In the accompanying paper we reported that intrasaccadic vergence enhancement during combined saccade–vergence eye movements reflects saccadic dynamics, which implies the involvement of saccadic burst signals. This involvement was not predicted by the Multiply Model of Zee et al. We propose a model wherein vergence enhancement is the result of a multiplicative interaction between a weighted saccadic burst signal and a nonvisual short-latency estimate of the vergence motor error at the time of the saccade. The enhancement of vergence velocity by saccades causes the vergence goal to be approached more rapidly than if no saccade had occurred. The adjustment of the postsaccadic vergence velocity to this faster reduction in vergence motor error occurred with a time course too fast for visual feedback. This implies the presence of an internal estimate of the progress of the movement and indicates that vergence responses are under the control of a local feedback mechanism. It also implies that the vergence enhancement signal is included in the vergence feedback loop and is an integral part of the vergence velocity command. Our multiplicative model is able to predict the peak velocity of the vergence enhancement as a function of cyclopean saccadic dynamics, smooth vergence dynamics, and saccade–vergence timing with remarkable precision. It performed equally well for both horizontal and vertical saccades with very similar parameters, suggesting a common mechanism for all saccadic directions. A saccade–vergence additive model is also presented, although it would require external switching elements. Possible neural implementations are discussed.
This paper explores alternatives to the Multiply Model (Busettini and Mays 2005; 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.
In the model in Fig. 1A the saccadic burst (SB) is multiplied with the smooth vergence velocity command (SĖ). 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 SĖ (Judge and Cumming 1986; Mays et al. 1986). In this model the CB1 cells have a projection to the multiplicative node (SĖ × 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 SĖ 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.
The data for this study, conducted using alert trained rhesus monkeys, are those from the preceding paper (Busettini and Mays 2005), 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 PẎPK. The vertical line VĠPK indicates the “saccade-related” peak vergence velocity (on trace VĠ) 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 (VĠ in Fig. 2) with that of a typical saccade-free smooth vergence movement of the same amplitude (smooth estimate SĖ).
The estimate of SĖ, 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 Ė 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 ĖPK usually coincided with the time of the overall saccade-related peak vergence velocity VĠPK, as in the case illustrated in Fig. 2. As a consequence, the enhancement velocity values ĖVGPK, i.e., the value of the enhancement velocity estimate at the time of the saccade-related peak vergence velocity VĠPK, and ĖPK were usually identical and we considered them to be interchangeable. SĖVGPK is the value of the smooth vergence velocity estimate at the time of the saccade-related peak vergence velocity VĠPK. SĖPYPK is the value of the smooth vergence velocity estimate at the time of the saccadic peak Pythagorean velocity PẎPK.
The values SĖVGPK and SĖPYPK, 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 (Ė) 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 VĠ (for VGME) and integrated SĖ (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 (VĠ+100) below the smooth vergence estimate (SĖ+100) must be linked to a nonvisual mechanism because it occurred too soon for the visual system to have produced this correction.
Moreover, the enhancement onset is the point at which the perturbation of the vergence motor error begins to develop, whereas the 100-ms latency used as the reference is the latency of the smooth vergence in response to a fully developed disparity error. This slowing is indicated as Ė+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 VĠ+100 to identify which value of SEME or VGME best predicts VĠ+100. The appendix provides a table with all the trace, event, and measurement symbols used herein.
Evidence for short-latency nonvisual vergence feedback
The single trial in Fig. 2 shows that the enhancement velocity trace Ė 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 VĠ from the smooth estimate SĖ at the 100-ms time mark from enhancement onset (i.e., Ė+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 VĠ+100 is determined by a short-latency internal estimate of the current vergence motor error. We computed the R2 of the linear correlations between VĠ+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 VĠ+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 VĠ+100 and the VGME+n and SEME+n point measures. Error lead zero matches the vergence velocity VĠ+100 with the current VGME+100 and SEME+100.
No biological system can respond with zero latency (CURR) and therefore we do not expect the peak of the correlation to occur at this point. An error lead of 100 ms matches the vergence velocity VĠ+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 SĖ on VĠ 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 VĠ+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 SĖ and of the associated VGME differ significantly during the accelerating phase of the smooth vergence response (Fig. 4, B and C).
As a direct consequence of their different temporal development, for the same saccadic dynamics we predict a different dependency of the vergence enhancement with the position of the saccade within the vergence response (vergence lead). In the case of a saccadic interaction at the level of the smooth vergence velocity command (Figs. 1A and 4B) we expect a gradual development of the enhancement with vergence lead. In the case of a saccadic interaction at the level of the vergence motor error (Figs. 1B and 4C), we expect a much more immediate development, with the peak of the enhancement effect at or soon after the onset of the presaccadic smooth vergence response. This difference in the temporal development can be exploited to test, for restricted ranges of saccadic dynamics, if the amount of vergence enhancement is better correlated with the value of the smooth vergence velocity around the time of the saccade or the value of the vergence motor error at similar times. The result of this test can be used as indirect evidence of the location of the saccade–vergence interaction. As estimate of the smooth vergence velocity command at the time of the saccade (Fig. 4B) we chose to use the value of the smooth vergence velocity estimate at the time of the saccadic peak Pythagorean velocity SĖPYPK. 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 SĖ 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 SĖPYPK 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 VĠPK as a function of SĖPYPK 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 SĖPYPK, as expected, the correlation is often poor. A similar pattern of poor correlation is also present for the enhancement peak ĖPK (gray dots). The similarities between the two scatterplots suggest that this additional variable is encoded in ĖPK.
Figure 5B uses the same data as those in Fig. 5A, with saccade-related peak vergence velocity VĠPK (black dots) and enhancement peak ĖPK (gray dots) plotted against the vergence motor error at the onset of the saccade (VGMESONS). The linear correlation between VĠPK and VGMESONS, expressed as R2 (observed vs. predicted) and t-value, was always as good as and often much better than that with SĖPYPK 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 ĖPK, 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 SĖVGPK, i.e., the smooth vergence velocity estimate at the time of the peak of the vergence enhancement. The hypothesis being tested here is that VĠPK is a linear combination of ĖVGPK (enhanced signals) and SĖVGPK (nonenhanced signals) and therefore for this analysis we preferred to use the value SĖVGPK instead of SĖPYPK. We measured the simultaneous linear contributions of VGMESONS and SĖVGPK in determining VĠPK 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 SĖVGPK, 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 SĖVGPK 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 SĖVGPK 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 SĖVGPK. 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 SĖVGPK, 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 ĖPK 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, PẎ ≠ 0), or when there is no saccade (PẎ = 0, VGME ≠ 0). We quantified this term as D × VGMESONS × PẎPK. 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 × VGMESONS × PẎPK + S × SĖVGPK. A linear term dependent on saccadic Pythagorean peak velocity alone, T × PẎPK, 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 × VGMESONS × PẎPK + S × SĖVGPK + T × PẎPK 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 × VGMESONS × PẎPK 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 × VGMESONS × PẎPK 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 × VGMESONS × PẎPK. We quantified this hypothesized saccade-related decrease of the enhancement by introducing the term 1 − V × PẎPK 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 × PẎPK. 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.
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 SĖVGPK. 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 × 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 PẎPK 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.
The parameter S, which is the weight of the smooth vergence velocity contribution to the overall response, was, on average, slightly larger than unity, supporting the idea of a nonenhanced smooth vergence component added to the CB2 cells. It is also possible that there may be a small secondary facilitation of the enhancement with higher smooth vergence velocities. Interestingly, with the exception of two cases, the value of T for convergence was always positive, i.e., in the direction of the (positive) vergence enhancement. If the divergence transients were the dominant effect in this element of the model, we would have expected a conflict between the initial transient divergence and the convergence enhancement and therefore a negative coefficient.
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 SĖPYPK in Eq. 1 with the value of VĠ at saccadic onset VĠSONS. 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 VĠ (green) accelerates rapidly and reaches the peak when the estimated smooth vergence velocity SĖ 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.
Can the interaction be additive?
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 × VGMESONS, released by the occurrence of the saccade, and of a purely saccadic cyclopean contribution P × PẎPK × (1 − V × PẎPK), the amplitude of which depends only on the saccadic metrics. The term S × SĖVGPK is, as before, the smooth nonenhanced vergence velocity contribution. The term T × PẎPK in Eq. 1 is now part of the term P × PẎPK × (1 − V × PẎPK). 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, PẎPK ≠ 0) and any VGME signal when a saccadic movement is not present (VGME ≠ 0, PẎPK = 0). Vergence enhancement has to be present only when both VGME and PẎ 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)].
Particularly interesting is the intrasaccadic large contribution of VGME alone, with an average coefficient of 12.8°/s per ° of vergence motor error and often responsible for more than 50% of the overall enhancement.
The discussion is centered on the analysis of possible neural implementations of Eqs. 1 and 3. Equation 2 is a modified version of Eq. 1 to estimate the enhancement for corrective saccades with identical neural implementation of Eq. 1. Local vergence feedback, which is common to all configurations, is discussed first.
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, where the enhancement is located with respect to the hypothetical “fast” component. This clearly implies that the enhancement has be integral part of the “fast” response or, in other words, that the “fast” system uses an efferent copy of the vergence command, including the enhancement, to control the progress of the movement. This would make the “fast” component a local feedback system, albeit open-loop with regard to the visual feedback. The possibility that the enhancement is preprogrammed inside the “fast” response is very unlikely because this preprogramming, which would have to be based purely on the visual stimulus, would also have to program when the saccade will occur within the response to predict the actual VGME value at that time, an enormously complex computation. In fact, our evidence strongly suggests that the enhancement is the product of the current vergence and saccadic signals, whatever they are at the time of the interaction, with no direct relationship to the visual stimulus per se.
Vergence enhancement also occurs during monocularly driven accommodative–vergence responses (Enright 1986) where there is no possibility of such preprogramming. Furthermore, we found no evidence that the “slow” component continues after the enhancement when the goal is reached at or immediately after the end of the saccade (Fig. 8). In the “Dual-Mode” model the “slow” component would necessarily continue until the visual feedback detects that the goal was already reached. This implies that both the “fast” and “slow” subsystems receive information from the local feedback loop. There is no evidence in the neurophysiological literature for a neural separation of the vergence response in two components. Indeed, all reported burst and burst-tonic cells in midbrain (Mays et al. 1986; Zhang et al. 1992) and cortex (Fukushima et al. 2002; Gamlin and Yoon 2000) fire during the entire vergence response, with no evidence for a separation in initial and completion components, and for smooth tracking in depth. These observations, in our view, strongly support the existence of a single vergence circuit with double feedback, as illustrated in Fig. 1B. We propose that the evidence from the work of Semmlow and collaborators (1986) of distinct initiation (or “fast”) and completion (or “slow”) subsystems may be the gradual shift of sensory recruitment from coarse to fine stereopsis cell subgroups and the combined action of two types of feedback with different delays.
Zee et al. (1992) were the first to propose a single smooth vergence model with a local vergence motor error feedback and included the enhancement, when present, in the internal loop. Their local feedback scheme was suggested by the discovery of vergence burst neurons by Mays et al. (1986) and Judge and Cumming (1986), which opened the possibility of a pulse-step arrangement similar to the saccadic system and, by extrapolation, suggested the existence of a vergence local feedback similar to the saccadic local feedback. Our paper is the first behavioral evidence supporting such an implementation by using a quantitative analysis of the postenhancement smooth vergence response. An important aspect not to be overlooked is that, for the saccadic system, the saccade is so fast that ordinarily no contribution from the visual feedback has enough time to intervene in the ongoing saccadic response. This is not the case for vergence, where the vergence responses are, when not enhanced, often three or four times longer than the visual delay, estimated to be around 100 ms. The information from the visual feedback is altered during the course of the movement and with enough time to alter the vergence response. Interestingly, the Zee et al. (1992) local feedback model of the smooth vergence system had as input a fixed desired vergence goal (ΔV) until the end of the vergence movement, as if the vergence system were a sample-and-hold circuit with no new update from the visual system until completion of the ongoing movement (i.e., for several hundreds of milliseconds). This is quite a puzzling assumption because a perturbation of the visual disparity error of the stimulus during an ongoing movement modifies the ongoing response with a visual latency (Alvarez et al. 2000). How can the vergence system respond to an external alteration of the visual stimulus (i.e., by continuously updating the information from visual feedback) but at the same time ignore the visual alterations associated with its own response?
Following the suggestion by Robinson et al. (1986) for the smooth pursuit system, we propose that the vergence local feedback information could be delivered to a positive feedback loop dynamically simulating the plant and the visual delay. This positive feedback loop signal would be used to cancel the negative visual feedback loop, therefore making the vergence system behave as a single local feedback loop system with a very short close-loop delay and thus inherently stable. This way, only discrepancies between the predicted and the actual visual feedback values would be detected and used to update the estimate of the current vergence motor error and, consequently, the response. In other words, if there are no changes in the visual stimulus (except those caused by the subject’s own response), there is no functional contribution from the visual feedback. This circuit would be also consistent with the double-component responses by Alvarez et al. (1998, 2000) where, as soon as the discrepancy between the predicted delayed visual information and the actual delayed visual information is above a certain threshold, a new vergence burst is generated. It is also possible that this update strategy may appear steplike and therefore misinterpreted as a preprogrammed behavior (Semmlow et al. 1994).
Our evidence that the enhancement is encoded in the local feedback loop, and therefore likely also encoded in the positive feedback loop, would make this arrangement functionally compatible with enhanced vergence responses. Interestingly, this goal-updating schema would also solve the conflict between the local feedback information, indicating that the goal is achieved and driving the vergence response to a quick end after a large vergence enhancement (Fig. 8), with the visual feedback information indicating that the goal is not achieved for at least another 100 ms.
Local vergence feedback: neural correlates
Unfortunately, there are no quantitative data on the temporal development of the various vergence-related cell types that can be used as temporal templates for a dynamical simulation. Nonetheless, there are some groups of vergence cells that are strong candidates for encoding vergence motor error or, even if not directly encoding it, of being part of a feedback loop.
The first possibility is that the short-latency nonvisual vergence motor error is carried by a subgroup of midbrain vergence burst cells. These cells typically show a very rapid buildup of activity about 22 ms before a vergence movement and their activity declines as the movement proceeds (Mays et al. 1986). Although these cells, which we identified as CB1 cells, have been described as having a vergence velocity signal, they might as easily be described as having a vergence motor error signal. Indeed, in open-loop investigations, vergence velocity has been found to be linearly proportional to binocular disparity (Rashbass and Westheimer 1961), which can be thought of as a vergence motor error signal. There is need for a signal transformation between the vergence motor error, which might be encoded by cells previously identified as CB1 cells with a large positive skew, and the smooth vergence velocity command encoded by the CB2 cells (compare the SEME and SĖ profiles of the estimated saccade-free smooth vergence response of the trial in Fig. 2).
The dynamics of the downstream vergence circuitry from the CB2 cells is necessarily very fast, generating saccadic-like enhanced vergence eye movements with velocities exceeding 400°/s. This implies that the dynamical transformation from VGME to the smooth vergence velocity command has to occur upstream from the CB2 cells. Such a transformation is indicated in Fig. 1B by the box labeled “vergence burst generator.” This approach sharply differs from the Multiply Model in Fig. 1 in Busettini and Mays (2005) and Fig. 1A, wherein during smooth vergence responses (i.e., with no saccades) the firing profiles of all CB1 and CB2 cells would be largely indistinguishable. We predict a much larger positive skew in the firing profile of these mislabeled “CB1” cells coding VGME with respect to the associated vergence velocity profiles than the skew in the true CB1 and CB2 firing profiles. This latter skewing effect, resulting only from the plant slow-pass filtering of the vergence velocity command, is expected to be quite small, considering how fast the vergence enhancement profiles can be.
Another possibility is that the vergence feedback loop is a cortico-midbrain-cortical loop involving the recently discovered vergence and accommodation cells in subregions of the frontal eye fields (Fukushima et al. 2002; Gamlin and Yoon 2000). Of particular interest is the firing profile of the cell reported in Fig. 1A in Gamlin and Yoon (2000), which clearly resembles a vergence motor error signal. Our data also suggest that the vergence feedback loop may have an overall delay around 40–50 ms, which would be consistent with cortical involvement. Other areas carrying vergence and accommodation signals are reported in the cerebellum and precerebellar nuclei (Gamlin et al. 1996; Zhang and Gamlin 1998) and focal lesions of these areas alter the vergence responses (Takagi et al. 2003). The function of these areas is still poorly understood.
At this time we do not know where the interaction is located and how it is structured. Figure 9 shows three possible neural implementations of Eq. 1. They are behaviorally indistinguishable in terms of oculomotor responses, but their neural circuitry presents, for each of them, specific features that could be directly tested with standard single-unit recordings or other nonhuman primate neurophysiological techniques.
Figure 9A, similar to Fig. 1B, illustrates a direct pure multiplicative implementation of Eq. 1. Vergence motor error and cyclopean saccadic burst converge on the multiplicative node and the result is added to the smooth vergence response at the level of the CB2 cells. The output of the multiplicative node is a weighted saccadic burst. There is no output from the node if VGME = 0 or SB = 0, which may be a very demanding requirement for large conjugate saccades or larger smooth saccade-free vergence responses. This model requires the existence of cells that are dynamically similar to saccadic burst neurons but that fire only during the enhancement, i.e., they are silent during smooth vergence responses and conjugate saccades. No such cells have been reported to date.
In Fig. 9B the vergence enhancement is obtained as the difference between saccadic bursts asymmetrically affected by VGME. The subtraction, in this model, is also implemented at the CB2 level. Although it has asymmetric saccadic bursts, this scheme is very different from the monocular models of vergence enhancement (Bruno et al. 1995; Chaturvedi and van Gisbergen 1999; King and Zhou 2002; Sylvestre and Cullen 2002; Zhou and King 1998). The two main hypotheses of monocular oculomotor circuits are the ability to generate a response for each eye related to what that eye sees, and that the asymmetric monocular bursts bypass the vergence pathway to directly drive the appropriate eye at the level of the motoneurons. The superior colliculus was considered the best candidate for the generation of these right- and left-eye asymmetric bursts (Chaturvedi and van Gisbergen 1999), although a detailed analysis of its behavior during asymmetric saccades (Walton and Mays 2003) failed to reveal any indication of three-dimensional (3-D) coding. Particularly striking was the absence of a modification of the motor fields in the intermediate and deep layers of the SC consistent with a monocular rotation of the saccadic direction to include the monocular horizontal asymmetry. For the hypothesis that the SC codes saccades in depth, this rotation was expected to be very evident for relatively small vertical saccades with large vergence enhancements, with the development of an important horizontal component.
The main and unexpected finding was a significant suppression in the firing rate of several collicular bursters for saccades during both convergence and divergence, which is not compatible with a right- or left-eye coding. Aniseikonic patterns, which would be an ideal stimulus for such SC-driven asymmetric saccades, generate only minor saccadic asymmetries, and larger asymmetries can be achieved only with the simultaneous activation of the smooth vergence system (Bush et al. 1995) or after prolonged adaptation (Oohira and Zee 1992). Furthermore, saccadic-related vergence enhancement is also observed during accommodative–vergence, when one eye is patched (Enright 1986). By comparing the velocity sensitivity of the medial rectus motoneurons to saccade-free smooth vergence, conjugate saccades, and vergence enhancement, we have strong preliminary data suggesting that the velocity sensitivity to vergence enhancement of these motoneurons consistently mirrors the sensitivity of the cell to the smooth vergence (Davison et al. 2004). This result, if confirmed, would imply that the entire vergence enhancement is encoded in the CBT vergence cells, which are known to monosynaptically connect to the medial rectus motoneurons (Zhang et al. 1991, 1992) and to carry the smooth vergence velocity and position command. As an indirect consequence, it would also mean that the reported monocular coding at the level of the abducens motoneurons (Sylvestre and Cullen 2002) is averaged out, without a detectable consequence at the oculomotor level.
As alternative to the SC, the vergence–saccade multiplicative interaction could be generated by a spatial reorganization during the vergence movement of the distributed vector coding of the saccadic premotor bursters downstream of the SC (Quaia and Optican 1997). Nonetheless, the resulting asymmetric saccadic component of this vector reorganization would still have to be fed into the vergence pathway. The observation that abducens internuclear neurons carry an inappropriate signal for ocular convergence (Gamlin et al. 1989) is also inconsistent with a well-organized monocular schema at the motoneuron level. The model in Fig. 9B would interpret the monocular coding of supposedly medium lead burst neurons (Zhou and King 1998) as a modulatory effect of VGME on a subpopulation of inhibitory (with respect to the CB2 cells) saccadic burst neurons, with the vergence system as the main target. It is also possible that these slowed saccadic bursts may still target, as cyclopean slowed saccadic bursts, the saccadic circuitry, and be responsible for the slowing of saccades during vergence. The slowing of activity at the SC level would be, in this view, an indirect effect of the SC being part of the saccadic local feedback loop.
Key properties of this model are that the absence of enhancement for conjugate saccades is obtained by the differential subtraction of identical saccadic bursts, and that the asymmetry is controlled by an inhibitory modulatory effect on the inhibitory branch to the CB2 cells. It also does not require the existence of cells that fire only during vergence enhancement. Our motoneuron data suggest that the enhancement is delivered to them by the same connections that carry the smooth vergence command, but we do not know whether and where the differential saccadic burst of the model in Fig. 9B is computed and where it is inserted in the smooth vergence response. Strong evidence for this model would be the identification of inhibitory connections between saccadic bursters with firing slowed during vergence (the “monocular saccadic bursts” in Zhou and King 1998?) and the CB2 vergence burst cells. A very interesting property of this model is that a subpopulation of pure vertical saccadic burst neurons would also show important alterations in their metrics during vergence, similar to those observed by Zhou and King (1998) for the horizontal medium lead burst neurons.
Figure 9C is a completely different interpretation of the vergence enhancement mechanism, with an excitatory multiplicative effect of the saccade on the VGME signal, which is seen by the vergence burst generator as a transiently enhanced VGME. In other words, the saccade transiently enhances the apparent goal of the vergence response. Strong evidence for this would be the finding that cells carrying VGME, perhaps in cortex, show saccade-related transient enhancement. Not knowing how the vergence velocity command is generated from VGME it is not possible, at this time, to estimate what type of response a brisk pulselike increase in the VGME would give as output of the vergence burst generator, now shared by both enhanced and nonenhanced signals. This transient saccadic enhancement of VGME is not related to the postsaccadic enhancement of ocular following responses (Kawano and Miles 1986) and ultrashort latency vergence (Busettini et al. 1996). The postsaccadic enhancement was shown to be related to the sweep on the retina of the visual scene associated with a preceding saccade. We can discount that this effect might be responsible for the intrasaccadic vergence enhancement because: 1) intrasaccadic vergence enhancement is concurrent with the saccade and 2) the targets used in this study are small crosses on a black background, which do not generate significant retinal sweep.
The classical model of a neuron is of a linear summing junction of weighted excitatory and/or inhibitory input signals. Nonetheless, there are several behavioral examples that are necessarily the direct result of a concurrent multiplicative interaction between two neuronal variables. Among them, the modulation of the linear vestibuloocular and ocular following responses with the inverse of the perceived distance in primates (Schwarz et al. 1989); the lateral localization of the prey by the space-specific auditory neurons in the owl’s inferior colliculus (Peña and Konishi 2001); the “gain field” multiplicative interaction between eye, head, and visual responses in area 7a of the primate parietal cortex (Salinas and Abbott 1996); and, perhaps the most common, the multiplicative enhancement of the firing of neurons by attention (V4: McAdams and Maunsell 1999; V1: Treue and Martínez-Trujillo 1999; MT and MST: Cook and Maunsell 2004; Treue and Maunsell 1999).
The simple linear summing interaction between vergence motor error and saccadic burst signals implemented in Eq. 3 is incompatible with the fact that there is no vergence enhancement during conjugate saccades (VGME = 0 and SB ≠ 0) and during vergence responses in the absence of a saccadic burst (SB = 0 and VGME ≠ 0). The second condition can be achieved by using the OPNs as an additional strong inhibitory input to the interaction node. In the absence of a saccade, the node could be inhibited by the OPNs, like the saccadic system, independently of the presence or absence of an ongoing VGME signal. The OPNs would therefore act as an on-off switch for the quite strong term D × VGMESONS of Eq. 3. Stimulation of the OPNs (Mays and Gamlin 1995) and of the rostral SC (Chaturvedi and Van Gisbergen 2000), which has connections with the OPNs (Büttner-Ennever and Horn 1994), slow an ongoing smooth vergence response, albeit never stop it, which would be compatible with a partial VGME signal still passing through the summing node in the absence of a saccade. To block the saccadic burst from reaching the downstream vergence pathway in the absence of an ongoing vergence we would need a subgroup of vergence inhibitory cells acting similarly to the OPNs for the vergence system. An enhancement would occur only if both saccadic and vergence OPNs are silent. These cells would pause, and thus release their inhibition on the summing node, only during an ongoing vergence movement, and continue firing otherwise, thus blocking conjugate saccadic bursts. In our study of the brain stem OPNs (Busettini and Mays 2003) no cell was found to pause for smooth saccade-free vergence responses or outside the saccade during combined saccade–vergence trials, but we cannot exclude their existence elsewhere.
The most puzzling aspect of an additive implementation is that a large saccade occurring near the end of the vergence response would still generate a large enhancement with, as a consequence, a large vergence overshoot. The amplitude of the additive saccadic contribution to the enhancement is independent of VGME and therefore of the timing of the saccade within the ongoing vergence movement, as long as VGME is different from zero and therefore the output from the summing node is not blocked. The data in Fig. 4A (and in Figs. 5 and 6 of the accompanying paper) show that this does not happen. Large saccades systematically occurred earlier in the vergence movement and only small saccades occurred later in the movement. Such a temporal distribution of the saccades can simulate a multiplicative effect, greatly reducing the possibility of large vergence enhancements later in the vergence movement. It may be possible to override this saccade–vergence timing strategy by eliciting large saccadic eye movements near the end of the vergence response with direct electrical microstimulation of the saccadic area of the frontal eye fields (Bruce et al. 1985; Robinson and Fuchs 1969) or of the intermediate/deep layers of the superior colliculus (Robinson 1972). The amplitude of the vergence enhancement for these electrically elicited large saccades, the timing of which within the ongoing vergence movement can be systematically selected by the investigator, may be a critical element in discriminating between an additive and a multiplicative interaction of ongoing vergence and saccadic signals.
The three multiplicative schemas of Fig. 9 and the additive model, with the appropriate synaptic excitatory and inhibitory connections, can be easily adapted to divergence responses as well, with the involvement of the divergence burst and burst-tonic neurons (Mays et al. 1986). These models implement the saccade–vergence interaction at the neural level.
Can the oculomotor plant directly contribute to the vergence enhancement by a mechanical modification of the vergence dynamics during the saccade? We presented evidence in the accompanying paper that the transient vergence also associated with conjugate saccades is too small to be responsible for the vergence enhancement. Nonetheless, the appearance in recent years (Demer 2002) of a new factor in oculomotor dynamics, the orbital pulley system, opens the possibility that at least part of the interaction may occur at the plant level. The presence of vergence cells that transiently increase their firing during the vergence enhancement (Mays and Gamlin 1995) would make a neural interaction more likely, but at this time there is no detailed quantitative analysis of the saccade–vergence interaction at the neural level that could support or exclude a plant contribution.
None of the models presented above accounts for the suppressive modulation of the vergence enhancement for the largest and fastest saccades, expressed by the coefficient V in the model equations. This aspect is addressed in the next section.
Short vergence lead effects: evidence for involvement of the superior colliculus?
The cyclopean saccadic signal present at the saccade–vergence interaction node, in both multiplicative and additive cases, may originate from the burst cells in the intermediate and deep layers of the superior colliculus (Sparks and Mays 1980). Supporting this view is the evidence from the report by Chaturvedi and van Gisbergen (1999) that stimulation of the superior colliculus during an ongoing vergence generates a vergence enhancement. The authors interpreted their data as evidence for the SC to be able to generate 3-D coded asymmetric saccades, but they could be also compatible with the SC remaining purely conjugate and simply generating the saccadic burst converging with VGME at the interaction node. Of particular interest is the fact, illustrated in Fig. 10, that the observed suppressive modulation for larger saccadic metrics (term 1 − V × PẎPK) is easily implemented by the spatial representation of the motor map in the superior colliculus (Sparks and Mays 1980). In this dual modulation, the multiplicative effect between VGME and the saccadic burst (and therefore with the peak velocity, term D × VGMESONS × PẎPK) is, at the same time, modulated by a suppressive vectorial weighting based on the size of the movement (term 1 − V × Ssize). This is simply achieved by a weaker spatial projection from the SC cells to the interaction node: the further caudal and/or away from midline is its motor map i.e., the larger the saccade, (decreasing thickness of the vertical arrows in the in Fig. 10, top).
We also used peak velocity for the vectorial weighting (term 1 − V × PẎPK) in our equations to limit the number of independent variables and to consider that part of the enhancement decrease for larger and faster saccades could be a true dynamical saturation (i.e., better correlated with saccadic velocity). Even if saccades are often slower during vergence, it seems that the slowing for larger saccades is, in relative terms, smaller than that for smaller saccades (Fig. 10 in Busettini and Mays 2005). As a consequence, a strong correlation between peak velocity and size for large saccades similar to the one found for conjugate saccades (Becker 1989) is preserved and a suppressive term in saccadic size for the largest saccades would give similar results. In several cases the depth of the effect, as in Fig. 4A, was much stronger than what would be expected from a simple plateaulike dynamical saturation.
Figure 10 also shows that the behavioral sensitivity of the parameter V is very strong. By just doubling its value, what seems like a simple dynamical saturation in some data subsets becomes a powerful suppression in others. The anatomical proximity between a subgroup of the vergence burst cells and the superior colliculus (Mays et al. 1986) makes such a connection feasible, but it is not known, at this time, whether the two clusters of vergence burst cells described in Fig. 9 of that report are functionally different with respect to the vergence enhancement and whether they have collicular connections. It is important to note that this hypothesized spatial mapping of the saccade–vergence interaction, although able to generate the suppressive term for the largest saccades, cannot, by itself, generate the multiplying effect, but only modulate its gain through the parameter V.
Our findings indicate that major revisions of the current models of the vergence system and of the saccade–vergence interactions are in order. We show that the saccade–vergence interaction is likely multiplicative and provide some indications how it may be implemented. Of equal consequence is our reinterpretation of reports of apparent monocular coding by some saccade-related cells and motoneurons. Moreover, we suggest new directions from which the analysis of the saccadic and vergence interactions should proceed at the neural level.
This research was supported by National Eye Institute Grant R01 EY-03463 to L. E. Mays and Core Grant P30 EY-03039.
We thank S. Hayley for computer programming, L. Millican, M. Bolding, and A. Yildirim for technical assistance, and L. Phillips for secretarial assistance.
Present address of L. E. Mays: Dept. of Computer Science, University of North Carolina at Charlotte, Charlotte, NC 28223.
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- Copyright © 2005 by the American Physiological Society