Modulation of saccade trajectories during sequential saccades

Abstract

The planning and execution of sequential saccades can overlap in time, and abrupt changes in neural activity in the oculomotor system can alter the normal trajectory of saccades. In this study, we analyzed saccade trajectories to assess the combined programming of sequential saccades. In two separate psychophysical experiments, subjects were instructed to make a sequence of two saccades. The results showed modulation of saccade curvature by the direction and amplitude of both the preceding and following saccade: saccade curvature is modulated in the direction of preceding saccades and away from the direction of following saccades. Moreover, larger preceding and following saccades have stronger effects on curvature. These results support the idea that sequential saccades are programmed concurrently. Finally, the amount of saccade curvature is correlated with the deviation of saccade start and end points, and the time of maximum deviation of saccade trajectories is highly consistent in both experiments. Based on this, we propose a novel benefit for the modulation of saccade trajectories by the oculomotor system: minimizing the saccadic error in sequential saccades.

NEW & NOTEWORTHY We show that in saccade sequences, saccade trajectory is modulated in the direction of the preceding saccade and away from the following saccade. The magnitude of this effect is correlated with preceding and following saccade amplitude. This confirms that programming of sequential saccades overlaps. Curvature is also correlated with the deviation of saccade start and end points. Thus, we propose a novel benefit for the modulation of saccade trajectories: minimizing end point error in sequential saccades.

INTRODUCTION

Saccades are ballistic eye movements allowing the fovea to capture high-resolution visual information from different parts of the visual scene (1). Ideally, saccade trajectories should be straight lines taking the shortest route between two fixation positions, but they often deviate significantly from a straight line (2–4).

Several different factors have been found to modulate saccadic trajectories. When subjects execute a saccade while maintaining covert attention on a peripheral location, saccades curved away from the locus of attention (5–8). Similarly, a suddenly appearing distractor can cause saccades to curve away from the location of the visual distractor (5–10), as well as auditory and somatosensory distractors (11). However, saccades can also curve toward irrelevant visual distractors when saccade latencies are relatively short (12–14). Ongoing competition between a target and distractor has been suggested as the explanation for saccade curvature toward a distractor, and evidence in favor of this idea has been found in two structures that play key roles in saccades, the superior colliculus (SC) and frontal eye field (FEF) of monkeys (12, 15).

Initially, it was suggested that curvature away from a distractor reflects the top-down inhibition of the distracting information in the oculomotor system, presumably occurring after the initial target/distractor competition has been resolved. In this model, distracter-related activity in the oculomotor system can initially deviate saccades toward the distractor location, but this activity will eventually be suppressed by an inhibitory top-down signal, causing saccades performed a longer time after distractor onset to curve away from the location of the distractor (9, 13, 16–19). However, persistent top-down inhibition of irrelevant target locations has not been observed in the activity of SC neurons, even when curvature away from a distractor is observed (20).

Therefore, two other mechanisms have been proposed to explain how visual attention or distractors are able to modulate saccade curvature: adaptation of long-lead burst neurons (LLBNs) in the brainstem (21) and interactions within the intermediate layers of the SC (22, 23). In both models, the later portion of the curved trajectory is driven by a downstream error-correction mechanism that detects the deviation of the eye’s path from the target location and attempts to provide an appropriate drive signal to decrease final saccade end point error. Parallel planning of sequential saccades may also modulate saccade curvature, because planning of sequential saccades can overlap in time (24–26). As a result, during sequential saccades, neural activity in the oculomotor system may be altered by the planning of a preceding or following saccade, resulting in modulation of saccade trajectories.

Indeed, saccades tend to curve in the same direction as preceding saccades. Sogo and Takeda (27) showed that saccades curve away from the previous fixation location during a free-viewing visual search task, consistent with the modulation of the saccade trajectories by visual attention. Moreover, recently Megardon et al. (28) showed that saccades curve in the same direction as the preceding saccade in a sequence of two instructed saccades. Are these saccade trajectory modulations only incidental side-effects arising from the oculomotor activity related to planning and executing a saccade sequence? To address this question, we investigated in greater depth how saccade trajectories are modified by the direction and amplitude of preceding and following saccades, and we discuss the potential benefits of saccadic trajectory modulation during sequential saccades.

METHODS

Subjects

Ten subjects, nine naive subjects and one author (R.A.), participated on a voluntary basis in this study (4 females and 6 males, aged 26–35 yr). Half of the subjects performed experiment 1 first and then experiment 2, whereas the other half performed the experiments in the reverse order (see the Procedure). All protocols were approved by the State University of New York College of Optometry Institutional Review Board, and subjects provided written, informed consent.

Apparatus

Subjects sat in a dark room with their heads stabilized via chin and forehead rests and their eyes at a distance of 114 cm from a 32 in. 1920 × 1080 IPS LCD with 120 Hz refresh rate (Display++ LCD Monitor, Cambridge Research Systems Ltd, Rochester, UK). Eye level was aligned with the center of the LCD. The stimuli were presented by PsychoPy, a presentation software package written in Python (29). For tracking and recording of eye movements, an SR-Research EyeLink 1000 Desktop Mount system was used at a sampling rate of 1,000 Hz to record the right eye position. A standard 13-point calibration followed by a validation procedure was used preceding all experimental sessions.

Procedure

Experiment 1: following saccades.

In this experiment, we asked whether the trajectory of the current saccade is modulated by the direction and amplitude of a subsequent (future) saccade in a sequence of movements. Each trial started with a red fixation circle presented on the horizontal midline, 5° above the center of the display (Fig. 1A). After a randomly chosen duration of 1,000 ± 250 ms, the fixation point disappeared and five horizontally aligned visual stimuli were simultaneously presented 10° below the fixation point at −10°, −5°, 0°, 5°, and 10° horizontal eccentricities, respectively, named far-left, close-left, middle, close-right, and far-right targets. Subjects were instructed to make a sequence of two saccades as quickly as possible; first, a vertical saccade toward the middle target and then a horizontal saccade to one of the other targets. The direction and amplitude of the second saccade was cued by the direction of a gap in the fixation circle, which pointed toward the second target position and was presented during the fixation period. Far second saccade targets were indicated by a larger angular deviation of the gap from the downward orientation compared with the close targets. In control trials, the gap in the fixation cue pointed straight downward, and subjects performed a single vertical saccade to the middle target. Each trial was terminated by presenting a blank screen after fixating on the final target for 400 ms. Each session contained 500 randomly interleaved trials (100 of each trial type). The fixation circle and target stimuli were rings with diameter 0.5° and 0.2° line thickness. The average duration of each trial and the experiment were 2,549 ms and 23 min across all subjects.

Figure 1.

A: schematic of the trial sequences and five trial types in experiment 1 (test saccade follows an initial saccade): 1) The fixation point appears and subjects start fixation; a small line cues the direction of the second saccade. 2) The fixation point disappears after 1,000 ± 250 ms, and simultaneously five peripheral visual stimuli appear. 3) Subjects first make a saccade to the middle target as quickly as possible. 4) A second saccade toward the final target is made and subjects are required to hold fixation for 400 ms. B: experiment 2 (test saccade precedes a subsequent saccade): 1) The fixation point is presented at one of the five locations depending on the trial type and the subject starts fixation. 2) After 1,000 ± 250 ms, the fixation circle disappears and simultaneously two targets appear on the midline. Subjects are instructed to perform 3) the first saccade horizontally to the upper target and 4) a second saccade to the lower target and hold fixation for 400 ms. C: schematic of the procedure for calculating saccadic curvature based on the area under the curve of saccadic trajectory from a line connecting the saccade start and end points. Note that clockwise curvatures (A₁ in this example) are defined as negative values and vice versa.

Experiment 2: preceding saccades.

In this experiment, we asked whether saccade trajectories can be modulated by the direction and amplitude of preceding saccades. The fixation circle was presented at 5° above the center of the display. Based on the trial type, the horizontal eccentricity of the fixation circle was chosen as −10°, −5°, 0°, 5°, and 10°, respectively, for far-left, close-left, middle, close-right, and far-right trials (Fig. 1B).

After the fixation point disappeared, two targets appeared on the midline; one horizontally aligned with the fixation point and another one 10° below. Subjects were instructed to perform the first saccade horizontally to the upper target and then the second saccade vertically to the lower target. Control trials were also included in this experiment, in which the fixation point appeared on the midline and subjects performed a single vertical saccade. The fixation point and visual stimuli were the same as in experiment 1. The average duration of each trial and the experiment were 2,394 ms and 22 min across all subjects.

Saccade Detection

Saccades were detected using a velocity threshold of the eye of 40°/s. Start and end points were marked when velocity fell below two standard deviations from the median saccade velocity during fixation. Saccades with gains less than 0.67 or more than 1.33 and saccades with intersaccadic intervals longer than 300 ms were excluded (3% of the trials).

Saccade Curvature

Saccade curvature was defined as the area under the curve of the saccade trajectory from a line connecting the saccade start and end points, divided by saccade amplitude (2). Clockwise saccade curvature was taken to be negative and vice versa (Fig. 1C). For a downward saccade, clockwise (positive) curvature denotes curvature toward the right.

Multiple Comparisons Correction

In the cases of multiple comparisons, we used Benjamini–Hochberg (BH) procedure (30) to control the false discovery rate at the level of 0.05. It works as follows:

1. sort P values from the smallest to the largest: P(1) < P(2) < … < P(m),

2. let k be the largest i for which P(i) < i/m × q, (q = 0.05),

3. reject the null hypothesis for i = 1, 2, 3, …, k.

The adjusted P value for a test is either the original P value times m/i or the adjusted P value for the next higher raw P value, whichever is smaller (31).

RESULTS

In the two experiments, we asked whether the curvature of a vertical “test” saccade is modulated by the direction and amplitude of a preceding or following saccade in a two-saccade sequence. Saccadic trajectories from three typical subjects in the two experiments are plotted in Fig. 2A. The left column illustrates data from single-saccade control trials and, as can be seen, saccade trajectories are not absolutely straight, but instead are somewhat idiosyncratic for each subject. The middle and right columns illustrate the trajectories of the test saccades in far-trials in experiment 1 (effect of a following saccade) and experiment 2 (effect of a preceding saccade). These panels also reveal some individual differences among subjects and show that the curvature modulations are not necessarily symmetric in the left and right trials for each individual subject.

Figure 2.

Saccade trajectories for typical subjects in experiments 1 and 2. Each row represents data from a typical subject. The left column is the saccade trajectories in the single-saccade control trials, when subjects performed only one saccade in both experiments. The middle and right columns represent data from the far trials, respectively in experiments 1 and 2, and the arrows indicate the following and preceding saccade directions. Individual differences are noticeable between the subjects, as well as asymmetry between the saccade trajectories in the right and left trials. All 200 control trials in experiments 1 and 2 and all 100 trials in each condition are presented here.

For each saccade, we calculated a curvature value as described in the methods. Box-and-whisker plots showing all the raw curvature values collected in this paper are presented in Fig. 3; each point represents saccade curvature in a single trial, and subjects are color-coded. The boxes indicate the lower and upper quartile of saccadic curvature in each trial type for each subject (subjects are color-coded), and the white horizontal stripes indicate the medians for each subject. The error bars (the whiskers) indicate 1.5 times the IQR (the distance between the upper and lower quartiles). Black circles represent the average saccade curvature for each subject, and the black horizontal lines indicate the average saccade curvature across all subjects for each trial type (thick lines) ± 1 standard deviation (thin lines). The results indicate that curvature of the test saccades tends to be modulated in the direction of the preceding saccade, but in the opposite direction of the following saccade. Moreover, the magnitude of this curvature change is larger in test saccades when the amplitude of the preceding or following saccade is larger.

Figure 3.

A descriptive analysis of saccade curvatures in experiment 1 (top) and experiment 2 (bottom). These box-and-whisker plots illustrate saccade curvatures in each trial type for each subject, and data from all single trials are presented on these plots. Each point represents data from a single trial; bars indicate the lower and upper quartile of saccadic curvature in each trial type for each subject (subjects are color-coded) and the white lines indicate the medians. The error bars (the whiskers) indicate 1.5 times the IQR (the distance between the upper and lower quartiles). Black circles represent the average saccade curvature for each subject, and black lines indicate the average saccade curvature across all subjects for each trial type (thick lines) ± 1 standard deviation (thin lines). P values are obtained from pairwise t tests corrected by Benjamini–Hochberg (BH) procedure.

To test the significance of these differences, we first ran a repeated-measures ANOVA (5 trial types × 10 subjects) on the average of saccade curvature in each trial type for each subject followed by pairwise t tests; the results showed significant differences in average saccade curvature in the different trial types in both experiments [F(4,36) = 21.238, P < 0.001 and F(4,36) = 29.498, P < 0.001, respectively for experiments 1 and 2). The results from pairwise t tests corrected by the BH procedure (see methods) showed significant differences between the control trials (trials with a single vertical saccade) and all of the other trial types (trials with saccade sequences) in experiments 1 and 2 (all P < 0.02), except for the close-right trial types in experiment 2 (P = 0.120). We also found significant differences between the far- and close-trial types in both experiments (all P < 0.02), except for the left trials in experiment 2 (P = 0.120, see Fig. 3).

To summarize the effects and to remove any bias due to the asymmetry between the saccade trajectories in the left- and right-trial types, we subtracted the average saccade curvature of the right-trial types from the left-trial types to compare saccade curvature in the close and far trials. This resulted in curvature values of 0.23° and 0.34° in experiment 1 and 0.37° and 0.49° in experiment 2, for close and far trials, respectively (see Fig. 4). Note that the results of these subtractions are positive in all subjects and trial types for both experiments, indicating that average curvature in left trials was greater (or more positive) than the right trials (see Figs. 3 and 4). A series of paired t tests followed by the BH procedure in both experiments showed significant differences between close- and far-trial types [t(9) = 5.105, P < 0.001 and t(9) = 2.787, P = 0.021; respectively for experiments 1 and 2; P values are adjusted by BH procedure] as well a significant difference from zero [close trials: t(9) = 5.368, P = 0.003 and t(9) = 3.889, P < 0.001; far-trials: t(9) = 6.562, P < 0.001 and t(9) = 6.183, P < 0.001; respectively for experiments 1 and 2; P values are adjusted by BH procedure].

Figure 4.

A: difference in saccade curvature of the left and the right trials, for far (red) and close (blue) second target (experiment 1, left) and fixation (experiment 2, right) position; the circles indicate data from each individual subject and the error bars indicate 95% confidence intervals across subjects. B: schematic of saccadic trajectories for far (red) and close (blue) trials (only one side is presented here): saccades curve away from the direction following saccades (experiment 1, left) and curve toward the direction of preceding saccades (experiment 2, right). This modulation of curvature is stronger for when the following or preceding saccades are larger (far trials).

To visualize the overall effects of following and preceding saccades on test saccade trajectories across left and right trials, we subtracted the test saccade trajectories of the right-trial types from the left-trial types. Figure 5A illustrates the average horizontal saccade deviation over the normalized saccadic duration (defined as the time of each data point from saccade onset, divided by the saccade duration) in each trial for close and far trials for each experiment. Interestingly, in close trials in experiment 1, the end of the test saccade trajectory appears to deviate toward the second target location. On the other hand, in experiment 2 the test saccade starting point is deviated toward the previous fixation, especially in far trials.

Figure 5.

Saccade trajectory deviation in each trial type as a function of time. A: horizontal component of the saccade trajectories from the left and right trials have been subtracted and plotted as a function of time. The arrows indicate the corresponding direction of preceding and flowing saccades. Thin lines indicate data from individual subjects and thick lines are the averages across all subjects; the shaded areas indicate 95% confidence intervals (CIs) across subjects. B: averaged saccade start, maximum deviation, and end points across all subjects. The same color codes as A of this figure have been used; the error bars indicate 95% CIs across subjects.

To examine these deviations in saccade end and starting points in more detail, we averaged the horizontal deviations across all subjects (Fig. 5B). The results show that the average horizontal deviation of saccade starting points in experiment 2 for close and far trials was −0.18° and −0.40°, significantly different from zero [t(9) = −3.667, P = 0.020 and t(9) = 2.793, P = 0, 0.041; respectively for close and far trials; P values adjusted by the BH procedure]. Moreover, the saccade end points for close and far trials in experiment 1 were 0.00° and −0.36° [t(9) = −0.027, P = 0.978 and t(9) = −3.309, P = 0.036; respectively for close and far trials; P values are adjusted by the BH procedure]. We also calculated the time and magnitude of the maximum horizontal deviation across all subjects (Fig. 5B) and found that the maximum trajectory deviation occurred at a similar time during the saccade for all trial types: 26, 31, 31, and 30 ms after saccade onset for experiments 1 and 2, respectively, and for close and far trials, there was no significant difference among these times (repeated-measures ANOVA (4 trial types × 10 subjects), F(3,27) = 1.963, P = 0.143, followed by pairwise t tests within each experiment [t(9) = 2.045, P = 0.142 and t(9) = −0.487, P = 0.637, respectively for experiments 1 and 2].

The aforementioned results suggest a connection between the curvature and end point deviation of the test saccade when a subsequent saccade was planned (experiment 1) as well as between curvature and the start point deviation of the test saccade when there was a preceding saccade (experiment 2). To examine this in more detail, first, for each subject, we divided the saccades into two groups: one group with low curvature and the other with high curvature by using a median split. Then, as in the previous analysis, we subtracted the saccade trajectories of the right-trial types from the left-trial types. The results are plotted in Fig. 6A; the solid and dashed lines represent saccades with higher and lower curvature, respectively. This figure indicates that in experiment 1, when saccades were more curved, their end points tended to deviate from the target less. Indeed, when we compared the horizontal positions of the saccade end points using paired t tests, we found significant differences in end point between saccades with higher and lower curvature [close-trials: t(9) = 2.919, P = 0.027; far-trials: t(9) = 3.648, P = 0.014; corrected using the BH procedure). We also found a significant difference in saccade start points for close trials [t(9) = −3.237, P = 0.020] but not for far trials [t(9) = −1.014, P = 0.336; corrected using the BH procedure].

Figure. 6.

The saccade trajectory deviation for saccades with high and low curvature separately. A: data for each subject and trial type were divided into saccades with high and low curvature and then the horizontal component of the saccade trajectories from the left and right trials were subtracted and plotted as a function of time. Arrows indicate the corresponding direction of preceding and following saccades. Blue dashed lines indicate data from saccades with lower curvature and the red solid lines indicate data from the saccades with higher curvature. The P values indicate the significance between the horizontal components of saccade start and end points, obtained by paired t test corrected by the Benjamini–Hochberg (BH) procedure. The shaded areas indicate 95% confidence intervals (CIs) across subjects. B: average correlation coefficient across all subjects between saccade curvature and saccade start and end points in experiment 1 (green) and experiment 2 (cyan). Filled triangles indicate significant difference between the averaged correlation and zero; the error bars indicate CIs across subjects.

On the other hand, in experiment 2, curvature was stronger for saccades with starting points that were more deviated from the target of the preceding saccade [close trials: t(9) = −6.990, P < 0.001; far trials: t(9) = −10.600, P < 0.001; corrected using the BH procedure], and we found no significant difference in saccade end point for higher and lower curvature saccades [close trials: t(9) = 1.317, P = 0.251; far trials: t(9) = 1.7638, P = 0.148; corrected using the BH procedure]. We also tested the correlation between the saccade start and end points (without any normalization by saccade duration) and saccade curvature for data from each individual subject in each trial type. The average correlation coefficients are plotted in Fig. 6B, t tests, corrected using the BH procedure, were run on each point to see if the averaged coefficients were different from zero (filled triangles represent significant coefficients).

Finally, we examined the relationship between saccade curvature and saccade latency or intersaccadic interval (ISI). We found that saccade curvature did not appear to be related to the latency of the first saccade or the ISI. The average correlations between curvature and the latency of the first saccade and ISI were not significantly different from zero in experiment 1 [t(9) = 0.293, P = 0.770; t(9) = −1.720, P = 0.093] and experiment 2 [t(9) = −1.735, P = 0.090 and t(9) = 0.732, P = 0.468, respectively for latency and ISI).

DISCUSSION

Our results show that in a sequence of two perpendicular saccades, curvature of the first saccade is modulated in the opposite direction of the following saccade and curvature of the second saccade is modulated in the same direction as the preceding saccade. The magnitude of these curvature modulations is correlated with the amplitude of the preceding or following saccades. Moreover, saccade trajectory analysis shows that, on average, saccades have their maximum trajectory deviation ∼20 ms after saccade initiation (average saccade duration ≈ 80 ms). Finally, our results show that saccade curvature is correlated with the magnitude of the deviation from the target position of the saccade starting and landing points. Specifically, when the test saccade was followed by a second saccade, deviation of the test saccade end point toward the second saccade goal was smaller when the curvature of the test saccade was larger. Moreover, when the test saccade was preceded by a saccade, curvature of the test saccade was larger when its starting point was more strongly deviated toward the previous fixation location.

These results suggest that saccade curvature may play a role in maintaining saccade accuracy during a sequence of saccades. Planning of sequential saccades may occur in parallel (24–26), and therefore planning of a following saccade can interfere with the execution of the current saccade, resulting in the deviation of the saccade end point in the same direction as the subsequent saccade. However, if changes in saccade curvature were only a distractive side effect of planning the following saccade, one would expect saccades with greater curvature modulations to land with more horizontal error relative to the target. Here, we found the opposite effect. Moreover, we found a significant correlation between saccade curvature and horizontal deviation (Fig. 6). This suggests that saccade curvature arises from a mechanism to compensate for this potential end point error induced by preparation of the following saccade. Our results also confirm combined planning of sequential saccades, as if they were independent, there should not be any modulation of the saccade trajectories by the other saccades in the sequence.

Neural Activity Associated with Saccade Curvature

Previous studies showed that, in a visual search task, saccade curvature toward or away from a distractor is correlated with the strength of SC activity occurring at the distractor site immediately before and during the saccade (12). Similar results were observed in the frontal eye field (FEF) (15). Moreover, a causal link between this activity and saccade curvature was established by showing that when an increase in activity with similar temporal patterning was artificially generated using electrical microstimulation that was subthreshold for evoking saccades, saccade curvature toward the location of the motor field of the stimulated site was observed, both in the SC (12) and FEF (15). On the other hand, if activity in a focal region of the superior colliculus is chemically inhibited, saccades tend to curve away from the inhibited location (32). These results are consistent with the idea that saccade curvature reflects the spatial pattern of activity across the SC and FEF motor maps.

Behavioral studies had suggested that the modulation of saccade trajectory by spatial attention reflected a top-down inhibition of the attended location within these motor maps, resulting in curvature away from the locus of attention (9, 16–19). White et al. (20) searched for the correlates of this top-down inhibition in the SC. In this study, monkeys were required to perform a simple reflexive saccadic task while ignoring irrelevant visual distractors. In agreement with human studies, their results showed that in this situation, monkeys’ saccades curve away from distractors. In White et al.’s (20) study, the authors expected to observe top-down inhibition of the distractor-related location in single-unit recordings in the superior colliculus, consistent with the initial models suggested for the modulation of saccade trajectory by visual attention. However, they did not find any evidence of persistent top-down inhibition associated with saccade curvature. Instead, their results showed a relationship between saccade deviation and distractor-evoked neural activity only during a short perisaccadic period that started ∼20 ms before saccadic onset, which is around the time of the SC movement-related burst of visuomotor SC neurons (33, 34).

Here, we suggest that the modulation of saccade trajectories in experiment 1 represents a mechanism for maintaining saccade accuracy. We speculate that, during planning or execution of the first saccade, visual attention is allocated to the second saccade target, increasing its corresponding neural activity in SC (35, 36). This overlapping neural activity associated with the first and second saccades can then deviate the first saccadic end point toward the second saccadic goal (37–39). Unlike the initial idea that a top-down inhibitory mechanism is used to cancel out this irreverent neural activity for the first saccade (9, 16–19), we propose that the correction of the saccade trajectory can be evoked by the neural activity that has been found by White et al. (20) around the time of saccade onset.

Previous saccade end point errors can also be corrected by modification of the subsequent saccade trajectory. Saccades often undershoot the target (40), which can explain why in experiment 2, the second saccade tends to start with a horizontal deviation toward the initial fixation point. When the first saccade is longer (far trials), the second saccade starts with greater horizontal deviation from the midline because saccadic gain to steady targets is about typically 95% (41). Similar to the results from experiment 1, we suggest that saccade curvature has a role in maintaining saccade accuracy by correcting the saccade trajectory during execution of the second saccade to minimize the final end point error. The significant correlation between the error of the saccade starting point and the magnitude of curvature is consistent with this hypothesis (Fig. 6). Therefore, parallel planning of sequential saccades not only has temporal benefits, but also improves saccadic accuracy.

In summary, results from the current study show that for sequential saccades, saccade curvature is modulated in the same direction as a preceding saccade and in the opposite direction of a following saccade. Moreover, the magnitude of this modulation is correlated with the amplitudes of both the preceding and following saccades. Finally, by observing correlations between start/end point error and the magnitude of saccade curvature, we propose that these saccade trajectory modulations represent a systemic mechanism to maintain saccade accuracy in the face of competing activity in the oculomotor system related to parallel planning of sequential saccades or to shifts of covert attention.

GRANTS

This work was supported by National Institutes of Health (NIH) Grant R01-EY030669 (to R.M.M.).

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

R.A. and R.M.M. conceived and designed research; R.A. performed experiments; R.A. and E.Y.Z. analyzed data; R.A. and R.M.M. interpreted results of experiments; R.A. prepared figures; R.A. drafted manuscript; R.A. and R.M.M. edited and revised manuscript; R.A., E.Y.Z., and R.M.M. approved final version of manuscript.