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Department of Vision Sciences and Vision Science Research Center, University of Alabama at Birmingham, Birmingham, Alabama
Submitted 27 December 2004; accepted in final form 18 May 2005
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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; Zee et al. 1992) for the intrasaccadic enhancement of vergence velocity during combined saccade–vergence eye movements, a model that was rejected in the accompanying report. The key reason for the rejection was the strong evidence for the expression of the dynamics of the associated saccade in the enhancement metrics, a signal that is not encoded by any of the types of cells involved in the original Multiply mechanism. Two implementations of a vergence-enhancement mechanism that involves a saccadic burst signal, encoding cyclopean (i.e., conjugate) saccadic dynamics, are proposed in Fig. 1, A and B. The key difference between the two models is in the location of the saccade–vergence interaction. In Fig. 1A the interaction is at the level of the smooth vergence velocity command, whereas in Fig. 1B the interaction is at the level of the vergence motor error signal, after the suggestion by Zee et al. (1992) that the smooth vergence system may be organized similarly to the saccadic system as a positional local feedback loop system.
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). In this schema, the vergence burst generator receives a visual estimate of the initial vergence motor error VGME0 (i.e., the initial disparity of the stimulus) and visual feedback (delayed by the visual processing). The output of this circuit is the smooth vergence velocity command, which may be encoded by a subgroup of vergence burst cells (CB1) located in midbrain. These cells have been described as having a temporal profile of activity following a positively skewed profile of the smooth vergence velocity (Judge and Cumming 1986; Mays et al. 1986). In this model the CB1 cells have a projection to the multiplicative node ( x SB), which also receives a copy of the cyclopean saccadic burst (velocity) command SB. The output from the multiplicative node is sent to other vergence burst cells, also located in midbrain, the CB2 subgroup. This subgroup also relays (connection in green) the direct smooth, nonenhanced vergence velocity signal, received from the CB1 cells, to the downstream vergence pathway. In the absence of a saccade, the multiplicative node, which in this schema is located outside the smooth vergence velocity generator, is silent, and the CB1 and CB2 subgroups are indistinguishable. The smooth branch also encodes vergence pursuit (Mays et al. 1986). During a saccade, the CB2 cells will carry, on top of the smooth vergence velocity command, the vergence enhancement (Mays and Gamlin 1995), which we propose to be a weighted version of the cyclopean saccadic burst.
The decision to place the enhancement node outside the circuit responsible for the smooth vergence command originated from the observation that the average smooth vergence velocity sensitivity of the midbrain convergence burst cells is quite high [4.45 spikes/(°/s), as is that of the midbrain divergence burst cells (–4.35 spikes/(°/s)] (Mays et al. 1986). This means that many of those cells cannot carry the intrasaccadic vergence velocities as high as 
400°/s in our data. Thus we have functionally separated the vergence system into a smooth component branch, with low dynamics and high velocity sensitivity, and an enhancement component branch, with saccadic-like dynamics and low velocity sensitivity. The matching alteration in the vergence tonic signal (vergence step) is obtained by integration of the velocity command (vergence pulse) from the CB2 cells in the vergence neural integrator (VG NI), and the two signals are added together at the level of the (con)vergence burst tonic cells (CBT). These CBT cells are known to monosynaptically project to the medial rectus subdivision of the oculomotor nuclei (Zhang et al. 1991, 1992), which innervates the medial rectus muscles. The result is a brisk symmetric intrasaccadic acceleration in the vergence response during the saccade, which is itself conjugate.
We presented evidence (Busettini and Mays 2003) that OPNs do not pause during saccade-free smooth vergence responses and that their tonic firing is only slightly modulated by the ongoing vergence command. We also verified that during a saccade–vergence combined response the OPNs pause during the saccade with only minor timing changes compared with conjugate saccades. This implies that the saccadic system is fully inhibited during smooth saccade-free vergence responses as well as during the pre- and postsaccadic periods of saccade-enhanced vergence trials. Thus these responses are necessarily generated by the smooth vergence system with no contributions from the saccadic system, and the saccade–vergence interaction is limited exclusively, in time, to the intrasaccadic period.
Additional vergence transients associated with the saccade per se, which are also present during purely conjugate saccades, are added to the overall vergence response, as illustrated in the preceding paper. Following the suggestion by Maxwell and King (1992) and Zee et al. (1992) that the transients are attributed to differences in abducting and adducting eye dynamics, we schematized them as plant related. A detailed analysis of the origin of these transients is discussed in Sylvestre et al. (2002). It is noteworthy that this model is applicable to both convergence and divergence movements, with the weighted saccadic contribution acting on the convergence and divergence burst cells (Mays et al. 1986), respectively, and to saccades in all directions.
The model in Fig. 1B is based on the suggestion by Zee et al. (1992) that the vergence control may be based on a local feedback arrangement (blue connection labeled LOCAL FEEDBACK). Local feedback may also be present in the schema in Fig. 1A, but it is not directly involved in the generation of the enhancement and it would not be directly detectable in the metrics of the vergence enhancement. Thus models of the smooth vergence system able to generate the observed CB1 and CBT signals without the need of local feedback, like the Dual-Mode Model of Hung et al. (1986), are compatible with the schema of Fig. 1A as well. The orange box labeled "VGME ESTIMATE" receives information about the initial (visual) vergence motor error associated with the stimulus VGME0, the (delayed) visual feedback information, and an internal efferent copy of the vergence motor command. The result is a rapid nonvisual evaluation of the progress of the movement as short-latency estimate of the remaining vergence motor error VGME. This signal is used by the (smooth) vergence burst generator (in green) to generate the smooth vergence velocity command, identical to the one in Fig. 1A. The external multiplicative interaction is, in this schema, between VGME and the cyclopean saccadic burst, and it is still added to the CB2 cells. An interesting aspect of this schema is that the CB2 cells would encode, in the enhancement, the same VGME that is used to generate the smooth vergence velocity command, which they also encode.
The smooth vergence velocity command has a Gaussian-like profile with a gradual initial acceleration. In contrast, we expect the initial estimate of VGME (VGME0) to be completed at or soon after the beginning of the movement. In fact, the open-loop initial acceleration of the vergence response is related to the initial (i.e., total) disparity error (Rashbass and Westheimer 1961). This means that VGME is already encoding a signal close to the initial, maximum value near or even before the beginning of the vergence response. This profile difference can be seen comparing the estimated temporal profiles of the and VGME signals entering the multiplying node in Fig. 1, A and B, respectively. For the same saccadic dynamics we predict, between the two models, a different dependency of the vergence enhancement with the timing of the saccade within the vergence response. We also predict that a vergence local feedback loop would have significant effects on the postsaccadic vergence profile. The enhancement of vergence velocity by a saccade reduces the residual vergence motor error more quickly than saccade-free smooth vergence alone. Therefore at some point after the saccade, the postsaccadic vergence velocity must be reduced below the smooth vergence velocity expected if no saccade had occurred to avoid a vergence overshoot. What feedback is used to make this adjustment? Is it possible that visual feedback is sufficient, or is the delay associated with the visual system too great for this task? It seems likely that the saccades that occur early in the vergence movement would allow enough time for visual feedback to adjust the later vergence response. Saccades that occur late in the vergence movement might not. If the enhancement-related decrease in postsaccadic vergence velocity occurs before any possible visually driven feedback correction, this would strongly suggest that the vergence enhancement contribution is continuously combined with the ongoing smooth vergence within the hypothesized local vergence feedback loop.
Currently there are two contrasting views regarding the brisk intrasaccadic vergence acceleration observed during saccade–vergence combined responses. The first is that intrasaccadic vergence enhancement is a true vergence signal, which is the case in the models in Fig. 1, A and B. This view is supported by the existence of vergence cells that increase their activity at the time of the intrasaccadic enhancement but do not fire for conjugate saccades (Mays and Gamlin 1995). Furthermore, we have preliminary evidence (Davison et al. 2004) that the velocity sensitivity of the medial rectus motoneurons to the vergence enhancement reflects the velocity sensitivity of the cell to the smooth vergence velocity and not to the saccadic input and that this is also preserved for purely vertical saccades. This implies that the enhancement is delivered to the motoneurons by the vergence pathway as a symmetric vergence command. The second view is that what is seen as an intrasaccadic enhancement is actually the result of two independent right- and left-eye (i.e., monocular) asymmetric saccadic bursts (Sylvestre and Cullen 2002; Zhou and King 1998). A largely qualitative attempt to merge the two views is reported in King and Zhou (2002), albeit their schema is applicable only to horizontal saccades. A similar limitation in applicability is also present in all other monocular implementations of the vergence enhancement (e.g., Bruno et al. 1995). The models in Fig. 1, A and B do not include monocular contributions to the vergence enhancement and a different interpretation of the results of Zhou and King (1998) and Sylvestre and Cullen (2002) is presented in the DISCUSSION.
Our goal, to behaviorally determine the nature of the saccadic and vergence neural signals involved in vergence enhancement and the modality of their interaction, may play a key role in this debate. Several neural implementations consistent with our results are presented in the DISCUSSION, with the illustration of the neural predictions associated with each model. These models are behaviorally indistinguishable and the neural predictions will have to be tested by single-unit recordings and/or other invasive neurophysiological techniques.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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), with additional measures, illustrated in Fig. 2. Although Fig. 2 shows data for a horizontal saccade with vergence, the same measurement procedures were used for vertical saccades with vergence and for conjugate saccades. The methodology for the computation of many of these parameters can be found in Busettini and Mays (2005) and only the new measures are described in detail here. Figure 2A (top) shows eye position traces, 2B (middle) shows vergence velocity traces, and 2C (bottom) shows the temporal profiles of the instantaneous vergence motor errors. The target step that the animal followed occurred at time 0 (not shown). Vergence onset and offset are indicated by the vertical lines marked VGONS and VGOFF, respectively. Total vergence change (TVC) was defined as the change in vergence between VGONS and VGOFF, including the contributions of the smooth vergence and, if present, of the enhancement(s) associated with the saccade(s) executed during the change in depth. An automatic multistep process determined saccadic onset (SONS) and end (SOFF). The interval between VGONS and SONS indicates the time between the onset of vergence and the onset of the saccade (vergence lead) and is identified by the horizontal gray bar in the second panel. The peak of the (conjugate) Pythagorean velocity is indicated by the vertical line at 
PK. The vertical line 
PK indicates the "saccade-related" peak vergence velocity (on trace ) during the saccade–vergence trial. Smooth vergence movements without saccades tended to be highly stereotyped, and so it was possible to directly compare the velocity of vergence associated with the saccade ( in Fig. 2) with that of a typical saccade-free smooth vergence movement of the same amplitude (smooth estimate ).
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, as illustrated in the accompanying paper, was performed only on primary saccades with vergence leads >5 ms, and all data and statistics, unless otherwise specified, are limited to those trials. A separate qualitative analysis was done on trials with vergence lead <5 ms and for corrective saccades. The trace 
is the difference between the vergence velocity associated with the saccade and the matched smooth vergence velocity estimate, and so indicates the degree of enhancement of the vergence velocity by the saccade. Because of the slow dynamics of smooth vergence, the time of the peak of the vergence velocity enhancement PK usually coincided with the time of the overall saccade-related peak vergence velocity PK, as in the case illustrated in Fig. 2. As a consequence, the enhancement velocity values VGPK, i.e., the value of the enhancement velocity estimate at the time of the saccade-related peak vergence velocity PK, and PK were usually identical and we considered them to be interchangeable. VGPK is the value of the smooth vergence velocity estimate at the time of the saccade-related peak vergence velocity PK. PYPK is the value of the smooth vergence velocity estimate at the time of the saccadic peak Pythagorean velocity PK.
The values VGPK and PYPK, as can be seen in Fig. 2, are also very similar because of the slow dynamics of the saccade-free smooth vergence estimate. An automatic multistep process determined the beginning of the enhancement (EONS), and the zero crossing (ZC) of the enhancement velocity around the end of the saccade was selected as an estimate of its end (EOFF). Using a two-point backward trapezoidal integration on the enhancement velocity trace between EONS and EOFF we computed the magnitude of the enhancement (enhancement area EA), i.e., the area covered by the enhancement velocity () within the interval EOFF – EONS.
To understand the nature of the vergence feedback loop we used the vergence enhancement as a physiological perturbation of the smooth vergence motor error. As shown in Fig. 2C, the vergence enhancement associated with the saccade causes a postenhancement reduction in the instantaneous vergence motor error (VGME) with respect to the smooth estimate of the instantaneous vergence motor error without saccadic enhancement (SEME). The temporal profiles of the two vergence motor errors were computed by subtracting from the total vergence change of the movement (TVC) the integrated (for VGME) and integrated (for SEME) traces using a backward trapezoidal integration with no temporal delays and with zero value at vergence onset VGONS. The shortest latency of visually driven disparity vergence in monkeys is around 60 ms (Busettini et al. 1996), but such latencies are obtained only with abrupt disparity shifts of large textured patterns after a centering saccade, and this short-latency system responds only to small disparities. For our small and impoverished stimuli, the animal having first to release fixation of the preceding target, and larger disparity steps, a more reasonable estimate of the average smooth vergence latency is around 100 ms (bars S in Fig. 7 of Busettini and Mays 2005). Thus the presence at 100 ms from enhancement onset (time line marked E+100) of a significant slowing of the postsaccadic vergence velocity (+100) below the smooth vergence estimate (+100) must be linked to a nonvisual mechanism because it occurred too soon for the visual system to have produced this correction.
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+100 in Fig. 2. To rule out that this change in the postsaccadic vergence velocity profile is a nonspecific postsaccadic suppression of the vergence system, the slowing should be correlated with the magnitude of the reduction in vergence motor error caused by the enhancement. To test this hypothesis and to provide an initial estimate of the time course of the feedback contribution, vergence motor error measures were taken every 10 ms from EONS to E+100 (Fig. 2 shows only the +100-ms point measures for clarity) and linearly correlated with +100 to identify which value of SEME or VGME best predicts +100. The APPENDIX provides a table with all the trace, event, and measurement symbols used herein. |
RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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The single trial in Fig. 2 shows that the enhancement velocity trace becomes negative soon after the end of the saccade and remains so at the E+100 point as well. This is expected if the postenhancement (smooth) vergence response were controlled by a short-latency, and thus nonvisual, vergence motor error that took into account the preceding vergence enhancement. To test this idea, we first measured enhancement duration. A correction based only on visual information would show a concentration of the enhancement ZCs after the visual latency, i.e., around 100 ms after enhancement onset. To have a sufficiently robust decrease of the vergence motor error, i.e., a sufficiently large enhancement area, the measurements of enhancement duration were made only on convergence–saccade trials with (positive) peak enhancement velocity >50°/s and on divergence–saccade trials with (negative) peak enhancement velocity < –50°/s. We limited this test to saccades of duration between 30 and 50 ms to provide a direct comparison between data sets and because there was a trend for longer saccades to show longer enhancement durations. The overall average of enhancement durations for the 16 convergence data sets was 47.1 ms (SD ± 9.2 ms; range 35.0 to 63.0 ms). For the 16 divergence data sets the overall average was 55.2 ms (SD ± 8.7 ms; range 43.7 to 73.8 ms). Furthermore, the average of the SDs for the convergence data sets was 9.6 ms (SD ± 2.6 ms; range 5.4 to 14.0 ms) and for the divergence data sets it was 12.6 ms (SD ± 2.2 ms; range 7.8 to 17.5 ms), indicating a robust ZC at the single trial level. Both convergence and divergence duration averages are <60 ms, implying a consistent reduction in vergence velocity from the smooth vergence estimate even before the shortest reported visual latencies (Busettini et al. 1996), and much earlier than the visual latencies typically observed with our stimulus configuration (i.e., 100 ms).
The finding of a short-latency decrease in postenhancement vergence velocity, alone, does not rule out that such a slowing may stem from a nonspecific postsaccadic suppression of the smooth vergence system. In other words, the slowing may be an effect associated with the occurrence of the saccade per se and not to the reduction in vergence motor error by the enhancement. From the Busettini and Mays (2003) report we can rule out that these postenhancement vergence responses are saccadic because the vast majority of omnipause neurons have resumed their tonic activity at this time and therefore the saccadic medium lead burst neurons must be silent. We linearly correlated the deviation of the vergence velocity from the smooth estimate at the 100-ms time mark from enhancement onset (i.e., +100 in Fig. 2) with saccadic peak Pythagorean velocity. The following tests were performed on all convergence and divergence data for which smooth vergence estimates were available, without any restrictions on peak enhancement velocity or saccadic duration. All linear correlation estimates included the constant term and the R2 are the observed versus predicted R2 measures (Systat). As reported by Sylvestre et al. (2002) and in our accompanying paper, vergence transients associated with saccades are well correlated with saccadic peak Pythagorean velocity and it is quite likely that if the postsaccadic vergence slowing is a nonspecific saccadic suppression it will also be related to saccadic dynamics. For the 16 convergence data sets, the average linear correlation R2 was only 0.05 (SD ±0.05; range 0.00 to 0.21). For the 16 divergence data sets the correlation was higher, but still weak, with an average R2 = 0.38 (SD ± 0.20; range 0.14 to 0.77). Similar results were obtained using saccadic size but there was essentially no relationship with saccadic duration.
The second test directly addressed the main hypothesis that +100 is determined by a short-latency internal estimate of the current vergence motor error. We computed the R2 of the linear correlations between +100 and each of the 11 values of the smooth vergence motor error estimates SEME taken every 10 ms from EONS to E+100 and the R2 of the linear correlations between +100 and each of the 11 values of the actual vergence motor error VGME (i.e., including the enhancement) at the same times. The overall averages of the average R2 values for the 16 convergence data sets are illustrated in Fig. 3 A and the overall averages of the average R2 values for the 16 divergence data sets are illustrated in Fig. 3B. Open circles are the average SEME-related R2 values, whereas the filled circles are the average VGME-related R2 values. The horizontal axis is the error lead, i.e., the separation in time between +100 and the VGME+n and SEME+n point measures. Error lead zero matches the vergence velocity +100 with the current VGME+100 and SEME+100.
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+100 with the VGME and SEME values at the enhancement onset (VGME+0 and SEME+0) and therefore they are separated in time by the estimated average visual latency (VIS). These two 0-ms R2 values are by definition the same because the enhancement has just started at enhancement onset and SEME and VGME are the same, leaving only random, small errors in the fitting of the estimated on inside the vergence lead period. These vergence errors would be the best predictors if the vergence system had only a visual feedback loop. For both convergence and divergence it is evident that the best prediction of +100 is obtained using the vergence motor error VGME with an error lead of approx 40–50 ms and that the quality of the prediction is much better than the (visual) prediction given by SEME (
VGME) at enhancement onset. The two asterisks in the plots indicate that the average R2 values for the VGME at the error leads 40 and 50 ms are not statistically different (P > 0.01) from each other. All other average values are significantly lower (P < 0.01). The peak of the VGME prediction is much higher than any SEME prediction, which excludes the possibility that the smooth vergence system has an internal feedback loop that does not include the enhancement. Furthermore, the average R2 peak values (0.64 ± 0.15 SD, range 0.42 to 0.87 for convergence; 0.74 ± 0.14 SD, range 0.45 to 0.90 for divergence) are much higher than the average R2 values obtained with saccadic peak velocity (0.05 and 0.38, respectively). This clearly indicates that the postsaccadic slowing of the vergence velocity is a true short-latency, nonvisual vergence velocity correction linked to the saccade-related decrease in postenhancement vergence motor error. The plots also suggest that the vergence local feedback loop has an overall delay, including the mechanical delay of the plant, of around 40–50 ms.
Location of the vergence–saccade interaction
The strong evidence for a fast, nonvisual vergence local feedback suggests two possible alternatives: 1) that the multiplicative interaction with the saccadic burst occurs at the level of the smooth vergence velocity command (Fig. 1A) and 2) that it occurs at the level of the vergence motor error estimate (Fig. 1B). In both models the result of the interaction is hypothesized to be added to the ongoing smooth vergence velocity command at the CB2 level. As illustrated in Fig. 4 A, there seems to be a direct interaction between the intensity of the estimated smooth vergence velocity at the time of the saccade (black dots) and the amount of vergence enhancement (gray dots). The much larger scatter of the gray dots, as shown in Figs. 5 and 6 of the accompanying paper, was related to cyclopean saccadic dynamics. These two observations are consistent with the need for the linear weighted summing junction (CB1* cells) in Busettini and Mays (2005) to be replaced by a multiplicative saccade–vergence element. The temporal profiles of the smooth vergence velocity command and of the associated VGME differ significantly during the accelerating phase of the smooth vergence response (Fig. 4, B and C).
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PYPK. As an estimate of the vergence motor error (Fig. 4C) we used the vergence motor error at saccadic onset VGMESONS.
We also tested other intrasaccadic measures between saccadic onset and enhancement peak and the results were comparable. The dynamics of the smooth vergence velocity, and even more so of the vergence motor error, are much slower than the saccadic dynamics, and there is only a relatively small variation in and VGME between saccadic onset and enhancement peak (Fig. 2). Our goal is to see whether, for similar saccadic dynamics, the enhancement is better related to PYPK or VGMESONS. Thus the analysis was performed within restricted ranges of peak saccadic velocity. Figure 5A shows an example of saccade-related peak vergence velocity PK as a function of PYPK for vertical saccades with peak Pythagorean velocity between 150 and 200°/s (animal 21 downward saccades). Convergence data are in the top right quadrant and divergence data are in the bottom left quadrant. Although peak vergence velocity (black dots) increases with PYPK, as expected, the correlation is often poor. A similar pattern of poor correlation is also present for the enhancement peak PK (gray dots). The similarities between the two scatterplots suggest that this additional variable is encoded in PK.
Figure 5B uses the same data as those in Fig. 5A, with saccade-related peak vergence velocity PK (black dots) and enhancement peak PK (gray dots) plotted against the vergence motor error at the onset of the saccade (VGMESONS). The linear correlation between PK and VGMESONS, expressed as R2 (observed vs. predicted) and t-value, was always as good as and often much better than that with PYPK for all data sets, including the example illustrated in Fig. 5, A and B. Similar, if not larger, relative improvements in the R2 were found for PK, which highlight the dominant contribution of VGME in determining the amplitude of the vergence enhancement. Figure 5, C and D show that the same observations apply to horizontal saccades as well (animal 21 leftward saccades).
The evidence strongly supports the contention that the saccade–vergence interaction is at the level of the vergence motor error signal (Fig. 1B). The model in Fig. 1B also implies (green path) a significant, independent contribution of the smooth vergence signal, quantifiable in our analysis by VGPK, i.e., the smooth vergence velocity estimate at the time of the peak of the vergence enhancement. The hypothesis being tested here is that PK is a linear combination of VGPK (enhanced signals) and VGPK (nonenhanced signals) and therefore for this analysis we preferred to use the value VGPK instead of PYPK. We measured the simultaneous linear contributions of VGMESONS and VGPK in determining PK for all data sets, after again restricting the saccadic dynamics from 150 to 200°/s.
Although we are aware that there is significant covariability between VGMESONS and VGPK, at least after the (smooth) acceleration period of the vergence response, and in such situations the double-linear correlation may be somewhat unstable, nonetheless the average coefficient for VGPK for the 16 restricted convergence data sets was 0.91 (±0.32 SD; range from 0.41 to 1.48), and the average coefficient for the 16 restricted divergence data sets was 0.89 (±0.36 SD; range from 0.28 to 1.69), which are close to unity. The values of R2 were remarkably high for all data sets, with an average of 0.88 (SD ±0.08; range from 0.69 to 0.96) for convergence and of 0.82 (SD 0.09; range from 0.63 to 0.94) for divergence. This test was repeated for different saccadic dynamics and, although the coefficient associated with VGMESONS varied with saccadic dynamics, as expected from the model in Fig. 1B, the coefficient associated with VGPK remained close to one and independent of saccadic dynamics.
The results therefore support the hypothesis of a linear superimposition, which we located at the level of the CB2 cells (Fig. 1B), of a vergence enhancement modulated by vergence motor error and saccadic dynamics to the ongoing smooth vergence velocity command. In this view the vergence burst generator is thus involved only in the generation of the nonenhanced (smooth) vergence velocity command, which we see in the data as VGPK. It is important to note that the postsaccadic nonenhanced (smooth) vergence velocity command is also modified by the enhancement, but only indirectly through the alteration of VGME caused by the enhancement. This also means that our methodology for estimating the CB1 firing from a matched saccade-free vergence velocity estimate is valid only in the first 40–50 ms of the enhancement, after which the CB1 firing is modified by the altered VGME. This is not a problem for our attempt to estimate VGPK, which occurred, in the vast majority of trials, well inside this interval. The main effect in our analysis might have been a slight underestimate of the enhancement area for the longest enhancements.
Building of the model equation
Figure 5 shows that for constant saccadic dynamics, assessed by the peak Pythagorean velocity, peak vergence enhancement PK can be represented by an equation linearly related to vergence motor error, a good estimate of which may be the value at saccadic onset, VGMESONS. We also know that there is a dependency with saccadic dynamics and that the crossed interaction has to be multiplicative. There is no vergence enhancement during conjugate saccades (VGME = 0, 
0), or when there is no saccade ( = 0, VGME 0). We quantified this term as D x VGMESONS x PK. The vergence enhancement is superimposed to the nonmodulated smooth vergence velocity component. This addition may not be perfectly linear and have a gain not equal to unity, and so we decided to allow for a gain factor S, giving: D x VGMESONS x PK + S x VGPK. A linear term dependent on saccadic Pythagorean peak velocity alone, T x PK, is also added to account for any dependency on saccadic metrics not directly modulated by VGME, like divergence/convergence transients, dynamical saturations at the motoneuron level, and other possible plant and neural interactions between the saccade and the enhanced vergence. However, equation D x VGMESONS x PK + S x VGPK + T x PK presents a major problem for enhancements occurring at short vergence leads, which is illustrated in Fig. 4A. We expect the initial estimate of VGME from the visual feedback (VGME0) to be completed at or soon after the beginning of the movement. The vast majority of the saccades observed at these short vergence leads are large, fast saccades (Busettini and Mays 2005). The product D x VGMESONS x PK would be maximal for these trials whereas, instead, we often had a quite dramatic drop in the vergence enhancement at the shortest vergence leads. Such a drop is unlikely the result of a simple "passive" dynamical saturation effect because the decrease is very strong and not plateaulike, and it is also seen in animals like 21, which had very small divergence transients during conjugate saccades.
Short vergence lead effects
At issue is whether the decrease in enhancement is explained by the fact that at very short vergence leads the vergence motor error signal may still be in the rising phase (i.e., a decrease linked to the temporal development of VGMESONS) and/or because the saccades that occurred at the shortest latencies were also often the largest (i.e., the drop is a decrease of the vergence enhancement specifically associated to the largest, fastest saccades). It is also possible that the product D x VGMESONS x PK is fully developed, but that the CB2 cells are dynamically unable to respond fully to the enhancement during the initial acceleration phases of the smooth component. Numerically, this effect would also translate into a dependency with vergence lead and therefore be indistinguishable from a slow temporal development of VGME. To discriminate between these alternatives, we first limited the total vergence change to a narrow range to restrict the dependency of the CB1- and VGME-related activity with the size of the vergence movement. Then, starting at the 5-ms vergence lead value, we selected consecutive 10-ms bands of vergence lead values, to restrict their variability with time. We can therefore determine whether, inside these bands, there is an independent negative multiplicative dependency with saccadic metrics in addition to the positive multiplicative effect given by the term D x VGMESONS x PK. We quantified this hypothesized saccade-related decrease of the enhancement by introducing the term 1 – V x PK to the main enhancement term, obtaining the full model equation
 | (1) |
The presence of a significant term V would be strong evidence that the decreases in the amplitude of the vergence enhancement observed for the shortest vergence leads (and largest saccades) are, at least in part, an effect directly related to saccadic metrics. A similar effect for horizontal and vertical saccades would also support the hypothesis that this is not a passive neural or mechanical effect at the plant level. As illustrated in the accompanying paper, the probability of having small saccades at very short vergence leads is small, as is the probability of having large saccades later in the vergence movement, making such a test possible on only a few data sets. Table 1 shows the application of Eq. 1 to the first seven 10-ms vergence lead bins, starting at 5 ms, for the downward saccades with convergence (top section) and leftward saccades with convergence (bottom section), both from animal 21. The test is particularly significant for these two data sets because this animal showed the smallest saccade-related vergence transients for conjugate saccades but among the most substantial decreases in enhancement amplitude for the shortest vergence leads. For all bins the 95% Wald confidence intervals (Systat) of the parameter V did not include the zero and its value was remarkably constant for the different bins. For the earliest vergence leads the smooth vergence velocity is still very small and the S estimates have no functional significance. Many of the R2 values of the model, even in these restricted data sets, were quite high. The overall evidence indicates the failure for large horizontal and vertical saccades to generate large vergence enhancements independent of the fact that they also occurred at the shortest vergence leads, which we modeled with the term 1 – V x PK. Thus the decrease of the enhancement for the shortest vergence leads is, at least in part, an indirect consequence of the fact that such trials also had the largest saccades.
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On the basis of these preliminary considerations we decided to apply Eq. 1 to the full data sets, with, as our only restrictions, a vergence lead of 
5 ms and the saccade to be a primary saccade because both conditions are needed to compute the smooth vergence estimate VGPK. An expansion of the model to saccades with vergence leads <5 ms and to corrective saccades will be described later. Table 2 shows the overall results for the 16 convergence and 16 divergence data sets (four animals x four saccadic directions). It is noteworthy that the R2 values are very high and the equation parameters are remarkably stable across animals and saccadic directions. Because of the covariance between saccadic peak velocity and saccadic size, replacing PK with saccadic size had only a minor effect on the quality of the model, mainly (slightly) reducing the consistency of the parameters (not shown). The suppressive effect with the largest saccadic metrics, quantified by the parameter V, was always different from zero, as indicated by the 95% Wald confidence interval, with the exclusion of one case (i.e., X01 rightward divergence). This is also the data set with the strongest divergence transients for conjugate saccades of similar direction and it is likely that the suppression was masked by an increasingly large contribution to the vergence enhancement by the divergence transients for the larger saccades.
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In the preceding paper (Table 1) we found that faster saccades generated higher enhancement peak velocities for the same enhancement area and it is possible that the parameter T, for convergence, reflects this property, masking the effect of the divergence transient. Whatever the origin of the term T, it should be noted that the average value of T for convergence was only 0.042. For a saccade of 500°/s, this means a contribution of only 21°/s to the overall vergence peak. As we illustrated in the subplots in Figs. 5 and 6 of Busettini and Mays (2005), for convergence the saccade-related vergence transients seem to play a minor role. For divergence the main feature was a much stronger contribution of the term T. Not only was the average value of T more than twice that for convergence, but the contribution of the actual vergence enhancement was smaller, as can be seen comparing the D and V values for convergence and divergence. A possible explanation is that, for divergence, the vergence enhancement, smaller per se as a possible result of a slower dynamics of divergence (in humans: Hung et al. 1997), amplifies quite significantly the (codirectional) saccadic divergence transient—modulated by saccadic dynamics alone—in a synergistic way. This possibility was also suggested by Maxwell and King (1992). From the behavior alone it is difficult to determine whether this synergy is neural or mechanical at the plant level. The high correlation, also for divergence, between the reduction in vergence motor error associated with the enhancement, which also includes such a contribution, and the slowing of the postsaccadic smooth vergence response would suggest it is neural because it is taken into account by the local vergence feedback loop.
One of the most important results illustrated by Table 2 is that the proposed model worked equally well and gave similar values of the parameters for both horizontal and vertical saccades. The fact that there were no consistent differences in the parameters with saccadic direction provides critical evidence that the mechanism generating the saccade-related vergence enhancement is similar for both horizontal and vertical saccades. Our data are not consistent with those published by van Leeuwen et al. (1998) who reported, in humans, smaller and more variable vergence enhancement for vertical saccades.
The predictive power of the model was even more evident by graphically comparing measured and predicted values. Some representative examples are illustrated in Fig. 6. An analysis of the residuals of the data sets with the lowest R2 showed some small secondary nonlinear interactions between the enhancement and the vergence motor error at the shortest vergence leads, effects not implemented in the model. The main results of such nonlinearities are a smaller enhancement estimate than the actual value for the highest enhancements, occurring at vergence leads around 50 ms. This can be seen comparing Fig. 6A1 with Fig. 6A2, Fig. 6B1 with Fig. 6B2, and Fig. 6D1 with Fig. 6D2 at the arrows.
Extension of the model to secondary saccades
The limitation we imposed that the saccade must be a primary saccade was so that we could compute a smooth vergence estimate and, by subtraction, an estimate of the enhancement. A preceding primary saccade, by altering the presaccadic smooth vergence response, made such an estimate impossible for corrective saccades. Corrective saccades are small, short-duration saccades occurring later in the vergence movement during the slow postprimary saccade (and postprimary enhancement) phase of the vergence movement. We can therefore as a first approximation, substitute PYPK in Eq. 1 with the value of at saccadic onset SONS. The new model equation is therefore
 | (2) |
With a small remaining vergence motor error and the usually small corrective saccades, we expect very little vergence enhancement. Figure 7 shows an example of the application of the modified enhancement model (Eq. 2) to a secondary dataset (secondary leftward saccades during convergence from animal X01). The modified model performed quite well, with a R2 of 0.82. This test was repeated on other secondary data sets with enough data with similar results, indicating that the requirement of the saccade to be a primary saccade, although needed for computational reasons, is not a model requirement. We see this result as further evidence that the vergence enhancement is not a visually preprogrammed response, but the result of an interaction between ongoing vergence and saccadic signals.
Extension of the model to negative vergence leads
Of particular interest is case B in Fig. 4C. This is the case where at the onset of the saccade there is no vergence motor error (and no smooth vergence) and the vergence motor error rapidly develops during the execution of the saccade. If the model is correct, we expect a very fast initial acceleration in the vergence response, much faster than the initial acceleration of the smooth vergence associated with a similar total vergence change, but with no detectable initial slow vergence before the abrupt acceleration. For large saccades and small vergence changes, a simultaneous start of the saccade and of the vergence response, including an initial transient not related to the actual goal as in Fig. 3A in Busettini and Mays (2005), was a common occurrence. Much less common, even when targets are predictable (Collewijn et al. 1997), are the cases where the saccade clearly precedes a large vergence response. In our data sets, with random presentation of stimuli, these were quite rare, with the smooth vergence having, in the vast majority of the cases, a shorter latency than the visually driven saccade. There were occasional trials where the animal started the vergence late or had an anticipatory non-visually guided saccade that, by chance, matched our criteria for acceptance.
Figure 8 shows three examples (A–C) of saccades during changes in depth with no detectable presaccadic vergence velocity. Figure 8A is an example of a leftward saccade during convergence. The vergence velocity (green) accelerates rapidly and reaches the peak when the estimated smooth vergence velocity is still in the early acceleration phase. The illustrated smooth vergence response is the single trial with the temporal profile closest to the average of all smooth responses of the animal achieving the same total change in vergence of the trial with the saccade. The same brisk, sudden acceleration is observed for divergence, as illustrated in the two rightward saccades examples in B and C. This is consistent with vergence enhancement being driven by a vergence motor error with rapid initial development, as hypothesized in Fig. 1B, with the smooth vergence component developing much more gradually. The saccade in C is much faster than the saccade in B. A comparison of the postenhancement vergence velocity profiles in Fig. 8, B and C clearly shows the powerful effect of the local vergence feedback loop. In C, the larger, faster saccade generates a much larger vergence enhancement. This results in a greater reduction in the postenhancement vergence motor error, which is detected by the vergence feedback loop. Consequently, the postenhancement smooth vergence velocity goes to zero much earlier than in B. Figure 8D is an extreme case of this fast postsaccadic correction, with the required change in vergence achieved almost entirely inside the saccade. There is very little, if any, postenhancement smooth vergence because it is rapidly cancelled by the feedback loop.
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We also tested the following equation, simulating a linear interaction between vergence motor error and saccadic burst signals
 | (3) |
In this equation the vergence enhancement is a linear sum of a vergence motor error contribution D x VGMESONS, released by the occurrence of the saccade, and of a purely saccadic cyclopean contribution P x PK x (1 – V x PK), the amplitude of which depends only on the saccadic metrics. The term S x VGPK is, as before, the smooth nonenhanced vergence velocity contribution. The term T x PK in Eq. 1 is now part of the term P x PK x (1 – V x PK). Equation 3, alone, is not sufficient. Active mechanisms must block any saccadic burst signal coming from this linear summing junction during conjugate saccades (VGME = 0, PK 0) and any VGME signal when a saccadic movement is not present (VGME 0, PK = 0). Vergence enhancement has to be present only when both VGME and are different from zero. It has to be noted that this condition is automatically implemented by a multiplicative interaction without the need of additional blocking elements. The results of the application of Eq. 3 to our data sets (the same of Table 2) are reported in Table 3. The R2 values of the additive model were not statistically different from the R2 values of the multiplicative model [P > 0.03; paired t-test of the R2 of the two models (Eqs. 1 and 3)].
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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Local vergence feedback: implications for smooth vergence models
The long delay of the visual feedback and the high open-loop gain required to achieve the smooth (nonenhanced) vergence velocity values that are observed in primates would make a vergence system based exclusively on a visual feedback inherently unstable (in humans: Hung et al. 1986). To deal with this problem, Hung et al. (1986) proposed a "Dual-Mode" model, in which there are two separate vergence subsystems. The first is an open-loop preprogrammed "fast" system, responsible for the fast dynamics of the smooth vergence response (Semmlow et al. 1994). A second "slow" subsystem uses the visual feedback loop as a continuous, albeit delayed, update of the progress of the movement and drives the eyes with high accuracy to the final goal. The "slow" system is necessarily slower and has a lower gain to maintain dynamical stability.
Our data show that there is a continuous correction of the postsaccadic vergence response with a latency 40–50 ms, irrespective of where the saccade is within the vergence response and, as a consequence,
