The suppression theory of saccade deviation

Deviation in saccade trajectory was first regarded as evidence for the premotor theory of attention [13]–[16]. The dominant view in the literature now attributes saccade deviations to top-down suppression (inhibition) of the distractor location unfolding over time: initially insufficient suppression of the distractor location causes deviation towards and once full suppression is in place it causes deviation away from distractors [17]. For convenience, we will refer to this theory as the “suppression theory”. The suppression theory of saccade deviation is in agreement with several lines of empirical findings. First, the amount of deviation away from distractors increases with saccade latency [6], [18], [19], but see [20]. When saccade latency is short there is not enough time for the top-down suppression to develop and thus weak deviation away from or even deviation towards distractors is observed. Second, previous studies of the superior colliculus (SC), a layered midbrain structure that contains a topographic motor map that encodes the vector of saccades [21], have demonstrated that saccades deviate away from the response field of an inactivated SC region [11], [22], [23]. Third, McPeek and colleagues [7], [8] found that distractor evoked neuronal activity in the SC and the frontal eye fields (FEF) is stronger when saccades deviated towards than when saccades deviated away from distractors. These findings support the idea that insufficient suppression leads to deviation towards distractors and suppression developing later in time leads to deviation away from distractors.

Despite its popularity in the literature, the validity of the suppression theory was challenged by a recent single-unit recording study by White, Theeuwes and Munoz [9]. In this study, the authors presented distractors 400 ms before target onset, so as to allow sufficient time for the suppression at the distractor location to build up. The results showed that saccades robustly deviated away from the distractors even though there was no reduction of neuronal activity at SC sites representing the distractor location. Instead, there was a trend for stronger deviation away from distractors that evoked stronger neuronal activity, the exact opposite pattern of results predicted by the suppression theory. These observations suggest that the generally accepted view that top-down suppression causes saccade deviations towards and away from distractors has to be revised.

The lateral interaction theory of saccade deviation

The lateral connection of neurons on the topographic motor map contained in the intermediate layers of the SC (SCi) is characterized by short distance excitation and long distance inhibition [24]–[26]. This lateral interaction can be captured by a neural field model [27], [28]. The neural field model has proven successful in simulating various saccade-related behavioral observations, including the global effect [29], [30] and trajectory deviations caused by lesion/inactivation [11] or visual distractor [10], [12]. It should be noted, however, that none of these computational studies has successfully simulated saccades deviating away from distractors. To fill up this gap, in a recent study [1], Wang, Kruijne and Theeuwes put forward a simple theory that claims that both deviation towards and away from visual distractors are caused by the lateral interactions in the SC. For convenience, we will refer to this theory as the “lateral interaction theory”.

The critical component of the lateral interaction theory is the shape of the lateral interaction profile in the SC. While most in vivo studies of the lateral interactions in the SC have focused on the SCi [31], in vitro studies have demonstrated similar interactions in the superficial layers of the SC (SCs) [32]. In addition, it is well known that the neuronal activity in the SC is modulated by the inhibitory projection from the substantia nigra pars reticulata (SNr) [33]. So, the lateral interaction kernel derived from in vivo cell-recordings [34], [35] reflects the overall interplay between the SCi, SCs and the SNr, rather than only the synaptic connections within the SCi. Following previous modeling work [10], [34], [35], we assumed that the lateral interaction profile in the SC is Mexican-hat shaped. As shown in Fig. 2A (gray line), the lateral interaction profile has an excitation zone and two inhibition zones. In a distractor paradigm, when the distractor and the target are close in space, the distractor and target evoked activity “bubbles” will excite each other and merge into one activity bubble peaked at an SC site representing to a location in between these two stimuli. This will lead to saccade trajectories deviating towards the distractor. However, when the distractor and target are placed at a distance where they compete with each other, the target evoked activity bubble receives non-uniform inhibition from the distractor evoked activity bubble. That is, the side close to the distractor (shaded in dark gray in Fig. 2A) receives stronger inhibition than the other side (shaded in light gray in Fig. 2A). In the same vein, the distractor also receives non-uniform inhibition from the target. As a result, after lateral competition, the peak of the target activity (sustained by a top-down signal after the visual input dissipates) is pushed away, leading to saccade trajectories deviating away from distractors.

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Figure 2. The lateral interaction theory and supporting evidence from the literature.

(A) A schematic illustration of why the lateral interactions in the SC can produce saccades deviating away from the distractors (redrawn from [1]), see text for detail. (B) Simulation results of Wang et al. [1]. Positive and negative values on the y-axis denote deviation towards and away from distractors, respectively. Thick and thin lines denote simulations using kernels of small and large excitation zones, respectively. (C) A graphical meta-analysis of studies that reported directional deviations in saccade trajectory. In Theeuwes and Godijn [6], the saccade target and the distractor could appear at previously stimulated or unstimulated locations; only trials in which both the target and distractor appeared at unstimulated locations were considered. In Van der Stigchel and Theeuwes [52], saccade deviation was binned according to saccade latencies; the data reported here is the average over all latency bins. The same procedure was applied to the data from [6], [19], [49], [52]–[54]. The data from White et al. [9] was collected from two monkeys; the target-distractor SOA was manipulated in this study, only the 0-ms SOA condition was included here. (D) A graphical review of studies that reported saccade deviations quantified with trajectory curvature. Note that the curvature measures differed drastically across studies and thus only the direction of trajectory curvature was considered in this analysis, with “+” and “−” signs on the y-axis denoting trajectories curving towards and away from distractors, respectively. The size of the symbols represents the number of experiments contributing to each data point.

https://doi.org/10.1371/journal.pone.0116382.g002

The simulation results of Wang et al. [1] are presented in Fig. 2B. As clearly shown in Fig. 2B, the model predicts that saccades deviate towards distractors that are close to the target and deviate away from distractors that are distal to the target. Due to lack of human neurophysiological data, the lateral interaction profile in the human SC is unknown. The simulation results using the lateral interaction kernel of Trappenberg et al. [35], which is based on monkey neurophysiology, is presented as a thin line, while the simulation results using a kernel with a much smaller excitation zone is presented as a thick line in Fig. 2B. The important message here is that the target-distractor separation at which the transition from deviation towards to deviation away occurs depends on the size of the excitation zone of the lateral interaction kernel.

Graphical meta-analysis of the literature

To validate the model predictions of Wang et al. [1] and to identify empirically significant issues for further experimentation, a graphical meta-analysis of the literature was performed. By scanning the reference lists of three recent review articles [2]–[4] and searching Google Scholar for empirical papers that cited those review articles, we identified 54 relevant studies (as of Nov 18, 2013). A study was included in the meta-analysis if it had one or more experiments that met the following criteria: a) healthy subjects were tested or, in case of a patient study, healthy controls were tested; b) used the distractor task (see Fig. 1A for illustration); and c) the target and distractor were peripheral onsets and were presented simultaneously to the participants. Studies that used endogenous targets (i.e., an arrow at fixation, pointing to a predefined target location) [36]–[38] or had multiple distractors [39]–[42] were not considered. Furthermore, studies that explored saccade trajectory deviation using visual search tasks [7], [8], [43] or attention tasks [13]–[15], [17], [44] were also excluded from the analysis. The results of the meta-analyses, which were based on the remaining 27 empirical papers, are presented in Fig. 2C and 2D.

Before discussing the meta-analysis results, we would like to point out that in the literature, two groups of methods exist for quantifying deviation in saccade trajectories [2]. One group of methods emphasizes the curvature of saccade trajectories, that is, how much a saccade trajectory deviates from the direct path between the start and endpoint of a saccade [45], while other methods examines the (initial, final or average) direction of saccade trajectories relative to the direction of the saccade target [46]. For convenience, we will refer to these two groups of trajectory deviation measures as “trajectory curvature” and “directional deviation”, respectively.

Because it is easy to calculate, a trajectory curvature measure named “maximum curvature” [45] has been frequently used in the literature [5]. Maximum curvature is defined as the maximum distance of the sample points to the straight path between the start and end of a saccade trajectory (see Fig. 1B), sometimes further divided by the amplitude of the same saccade [18]. One often used directional deviation measure is “initial directional deviation”, defined as the direction of an early (e.g., the fifth) sample point of a saccade trajectory, relative to the target direction [46] (see Fig. 1C). Because Wang et al. [1] used a 1-dimensional neural field model that encoded only the saccade direction, their simulation results were about the directional deviation rather than the curvature of saccade trajectories.

Studies that examined directional deviations [6], [9], [19], [46]–[55] are summarized in Fig. 2C. A careful examination of Fig. 2C reveals several interesting observations. First, in agreement with the simulation results of Wang et al. [1], a transition from deviation towards distractors to deviation away from distractors emerges as the target-distractor angular separation increases. Second, the simulation results obtained using a kernel of a small excitation zone (thick line in Fig. 2B) seem to agree with behavioral findings more than those obtained using a kernel of a relatively large excitation zone (thin line in Fig. 2B). With a large excitation zone, the transition from deviation towards to deviation away occurs at a fairly large target-distractor separation (∼90°), while empirical results suggest that the transition occurs at a target-distractor separation of about 40°. Third, previous studies were mainly concerned with relatively small target-distractor separations. The simulation results of Wang et al. [1], which suggest that the amount of deviation away from distractors decreases as target-distractor separation increases, cannot be verified by simply synthesizing data available in the literature. To better characterize the relationship between saccade deviation and target-distractor separation with behavioral experiments, parametric manipulation of the target-distractor angular separation is needed. Finally, stimulus eccentricity (represented by the symbol size in Fig. 2C) seems to also play a role. Deviations in the “away” direction were generally weaker for more eccentric targets (and distractors).

For completeness, we also performed a graphical meta-analysis of studies that reported the curvature of saccade trajectories [5], [18], [20], [46], [48], [49], [56]–[67]. Because trajectory curvature measures varied drastically across studies, it is not possible to do a quantitative review (like the one presented in Fig. 2C), unless we reanalyze the raw data of all these studies. Thus, only the direction of trajectory curvature, i.e., towards (+) or away from (−) distractors, was considered in this analysis. The results are presented in Fig. 2D, with the size of symbols representing the number of experiments contributing to each data point. It is clear from Fig. 2D that, when measured with trajectory curvature, saccades also deviate towards close distractors and deviate away from remote distractors.

Purpose of the present study

As shown in Fig. 2B, the amount of deviation towards distractors generated by the neural field model of Wang et al. [1] was significantly larger than those observed in previous behavioral studies (Fig. 2C). This is likely due to the fact that Wang et al. [1] did not consider the fixation activity at the rostral pole of the SC, which globally suppresses neuronal activity evoked by both the target and distractor. To address this issue, simulations considering the effect of SC fixation activity were first performed. Predictions generated by these simulations were then verified with behavioral experiments, in which both the strength of fixation activity and the angular distance between the target and the distractor were manipulated. The latter manipulation was included because, as clearly shown in Fig. 2C, large target-distractor distance (>60°) is largely unexplored in the literature.

Fixation activity and saccade deviation: A conceptual analysis

In a distractor paradigm, how saccade direction and amplitude are affected by fixation activity is graphically analyzed in Fig. 3. The color gradient in Fig. 3A represents the strength of connections originating from the rostral pole of the SC, i.e., the fixation zone. When appearing in the periphery, due to lateral inhibition, the target and distractor evoked activities receive inhibition from the fixation zone. The effect of this fixation-related inhibition is two-fold. First, because the lateral interaction profile is Mexican-hat shaped, as illustrated in Fig. 3B, the target evoked activity will drift away from the fixation zone (along Slice 1 in Fig. 3A). The stronger the fixation activity the further the drift, the larger the saccade amplitude. A second and more interesting effect of the fixation-related inhibition is illustrated in Fig. 3C. Because of the Mexican-hat shaped interaction profile, there exists a non-uniform inhibition along the path where the distractor and target interact (Slice 2 in Fig. 3A). As a result, saccades to the target will be pushed away from the distractor by the fixation activity. The stronger the fixation activity, the stronger the deviation away from the distractor. Importantly, as can be inferred from Fig. 3C, the effect of fixation-related inhibition on saccade deviation depends on the distance between the target and the distractor. When the target and the distractor are far apart, the strength of fixation activity should have little or no effect on saccade deviation.

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Figure 3. The strength of fixation activity modulates saccade trajectory deviation.

(A) The motor map in the SC, drawn from the equations and parameters given by van Gisbergen, van Opstal and Tax [79]. The color gradient represents the strength of connections originating from the fixation zone (the rostral pole of the SC). T: Target; D: Distractor; F: Fixation. (B) Non-uniform inhibition from the fixation zone can cause the target-evoked activity to drift away from the fixation, see text for details. (C) The inhibition from the fixation zone can also cause the target-evoked activity to drift away from the distractor, see text for details. (D) Saccade deviations obtained from simulations in a neural field model of the SC [1], [35], assuming that the fixation activity was either weak or strong.

https://doi.org/10.1371/journal.pone.0116382.g003

Model architecture

To demonstrate the idea that the strength of fixation activity modulates deviations in saccade direction, simulations were performed in a 1-dimensional neural field model of the SC [1]. The model, which has n = 1000 nodes (leaky integrators), roughly represents 5-mm of SC tissue encoding the straight path through the target and distractor (see Fig. 3A). Equation 1 defines the connection strength (w_ij) between two nodes. Because our graphical meta-analysis of the literature suggests that an interaction kernel with a small excitation zone could better predict human behavioral data (see Fig. 2B and 2C), the following parameters were used in our simulations: a = 144, b = 24, c = 9, σ_a = 0.25 mm, σ_b = 1.5 mm. The internal dynamics of a node is described in Equation 2, where τ = 10 ms. A sigmoid gain function is used to relate the discharge level of a node to its internal state, where β = 0.08.(1)(2)(3)

Nodes in the network receive both excitatory () and inhibitory ( and ) inputs. The excitatory input was further dissected into exogenous (visual) and endogenous (top-down) inputs [35], [68]. It should be noted that the endogenous input represents a top-down selection of the target and thus was only applied to the target location. The excitatory inputs were assumed to have a Gaussian spatial shape (see Equation 4). In our simulations, the width of the excitatory inputs were fixed at σ_e = 0.53 mm, close to estimations that are based on cell-recordings in the SC [24]. The temporal dynamics of the exogenous and endogenous inputs are described in Equations 5 and 6, respectively. As in previous modeling work [35], the exogenous input reached the SC 70 ms after stimulus onset (t_on) while the endogenous input reached the SC 50 ms later, i.e.,  = 70 ms,  = 120 ms. For all simulations, the strength of exogenous and endogenous excitatory inputs were set to e_exo = 30 and e_endo = 15, respectively. The exogenous input was transient and decayed exponentially (τ = 10 ms). The endogenous input was sustained and was turned off when the saccade initiation threshold (80% of the maximum discharge level) was crossed (t_off). For simplicity, the inhibition from the substantia nigra pars reticulata (SNr) was fixed at  = −16 for all nodes.(4)(5)(6)

In our simulations, it was assumed that that target and distractor always appeared at locations mirroring the horizontal meridian. Thus, the inhibition coming from the fixation zone could be approximated with a sustained Gaussian-shaped inhibitory input (Equation 7), centered at the midpoint between the target and distractor (x_c). The width of this input was set to σ_fix = 0.7 mm, while the strength of this input was set to either weak (f = −0.5) or strong (f = −1.8). Fixation neurons at the rostral pole of the SC are characterized by tonic discharge during active fixation and pause during saccades [69]. Thus, the inhibitory input coming from the fixation zone was applied to the model neurons from the beginning of each simulation trial and was turned off after the saccade initiation threshold was crossed (t_off), see Equation 8.(7)(8)

Simulation results

The simulation results are presented in Fig. 3D. First and foremost, replicating previous findings [1], saccades deviated towards close distractors and away from remote distractors. Second, when inhibition from the fixation zone of the SC was considered, the amount of deviation towards distractors reduced to a range normally reported in previous empirical studies (about 1°–7°). Third, fixation activity modulated the amount of directional deviation, with strong fixation activity causing a shift in the “away” direction. Last but not least, as has been discussed previously, the modulatory effect of fixation activity on saccade deviation was weak (largely absent) for relatively large target-distractor separations. These simulation results provided us with testable predictions for further behavioral experimentation.

Materials and Methods

The human research protocol described here was approved by the local ethical committee at Vrije Universiteit and all participants gave written informed consent.

Results

Due to technical issues, one participant (No. 14) completed partial (2/3) of the experimental trials. Careful off-line inspection of the eye movement data identified that the experimental script failed to recycle a small number of error trials (0.54%). These trials were excluded from the analyses. For successfully completed trials, those were excluded from the analyses if a) the SRT was shorter than 80 ms (6.16%) or longer than 500 ms (1.22%), b) the initial saccade direction deviated more than 30° from the target direction (2.64%), or c) the starting point of the primary saccade deviated more than 1.5° from the fixation cross (1.40%). After data cleansing, 88.91% of the trials remained.

The mean directional deviation, trajectory curvature, saccade amplitude and SRT of each experimental cell are presented in Fig. 4. Repeated measures ANOVAs of these measures, with variables condition (gap vs. overlap) and target-distractor separation (15°–150°), were performed and the results are presented below.

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Figure 4. Mean directional deviation (A), trajectory curvature (B), saccade amplitude (C) and SRT (D) for each target-distractor separation in the gap and overlap conditions in Experiment 1.

Error bars denote ±1 SE; for clarity, only one side of the error bars is drawn. In (C) and (D), thick and thin horizontal lines denote distractor-absent trials in the overlap and gap conditions, respectively.

https://doi.org/10.1371/journal.pone.0116382.g004

Discussion

Simulations using a neural field model of the SC showed that task irrelevant visual distractors can cause the direction of saccades to deviate towards or away from the distractors, depending on the angular distance between the target and the distractor [1]. The simulation results presented here suggest that the amount of saccade deviation also depends on the strength of fixation activity at the rostral pole of the SC (see Fig. 3D). To verify this prediction, a behavioral experiment manipulating the temporal gap/overlap between fixation offset and target onset was performed. The primary results of interest are those presented in Fig. 4A, i.e., deviations in initial saccade direction. It is clear that the behavioral results resemble those produced by the neural field model (Fig. 3D), supporting the lateral interaction theory of saccade deviation [1]. In addition to deviations in initial saccade direction, here we also report saccade deviations quantified with a trajectory curvature measure [5], [18]. As shown in Fig. 4B, when measured with trajectory curvature, the amount of deviation also varied with the manipulation of target-distractor separation and temporal gap/overlap.

One important finding of the present experiment is that saccade amplitudes were found to be larger in the overlap than in the gap condition (see Fig. 4C). This confirms a novel prediction of the lateral interaction theory. Because the lateral connection in the SC is Mexican-hat shaped, when the target appears in the periphery, the target evoked activity will be pushed away by the fixation activity (see Fig. 3B). As a result, the stronger the fixation activity, the larger the saccade amplitude. It is important to note that, although not statistically reliable, a similar pattern of results has been reported in an early study by Kingston and Klein [78]. This effect deserves further study.

In the literature, several researchers have reported that short-latency saccades are accompanied by deviation towards distractors and long-latency saccades are accompanied by deviation away from distractors [6], [18]. This observation has been regarded as evidence for the suppression theory because suppression at the distractor location takes time to develop. As shown in Fig. 4D, SRTs were generally slower in the overlap condition and this difference was largely unaffected by the target-distractor separation. According to the suppression theory, deviation towards distractors should be observed in the gap condition while deviation away should be observed in the overlap condition, regardless of the target-distractor distance. However, as shown in Fig. 4A and 4B, when the distractor was distal to the target (>90°), the amount of deviation was statistically equivalent for the gap (short SRT) and overlap (long SRT) conditions, see also [49].

Method

The human research protocol reported here was approved by the local ethical committee at Hangzhou Normal University and all participants gave written informed consent.

Results

Successfully completed trials were further cleansed to improve data quality. Trials were excluded from the analyses if the SRT was shorter than 80 ms or longer than 550 ms (1.72%) or the starting point of the primary saccade deviated more than 2.0° from the fixation cross (4.16%). Based on the criteria given by Van Selst and Jolicoeur [80], a trial was also excluded if the directional deviation from the target direction was above or below 2.35 standard deviations from the mean (2.18%). After data cleansing, 91.17% of the trials remained.

Dependent measures of interest included initial directional deviation, maximum curvature, and SRT. Unlike Experiment 1 where stimulus eccentricity was fixed in all conditions, multiple eccentricity was tested in Experiment 2. To make comparisons across different eccentricities, initial saccade direction was calculated with a sample point where the eyes had travelled approximately 20% of the total duration and maximum curvature was further divided by the amplitude of the saccade. Mean directional deviation, trajectory curvature, and SRT of each condition are presented in Fig. 5.

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Figure 5. Mean directional deviation (A), trajectory curvature (B), and SRT (C) for each condition in Experiment 2.

Error bars denote ±1 SE; for clarity, only one side of the error bars is drawn in (C).

https://doi.org/10.1371/journal.pone.0116382.g005

Discussion

On the basis of the results of the present experiment, we argue that the strength of the fixation activation in the rostral pole of the SC modulates the strength (and the direction) of deviations of saccade trajectories. As can be easily inferred from Fig. 3B, the effect of the fixation activation first increases and then decreases with stimulus eccentricity. Thus, the theory presented here predicts that the strength of saccade trajectory deviations should vary with stimulus eccentricity, a prediction that was confirmed by Experiment 2. As clearly shown in Fig. 5A, the directional deviation decreased as the stimulus eccentricity increased from 12° to 24°. An increase in directional deviation from 4° to 12° was also observed. This observation, however, was not statistically reliable, because the directional deviation for the 4° eccentricity was highly variable across participants. This variability was likely contributed to by two factors: a) the size of the fixation zone in the SC might be highly variable across participants, and b) the initial saccade direction was estimated with a much earlier gaze sample than that for the 12° and 24° eccentricities.

Fixation activity and saccade deviation

Saccade latency is usually shortened when the fixation stimulus is removed before target onset, i.e., the gap effect [76]. When the fixation stimulus remains visible after target onset, however, saccade latency is usually prolonged [75]. The manipulation of temporal gap/overlap between fixation offset and target onset has been used in several recent studies to explore the relationship between saccade latency and saccade deviation [6], [18], [19]. One interesting finding of this line of study is that saccade deviation seems to vary with saccade latency (for failure to observe such an effect, see [9], [20]). For instance, McSorley and colleagues [18] demonstrated that short SRTs were accompanied by trajectories curving towards distractors while long SRTs were accompanied by trajectories curving away from distractors. Similar results were also observed in the present behavioral experiment, but only when the target-distractor separation was relatively small (see Fig. 4B). Such observations have been widely regarded as evidence for the suppression theory which argues that suppression at the distractor location takes time to develop. The most significant contribution of the present study is that we show that the not always observed correlation between SRT and saccade deviation is caused by the manipulation of temporal gap/overlap, which in turn affects the strength of fixation activity the SC [70], [71].

A general explanation for deviation away

The present study and our previous modeling work [1] emphasized the role of the lateral interactions in the SC in generating deviation away from distractors. Here we would like to point out that the lateral interaction in the SC is just one implementation of a much more general principle underpinning deviation of saccade direction. This general principle is non-uniform inhibition or suppression of target activation (see Fig. 2A and Fig. 3C). In addition to the Mexican-hat shaped lateral interaction which could give rise to a non-uniform inhibition from the distractor, previous studies have identified several factors that may cause non-uniform inhibition/suppression of target activation. These factors include, but are not limited to, pharmacological inactivation of the SC [22], [23] and inhibition of return (IOR) [55], [81]. When an SC site is inactivated, there will be a gradient of suppression surrounding the infusion site. When a target appears at a location close to the response field of the infused SC site, due to uneven suppression, saccades will be pushed away (see Fig. 3C). Rather than using pharmacological methods, in a recent study, we successfully produced one such uneven (Gaussian shaped) inhibition behaviorally, taking advantage of a behavioral phenomenon called IOR [82]–[84], see also [6]. When a target is presented close to a recently visually stimulated location, response times (RTs) are usually slower than when the same target appears at a location that has not been stimulated. This RT cost has a spatial gradient, as the distance between the stimulated location and the target increases RT decreases [85], [86]. When the angular separation between the stimulated location and the target was varied, saccades deviated away from the stimulated location even when the separation was only 15° [81]. In contrast to distractor induced deviation away which could only emerge when the distractor is relatively distal to the target (>30°; see Fig. 2C and Fig. 4A), IOR or inactivation can induce deviation away when the saccade target is presented very close to the location suppressed by IOR [81] or inactivation [22]. It should be noted that there is abundant evidence supporting the notion that IOR mainly affects the visual pathway [25], [87]–[89]. Considering the fact that inactivation directly suppresses neuronal activity in the SC, it is safe to conclude that deviation away can be caused by non-uniform suppression of target activation at various stages of processing. This general theory is in contrast to the suppression theory which emphasizes the suppression of distractor activation.