Response of supraoculomotor area neurons during combined saccade-vergence movements

Abstract

Combined saccade-vergence movements allow humans and other primates to align their eyes with objects of interest in three-dimensions. In the absence of saccades, vergence movements are typically slow, symmetrical movements of the two eyes in opposite directions. However, combined saccade-vergence movements produce vergence velocities that exceed values observed during vergence alone. This phenomenon is often called “vergence enhancement”, or “saccade-facilitated vergence,” though it is important to consider that rapid vergence changes, known as “vergence transients,” are also observed during conjugate saccades. We developed a visual target array that allows monkeys to make saccades in all directions between targets spaced at distances that correspond to ~1° intervals of vergence angle relative to the monkey. We recorded the activity of vergence-sensitive neurons in the supra-oculomotor area (SOA), located dorsal and lateral to the oculomotor nucleus while monkeys made saccades with vergence amplitudes ranging from 0 to 10°. The primary focus of this study was to test the hypothesis that neurons in the SOA fire a high frequency burst of spikes during saccades that could generate the enhanced vergence. We found that individual neurons encode vergence velocity during both saccadic and non-saccadic vergence, yet firing rates were insufficient to produce the observed enhancement of vergence velocity. Our results are consistent with the hypothesis that slow vergence changes are encoded by the SOA while fast vergence movements require an additional contribution from the saccadic system.

NEW & NOTEWORTHY Research into combined saccade-vergence movements has so far focused on exploring the saccadic neural circuitry, leading to diverging hypotheses regarding the role of the vergence system in this behavior. In this study, we report the first quantitative analysis of the discharge of individual neurons that encode vergence velocity in the monkey brain stem during combined saccade-vergence movements.

INTRODUCTION

Saccades are conjugate eye movements that rapidly align the foveae with an object of interest. In contrast, vergence eye movements are disconjugate and move the eyes in opposite directions to allow them to converge on an object at a different depth. Much of our knowledge of the neural mechanisms underlying saccadic and vergence eye movements comes from experiments designed to isolate these systems and study their circuitry independently. Although this is a useful experimental technique, most movements of the eyes combine both saccadic and vergence components. This is true simply because objects in the real world exist at a range of positions in three dimensions.

Researchers who have studied combined saccade-vergence behavior have reported that vergence angle changes more rapidly than during symmetric vergence movements without saccades (Enright 1984, 1992; Maxwell and King 1992; Ono et al. 1978). This phenomenon has been called both “vergence enhancement” and “saccade-facilitated vergence,” names that highlight the different mechanisms that have been proposed to account for the effect.

In fact, the debate goes back to the fundamental organization of the oculomotor system, epitomized by the differing hypotheses of Hering and von Helmholtz. Briefly, under Hering's hypothesis of 1868 (translated in Hering 1977), the brain treats the two eyes as a single organ and controls them with combinations of version and vergence movements, whereas von Helmholtz argued in 1866 that the two eyes are instead controlled independently (translated in von Helmholtz 1924). Behavioral studies have not produced sufficient evidence to reject either of these long-standing hypotheses, but the fact that they make very different predictions about the underlying neural mechanisms has encouraged researchers to probe this question more deeply.

Initially, the discovery of individual neurons near the oculomotor nucleus, including in the supraoculomotor area (SOA), that encode vergence angle without regard for the positions of either eye individually was seen as strong evidence in favor of Hering's hypothesis (Mays 1984, 1998). These so-called near-response cells, because they increased their firing rates when animals viewed near targets, could provide the vergence-specific commands that would be combined with conjugate saccadic commands, as predicted by Hering (Mays and Gamlin 1995; Zee et al. 1992). Near-response cells in this region have also been shown to project to the medial rectus subdivision of the oculomotor nucleus (Zhang et al. 1992). One challenge for this view is to explain how vergence velocity is “enhanced” during saccade-vergence to levels that are not seen during nonsaccadic vergence. Some researchers have suggested that there could be an interaction between the saccadic and vergence systems, such that a copy of the saccadic command is used to drive a subset of vergence premotor neurons to fire a burst of spikes only during saccade-vergence (Busettini and Mays 2003, 2005a).

Notwithstanding the discoveries supporting Hering's hypothesis, a series of studies has also revealed that individual neurons in brain stem regions previously thought to encode conjugate eye movements may actually preferentially encode the movements of one eye; a result more consistent with von Helmholtz's hypothesis. These areas include the pontine paramedian reticular formation (PPRF), the nucleus prepositus hyoglossus (NPH), central mesencephalic reticular formation (cMRF), and superior colliculus (SC) (Cullen and Van Horn 2012; King 2011; Kumar et al. 2006; Sylvestre et al. 2003; Waitzman et al. 2008; Zhou and King 1996, 1998). Such an arrangement would allow for individual control of the two eyes during disjunctive saccades without a need for an additional vergence command. Based on a quantitative analysis of saccadic burst neurons during saccade-vergence, Van Horn and colleagues (2008) concluded that neuronal activity was largely sufficient to generate the observed action of lateral rectus motoneurons during saccade-vergence. Instead of enhancing the activity of vergence-specific near-response cells, populations of monocular saccadic burst neurons would dynamically control the unequal saccades necessary to “facilitate” vergence. The role of previously identified near-response cells would be limited to controlling “slow vergence” movements that occur before and after saccades, to maintain appropriate eye alignment during fixation (Cullen and Van Horn 2011; Dubrovsky and Cullen 2002; King 2011) and pursuit in depth (Van Horn et al. 2013).

In addition to near-response cells that encode vergence angle during fixation, convergence burst and burst-tonic neurons have also been described in the SOA (Mays et al. 1986; Mays and Gamlin 1995). These cells increase their firing rates during convergence above what would be expected based on the vergence angle, suggesting a sensitivity to vergence velocity, but their activity has not been quantified during saccade-vergence. It is unclear whether these cells could be responsible for generating the rapid vergence changes observed during disjunctive saccades. To account for the reported enhancement of vergence velocity, peak firing rates of SOA neurons during saccade-vergence movements would need to be substantially higher than what has previously been reported for velocity-sensitive neurons in this region during nonsaccadic vergence movements (Gamlin 2002; Mays et al. 1986).

Recent studies of the central mesencephalic reticular formation (cMRF) suggest a plausible mechanism for combined saccade- and vergence-related signals to reach the SOA. The cMRF contains saccadic burst neurons and has been shown to project to SOA (Bohlen et al. 2016; Waitzman et al. 1996). Waitzman et al. (2008) reported that these neurons carry monocular saccadic commands.

During conjugate saccades, the alignment of the two eyes is often unstable, creating what are called “vergence transients” (Collewijn et al. 1988). These are transient changes in vergence angle that can produce vergence velocities exceeding 100°/s during conjugate saccades. Although the transients vary idiosyncratically between subjects, they are often described as an initial divergence followed by convergence that returns eye alignment to the original vergence angle (Busettini and Mays 2005a; Collewijn et al. 1988; Maxwell and King 1992). This simple description led to a variety of hypothesized mechanisms, such as a difference in timing between the adducting and abducting eye due to differing final neuronal pathways, (Maxwell and King 1992; Zee et al. 1992) or differences introduced by the oculomotor plants being driven in different directions (Collewijn et al. 1988). A more thorough investigation of vergence transients during longer saccades and head-free gaze shifts suggests that these simple explanations are insufficient (Sylvestre et al. 2002). Longer duration saccades that do not have “bell-shaped” velocity profiles are associated with multiphasic vergence transients with oscillatory properties that are not explained by the previously mentioned mechanisms, suggesting the more complex transients are a result of disjunctive saccadic commands.

Previous studies have estimated the vergence velocity sensitivity of SOA neurons during nonsaccadic vergence (Mays et al. 1986). If these same neurons display peak firing rates well above the previously observed values when there is an accompanying saccade (>500 spikes/s, for example), then this would be compelling evidence to support models that predict that near-response cells encode the enhancement of vergence velocity (Busettini and Mays 2005a; King and Zhou 2002; Zee et al. 1992). Alternatively, if the peak firing rates of SOA neurons during combined saccade-vergence movements are similar to what has been previously reported for vergence movements in the absence of saccades, then this would be evidence that SOA neurons do not encode the reported enhancement, at least not in the form of the predicted high-frequency burst. The goal of the present study was to determine whether SOA neurons show the predicted high-frequency burst during saccades that accompany vergence.

METHODS

Subjects and surgical procedures.

Two female juvenile rhesus macaque monkeys (Macaca mulatta) were used in this study. To prepare for neurophysiological experiments, the animals underwent two sterile surgeries in a dedicated surgical suite. All procedures were in compliance with the National Institutes of Health Guide for the Care and Use of Laboratory Animals and the ARVO Statement for the Use of Animals in Ophthalmic and Vision Research. Experimental protocols were approved by the Institutional Animal Care and Use Committee (IACUC) of the University of Washington. Detailed descriptions of our surgical procedures can be found in our previously published studies (Mustari et al. 2001; Ono and Mustari 2007). Briefly, a titanium post (Crist Instruments, Hagerstown, MD) was affixed to the skull so that the head could be stabilized during recording sessions. Eye position was measured using search coils, implanted underneath the conjunctiva of both eyes (Fuchs and Robinson 1966; Judge et al. 1980). A recording chamber was implanted over a craniotomy, positioned so that the SOA, near the caudal half of oculomotor nucleus, could be reached with tracks near the center of the chamber. Placement of chambers was aided by preimplant structural MRIs.

Behavioral tasks and visual display.

For the duration of each experimental session the animals sat, with their heads stabilized, in a specially designed primate chair at the center of a 1-m magnetic coil frame (CNC Engineering). Visual targets were presented using a custom-designed array of red, plus-shaped LEDs, which we call the “vergence array.” The array consisted of 60 individual targets arranged in 5 columns and 12 rows positioned at 12 different distances in front of the monkey as follows: 10.2, 11.0, 11.9, 13.1, 14.4, 16.0, 18.1, 20.7, 24.2, 29.0, 36.3, and 48.5 cm. For a monkey with a 25-mm interpupillary distance, these values corresponded to ~1° steps of vergence angle. The absolute target size was scaled with distance, such that all targets subtended 1° of visual angle. The central column was aligned with the animal's midsagittal plane, and the array was adjustable so that the columns immediately to the left and right aligned with their respective eye. The most lateral columns were angled at 20° so that each target could be viewed by both eyes without obstruction (Fig. 1, A and B). Additionally, the height of the array was adjusted so that the central row of targets was aligned with the eyes.

Fig. 1.

Diagram of target display apparatus and examples of behavior. Visual targets were presented using an array of 60 plus-shaped LEDs at distances ranging from 10.2 to 48.5 cm. The size of each LED was scaled with distance such that each target subtended 1° of visual angle. A: top view of apparatus showing the positioning of the plus-shaped LEDs with respect to distance and horizontal displacement. Five columns of targets are attached to triangular panels and organized as shown, adjusted to the interpupillary distance of each monkey. B: side view of the middle columns of the display showing the range of vertical displacements. Each triangular panel contains 12 LEDs arranged at intervals corresponding to 1° changes in vergence angle. C: example saccade-vergence. D: example of spontaneous nonsaccadic vergence. For each plot, we show the change in conjugate vertical eye position (pink), left and right horizontal eye positions (dark blue, red, respectively), vergence position (green), and vergence velocity (light blue). Note that position traces are shifted for display purposes to show change in position rather than absolute position. The onset of the vergence movements are marked, and the period of the saccade is highlighted with a gray box.

Targets were randomly illuminated, one at a time, and monkeys received an applesauce reward for aligning both eyes with the target. After 1–4 s of fixation, the target was switched off at the same time that a different target was illuminated. This arrangement of visual targets enabled us to elicit saccades with a wide range of version and vergence amplitudes (Fig. 1C). For example, shifting the illuminated target to the corresponding location in a different column should elicit a horizontal conjugate saccade. Vertical and oblique saccades should always have a vergence change of at least 1°. However, a target step between the two farthest targets in a given column should elicit a 23° vertical saccade with ~1° of vergence. The amount of vergence change that actually accompanies each saccade is dependent on the accuracy of the monkey. Sometimes, illuminating a target that required no change in vergence angle would elicit a small converging or diverging saccade that was often corrected by postsaccadic vergence movements. We therefore defined conjugate saccades as saccades accompanied by less than 1° of vergence change rather than by the location of the visual targets.

One limitation of this design is that we could not elicit symmetric vergence movements. Despite this, we were able to assess sensitivity to nonsaccadic vergence because monkeys often made spontaneous nonsaccadic vergence movements between saccades (Fig. 1D). In addition, both monkeys sometimes made incorrect conjugate saccades between targets at different distances, with the required vergence change occurring after the saccade. This occurred on a minority of trials.

Unit recording and localization of SOA.

Single-unit, extracellular neural activity was recorded using tungsten in glass microelectrodes (Frederick Haer, Brunswick, ME). The SOA was identified by the presence of vergence-related modulation located immediately dorsal and lateral to the oculomotor nucleus (Mays 1984). In an effort to avoid the nearby central mesencephalic reticular formation, all recorded cells were within 2 mm of the lateral edge of the oculomotor nucleus. The location corresponded to expectations from the MRIs for each animal.

Data analysis.

Experimental control and data acquisition were accomplished with Cambridge Electronics hardware (CED 1401) using Spike2 software for data visualization and storage. Offline analysis was performed in MATLAB (MathWorks, Natick, MA) and R (www.R-project.org) using custom software. Unit isolation and spike times were confirmed using both a voltage threshold and a spike-sorting algorithm (Hill et al. 2011). For some analyses, spike times were converted to spike density functions by convolving them with a Gaussian kernel with SD of 10 ms. Eye velocity was calculated using 7-point parabolic differentiation. Saccades were detected using a velocity threshold (20°/s) using the vectorial velocity to capture saccades in all directions. We defined vergence velocity as the horizontal velocity of the left eye minus the horizontal velocity of the right eye. Vergence lead was calculated using a 3°/s vergence velocity threshold, counting backward from saccade onset to find the last time vergence velocity was below the threshold. Multiple linear regression was used to estimate neuronal sensitivity with confidence intervals calculated using nonparametric bootstrapping with 1,999 iterations. For this analysis, we identified converging and diverging saccades and randomly sampled, with replacement, an equal number of each type plus 200 ms before and after each saccade. We used this new data set to estimate the parameters of the model. Confidence intervals were calculated based on the quantiles of the resulting distribution (Carpenter and Bithell 2000). To assess the fit of our models, we used a measure of variance accounted for (VAF) that has been used in similar studies (Sylvestre and Cullen 1999; Van Horn et al. 2013), calculated as one minus the ratio of the variance of the residuals to the variance of the prediction. This is equivalent to the coefficient of determination (R²) defined with the possibility for values below zero.

Vergence transients.

Previous studies of near-response cells demonstrated that they do not modulate their activity during conjugate saccades (Mays 1984; Mays et al. 1986) despite these high-velocity vergence transients, so any calculation of sensitivity to vergence velocity would be reduced if conjugate saccades were included in the data set. We omitted conjugate saccades from our modeling analysis to avoid this problem. Despite this, the role of vergence transients is still important for interpreting our results. There is significant evidence that vergence transients also influence vergence velocity during converging and diverging saccades. During some converging saccades, the eyes initially diverge before making the appropriate convergent movement. The timing of the saccade relative to the onset of the vergence movement (the vergence lead) is highly predictive for the appearance of this inappropriate divergence, such that saccades that begin 50 ms or more after vergence onset rarely show any divergence at all (Busettini and Mays 2005a). Further, the peak vergence velocity during converging saccades is correlated with the conjugate saccade metrics. Together, this suggests that the vergence velocity observed during saccades with vergence is a combination of both a transient and a vergence movement. Although it appears that transients are produced by the saccadic system, the origination of the vergence command remains unresolved.

The presence of vergence transients also created problems for our ability to use statistical techniques to calculate the latency of the neurons in our sample. Diverging transients made as part of a converging saccade obscure the movement onset and lead to implausibly long delays (>150 ms) for some cells. This results in a misalignment between the burst of spikes and the saccade, which leads to meaningless values for sensitivity. Because the presence of diverging transients was not under experimental control, the magnitude of this problem varied. Rather than adjust the algorithm to produce values we found plausible, we chose a standard delay of 20 ms for each cell. Mays and colleagues (1986) found a mean value of 21.8 ms with SD of 12.5 ms for their convergence burst cells, and 20 ms represented the most common delay we found using their technique with our cells. An important distinction is that they did not evaluate saccadic movements and therefore did not have the same challenges with transients.

RESULTS

We recorded a total of 55 vergence-sensitive neurons in SOA from two monkeys (32 from monkey B and 23 from monkey O), made up of 45 near-response cells and 10 far-response cells. Data from all of these cells are shown in each summary figure.

The primary focus of this paper was to determine whether vergence-sensitive cells in the SOA display a high-frequency burst of spikes during saccade-vergence movements that could encode vergence velocity. The majority of neurons we recorded did not produce a burst for any movements, despite clear vergence-related tonic activity. Some neurons did show vergence velocity-related increases in firing rate, but none approached the firing rates anticipated by previous studies. To illustrate this, in Fig. 2A we plot the peak firing rate of a velocity-sensitive near-response cell as a function of the peak vergence velocity observed during saccade-vergence movements in all directions. The firing rate during saccades with peak velocities of 75°/s is nowhere near the 500 spikes/s that we predicted would be necessary to encode the enhanced vergence velocity in the introduction. The regression lines for all of the cells in our sample are shown in Fig. 2B.

Fig. 2.

Vergence velocity sensitivity of SOA neurons. A: peak firing rate as a function of peak vergence velocity during saccade-vergence for a vergence velocity-sensitive near-response cell. Each point represents the peak values recorded during an individual converging or diverging saccade made while the unit was recorded. This plot includes horizontal, vertical, and oblique saccade directions. Negative values indicate divergence. The blue line is the least-squares regression for movements in the cell’s preferred direction: convergence. B: regression lines for preferred (on-direction) and nonpreferred (off-direction) saccade-vergence movements for all cells. For near-response cells, the preferred direction is convergence whereas the preferred direction of far-response cells is divergence. C–F: perimovement histograms from 2 near-response cells, one with strong vergence-velocity sensitivity (C, D) and one with weak sensitivity to vergence velocity (E, F). C and E: perimovement histograms for converging saccades. D and F: perimovement histograms for diverging saccades. From top to bottom are: spike rasters, normalized perimovement histogram, horizontal eye position (left, blue; right, red), vertical eye position (purple), and vergence angle (horizontal left eye position minus horizontal right eye position; green), shown magnified 10×. Notice that eye movements are shown from many directions for each panel, indicating the activity is not related to conjugate eye movement parameters or the movement of either eye. Also note that both the strongly and weakly velocity-sensitive cells pause their firing during saccades with off-direction vergence movements.

To illustrate the differences between cells with strong and weak vergence velocity responses, in Fig. 2, C–F, we show the activity of two neurons during converging and diverging saccades. The activity of each of these cells is consistently related to the change in vergence, even though each panel includes horizontal, vertical, and oblique saccades in many directions. The near-response cell with strong vergence velocity sensitivity ceases firing shortly before diverging saccades (Fig. 2D) and reaches firing rates during converging saccades that well exceed the tonic firing rate during fixation (Fig. 2C), producing what could be called a burst of spikes. The other near-response cell with weak velocity sensitivity also pauses or significantly decreases its firing rate during off-direction, diverging saccades (Fig. 2F), but does not burst during converging saccades. Nevertheless, there is a small but consistent increase in firing rate during the movements above what would be expected based on vergence position, suggesting a sensitivity to vergence velocity.

In Fig. 3, we show the response of a near-response cell during a conjugate saccade (Fig. 3A), spontaneous nonsaccadic vergence (Fig. 3B), and a combined saccade-vergence movement (Fig. 3C). During fixation, the tonic activity of the cell is related to vergence position, and the firing rate increases during convergence. In the conjugate saccade example, the vergence transient is seen as a rapid divergence followed by convergence during the saccade. In agreement with previous studies, none of the SOA cells we recorded encoded these transients; the cell fires faster during nonsaccadic vergence, even though peak vergence velocity is actually lower than is observed during the conjugate saccade. In the combined saccade-vergence movement, although peak vergence velocity is 10-fold faster than the nonsaccadic vergence, there is no equivalent increase in the firing rate of the cell. During combined saccade-vergence, the vergence movement typically begins before the saccade and often continues for some time after the saccade ends. The period between the beginning of the vergence movement and the saccade is called the vergence lead. A short vergence lead (<30 ms) has been previously shown to be associated with the presence of a divergence transient during converging saccades (Busettini and Mays 2005a), indicated in this example by the arrow. Notice that the cell begins firing and the eyes begin to converge before the divergence transient associated with the onset of the saccade.

Fig. 3.

Activity of an SOA near-response cell during 3 movement types. A: a conjugate saccade. B: a nonsaccadic vergence movement. C: a combined saccade-vergence movement. For each plot, we show the change in conjugate vertical eye position (pink), left and right horizontal eye positions (dark blue, red, respectively), vergence position (green), vergence velocity (light blue), spike rasters (white), and spike density function (black). Note that position traces are shifted for display purposes to show change in position rather than absolute position. The arrow in C indicates the remnant of the vergence transient. Saccades are marked with gray boxes.

Although firing rates did not reach levels sufficient to encode enhanced vergence velocity during saccade-vergence, the cells were active and there was a correlation between peak firing rate and peak vergence velocity (Fig. 2A). We wanted to test whether the cells could also dynamically encode the behavior. To test this, we modeled the firing rate of the cells using a simple linear model including terms for vergence velocity and vergence angle (position):

$$\text{FR}(t)=\text{κ}VG(t+t_d)+r\dot{V}G(t+t_d)+b$$ (1)

where VG and V̇G are vergence position and velocity, κ and r represent sensitivity to vergence position and velocity, respectively, and t_d accounts for delays in neural processing. This model fit the data quite well for the example cell (VAF = 0.34) and the population in general (VAF = 0.36 ± 0.21) when all movements were included (Table 1). However, when we considered saccadic and nonsaccadic vergence separately, the model was better at predicting nonsaccadic vergence in 51/55 cells (VAF_saccadic = 0.25 ± 0.17; VAF_nonsaccadic = 0.39 ± 0.22). This suggests that the cells are dynamically encoding at least part of the saccadic vergence, if not the enhancement. Sensitivity to vergence velocity (r) varied widely among the population (mean ± SD = 0.41 ± 0.33, min = 0.06, max = 1.66), so we used nonparametric bootstrapping to estimate confidence intervals and determine whether terms were significant (see methods). For each bootstrap iteration, we sampled, with replacement, the number of converging or diverging saccades equivalent to the number of saccades made during recording of the cell (converging: mean = 103, min = 10, max = 399; diverging: mean = 107, min = 14, max = 502). As expected, 95% confidence intervals for sensitivity to vergence position (k) did not include zero for any of the neurons in our sample. Surprisingly however, 95% confidence intervals did not include zero for sensitivity to vergence velocity (r) either. This indicates that sensitivity to vergence velocity is distributed to varying degrees throughout the SOA rather than in a separate subpopulation of velocity-sensitive cells.

Table 1.

Mean regression coefficients calculated using Eq. 1

r	κ	b
0.41 ± 0.33	4.73 ± 3.17	34.19 ± 25.88

Values are mean regression coefficients ± SD; n = 55. Sensitivity to vergence velocity and position are represented by r and κ, respectively, and b represents the bias. Sensitivities were estimated while monkeys fixated the visual targets shown in Fig. 1, made saccades between targets at different distances, and made spontaneous adjustments to vergence position between saccades.

We have seen that the model is better at predicting nonsaccadic vergence, and that this is likely due to the firing rate of the cell failing to increase proportionally with enhanced saccadic vergence. To quantify the difference between saccadic and nonsaccadic vergence, we expand the vergence velocity parameters of Eq. 1 to include separate parameters representing the sensitivity of the neurons to saccadic and nonsaccadic vergence velocity. This resulted in the following equation:

$$\text{FR}(t)=\text{κ}VG(t+t_d)+r_{\text{s}}\dot{V}{G}_{\text{s}}(t+t_d)+r_{\text{n}}\dot{V}{G}_{\text{n}}(t+t_d)+b$$ (2)

where VG represents vergence angle, V̇G_s represents vergence velocity during saccades, V̇G_n represents vergence velocity without saccades, κ represents the sensitivity to vergence angle, and r_s and r_n represent the sensitivities to saccadic and nonsaccadic vergence velocity, respectively (Table 2). We defined saccadic vergence as vergence change that occurs during a saccade.

Table 2.

Mean regression coefficients calculated using Eq. 2

rs	rn	κ	b
0.35 ± 0.27	1.12 ± 1.02	4.69 ± 3.17	34.13 ± 25.95

Values are mean regression coefficients ± SD; n = 55. Sensitivity to vergence velocity is separated into 2 terms representing sensitivity during saccadic (r_s) and nonsaccadic (r_n) vergence velocity. Saccadic vergence velocity includes all vergence movement during saccades made between targets at different distances, which likely includes vergence transients. Conjugate saccades were omitted from this analysis.

We then used the bootstrapping procedure described above to estimate 95% confidence intervals for the parameters. Parameters with overlapping confidence intervals are not statistically different and could be replaced by a single term, indicating no significant difference in the vergence velocity sensitivity of the cell during saccadic and nonsaccadic vergence, whereas parameters with confidence intervals that do not overlap indicate a significant difference. Confidence intervals were said to overlap if any points were contained in both intervals, as we show in Fig. 4, A and B. Overall, mean sensitivity to nonsaccadic vergence was significantly greater (Fig. 4C). For the majority of SOA neurons (42/55), sensitivity to nonsaccadic vergence velocity was significantly greater (Fig. 4D). The remainder, 13/55, did not show a significant difference between the parameters. None of the SOA neurons showed a significantly greater sensitivity to saccadic vergence velocity. Additionally, all cells showed a significant sensitivity to saccadic vergence velocity, meaning the confidence intervals did not include zero. In Fig. 4D, we compare the sensitivity of each neuron to saccadic and nonsaccadic vergence velocity. Bootstrap confidence intervals are shown, and cells without a significant difference between parameters are highlighted in red. It should be noted that all cells with sensitivity to nonsaccadic vergence velocity greater than ~1.1 showed a significant difference. Far-response cells have negative sensitivities to vergence velocity, indicating that these cells reduce their firing rates during converging movements and increase them during diverging movements. When summarizing the whole population, as in Fig. 4C, we considered the absolute value of the fit parameters of far-response cells, which corresponds to the sensitivity for movements in the preferred direction.

Fig. 4.

Comparison of sensitivity to vergence velocity during saccadic and nonsaccadic convergence. A and B: demonstration of the nonparametric bootstrapping procedure used to calculate confidence intervals for the parameters. The bar under each histogram extends from the 2.5 to 97.5th percentile and indicates the 95% basic bootstrap confidence interval for the parameters. Confidence intervals that do not overlap (A) indicate the difference is significant. C: box plots comparing the sensitivity of the population of cells to vergence velocity during saccadic and nonsaccadic convergence. The top of the box indicates the 95th percentile, the bottom indicates the 25th percentile, the middle line indicates the median, the whiskers extend 2.5 times the height of the box, and additional outlies are plotted separately. D: comparison of vergence velocity sensitivity during saccadic and nonsaccadic convergence. Each point represents the sensitivities of a single SOA neuron. Crosses indicate the 95% bootstrap confidence intervals. Points above the unity line (black) have a greater sensitivity to nonsaccadic vergence. A negative sensitivity to convergence velocity indicates cells that reduced their firing rates during convergence. Cells with confidence intervals that overlap for the 2 terms (as in B) are colored red to indicate the difference is not significant.

The fact that sensitivity to vergence velocity is reduced in this population during saccadic vergence suggests that an additional mechanism drives vergence velocity during saccades. However, the neurons do not cease their firing during saccades, indicating some contribution to the movement. If the sensitivities calculated during nonsaccadic vergence represent the true sensitivities of the neurons, we can estimate the vergence velocity that is encoded by the cells. To calculate this, we created a new model to predict vergence velocity using the firing rate of the cell and the vergence angle, to account for tonic firing during fixation:

$$\dot{V}G(t+t_d)={\text{κ}}_{\text{v}}VG(t+t_{\text{d}})+r_{\text{FR}}\text{FR}(t)+b$$ (3)

With the new terms r_FR representing the expected vergence velocity given the firing rate of the neuron (°/s per spikes/s), and κ_v accounting for the tonic activity associated with vergence angle. We fit the parameters of this model using nonsaccadic data and then used it to predict the vergence velocity expected by the cell during saccades. In Fig. 5, A–C, we show how this model performs to predict the vergence velocity seen in the example movements from Fig. 3. The model does not predict any significant vergence movement during the conjugate saccade (Fig. 5A), it accurately predicts peak vergence velocity during nonsaccadic vergence (Fig. 5B), but it completely fails to predict the enhancement seen during saccade-vergence (Fig. 5C). In Fig. 5D, we compare the actual and predicted vergence velocity. Consistent with the example, the model always underestimates the peak firing rate during saccade-vergence. This is not a surprising result given that the firing rate does not increase proportionally during saccade-vergence, and it is a simple linear model. Nevertheless, note that the model is successful in predicting the pre and postsaccadic vergence.

Fig. 5.

Predicting vergence velocity from neuronal activity. We use the model described by Eq. 3 to predict vergence velocity for the 3 example movements shown in Fig. 3 (actual: light blue; prediction: orange). The parameters of the model were fit using only nonsaccadic data. A: during the conjugate saccade the model does not predict significant vergence movement. The divergence-convergence oscillation shown is due to the transient introduced by the conjugate saccade (see Fig. 3). B: the parameters of the model are appropriate to predict peak vergence velocity during nonsaccadic vergence. C: the model fails to predict the large vergence enhancement in the combined saccade-vergence movement but does predict the pre- and postsaccadic vergence movement. Note that the model also predicts that vergence velocity will be highest during the saccade. D: comparison of the actual vs. predicted peak vergence velocity for all converging saccades made while this neuron was recorded. The least-squares regression line is shown. The small slope indicates the model consistently fails to predict the enhanced vergence velocity. Saccades are marked with gray boxes.

To estimate the effect that vergence transients have on saccade-vergence, we first verified that the time between the onset of presaccadic vergence and the initiation of the saccade (vergence lead) was predictive of whether a counterproductive vergence movement would be observed at the beginning of the saccade—a remnant of the vergence transient (Fig. 6A); then we estimated the expected transient based on conjugate saccades with similar direction and conjugate velocity, and mathematically subtracted this estimate from the observed vergence velocity to produce several examples (Fig. 6, B–E).

Fig. 6.

The effect of vergence transients on converging saccades. A: minimum vergence velocity as a function of vergence lead during converging saccades. Negative values indicate that the eyes diverge. Vergence lead is defined as the time between vergence onset and the beginning of the saccade. B–E: estimating the effect of vergence transients. Each example is the vergence velocity observed during a converging saccade-vergence movement, aligned by the time of vergence onset. Transients were estimated (blue) by comparison with conjugate saccades of similar direction and peak velocity from the same animal and then subtracted from the original velocity. This results in an estimate of vergence velocity without the effect of the saccade-induced transient (red). The examples shown in B–D demonstrate how the transient can be visible, partially or mostly obscured by the enhancement. The example shown in E highlights the failure of this technique when saccade-vergence movements are for longer duration than similar conjugate saccades.

DISCUSSION

The goal of this study was to test the hypothesis that the activity of vergence-sensitive cells in the SOA is enhanced such that they can encode vergence velocity during saccade-vergence. Although we found cells sensitive to vergence velocity during saccade-vergence, none increased their activity sufficiently to encode the enhanced vergence velocity. This result is inconsistent with the hypothesis. Instead, our results are more consistent with the idea that the saccadic system is largely responsible for the enhancement of vergence velocity during saccade-vergence, while vergence-specific neurons, such as SOA near-response cells, maintain vergence between saccades through slow vergence movements. However, because SOA neurons also dynamically encode vergence velocity during disjunctive saccades and project monosynaptically to medial rectus motor neurons in the oculomotor nucleus, their contribution to saccade-vergence cannot be dismissed.

Prior to our study, Van Horn and colleagues (2008) identified saccadic burst neurons in the pontine paramedian reticular formation (PPRF) that preferentially encode the movement of a single eye during disjunctive saccades. They determined, through a quantitative analysis, that the activity of these cells was “largely sufficient to drive abducens motoneurons during disconjugate saccades.” This study left open the possibility that an additional signal to the medial rectus motor neurons would be required, which had been suggested to originate in the SOA (King and Zhou 2002). Although researchers had previously identified cells that encode vergence velocity in this region (Mays et al. 1986), none had quantified the activity of these cells during saccade-vergence movements, when vergence velocity is enhanced.

Although none of the cells we recorded from either animal increased their firing rates sufficiently during saccade-vergence to encode the observed enhancement, Busettini and Mays (2005b) proposed that only a subset of the neurons in the SOA would encode vergence enhancement, rather than the entire population. This makes their hypothesis more difficult to reject, but we did not encounter any such cells in our study. However, we did record neurons with a wide range of sensitivities to vergence velocity, suggesting that contribution from SOA cells to vergence movements is not uniform, potentially allowing cells to perform different roles. Our study demonstrates that vergence-velocity sensitivity is distributed throughout the population of vergence-sensitive cells in the SOA, rather than as separate populations of tonic and burst-tonic cells. Velocity sensitivity can be observed as an increase in firing rate during vergence movements above what would be expected for the current vergence angle. We have avoided referring to the activity of these cells during saccade-vergence as a “burst” since the period of increased firing rates extends throughout the entire movement, including pre- and postsaccadic vergence, although such activity could be called a burst in the most strongly velocity-sensitive cells.

Busettini and Mays (2005a) demonstrated that the time between the onset of presaccadic vergence and the initiation of the saccade (vergence lead) was predictive of whether a counterproductive vergence movement would be observed at the beginning of the saccade—a remnant of the vergence transient. Saccades with longer vergence leads do not show this behavior, which the authors interpreted to mean that the vergence system needs time to “build up” its activity to obscure the vergence transient, consisting of rapid intrasaccadic divergence and convergence that is observed during conjugate saccades. Our behavioral results confirm that vergence lead is an important predictive factor for these inappropriate vergence movements (Fig. 6A), but we did not find evidence that the vergence-related activity in the SOA could build up sufficiently to cancel out large vergence transients, which can exceed 150°/s. Van Horn and colleagues (2008) determined that saccadic burst neurons in the PPRF are largely responsible for producing the activity of abducens motor neurons during disconjugate saccades, and actively contribute to disjunctive vertical saccades (Van Horn and Cullen 2008), although they did not directly address whether this includes producing the vergence transient, as was suggested by Sylvestre and colleagues (2002). If activity in PPRF is responsible for both the enhancement and the transient, then it remains unexplained why a short vergence lead is associated with a divergence movement before a converging saccade, since the presaccadic vergence movement is produced while the saccadic burst generators are silent.

Busettini and Mays (2005a) also showed that transients are idiosyncratic, but are predictable based on saccade direction and peak conjugate velocity. Mathematically removing the expected transient, as we did in Fig. 6, B–D, not only removes the inappropriate divergence, but also suggests that enhancement begins with saccade onset. The example in Fig. 6E shows the limitations of this technique. If the duration of the converging saccade is longer than the transient, or if the estimated transient is not accurate, the result is difficult to interpret. Compounding this is that there is no objective way to determine the accuracy of the estimated transient. Regardless, removing the transient has the effect of increasing vergence velocity at the beginning of the saccade, and often increases, rather than decreases, peak vergence velocity. This means that even if we were able to remove the effect of the transients, which we know SOA does not encode, the remaining vergence velocity is still too fast to be the result of the activity of SOA near-response cells alone. As discussed above, additional input may come from the saccadic burst neurons in the PPRF (Van Horn et al. 2008).

Cells encoding slow vergence, but not fast saccade-vergence, have been described in the rostral superior colliculus (rSC) by Van Horn and colleagues (2013). Unlike the cells that we recorded in the SOA, vergence-sensitive cells in the rSC were largely unresponsive during disjunctive saccades, but become active during postsaccadic slow vergence and during vergence pursuit. In contrast, SOA neurons described in our study are active during all phases of the saccade-vergence movement and demonstrate significant sensitivity to vergence velocity throughout.

Our study did not find evidence that vergence velocity cells in the SOA have appropriate response dynamics to produce the observed vergence enhancement or vergence transients. Other brain regions that have been shown to contain individual neurons encoding vergence have yet to be investigated during saccade-vergence tasks. Further studies are needed to determine the contribution of vergence-specific circuits to saccade-vergence. Cells encoding vergence velocity during slow vergence movements have been reported in the nucleus reticularis tegmenti pontis (NRTP), a region that also encodes saccadic eye movements and projects exclusively to the cerebellum (Gamlin and Clarke 1995). The role of the cerebellum in generating saccade-vergence movements has not been established, but both saccadic and vergence sensitive cells have been identified in oculomotor regions (Zhang and Gamlin 1998). Even if there is no direct interaction between the saccadic system and vergence-specific regions, the coordination of multiple, independent vergence systems (both saccadic and nonsaccadic) is still an important unresolved issue, particularly given our results here demonstrating SOA neurons continue to fire uninterrupted during saccade-vergence.

GRANTS

This work was supported by National Eye Institute Grants EY-024848 (M. M. G. Walton); and EY-06069 and EY-013308 (M. J. Mustari); Office of Research Infrastructure Programs (ORIP) Grant P51-OD-010425; and Research to Prevent Blindness.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

M.M.W. and M.J.M. conceived and designed research; A.C.P. and M.M.W. performed experiments; A.C.P. analyzed data; A.C.P. and M.M.W. interpreted results of experiments; A.C.P. prepared figures; A.C.P. drafted manuscript; A.C.P., M.M.W., and M.J.M. edited and revised manuscript; A.C.P., M.M.W., and M.J.M. approved final version of manuscript.