New Mechanism That Accounts for Position Sensitivity of Saccades Evoked in Response to Stimulation of Superior Colliculus

A. K. Moschovakis1, 2, Y. Dalezios1, 2, J. Petit3, and A. A. Grantyn3

1 Institute of Applied and Computational Mathematics, Foundation for Research and Technology, Hellas; and 2 Department of Basic Sciences, Faculty of Medicine, University of Crete, Crete, Greece; and 3 Laboratoire de Physiologie de la Perception et de l'Action, Centre National de la Recherche Scientifique-College de France, Paris, France

    ABSTRACT
Abstract
Introduction
Methods
Results
Discussion
References

Moschovakis, A. K., Y. Dalezios, J. Petit, and A. A. Grantyn. New mechanism that accounts for position sensitivity of saccades evoked in response to stimulation of superior colliculus. J. Neurophysiol. 80: 3373-3379, 1998. Electrical stimulation of the feline superior colliculus (SC) is known to evoke saccades whose size depends on the site stimulated (the "characteristic vector" of evoked saccades) and the initial position of the eyes. Similar stimuli were recently shown to produce slow drifts that are presumably caused by relatively direct projections of the SC onto extraocular motoneurons. Both slow and fast evoked eye movements are similarly affected by the initial position of the eyes, despite their dissimilar metrics, kinematics, and anatomic substrates. We tested the hypothesis that the position sensitivity of evoked saccades is due to the superposition of largely position-invariant saccades and position-dependent slow drifts. We show that such a mechanism can account for the fact that the position sensitivity of evoked saccades increases together with the size of their characteristic vector. Consistent with it, the position sensitivity of saccades drops considerably when the contribution of slow drifts is minimal as, for example, when there is no overlap between evoked saccades and short-duration trains of high-frequency stimuli.

    INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References

Electrical stimulation of the superior colliculus (SC) was long known to generate saccades. Early experiments in the monkey emphasized the fact that the size and direction of evoked saccades depend on the site stimulated so that the rostral SC causes small saccades, the caudal large saccades, the medial upward saccades, and the lateral downward saccades (Robinson 1972). Otherwise, saccade metrics were not thought to depend on parameters of stimulation (e.g., intensity, frequency, and duration) or on the initial position of the eyes (Robinson 1972; Schiller and Stryker 1972). In contrast, electrical stimulation of the feline SC (Guitton et al. 1980; McIlwain 1986, 1990; Straschill and Rieger 1973) and more recently of the caudal primate SC (Cowie and Robinson 1994; Freedman et al. 1996; Segraves and Goldberg 1992) has shown that the size of evoked saccades depends on the initial position of the eyes. This phenomenon attracted considerable attention over the past 20 years, and several mechanisms were proposed to account for it. These are presented in the DISCUSSION, and their relative merits are discussed. Whatever else can be said for or against them, they do not explain why the position sensitivity of evoked saccades is stronger for saccades evoked from caudal SC sites and weaker or absent for saccades evoked from rostral SC sites (McIlwain 1990). Because the rostral SC encodes small saccades while the caudal SC encodes large saccades it is reasonable to expect that the position sensitivity of saccades is correlated with their size. The existence of such a relationship was documented for the SC in the cat (Grantyn et al. 1996) and the monkey (Azuma et al. 1996) and for the frontal and supplementary eye fields in the monkey (Russo and Bruce 1993).

Besides saccades, electrical stimulation of the SC was recently shown to evoke slow movements in both the cat (Grantyn et al. 1996; Missal et al. 1996) and the monkey (Breznen et al. 1996). In the cat, induced slow drifts follow saccades and last until the end of the stimulation. Their size depends on the frequency of the electrical stimulation, and it was argued that they might be due to SC projections that bypass the burst generator of the oculomotor system (Grantyn et al. 1996). Despite their dissimilar kinematics and presumably different anatomic substrates, the metrics of slow drifts and saccades are similarly affected by the initial position of the eyes, and their position sensitivity is similarly correlated with the size of their characteristic vectors. Conceivably, a single mechanism could account for the position sensitivity of both. Here we hypothesize that the position sensitivity of saccades may be due to position-sensitive slow drifts superimposed onto position invariant saccades. We then describe experiments that were performed to test this "superposition hypothesis" and demonstrate that such a mechanism can account for the correlation between the size and the position sensitivity of evoked saccades.

    METHODS
Abstract
Introduction
Methods
Results
Discussion
References

Data were obtained from 10 adult cats weighing 3-4 kg, surgically prepared for electrical recording and stimulation as described elsewhere (Grantyn et al. 1996). Briefly, stainless steel bolts were cemented onto the frontal and temporal bones for painless head fixation, and a search coil consisting of three loops of Teflon insulated stainless steel wire was wound under the insertions of the extraocular muscles under pentobarbital anesthesia (30 mg/kg) and sterile conditions. After craniotomy, a plastic chamber (~1 cm diam) was cemented onto the bone at stereotaxic coordinates appropriate for the lowering of vertically oriented electrodes into the SC. In between experimental sessions, the chamber was filled with a gel containing dexamethasone and antibiotic (neomycine) and closed with a cap. Experiments started >= 1 wk postoperatively. Body movements were restrained with a cloth bag, and the head was fixed to the stereotaxic frame by means of the implanted bolts. Instantaneous horizontal and vertical eye position was recorded with the search coil method. Protocols were consistent with European Union directive 86/609 and were approved by an ethics committee.

During recording sessions, the animals faced a featureless screen in a dimly illuminated room. We used noises and spots of light to make them look in all directions so that saccades evoked from each stimulus site would start from initial positions throughout the oculomotor range. Cats did not receive any reward for gaze shifts toward these transiently presented visual or auditory stimuli, which therefore did not serve as targets for attentive fixation. Still they were efficient enough to keep the animals alert. Periods of reduced alertness were reliably identified by instability of eye position and the presence of slow pendular eye movements. Saccades elicited during such periods were excluded from analysis. For each animal, the gain was calibrated by rotating the field coils around the vertical and horizontal axes with excursions of ±5°, and the straight ahead eye position was calibrated by averaging samples of instantaneous eye position obtained while the animal was tracking an object that moved vertically in the midsagittal plane by a computer-controlled mechanical device (horizontal zero) or horizontally on a plane passing through the center of its eyes (vertical zero). Stereotaxic technique was used to lower electrodes toward the SC. Glass-insulated tungsten electrodes were used for stimulation. The uninsulated portion of the tungsten wire was etched to a tip diameter of ~5 µm and had a length of ~100 µm. In some experiments stimulation was applied through micropipettes filled with a 2-M solution of NaCl. These electrodes were part of arrays bearing a pipette for pressure injection of biocytin at the stimulation site. To minimize damage to the SC, only one or, exceptionally, two tracks were run in each colliculus. Because the results of anatomic tracing are not the subject of this report, the reader is referred to our earlier description of the injection technique and of histological procedures (Grantyn et al. 1996). Suffice it to say that local labeling by biocytin ensured the exact determination of the location of stimulation sites. At the end of experiments, the animals were euthanized by an overdose of pentobarbital and perfused transcardially with saline followed by a solution of fixative. Tissue blocks were cut serially on a freezing microtome and processed with standard histochemical procedures to visualize biocytin.

Stimuli used to activate the SC were trains of monopolar pulses (0.4-ms pulse duration). Because evoked saccade metrics depend on the set of stimulation parameters, these were the same in all experiments. Current intensity was equal to 2 times threshold (20-50 µA), and unless indicated otherwise stimulus trains consisted in 70 pulses, and the intervals between these were equal to 5 ms (frequency 200 Hz). The instantaneous position of the animals' eyes was sampled at a rate of 500 Hz and analyzed off-line with the help of a microcomputer running the Spike2 piece of software (Cambridge Electronic Design, Cambridge, UK). Eye velocity was calculated off-line through software differentiation of the position trace; the digital filter cutoff frequency was 70 Hz. To analyze saccades, we marked their onset and offset as well as the onset and offset of the stimulus trains with the help of cross-hairs. There was seldom any ambiguity as to when saccades started or stopped as these points corresponded to sharp inflections on the eye position traces. In ambiguous cases, the end of the saccade was marked from the sharp inflection on the eye velocity trace. The computer then stored the horizontal and vertical eye position at the beginning (H1, V1) and at the end (H2, V2) of saccades, saccade latency (L), saccade duration (Sd), horizontal (h) and vertical (v) eye displacement as well as horizontal (&Hdot;max) and vertical (Vmax) peak eye velocity. Linear regressions between h and Sd were used to determine the intercept and slope of the main sequence relationship of evoked saccades (Evinger and Fuchs 1978; Olivier et al. 1993; Straschill and Rieger 1973). Evoked saccades with latencies >100 ms were excluded from analysis. We also excluded the second or third saccade in staircases of evoked saccades.

    RESULTS
Abstract
Introduction
Methods
Results
Discussion
References

Figure 1A provides examples of eye movements evoked in response to identical stimuli (current intensity: 2 × T; frequency: 200 Hz; number of pulses: 70; train duration: 350 ms) applied to a single site in the intermediate layers of the left SC. As shown here, the horizontal component of evoked saccades can be small or large, depending on the initial horizontal position of the eyes. Figure 1B is a plot of the size of the horizontal component of saccades (Delta H) evoked in response to similar stimulation of a different site in the right SC as a function of initial horizontal eye position (H1). The solid line is the linear regression line through the data and obeys the expression
Δ<IT>H = S<SUB>H</SUB>+ k<SUB>H</SUB>H</IT><SUB>1</SUB> (1)
The intercept SH is the horizontal component of the "characteristic" vector of evoked saccades (McIlwain 1988b). It is a constant equal to the horizontal component of the saccades (-7.2° in the case of Fig. 1B) that would have been produced had the eyes started to move from the primary position. The coefficient kH provides a measure of the influence exerted by the initial position of the eyes on the size of the movement. Values close to -1 are indicative of extreme position sensitivity. A line of this slope would describe the relationship between Delta H and H1, were the eyes to end at the same position from any point of departure ("goal-directed" movements). On the other hand, values of kH close to 0 indicate that elicited movements are not sensitive to the initial position of the eyes and that evoked saccades are always of the same size ("fixed vector" movements). In the example of Fig. 1B it is equal to -0.52, i.e., it has a value intermediate between the two extremes above.


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FIG. 1. A: examples of eye movements evoked in response to the electrical stimulation of a single site in the left superior colliculus (SC) with identical stimulus parameters (70 pulses at 2 × T). Dashed lines indicate 0 horizontal eye position. Boxes on the time axis indicates the onset and duration of stimulus trains. The presence of slow drifts is indicated by arrows. B: plot of initial horizontal eye position (abscissa) vs. horizontal eye displacement (ordinate) of saccades evoked in response to the electrical stimulation of the SC. The solid line is the least-squares regression line through the data and obeys the equation displayed. C: plot of the horizontal position sensitivity (kH) of saccades evoked in response to stimulation of the feline SC (at 2 × T) against the horizontal component of their characteristic vectors (SH). Each solid circle is from a different stimulation site and often from a different animal. The solid line is the least-squares regression line through the data and obeys the equation displayed. Saccades evoked from the right SC were reflected to appear positive (rightward).

Saccades evoked from 20 collicular sites in response to the same stimulus parameters were analyzed in the same manner. The correlation coefficients of the regression analyses ranged between 0.66 and 0.99 (mean ± SD: 0.88 ± 0.08). Their slopes (horizontal position sensitivity) are plotted against their intercepts (size of the horizontal component of their characteristic vectors) in Fig. 1C. Clearly, saccades with small characteristic vectors (as small as 1°) had a small position sensitivity (approximately -0.4). On the other hand, saccades with large characteristic vectors (as great as 14°) had a substantial position sensitivity (approximately -0.7). In between these two extremes, the position sensitivity of evoked saccades increased together with the size of characteristic vectors. The correlation coefficient of the regression line fit to this data is equal to 0.59 and is statistically significant (analysis of variance, F = 9.4, P = 0.007). Although, in this and the following paragraphs we focus on horizontal components of saccades, a similar relationship was described for the vertical components of saccades (Grantyn et al. 1996).

Besides saccades, electrical stimulation of the feline SC evokes slow drifts (Fig. 1A, arrowheads). The metrics of slow drifts are as sensitive to the initial position of the eyes as those of saccades, but unlike saccades their size depends on the duration and the frequency of stimulation, and their time course can be fit with exponential curves whose time constant is roughly equal to the time constant of the oculomotor plant (Grantyn et al. 1996). Accordingly, these authors suggested that evoked slow drifts are due to the activation of oligosynaptic projections of the SC onto extraocular motoneurons, which may involve the neural integrator but need not involve the saccadic burst generator of the oculomotor system. Because of these projections, high-frequency, long-duration SC stimulation (such as the one employed in this and other studies) would force motoneurons to discharge at a high rate for the duration of the stimulation. Because of the good correlation between motoneuron firing rate and eye position (Robinson 1970), the eyes would tend to move to the same position in the orbit (E) whatever their point of departure (E1). Because the magnitude of eye displacement (E - E1) would in this case depend on the initial position of the eyes (E1), a mechanism such as this would account for the position sensitivity of slow drifts evoked from the SC. How could this explain the position sensitivity of evoked saccades?

To answer this, suppose that the unknown variables that affect saccade latency also affect drift latency so that statistical distributions of saccade and drift latencies are similar and largely overlapping. If this were the case, some of the eye displacement during evoked saccades would be due to superimposed slow drifts as diagrammatically illustrated in Fig. 2A (stippled). As shown here, the total displacement of the eyes (SH + G) is equal to a slow drift displacement (G) added onto the saccadic displacement (SH). Would the position sensitivity of the slow drift account for the position sensitivity of the evoked movement even if the saccadic displacement were position invariant (equal to the "fixed vector" SH)? Although there is no a priori reason why this should be so, the following considerations suggest an affirmative answer. To simplify the argument, we present an evaluation of the size of G' (Fig. 2A) from the linear approximation (thin solid line) to the slow drift (stippled) for the case where saccade latencies and drift latencies are approximately the same. First, consider that, if the eye started from position E1 and executed just the slow drift, its excursion would be such as to reach position E within a period of time roughly equal to three times the time constant of the drift (tau ). From the linear approximation of Fig. 2A, it follows that
<IT>G</IT>′/<IT>S<SUB>d</SUB></IT>= (<IT>E − E</IT><SUB>1</SUB>)/3τ (2)
From the slope of the main sequence curve (beta ), the duration of the saccade (Sd) can be expressed as beta ·SH. Substituting and rearranging one obtains
<IT>G</IT>′ = (<IT>E − E</IT><SUB>1</SUB>)⋅β⋅<IT>S</IT><SUB><IT>H</IT></SUB>/3τ = <IT>E</IT>⋅β⋅<IT>S</IT><SUB><IT>H</IT></SUB>/3τ − <IT>E</IT><SUB>1</SUB>⋅β⋅<IT>S</IT><SUB><IT>H</IT></SUB>/3τ (3)
Because we assumed that, in the absence of a saccade, drifts would move the eyes always to the same position in the orbit (E), the first term on the right-hand side of this expression is a constant. The second term is equal to the initial position of the eyes (E1) weighed by a coefficient of proportionality (-beta ·SH/3tau ), which describes the position sensitivity of the movements (as does kH in Eq. 1). That SH is in the numerator explains why the position sensitivity of evoked saccades increases together with the size of their characteristic vector.


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FIG. 2. Typical eye movement evoked in response to the electrical stimulation of the SC (thick solid line) and a theoretical slow drift (stippled line) that starts from the same position and is superimposed on the rapid movement. E1, initial eye position; E2, eye position at the end of the saccade; E, final eye position to be reached by slow drifts of long duration in the absence of a saccade; G, contribution of the slow drift to saccade size; G', linear approximation to slow drift displacement; Sd, saccade duration; tau , time constant of the drift. B: plot of the experimentally determined (solid circles) and theoretically estimated (open circles) values of the horizontal position sensitivity of saccades against the horizontal component of the characteristic vectors of evoked saccades. Solid lines were produced from the equation displayed and for the extreme values of D, beta , and tau  encountered in our experiments (indicated on the plot). The dashed region corresponds to curves that would be obtained with intermediate values of D, beta , and tau . Inset: frequency histogram of the difference (abscissa) between the coefficients of saccadic position sensitivity, experimentally determined and theoretically estimated for each SC site (number of sites; ordinate). C: plots of initial horizontal eye position (H1; abscissa) vs. horizontal eye displacement (Delta H; ordinate) of rapid eye movements produced in response to short, high-frequency stimulation of the SC. Movements with latencies shorter than (solid circles) and longer than (open circles) the duration of the stimulus train are plotted separately. The solid lines are the least-squares regression lines through the data and obey the equations displayed.

It should be noted that in the schematic drawing of Fig. 2A we assumed that the onset of the evoked saccade coincides with that of the drift. It can be shown that differences in timing of the two events would not compromise the validity of Eq. 3. To give an example, a delay of drift onset equal to 10 ms relative to saccade onset reduces the position sensitivity of saccades only by 0.03 (10/300 after substituting in Eq. 3) for drifts that have a time constant equal to 100 ms. Also, the position sensitivity of evoked movements estimated from an exact evaluation of the size of G that takes into consideration the exponential time course of drifts follows the somewhat more complex formula (derived in the APPENDIX )
<IT>k<SUB>H</SUB></IT>= −[1 − <IT>e</IT><SUP>−(<IT>D</IT>+β<IT>S<SUB>H</SUB></IT>)/τ</SUP> (4)
where D is the intercept of the main sequence curve, beta  its slope, and tau  the time constant of the drift. Curves obeying this expression are illustrated in Fig. 2B (solid lines) for extreme values of tau , D, and beta  that were determined experimentally, after plotting the duration of the horizontal components of evoked saccades against their size. Roughly similar values of D and beta  were reported before for both natural (D = 20 ms, beta  = 2.5-5.2 ms/deg) (Evinger and Fuchs 1978) (beta  = 3.7-5.2 ms/deg) (Olivier et al. 1993) and evoked (D = 40 ms, beta  = 3.2 ms/deg) (Straschill and Rieger 1973) saccades. The values of tau  were also experimentally determined from exponential curve fits of the drifts we observed in our experiments. The shaded area between the two curves is occupied by curves that apply to intermediate values of tau , D, and beta . As shown in Fig. 2B, this area covers the values of kH versus SH for saccades evoked from all the SC sites we explored (solid circles), thus demonstrating that such a family of curves can account for the position sensitivity of evoked saccades and its relationship with the size of their characteristic vectors.

Because the amplitude and position sensitivity of drifts depend on the site stimulated, it is important to show that it is the drifts evoked from a particular site that account for the position sensitivity of the saccades evoked from the same site. To this end, we used a least-squares exponential curve fitting algorithm to evaluate the time constant of 10-20 randomly selected drifts evoked from each one of the stimulated SC sites. We then used these values to reconstruct the portions of drifts temporally overlapping saccades. To estimate the position sensitivity of saccades for each one of the sites stimulated we used Eq. 4, thus assuming that the superimposed slow drifts endow saccades with the position sensitivity they display. To obtain this theoretical estimate, we replaced SH with the characteristic vector of the saccades evoked from that site, D and beta  with the values experimentally determined from the main sequence curve of the cat in which the site was stimulated, and tau  with the average time constant of the drifts evoked from the same site. Such theoretical estimates of saccadic position sensitivities are plotted as open circles in Fig. 2B. The inset in Fig. 2B is a histogram of the difference between the experimentally determined and the theoretically estimated values of saccadic position sensitivity, both for the same SC site. As shown here, differences can be greater (experimental values higher than the estimated values) or smaller (experimental values lower than the estimated values) than zero and are generally small (<0.2). The average difference between the experimentally determined and the estimated saccadic position sensitivities is -0.04, a value that does not differ significantly from zero (t-test, t = -1.42, P = 0.17).

To directly test the hypothesis that the position sensitivity of evoked saccades is due to the superposition of largely position-invariant saccades and position-dependent slow drifts, we would need to study the position sensitivity of evoked saccades after abolishing evoked slow drifts. This is not feasible, given the anatomy of SC projections to the brain stem (see DISCUSSION). Instead, we used high-frequency (300 Hz) short-duration (15 pulses) trains to take advantage of the fact that their duration (47 ms) could be smaller than the latency of some evoked saccades. We then separated saccades into those that overlapped the stimulus train (saccades whose latency was <47 ms) and those that did not (saccades whose latency was >47 ms). We predicted that, in the latter case, the contribution of the slow drifts to saccades would be substantially smaller and that this should reduce both the size of the characteristic vector and the position sensitivity of evoked saccades. This was indeed the case. As shown in Fig. 2C, the position sensitivity of saccades is equal to 0.33 when they overlap with the stimulus train (solid circles), but it drops to 0.15 when saccades evoked from the same site and in response to an identical stimulus do not overlap with it (open circles).

It might be argued that the drop of the position sensitivity is due to the small size of the possibly truncated saccades that are evoked by stimuli of such short duration (McIlwain 1990; Paré et al. 1994). To examine whether this is the case, we compared the position sensitivity of saccades evoked in response to short and long trains of pulses after matching the two groups so that the size of their characteristic vectors was indistinguishable. The characteristic vectors of saccades evoked from 14 SC sites in response to high-frequency/short-duration stimulation ranged between 1.6 and 5.3° (2.9° ± 0.99; mean ± SD). To match these, we selected 16 SC sites that evoked saccades in response to low frequency/long duration stimulation with characteristic vectors ranging between 0.7 and 5.2° (2.9° ± 1.75). Despite the fact that the characteristic vectors of the two groups did not differ (unpaired t-test, t = 0.056, df = 28), the position sensitivity of saccades evoked in response to long duration pulse trains (0.48 ± 0.11) was significantly higher (t = 10, P < 0.0001) than the position sensitivity of saccades evoked in response to short-duration pulse trains (0.15 ± 0.06).

    DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References

Several previously proposed mechanisms attempted to account for the position sensitivity of saccades electrically evoked from the SC. The first one is the "goal hypothesis," which assumes that it is the final postsaccadic position of the eyes in the orbit (a "goal") that is place coded in the SC (Straschill and Rieger 1973) instead of an eye displacement of constant amplitude and direction (a fixed vector). These authors did not propose any theoretical explanation as to how the retinotopic visual input could be transformed into postsaccadic eye position corresponding to a goal. McIlwain (1988a) attempted to provide such an explanation by assuming that the SC implements a saccadic controller, the front stage of which adds an eye position signal (E1) onto the place coded retinal error signal (re). Thus, the output of the controller is equal to the desired postsaccadic position of the eyes (E2) in the orbit. McIlwain suggested that an electrical stimulus applied to the SC reproduces the re signal but also interferes with the gain factor (g) of the E1 signal so that it becomes smaller than unity (0 < g < 1). The desired eye displacement command (Delta E) exiting the burst generator will be equal to re gE1 - E1. The subtraction of E1 occurs at a later stage and is dictated by the fact that Delta E = E2 - E1. After rearranging the expression of the previous sentence one obtains Delta E = re - (1 - gE1. This expression is the same as Eq. 1 if one substitutes re by SH and -(1 - g) by kH. The goal hypothesis would therefore formally account for the position sensitivity of evoked saccades. Unfortunately, the saccadic controller it employs is not supported by experimental data (discussed in Moschovakis 1996a,b; Moschovakis and Highstein 1994; Moschovakis et al. 1996).

A second hypothesis ("gaze hypothesis") assumes that the SC encodes gaze displacements, i.e., the sum of eye and head displacements (Freedman et al. 1996; Guitton et al. 1980; Paré et al. 1994). It is thought that such commands are decomposed downstream from the SC into separate commands to eye and head controllers in such a way that the contribution of the eye movement decreases while the contribution of the head movement increases when initial eye position shifts in the direction of the desired movement. When the head is immobilized, stimulus-evoked gaze shifts are now accomplished by the eyes alone; these decrease in amplitude in proportion to the contribution of the head displacement that would be observed in the head-free condition. This explains why head-fixed evoked saccades are sensitive to initial eye position as well as why head-free evoked gaze shifts are not (Freedman et al. 1996; Paré et al. 1994). Although this is a plausible explanation of the position sensitivity of evoked saccades, the gaze hypothesis has certain limitations. For example, it cannot account for the position sensitivity of saccades evoked in response to the electrical stimulation of several brain regions (striate cortex, frontal eye field, and supplementary eye field) in head-fixed animals (reviewed in McIlwain 1988a; Russo and Bruce 1993; Schlag and Schlag-Rey 1987) because stimulation of the same regions does not evoke head movements in head-free animals. Further, the neural mechanisms underlying the decomposition of collicular gaze displacement commands into eye- and head-related components were not explored. Finally, it remains to be seen whether the gaze hypothesis can account for two phenomena analyzed in this report. These are, first, the positive correlation between the size of the characteristic vector and the position sensitivity of evoked saccades and, second, the decrement of position sensitivity of saccades evoked in response to stimulus trains that do not temporally overlap with the saccades.

A third mechanism alludes to a missing signal of possible cerebellar origin ("cerebellar hypothesis") (Russo and Bruce 1993; Segraves and Goldberg 1992). This hypothesis assumes that during saccades the cerebellum compensates for position-dependent orbital nonlinearities. It further assumes that electrical stimulation of the SC evokes saccades without engaging the cerebellum. As a consequence, orbital nonlinearities would remain uncompensated during electrically evoked saccades, and thus saccade size would depend on the initial position of the eyes (Russo and Bruce 1993; Segraves and Goldberg 1992). However, it is not clear whether the cerebellar hypothesis can explain the correlation between the size of the characteristic vector and the position sensitivity of electrically evoked saccades, nor is it clear that it can explain why the position sensitivity of saccades drops considerably when they do not overlap with the stimulus train used to evoke them.

The fourth mechanism is the herein proposed "superposition hypothesis." It rests on the assumption that position-sensitive slow drifts temporally overlap position-invariant saccades. This assumption is reasonable considering that position sensitive slow drifts have been shown to follow most of the saccades that are electrically evoked from the SC (Grantyn et al. 1996). It further rests on the assumption that slow drifts evoked from the SC are due to anatomic projections that bypass the burst generator. This is consistent with the fact that their size depends on the frequency of stimulation while their time course is reminiscent of the expected step response of the feline oculomotor plant (Grantyn et al. 1996). It is also consistent with the fact that not all tectomotoneuronal projections are routed via the burst generator. Axons originating in the SC have been shown to deploy terminal fields within the abducens nucleus of the cat (Grantyn and Berthoz 1985; Grantyn and Grantyn 1982; Olivier et al. 1993) and to establish monosynaptic connections with abducens motoneurons (Grantyn and Grantyn 1976). There is ample anatomic evidence to suggest that the nucleus prepositus hypoglossi (a presumed site of the horizontal neural integrator) could also mediate a tectal projection to extraocular motoneurons (Grantyn and Berthoz 1985; Grantyn and Grantyn 1982; Olivier et al. 1993). Tectal efferents are also distributed among reticulospinal neurons, which in turn project to the abducens nucleus (Grantyn and Berthoz 1987; Grantyn et al. 1980). The same reticulospinal neurons make substantial collateral connections with the nucleus prepositus hypoglossi and the medial vestibular nucleus (Grantyn and Berthoz 1987; Grantyn et al. 1980, 1992), thus giving the SC indirect access to these nuclei. The existence of similar, albeit less direct, pathways was demonstrated in the vertical system (Isa and Itouji 1992; Isa and Naito 1994), thus permitting the formulation of a similar argument for vertical saccades. The assumption that tectooculomotor connections bypassing the burst generator may be responsible for the generation of slow drifts is therefore well supported by neuroanatomical data. Starting from this assumption, we predicted that the position sensitivity of saccades would drop if they did not overlap with the stimulus train used to evoke them, a prediction that we were able to verify experimentally. Further, we could show that the relationship between the position sensitivity (kH) of evoked rapid eye movements and their characteristic vectors (SH) is of the form kH = -(1 - e-(D+beta SH)/tau ), which accounts for the positive correlation between SH and kH. This relationship also demonstrates that the position sensitivity of evoked rapid eye movements increases together with the slope of the main sequence curve (beta ) and in inverse proportion to the time constant (tau ) of the drift. The values that these constants obtain in cats can account for the fact that estimates of the position sensitivity of evoked rapid eye movements cluster around 0.5 in this species. The much smaller value that beta  obtains in the monkey (by a factor of >= 5) (Robinson 1981) could account for the fact that the position sensitivity of rapid eye movements evoked in response to the electrical stimulation of the SC can be smaller in primates unless areas responsible for saccades of large amplitude are considered.

Taken in isolation, neither the superposition hypothesis nor the alternative mechanisms discussed can explain the ipsiversive direction of evoked saccades when the eyes start from extreme contralateral positions. Take, for example, the goal hypothesis, where it is theoretically possible to find values of E1 such that the sign of Delta E is reversed [if (1 - gE1 > re]. Clearly, the SC commands would have to be routed to the ipsiversive burst generator for these saccades to be executed. Yet, there is no indication that the output of one SC is routed to the burst generator of one or the other side of the brain depending on the sign of re - (1 - gE1. Similar arguments apply to the other hypotheses we considered in the previous paragraphs. However, it should be noted that electrical stimulation of the caudal edge of the feline SC evokes saccades toward primary position (centering saccades) (Guitton et al. 1980; McIlwain 1986). It was argued that spread of electrical activation to the caudal pole of the SC would add a centering component to the evoked saccades, thus accounting for the reversed direction of evoked saccades that start from extreme contralateral positions (McIlwain 1986). Both the superposition and the other hypotheses discussed in the previous paragraphs would explain the reversed direction of evoked saccades if they were combined with such a mechanism.

    ACKNOWLEDGEMENTS

   We thank A. Kalaitzakis for help with the data analysis and two anonymous referees for comments.

  We acknowledge the financial support of Human Capital and Mobility Grant ERBCHRXCT-940559.

    APPENDIX

Exponential drifts such as the one illustrated in Fig. 2A follow a time course described by the expression E(t) = a - be-t/tau , where a = E and b = E - E1 as determined from the boundary conditions E(t) = E1 at time t = 0 and E(t) = E at t = infinity . The size of the drift (G) equals E(Sd) - E1 where E(Sd) is the position that would have been reached by the eyes at the end of the saccade had the saccade not occurred (i.e., eye displacement would be due to the drift alone). Substituting and rearranging one obtains G = E - E1 - (E - E1)e-Sd/tau where Sd = (D + beta SH). Therefore, G = E - E e-(D+beta SH)/tau -E1(1 - e-(D+beta SH)/tau ). The coefficient of proportionality of E1 in the latter expression [-(1 - e-(D+beta SH)/tau )] is the expression that describes the position sensitivity in Eq. 4.

    FOOTNOTES

  Address reprint requests to A. K. Moschovakis, Dept. of Basic Sciences, Faculty of Medicine, School of Health Sciences, University of Crete, P.O. Box 1393, Iraklion, Crete, Greece.

  Received 9 June 1998; accepted in final form 9 September 1998.

    REFERENCES
Abstract
Introduction
Methods
Results
Discussion
References

0022-3077/98 $5.00 Copyright ©1998 The American Physiological Society