Fig 1.
Screen and retinal images during the pursuit eye movement.
The subject performs pursuit eye movements upon a target moving horizontally to the left on a screen with static background dots (a). On the retinal image during the pursuit, the target is relatively stable on the fovea, while the “static” dots are induced to move toward the right (b). Note that the normal inversion of the visual field on the retina is ignored in this diagram for the sake of clarifying the trade-off of retinal vs. screen motion during pursuit eye movement.
Fig 2.
An MSTd cell that responds to both a large field dots moving to the right and to pursuit of a target moving to the left on a dark background.
The height of the gray vertical bar indicates 250 spikes per second. Adapted from Komatsu and Wurtz (1988).
Fig 3.
Pursuit compensation of MSTd neurons.
MT neurons are tuned to retinal velocity. Thus, for different eye movement velocities, the velocity tuning curves of MT neurons shift away from the velocity tuning curve for the fixation condition in screen coordinates (c and d). Unlike MT neurons, MSTd neurons can compensate for the visual motion induced by pursuit to represent the real velocity on screen rather than the retinal velocity. The compensation is indicated by the overlapping velocity tuning curves in the screen reference frame for different eye movement velocities (a), as well as the shifting of the same curves in the retinal frame (b). The shifting distance of each curve depends on the pursuit speed. For a perfect compensation, the shift distance should be equal to the speed of the pursuit but in the opposite direction. Different colors represent different pursuit velocities as shown in the legends in (a). Adapted from Inaba et al. (2011).
Fig 4.
The MSTd computation contains five stages: 1) calculate the summation of MT responses and calculate the exponential form of the MT summation, 2) define pursuit input as a function of pursuit velocity with the mirrored visual tuning function (see text), 3) calculate the result of divisive interaction between the MT and pursuit responses, 4) use the result as the input to a simple shunting computation and 5) solve the shunting equation in its equilibrium state.
Fig 5.
The log-Gaussian function of MT velocity tuning and the input to the model MSTd neuron.
(a) Three examples of the velocity tuning curves of model MT neurons with the preferred velocity parameter μ set at 10, 20 and 30 degrees per second. (b) The summing weights follow a power function of preferred speed with a negative power. The response is assumed to be negative when the preferred direction of MT neurons is opposite to their projecting MSTd neuron. In each plot, the x-axis is the retinal velocity in degrees per second, and the y-axis is unit-less since the responses are normalized.
Fig 6.
Model MSTd responses as a function of retinal visual velocity for different pursuit velocities compared to single function fit.
The original MSTd velocity tuning data and the fitting function from Inaba et al. (2011) are shown in filled circle and solid line, respectively. The velocity tuning curve during the fixation, the pursuit to the preferred direction, and the pursuit to the anti-preferred direction conditions are shown in black, red, and green, respectively. For preferred pursuit direction (red lines), the relative intensity ratio of the visual motion signal to the pursuit signal is stronger than that for the anti-preferred pursuit direction (see text for details).
Fig 7.
An example of a predicted compensatory pursuit neuron with similar velocity tuning of pursuit and visual motion.
The black dots and line show the tuning and corresponding fit of visual motion, while the gray open dots and line show those of pursuit. Adapted from Churchland and Lisberger (2005).
Fig 8.
Different pursuit modulations of velocity tuning in compensatory and non-compensatory pursuit neurons.
We assume both neurons prefer visual motion to the right. Correspondingly, the compensatory pursuit neuron should show a preferred direction of pursuit to the right, while the non-compensatory pursuit neuron should show a preferred direction of pursuit to the left. According to our analysis, if we know the neuron’s preferred direction of both pursuit and visual motion, we should be able to tell if the neuron is a compensatory pursuit neuron or a non-compensatory pursuit neuron. Diagrams of the retinal velocity tuning of visual motion during pursuit to the left and right directions are shown in Fig 8. Red lines represent pursuit to the right (preferred visual motion direction); blue lines represent pursuit to the left (null visual motion direction). The black arrows show the shift direction of these tuning curves when plotted against the screen velocity instead of the retinal velocity. The compensatory pursuit neuron compensates for the pursuit irrespective of the pursuit direction by converging the tuning curves in the screen frame, while the non-compensatory pursuit neuron spreads out the velocity tuning curves for different pursuit directions in the screen frame.
Fig 9.
Component compensation versus vector summation as a single-cell level mechanism of pursuit compensation.
(a) Pursuit (red arrow) induces a motion component (dashed red arrow) for the moving background (black dot). Thus, the motion on retina (purple arrow) is a vector sum of the motion on screen (blue arrow) and the motion component induced by the pursuit. A compensation mechanism can help the neuron respond to the same motion on screen similarly, whether there is pursuit or not. The goal is to code the motion on screen correctly, even when input from the retina is changed due to pursuit. (b) Two possible pursuit compensation mechanisms. Component compensation can be done by the mechanism suggested by our model. The MSTd neuron responds (horizontal dashed black arrow) to the motion input from MT (purple arrow). The response is adjusted by the pursuit input (red arrow). This adjustment can be achieved by the divisive interaction between the visual motion component along the preferred direction (horizontal dashed black arrow) and the pursuit (red arrow). Then, the MSTd neuron responds similarly to the same motion on screen, with or without pursuit (horizontal dashed blue arrows). In the component compensation approach, only the component of the actual motion on screen along the preferred direction is represented. However, this single MSTd neuron can show similar direction tuning under pursuit and fixation conditions (responses to dashed blue arrows). The vector summation mechanism can compensate for the pursuit and reveal both the speed and direction of the actual motion on screen. However, for the vector summation to work, the direction and speed of both the visual motion and pursuit vectors should be represented in neural responses, but the angle between these two vectors (θ) should also be represented in neural responses. Perfect representation of such information is difficult to implement in a single neuron. Thus, we suggest that component compensation can happen on a single-cell level in MSTd neurons first, so that the visual motion component along the neuron’s preferred direction can be represented. Then the population responses of these MSTd neurons with different preferred directions can be pooled together to represent precisely the actual motion on screen in the presence of pursuit eye movement.
Fig 10.
Direction-selective responses of the MSTd neuron shown in Fig 3 to the background motion on the screen during fixation (black arrows/lines) and pursuit in the preferred direction (red arrows/lines).
(a) Motion on retina as a result of pursuit. Each arrow represents the motion of the background toward one of the eight directions. For the same background motion on screen for the fixation (black arrows) and pursuit conditions (red arrows), the motion on retina during pursuit is different from those during fixation. (b) The MSTd neuron shows similar direction tuning with or without pursuit. Our modeled neuron also shows similar direction tuning to the MSTd neuron during fixation (black line) and pursuit to preferred, preferred+90 degrees, anti-preferred, and anti-preferred+90 degrees direction (red, cyan, green and blue lines, respectively). (a) and the left plot in (b) are adapted from Inaba et al. (2011).