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The Journal of Neuroscience, January 1, 2000, 20(1):495-510
Spatial and Temporal Structure of Receptive Fields in Primate Somatosensory Area 3b: Effects of Stimulus Scanning Direction and Orientation
James J. DiCarlo and Kenneth O. Johnson Krieger Mind/Brain Institute, Departments of Neuroscience and Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland 21218
ABSTRACT
TOP
ABSTRACT
INTRODUCTION
This is the third in a series of studies of the neural representation of tactile spatial form in somatosensory cortical area 3b of the alert monkey. We previously studied the spatial structure of >350 fingerpad receptive fields (RFs) with random-dot patterns scanned in one direction (DiCarlo et al., 1998
) and at varying velocities (DiCarlo and Johnson, 1999
Key words: receptive field; reverse correlation; somatosensory; monkey; cortex; cortical layer; orientation sensitivity
INTRODUCTION
This is the third in a series of studies of the spatial and temporal response properties of area 3b neurons with receptive fields (RFs) on the distal fingerpads. Each study used scanned, random-dot stimuli and regression analysis to estimate RF structure. The first study (DiCarlo et al., 1998
The second study (DiCarlo and Johnson, 1999
The simplest explanation for this invariance in spatial structure is that the excitatory and inhibitory effects in area 3b are all brief and synchronous. But this explanation fails to account for the large changes in excitatory and inhibitory intensity with changes in scanning velocity and the studies that show substantial inhibitory delay in comparison with excitation. An alternative explanation based on the cancellation of overlapping excitation and inhibition accounts for all these observations (DiCarlo and Johnson, 1999
In this study, random-dot patterns and bars were scanned in up to eight directions over the RF of each neuron. RFs were determined from the responses to random-dot stimulation in each direction. The central excitatory region and a portion of the inhibition of each RF were unaffected by direction. The remaining inhibition was affected in the manner expected of a temporally lagged component. The data were well described by a spatial-temporal RF model containing an excitatory component, a spatially offset, temporally synchronous inhibitory component, and a delayed inhibitory component that overlaps the excitation. Orientation sensitivity, measured separately by scanned bars, was predicted accurately by this RF model. Both orientation sensitivity and the RF components related to orientation sensitivity were more prominent in the infragranular and supragranular layers than in layer IV.
MATERIALS AND METHODS
Animals and surgery. Two rhesus monkeys (Macaca mulatta) weighing 4-5 kg were used in this study. Each animal was trained to perform a visual detection task during the presentation of tactile stimuli; the purpose was to maintain the animal in a constant, alert state during recording periods. After the animal was performing the task nearly perfectly, which took a few weeks, a head-holding device and recording chamber were attached to the skull. Surgical anesthesia was induced with ketamine HCl (33 mg/kg, i.m.) and maintained with pentobarbital (10 mg · kg
1 · hr
Recording. Electrophysiological recordings were done with techniques described previously (DiCarlo et al., 1998
at 1000 Hz). Each electrode was coated with one of two fluorescent dyes (DiI or DiI-C5; Molecular Probes, Eugene, OR), which were used later to identify the recording locations (DiCarlo et al., 1996
Stimuli. The primary stimulus patterns were arrays of raised dots distributed randomly within a rectangular region 28 mm wide and 250 mm (first monkey) or 175 mm (second monkey) long (for details, see DiCarlo et al., 1998
The dot pattern was wrapped around and glued to a cylindrical drum, 320 mm in circumference, which was mounted on a rotating drum stimulator (see DiCarlo and Johnson, 1999
After one or more neurons with overlapping RF locations were isolated with one or more of the electrodes, the drum with the random-dot pattern was positioned over the fingerpad so that all the RFs were in the cutaneous region contacting the drum surface. The scanning velocity was 40 mm/sec in all scanning directions. Contact force was set at 0.3 N (Johnson and Phillips, 1988
The experimental design called for stimuli to be scanned in four or eight directions: 0 (proximal-to-distal), 45, 90 (left-to-right), 135, 180 (distal-to-proximal), 225, 270 (right-to-left), and 315°. Because the stimulus sequence was lengthy and not all neurons could be held for the entire sequence, the stimulus order (0, 180, 90, 270, 45, 135, 225, and 315°) was designed to produce the greatest possible range of directions at any stopping point. When four scanning directions were used, the order was 0, 90, 180, and 270°. When the neural recording was still stable after all scanning directions had been studied, the 0° direction was repeated.
The drum was positioned initially so the cutaneous contact region was within the random-dot pattern and the center of the contact region was ~5 mm from the edge of the long side of the pattern. After each revolution the drum was stepped 400 µm along its axis of rotation. The drum typically completed 25-40 revolutions in each scanning direction and therefore stepped 10-16 mm across the pattern. Before each new scanning direction, the drum was translated back to its starting location to ensure that approximately the same random-dot pattern was scanned across the neuron's RF in each scanning direction. Four directions and a repeated first direction required 20 min; eight directions required 36 min.
Before applying the stimulator, a thin latex sheet (~50 µm thick; Carter-Wallace, New York, NY) was positioned over the fingerpad, and glycerin was applied to the drum's surface to eliminate friction between the drum and the latex. The latex sheet was tethered in all directions by gluing its edges to a 20-mm-diameter aperture in the center of a thin (6 µm), 10 × 10 cm Mylar sheet (DuPont, Wilmington, DE). A square Plexiglas frame positioned horizontally over the fingerpad (see DiCarlo and Johnson, 1999
Responses. The action potential times were recorded with a resolution of 0.1 msec. The data collected at each scanning direction from each neuron were maintained as a separate data set. Within each of these data sets the action potentials were assigned two-dimensional (x, y) locations in relation to the drum surface (Johnson and Phillips, 1988
Receptive field estimation. The responses in each scanning direction were used to obtain independent linear RF estimates for each direction. The method used to estimate each RF was the same as in both our previous studies (DiCarlo et al., 1998
The firing pattern evoked by the random-dot stimulus at each scanning direction was used to infer the two-dimensional pattern of excitation and inhibition on the skin surface. We assumed that each small region of skin had a positive, negative, or zero effect on the firing rate when stimulated and that the instantaneous firing rate was equal to the sum of these effects. Specifically, we subdivided a 10 × 10 mm square region of skin containing the RF into a grid of 625 (25 × 25) subregions, each 0.4 × 0.4 mm square. We then determined the contribution of each subregion to the observed neural response with multiple regression. The grid of 625 positive (excitatory) and negative (inhibitory) values are the weights that produce the best (least-squared error) approximation of the observed firing rates when convolved with the stimulus pattern. The units of these weights are impulses per second (ips) per millimeter of indentation. The integral of the excitatory (inhibitory) weights is referred to as the excitatory (inhibitory) mass of the RF (see DiCarlo et al., 1998
The three-component RF model. To describe the effect of scanning direction on each neuron's RF, we constructed an RF model with three Gaussian subfields, one for each of the three RF components described in the introductory remarks. We refer to these three components as the (1) excitatory, (2) fixed inhibitory, and (3) lagged inhibitory components. Each Gaussian subfield has the form:
(1)
in which (x, y) represent mediolateral and proximodistal locations on the skin surface, (µx, µy) represents the center of the subfield, (vx, vy) represents the stimulus velocity vector, and
represents the delay of the peak of excitation or inhibition with respect to skin stimulation. The parameters a,
x,
together specify the amplitude, spread, orientation, and elongation of the excitatory (a > 0) or inhibitory (a < 0) component represented by the Gaussian function.
Each component is delayed with respect to skin stimulation, and therefore the effect of each component is displaced from its true center by an amount and direction that is proportional to (vx, vy) and
In each scanning direction, the RF predicted by the three-component model is the sum of the excitatory, the fixed inhibitory, and the lagged inhibitory components (E, excitatory; IF, fixed inhibitory; and IL, lagged inhibitory):
Therefore the three-component model of each neuron's RF is described by 19 parameters (six parameters for each of the three Gaussian components, µx, µy, a,
(2) The data from the present study include the effects of changes in direction. Our previous study (DiCarlo and Johnson, 1999
The solution was unstable when scanning direction had a small effect on RF structure in comparison with the variability of the RF estimates. That occurs, for example, when the lag (
Orientation sensitivity. Some neurons were studied with three raised bars as well as with the random-dot patterns. The bars were constructed from photosensitive plastic sheets, mounted on a 320-mm-circumference drum, and applied to the skin in exactly the same way as the random dots. Each bar was 400 µm high (relief from the surface) and 500 µm wide at its top, with sides that sloped away at 60° with respect to the surface of the stimulus pattern. The bars were oriented orthogonal to and at ±45° (clockwise) in relation to the scanning direction. The bars were long enough (at least 30 mm long) so that the end of a bar never touched the skin and were spaced far enough apart (at least 30 mm between bars) so that two bars were never on the skin at the same time. The bar pattern was scanned over the neuron's RF 8-25 times in each of eight scan directions separated by 45° as in the random-dot scans.
The reason for including bars at ±45° was to examine the responses for any interaction between scanning direction and stimulus orientation. In fact, the orientation sensitivities and preferred orientations obtained from the three bars were essentially identical. For example, if the peak response to the orthogonal bar occurred with a proximal-to-distal scan, then the peak response to the bar oriented at
45° occurred when the scanning direction was rotated +45° from the proximal-to-distal scan. The data from all three bars were combined for this reason.
A summary measure of the response to each bar scanned in each direction (24 response values) was computed by binning the neuron's spikes from all repeated scans (8-25 repetitions) in 400 µm (10 msec) bins, smoothing the resulting histogram (70 msec boxcar filter), and taking the response to be the peak of the resulting histogram (e.g., see Fig. 12). The orientation sensitivity was measured by plotting the data in polar coordinates and fitting an ellipse to the data points (i.e., the ellipse with least mean squared error measured on the radial dimension). In all those cases in which a neuron was studied with both the bars and the random-dot pattern, the responses to the bars were predicted by convolving the three-component RF model with a bar (400 µm in relief and 400 µm in width) moving orthogonal to its long axis. Sixteen evenly spaced scanning directions were simulated, and the response in each direction was measured as the peak value of the simulated response histogram smoothed with a 70 msec wide boxcar filter (i.e., exactly the same measure used to describe the actual neural data). An ellipse was fitted to the predicted data in exactly the same way as the observed data (see Fig. 12).
Histology. Histological methods and the methods for coating the electrodes with fluorescent dyes (DiI or DiI-C5) are described by DiCarlo et al. (1996)
RESULTS
We studied all well isolated neurons in area 3b that had an RF on one of the distal fingerpads. A neuron was excluded only if the finger and the stimulator could not be positioned to bring the RF, mapped with a manual probe, well within the contact region between the skin and stimulus surface. Even neurons that were marginally responsive to manual probing were studied with the idea that the random-dot pattern might uncover responsiveness that was not evident with simpler stimuli. One hundred sixty-two neurons in three hemispheres of two monkeys were studied with random-dot patterns scanned in at least two directions.
The essential result was that all area 3b RFs were affected by the scanning direction. After examination of the entire population of neurons, it became clear that the most parsimonious hypothesis that might explain these effects was that each neuron's RFs had three components: (1) a region of excitation, (2) one or more regions of inhibition whose locations were fixed in relation to the excitatory center and were unaffected by changes in scanning direction, and (3) a region of inhibition whose position depended on the scanning direction. In the following sections, we describe the neural response and RF data that led to this three-component hypothesis. We then generate a quantitative model consisting of three Gaussian subfields to test the adequacy of this hypothesis.
All area 3b neuronal responses were affected by the scanning direction. This is the expected result unless a neuron's RF is circularly symmetric; almost none of the RFs that we have studied in area 3b are circularly symmetric (DiCarlo et al., 1998
D) over the RF, the neuron responded best when dots clustered in groups with distal-right to proximal-left orientations in relation to the fingerpad passed over the neuron's RF. That response pattern suggests that the RF has regions of excitation and inhibition offset from each other in the orthogonal direction (distal-left to proximal-right); that is, in fact, what emerged when the RF was estimated (Fig. 1, RF to the right of the top raster). If the RF structure were unaffected by scanning direction, the response patterns in different scanning directions would appear the same but simply rotated to match the change in alignment between the finger and the stimulus pattern (i.e., the neuron would always respond best to dot clusters with a distal-right to proximal-left orientation on the skin). When the pattern was rotated 90° and scanned from left to right (Fig. 1, second raster), the response was as expected. The D
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Figure 1. Effect of scanning direction on the response and RF of a typical area 3b neuron. Part of the random-dot pattern (~40% of the entire pattern) is shown at the top. Each dot on the plot illustrates the location of a stimulus element, 400 µm in relief and 500 µm in diameter. The neuron's responses in each scanning direction is shown as a spatial raster. Each tick mark represents a single action potential plotted at the stimulus position (top) when the action potential occurred (time flows from left to right across each raster). The box in each raster shows the neuron's response in each scanning direction to the same stimulus region (also identified with a box). The RF estimated from the response to each scanning direction is shown in two orientations on the right side of each raster. Each RF is plotted as if viewing the skin through the back of the finger (i.e., from the neuron's point of view). RFs in the left column are plotted so the finger orientation in relation to the random-dot pattern (top panel) is the same as in the experiment; RFs in the right column are plotted so the finger points toward the top of the figure (see labels next to each RF; L indicates the left side of the finger when viewed through the dorsum of the finger with the tip pointing up). Each RF is represented by a 10 × 10 mm gray scale image in which bins that are darker than the gray background represent skin regions in which raised stimuli (dots) had an excitatory effect on the neuron's response; bins that are lighter than the gray background represent skin regions in which raised stimuli had an inhibitory effect on the neuron's response. The peak excitatory values in the four RFs are (top to bottom) 50, 39, 77, and 83 ips/mm. The corresponding peak inhibitory values are 31, 28, 53, and 67 ips/mm. Pattern motion in relation to the skin can be visualized by placing a fingerpad on the random-dot pattern in the orientation specified by the labels in the leftmost RF and scanning the finger from left to right across the pattern. For example, for the proximal-to-distal scanning direction (top spike raster), the finger should be placed on the stimulus pattern (top panel), pointed toward the left side of the page, and then scanned to the right side of the page.
The reason for the change in response properties between scanning directions can be seen by examining the RFs in Figure 1. The RFs change with scanning direction. For example, RFs derived from two scanning directions (L
To test the adequacy of this three-component description on the entire population, the RFs of each neuron in the study were fitted with the model illustrated in Figure 2 in which the three RF components are represented by Gaussian functions (see Materials and Methods). The aim was not to capture the exact shape of the individual components but instead to assess the validity of the three-component description and to obtain an estimate of the locations, sizes, and magnitudes of the three components. In fitting the model, the Gaussian functions representing the RF components were allowed to vary in intensity, spatial location, and spatial spread (i.e., overall area including possible spatial elongation and orientation). The two inhibitory components were allowed to overlap the excitation, just as inhibition and excitation are known to overlap in the RFs of area 3b neurons (Laskin and Spencer, 1979
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Figure 2. Three-component Gaussian model. Three ellipses in each panel represent isoamplitude contours around Gaussian functions describing three RF components (excitatory, fixed inhibitory, and lagged inhibitory). The RF predicted by the model in each scanning direction (i.e., each panel) is the sum of these three Gaussian functions. Only the lagged inhibitory component changes its apparent RF location as scanning direction changes. This change in apparent RF location is the expected change if the lagged inhibitory component was temporally delayed from the excitatory and fixed inhibitory component. The locations of the fixed inhibitory center and the lag center in relation to the excitatory subfield are identified by the two thin arrows originating from the center of the excitatory component. The displacement of the lagged inhibitory component from the lag center is indicated by the thick, gray arrow. The tail of the gray arrow is at the lag center; the arrow direction corresponds to the stimulus direction across the RF (i.e., scanning direction). The tip of the gray arrow specifies the apparent location of the lagged inhibitory center (see Materials and Methods for details.)
An iterative gradient descent method (Press et al., 1992
90° had RF noise indices <30% (DiCarlo et al., 1998
Figures 3-7 show five examples of the effects of scanning direction on RF structure and the degree to which the three-component model fits the data. Figure 3 displays results from the same neuron as in Figure 1. Three RF panels are displayed for each scanning direction. The left panel in each group (except the bottom group) is the RF estimated from the neuron's response in the indicated scanning direction. The middle panel is the RF predicted by the three-component model (i.e., the summed effect of the excitatory component and the two inhibitory components illustrated in Fig. 2). Visual comparison of the left and middle panels provides an indication of the degree to which the three-component model captures the essential spatial structure of the observed RF. The peak excitatory values range from 30 to 133 imp · sec
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Figure 3. RFs in four scanning directions and model predictions. The neuron is the same as in Figure 1. The three squares in each group display the RF estimated from the raw data (left), the RF predicted by the three-component model (middle), and the positions of the model Gaussian components (right). The ellipses in the right square in each group are isoamplitude contours at 1.5 SD. The scanning direction is shown above each group. As in Figure 1, each RF is plotted as if it were viewed through the dorsum of the finger (i.e., from the neuron's point of view) with the finger pointed toward the top of the figure; the effect of relative motion between the finger and the stimulus pattern on the RF can be visualized by placing a fingerpad in the center of the figure and sliding it along the arrow labeled finger "motion" toward the RF of interest. Note how the locations of the model's excitatory (solid ellipse) and fixed inhibitory (dashed ellipse) components are unaffected by scanning direction and, similarly, how the lagged inhibitory component (dotted ellipse) trails the lag center by a fixed distance in each direction (see Fig. 2). The arrow in each right square corresponds to the gray arrow in Figure 2. The degree to which the model accounts for RF structure in each direction can be seen by comparing the left and middle panels in each group. The absolute values of the ratios of the peak excitatory values to the peak inhibitory values (peak E/I ratios) in the observed RFs are (clockwise from proximal to distal, bottom panel) 1.6, 1.4, 1.5, and 1.2. The comparable predicted peak E/I ratios are 0.9, 1.5, 1.7, and 1.3. The RF illustrated at the left of the bottom row was determined from responses without the latex intermediate (see Materials and Methods and Results).
The lagged inhibitory region in the model in Figure 3 trails 0.99 mm behind a lag center 0.64 mm below (proximal) and slightly to the left of the excitatory center. If the lag is due to a temporal delay between excitation and the lagged inhibition, that delay is 25 msec (0.99 mm at 40 mm/sec). Because the lag center is proximal to the excitatory center, the lagged inhibition overlaps and cancels a fraction of the excitation almost maximally when the scanning direction is P
Figures 4-7 illustrate four more RFs with a range of structural features. The points to note in assessing the adequacy of the three-component model are the degree to which the predicted inhibitory geometry (middle panel) matches the observed inhibitory geometry (left panel) and the degree to which the predicted inhibitory intensity matches the observed inhibitory intensity. The model predicts that the most intense inhibition will usually be produced when the stimulus is scanned along a line passing from the lag center to the center of fixed inhibition. In this case, the lagged and fixed inhibition will overlap and sum. According to the model, the opposite scanning direction should produce inhibition that is spread over a larger region and is less dense. In general, both predictions are satisfied. Note that the objective is not to determine whether the RF subfields are fitted by Gaussian functions but rather it is to assess the hypothesis that each RF is composed of subfields of three types. The prediction based on the three-component model highlights RF features that may deviate from this general hypothesis. In some cases there are consistent deviations from the Gaussian model, but in every case they consist of an additional region of fixed inhibition. Those cases indicate deviation from the three-component Gaussian model but at the same time conformity to the more general three-component hypothesis, which is the real object of the analysis.
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Figure 4. RF example in which the regions of fixed and lagged inhibition are elongated and the lag center is near the excitatory center. The observed (predicted) peak E/I ratios are (clockwise from proximal to distal) 1.4 (1.8), 2.1 (2.6), 2.6 (2.7), and 2.4 (2.6). Details as in Figure 3.
Figure 4 illustrates an example in which the regions of fixed and lagged inhibition are elongated and the lag center is near the excitatory center. The lag in Figure 4, 1.23 mm, is equivalent to a 30 msec delay between excitation and the lagged component of inhibition. In two of the four scanning directions (scanning directions R
Figure 5 illustrates an RF with more than one region of fixed inhibition as well as a region of lagged inhibition. This RF has a strong fixed inhibitory component in the proximal, left part of each RF and a separate region of weaker fixed inhibition in the distal, right part of each RF. To reach the best solution, the three-component model-fitting algorithm assigned the fixed component to the stronger of the two fixed inhibitory components
the inhibition in the proximal, left portion of the RF. In three of the four scanning directions the main model error is the failure to account for the fixed inhibition distal and slightly to the right of the excitation. In the fourth, P
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Figure 5. RF example in which there is more than one region of fixed inhibition. The observed (predicted) peak E/I ratios are (clockwise from proximal to distal) 1.7 (2.6), 2.5 (2.6), 1.2 (1.6), and 1.5 (1.8). Details as in Figure 3.
Figure 6 illustrates a neuron held long enough to obtain full scans in eight directions. The lagged inhibitory area in this example is large compared with the excitatory area, which produces something close to surround inhibition in some scanning directions. Because the lagged inhibition is so large, there is overlap between the fixed and lagged inhibition in several scan directions. The intense inhibition in the distal, left part of the RFs derived from the responses in three directions (Fig. 6, three RFs in the bottom right quadrant) is accounted for well by summation between the model's overlapping fixed and lagged inhibition. The lag illustrated in Figure 6 is equivalent to a 25 msec delay between excitation and inhibition.
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Figure 6. RF example in which a neuron was held long enough to obtain full scans in eight directions and the lagged inhibitory area is large in comparison with the excitatory area. The observed (predicted) peak E/I ratios are (clockwise from proximal to distal) 1.1 (1.2), 1.7 (1.7), 1.8 (1.9), 2.5 (2.2), 2.2 (2.2), 1.9 (1.7), 1.2 (1.3), and 1.1 (1.2). Details as in Figure 3, except that eight scanning directions were studied.
Figure 7 illustrates a neuron in which the excitatory area is small, both the fixed and the lagged inhibitory areas are large when compared with the excitatory area, and both regions overlap the excitatory region. The lagged inhibitory area is 3.6 times larger than the excitatory area, and its mass is 3.5 times larger than the fixed inhibitory mass. The lag center is offset from the excitatory center by a distance that is a large fraction of the radius of the excitatory area (0.45×). The primary discrepancy between the model and the observed data in this case is the failure to account for a region of fixed inhibition in the proximal-right part of the RF. In comparing the predicted and observed RFs, it can be seen that there is a region of inhibition in the proximal-right part of each RF that is stronger than predicted by the model. As before, that could have been rectified by allowing the model to incorporate a second region of fixed inhibition. The lag illustrated in Figure 7 is equivalent to an 18 msec delay.
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Figure 7. RF example in which the inhibitory areas are large in comparison with the excitatory area, which results in surround inhibition in some scanning directions. The observed (predicted) peak E/I ratios are (clockwise from proximal to distal) 1.3 (1.2), 1.5 (1.4), 1.6 (1.6), and 1.6 (1.6). Details as in Figure 3.
Goodness of fit
Figures 3-7 provide a qualitative summary of typical fits between the three-Gaussian model and RFs derived from responses in multiple scanning directions. Product-moment correlation coefficients displayed in Figure 8 provide a quantitative summary of the fits for all neurons studied. Specifically, each observed RF bin value was paired with the corresponding RF bin value predicted by the three-Gaussian model, and the correlation between all such pairs for a single neuron was computed. On average, 3200 RF points contributed to each correlation calculation (i.e., 625 RF bin values in each of 5.1 scanning directions, on average). The mean correlation was 0.81 (SD, 0.09). If the model had allowed for two regions of fixed inhibition, many correlations would have been higher. The high correlation between the predicted and observed RFs is remarkable for several reasons: (1) the Gaussian components were not intended to capture the details of the shapes of the RF regions; (2) the three-Gaussian model includes only 19 parameters to describe up to 5000 RF bin values (8 scanning directions × 625 bin values in each RF); and (3) noise in the observed RFs accounts for a large part of the lack of correlation between the predicted and observed RFs (DiCarlo et al., 1998
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Figure 8. Model fit. The fit between the RF predicted by the three-component model (middle RFs in Figs. 3-7) and the observed RF (left RFs in Figs. 3-7) was computed as the correlation on a bin-by-bin basis for each of the 62 neurons. The histogram represents these 62 correlation values.
Summary of the three response components
No simple graphical summary of the RF components that we could find fully captured the range of RF structures. (The 19 parameters that describe the three RF components for all 62 neurons can be obtained from the authors.) Scatter plots of the areas and masses (intensities) of the three estimated RF components are shown in Figure 9. The distribution of excitatory areas is nearly identical to the distribution of excitatory areas in the larger sample reported earlier. The geometric mean excitatory area in the sample shown in Figure 9 is 13.1 mm2; the comparable area in the earlier study was 12.6 mm2 (DiCarlo et al., 1998
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Figure 9. Areas (top row) and masses (bottom row) of the three RF response components computed from the three-component model. The area of each excitatory or inhibitory component was defined as the area within 2.15 SDs of its center. The mass of each component was defined as the sum of the absolute bin values within 2.15 SDs of its center.
On average, the Gaussian fixed inhibitory area (mean, 13.4 mm2) was approximately equal to the excitatory area (mean, 13.1 mm2; Fig. 9, top left), but its mass (mean, 571 mass units) was only ~25% as large as the average excitatory mass (mean, 2440 mass units; Fig. 9, bottom left). The average lagged inhibitory area (mean, 24.0 mm2) was 80% greater than the average excitatory area (Fig. 9, top middle); the average lagged inhibitory mass (1781 mass units) was ~30% less than the average excitatory mass (Fig. 9, bottom middle). The average lagged-inhibitory area and mass were 80 and 200% greater than the average fixed inhibitory area and mass, respectively (Fig. 9, top and bottom right). In making these comparisons it must be borne in mind that the lagged inhibition overlapped the excitation more than did the fixed inhibition (compare Figs. 3, 8); therefore, it was canceled more by the excitation, and a smaller fraction of the lagged inhibition contributed to the net (i.e., observed) inhibition.
RF component locations have a predictable effect on a neuron's response properties. For example, the vector arising at the center of fixed inhibition and pointing toward the center of excitation defines a predicted orientation sensitivity to spatial stimulus gradients (see below). Figure 10, left panel, shows that the Gaussian fixed inhibitory component is most frequently 1-3 mm from the center of excitation, and it occurs on all sides of the central excitatory region. Analysis of the locations of the fixed inhibitory regions revealed a small but statistically significant lack of uniformity (p < 0.005; n = 62, Kuiper's test for uniformity of a circular distribution; Mardia, 1972
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Figure 10. Inhibitory offsets from the center of excitation. The left graph displays the locations of the centers of the fixed inhibitory components in relation to the centers of the excitatory components for the entire sample of 62 neurons. The right graph displays the locations of the lag centers of the lagged inhibitory components in relation to the centers of the excitatory components. The data in both plots are displayed with the abscissa aligned from left to right. No obvious lateral bias is apparent when the data are plotted in these coordinates or in radial-ulnar coordinates. This is supported by statistical analyses (see Results).
The lagged inhibitory component appears in the RF in each scanning direction at a position that lags a point (lag center) near the excitatory center by a fixed distance as described previously (see Fig. 2). An offset between the lag center and the center of excitation can result in directional sensitivity (Barlow and Levick, 1965
Effect of scanning direction on firing rate
With a few exceptions (e.g., Fig. 1), scanning direction had no discernible effect or only a small effect on firing rate. Figure 11 shows the average firing rates of 26 neurons that (1) were studied long enough to obtain scans in all eight directions plus a repeated scan in the original proximal-to-distal direction and (2) yielded a response (mean impulse rate) to the final P
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Figure 11. Effect of scanning direction on mean firing rate. Twenty-six neurons studied with eight scanning directions are shown. Left panel, Mean firing rate versus scanning direction. The direction yielding the largest mean firing rate ("best direction") is shown at the middle of the plot. Right panel, The abscissa is the overall mean firing rate (average firing rate over all scanning directions). The ordinate is the ratio of the firing rate in the best direction to the firing rate in the opposite direction. The dashed curve in the left panel illustrates one of the most selective responses (mean rate, 10 ips; directional index, 3.3).
Orientation sensitivity
It is clear from the responses of neurons to random-dot patterns that many neurons are sensitive to dot clusters with certain orientations (e.g., Fig. 1 and comparable rasters in DiCarlo et al., 1998
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Figure 12. Orientation sensitivity and its prediction by the three-component model. The top panel illustrates the responses of one of the more orientation-selective neurons that was also studied with the random-dot patterns. Each raster plot shows spikes (tick marks) produced in response to eight repeated scans of a single, raised bar scanned in a particular direction across the neuron's RF. The histogram above each raster shows the spike data binned across trials and filtered (see Materials and Methods). The peak value of each histogram was taken as the neuron's response in that scanning direction and these values are plotted as open circles along the radial lines in the middle polar plot (error bars are SDs computed by bootstrap; Efron and Tibshirani, 1993
How well does the three-component RF model derived in the first part of this paper predict the observed neural responses to scanned, oriented bars? We used each of the 62 three-component models to predict each neuron's response to a bar scanned in 16 evenly spaced directions and summarized these predicted responses with an ellipse in exactly the same way as the observed responses. The distributions of predicted orientation sensitivities and preferred orientations (data not shown) were similar to the distributions shown in Figure 12, bottom, which indicates that scanned, oriented bars do not produce orientation sensitivity beyond that predicted by linear RFs. The predicted orientation sensitivity was most strongly dependent on the strength of the fixed inhibition in comparison with the excitatory mass; the correlation between predicted orientation sensitivity and the ratio between fixed inhibitory and excitatory mass was 0.46 (p < 0.001). Of these 62 neurons, 24 were also studied with scanned, oriented bars. The left middle scatter plot in Figure 12 shows that the predicted orientation sensitivity was within 50% of the observed orientation sensitivity for 96% (23 of 24) of these neurons (Pearson's correlation coefficient = 0.714; p < 0.01). Nineteen of these 24 neurons had observed orientation sensitivities >1.2, and the right middle scatter plot in Figure 12 shows that, for these neurons, the preferred orientation predicted by the three-component RF model was strongly related to the observed preferred orientation. If the observed and predicted orientations were unrelated, the differences between them would be uniformly distributed between
In summary, area 3b neurons exhibit a range of orientation sensitivities to scanned bars, and that range is consistent with the range of sensitivities predicted by the three-component RF models determined with scanned random dots. For most neurons, the three-component RF model provides a good description of the neuron's sensitivity to orientation and its preferred orientation. The ability of each neuron's three-component RF model to predict both the degree of orientation sensitivity and the preferred orientation suggests that it has indeed captured some of the salient neural response properties. This is especially striking considering that (1) the three-component models are "meta-models" in that they are condensed descriptions of RF estimates that are themselves incomplete (i.e., linear) descriptions of the actual neural responses (see DiCarlo et al., 1998
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Figure 13. Relationship of orientation sensitivity and RF mass ratio to cortical layer. The abscissa of both plots is the cortical layer in which each neuron was recorded (see Materials and Methods). The ordinate of the left plot is the observed orientation sensitivity (fitted ellipse aspect ratio; see Results). Forty area 3b neurons whose cortical layer and orientation sensitivity were both determined are shown. The ordinate of the right plot is the ratio of the mass of the fixed inhibitory RF component and the mass of the excitatory RF component. Twenty-seven area 3b neurons whose cortical layer and three-component RF models were both determined are shown. The thick bars indicate the mean value in each cortical layer.
Relationship to cortical layer
The results of this study and our previous studies (DiCarlo et al., 1998
