Article Figures & Data
Figures
- Figure 1.
Ocular following responses are modulated by the size of the motion stimulus. a, Mean eye velocity profiles of ocular following responses triggered by a vertical, rightward drifting grating at constant spatial and temporal frequencies (experiment 1). The motion stimulus was presented behind a circular aperture of increasing diameters. As this diameter increased from 3.6° to 14.2°, the initial eye velocity increased (continuous lines). For larger and larger stimuli, initial eye velocity gradually decreased (broken lines). Right-hand numbers are grating patch diameters. b, Mean eye velocity profiles of ocular following driven by the same grating motion presented within a large (diameter, >50°) patch. The central portion of the stimulus was covered by a mean luminance patch of increasing diameter, as indicated by the numbers at the right-end of each curve. Data are illustrated for the two monkeys, No and Pe. Notice that the small initial dip in eye velocity seen at ∼20 ms for monkey No resulted from the subtraction of the mean velocity profile of the catch trials, where a tiny, idiosyncratic deflection was present at the end of fixation. Such an artifact occurred at very short latency (<20 ms) and therefore did not impact our quantitative analysis of response amplitudes. c, d, Mean change in position during the early (c; 60–70 ms) and late (d; 90–100 ms) time windows, plotted as a function of the grating patch diameter (blue curves) or inner mean luminance patch diameter (red curves). Data are the mean ± SE, over >150 trials for each condition. Left-hand and right-hand columns are data from monkeys No and Pe, respectively.
- Figure 2.
Characteristics of spatial summation for ocular following. a, Three different shapes of a spatial summation function are plotted to illustrate how different characteristic parameters can be extracted to describe relationships between stimulus size and response strength. Top and bottom horizontal lines illustrate the maximum (Ropt) and plateau (Rasy) OFR amplitude levels. The GSA is defined as the first smallest stimulus diameter for which response amplitude reached 95% of the maximum level (light blue symbol). They correspond to a stimulus size covering 95% of a central driving field, schematized as a Gaussian profile drawn over the visual field. SExt is the first stimulus diameter yielding to a response amplitude within 5% of the plateau level (Rasy). This would correspond to the size of the stimulus covering the driving field but also a large portion of a peripheral, inhibitory surround field. The SSI is the ratio between the plateau and maximum levels of the raw data. b, Theoretical relationship between response amplitude and the size of the central, occluding mean luminance patch of the ring stimulus. The AMD is the first inner diameter for which the response amplitude reached 5% of the smallest response, as observed with the largest mean luminance patch. This value characterizes the portion of the visual field from which no significant motion signals can be used to drive ocular following. GSA, SExt, SSI, and AMD were computed for each monkey and each motion direction or speed. c, GSA, SExt, and AMD mean values (mean ±SE across monkeys and directions) are plotted for five different time windows covering the entire open-loop period of the ocular responses. d, GSA and SExt are plotted one against each other. Dotted lines correspond to a ratio of 1, 2, or 3 between the two spatial parameters. Data are both individual estimates (each monkey and direction) and mean values (error bars are the SE across monkeys and directions) for each of the five time windows. To illustrate the temporal dynamics, mean values for successive time windows are plotted with increasing gray levels.
- Figure 3.
Spatial summation function is velocity independent. a, b, The spatial summation function of ocular following is plotted against the grating patch size for rightward (a) and leftward (b) motion directions and, in each one, for three different speeds (15, 30, and 45°/s; experiment 2). Top and bottom rows plot the results for monkey No and Pe, respectively. Data are the mean changes in position (±SE) over the 85–105 ms time window.
- Figure 4.
Spatial summation is spatial frequency sensitive. Mean eye velocity profiles are plotted for nine representative grating patch sizes (experiment 3; diameter, 3.55–53.25°). Broken lines illustrate decreasing eye velocity responses when increasing stimulus sizes. The mean initial eye peaks of acceleration are plotted against stimulus diameters. Corresponding dots and curves are of the same color. Each moving grating was presented at six different spatial frequencies, ranging from 0.12 to 1.41 cpd in Monkey No.
- Figure 5.
Mean stimulus spatial frequency shapes the spatial summation function. Early spatial summation functions are plotted for each of the six mean spatial frequencies (experiment 3). For the three highest spatial frequencies (0.72, 1.06, and 1.41 cpd), an additional experiment was run with a complementary set of smaller grating disk sizes. This experiment with smaller diameters maps more precisely the change in ocular following over the gray-shaded area of the original spatial summation function. Only data (mean ± SE, n > 150) for rightward grating movements are illustrated, as the results with the leftward direction were essentially the same. a, b, Monkey No (a) and Monkey Pe (b).
- Figure 6.
Contribution of peripheral motion changes with mean spatial frequency. Changes in early eye position (mean ± SE, n > 150 trials) are plotted against the diameter of the uniform circular patch covering the center of a large rightward motion stimulus (experiment 3). Each column corresponds to a given grating spatial frequency, ranging from 0.12 to 1.41 cpd. Dotted blue curves indicate the OFR spatial summation for the same mean spatial frequency, replotted from Figure 5. a, b, Monkey No (a) and Monkey Pe (b).
- Figure 7.
Relationships between spatial frequency and spatial summation. Mean (± SD; across animals and directions) characteristic indices of spatial summation are plotted against grating spatial frequency. Open and closed symbols illustrate the change in eye position over early and late time windows (65 -85 and 85 -105 ms, respectively). a, GSA. b, SExt. c, SSI. d, AMD. See Figure 2, a and b, for a description of these indices.
- Figure 8.
Surround inhibition is not because of line endings in the peripheral visual field. A masking ring (mean luminance) of 3.4° width and of increasing eccentricity is superimposed to a large grating patch (experiment 4). Such a mask introduces line-ending motion of an average direction identical to the moving grating. The left column shows mean eye velocity profiles, obtained with a masking uniform annulus of increasing eccentricity, placed over a leftward grating motion. The right column shows the change in eye position measured across three successive 20 ms time windows, plotted against the inner diameter of the mean luminance ring. Data are the mean ± SE (n > 100 trials). Closed and open symbols correspond to leftward and rightward grating motion directions, respectively. a, b, Monkey No (a) and (b) Monkey Pe.
- Figure 9.
A difference-of-Gaussians model of OFR spatial summation. a, A DoG model was fitted to the individual relationships between the change in eye position and stimulus size (blue dots) for each spatial frequency condition. A simple exponential decay function was fitted to the individual relationships between each change in eye position and the diameter of the central patch of mean luminance (red dots). Blue and red curves are best-fit functions, for Monkey Pe and for both rightward and leftward grating motions. Data are replotted from Figures 5 and 7. b, c, Best-fit σ(e,i) parameters of center (b) and surround (c) Gaussian functions are plotted against grating spatial frequency, respectively. For both parameters, grating directions are plotted independently, for each monkey, together with the grand average values (continuous lines). In c, the dashed line replots the exponential decay of σ(e) from b to allow direct comparison. d, The two sets of best-fit σ(e,i) parameters are plotted against each other. Broken lines are the theoretical linear relationships with a gain of 1 or 2. e, The gain g(e,i) parameters of both central and surround Gaussians are plotted against grating spatial frequency, with confidence intervals. Continuous lines are best-fit Gaussian functions for either g(e) or g(i). f, The ratio between excitatory and inhibitory gains (gi/ge), corresponding to the SSI computed above, is plotted against spatial frequency. g, Mean values of the best-fit τ parameter, as a function of spatial frequency. The insets illustrate best-fit functions for rightward motion (monkey Pe), replotted from a. In e–g, data are the mean (±SD) across monkeys and directions.
Tables
SF (cpd) σe σi (σi /σe) ge gi gi/ge 0.12 12.96 ± 6.8 25.21 ± 0.04 2.15 ± 0.6 0.009 ± 0.005 0.008 ± 0.004 1.01 ± 0.22 0.18 3.98 ± 0.8 11.84 ± 2.14 3.03 ± 0.59 0.008 ± 0.005 0.005 ± 0.004 0.66 ± 0.17 0.36 4.18 ± 0.8 7.6 ± 2.1 1.85 ± 0.48 0.017 ± 0.003 0.009 ± 0.005 0.51 ± 0.29 0.72 3.04 ± 1.79 5.43 ± 1.98 2.10 ± 0.7 0.016 ± 0.01 0.16 ± 0.011 0.56 ± 0.34 1.06 2.62 ± 2.38 4.85 ± 2.93 2.98 ± 1.66 0.007 ± 0.006 0.004 ± 0.002 0.46 ± 0.09 1.41 2.36 ± 1.31 4.88 ± 2.2 2.36 ± 0.85 0.004 ± 0.003 0.001 ± 0.001 0.36 ± 0.38
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