January 2008
Volume 49, Issue 1
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Eye Movements, Strabismus, Amblyopia and Neuro-ophthalmology  |   January 2008
How the Brain Obeys Hering’s Law: A TMS Study of the Posterior Parietal Cortex
Author Affiliations
  • Marine Vernet
    From the IRIS Group, CNRS–Collège de France, Paris, France;
    University of Pierre and Marie Curie (Paris VI), Paris, France;
  • Qing Yang
    From the IRIS Group, CNRS–Collège de France, Paris, France;
  • Gintautas Daunys
    From the IRIS Group, CNRS–Collège de France, Paris, France;
    Department of Radioengineering, Siauliai University, Siauliai, Lithuania;
  • Christophe Orssaud
    From the IRIS Group, CNRS–Collège de France, Paris, France;
    Service Ophtalmologie, Hôpital Européen Georges Pompidou, Paris, France; and
  • Thomas Eggert
    From the IRIS Group, CNRS–Collège de France, Paris, France;
    Departement of Neurology, Ludwig-Maximilians Universität, Munich, Germany.
  • Zoï Kapoula
    From the IRIS Group, CNRS–Collège de France, Paris, France;
Investigative Ophthalmology & Visual Science January 2008, Vol.49, 230-237. doi:10.1167/iovs.07-0854
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      Marine Vernet, Qing Yang, Gintautas Daunys, Christophe Orssaud, Thomas Eggert, Zoï Kapoula; How the Brain Obeys Hering’s Law: A TMS Study of the Posterior Parietal Cortex. Invest. Ophthalmol. Vis. Sci. 2008;49(1):230-237. doi: 10.1167/iovs.07-0854.

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      © 2016 Association for Research in Vision and Ophthalmology.

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Abstract

purpose. Human ocular saccades are not perfectly yoked; the origin of this disconjugacy (muscular versus central) remains controversial. The purpose of this study was to test a cortical influence on the binocular coordination of saccades.

methods. The authors used a gap paradigm to elicit vertical or horizontal saccades of 10°, randomly interleaved; transcranial magnetic stimulation (TMS) was applied on the posterior parietal cortex (PPC) 100 ms after the target onset.

results. TMS of the left or right PPC increased (i) the misalignment of the eyes during the presaccadic fixation period; (ii) the size difference between the saccades of the eyes, called disconjugacy; the increase of disconjugacy was significant for rightward and downward saccades after TMS of the right PPC and for downward saccades after TMS of the left PPC.

conclusions. The authors conclude that the PPC is actively involved in maintaining eye alignment during fixation and in the control of binocular coordination of saccades.

Saccades are rapid eye movements that bring the object of interest on the fovea, where fine vision is possible. The two eyes move in the same direction and by the same amplitude. How the brain controls the binocular coordination of the saccade has been an issue of controversy since 1868. Helmoltz 1 speculated that there was one command center for each eye and that binocular coordination would be the result of learning and visual experience. On the contrary, Hering 2 postulated that the brain sends a unique command to each eye so that they move as a uniform organ; binocular coordination would be innate. 
However, during a saccade, the two eyes are not perfectly yoked. For horizontal saccades, Collewijn et al. 3 characterized for the first time in four subjects a transient disconjugacy: during the acceleration phase of the saccade, the vergence angle becomes more divergent (between 1° and 3°) because of larger movement of the abducting eye, and then it becomes more convergent. At the end of the pulse component of the saccade, there is still a residual divergence so the saccade is followed by a convergent postsaccadic drift that reduces or eliminates this residual divergence. In contrast, the vertical misalignment between the two eyes during vertical saccades is small (inferior to 1° for a saccade of 20°) but was consistent in two subjects among the three subjects studied. 4 A subsequent study (Zee et al. 5 ) confirmed the observation of a transient saccade disconjugacy in humans. 
The pattern of this stereotyped disconjugacy evolves during life. Yang and Kapoula 6 showed that in children younger than 12 years, horizontal saccades made at near distance present also a small transient disconjugacy, but the rate of divergent disconjugacy is lower, approximately 67% in children between 4.5 and 6 years of age compared with 80% in adults. Moreover, the disconjugacy remaining at the end of the saccade is below 0.5° in adults, but it could reach 2° in children for saccades of 20°. It is only around the age of 12 years that children acquire a quality of binocular coordination—small and stereotyped disconjugacy of saccades at either far or close distance—similar to that of adults. 
Several explanations have been proposed for the origin of the transient disconjugacy of saccades. First, mild asymmetry of viscoelastic properties between the lateral rectus muscle of one eye and the medial rectus muscle of the other eye, coactivated during horizontal saccades, may exist. 3 5 However, muscular asymmetry would also be reflected in saccade dynamics, such as in peak velocity difference between the eyes. Yet disconjugacy—the asymmetry between the amplitudes of each eye—depends on depth, whereas mild asymmetry of peak velocity of the eyes is not a function of depth. 6 As a consequence, transient disconjugacy cannot be entirely caused by a muscular phenomenon, even if we cannot exclude a contribution of such peripheral cause. 
Another asymmetry considered by Zee et al. 5 concerns the length of innervation circuitry of the lateral rectus muscle of one eye and the medial rectus muscle of the other eye: the abducens nucleus innervates the ipsilateral lateral rectus muscle directly, and the contralateral medial rectus motoneurons indirectly, through abducens internuclear neurons. 7 Thus, one could expect a conjugate command for saccades to arrive earlier at the lateral rectus than at the medial rectus; this delay has been modeled by Zee et al. 5 However, although the motor and premotor circuits are mature from the age of 4, because the saccades of young children are as fast as those of adults, 8 binocular coordination is not optimal until the age of 12. 6 Asymmetries between the lengths of innervation circuitry could consequently partially explain the disconjugacy of saccades but not its development during childhood. To summarize, the development of coordination during childhood is contrary to the idea of an innate coordination and does not support the peripheral asymmetries (muscular, circuitry) as unique causes of observed disconjugacy. 
The dominant pattern of divergent disconjugacy during saccades observed in adults can be modified by visually induced adaptation mechanisms, such as in experiments in which disparate images are presented to the eyes. 9 10 11 12 Possible mechanisms for this adaptive learning could involve modification of the saccadic signal for each eye individually or the issuing of a rapid vergence command linked to the saccade command. 10 These studies suggest that central mechanisms are involved in the coordination of saccades. The cerebellum is an important site of oculomotor adaptation in general, 13 14 but other cerebral structures, such as the posterior parietal cortex (PPC), may also be involved. The hypothesis is compatible with known physiology. Indeed, Gnadt and Mays 15 have shown in monkey posterior parietal cortex the existence of activity coding for position and desired change of gaze in a three-dimensional spatial system. This activity still exists when there is no visual target. Perhaps the brain stem circuitry is calibrated by the cerebellum and the PPC modulated these two lower circuits, subtending binocular coordination. 
In this study, we hypothesized that the binocular coordination is controlled at least partly by the posterior parietal cortex. In a previous transcranial magnetic stimulation (TMS) study, Elkington et al. 16 showed that the TMS of the PPC increased the divergence of the eyes before the saccade, indicating that the PPC is involved in static vergence control before eye movements. Thus, the PPC could be a privileged cortical place for the control of binocular coordination of saccades, i.e., accurate control in three-dimensional space during saccades. Other TMS studies showed that the PPC is involved in the initiation of saccade and vergence movements. 17 18 19 20 21 In these five TMS studies, the binocular coordination aspect was ignored. Our study focuses on the binocular coordination of saccades and the binocular alignment of the eyes during fixation before the saccade and during postsaccadic drift. 
Materials and Methods
Subjects
Twelve adult subjects were tested. Their ages ranged from 20 to 49 years (mean, 24.7 ± 8.3 years). All subjects were healthy and did not have any neurologic, neuro-otologic, or ophthalmologic symptoms. They had normal or corrected-to-normal vision. Binocular vision was assessed with the TITMUS test of stereoacuity. All individual scores were normal (40″ of arc or better). Each participant gave informed consent to participate in the experiment. This investigation was approved by the local ethics committee and was consistent with the Declaration of Helsinki. 
Transcranial Magnetic Stimulation
In the TMS blocks, single-pulse stimulation was applied on the right or the left PPC with a magnetic stimulator (model 200; MagStim; Withland, Wales, UK). Maximum stimulator output was 2.2 T; the coil has a figure-of-eight (each wing 70-mm diameter) allowing focal stimulation. The time of increase of the pulse was 5 μs, and the decay lasted 160 μs. A click occurred simultaneously with the pulse. 
To define motor thresholds, the intersection of the wings of the coil was applied on the motor hand area, and the intensity of the stimulator was increased until it reached a value for which visible jerks of contralateral hand muscles occurred. For our group of subjects, the motor threshold ranked from 35% to 60% of total stimulator output. During PPC stimulation, the intensity was between 45% and 65%, depending on the subject. Such values, above the motor threshold, did not cause blinks. 
The left or right PPC was stimulated by placing the coil 3 cm posteriorly and 3 cm laterally to the vertex, tangentially to the skull, to obtain a well-focalized stimulation of this area. The coil was placed on the scalp with its handle oriented backward and 45° leftward (for stimulation of the left PPC) or rightward (for stimulation of the right PPC) relative to the midline. Similar procedures for localization, coil placement, and stimulation capacity have been used by our group and other groups. 16 19 20 22 TMS was delivered 100 ms after the target onset. 
For the blocks without TMS, stimulation was also delivered 100 ms after the onset of the target, but the coil was placed 30 cm over the head of the subject and oriented toward the ceiling to provide the same auditory input in both conditions (TMS/no TMS). A second coil, unlinked to the magnetic stimulator, was placed over the subject head, to conserve the same somatosensory clues as during the real stimulation. 18 19 20  
Stimuli/Visual Display
The visual display, shown in Figure 1A , was composed by five white luminous dots (angular size, 0.2°), presented on a black computer screen placed at 57 cm from the subject (the required convergence angle was approximately 6°). One of these five dots was at the center of the screen, two were at an eccentricity of ±10° horizontally, and two were at an eccentricity of ±10° vertically. 
In a dark room, each subject was comfortably seated in an adapted chair with a medical collar to stabilize the head. Each subject viewed binocularly. During the calibration task and the oculomotor task, dots were highly visible because only one was lit at a time. 
Main Oculomotor Task
To elicit short-latency reflexive eye movements, we used a gap paradigm (Fig. 1B) . Each trial started by lighting the central dot during approximately 1500 ms (SD 100 ms, to avoid predictability of the exact moment of the target onset). After this fixation period, the fixation dot was turned off. After a gap of 200 ms, a target—one of the horizontally or vertically eccentric dots—appeared for 1500 ms. This paradigm called for saccades of 10°. During the blocks with TMS, stimulation was applied 100 ms after the target onset. Successive trials were separated by periods of 1000 ms, with all dots turned off. Each block lasted 5 minutes. The instruction given to the subject was to look at the light dot as accurately and as rapidly as possible. 
During each session, the subject performed three blocks: one block of trials with TMS of the left PPC, one block of trials with TMS of the right PPC, and one block without stimulation. Each block included 60 trials (15 upward saccades, 15 downward saccades, 15 leftward saccades, 15 rightward saccades). The four directions were randomized to avoid predictability of the direction. In the blocks with TMS, stimulation was not delivered for 2 trials of each direction (13% of the trials) to avert the predictability of the TMS release. The order of the blocks was randomized. 
Calibration Task
Before each block of the oculomotor task, the subject made a sequence of saccades between the white dots in all four directions; each dot was turned on during 1000 ms (a period allowing accurate and stable fixation). The calibration factors for each eye were extracted from these recordings. 
Eye Movement Recording
Horizontal and vertical eye movements were recorded binocularly (EyeLink II device; SR Research Ltd., Mississauga, Ontario, Canada). Each channel was sampled at 250 Hz. The system has a resolution of 0.025°. 
Data Analysis
Calibration factors of each eye were extracted from the saccades recorded during the calibration task. A calibration was run on the vertical and horizontal signals with a linear function to fit the calibration data. From the two individual calibrated horizontal eye position signals, we derived the horizontal conjugate signal (mean of the two horizontal eyes position) and the horizontal disconjugacy signal (left-right eye horizontal position difference); from the vertical eye position signals, we derived the vertical conjugate signal (mean of the two vertical eyes position) and the vertical disconjugacy signal (left-right eye vertical position difference). Examples of saccades from one subject in each condition are shown in Figure 2
The onset of horizontal or vertical saccades was defined as the time when the eye velocity of the conjugate signal exceeded 45°/s; saccade offset was defined as the time when the eye velocity dropped below 10% of the v max. The onset and the offset of the saccades are indicated by i and p in Figure 2 . These criteria are standard and are used in several other studies. 17 23 The automatic placement of the markers by the computer was verified by visual inspection of the individual eye movement traces. The end of the postsaccadic drift, noted f in Figure 2 , was defined at the time at which eye positions are stable, or before a corrective saccade. From these markers, we measured the latency of eye movements and the amplitude of the saccade. We then calculated the change in the alignment of the eyes during the presaccadic period (between TMS and i), the disconjugacy change during the saccade (between i and p), and the disconjugacy change during the postsaccadic drift (between p and f). The change in the alignment of the eyes during the initial fixation directed at the center of the screen was expressed in degrees. The disconjugacy of the saccade and the disconjugate postsaccadic drift was expressed in percentage of the saccade amplitude. This choice takes into account possible modifications of saccade amplitude in the TMS blocks. 
We also measured the percentages of saccade with negative misalignment or disconjugacy. For horizontal saccades, negative misalignment or disconjugacy means a divergent change, whereas positive misalignment or disconjugacy means a convergent change. Similarly, for vertical saccades, negative misalignment or disconjugacy means that the left eye is hypodeviated compared with the right eye, whereas positive misalignment or disconjugacy means that the left eye is hyperdeviated. For instance, during an upward saccade, a negative disconjugacy is observed when the right eye moves up higher than the left eye; during a downward saccade, a negative disconjugacy is observed when the left eye moves down lower than the right eye. 
Saccades in the wrong direction, saccades contaminated by blinks, saccades with latency shorter than 100 ms, and saccades with amplitude below 50% or above 150% of required amplitude were removed from the analysis. In total, 20% of the movements were rejected; the most frequent reason was blinks. 
Measures and Statistical Analysis
One-way repeated-measures ANOVA was applied on the absolute value of the measure of alignment of the eyes during the presaccadic fixation period, to test the effect of TMS. The fixed factor is the TMS condition (no TMS, TMS of the left PPC, TMS of the right PPC), and the random factor is the subject. Least significant difference (LSD) test of Fisher was then used for post hoc two-by-two comparisons. For the absolute value of disconjugacy of saccade and the disconjugate postsaccadic drift, expressed in percentage of the saccade amplitude, the nonparametric Friedman test was used to test the effect of TMS. Post hoc two-by-two comparisons were tested with the Wilcoxon test. The Friedman test was then used for the percentages of saccade with negative misalignment of disconjugacy. All statistical tests were conducted on individual means based on 11 individual trials on average (range, 5–15); 84% of individual means were based on more than eight trials. 
Results
Qualitative Observations
Figures 2B and 2Cpresent typical binocular recording of horizontal and vertical saccades after TMS of the left and of the right PPC, respectively. A perturbation of the alignment of the eyes before the saccade is seen for almost all cases shown (see disconjugacy traces between the TMS and i). In addition, substantial disconjugacy during the saccade (compared with the no-TMS condition; Fig 2A ) can be seen in the traces of individual eye positions and in the disconjugacy trace between i and p, with the major change of disconjugacy occurring during the rightward and downward saccades. 
Binocular Alignment of the Eyes during Presaccadic Fixation
Figure 3presents the group mean (absolute value) of change in the alignment of the eyes during the fixation period preceding horizontal saccades (12 subjects) and vertical saccades (11 subjects). ANOVA showed that TMS caused a significant increase of misalignment during the presaccadic fixation (F 2,22 = 5.14; P < 0.05 for fixation before leftward saccade; F 2,22 = 4.51; P < 0.05 before rightward saccade; F 2,20 = 3.82; P < 0.05 before downward saccade; F 2,20 = 5.74; P < 0.05 before upward saccade). The LSD post hoc Fisher test showed that the increase of misalignment was significant (P < 0.05) for all directions when TMS was applied on the right PPC and for rightward and upward saccades when TMS was applied on the left PPC. 
Horizontal misalignment of the eyes before horizontal saccades could be divergent (negative) or convergent (positive), with a dominance of divergence (see percentages in Fig. 3 ). Vertical misalignment of the eyes before vertical saccades could be negative (left eye hypodeviated compared with the right eye) or positive (left eye hyperdeviated) at similar rates (percentages in Fig. 3 ). These percentages did not statistically change with TMS (Friedman test; all P > 0.05). Separate examinations of positive and negative misalignment confirmed that both positive and negative misalignment increased with TMS of the left or right PPC. 
Disconjugacy of the Saccade
The ANOVA showed that the TMS had no effect on the conjugate saccade amplitude for saccades to left, right, and down. TMS had only a significant effect on upward saccades (F 2,18 = 7.90; P < 0.01). The LSD post hoc Fisher test showed that the amplitude of upward saccades significantly decreased with TMS of the left PPC (from 9.5° ± 1.4° to 8.5° ± 1.3°; P < 0.01). To account for such saccade amplitude changes, saccade disconjugacy was expressed as a percentage of the conjugate amplitude of the saccade. 
Figure 4shows the group mean (absolute value) of disconjugacy, as a percentage of saccade amplitude, during horizontal saccades (12 subjects) and vertical saccades (12 subjects for downward saccades, 10 subjects for upward saccades). The Friedmann test showed that TMS had a significant effect on disconjugacy during rightward saccades (χ2 = 8.17; df = 2; P < 0.05) and downward saccades (χ2 = 8.67; df = 2; P < 0.05). The Wilcoxon test showed that TMS of the right PPC caused a significant increase in disconjugacy during rightward and downward saccades, whereas TMS of the left PPC caused a significant increase in disconjugacy during downward saccades (P < 0.05). Examination of the individual data shows, for leftward or upward saccades, an increase of disconjugacy for many subjects (9 and 7 subjects, respectively), but the change did not reach significance because of intersubject variability. Thus, one can conclude that TMS significantly affected the binocular coordination of rightward and downward saccades. Data are insufficient for conclusions about the other directions. 
The group means disconjugacy in degrees is also shown in Figure 4 . The initial (no TMS) values of disconjugacy is small and compatible with those found in the existing literature, 3 4 5 indicating a fair natural binocular coordination of saccades. The increase of disconjugacy induced by TMS was in the range of the existing natural disconjugacy, approximately 0.2°, but was statistically significant. 
Horizontal natural disconjugacy could be negative or positive—divergent or convergent—with a predominance of divergence. Vertical natural disconjugacy could be negative or positive—with left eye hypodeviated or hyperdeviated—at similar rates. TMS did not influence these percentages (Friedman test; P > 0.05 for all). Separate examinations of positive and negative disconjugacy showed that TMS of the right PPC increased divergent disconjugacy during rightward saccades. During downward saccades, TMS of the right PPC increased negative and positive disconjugacy. During upward saccades, TMS of the left PPC increased positive disconjugacy. 
Postsaccadic Drift Disconjugacy
Figure 5shows the group mean (absolute value) of disconjugacy, in percentage of saccade amplitude, during postsaccadic drift (11 subjects for upward saccades, 12 subjects for the other directions). The Friedman test showed that TMS had no effect on disconjugacy during postsaccadic drift. 
Figure 5also shows the percentage of divergent postsaccadic drift after horizontal saccades or the percentage of postsaccadic drift with the left eye hypodeviated after vertical saccades. After horizontal saccades, the postsaccadic drift was predominately convergent. This propensity to converge compensates the divergent angle induced during the saccade. After vertical saccades, the postsaccadic drift had a slight predominance for positive disconjugacy (with left eye drift more upward than right eye drift). 
Discussion
TMS Disturbs the Static Alignment of the Eyes before Saccades
Elkington et al. 16 observed that stimulation of right or left PPC applied 80 ms after target onset significantly increased divergence before leftward and rightward saccades of 5°. Their study was limited to two subjects. In the present study, the change of the small misalignment of the eyes before the saccade in no-TMS blocks could be divergent (65% on average; range 10%–100%, depending on subject) or convergent. The TMS did not change this ratio. However, we observed that the TMS of the right or left PPC increased the misalignment of the eyes before leftward and rightward saccades. When the TMS was applied to the right PPC, this increase was significant for leftward and rightward saccades, and when the TMS was applied to the left PPC, this increase was significant for rightward saccades. These modifications were caused by increased divergent or convergent misalignment of the eyes. Our results extended the results of Elkington et al., 16 showing that static vergence angle before saccade could become more divergent or more convergent. The examples shown in Figures 2B and 2Cshow that the misalignment of the eyes induced by TMS before saccade was not modified by a slow regular vergence movement. The misalignment consisted of small, irregular oscillations. The TMS of the PPC did not elicit a vergence command but disrupted the normal sustained process of static eye alignment. The fact that the parietal cortex could be involved in keeping the eyes aligned during fixation is also supported by electrophysiologic studies. Recordings in the parietal cortex of monkeys have shown that visual fixation neurons could have a strong selectivity in both the direction and the depth of fixation, even in the dark. 24  
Ramat et al. 25 observed conjugate oscillations (around 30 Hz) after large saccade vergence movements. They attributed these oscillations to the failure of the pause cells. The vergence oscillations we observed were also of high frequency (10–30 Hz). Their amplitude was approximately 0.8° (Figs. 2B 2C) . Conjugate oscillations of smaller amplitude also occurred. Thus, it is possible that the PPC controls the fixation stability in direction and depth, thanks to an interaction with the omnipauser cells in the brain stem through its projection to the superior colliculus. 
Importantly, the TMS also modified the vertical alignment between the eyes before vertical saccades: TMS of the right PPC modified vertical alignment before upward and downward saccades, and TMS of the left PPC modified vertical alignment before upward saccades. These new results extend the observations of Elkington et al. 16 limited to fixation before horizontal saccades and suggest that the PPC actively controls the alignment of the eyes during presaccadic fixation, irrespective of the direction of the upcoming horizontal or vertical saccades. 
TMS Causes Binocular Coordination to Deteriorate during Saccade
Another important result of this study is that binocular coordination during saccades could be modified by TMS of the right or left PPC. TMS of the right PPC caused a significant increase of the disconjugacy during rightward and downward saccades, and TMS of the left PPC caused a significant increase of the disconjugacy during downward saccades. This result clearly argues against interpretations according to which the intrasaccadic transient disconjugacy is entirely a peripheral phenomenon. Indeed, TMS inhibits only the superior layers of the cortex located under the coil. Stimulation could not interfere directly with the muscular activity or with the brain stem saccadic generator activity. 
Given that TMS decreased the conjugate amplitude of upward saccades only and increased the disconjugacy of rightward and downward saccades, we suggest that the change in the disconjugacy of saccade was not mediated by changing the saccade signals; rather, we suggest a central vergence command coupled to the saccade signals. In line with Hering, 2 modification of the binocular coordination of the saccade could have two origins. The first is that the PPC disturbs the hypothetical vergence command before, during, and after the saccade. Indeed, the PPC is implicated in coding saccade and vergence. 15 However, this explanation is probably misleading. Observation of the saccade trajectories and morphologies of changes between the no-TMS and the TMS conditions does not show continuity between the change of the alignment of the eyes before the saccade and the change of disconjugacy during the saccades (see, for instance, the disconjugacy change before and during rightward saccade; Figs. 2A 2C ). Consequently, our results sustain the hypothesis of distinct mechanisms for the two phenomena, the misalignment before the saccade and the disconjugacy of the saccade. The disconjugacy during saccade could be partly attributed to a rapid horizontal or vertical vergence mechanism that could be controlled by the PPC. Such a mechanism would be naturally used to reduce peripheral (muscular and circuitry) asymmetries and to keep the disconjugacy of the saccade small. TMS of the PPC would disturb the magnitude of this initially small command, leading to a more important disconjugacy. Next we will discuss these findings in the context of existing models on saccade–vergence interaction. 
Models of Saccade–Vergence Interaction
Several studies of gaze shift, both in direction and in depth, revealed unequally sized saccades in the two eyes, allowing the vergence angle to be adjusted for depth during the saccade itself. The acceleration of the vergence by the saccade 26 and the slowing of the saccade by the vergence 27 resulted, for some investigators, 5 28 from the interaction between the saccade and the vergence subsystems. Zee et al. 5 supposed in their model that this coupling could be made through the omnipauser neurons (located in the nucleus raphe interpositus), which inhibit the saccadic system and could also partially inhibit the vergence system. More recently, Busettini and Mays 28 proposed a new model in which the acceleration of the vergence by the saccade would result from a multiplicative interaction between the position command driving the saccade system and an estimation of the vergence motor error driving the vergence system. An internal mechanism of feedback would control the movement progression; this feedback is suggested to be a cortico-midbrain-cortical loop. This model is meant to explain mainly saccade–vergence interaction for gaze shift in direction and in depth. The transient disconjugacy of the saccades is still localized at the stage of motor nucleus. Yet the model supposes a cortico-midbrain-cortical loop that could also account for the control of the transient disconjugacy occurring for saccade to targets at a frontoparallel plane. 
Vertical saccades can naturally be of different size when targets are placed laterally at near distance; in such case, because of the inter-ocular distance, the vertical deviation is different for the two eyes. Ygge and Zee 29 suggest the existence of a preprogrammed disconjugacy and a central representation of a three-dimensional map of vertical saccade “yoking.” Such a mechanism could be useful in cases of vertical disparities, naturally occurring for objects aligned vertically and closer to one eye, which are frequent in everyday life. Such a mechanism would exist for all saccades, including saccades along the midsagittal plane. A smaller “vertical vergence” could be learned and programmed to occur during every vertical saccade. The modification by the TMS of the vertical saccade disconjugacy during vertical saccades could reflect a modification of this vertical vergence command. 
The PPC could be a cortical area implicated in the elaboration of vertical and horizontal fast vergence signals used to control intrasaccadic disconjugacy. Indeed, neurons in monkey parietal area LIP are thought to encode in three-dimensional space the premotor signal for directing gaze. 15 Control of the binocular coordination of saccades by the PPC could have been modified by TMS. We thus conclude that there is a cortical intervention in the binocular coordination of horizontal and vertical saccades. This intervention is useful in everyday life, where pure saccades rarely occur. Most eye movements are a combination of saccades and vergence. Small, horizontal, transient disconjugacy during saccades could be a preparation for the most frequent movements, as suggested by Collewijn et al. 3 Similarly, for vertical saccades, the mild vertical misalignment could be reminiscent of naturally required disconjugacy when vertical targets are at near and are laterally placed. 
Binocular coordination of horizontal saccades and, to less extent, of vertical saccades were found to be rapidly modified in an adaptive way. 9 10 11 12 29 The speed of such adaptation could be explained by the fact that adaptation uses naturally existing mechanisms of saccade-vergence interaction, subtending the quality of the binocular coordination of saccade. The influence of PPC on the natural disconjugacy clearly supports the hypothesis of a disconjugacy partly controlled by the cortex. 
We suggest that the horizontal or vertical transient disconjugacy is the manifestation of a “deliberate” binocular error signal of depth. This signal would be learned, allowing motor and sensory plasticity throughout life. This is consistent with the necessity of learning and adaptation for binocular coordination, suggested by Helmoltz. 1 Our results indicate a cortical control of binocular coordination, compatible with the models of Busettini and Mays 28 and in line with Hering’s 2 ideas for the existence of two distinct systems of conjugate saccades and divergence, both obeying on the law of equal innervation. Existing models should be extended to consider saccade–vergence interaction as a permanent control mechanism that even occurs during saccade to frontoparallel plane. The model suggested by Zhou and King 30 sets learning mechanisms downstream, at the level of oculomotor nuclei. This was not compatible with the evidence provided here for a cortical influence of the PPC. 
 
Figure 1.
 
Experimental design. (A) Spatial arrangement: black computer screen, 57 cm from the subject, with 5 white dots (1 central, 4 at ± 10° horizontally and vertically). (B) Temporal arrangement. The gap (time between fixation offset and target onset) lasted 200 ms. TMS was applied 100 ms after target onset.
Figure 1.
 
Experimental design. (A) Spatial arrangement: black computer screen, 57 cm from the subject, with 5 white dots (1 central, 4 at ± 10° horizontally and vertically). (B) Temporal arrangement. The gap (time between fixation offset and target onset) lasted 200 ms. TMS was applied 100 ms after target onset.
Figure 2.
 
Sample traces during saccades toward each direction for the no TMS condition (A), left PPC stimulation (B), and right PPC stimulation (C). First line: left eye (L) and right eye (R) horizontal positions (for left and right saccades) or vertical positions (for down and up saccades) positions. Second line: horizontal (for left and right) or vertical (for down and up) conjugate components. Third line: horizontal (for left and right) or vertical (for down and up) disconjugacy components (left-right eye position differences). The target appears at time 0. TMS is applied at 100 ms (placebo stimulation for A and real stimulation for B and C). i, p, and f indicate, respectively, the initiation of the saccade, the end of the saccade, and the end of the postsaccadic drift.
Figure 2.
 
Sample traces during saccades toward each direction for the no TMS condition (A), left PPC stimulation (B), and right PPC stimulation (C). First line: left eye (L) and right eye (R) horizontal positions (for left and right saccades) or vertical positions (for down and up saccades) positions. Second line: horizontal (for left and right) or vertical (for down and up) conjugate components. Third line: horizontal (for left and right) or vertical (for down and up) disconjugacy components (left-right eye position differences). The target appears at time 0. TMS is applied at 100 ms (placebo stimulation for A and real stimulation for B and C). i, p, and f indicate, respectively, the initiation of the saccade, the end of the saccade, and the end of the postsaccadic drift.
Figure 3.
 
Group means and standard errors of the change of the horizontal (for left and right) or vertical (for down and up) alignment of the eyes (absolute value of left-right eye position difference, in degrees) during presaccadic fixation, between the time of TMS application and the initiation of the saccades. Asterisks: significant differences between TMS of the left and right PPC conditions and the no TMS condition. Mean percentage of divergent misalignment of the eyes before horizontal saccades or negative misalignment (with left eye hypodeviated) before vertical saccades is indicated above the bars.
Figure 3.
 
Group means and standard errors of the change of the horizontal (for left and right) or vertical (for down and up) alignment of the eyes (absolute value of left-right eye position difference, in degrees) during presaccadic fixation, between the time of TMS application and the initiation of the saccades. Asterisks: significant differences between TMS of the left and right PPC conditions and the no TMS condition. Mean percentage of divergent misalignment of the eyes before horizontal saccades or negative misalignment (with left eye hypodeviated) before vertical saccades is indicated above the bars.
Figure 4.
 
Group means and standard errors of horizontal or vertical disconjugacy (absolute value in percentage of saccade amplitude; correspondence in degrees indicated inside the group mean bars) during horizontal or vertical saccades. Asterisks: significant differences between TMS of the left and right PPC conditions and the no TMS condition. The percentage of divergent disconjugacy during horizontal saccades or negative disconjugacy (with left eye hypodeviated) during vertical saccades is indicated above the bars.
Figure 4.
 
Group means and standard errors of horizontal or vertical disconjugacy (absolute value in percentage of saccade amplitude; correspondence in degrees indicated inside the group mean bars) during horizontal or vertical saccades. Asterisks: significant differences between TMS of the left and right PPC conditions and the no TMS condition. The percentage of divergent disconjugacy during horizontal saccades or negative disconjugacy (with left eye hypodeviated) during vertical saccades is indicated above the bars.
Figure 5.
 
Group means and standard errors of horizontal or vertical disconjugacy (absolute value in percentage of saccade amplitude; correspondence in degrees indicated inside the group mean bars) during the postsaccadic drift after a saccade. The percentage of divergent disconjugacy after horizontal saccades or negative disconjugacy (with left eye hypodeviated) after vertical saccades is indicated above the bars.
Figure 5.
 
Group means and standard errors of horizontal or vertical disconjugacy (absolute value in percentage of saccade amplitude; correspondence in degrees indicated inside the group mean bars) during the postsaccadic drift after a saccade. The percentage of divergent disconjugacy after horizontal saccades or negative disconjugacy (with left eye hypodeviated) after vertical saccades is indicated above the bars.
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Figure 1.
 
Experimental design. (A) Spatial arrangement: black computer screen, 57 cm from the subject, with 5 white dots (1 central, 4 at ± 10° horizontally and vertically). (B) Temporal arrangement. The gap (time between fixation offset and target onset) lasted 200 ms. TMS was applied 100 ms after target onset.
Figure 1.
 
Experimental design. (A) Spatial arrangement: black computer screen, 57 cm from the subject, with 5 white dots (1 central, 4 at ± 10° horizontally and vertically). (B) Temporal arrangement. The gap (time between fixation offset and target onset) lasted 200 ms. TMS was applied 100 ms after target onset.
Figure 2.
 
Sample traces during saccades toward each direction for the no TMS condition (A), left PPC stimulation (B), and right PPC stimulation (C). First line: left eye (L) and right eye (R) horizontal positions (for left and right saccades) or vertical positions (for down and up saccades) positions. Second line: horizontal (for left and right) or vertical (for down and up) conjugate components. Third line: horizontal (for left and right) or vertical (for down and up) disconjugacy components (left-right eye position differences). The target appears at time 0. TMS is applied at 100 ms (placebo stimulation for A and real stimulation for B and C). i, p, and f indicate, respectively, the initiation of the saccade, the end of the saccade, and the end of the postsaccadic drift.
Figure 2.
 
Sample traces during saccades toward each direction for the no TMS condition (A), left PPC stimulation (B), and right PPC stimulation (C). First line: left eye (L) and right eye (R) horizontal positions (for left and right saccades) or vertical positions (for down and up saccades) positions. Second line: horizontal (for left and right) or vertical (for down and up) conjugate components. Third line: horizontal (for left and right) or vertical (for down and up) disconjugacy components (left-right eye position differences). The target appears at time 0. TMS is applied at 100 ms (placebo stimulation for A and real stimulation for B and C). i, p, and f indicate, respectively, the initiation of the saccade, the end of the saccade, and the end of the postsaccadic drift.
Figure 3.
 
Group means and standard errors of the change of the horizontal (for left and right) or vertical (for down and up) alignment of the eyes (absolute value of left-right eye position difference, in degrees) during presaccadic fixation, between the time of TMS application and the initiation of the saccades. Asterisks: significant differences between TMS of the left and right PPC conditions and the no TMS condition. Mean percentage of divergent misalignment of the eyes before horizontal saccades or negative misalignment (with left eye hypodeviated) before vertical saccades is indicated above the bars.
Figure 3.
 
Group means and standard errors of the change of the horizontal (for left and right) or vertical (for down and up) alignment of the eyes (absolute value of left-right eye position difference, in degrees) during presaccadic fixation, between the time of TMS application and the initiation of the saccades. Asterisks: significant differences between TMS of the left and right PPC conditions and the no TMS condition. Mean percentage of divergent misalignment of the eyes before horizontal saccades or negative misalignment (with left eye hypodeviated) before vertical saccades is indicated above the bars.
Figure 4.
 
Group means and standard errors of horizontal or vertical disconjugacy (absolute value in percentage of saccade amplitude; correspondence in degrees indicated inside the group mean bars) during horizontal or vertical saccades. Asterisks: significant differences between TMS of the left and right PPC conditions and the no TMS condition. The percentage of divergent disconjugacy during horizontal saccades or negative disconjugacy (with left eye hypodeviated) during vertical saccades is indicated above the bars.
Figure 4.
 
Group means and standard errors of horizontal or vertical disconjugacy (absolute value in percentage of saccade amplitude; correspondence in degrees indicated inside the group mean bars) during horizontal or vertical saccades. Asterisks: significant differences between TMS of the left and right PPC conditions and the no TMS condition. The percentage of divergent disconjugacy during horizontal saccades or negative disconjugacy (with left eye hypodeviated) during vertical saccades is indicated above the bars.
Figure 5.
 
Group means and standard errors of horizontal or vertical disconjugacy (absolute value in percentage of saccade amplitude; correspondence in degrees indicated inside the group mean bars) during the postsaccadic drift after a saccade. The percentage of divergent disconjugacy after horizontal saccades or negative disconjugacy (with left eye hypodeviated) after vertical saccades is indicated above the bars.
Figure 5.
 
Group means and standard errors of horizontal or vertical disconjugacy (absolute value in percentage of saccade amplitude; correspondence in degrees indicated inside the group mean bars) during the postsaccadic drift after a saccade. The percentage of divergent disconjugacy after horizontal saccades or negative disconjugacy (with left eye hypodeviated) after vertical saccades is indicated above the bars.
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