of the contrast of the inhibitory stim-
ulus (i.e., the surround). A dashed line indicates the re-
sponse level of the cell when the contrast of the surround is
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LENGTH AND WIDTH TUNING IN STRIATE CORTEX 361
0%. It is clear from Fig. 1 OA that the strength of end-inhibi-
tion increases monotonically as a function of surround con-
trast. The cell’s response is completely suppressed when the
contrast of the surround reaches 20%. Similar results have
been obtained for several other cells that exhibited either
end- or side-inhibition.
Let us now consider the effect of an inhibitory stimulus
on the excitatory contrast-response function. Figure 10 B
shows contrast-response functions for the same end-inhib-
ited complex cell as in Fig. 1OA. For these tests, the contrast
of the excitatory grating patch (i.e., the center) is varied,
whereas the contrast of the surround is fixed at one of four
values: 0% (O), 5% (a), 9% (Cl), or 12% (
q
) . Note that the
data are plotted on log-log coordinates. Qualitatively the
presence of the surround appears to cause either a rightward
or downward shift of the contrast-response function.
To quantitatively assess the shift of the contrast-response
functions shown in Fig. 1 OB, these data have been fit with a
hyperbolic ratio function. Albrecht and Hamilton ( 1982)
have shown that this function provides a good fit to con-
trast-response functions for most cortical cells. The hyper-
bolic ratio is formulated as
R(c) = R,,, Cn
cn + c;,
(6)
where
R,,, ,
n,
and c,~ are free parameters and c denotes
contrast. To examine whether the contrast-response func-
tions move rightward or downward as surround contrast
increases, we have fit hyperbolic ratio functions to all four
sets of contrast-response data simultaneously (by minimiz-
ing the total sum squared error, pooled across the 4 data sets
corresponding to surround contrasts of 0, 5, 9, and 12%).
The solid curves in Fig. 1OC show the results of this fit. If
the contrast-response curve shifts laterally as a function of
surround contrast, then the semi-saturation coefficient, c,~,
should change, but the saturation level,
R,,,,
and the expo-
nent,
n,
should remain constant. Alternatively, if the con-
trast-response curve shifts downward as surround contrast
increases, then R,,, should decrease while
n
and c50 remain
constant. Figure 10,
D-F,
shows the values of
R,,,
,
n,
and
Cam, respectively, as a function of the contrast of the inhibi-
tory stimulus. These parameter values are obtained from
the fit shown in Fig. 1OC. Note that
R,,,
and
n
exhibit little
change as a function of surround contrast, although there is
a tendency for
n
to decrease somewhat. On the other hand,
csO increases dramatically (almost 4-fold) with surround
contrast, a result that is consistent with the expectation for a
rightward shift of the contrast-response function. Further-
more, if
R,,,
is constrained to have the same value for each
surround contrast (while
n
and c,, vary as before), then the
total sum squared error of the fit increases by only 2%.
However, if c,~ is constrained to have the same value for
each surround contrast (whereas
R,,,
and
n
are varied inde-
pendently), then the total sum squared error increases by
56%. We conclude, on the basis of these analyses, that the
data of Fig. 1 OB are consistent with a rightward, rather than
a downward, shift of the contrast-response function. Thus
the influence of end- and side-inhibition on contrast re-
sponse properties appears to be similar to the effects of
cross-orientation inhibition ( Bonds 1989 ) or contrast adap-
tation (Ohzawa et al. 1985) which are thought to be me-
diated by a divisive mechanism (Heeger 1992).
Laminar analysis
For 64 of the 88 cells studied here, histological analysis
was successful in determining the laminar locations of the
neurons. Figure 11 summarizes the results of this laminar
analysis. Figure 11 A shows %EI plotted against laminar lo-
cation (i.e., layer) for 2 1 complex cells (0) and 43 simple
cells
(A).
Points plotted halfway between two different
layers indicate cells that are located on the border between
these layers. Note that all but one of the neurons in Layer 4
are simple cells and that all three of the neurons in Layer 5
are complex cells. These results are consistent with those
reported by Gilbert ( 1977 ) . The data of Fig. 11 A show that
end-inhibited cells are found in all layers of the cortex.
Moreover, the distribution of %EI is roughly uniform
within each layer (with the possible exception of Layer 5,
where the sample is small). Similar findings have been re-
ported by Gilbert ( 1977) who studied the length tuning of
cortical cells using bar stimuli. One difference between the
results reported here and those of Gilbert concerns the pro-
portion of Layer 6 cells that exhibit end-inhibition. Gilbert
( 1977 ) reports that end-inhibited cells are rarely found in
Layer 6, whereas Fig. 11 A shows that several Layer 6 cells
are strongly end-inhibited.
Figure 11 B shows Lopt plotted against laminar location
for the same population of cells shown in Fig. 11 A. It is
clear that each lamina contains a considerable range of op-
timal lengths. Consider, in particular, the distribution of
L,,, within Layer 6, as there is some disagreement in the
literature concerning the proportion of cells in this layer
that have long receptive fields. Gilbert ( 1977) reports that
63% of cells in Layer 6 have receptive fields longer than 6”,
whereas Grieve and Sillito ( 199 la) state that only 24% of
Layer 6 neurons have receptive fields longer than 6’. Our
data (Fig. 11 B) show that 27% (8 /30) of Layer 6 cells in
this study have optimal lengths >6O, a result that is very
similar to that of Grieve and Sillito ( 199 1 a).
Differences between the results reported here (Fig. 11, A
and B) and those of Gilbert ( 1977) may be partially ex-
plained by the following observations. Gilbert ( 1977) re-
ports that most Layer 6 cells have receptive fields longer
than 6” and exhibit no end-inhibition. Overall, the data of
Fig. 11, A and
B,
do not confirm this finding, but a subpopu-
lation of Layer 6 cells in this study does exhibit the type of
behavior reported by Gilbert. As shown in Fig. 4, most of
the cells with receptive fields longer than 6” belong to a
group of neurons (indicated by half-filled symbols) that ex-
hibit pronounced side-inhibition, but no end-inhibition.
Eight of these 11 cells were recorded from Layer 6. As noted
above, cells belonging to this group do not respond well to
round or square patches of grating, regardless of size, but
they do respond well to long, thin bars. Because Gilbert
( 1977 ) used bar stimuli and we have used grating stimuli, it
is possible that Gilbert encountered a greater proportion of
cells with long receptive fields and no end-inhibition. How-
ever, it should be noted that the study of Grieve and Sillito
( 199 la) was also performed using bar stimuli, and their
results concerning Layer 6 neurons are very similar to ours.
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362 G. C. DEANGELIS, R. D. FREEMAN, AND I. OHZAWA
1 213 4 5 6
1 213 4 5 6
IO-
Layer Layer
FIG. 11. Laminar analysis of length and width tuning parameters. A : %EI is plotted against layer for a population of 64
neurons. Triangles: simple cells
(n
= 43 ). Circles: complex cells
(n
= 2 1). Most cells were unambiguously classified as
residing within Layers 2/ 3, 4, 5, or 6, and these data are plotted at the appropriate abscissa. For a few cells the laminar
location could not be clearly determined, because these neurons were located on the border between 2 laminae. Symbols
denoting these cells are plotted halfway between the abscissas corresponding to the relevant laminae. B: Lopt is plotted here
vs. layer for the same population of cells shown in A. Note that there are several neurons in Layer 6 with exceptionally long
(~6” ) receptive fields. C: laminar distribution of %SI. D: laminar distribution of Wept.
Figure 11 C shows %SI plotted against layer for the same
population of neurons described above. Overall, there ap-
pears to be no laminar specialization with respect to the
strength of side-inhibition. Similarly, Fig. 11 D shows that
cells from all laminae exhibit similar distributions of Wept .
Thus the only clear laminar specialization observed in this
study involves the group of Layer 6 cells with long receptive
fields that exhibit strong side-inhibition but no end-inhibi-
tion (see Fig. 4).
of length and/or width tuning have been obtained through
both the dominant and nondominant eyes. These data are
summarized in Fig. 12. Figure 12A shows a comparison of
the two eyes with respect to the strength of end-inhibition
(%EI). Most of the data points are clustered around the
diagonal line, indicating that the strength of end-inhibition
is generally well matched for the two eyes. Linear regression
analysis yields a correlation coefficient of 0.925, which is
significant (P < 0.001). The best-fitting straight line (not
shown) has a slope of 0.94 and an intercept of 7.5%. Figure
12 B shows a comparison of L,,, measured through the dom-
inant and nondominant eyes for the same population of
cells as in Fig. 12A. Again most of the points cluster closely
around the diagonal line. In this case the correlation coeffi-
cient is 0.89, which is also significant (P < 0.001). The
regression line (not shown) has a slope of 1 .O 1 and an inter-
cept of 0.15’. Together, Fig. 12, A and B, shows that the
length tuning of cortical cells is closely matched between
the dominant and nondominant eyes. In this regard length
tuning is similar to orientation and spatial frequency selec-
tivity (see Skottun and Freeman 1984).
Figure 12, Cand D, shows width tuning data for 27 binoc-
ular cells ( 14 simple and 13 complex). Figure 12C shows
that there is generally agreement between measurements of
Comparison of the two eyes
All of the results described above have been obtained by
applying visual stimulation to the dominant eye for each
neuron. The question arises as to whether the length and
width tuning measured through the nondominant eye is
similar to that measured through the dominant eye. For
example, it has been suggested (Rogers and Cagenello
1989) that differences in length tuning between the two
eyes may be useful for computing three-dimensional sur-
face structure
(see DISCUSSION).
Thus it is of interest to
make a quantitative comparison between length and width
tuning curves for the two eyes.
For 28 cells ( 14 simple and 14 complex), measurements
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LENGTH AND WIDTH TUNING IN STRIATE CORTEX
363
A
100
L T
80
w
To’
b
- 80
CT)
N=28
1
6
I I I I I
20 40 60 80 100
Dominant El (%)
N=27
t
I I I I
I I I I t
0 20 40 60 80 100
Dominant SI (%)
u
- 8--
E
-I 6--
z
E
.- 4”.
E
0
D
%?
8
t
1 I I I
I
I I
I
t
0 2 4 6 8 10
Dominant Lopt (deg)
6
i i
i; i3
Dominant Wept (deg)
FIG. 12. Comparison of length and width tuning parameters obtained for the dominant and nondominant eyes. In each of
the 4 panels, values obtained by stimulation through the nondominant and dominant eyes are plotted on the vertical and
horizontal axes, respectively. Diagonal lines: perfect correspondence between parameter values for the 2 eyes. A: %EI. B:
L opt. C: %SI. D: Wept.
See text for additional details.
%SI obtained through the two eyes. The correlation coeffi-
cient is 0.87 (P < 0.00 1); the regression line (not shown)
has a slope of 0.86 and an intercept of 3.4%. Figure 12 D
shows the relationship between measurements of Wept for
the dominant and nondominant eyes. In this case the corre-
lation coefficient is 0.73, which is significant (P < 0.00 1).
The best-fitting straight line (not shown) has a slope of 0.67
and an intercept of 1.5 O. Note that the correlation between
WOPt for the two eyes (D) is somewhat weaker than the
correlation between Lopt for the two eyes (B).
Dichoptic measurements ofend- and side-inhibition
Several different models have been proposed to explain
the generation of end-inhibition in the visual pathway (see
DISCUSSION).
Some of these models (e.g., Bolz and Gilbert
1986; Dobbins et al. 1987, 1989; Hubel and Wiesel 1965)
propose that end-inhibition arises through intracortical
connections, whereas others (Cleland et al. 1983; Rose
1979) postulate that end-inhibition in the cortex derives
solely from the length tuning properties of cells in the LGN.
One way to distinguish between these different models is to
measure end-inhibition (or side-inhibition) dichoptically,
as described below. If end-inhibition (or side-inhibition) is
mediated dichoptically, then it cannot be explained solely
on the basis of subcortical mechanisms (Cleland et al. 1983;
Rose 1979) because binocular interactions are known to
occur almost exclusively within the cortex (e.g., Hubel and
Wiesel 1961, 1962).
Figure 13A shows monoptic and dichoptic measure-
ments of end-inhibition for a binocular complex cell. A
monoptic length tuning curve (filled circles) is obtained by
stimulating the dominant eye with variable-length patches
of drifting sinusoidal gratings as previously illustrated in
Fig. 1 B. Note that the response of this cell is completely
suppressed for stimuli longer than - 5 O. Thus there are po-
tent end-inhibitory regions around the receptive field of the
dominant eye. A dichoptic length tuning curve (open cir-
cles) is obtained using the stimulus arrangement depicted
above Fig. 13A. The dominant eye is stimulated with a
rectangular patch of drifting grating that is contained
within the excitatory receptive field (thick square). For the
nondominant eye there is no stimulus presented within the
excitatory receptive field. Instead, two patches of grating
extend outward from the receptive field into the end-inhibi-
tory regions of the nondominant eye. By varying the length
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G. C. DEANGELIS, R. D. FREEMAN, AND I. OHZAWA
Dom. Eye
Non-Dom. Eye
Dom. Eye
Non-Dom. Eye
B
819-38
12
8
496-22
0
819-21
k 1 r
4
0 2 4 6 8
IO
Length, L (deg)
8
T
458-l 1
6--
I
I I I
I
1 I
0
5
IO 15 20
Width, W (deg)
FIG.
13. Dichoptic measurements of end- and side-inhibition. A : filled circles: standard monoptic length tuning curve for
an end-inhibited complex cell ( CeZZ 819-38). These data are obtained by stimulating through the dominant eye, as depicted
in Fig. 1 B. Open circles: dichoptic length tuning curve for this complex cell. The dichoptic measurement is obtained using
the stimulus configuration shown directly above A. The dominant eye is stimulated with a rectangular patch of grating ( 3”
wide by 1.25 O long), having optimal orientation ( 5 O from horizontal) and spatial frequency (0.5 cycles per degree), which is
confined within the excitatory receptive field (thick square). The contrast is 50%. No stimulus is presented within the
excitatory receptive field of the nondominant eye. Instead, the end-inhibitory regions of the nondominant eye are stimulated
with grating patches that have optimal orientation and spatial frequency and a contrast of 50%. The total length, L, of the
inhibitory stimulus (from end to end, including the blank space corresponding to the excitatory receptive field of the
nondominant eye) is varied from 1.25 to 20”. Note that the monoptic and dichoptic tuning curves parallel one another,
starting at the optimal length (L = 1.25 O ) for excitation. B: filled and open circles: monoptic and dichoptic width tuning
curves, respectively, for a side-inhibited complex cell ( Cell 496-22). The stimulus configuration (shown above B) is similar
to that illustrated in A, except that side-inhibitory regions are stimulated in the nondominant eye. The total width, IV, of the
inhibitory stimulus is varied from 3 to 18’. C: monoptic and dichoptic length tuning curves (filled and open circles,
respectively) for another end-inhibited complex cell (Cell 819-21). In this case, end-inhibition is weaker during dichoptic
stimulation than during monoptic stimulation. D: monoptic and dichoptic width tuning curves (filled and open triangles,
respectively) for a side-inhibited simple cell ( Cell 458-11) .
of these inhibitory stimuli while keeping their inner bound-
aries fixed, a dichoptic length tuning curve is constructed.
Notice that the dichoptic length tuning curve (Fig. 13A,
open circles) starts at the peak of the monoptic curve (filled
circles) and that the two curves decline roughly in parallel.
Clearly the end-inhibitory regions in the dominant and
nondominant eyes have a similar effect on the response
elicited by stimulating the excitatory receptive field of the
dominant eye. It may be concluded, therefore, that end-in-
hibition is mediated dichoptically for this cell. It should be
noted that for two cells we repeated this test with the re-
versed eye-stimulus arrangement, namely the excitatory
stimulus presented to the nondominant eye and the inhibi-
tory gratings presented to the dominant eye; the results
were quite similar.
Figure 13B shows monoptic and dichoptic measure-
ments of side-inhibition for another binocular complex
cell. The monoptic width tuning curve (filled circles) is ob-
tained by stimulating the dominant eye with rectangular
grating patches of optimal length and variable width (see
Fig. 1A). The stimulus configuration for the dichoptic
width tuning measurement is shown above Fig. 13B.
Again, the dominant eye is stimulated with an optimally
sized patch of grating. For the nondominant eye, grating
patches extend outward from the excitatory receptive field
into the side-inhibitory regions. The total width, W, of the
inhibitory stimulus is varied from 3O up to 18 O. There is a
good match between the monoptic (filled circles) and di-
choptic (open circles) width tuning curves in Fig. 13
B,
in-
dicating that side-inhibition is mediated dichoptically for
this cell.
For the cells shown in Fig. 13, A and
B,
inhibition ap-
pears to be as strong in the dichoptic tests as it is in the
monoptic tests. However, this is not always the case. Figure
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LENGTH AND WIDTH TUNING IN STRIATE CORTEX 365
13C shows monoptic and dichoptic length tuning curves
for a complex cell. In this case, end-inhibition is weaker in
the dichoptic measurement (open circles) than in the mon-
optic test (filled circles). Similar results have been obtained
for several cells in this study (see Fig. 14). Notice also that
there appears to be some disinhibition in the dichoptic
length tuning curve. Response decreases with length up to
- 5 O, after which the response increases a bit.
Figure 13 D illustrates another type of behavior that has
been observed in a couple of instances. For this simple cell,
the dichoptic response (open triangles) initially increases as
a function of width and then drops sharply. Because it was
repeatable, this behavior probably reflects some overlap be-
tween the excitatory receptive field and the side-inhibitory
regions associated with the nondominant eye. Increasing
the width of the grating patches presented to the nondomi-
nant eye initially adds to the response produced by stimula-
tion of the dominant eye. Further increase in the width of
the stimulus causes the cell’s response to be suppressed be-
low the level produced when only the dominant eye is stim-
ulated.
Dichoptic measurements of length or width tuning have
been performed on a total of 13 cells. Figure 14 shows a
scatter diagram in which the strength of inhibition observed
in dichoptic tests is plotted against that measured in mon-
optic tests. Percent inhibition is defined as shown in Fig.
3A. Filled and open symbols denote measurements of end-
and side-inhibition, respectively. Triangles represent sim-
ple cells and circles represent complex cells. Two points
should be made regarding the data of Fig. 14. First, all of the
cells exhibit some degree of inhibition in dichoptic tests.
Second, for many cells, inhibition is considerably stronger
in monoptic tests than in dichoptic tests (i.e., most of the
? 80
0
5
.-
-g
60
.-
AZ
s
-
.g
4c
Ei-
5
fi
20
L
I
0
I I
I I
I I I I 4
20 40 60 80 100
Monoptic Inhibition (%)
FIG. 14. Comparison of the strengths of inhibition in monoptic and
dichoptic tests. Percent inhibition measured in response to dichoptic stimu-
lation (see Fig. 13 ) is plotted on the vertical axis, and percent inhibition
obtained monoptically (see Fig. 1) is plotted on the horizontal axis. Data
are shown for 13 neurons, of which 6 are simple cells (triangles) and 7 are
complex cells (circles). Filled symbols: cells for which end-inhibition was
studied. Open symbols: cells for which side-inhibition was studied. Diago-
nal line: perfect correspondence between the strengths of monoptic and
dichoptic inhibition. Average values of percent inhibition are 70.4% for the
monoptic tests and 57.4% for the dichoptic tests.
A
326-29
50
- T
-- ----------------_
a,
r.
--A
$f IO
2
0
f, : ,
0.2 1 2 3
Spatial Frequency (cycles/deg)
B
0
1
I I I
I
a I I I -I
100
145
190 235 280 325
Orientation (deg)
FIG. 15. Tuning characteristics of end-inhibition, measured both mon-
optically and dichoptically, for a simple cell (Cell 326-29). A : filled trian-
gles: spatial frequency tuning of end-inhibition, measured monoptically
for the dominant eye. The stimulus configuration used is similar to that
shown in Fig. 5D. Open triangles: results of a dichoptic measurement of
the spatial frequency tuning of inhibition. The stimulus configuration used
for this dichoptic test is similar to that shown in Fig. 13A, except that the
inhibitory grating patches presented to the nondominant eye have variable
spatial frequency. Note that the monoptic and dichoptic tuning curves
have a similar shape, although end-inhibition is weaker in the dichoptic
test. Horizontal dashed line: response when only the dominant eye is stimu-
lated with a grating of optimal dimensions. B: filled and open triangles:
monoptic and dichoptic measurements, respectively, of the orientation
tuning of end-inhibition. These measurements are obtained as described
above, except that the orientation, rather than the spatial frequency, of the
inhibitory gratings is varied.
points lie below the diagonal). These results are not compat-
ible with models (Cleland et al. 1983; Rose 1979) in which
end-inhibition (or side-inhibition) derives solely from sub-
cortical mechanisms
(see DISCUSSION).
Dichoptic tuning characteristics
For three binocular cells it was possible to examine the
tuning characteristics of inhibition both monoptically and
dichoptically. Data for one of these neurons, an end-inhib-
ited simple cell, are shown in Fig. 15. Figure 154 shows the
spatial frequency tuning of end-inhibition, measured mon-
optically (filled triangles) and dichoptically (open trian-
gles). In the monoptic test, both the excitatory and inhibi-
tory stimuli are presented to the dominant eye, as shown in
Fig. 5 D. For the dichoptic measurement, an optimally
sized patch of grating is presented within the receptive field
of the dominant eye and the nondominant eye is stimulated
with patches of gratings that are confined to end-inhibitory
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366
G. C. DEANGELIS, R. D. FREEMAN, AND I. OHZAWA
regions (as shown in Fig. 134. The spatial frequency tun-
ing of inhibition is similar in shape for the monoptic and
dichoptic tests, but the inhibition is weaker over most of the
spatial frequency range in the dichoptic test. Figure 15
B
shows orientation tuning curves for end-inhibition mea-
sured monoptically (filled triangles) and dichoptically
(open triangles). The two results are similar, except that the
orientation tuning is slightly broader in the dichoptic test.
Very similar findings have been obtained for the other two
binocular cells that were tested dichoptically with respect to
orientation and spatial frequency tuning. The fact that
monoptic and dichoptic measurements yield similar tuning
characteristics suggests that end- and side-inhibition are
mediated by a pool of binocular (i.e., cortical) neurons.
We now consider whether end-inhibition is selective for
binocular position (or phase) disparity. This question is of
interest because disparity-tuned inhibition originating from
regions surrounding the excitatory receptive field could
serve as a neural mechanism for discriminating local
changes in depth within an image
(see DISCUSSION).
Such a
mechanism would be useful for figure-ground segregation
or for the encoding of three-dimensional surface curvature
(e.g., Rogers and Cagenello 1989). Figure 16 examines this
idea for the same binocular simple cell as described in Fig.
15. Figure 16A shows the excitatory response of this simple
cell (filled triangles) as a function of the relative spatial
phase (or disparity) between gratings presented to the domi-
nant and nondominant eyes. Like virtually all binocular
simple cells, this neuron is highly selective for relative inter-
ocular phase (see Ohzawa and Freeman 1986). In other
words, the excitatory response of the cell is disparity selec-
tive. Figure 16
B
shows the disparity selectivity of end-inhi-
bition for this cell. To obtain these data, the excitatory re-
ceptive field of the dominant eye is stimulated with a patch
of grating having optimal orientation, spatial frequency,
length, and width. The end-inhibitory regions of both eyes
are stimulated with grating patches having the same orienta-
tion and spatial frequency as the excitatory stimulus (see
the schematic above Fig. 16
B).
Filled triangles show the
cell’s response as the relative spatial phase between the in-
hibitory gratings presented to the two eyes is varied over
360°. This is equivalent to testing the end-inhibitory re-
gions with different binocular disparities. The dashed line
shows the cell’s response level when only the excitatory re-
ceptive field of the dominant eye is stimulated. Clearly,
there is no dependence of the strength of inhibition on in-
terocular phase difference (or binocular disparity). Similar
results have been obtained for a side-inhibited complex cell.
Thus there is no evidence as of yet for disparity-selective
center-surround interactions in the cat’s striate cortex (see
DISCUSSION).
Relationship of length and width tuning curves to receptive
field maps
Detailed maps of the spatial receptive field structure of
cortical cells can be obtained using a technique known as
reverse correlation (see DeAngelis et al. 1993a; Jones and
Palmer 1987a for details). In this study the lengths and
widths of receptive fields have been determined by present-
ing grating patches of variable dimensions. Valuable insight
Dom. Eye
A
Non-Dom. Eye
-s
326-29
z 50
t
0
01, , , , , , , , ,
I I I I I I I
0 90 180 270 360
Dom. Eye
Non-Dom. Eye
B
”
I I I I I I
1 I I I I I I
0 90 180 270 360
Relative Spatial Phase (deg)
FIG. 16. Binocular spatial phase (i.e., disparity) tuning of excitation and
end-inhibition for a simple cell (Cell 326-29). A : disparity tuning of exci-
tation. Filled triangles: cell’s response as a function of the relative spatial
phase between gratings presented to the dominant and nondominant eyes.
Each eye is stimulated with a patch of grating (2” wide by 1 O long) that is
confined within the excitatory receptive field (as determined from monoc-
ular length and width tuning curves). These stimuli have a spatial fre-
quency of 0.9 cycles per degree and a contrast of 50%, and are oriented 40”
from vertical. Open square on
right
side of graph: cell’s response when only
the dominant (right) eye is stimulated. Similarly, an open circle shows the
cell’s response when only the nondominant eye is stimulated.
B:
binocular
disparity tuning of end-inhibition. The stimulus configuration is shown
directly above the graph. The excitatory receptive field of the dominant eye
is stimulated with an optimally sized patch of grating to produce a baseline
response level (dashed line). No stimulus is presented within the excit-
atory receptive field of the nondominant eye. Grating patches are pre-
sented to each eye within the end-inhibitory regions. These inhibitory stim-
uli have the same orientation, spatial frequency, and contrast as the excit-
atory grating patch. Filled triangles: cell’s response as a function of the
relative spatial phase between the inhibitory stimuli presented to the 2
eyes. Note that the strength of suppression is roughly independent of the
interocular phase difference.
can be gained by comparing these grating measurements
with receptive field maps obtained using reverse correla-
tion. Data for three neurons are shown in Fig. 17, two sim-
ple cells (A and C) and a complex cell
(B)
. For each cell, a
two-dimensional spatial receptive field profile (similar to
those described by Jones and Palmer 1987a) is shown on
the left, with length and width tuning curves on the
right.
Consider the simple cell shown in Fig. 17A. The receptive
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LENGTH AND WIDTH TUNING IN STRIATE CORTEX
367
0
0
@
a
A
0
w (deg) 8
25
20
15
10
5
0
50-
40--
30.-
i‘:
20..
IO-
0 5 10 15 20
Width, W (deg)
50
T
186-06
0
I
0 5 IO 15 20
Length, L (deg)
FIG.
17. Comparison of receptive field maps, obtained using the reverse correlation technique, with length and width
tuning curves. A : data are shown here for a simple cell ( Cell 326-26). A 2-dimensional spatial receptive field profile is shown
on the
left
(see DeAngelis et al. 1993a for a complete description of the procedures used to obtain this profile). This receptive
field map subtends 7”
X
7 O. The reverse correlation delay used to obtain this profile was 70 ms. Solid contours delimit
subregions that are responsive to bright stimuli (i.e.,
ON
subregions), whereas dashed contours indicate dark-excitatory (i.e.,
OFF)
subregions. The axis of the cell’s preferred orientation is parallel to the vertical (i.e., length) axis of the receptive field
map. Width and length tuning curves for this simple cell are shown to the
right
of the receptive field map. To obtain these
curves, rectangular patches of drifting grating are centered at the spatial coordinate indicated by a small black spot on the
receptive field profile. Clearly the grating stimuli are well-centered on the receptive field. This cell exhibits both side- and
end-inhibition.
B:
data are shown here for a complex cell (Cell 905-21) in the same format as described above. The spatial
receptive field profile
(left)
for this cell is obtained from responses to small bright bars (see footnote in text). Width and
length tuning curves are obtained in response to grating patches centered at the location shown as a black spot on the
receptive field profile. C: data for another simple cell
( CeZZ 186-06).
This cell exhibits some end-inhibition but no side-inhi-
bition.
field map for this neuron (left) shows a central bright-exci-
curve for this cell (right) shows that response starts to de-
tatory (ON) subregion (solid contours), which is flanked on
cline for stimuli longer than - 6 O, and the reverse correla-
either side by dark-excitatory (OFF) subregions (dashed tion map shows that the excitatory receptive field is -6’
contours). Overall, the receptive field of this cell is - 3.5’ long.
wide and 6O long. The width and length tuning curves
Figure 17
B
shows data for a complex cell that exhibits
(right) show that the cell exhibits mild side- and end-inhibi-
end- and side-inhibition. In this case, the reverse correla-
tion, respectively. Comparison of these curves with the re-
tion map* shows that the excitatory receptive field is no
ceptive field map suggests that the end- and side-inhibitory
regions do not overlap with the excitatory receptive field.
2 For the simple cells shown in Fig. 17, A and C, reverse correlation maps
For
example, response
increases with the width of a grating
are obtained by taking the difference between responses to bright and dark
patch up to
- 4”, after which further
increasing
the width of
bar stimuli (see DeAngelis et al. 1993a,b; Jones and Palmer 1987a). For
complex cells, reverse correlation maps obtained using bright and dark
a grating reduces the cell’s response. Because the excitatory
bars are completely overlapping and similar in structure (see Fig. 1 of
receptive field map (left) is certainly no wider than 4”, side-
Ohzawa et al. 1990). For the complex cell of Fig. 17
B,
the reverse correla-
inhibition appears to originate from regions that are outside
tion map was obtained from responses to bright bars. The map obtained
f
rom
of the excitatory receptive field. Similarly, the length tuning
responses to dark barsis nearly identical to that obtained with bright
bars.
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368
G. C. DEANGELIS, R. D. FREEMAN, AND I. OHZAWA
larger than 4” wide and 4” long. Tuning curves for this cell
(right) show that response increases with the length and
width of a grating stimulus up to -4O, after which further
increasing the size of a grating patch produces inhibition.
Again, comparison of these curves with the receptive field
map suggests that inhibition arises from regions located
outside of the excitatory receptive field. A similar conclu-
sion can be drawn for the simple cell of Fig. 17C, which
shows end-inhibition but no side-inhibition. In this case,
response increases with the length of a grating patch up to
- 6”, which corresponds well with the length of the excit-
atory receptive field as determined from the reverse correla-
tion mapping.
Overall, receptive field maps have been compared with
length and width tuning curves for 12 simple cells and 4
complex cells. Previous studies report that the end-inhibi-
tory regions (Orban et al. 1979b; Sillito 1977) or side-inhibi-
tory regions (Born and Tootell 199 1) of some cells may
overlap the excitatory receptive field to a considerable ex-
tent. Indeed, there does seem to be some overlap between
excitatory and inhibitory regions for a few of the cells stud-
ied here. However, in most cases, the amount of overlap
between the excitatory receptive field (as mapped using the
reverse correlation technique) and the end- or side-inhibi-
tory regions seems minimal (see DIscussIoN for more on
this point). We cannot rule out the possibility, however,
that the weakest flanks of the excitatory receptive field do
not show up in our reverse correlation maps because of the
presence of a response threshold (see Tadmor and Tolhurst
1989). Also, it is possible that weak, peripheral flanks of the
receptive field are suppressed by overlapping end- or side-
inhibitory regions.
DISCUSSION
There have been many studies of inhibitory regions that
surround the receptive fields of visual cortical cells. Several
investigators (e.g., Bodis-Wollner et al. 1976; Bolz and Gil-
bert 1986; Dreher 1972; Gilbert 1977; Hubel and Wiesel
1965; Orban et al. 1979a,b; Rose 1977; Yamane et al. 1985 )
have studied the length tuning characteristics of cortical
cells with the use of optimally oriented bars of light. As
pointed out by DeValois et al. ( 1985), these studies are
limited to an analysis of inhibitory regions that lie along the
axis of a cell’s preferred orientation (i.e., end-inhibitory re-
gions) . Other investigators (Born and Tootell 199 1; DeVa-
lois et al. 1985; Foster et al. 1985; Maffei and Fiorentini
1976; von der Heydt et al. 1992) have studied inhibitory
regions located along the sides of the receptive field using
gratings of variable width (or number of cycles). However,
width and length tuning have not been directly compared
in these studies. Some researchers (e.g., Blakemore and To-
bin 1972; Fries et al. 1977; Nelson and Frost 1978) have
studied inhibitory regions using a suppressive stimulus that
completely surrounds the excitatory receptive field (i.e., a
grating annulus). These studies make no attempt to local-
ize the regions that produce inhibition.
Apparently, the study we report here is the first to quanti-
tatively characterize both the length and width tuning of a
population of neurons in the primary visual cortex. The
findings of this study can be summarized as three main
points. 1) The data reported here show that most cells ex-
hibit similar degrees of end- and side-inhibition. Thus
many cells in the striate cortex have inhibitory regions that
completely surround the excitatory receptive field (e.g., Fig.
2, A and B). However, some cells exhibit either end-inhibi-
tion or side-inhibition, but not both. The group of cells that
exhibits only side-inhibition appears to be physiologically
and anatomically distinct in that these neurons generally
have long receptive fields (see Fig. 4B) and are located
within Layer 6. 2) The results of this study show that end-
and side-inhibitory regions have similar selectivities for ori-
entation, spatial frequency, and spatial phase. End- and
side-inhibition are usually strongest at orientations and
spatial frequencies that are close to the optimal values for
producing excitation. However, orientation and spatial fre-
quency tuning curves for inhibition are generally much
broader than those for excitation, suggesting that inhibition
is mediated by a pool of neurons. This idea is also supported
by the observation that the strength of inhibition is gener-
ally not dependent on the relative positions (or spatial
phases) of the excitatory and inhibitory stimuli. 3) The data
show that end- and side-inhibition are mediated dichopti-
tally, indicating that these phenomena cannot be explained
solely on the basis of subcortical mechanisms.
Relationship to previousfindings
As noted above, several different methods have been
used in previous studies to examine the properties of inhibi-
tory regions that lie around the excitatory receptive field.
Many of the findings reported here are in accord with the
results of previous studies. However, there are some notable
exceptions. Maffei and Fiorentini ( 1976) report that stimu-
lation of regions outside of the excitatory receptive field can
facilitate the response of some cells. In contrast, we have
not observed facilitatory effects in this study. Maffei and
Fiorentini ( 1976) also report that, for 85% of cells studied,
inhibition is either nonspecific or very broadly tuned for
orientation. Similarly, Fries et al. ( 1977) distinguish be-
tween two groups of cells: one for which the orientation
tuning of inhibition is similar to (but broader than) the
orientation tuning of excitation and another for which the
strength of inhibition is roughly independent of orienta-
tion. Nelson and Frost ( 1978 ) report that “some cells dis-
played, in effect, nonoriented inhibition to which the orien-
tation-selective component is added.” For virtually all cells
studied here, inhibition is tuned, albeit somewhat broadly,
for the orientation of a stimulus placed in regions surround-
ing the classical excitatory receptive field (see also Born and
Tootell 199 1 for a similar result).
It is likely that some of the discrepancies between this and
previous studies are due to inadequate methods used in
previous investigations for determining the extent of the
excitatory receptive field. Many studies of surround proper-
ties (e.g., Blakemore and Tobin 1972; Born and Tootell
199 1; Fries et al. 1977; Gilbert and Wiesel 1990; Knierim
and Van Essen 1992; Maffei and Fiorentini 1976; Sillito
1977) have used small bar stimuli to determine the bound-
aries of the excitatory receptive field. In most of these stud-
ies the extent of the excitatory receptive field is determined
qualitatively, by listening to the responses of a cell. More-
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LENGTH AND WIDTH TUNING IN STRIATE CORTEX 369
over, in most cases, only bright bars are used to map the
receptive field. These hand-plotted estimates of the recep-
tive field are similar to the minimum response fields ob-
tained by Barlow et al. ( 1967). For example, Fries et al.
( 1977) state that “only areas in which a moving light stimu-
lus evoked a clear excitatory response were considered to be
within the receptive field.” Because of their qualitative na-
ture, these methods are likely to underestimate the size of a
cell’s excitatory receptive field. This is especially problem-
atic for studies of the regions that supposedly “surround”
the classical receptive field. If one’s estimate of the excit-
atory receptive field is too small, then stimuli that are
thought to be placed in the surround may actually stimulate
substantial portions of the receptive field itself. This is a
likely explanation for the finding (Maffei and Fiorentini
1976 ) that regions located “outside” of the receptive field
can be facilitatory (see DeAngelis et al. 1992 for a lengthy
discussion of these issues).
Erroneous estimates of the extent of the excitatory recep-
tive field may also explain some of the varied findings (e.g.,
Born and Tootell 199 1; Fries et al. 1977; Maffei and Fioren-
tini 1976; Nelson and Frost 1978) concerning the orienta-
tion selectivity of inhibition. We have recently shown that
virtually all cells in the cat’s striate cortex have suppressive
regions that are coextensive with the excitatory receptive
field and nonspecific for stimulus orientation ( DeAngelis et
al. 1992). In this study, we show that the responses of many
cells are suppressed by the presence of stimuli located out-
side of the excitatory receptive field and that this form of
inhibition (or suppression) is tuned to the optimal orienta-
tion for excitation. If one underestimates the size of the
excitatory receptive field by hand-plotting with a small bar
stimulus, then the presence of a stimulus that is supposedly
confined to the surrounding regions may elicit either or
both of these two types of suppression. This is a likely expla-
nation for the results of previous studies (e.g., Fries et al.
1977; Knierim and Van Essen 1992; Maffei and Fiorentini
1976) in which stimulation of regions outside the classical
receptive field sometimes produced inhibition that was non-
specific for orientation.
In our study, quantitative measurements of the size of a
cell’s receptive field have been obtained by systematically
varying the length and width of a rectangular patch of drift-
ing sinusoidal grating. For cells that exhibit end- or side-in-
hibition, the length or width of the excitatory receptive field
is taken as the value at which the length-response or width-
response curve reaches its maximum amplitude (see Fig.
3). If end- and side-inhibitory regions overlap extensively
with the excitatory receptive field, then our estimates of the
size of the excitatory receptive field may be erroneously
small. Indeed, it has been shown (Born and Tootell 199 1;
Orban et al. 1979b; Sillito 1977) that inhibitory regions
overlap the excitatory receptive field to some degree. How-
ever, several of the findings that we report here suggest that
the degree of overlap for most cells is fairly small. Figure 17
shows that estimates of the size of the excitatory receptive
field derived from responses to gratings are consistent with
estimates obtained from detailed two-dimensional recep-
tive field profiles. Moreover, if excitatory and inhibitory
areas overlap extensively, then a cell’s response should be
markedly dependent on the relative spatial phase between a
stimulus that has optimal dimensions (based on length-
and width-response curves) and a stimulus that is confined
to the surrounding regions. Yet only 3 cells out of 20 show a
phase sensitivity index >0.4 (Fig. SC), indicating that most
cells exhibit only a small amount of overlap between the
excitatory receptive field and the surrounding inhibitory
regions. Furthermore, if end- and side-inhibitory regions
overlap the receptive field extensively, then orientation
tuning curves for end- or side-inhibition should show a sub-
stantial component of non-orientation-specific suppression
(i.e., cross-orientation inhibition). A mixture of orienta-
tion-specific and nonspecific inhibition has been observed
in a few instances (see Fig. 7 of DeAngelis et al. 1992)) but
this mixture is rare in the data reported here.
Implications fir models ofend- (and side-) inhibition
The neuronal connectivity underlying the generation of
end- and side-inhibition is not well understood. Several dif-
ferent types of models have been proposed to account for
the length tuning of neurons in the visual cortex. In this
section, we consider how the findings of this study con-
strain possible models for end-inhibition. Although formal
models for the generation of side-inhibition have not been
proposed, most of the discussion below applies equally well
to the mechanisms that underlie width tuning.
It is well known that neurons in the cat’s LGN have a
center-surround receptive field structure (e.g., Hubel and
Wiesel 196 I). As a result, most LGN cells are somewhat
tuned for the length of a bar stimulus (e.g., Cleland et al.
1983; Jones and Sillito 199 1; Murphy and Sillito 1987; Sil-
lito et al. 1993; but see Jones and Sillito 1990). On the basis
of this fact, it has been suggested (Cleland et al. 1983; Rose
1979; Schiller et al. 1976a) that the length tuning of cortical
neurons derives from that already present in the LGN. In-
deed, Cleland et al. ( 1983 ) show that a basic model, in
which the simple cell receives a weighted sum of geniculate
inputs (see Ferster 1987; Hubel and Wiesel 1962) can ac-
count for a variety of types of length tuning in the cortex. It
is also well known, however, that most cells in the LGN can
only be excited by stimulation through one eye-they are
rarely binocular (Bishop et al. 1959; Erulkar and Fillenz
1960; Hubel and Wiesel 196 1). Yet this study shows that
end- and side-inhibition are mediated dichoptically for bin-
ocular cells in the striate cortex (see Figs. 13 and 14). If
end- and side-inhibition were to arise from the LGN, genic-
ulate cells would have to exhibit strong binocular interac-
tions to account for dichoptic inhibition in the cortex. Al-
though many geniculate neurons do exhibit response sup-
pression when stimulated dichoptically, the magnitude of
the effect is generally quite small (Kato et al. 198 1; Xue et
al. 1987). Moreover, Kato et al. ( 198 1) report that the di-
choptic suppression exhibited by LGN cells is not orienta-
tion dependent. Thus it is difficult to see how a geniculate-
based model for length tuning (e.g., Cleland et al. 1983)
could account for the fact that end-inhibition in the cortex
is orientation specific (see Figs. 7 and 15 ) . We believe, there-
fore, that it is very unlikely that the length and width tuning
of cortical cells derives solely from the response properties
of neurons in the LGN.
Other models for the generation of end-inhibition rely
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370 G. C. DEANGELIS, R. D. FREEMAN, AND I. OHZAWA
exclusively on intracortical inhibitory interactions. One
currently popular idea is that end-inhibition is generated
through intracortical inhibition from Layer 6 neurons that
possess long receptive fields (Bolz and Gilbert 1986; Dob-
bins et al. 1987, 1989). Support for this idea comes from
experiments (Bolz and Gilbert 1986) showing that cells in
the upper layers of the cortex lose their end-inhibition fol-
lowing inactivation of Layer 6 with y-aminobutyric acid.
On the basis of this finding, Bolz and Gilbert ( 1986) suggest
that a Layer 4 neuron with a small receptive field receives
inhibition from a Layer 6 cell with a long receptive field,
thus producing end-inhibition. A quantitative version of
this model, in which a simple cell with a long receptive field
(modeled as a Gabor function) inhibits another simple cell
with a short receptive field, has been formulated by Dob-
bins et al. ( 1987, 1989). The findings reported here are
inconsistent with the model of Dobbins et al. ( 1987, 1989)
in several respects. First, their model predicts that the
strength of end-inhibition should be markedly dependent
on the relative spatial phase between a grating confined to
the excitatory receptive field and a grating confined to the
inhibitory end-zones. The data of Fig. 9 show that the
strength of inhibition is generally independent of spatial
phase, suggesting that inhibition is mediated either by com-
plex cells or by a group of simple cells having spatially inco-
herent receptive fields (i.e., fields with random spatial
phase). In addition, the orientation and spatial frequency
tuning of inhibition are considerably broader than the tun-
ing of excitation (see Figs. 6 and 8 ), indicating that inhibi-
tion is mediated by a pool of neurons rather than by a single
cell.
An interesting finding of our study, with regard to the
model of Bolz and Gilbert ( 1986) and Dobbins et al. ( 1987,
1989), is that virtually all of the Layer 6 cells with long
receptive fields exhibit side-inhibition but no end-inhibi-
tion (see Fig. 4). If end-inhibition is actually generated
through interlaminar feedback from Layer 6 neurons, then
it may be necessary to postulate a different mechanism for
the generation of side-inhibition, because this phenomenon
is already exhibited by Layer 6 neurons with long receptive
fields. Grieve and Sillito ( 199 1 b) have repeated the experi-
ments of Bolz and Gilbert ( 1986). Although they have con-
firmed the finding that length tuning is weakened by local
blockade of Layer 6, Grieve and Sillito ( 199 lb) conclude
that this effect is due to the loss of an excitatory influence
from Layer 6 rather than the loss of inhibition. Thus the
role of Layer 6 neurons in the generation of end-inhibition
may be different than previously thought.
Hubel and Wiesel ( 1965) suggested that the end-inhibi-
tory regions of cortical cells arise through intracortical inhi-
bition from neurons with spatially offset receptive fields. A
simple extension of this model seems to account for most of
the properties of end- and side-inhibition reported here. As-
sume that a given cortical cell receives inhibitory contacts
from a group of neurons, each of which has a receptive field
that is spatially offset (along some arbitrary direction) from
that of the cell being recorded. In essence, the receptive
fields of this inhibitory pool of neurons would form an an-
nulus around the receptive field of the cell being studied,
thus producing both end- and side-inhibition. If the inhibi-
tory
contacts were limited to neurons having receptive
fields located only along the ends or sides of the receptive
field of the cell being recorded, then only end- or side-inhi-
bition would be observed. To be feasible this scheme re-
quires long-range inhibitory connections between neurons
with nonoverlapping receptive fields. Moreover, these long-
range connections must only connect cells with similar ori-
entation preferences, so that end- and side-inhibition are
tuned to the same orientation as excitation. Indeed, long-
range horizontal connections between neurons of like orien-
tation preferences have been shown to exist in the cat’s
striate cortex ( Gilbert and Wiesel 1983, 1989 ) , and ana-
tomic studies show that -20% of these connections may be
inhibitory ( McGuire et al. 199 1). Thus a generalized ver-
sion of the Hubel and Wiesel ( 1965) scheme remains a
plausible model for the generation of end- and side-inhibi-
tion.
The fact that end- and side-inhibition are mediated di-
choptically supports a model, like that described above,
that relies primarily on intracortical inhibitory processes It
is possible, however, that length and width tuning are gen-
erated by a combination of intracortical and subcortical
mechanisms. Murphy and Sillito ( 1987) have shown that
the length tuning of neurons in the LGN is augmented by
corticofugal feedback from Layer 6. Recently, Sillito et al.
( 1993) have shown that this corticofugal feedback imparts
onto LGN cells a component of length tuning that is orien-
tation specific. Thus the length tuning of LGN neurons is
strongest when the surrounding (inhibitory) stimulus has
the same orientation as the excitatory stimulus, a finding
that is similar to that reported here. When the corticofugal
pathway is silenced, LGN cells display a residual compo-
nent of length tuning, presumably derived from their
center-surround receptive field structure, which is non-ori-
entation specific. On the basis of these findings, Sillito et al.
suggest that end-inhibition is an emergent property of pro-
cessing that occurs within the corticogeniculate loop. The
findings of our study do not rule out, nor are they inconsis-
tent with, this possibility. To test whether corticogeniculate
feedback is essential to the presence of end- and side-inhibi-
tion in the cortex, it would be desirable to reversibly inacti-
vate the corticofugal projection while recording from single
neurons in the cortex.
Functional role of‘end- and side-inhibition
It has often been suggested (see Chapman and Stryker
1992; Ferster and Koch 1987; Martin 1988 for review) that
intracortical inhibitory processes serve to sharpen the stimu-
lus selectivity of cortical neurons. Perhaps the most striking
feature of cortical cells, as compared with neurons at earlier
stages in the visual pathway, is their sensitivity to stimulus
orientation. One proposal to account for the generation of
orientation selectivity in the cortex involves cross-orienta-
tion inhibition (Bonds 1989; Morrone et al. 1982; see Fer-
ster and Koch 1987 for an overview) between neurons
tuned to roughly orthogonal orientations. We have recently
shown that this mechanism is unlikely to enhance orienta-
tion tuning, because the strength of suppression is approxi-
mately independent of orientation ( DeAngelis et al. 1992).
Instead, this nonspecific suppression may serve as a neural
mechanism for contrast normalization (Bonds
Heeger 1992; Robson 1988).
1991;
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LENGTH AND WIDTH TUNING IN STRIATE CORTEX 371
In this study, we show that inhibition from regions
surrounding the excitatory (i.e., classical) receptive field is
tuned to the same orientation that produces maximal exci-
tation, and that the orientation selectivity of this surround
inhibition is somewhat broader than the tuning for excita-
tion. On the basis of similar observations, it has been sug-
gested (e.g., Benevento et al. 1972; Nelson and Frost 1978)
that surround inhibition serves to refine the orientation se-
lectivity of cortical cells. “Because the peripheral inhibition
is more broadly tuned than excitation,” state Nelson and
Frost ( 1978 ), “it would serve to sharpen orientation tuning
curves by reducing their flanks.” However, this interpreta-
tion relies on the assumption that the inhibition is subtrac-
tive in nature. If surround inhibition is subtractive, then it
could serve to sharpen orientation tuning to some extent.
On the other hand, if surround inhibition is divisive (as
reported for cross-orientation inhibition; see Bonds 1989;
Heeger 1992), then it may actually act to broaden the orien-
tation tuning curves of cortical cells. The data reported here
(Fig. 10) suggest that surround inhibition causes a right-
ward shift of the contrast-response function on logarithmic
coordinates. This behavior may be consistent with a divi-
sive mechanism for inhibition (Heeger 1992). In addition,
quantitative receptive field mapping studies (Jones and
Palmer 1987b; Szulborski and Palmer 199 1) show that ori-
entation selectivity can be predicted reasonably well on the
basis of the two-dimensional spatial structure of the excit-
atory receptive field (see DeAngelis et al. 1992 for more on
this point). Thus, although further research is needed to
clarify the nature of the inhibition produced by surround
stimulation, the findings reported here do not lend much
support to the idea that the function of surround inhibition
is to refine orientation selectivity.
If surround inhibition does not serve to enhance stimulus
selectivity, then what is its function? Several different ideas
have been proposed, as discussed below. Hubel and Wiesel
( 1965 ), after discovering end-inhibited neurons in the cat’s
extrastriate cortex, speculated that these neurons might be
useful for signaling the presence of curved stimuli or stimuli
that contain corners. Indeed, it has been shown (Dobbins et
al. 1987; Orban et al. 1987b) that end-stopped cells are
selective for the degree of curvature of line stimuli. It is not
clear, however, whether end-inhibition exists for this pur-
pose or whether curvature selectivity is simply an epiphe-
nomenon. Rogers and Cagenello ( 1989) show that small
differences in curvature between contours presented to the
two eyes can be utilized to perceive three-dimensional sur-
face structure. Thus they suggest that neurons tuned to
small interocular differences in curvature may serve as a
neural mechanism for surface reconstruction. Differential
curvature selectivity in the two eyes could result from the
existence of different length tuning properties for the two
eyes. However, the data of Fig. 12, A and B, show that most
cells in the striate cortex have nearly identical length tuning
properties for the dominant and nondominant eyes, sug-
gesting that the two eyes should be similar in their curvature
selectivity. There are a few cells, however, for which length
tuning curves obtained through the two eyes are dissimilar.
These neurons could potentially encode binocular curva-
ture disparity, although this possibility has not been tested
directly.
Perhaps surround inhibition in the striate cortex has a
function similar to the types of surround inhibition that
have been observed in other visual areas. There is consider-
able evidence that cells in extrastriate visual areas, particu-
larly those areas thought to be involved in motion process-
ing, have complicated stimulus-specific surround mecha-
nisms. Von Grunau and Frost ( 1983) report that some cells
in the cat’s lateral suprasylvian cortex respond optimally
when stimuli presented within the surround move in the
direction opposite to stimuli that are presented within the
receptive field. Similarly, Frost and Nakayama ( 1983 ) de-
scribe neurons in the pigeon’s optic tectum that respond
optimally when a random dot background moves in the
direction opposite to an excitatory spot stimulus, regardless
of the direction of motion of the spot stimulus. In the pri-
mate, it has been reported (e.g., Allman et al. 1985; Tanaka
et al. 1984) that neurons in area MT often respond opti-
mally when the excitatory receptive field and its surround-
ing regions are stimulated with different (i.e., antagonistic)
motions. Direction-specific interactions between an opti-
mally oriented bar stimulus and a textured background
have also been reported for neurons in Area 17 of the cat
(Orban et al. 1987a). Theoretical studies (e.g., Loomis and
Nakayama 1973; Nakayama and Loomis 1974) have sug-
gested that these types of motion-selective surround mecha-
nisms may be used by the visual system to perform figure-
ground segregation or to compute depth from optical flow
patterns.
Whereas cells in extrastriate visual areas exhibit motion-
selective surround mechanisms, cells in the striate cortex
show orientation-selective surround inhibition (e.g., Fig.
7). The work of Julesz ( 198 1, 1984) has shown that local
differences in the orientation of line segments, as well as
other features such as line terminations, provide powerful
cues (or “textons”) for preattentive texture discrimination.
Neurons in the striate cortex that exhibit orientation-selec-
tive surround inhibition should be able to encode local dif-
ferences in orientation, as well as line terminations, that
allow texture boundaries to “pop out.” Recently, Knierim
and Van Essen ( 1992) have studied the responses of VI
neurons in the awake monkey to texture patterns that re-
semble those used in psychophysical pop-out experiments.
They report that many cells respond optimally when there
is a large difference in orientation between texture elements
confined to the excitatory receptive field and those pre-
sented to the surrounding regions. Moreover, this orienta-
tion-selective suppression can be elicited from surrounding
regions either at the ends of the receptive field or along the
sides. Similar findings concerning responses to texture
borders have been reported for cortical neurons in the cat
(Nothdurft and Li 1984,1985 ) and the monkey (Nothdurft
et al. 1992). Thus there is evidence to suggest that end- and
side-inhibited cells may be involved in performing image
segmentation.
In addition to local differences in orientation, differences
in binocular disparity between adjacent regions of an image
can be used as cues for figure-ground segregation ( e.g., Ju-
lesz 1964, 1984). If the classical receptive field and its
surrounding regions are antagonistically tuned for binocu-
lar disparity, cortical cells could serve to encode local
changes in depth, such as those which occur when an object
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372 G. C. DEANGELIS, R. D. FREEMAN, AND I. OHZAWA
in the foreground occludes an object in the background.
Because neural signals from the two eyes first converge in
the cortex, and because some cortical neurons exhibit inhib-
itory surrounds, it is plausible that disparity-selective
center-surround interactions could be exhibited by cells in
the striate cortex. This possibility has been examined for a
couple of cells (e.g., Fig. 16). However, the data reported
here do not show any center-surround antagonism in the
domain of binocular disparity, suggesting that local changes
in disparity may not be encoded by this type of mechanism
in the striate cortex. However, this conclusion may be pre-
mature, because only two neurons have been tested. It
would be interesting to examine cells in higher cortical
areas to see whether they exhibit disparity-selective
surround inhibition.
u I
processing.
In summary, we have studied the impact of stimulating
regions of visual space that surround the classical receptive
fields of cortical visual neurons. Our findings show that
many cells have inhibitory regions that completely
surround the excitatory receptive field. The tuning charac-
teristics and dichoptic response properties of surround inhi-
With regard to depth perception, it has also been pro-
posed that end-inhibition allows neurons tuned to horizon-
bition suggest that it is mediated via long-range inhibitory
tal orientations to encode binocular disparity information
(Maske et al. 1986). Finally, it should be mentioned that
end-inhibited cells have also been implicated in the neural
processing of illusory contours (Heitger et al. 1992; Peter-
hans and von der Heydt 1989; von der Heydt and Peterhans
1989). At this time, however, it is difficult to assign a spe-
cific functional role to end- and side-inhibition, because
none of the possible functions described above are clearly
favored by experimental results. It may simply be the case
that end- and side-inhibition reflect a general neural archi-
tecture that is useful for manv different aspects of visual
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