Article Figures & Data
Figures
- Fig. 1.
A, Schematic illustration of the elementary stimuli (squares of light, 0.4 × 0.4°) presented at seven horizontally shifted positions within the foveal representation of the visual field. B, Composite stimuli were assembled from combinations of the elementary stimuli and were presented at six different separation distances of 0.4–2.4°. The left stimulus component was kept at a fixed nasal position. C,Illustration of the noncentered field approach. Stimuli, indicated by the small gray square, were presented independent of the locations of the RFs of the measured neurons (schematically illustrated by gray ellipses). The frame with the cross-hair illustrates the analyzed portion of the visual space (2.8 × 2.0).D–F, Illustration of the Gaussian interpolation method to construct the DPA. D1, The grid of stimuli used (36 circles, each 0.64° in diameter) to measure the RF profile of each neuron was centered on the hand-plotted RF (response plane technique).D2, The RF profile constructed from responses to this stimulus grid was smoothed (D3) with a Gaussian filter (width, 0.64°). The RF center was determined as the location of the centroid of this smoothed RF profile. D4, The contribution of each cell to the population representations was always centered on this location and was weighted with the current firing rate of the neuron, illustrated as vertical bars of varying length. This weighting factor was normalized to the maximal firing rate of each neuron. E, The DPA was obtained by Gaussian interpolation (width, 0.6°) of the weighted firing rates and by a subsequent convolution with an unweighted Gaussian (width, 0.64°).F, View of the distribution of population activation using gray levels to indicate activation. The location of the stimulus is indicated by the small square outlined in black together with the stimulus frame. In a second approach, one-dimensional DPAs were derived by means of an OLE; see Materials and Methods and Figure 2C.
- Fig. 2.
A, Average RF, corresponding to the tuning for location, of all 178 recorded neurons. Based on the peak responses in the PSTHs (40–65 msec after stimulus onset) each RF profile was smoothed by convolution with a Gaussian in two dimensions (width, 0.64°). RF centers were derived by calculating the centroid of each profile (compare Fig. 1D3). For summation, the smoothed profiles were added with respect to their RF centers. The SD was 0.6° (calculated for that part of the resulting average RF profile, which exceeded half of the maximal amplitude). This value of average RF width matches the typical RF sizes found in area 17 of the cat (Orban, 1984). The vertical arrow indicates the spatial extension in terms of visual field coordinates. B, Population representations of the elementary stimuli computed as two-dimensional DPAs over visual space after Gaussian interpolation (compare Fig. 1). The construction was based on the activity of 178 neurons. DPAs were computed in the time interval between 40 and 65 msec after stimulus onset corresponding to the peak responses in the PSTHs. The activation level is shown in a color scale normalized to maximal activation separately for each stimulus (calibration bar at bottom right). Redindicates high levels of activation. The frame outlined inwhite depicts the area of the visual field investigated as described in Figure 1C. In addition, the stimulus is shown as a square outlined in white. Note that for each stimulus the focal zone of activation is approximately centered on the stimulus location. C, DPAs derived by means of an OLE for all seven elementary stimuli used. DPAs were assumed as Gaussian profiles centered on each respective stimulus position. As in the interpolation procedure, neural activity was integrated between 40 and 65 msec after stimulus onset. The width of the estimated Gaussian was chosen 0.6° to match the average RF width (tuning curve) of all neurons measured (compare Fig.2A). The maxima of the OLE-derived distributions were aligned accurately on the position of each stimulus.
- Fig. 3.
Two-dimensional DPAs of adjacent elementary stimuli (top and bottom) derived by Gaussian interpolation. The DPAs were obtained for consecutive intervals of 10 msec duration covering the period from 30 to 80 msec after stimulus onset. Same conventions as in Figure2B. Each example was normalized separately. As for the OLE-derived DPAs (compare Fig. 4), the distributions grow and decay gradually, and their maximum is always located near the position of the stimulus. Although the two stimuli are at neighboring locations, differences of the spatial representations are apparent throughout the time course of the response. For all elementary stimuli, the average latency of maximal activation was 54 ± 4 msec.
- Fig. 4.
The temporal evolution of two OLE-derived DPAs of the same elementary stimuli (A, B, vertical linesindicate position) as shown in Figure 3. The DPAs are depicted in 10 msec time intervals covering the period from 30 to 80 msec. The distributions grow and decay, gradually reaching maximum activity at 53 ± 5 msec (average of all seven elementary stimuli) after stimulus onset. The position of the maximum of each distribution closely approximates the stimulus position of the elementary stimulus throughout the time course of the neural population response, yet less accurately in the late time epoch.
- Fig. 5.
Constructed versus real position of the elementary stimuli using the averaged spike activity during the entire time course of responses (30–80 msec). The position of the maximum of the DPA is shown for the seven elementary stimuli as a function of the real stimulus position. The dotted line indicates the perfect match between estimated and real stimulus position. A,The two-dimensional distributions as shown in Figure2B were summed along the vertical axis to obtain the horizontal position of the maximum only. Using the Gaussian interpolation method, stimulus position can be estimated as well, but less accurate as compared to the OLE-derived DPAs (average deviation for all elementary stimuli, 0.20 ± 0.11°). B,Examination of the OLE-derived DPAs proved that the estimator accounts for a high spatial accuracy during the entire neural activation (average deviation for all elementary stimuli, 0.02 ± 0.02°).
- Fig. 6.
The measured two-dimensional DPAs (top) of composite stimuli (from left toright, 0.4–2.4° separation) were compared to the superpositions of the representations of their component elementary stimuli (bottom). The DPAs were based on spike activity of 178 cells averaged over the time interval from 30 to 80 msec after stimulus onset. Same conventions as in Figure 2B, the color scale was normalized to peak activation separately for each column. For small stimulus separation, note the remarkably reduced level of activation for the measured as compared to the superimposed responses. The bimodal distribution recorded for the largest stimulus separation comes close to match the superposition. However, inhibitory interaction can still be observed.
- Fig. 7.
The OLE-derived DPAs for the composite stimuli as depicted in Figure 6. Solid lines mark the measured activations, and dashed lines show the calculated superpositions (vertical lines mark stimulus positions). Peak activation was uniformly normalized. As demonstrated for the interpolated two-dimensional DPAs, the level of measured activation was systematically reduced for smaller stimulus separations but approached linear superposition for larger separations. The transition from monomodal to bimodal distributions was found between 1.2 and 1.6° separation. A slight asymmetry of the amplitudes between the representations of the left and the right stimulus component was found for the measured as compared to the superimposed distributions for stimulus separations of 1.2 and 1.6°.
- Fig. 8.
Reduction of the DPA magnitude induced by composite stimuli as a function of separation between the two component stimuli, calculated for the time-averaged responses (30–80 msec). The total activation in the distribution was expressed as percentage of the total activation in the superposition. The dashed linemarks results from the OLE-derived DPAs, the dotted linedepicts results from the two-dimensional distributions (Gaussian interpolation). For both ways of construction, inhibition was strongest for zero distance (66% for the OLE-derived, 68% for the interpolated data) and decreased almost monotonically with increasing distance, but was still present at the largest separation tested (2.4°).
- Fig. 9.
Time-resolved analysis of interaction effects based on integrals of DPAs in a 0.8° wide band around the location of the nasally positioned elementary stimulus (A, vertical arrow). The different composite stimuli are shown in columnA. Column B contrasts the OLE-derived DPAs to composite stimuli (solid line) with the responses to the single nasally positioned elementary stimulus (dashed line). At small distances, the activation to composite stimuli had a significantly smaller latency accompanied by an earlier onset of the decay of the population activity as compared to the elementary stimuli. The late part of the responses to the composite stimuli was characterized by an overall inhibition. Thearrow marks that peak activation in response to the composite stimulus of largest separation is still below activity measured in the single stimulus condition. Column Cdisplays results of simulations of the dynamic neural field model scaled to match the experimental stimulus conditions. Parameter values used for this simulation are: Au = 5.2,Av = 4, ςu = 15, ςv = 25, As = 4,Bs = 10, b = 1,h = − 3, τ = 15. The arrowmarks that inhibition can still be seen at the largest probed distances between the component stimuli.
- Fig. 10.
Interaction effects analyzed in two separate time intervals. The OLE-derived DPAs were integrated within a band of 0.8° width around the nasally positioned stimulus component. For the early response epoch, between 30 and 45 msec after stimulus onset, we computed the relative difference between the activation in the distribution of the composite stimulus and the superposition. This difference (solid line) is shown as a function of the spatial separation of the two stimulus components. Note that the positive values peaking at 1.6° with 58% enhancement remain positive up to 2.0°. This excess activation is indicative of excitatory interaction in this early response time interval. For the response epoch between 45 and 80 msec, we computed the relative difference between the activation in the distribution of composite stimuli, and the activation in response to the single nasally positioned elementary stimulus (dashed line). For all separations, this difference was negative, reaching ∼25% inhibition at 2.0°, indicative for inhibitory interaction. The distinct inhibition still present at the largest separation makes it unlikely that a local saturation effect can explain this observation. For the two epochs, the different types of analysis used provide a conservative estimate: for excitatory interaction in the first case, for inhibitory interaction in the second case (for details, see Results).
- Fig. 11.
Spatial repulsion effect. Repulsion was computed in the time slices between 60 and 80 msec after stimulus onset where inhibition is dominant. The distances between the activity peaks in the bimodal DPAs (OLE-derived) for stimulus separations of 1.6–2.4° were compared to the respective superpositions. Differences were depicted as shifts of repulsion dependent on stimulus separation. Maximal spatial shift amounts to 0.3°.
- Fig. 12.
Simulation of the repulsion effect. Shown are the simulated DPAs in response to the composite stimuli of 2.0° (A) and 2.4° (B) separation (solid lines). These are compared to the superpositions (dashed lines). The two vertical lines mark the position of the elementary stimuli. The same values of the model parameters were used as in Figure9C. Repulsion is manifested by an outward shift of the maxima.
- Fig. 13.
Effect of a nonhomogeneous, position-dependent evolution of field activity. The time-averaged response period of the superposition (dashed line) and the response to composite stimuli (solid line) are compared for a separation of 1.6°. A reduction of input strength (30% in the simulation shown here) for the right stimulus leads to a delay in temporal evolution at this particular field site. Because this reduction has little effect on the response maximum in the single stimulus condition, the time-averaged superposition profile is still symmetric. As a result of field interactions, a significant decrease of activity at the right position occurs when the two stimuli are applied together.
