Article Figures & Data
Figures
- Figure 1.
Schematic illustration of dynamic perspective cues. An observer translates rightward over time while maintaining fixation on a world-fixed target (red cross). As the observer translates, the eye counterrotates (angular position = α) to maintain fixation. This induces a perspective distortion of the visual scene (here a checkerboard) under planar image projection, as the gaze angle of the eye changes relative to the checkerboard. The image of the checkerboard (bottom) rotates around the fixation point such that the rightmost edge appears closer compared with the leftmost edge. This distortion is known as a dynamic perspective cue and provides information about eye rotation relative to the scene.
- Figure 2.
Definition of stimulus directions and schematic illustrations of the EO and DP stimulus conditions. A, The eight rotation directions used in all stimulus conditions. Each rotation direction, θ, arises from one particular combination of 4 rotation axes and 2 rotation phases (values given in parentheses). Each trial involves one cycle of sinusoidal movement (at 0.5 Hz), and rotation direction is defined as the direction during the middle half-cycle of movement. B, Eye Only condition. Left, In this illustration, the fixation target (white cross) translates along an axis of 0° and the monkey pursues the target. Background triangles are turned off. Right, Eye position as a function of time, illustrating the real (purple) eye movement. The purple curve assumes perfect pursuit such that eye position is equal to target position. As visual cues to rotation are lacking in this condition, no curve is shown corresponding to simulated eye rotation. C, Dynamic Perspective condition. Left, The eye of the monkey remains fixated on a screen-centered target, while background motion simulates the combination of eye rotation and translation. Right, Visually simulated rotation (green dashed curve) follows the same sinusoidal profile as real eye rotation in B, while real eye rotation is absent (purple line). Dashed vertical lines in B and C indicate the time period during which data are analyzed.
- Figure 3.
Data from an example MU (left column) and SU (right column) pair recorded simultaneously. A, Mean spike rates are plotted as a function of 2D motion direction and fit with a wrapped Gaussian function (solid curves). B, Mean spike rates are plotted as a function of 2D motion speed and fit with a Gamma function (solid curves). C, Mean spike rates are plotted as a function of real and simulated rotation direction for the EO (purple circles) and DP (green triangles) conditions, respectively. Smooth curves show fits of a unimodal or bimodal von Mises function (see Materials and Methods). Error bars in all panels indicate SEM.
- Figure 4.
Summary of direction preferences for eye rotation in the EO (left column) and DP (right column) conditions. A, Distribution of rotation direction preferences for SUs recorded in the EO condition. Only SUs with significant tuning for rotation direction (ANOVA, p < 0.05) in this condition were included. Data from monkeys m39 (black) and m31 (blue) are shown separately (N = 16 for m39, N = 55 for m31). B, Distribution of SU rotation preferences for the DP condition. SUs with significant rotation tuning (ANOVA, p < 0.05) in the DP condition were included (N = 12 for m39, N = 55 for m31). C, Same as A, but for MU activity (N = 78 for m39, N = 147 for m31). D, Same as B, but for MU activity (N = 48 for m39, N = 133 for m31). E, Comparison of rotation direction preferences MU and SU activity recorded from the same channel. Data were included if both MU and SU responses had significant rotation tuning (ANOVA, p < 0.05) in the EO condition (N = 11 for m39, N = 25 for m31). Data points in the scatter plot were wrapped to lie between diagonal lines corresponding to differences of ±180°. Inset displays the difference distribution between MU and SU direction preferences. F, Same as E but for the DP condition. Channels were included if both MU and SU responses had significant rotation tuning (ANOVA, p < 0.05) in the DP condition (N = 8 for m39, N = 21 for m31).
- Figure 5.
Comparison of rotation direction tuning properties between EO and DP conditions. A, The magnitude of response of each unit (difference in response between the peak and trough of the rotation tuning curve) in the EO condition is plotted against response magnitude in the DP condition. Color denotes monkey (black for m39, blue for m31), shape denotes rotation tuning significance [upward triangle, EO and DP tuning both significant (N = 30 for m39, N = 165 for m31); circle, only EO tuning significant (N = 65 for m39, N = 37 for m31); square, only DP tuning is significant (N = 31 for m39, N = 23 for m31); downward triangle, the tuning of neither condition was significant (N = 150 for m39, N = 61 for m31)], and symbol fill denotes MU or SU (solid for SU, open for MU). Solid line indicates the unity–slope diagonal. All MSTd units were included regardless of significance of rotation tuning. B, Comparison of tuning strength, as quantified by the DirDI, between EO and DP conditions. Format is the same as in A. All MSTd units were included regardless of the significance of rotation tuning. C, Comparison of rotation direction preferences between EO and DP conditions. This panel includes MU activity recorded from m39 (black, N = 23) and m31 (blue, N = 117). For units with bimodal direction tuning in either condition (71 of 140), the smallest difference between peaks in the two conditions was used. All MUs with significant rotation tuning (ANOVA, p < 0.05) in both the EO and DP conditions were included. Inset displays the difference distribution between rotation preferences for the two conditions. Format is the same as in Figure 4E. D, Same as C but for SUs (N = 7 for m39, N = 48 for m31) with significant rotation tuning (ANOVA, p < 0.05) in both EO and DP conditions. Format is the same as in C; 29 of 55 SUs had bimodal direction tuning. E, Rotation preferences of units in the EO condition plotted against their preferences for 2D motion direction (N = 94 for m39, N = 202 for m31). Units with significant tuning in the EO condition (ANOVA, p < 0.05) and 2D direction tuning protocol (ANOVA, p < 0.05) were included (34 of 94 with bimodal EO tuning for m39; 49 of 202 bimodal for m31). Inset, Histogram (top right) shows the distribution of differences between EO and 2D direction preferences. For units with bimodal tuning in the EO condition, the direction at the largest peak was used. Color denotes monkey (black for m39, blue for m31), symbol fill denotes unit type (open for MU, solid for SU), and symbol shape denotes tuning modality (circle for unimodal, square for bimodal). Note that axis ranges are expanded such that all data points wrap between the black diagonal lines corresponding to differences of ±180°. F, Same as in E but for rotation direction preference in the DP condition (N = 60 for m39, N = 188 for m31). Units with significant tuning in the DP condition (ANOVA, p < 0.05) and significant tuning for the 2D direction tuning protocol (ANOVA, p < 0.05) were included (12 of 60 with bimodal DP tuning for m39; 61 of 188 bimodal for m31). Format is the same as in E.
- Figure 6.
Are responses in the DP condition driven by selectivity for 2D motion? A, Schematic depiction of a stimulus for measuring tuning for 2D motion direction. The white circle indicates the receptive field, and the white arrow indicates the preferred 2D motion direction (rightward, 0°). B, A pure leftward rotation of the eye produces rightward image motion of the stationary background elements (green triangles). C, When the eye translates rightward while counterrotating to the left to maintain fixation on a world-fixed target (black cross), near and far background elements in the scene (green triangles) move in opposite directions and with speeds that depend on their distance relative to the fixation point. D, The absolute difference between rotation direction preferences in the DP condition and 2D motion direction preferences (|DP rotation – 2D motion preference|) is plotted as a function of speed preference for a subpopulation of MSTd neurons. Marginal histograms show distributions of direction differences and speed preferences. All MSTd units (solid fill for SU, open fill for MU) from m39 (black) and m31 (blue) with significant tuning for speed and for rotation in the DP condition (ANOVA, p < 0.05) were included. E, Expected responses for near triangles are plotted against expected responses for far triangles (see text for details). Same subpopulation of units as in D. The black line denotes the unity slope diagonal, while the dashed gray line indicates a fourfold response ratio (near/far). Color denotes monkey (black for m39, blue for m31).
- Figure 7.
Schematic illustration of stimulus configurations for the Congruent (left column) and Incongruent (right column) conditions. A, Illustration of the Congruent stimulus condition for a movement axis of 0°. Left, The entire scene (including fixation point) translates back and forth sinusoidally (Movie 3), while the monkey maintains fixation on the target (white cross). Right, This configuration produces dynamic perspective cues (simulated rotation, dashed green curve) that are consistent with the actual rotation of the eye (magenta curve). Dashed vertical lines, Data analysis window. B, Illustration of the Incongruent condition. Left, While the scene (including fixation target) translates laterally in front of the monkey, the cloud of background triangles counterrotates around the fixation point to visually simulate eye rotation in the opposite direction. Right, This configuration produces visual cues to eye rotation (dashed green) that are in antiphase to real eye rotation (magenta). C, Top-down illustration of the Congruent condition for a case in which the eye translates leftward and counterrotates rightward (θ = 0°). α denotes the angular position of the eye. β0 refers to the angle of the background relative to the line of sight. Note that, in this schematic, the background is shown as a plane of triangles for clarity of visual illustration; the actual background was a 3D cloud of triangles. D, Top-down illustration of the Incongruent condition for the case of leftward eye translation (θ = 0°). The background elements (green triangles) rotate around the fixation point such that the angle of the background relative to the line of sight (β) is consistent with that produced by leftward eye rotation in the Congruent condition (see E). E, Top-down illustration of the Congruent condition for the case of rightward eye translation and leftward eye rotation (θ = 180°). Format is the same as in C. F, Top-down illustration of the Incongruent condition for the case of rightward eye translation and leftward eye rotation (θ = 180°). Note that the angle of the background relative to the line of sight is consistent with that produced by rightward eye rotation in the Congruent condition (C). Format is the same as in D.
- Figure 8.
Responses of an example multiunit to Congruent and Incongruent conditions, along with predictions of a weighted summation model. A, Rotation direction tuning of an example MU in the EO condition. B, Rotation tuning of the same MU in the DP condition (black symbols). The gray curve shows the tuning curve shifted by 180° (which corresponds to a predictor of responses in the Incongruent condition). C, Responses of the same example MU in the Congruent condition (black symbols, line), along with the best fit of a weighted linear summation model (red squares, dashed line). D, Responses of the same MU to the Incongruent condition (black) and the best fit of the linear model (red). Note that the second response peak near 270° reflects the contribution from DP cues, which are shifted by 180° in the stimulus (B, gray line). Error bars in all panels represent the SEM.
- Figure 9.
Predictions of weighted summation model for an example single unit with a substantial contribution from retinal slip. A, B, Rotation direction tuning for the EO and DP conditions, respectively. Format is the same as in Figure 8, A and B. C, D, Predicted responses of the same example SU to retinal slip associated with eye movements in the Congruent and Incongruent conditions, respectively. See text for details regarding computation of the retinal slip predictor. E, Measured (black symbols, solid line) responses of the example SU in the Congruent condition, plotted together with predictions of two versions of the weighted summation model that either includes (blue triangles, dotted lines) or does not include (red squares, dashed line) the retinal slip predictor. F, Measured responses and model fits for the Incongruent condition. Format is the same as in E.
- Figure 10.
Population summary of linear model performance. A, VAF without the RS factor is plotted against VAF with the RS factor for m39 (black) and m31 (blue). Open and filled symbols denote MU and SU activity, respectively. Triangles denote units for which the retinal slip factor significantly improves model predictions (7 of 29 units for m39; 11 of 68 for m31; sequential F test, p < 0.05), whereas circles denote units for which the retinal slip contribution is not significant. Units with significant tuning for basic protocols (2D motion and speed), significant tuning for both EO and DP conditions, and significant tuning for (at least) one of the combined conditions were included. B, Model weights on responses to the EO condition are plotted against weights on responses to the DP condition for m39 (black) and m31 (blue). Data are shown for the same populations of units as in A. Open and filled symbols denote MU and SU activity, respectively.
Movies
- Movie 1.
EO condition. In this condition, the background triangles are turned off as the fixation target (+) translates in front of the animal. The animal remains stationary and is required to make smooth pursuit eye movements to track the cross. All four rotation axes and both motion phases are shown, for a total of eight unique directions of eye rotation (as defined in Fig. 2A).
- Movie 2.
DP condition. In the DP condition, the background optic flow simulates the visual input received during smooth eye movements in the Congruent condition. The stationary monkey fixates on the cross in the center of the screen and passively fixates while viewing the stimulus.
- Movie 3.
Congruent condition. In the Congruent condition, the background triangles and fixation point translate together along one of the four axes of motion. The stationary monkey must make smooth pursuit movements to track the fixation cross. Rotational optic flow (dynamic perspective cues) is produced by the combination of scene translation and eye rotation.
- Movie 4.
Incongruent condition. Scene translation and eye movements are the same as in the Congruent condition. The key difference is that background triangles rotate around the fixation target to produce a rotational optic flow pattern that is consistent with the eye moving in the opposite direction.
