Alteration of the microsaccadic velocity-amplitude main sequence relationship after visual transients: implications for models of saccade control

Abstract

Microsaccades occur during gaze fixation to correct for miniscule foveal motor errors. The mechanisms governing such fine oculomotor control are still not fully understood. In this study, we explored microsaccade control by analyzing the impacts of transient visual stimuli on these movements' kinematics. We found that such kinematics can be altered in systematic ways depending on the timing and spatial geometry of visual transients relative to the movement goals. In two male rhesus macaques, we presented peripheral or foveal visual transients during an otherwise stable period of fixation. Such transients resulted in well-known reductions in microsaccade frequency, and our goal was to investigate whether microsaccade kinematics would additionally be altered. We found that both microsaccade timing and amplitude were modulated by the visual transients, and in predictable manners by these transients' timing and geometry. Interestingly, modulations in the peak velocity of the same movements were not proportional to the observed amplitude modulations, suggesting a violation of the well-known "main sequence" relationship between microsaccade amplitude and peak velocity. We hypothesize that visual stimulation during movement preparation affects not only the saccadic "Go" system driving eye movements but also a "Pause" system inhibiting them. If the Pause system happens to be already turned off despite the new visual input, movement kinematics can be altered by the readout of additional visually evoked spikes in the Go system coding for the flash location. Our results demonstrate precise control over individual microscopic saccades and provide testable hypotheses for mechanisms of saccade control in general.NEW & NOTEWORTHY Microsaccadic eye movements play an important role in several aspects of visual perception and cognition. However, the mechanisms for microsaccade control are still not fully understood. We found that microsaccade kinematics can be altered in a systematic manner by visual transients, revealing a previously unappreciated and exquisite level of control by the oculomotor system of even the smallest saccades. Our results suggest precise temporal interaction between visual, motor, and inhibitory signals in microsaccade control.

Keywords: microsaccades; omnipause neurons; saccades; saccadic inhibition; superior colliculus.

Fig. 1.

The phenomenon of kinematic alteration. A: schematic of the phenomenon from a typical scenario from the literature (Buonocore et al. 2016; Reingold and Stampe 2002). Top panel shows radial eye position for 2 hypothetical saccades. In blue, the saccade is triggered without a preceding visual flash; in red, a flash consisting of 2 horizontal full-screen white bars (see inset) appears right before saccade onset and after the point of no return (gray vertical line). The saccade amplitudes are different even though peak velocity (shown in bottom panel) is minimally affected. Thus the post-flash saccade violates the main sequence relationship and has different kinematics from the no-flash movement. Note how eye velocity decelerates slightly faster for the post-flash saccade compared with the no-flash saccade, contributing to the reduced amplitude in the former movement. B: in this study, we were interested in the role of flash-induced visual responses in spatial structures such as the superior colliculus (SC). If the post-flash saccade is triggered at the time of visual response occurrence, then readout of spatial maps would have access not only to the saccade-related spikes (blue) but also to the visual spikes. C: spatially, the visual spikes would alter the center of mass of activity being read out by the oculomotor system to specify saccade end point. In this example, the SC map (Hafed and Chen 2016) would have a center of mass less eccentric than the blue saccade-related burst, which could explain the lower saccade amplitude in A. We explored the implications of this mechanism in this study.

Fig. 2.

Interactions between the spatial geometry of visual stimulus location and the saccade goal location in the phenomenon of kinematic alteration (experiment 1). A: in experiment 1, a microsaccade was planned to a near eccentricity, whereas a visual stimulus was presented peripherally. We confirmed this spatial dissociation by plotting the distribution of microsaccade amplitudes observed in the interval from −150 to 205 ms relative to peripheral stimulus onset. Median microsaccade amplitude was 13.18 min arc, more than an order of magnitude less eccentric than the peripheral stimulus location (materials and methods). This is consistent with previous observations in monkeys and humans (Chen and Hafed 2013; Hafed et al. 2009; Hafed 2013). The histogram shown was normalized by the total number of observations (9,314 microsaccades from both monkeys). B: on a model of the SC map (Hafed and Chen 2016), the spatial dissociation is shown for a microsaccade either toward the flash location (top) or opposite it (bottom). In each case, the blue region of the spatial map would be the region of movement-related spiking activity at the time of movement execution, and the red region would be the region of stimulus-induced visual spikes that would occur after stimulus onset. Spatial readout of the map in the 2 scenarios predicts different patterns of executed saccade amplitudes. C: stimulus onset resulted in microsaccadic inhibition, as expected. graphs show the proportion of trials containing either “toward” (bluish color) or “opposite” (brownish color) microsaccades as a function of time after stimulus onset. Classic microsaccadic inhibition occurred. Note that the strong postinhibition difference between toward and opposite movements is expected given previous results (e.g., Tian et al. 2016). D: time courses of microsaccade radial amplitude as a function of time relative to peripheral stimulus onset. Near the time of microsaccadic inhibition (e.g., shaded region), microsaccade amplitude was modulated in a manner consistent with the predictions of spatial readout of oculomotor maps as in B. Toward microsaccades were consistently larger than opposite microsaccades. E: microsaccade peak velocity was also modulated, and one of our purposes in this study was to explore the relationships between the amplitude and peak velocity modulations (e.g., Figs. 4 and 7). Error bars denote 95% confidence intervals (c.i.).

Fig. 3.

Kinematic alteration of microsaccades occurring after peripheral stimulus onset. A: each column shows a pair of microsaccades that are matched for peak velocity. The pair at left is from monkey N, and the two pairs at middle and right are from monkey P. In the top row, radial eye position shows that the microsaccade toward the peripheral flash (bluish color) within a pair was larger than the microsaccade opposite the peripheral flash (brownish color) when these microsaccades were triggered during the microsaccadic inhibition period of Fig. 2C. This happened even though radial peak velocity was matched (bottom row). The 3 pairs were chosen to sample different microsaccade amplitudes (also see Fig. 8). B: a similar analysis to that in A but for pairs of movements that were matched for amplitude. In this case, even though the “toward” and “opposite” microsaccades within a pair were matched in radial amplitude, the peak velocity of the opposite microsaccade was larger, suggesting that a larger movement may have been planned, but there was spatial interaction like that shown in Fig. 2B, bottom, altering the executed microsaccade. Once again, the pair at left is from monkey N, and the two remaining pairs are from monkey P; also, the pairs were chosen to sample different amplitudes (also see Fig. 8). Figure 4 shows population summaries consistent with the example results presented in this figure, and the figure would be more suitable for inspecting velocity trajectories (beyond just peak velocity) more closely. This is because inspecting velocity trajectories for individual traces is less reliable given the low-velocity ripples associated with the differentiation operation needed to compute velocity (materials and methods).

Fig. 4.

Consistency of kinematic alterations of microsaccades between “toward” and “opposite” movements occurring near the time of microsaccadic inhibition. A and C: for each monkey, we selected all microsaccades occurring within 40–100 ms after peripheral stimulus onset (Fig. 2B) that had a certain peak velocity (see the eye velocity trace in each panel and the horizontal red arrow). For those microsaccades, we plotted the average radial eye position trace. Toward microsaccades were consistently bigger than opposite movements despite matched peak velocities. Note that the velocity traces suggest faster deceleration for the opposite movements (diagonal red arrows), which contributes to the reduced amplitudes (as is the case with large saccades; e.g., Figs. 1 and 10). B and D: for all microsaccades occurring 40–100 ms after stimulus onset (regardless of peak velocity), we plotted the ratio of peak velocity to movement amplitude. This ratio was different between toward and opposite microsaccades in each monkey. Thus, in addition to amplitude and velocity variations (Fig. 2, D and E), the kinematics of microsaccades were also altered by the recently appearing visual flash. The gray data show the same ratio but for microsaccades occurring from −100 to −40 ms from stimulus onset. Error bars in all panels denote 95% confidence intervals.

Fig. 5.

Exploring microsaccadic inhibition and kinematic alterations when the flash and movement goal are almost colocalized (experiment 2). A: the logic of experiment 2. If a microsaccade is triggered to correct for a foveal motor error, then the fixation spot (a white “frame” of pixels with a hole in the middle) is close to the movement goal of the microsaccade (top). Thus introducing a transient flash on the fixation spot makes the flash-related and movement-related spikes in oculomotor maps like the SC map model shown (Hafed and Chen 2016) almost colocalized. B: in each monkey (i.e., within each row), we plotted the distribution of landing eye positions at microsaccade end for either “toward” (left plot) or “opposite” (right plot) microsaccades. Toward and opposite movements were classified according to the inset polar plots in C, showing microsaccade angle relative to the axis connecting eye position at movement onset and the center of the fixation spot (Materials And Methods). Toward microsaccades brought gaze closer to the fixation spot (also shown in more detail in C). Moreover, there were many more toward than opposite microsaccades. C: for either toward or opposite microsaccades, and for each monkey individually, we plotted a normalized histogram of the final eye position after microsaccade end (i.e., the final foveal motor error). Toward microsaccades consistently decreased eye position error (compare bluish and brownish histograms in each monkey; P < 0.00001 for each monkey, Wilcoxon rank sum test). Note that the histograms were normalized to facilitate viewing of the different landing eye position errors. In reality, there were very few opposite microsaccades (see B and Fig. 6A).

Fig. 6.

Microsaccadic inhibition occurs even when flash and movement goal location are almost colocalized and foveal. A: we plotted the proportion of trials containing microsaccades as a function of time from foveal flash onset. Regardless of microsaccade direction relative to the flash location (either bluish or brownish curve), robust microsaccadic inhibition occurred. This was particularly true for toward movements (bluish curve) even though the flash was almost perfectly colocalized with the movement goal (Fig. 5A). Also, note that the frequency of opposite microsaccades is much less than that of toward movements (compare bluish and brownish curves). This is consistent with observations that microsaccades occur to primarily correct instantaneous foveal motor error (Tian et al. 2016). Error bars denote 95% confidence intervals. B: microsaccade amplitude distribution in the present experiment (similar to how it was computed in Fig. 2A), demonstrating the small scale of movement goal and stimulus locations that we tested in this portion of our study.

Fig. 7.

Microsaccade kinematic alteration with a foveal flash. A: for “toward” microsaccades (Figs. 5 and 6), we plotted time courses of rate (top row), amplitude (second row), peak velocity (third row), and ratio of peak velocity to amplitude (bottom row). In each monkey, microsaccadic inhibition occurred despite the proximity of movement goal and flash location (top row). Around the inhibition period, movement amplitude (second row) and peak velocity (third row) increased, consistent with spatial readout predictions (Figs. 2–4 and 5A). Moreover, the peak velocity increase was not proportional with the amplitude increase, resulting in a transient dip in ratio of peak velocity to movement amplitude (bottom row). This suggests an alteration in microsaccade kinematics. B: the alterations observed in A resulted in post-flash microsaccades that landed more accurately at the goal location than those without the flash, consistent with the hypothesis that spatial readout “pulls” the microsaccades toward the flash location. For each monkey, we plotted the foveal error at microsaccade end (i.e., the remaining distance to the fixation point center after microsaccade end) for movements occurring either shortly after the flash (bluish) or before the flash (gray). There was a small but systematic reduction in foveal error in each animal for movements occurring right after the flash (median error with the flash was 3.9 and 3.6 min arc in monkeys N and P, respectively, whereas it was 4.2 and 4.4 min arc before the flash; P < 0.002 for each monkey). This suggests that the flash had a functional impact of increasing microsaccade landing accuracy. C: microsaccade kinematic alterations can also be seen when peak velocity is plotted against amplitude (i.e., the main sequence curve). For baseline microsaccades (−150 to 0 ms from flash onset), we fitted the main sequence curve and obtained 95% confidence intervals (materials and methods). For toward movements occurring 5–205 ms after flash onset, we then plotted the trajectory of peak velocity and amplitude from the curves in A (in steps of 10 ms). The black circle indicates time 5 ms, and the phase plane curves show progress from 5 ms onward. Microsaccades were consistently deviated from the baseline curve. Note that the monkey had different peak velocities (compare black curves), and this was due to different amounts of microsaccade curvature between the animals. Error bars in all panels show 95% confidence intervals.

Fig. 8.

Alteration of microsaccade kinematics regardless of microsaccade amplitude. In each monkey (A and B), we plotted an index of kinematic alteration (materials and methods) similar to the one used in Buonocore et al. (2016), and we plotted it for different microsaccade amplitude bins (x-axis in each graph; bin width = ±3 min arc around each shown bin center). Each graph shows a different time period relative to flash onset. For microsaccades very close (leftmost column) or very far (rightmost column) from the time of flash onset, no strong kinematic alteration occurred. However, near the microsaccadic inhibition period (i.e., when visual spikes are expected to interact with movement-related spikes in Fig. 1), kinematic alteration like that in Fig. 7 was observed, and this happened for all microsaccade amplitude bins. Thus kinematic alteration occurs even for the smallest possible saccades. Note that the effect was longer lived in monkey P than in monkey N, but so was this monkey’s inhibition period, as well (see insets). Error bars denote 95% confidence intervals.

Fig. 9.

Free-viewing task of experiment 3 and its analysis. A: the monkey scanned a cloud pattern, and a transient full-screen flash occurred at a random time. Example eye movement scan paths are shown in cyan. B: we selected either baseline saccades occurring 20–200 ms before flash onset (black example saccade) or post-flash saccades occurring 50–150 ms after flash onset (brownish example saccade). Saccades were chosen such that, relative to the flash geometry (i.e., the screen extent), their starting and ending eye positions fell within the gray regions shown. Specifically, we split the screen into 9 equally sized virtual tiles; any saccade starting from a large region of 4 contiguous tiles abutting one corner of the display (e.g., the large gray box) and ending into a single tile in the opposite corner (e.g., the small gray box) was considered as a saccade for which the flash (i.e., the full-screen stimulus) had a center of mass less eccentric than the saccade goal location (similar to opposite movements in our earlier analyses with microsaccades). Note that we repeated this tiling procedure for all other corners of the screen. Thus, with such selection, we ensured that the center of mass of visual spikes associated with the full-screen flash was less eccentric than the center of mass of the saccade goal location (as in the schematic scenario of Fig. 1C), which would allow replication of previous human experiments (it is also conceptually similar to opposite microsaccades in Fig. 2). C: we confirmed that for these saccades, saccadic inhibition occurred in the monkey (e.g., gray region), as with earlier human experiments and our earlier microsaccade experiments. Error bars denote 95% confidence intervals.

Fig. 10.

Kinematic alteration for large monkey saccades. A: we plotted the main sequence curve for baseline saccades (black) or post-flash saccades (brownish) after saccades were selected according to the criteria of Fig. 9B. The main sequence curves were close to each other, because the flash was too close in time to the saccade onset (visual spikes would arrive too late after the saccade has been triggered to influence it). B: however, for saccades occurring near saccadic inhibition time (i.e., when visual spikes would coincide with saccade triggering), the main sequence curve was consistently elevated, especially for larger saccades. This is consistent with results of previous human experiments (Buonocore et al. 2016) and also with our microsaccade results from earlier figures (for opposite microsaccades). C: for an example saccade amplitude bin from B (all saccades with amplitude 13.5 ± 1.5°), we could confirm that peak velocity was consistently elevated for the same movement amplitude. D: we repeated the analysis shown in C but for other saccade amplitude bins centered on 8°, 10°, 12°, and 14°. Each bin included saccades ±0.5° in amplitude relative to the bin center. As expected from data in B, peak velocity alterations were consistent for all the different saccade amplitudes, except for 8° saccades (this is likely due to the small saccade size relative to the flash center of mass). Error bars denote 95% confidence intervals.

Fig. 11.

Hypothesized mechanism for saccadic inhibition and kinematic alterations. A: visual transients result in visual input to a variety of oculomotor structures (red). Among these structures are spatial ones (e.g., the SC) in which spatial readout of activity would be altered by the visual spikes present at movement triggering (blue “Go” system). Additionally, other structures (e.g., omnipause neurons, OPNs) are part of a “Pause” system (black) that helps gate saccades and influence saccade timing. If the Pause system happens to be already in the “off” state at the time of presence of visual spikes in the Go system (e.g., Fig. 1C; i.e., the saccade is being executed), then spatial readout of the Go system would alter movement kinematics. B: saccadic inhibition may be a result of the timing of visual inputs arriving to the Pause and Go systems. In the scenario at left, the visual stimulus appears early enough before pause onset such that visual input to the Pause system delays any potential eye movement triggering (red arrows). In this case, saccades are delayed, explaining the classic saccadic inhibition “dip” in reaction time distributions. In the scenario at right, the saccade is triggered nonetheless such that at the time of pause in the Pause system (i.e., at the time of saccade execution), visual spikes are present anyway in the Go system and can alter saccade kinematics. Note that the visual spikes may also contribute to reactivating the Pause system a bit early (red arrow) and truncating saccades. Therefore, saccade amplitudes and peak velocities can still be altered by the visual input, even if some truncation may still occur in the same movements.