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# A distributed saccade-associated network encodes high velocity conjugate and monocular eye movements in the zebrafish hindbrain

## Abstract

Saccades are rapid eye movements that redirect gaze. Their magnitudes and directions are tightly controlled by the oculomotor system, which is capable of generating conjugate, monocular, convergent and divergent saccades. Recent studies suggest a mainly monocular control of saccades in mammals, although the development of binocular control and the interaction of different functional populations is less well understood. For zebrafish, a well-established model in sensorimotor research, the nature of binocular control in this key oculomotor behavior is unknown. Here, we use the optokinetic response and calcium imaging to characterize how the developing zebrafish oculomotor system encodes the diverse repertoire of saccades. We find that neurons with phasic saccade-associated activity (putative burst neurons) are most frequent in dorsal regions of the hindbrain and show elements of both monocular and binocular encoding, revealing a mix of the response types originally hypothesized by Helmholtz and Hering. Additionally, we observed a certain degree of behavior-specific recruitment in individual neurons. Surprisingly, calcium activity is only weakly tuned to saccade size. Instead, saccade size is apparently controlled by a push–pull mechanism of opposing burst neuron populations. Our study reveals the basic layout of a developing vertebrate saccade system and provides a perspective into the evolution of the oculomotor system.

## Introduction

Bilateral coordination of muscle control is a necessary feature of behavior in all bilaterally symmetric animals. As humans, we alternate the movements of our limbs between bilateral (both in-phase and anti-phase) and unilateral states throughout the day1. In contrast, our eyes appear to be firmly yoked to each other, pulled apart only through experimental strategies such as Mueller’s paradigm2. Yet, during REM sleep the eyes can move independently, performing conjugate, monocular, and vergence eye movements, capable even of moving along orthogonal axes3. The ability of the oculomotor system to generate two such behaviorally distinct states, one characterized by bilaterally coupled gaze interspersed with fast reorienting conjugate eye movements (saccades), the other by uniocular independence, provides hints towards the underlying circuits, which are not yet fully understood.

Saccades are high velocity eye movements which are driven by excitatory burst neurons (EBNs) in the brainstem4. The majority of saccades are conjugate, and it is therefore difficult to determine whether they are executed via a single neural command sent to both eyes (argued by Ewald Hering and known as “Hering’s Law of equal innervation”), or via two individual commands defined by separate systems but performed synchronously (suggested by Hermann von Helmholtz). This debate has provided a framework for much of the research into conjugate and vergence eye movements in monkey (reviewed in5,6,7). In monkey, this dichotomy has not been completely resolved, though a Helmholtzian model has recently come into favor8,9,10. Importantly, 80% of EBNs11 and the majority of abducens motoneurons12 have been shown to encode saccades in a monocular fashion. In favour of a Heringian model, however, are findings that lesions both of the paramedian pontine reticular formation (PPRF)13 and medial longitudinal fasciculus (MLF)4, can disrupt conjugate but not convergent gaze, and the existence of a vergence center in the midbrain14. A key strategy throughout these experiments has been the characterization of neuronal firing during conjugate versus disconjugate saccades. A schematic illustrating the burst neuron populations required for each hypothesis, and how their expected response profiles differ for different saccade types is shown in Fig. 1.

Larval zebrafish are a promising vertebrate model to investigate the development of bilateral oculomotor control, because the activity of complete brain areas can be recorded at cellular resolution in the developing animal15. Though the primate system is more complex than that seen in teleost fish, common structures and principles have been shown to underlie the generation of eye movements and may provide insights into an evolutionarily conserved common circuit motif. Recently, Brysch, Leyden and Arrenberg16 showed that for low velocity (slow phase) and position encoding neurons, the zebrafish oculomotor system appears to be overwhelmingly monocular, though a large population of binocular neurons (28.6%) was also found. Similarly, Debowy and Baker17 found that the adult goldfish velocity-to-position neural integrator for horizontal eye movements contained both monocular and conjugate neurons.

Recent studies have started to characterize the zebrafish saccadic burst generator. The first indications of its location were uncovered by Schoonheim, Arrenberg and colleagues18, who were able to elicit saccades via stimulation of neurons in the vicinity of hindbrain rhombomere 5 (also shown by Wolf and Dubreuil19). Ramirez and Aksay20 reported three distinct types of saccade-related neurons: neurons which fire tonically after saccades, neurons which fire a burst at saccade onset, and ramping neurons which start increasing their firing rate a few seconds before a saccade. These ramping neurons have been hypothesized to be responsible for saccade initiation, by a mechanism possibly involving the anterior rhombencephalic turning region (ARTR) and a neuronal population in rhombomere 719,21.

Our study helps to fill the gap in knowledge that currently exists between command structures and motor output by revealing the nature of bilateral control of saccades. We investigated whether horizontal saccades are encoded binocularly (via summation of conjugate and vergence commands) or monocularly (via independent commands), and how saccade size is determined. We identified putative burst neurons in the hindbrain and found that neural recruitment was biased towards certain saccade types for each neuron, suggesting a certain level of binocular and monocular saccade-type specificity across putative burst neuron populations, which is neither in line with Helmholtz’s nor Hering’s hypotheses. Furthermore, these neurons were also active during small-size saccades in the OFF direction and appeared only weakly tuned to saccade magnitude, suggesting that saccade size is encoded via a push–pull mechanism between opposing burst neuron populations.

## Results

### Zebrafish larvae are capable of conjugate, monocular and disconjugate saccades

In this study we investigated the monocular and binocular encoding of horizontal saccades within the hindbrain using calcium imaging in semi-restrained zebrafish larvae during optokinetic behavior (Fig. 2a). Since a large fraction of saccades are binocular conjugate eye movements, the naturally occurring correlations of left and right eye movements impede the identification of eye-specific neural activity correlations. We therefore designed a stimulus protocol to experimentally enrich larval zebrafish oculomotor behavior with monocular, convergent, and divergent eye movements (Fig. 2b). This stimulus protocol consisted of a moving bar stimulus being presented to each eye, with alternating phases, during which the velocity of the bar stimulus sometimes differed in magnitude between the two eyes, or had opposite signs (Fig. 2c). This stimulus protocol reliably evoked optokinetic responses, which are characterized by slow velocity eye movements in the direction of stimulus motion. When the eyes reach the periphery, fast resetting eye movements (saccades) occur to enable the next slow phase. For continuous stimulus rotation, this would result in optokinetic nystagmus (repetitions of slow phase and saccade). Calcium signals of oculomotor neurons are difficult to analyze during nystagmus, since the time points of eye position and eye velocity changes are highly correlated. Therefore, to disambiguate eye velocity and eye position related neural activity16, we paused stimulus motion for 5–7 s after automatic detection of a saccade and then switched its direction for both eyes (Fig. 2d). Since we focused on neurons active during saccades, we removed neurons from analysis which showed tuning to eye position (two example neurons are shown for comparison in Fig. 2d, see “Methods”).

Zebrafish performed horizontal saccades with diverse magnitudes and directions in each recording (Fig. 3a). Saccades were categorized based on the direction and conjugacy of both eyes (RE: right eye; LE: left eye). The following eight categories were defined: monocular temporal-nasal (LETNmono, RETNmono), monocular nasal-temporal (RENTmono, LENTmono), divergent (DIV), convergent (CONV), clockwise (CW, i.e. rightward), and counter-clockwise (CCW, i.e. leftward) saccades. In the convergent–divergent/translational stimulus phase, 38% of saccades were of disconjugate nature (monocular or vergence eye movements), which represents a six-fold enrichment of disconjugate saccades relative to the observed behavior during the conjugate/rotational stimulus phase (Fig. 3b). Notably, conjugate saccades are still the most frequent saccade type in any of the employed stimulus phases. We did not systematically assess the vertical component of these eye movements, which are small during horizontal stimulation (unpublished observation).

### Spontaneous larval saccades conform to the main sequence

The term main sequence describes the stereotyped relationship between maximal saccadic velocity and saccade magnitude22. This relationship has been reported throughout human and monkey saccade literature, and has been used as a tool to identify alterations in saccade kinematics in order to probe the circuitry driving them23,24. Separate high-speed recordings of spontaneous saccades in the absence of moving visual stimuli (but in a lit environment) showed that larval zebrafish eye movements also conform to the main sequence (Fig. 3c), reaching speeds of 800°/s for large saccades (for previous reports, see25,26). Saccade magnitude and velocity are correlated (R2 = 0.5).

To identify whether saccades are driven by mainly monocular coding neurons (Helmholtz’s hypothesis) or binocular coding neurons (Hering’s hypothesis), we labelled each saccade event according to the (mutually exclusive) saccade types (CW, CCW, RETNmono, RENTmono, LETNmono, LENTmono, CONV, DIV; 8 in total), and according to the occurring horizontal eye movements of both eyes during the saccade event (RETN, RENT, LETN, LENT; 4 possibilities). Whilst the first eight labels were distinct, the final four labels (RETN, RENT, LETN, LENT) were applied to different combinations of saccade types, e.g. RENT occurs during the CW, RENTmono and divergent saccade types. We reasoned that if the burst system was organized according to Hering’s hypothesis, then we would find individual neurons active during conjugate and monocular saccades, or active during vergence and monocular saccades. In contrast, following Helmholtz’s hypothesis, many neurons should be active for all three types: conjugate, monocular and vergence saccades. These activity combinations are shown in Fig. 1.

We were aware of the possibility that the monocular neuron types had been detected by chance given their smaller numbers, the high numbers of recorded burst neurons in total, and the lack of clear anatomical clustering (Fig. S2). However, neurons active during CW or CCW are not significantly active during monocular eye movements (see peri-saccadic activity maps in Fig. 4b), and so the motoneuron drive during monocular eye movements cannot come from these conjugate populations. We thus carried out a permutation analysis to determine whether or not the classification of a small population of the LENTmono functional type could be attributed to chance given the large number of identified ROIs. To test this, we used our algorithm to search for neurons that appear to encode a randomly chosen diverse set of saccades. The probability of identifying a monocular population of this size or larger by chance was (p < 0.0001; comparison to all identified LENTmono encoding neurons). Furthermore, the average anatomical locations of exclusively monocular neurons were both significantly more lateral (permutation test: p = 0.0055, α = 0.0167 (0.05/3)) and also more caudal (permutation test: p = 0.0085, α = 0.0167 (0.05/3)) than those of a randomly chosen selection of identified neurons. Therefore, a small subset of neurons is active exclusively during monocular, but not conjugate movements. The drive during monocular eye movements appears to originate from the combined activity of these monocular-only neurons and Helmholtz-like neurons (ranks 4, 6, 8 and 9), which might form a continuum instead of being clearly separated response types.

In the case of conjugate neurons (CW-LETN-RENT and CCW-LENT-RETN), the neurons appeared to encode both eyes. However, smaller numbers of conjugate neurons with preference for a single eye were found as well (cf. ranks 11, 13, 19–20). To determine the position of the conjugate SA neurons within the zebrafish hindbrain, we generated anatomical maps of the two most frequent SA neuron types (significantly active for conjugate saccades, Fig. 5a,b). The vast majority of SA neurons of the conjugate type are located in rhombomeres 4–6 in the hemisphere ipsilateral to the encoded eye movement direction (ipsiversive), whereas contraversive SA neurons are less frequent and located more caudally (rhombomeres 5–7). In contrast to this lateralization of conjugate-related SA neurons (average lateralization index 0.44), Helmholtz-like monocular neurons (Fig. 5c) were not lateralized to a single hemisphere (average lateralization index: 0.09). Furthermore, within each hemisphere, conjugate-related SA neurons were located more medial (Two sample t-test, p = 4.4 × 10−11) more rostral (Two sample t-test, p = 3.6 × 10−6) and more dorsal (Two sample t-test, p = 5 × 10−9) than Helmholtz-like monocular SA neurons (Fig. 5b,c, Fig. S2). Overall, neurons with saccade-related phasic activity are widely distributed throughout the hindbrain, with clusters of higher density in the more dorsal and medial regions of rhombomeres 4 to 7 (Fig. 5d, Fig. S3).

### Tuning to saccade size: evidence for a push–pull mechanism

Our STA analysis revealed that the majority of neurons were significantly correlated with saccades in one direction only. However, many of the SA neurons also fired during many OFF direction saccades. An analysis of peri-saccadic z-scores according to saccade size and direction showed that the same characteristic activation—albeit at smaller magnitude—was present for saccades in the OFF direction (Fig. 6a,b).

## Discussion

In this study we characterized the saccade-associated network of the larval zebrafish hindbrain by determining the response profile of identified neurons to a range of saccade types. These putative burst neurons showed a clear preference for either leftward or rightward saccades and we observed distinct functional neuron types related to conjugate, monocular, and convergent saccades. Furthermore, we present evidence for a push–pull mechanism specifying conjugate saccade magnitude in combination with saccade size tuning.

### Evidence for Helmholtz-like populations

In other species, especially in macaque monkeys, the existence of monocular versus binocular coding schemes for eye movements has already been studied extensively, with evidence favoring a mostly monocular encoding of burst neurons9,11,27. In our neuron type classification scheme, such a Helmholtzian (i.e. monocular, unidirectional) system would rely on four populations (shown in Fig. 1), each active during one of the four possible monocular eye movements and also during corresponding conjugate and disconjugate eye movements, for example a neuron specifically encoding right eye temporal-nasal movements would be classified as type CCW-RETN-RETNmono-CONV (first row, Fig. 1). In our analysis these strict Helmholtzian neurons were rarely found (12 total: divided among 4 different classifications), likely because some of the saccade types (e.g. monocular and vergence saccades) were too infrequent to enable a significant result for these saccade types in our STA analysis in any given recording. When inspecting the population activity of the neuron types with ranks 4, 6, 8 and 9 (Fig. 4), it is evident that these neurons are quite similar to Helmholtzian neurons, in terms of their lack of behavioral specificity; we therefore have referred to them as “Helmholtz-like” neurons. These neurons only reach significant STA activity levels, when events from all saccade types (containing the monocular eye movement in question) are pooled. The fact that their activity during conjugate saccades is not significant, an observation which cannot be explained by undersampling, means they are unlikely to be “pure” Helmholtzian neurons. To determine how distinct Helmholtz-like and conjugate populations are, we carried out principal component analysis (PCA) based on their responses to different saccade categories. The PCA and its interpretation is complicated by the scarcity of activity data for certain saccade types. Our analysis of principal components does—however—suggest that the identified response types do not form distinct clusters and instead form continuous distributions (see Fig. S4).

### Evidence for vergence and conjugate neurons

Vergence-associated burst neurons have been found in the brainstem of primates28,29,30,31, most frequently in the midbrain. These neurons conform to Hering’s hypothesis, according to which a monocular saccade is generated by the combined activity of a vergence and a conjugacy center (where the drive is combined in the moving eye and cancels out for the resting eye). In our classification scheme, we would expect four Heringian populations: a rightward population (CW-LETN-RENT-LETNmono-RENTmono), a leftward population (CCW-LENT-RETN-LENTmono-RETNmono), and two vergence populations (LETNmono-RETNmono-CONV and LENTmono-RENTmono-DIV) (shown in Fig. 1). For pure conjugate movements only the leftward or the rightward population would be active, for pure convergence only the vergence population, and for monocular movements two populations would be active. The two identified conjugate neuron types (CW-LETN-RENT, CCW-LENT-RETN) closely resemble the pure conjugate Heringian types. Their presence at high numbers suggests a certain degree of binocular saccade encoding, especially since activity during conjugate saccades is smaller for the identified Helmholtz-like neurons. We also detected a sizable population of convergence-specific neurons. However, their inconsistent activity during monocular saccades (Fig. 4) argues against a purely Heringian system. In the macaque, a modulation of vergence burst neuron activity based on the binocular context is also present. A recent study described midbrain burst neurons that are active during disjunctive saccades, but inactive during conjugate or symmetric vergence saccades32. In our study, we did not record in the midbrain and further investigation is needed to reveal its role for convergent saccades in zebrafish. Convergent saccades increase the binocular overlap of the visual field, and occur frequently during zebrafish prey capture33. As this behavior is important for foraging, and is functionally distinct from optokinetic saccades (in that it does not seek to reduce retinal slip), it is perhaps less surprising that a separate population of convergent-exclusive neurons exists.

### Saccade-type specific neurons challenge both hypotheses

Based on the findings described above, the saccadic control system neither fully conformed to Hering’s nor to Helmholtz’s hypothesis. Instead, the identified neuronal populations showed evidence in favor of both monocular and binocular encoding of saccades. Whilst the majority of identified SA neuron populations were significantly elevated during a particular saccade type or behavior, reminiscent of labelled lines, it is important to note that this should be considered a preferential recruitment rather than true exclusivity. An interesting characteristic of this system is that it suggests burst neuron recruitment is more binocular than monocular in the sense that activity depends on what both eyes are doing during the saccade- a finding which is more in line with a Heringian view.

### Push–pull dynamics may determine saccade size

Previous research in primates has demonstrated that though saccadic neurons are tuned to a specific direction (the ON direction), they are known to still fire a small number of bursts during OFF direction saccades34. Cullen and Guitton35 systematically analyzed the firing patterns of inhibitory burst neurons and found that half of the neurons recorded had a similar but attenuated rate of firing in the OFF direction. In agreement with these previous studies, our data shows that while zebrafish SA neurons are direction-selective, they also fire at lower magnitude and less reliably during saccades into the OFF direction. Van Gisbergen, Robinson and Gielen36 suggested that burst neurons activate motoneurons via a push–pull system, where motoneurons in the right half of the abducens nucleus integrate excitatory and inhibitory burst neuron input from the right and the left hemisphere, respectively. Thus, small-size saccades occur when the bilateral drive generated by the burst system almost completely cancels out at the level of the level of the motoneurons. Our data is in good agreement with such a push–pull system, though we cannot establish the precise temporal relationships as has been identified for different types of primate burst neurons, nor do we have knowledge about the excitatory or inhibitory nature of each recorded neuron. We found that even monocular and Helmholtz-like neurons are recruited during small conjugate saccades (Fig. 7), which is somewhat surprising given that they are not recruited during larger conjugate saccades. Further research is necessary to characterize the interactions between these populations, and determine at what circuit level the observed opposing activity of CW and CCW encoding neurons is integrated.

### Potential recruitment of vestibular and locomotor systems

When comparing conjugate (left side in Fig. 7) and disconjugate populations (right side in Fig. 7), it is salient that high levels of activity occur during disconjugate eye movements across the identified populations. It is possible that our disconjugate/translational stimuli frequently resulted in the activation of neural circuits involved in locomotion or body posture changes. Therefore, many of our putative burst neurons, especially the disconjugate types, might not be directly related to saccade generation.

We expected the oculomotor circuits to be bilaterally symmetric. However, we observed more conjugate neurons encoding CW saccades than CCW saccades (517 vs. 442 neurons), and more Helmholtz-like neurons encoding left than encoding right eye movements (395 vs. 324). These asymmetric results could potentially be explained by hidden experimental bias (unequal sampling, hardware setup asymmetries). Our analysis also produced many response types for which only very few neurons were identified (Supplementary Table S2). These response types were likely detected at chance or even below chance levels and thus should play a subordinate role in saccadic control. Many of these small-size response populations were not found in every recorded animal, which could have been caused by behavioral bias across recordings and animals, or by true inter-individual circuit differences at this developmental stage.

A previous study suggested that zebrafish burst neurons were located ipsiversively18. Indeed, this was the case for the majority of conjugate (but not monocular) neurons found in this study, though some were located contraversively (average lateralization index = 0.44). Generally, our study only revealed correlations and had a low temporal resolution when compared to electrophysiological approaches. It is therefore likely that many of the identified neurons belong to populations performing functions other than facilitating the saccades, as discussed above. Further investigation is needed to identify the burst neurons causally involved in triggering saccades, and to determine their excitatory and inhibitory interactions.

### Monocularity in comparison to other species

Amongst lateral-eyed animals, an ability to uncouple the eyes during slow phase eye movements is not unusual and can be seen in sandlance, pipefish37, mantis shrimp38, chameleon39, and also in goldfish during early development40. For goldfish, this ability decreases with time, as shown by Beck, Gilland and colleagues40. Much less common, however, is the ability to carry out truly monocular saccades as seen in adult sandlance37. The pipefish was shown not to have complete independence, similar to results seen in zebrafish larvae37,40, and indeed in our study we could only induce monocular saccades with somewhat unnatural disjunctive stimuli. This raises the question of the ethological relevance of monocular saccades. Adult goldfish have been shown to carry out highly disjunctive saccades whilst swimming, in order to compensate for head turns, and monocular saccades may be an extension of this41. As the ability to carry out even slow velocity monocular eye movements decreases as zebrafish develop40, it is questionable whether these monocular saccades will remain in adult zebrafish. The possibility that this level of monocularity is a stage in development points towards Helmholtz theory of conjugacy as a learned behavior.

## Conclusion

In conclusion, our characterization of zebrafish burst neuron types starts to reveal the layout of binocular saccadic control in a developing vertebrate. A rich diversity of functional saccade-associated populations are present in the hindbrain and interact in order to generate a wider range of behaviors. Together with the tuning properties of position and low velocity encoding neurons16, our findings advance the understanding of larval zebrafish oculomotor behavior at cellular resolution, and suggest coding strategies which may prove to be conserved in other vertebrates.

## Methods

### Zebrafish

Animal experiments and all experimental protocols were approved by the responsible ethics committee of the Regierungspräsidium Tübingen in accordance with German federal law and Baden-Württemberg state law. All animal procedures also conformed to the institutional guidelines of the University of Tübingen. The study was carried out in compliance with the ARRIVE guidelines. 5–7 dpf Tg(elavl3:nls-GCaMP6s)mpn400 zebrafish larvae were used42. All zebrafish used were homozygous for the mitfa mutation43. Zebrafish were reared in E3 solution at 29 °C on a 14/10 light/dark cycle.

### High-speed camera recordings

High-speed camera recordings were carried out using an iN8-S1 IDT high-speed camera mounted on a stereomicroscope at a frame rate of 750 Hz. Larval zebrafish were embedded in 1.6% agarose; the agarose was then removed from around the eyes to allow unimpeded eye movements. No moving visual stimuli were presented, but the recording chamber (Petri dish lid) was lit. Ten recordings, each 1 s in duration and containing one spontaneous saccade were made of each fish. Recordings were initiated via a motion trigger. Each eye was analyzed separately in the recordings. Saccades were detected when the eye exceeded a velocity of 100°/s for at least 6.67 ms (5 consecutive frames). This step ensured that all included events were saccades; while binocular saccades of sub-threshold velocity did sometimes occur as well (and were excluded from further analysis in the main sequence plot). In line with Gibaldi and Sabatini44, the maximum velocity was taken as the highest frame-to-frame velocity. The magnitude of the saccade was taken as the difference between the eye position when the eye began to move in the direction of the saccade, and the eye position when the eyes ceased to move in that direction. Only saccades where data was available for 100 frames before the onset and 500 frames after the onset were analyzed. If more than one saccade was detected in an eye, that individual eye trace was not analyzed. 249 recordings were used, taken from a total of 24 fish: analyzing each eye separately a total of 366 saccades were used to generate the plot.

### Visual stimulation

Experiments were carried out using the animal preparation, optical stimulation setup, and microscope setup described previously16, and shown in Fig. 2a. Briefly, larvae were first embedded in 1.6% low melting point agarose in E3. The agarose surrounding both eyes was removed such that both eyes were free to move through a full range of horizontal positions (approximately 30°-40° of dynamical range in each fish). Larvae were then placed under the two-photon microscope. A custom built, 360° surround, square LED arena was used to stimulate the eyes. Previous experiments have elicited disconjugate slow phase eye movements by presenting a moving bar stimulus to one eye, and a stationary stimulus to the other eye: we found that while this stimulus uncoupled slow phase eye movements, the vast majority of the saccades recorded in this condition are conjugate. For this reason, both eyes were provided with moving stimuli throughout the experiment, and uncoupling was achieved by stimuli moving in opposite directions at differing speeds. An opaque black card was also placed directly in front of the arena, at the area of binocular overlap, obscuring an arc of ~ 70°, which allowed both eyes to receive entirely independent stimuli (ignoring potential stimulus reflections). The eyes were then stimulated using a four-stage stimulus protocol, in which the pattern (spatial frequency) of the stimulus was kept the same, but the velocity was altered. In the first two phases the direction and absolute horizontal velocity of the stimulus differed for each eye (unbalanced monocular stimulation). During the third phase the direction and velocity were the same for both eyes (conjugate/rotational stimulus), and during the fourth phase the direction differed but the absolute velocity was the same (convergent-divergent/translational stimulus). The protocol included saccade-triggered motion pauses of 5–7 s followed by stimulus direction reversal. These saccade-triggered stationary periods were used to disentangle position neurons from putative burst neurons. The stimulus presentation lasted 20.8 min per recording and optical plane. Eye position was simultaneously tracked using a CMOS camera (The Imaging Source GmbH, Bremen, Germany) and analyzed using a precursory version of ZebEyeTrack45.

Calcium imaging was performed using a MOM microscope (Sutter Instruments, Novato, CA, USA), Coherent Vision-S Ti-Sa laser and a 25 × objective (Nikon CFI75, Tokyo, Japan). Imaging was carried out at a frequency of 2 Hz, a magnification of 1.5x, and at a wavelength of 920 nm for a duration of 2550 frames. For anatomical registration, we used the same registration framework described in Brysch, Leyden and Arrenberg16. Since the Mauthner neurons did not express the calcium indicator in our transgenic line, the gap in expression in rhombomere 4 corresponding to their somata was instead used as the registration landmark. Imaging was carried out at 10 µm intervals along the optical axis, and multiple recordings were carried out in each fish in different planes. In the range from -80 µm to 40 µm each dorsal–ventral level within the hindbrain was imaged 7–12 times per 10 µm, a further 4 recordings were made at -90 µm and 50 µm, 3 recordings were made at 60 µm and one recording at 70 µm. In total 146 optical planes were recorded in 30 fish. Imaging was stopped when larvae ceased to reliably perform saccades during the conjugate phase. Since some of the saccade types were infrequent, many individual fish did not show the complete set of observable saccade types in a given recording. For example, divergent saccades were observed in 95 out of 146 recordings, out of which only 6 recordings contained the minimum required amount of 6 saccades. 97 out of 146 recordings were missing one type of saccade, none contained at least 6 of each type of saccade.

### Saccade-triggered average (STA) of neuronal activity

Saccade timepoints corresponded to those timepoints in which the eye velocity exceeded 8°/s (as judged from the high velocity regressors). Saccades which overlapped temporally were first removed. An exclusion size of 3 s was used, corresponding approximately to the signal decay kinetics (tau) of the calcium indicator (3.1 s). This step ensured that neural activity could be conclusively correlated with known saccades, and it reduced the risk of misclassification of burst neurons as ramp neurons due to residual activity. 30.6% of the saccadic events were removed from further analysis due to temporal overlap. Each remaining saccade was categorized into one of the 8 unambiguous categories CW/CCW/RENTmono/LETNmono/RETNmono/LENTmono/CONV/DIV and in addition the matching ambiguous categories RENT/LETN/RETN/LENT were assigned (see Table S1). For example, each CW saccade was assigned CW, RENT, and LETN. CW and CCW timepoints were taken from the intersection of left and right eye conjugate regressors (i.e., occurrence of binocular conjugate saccade).

For each ROI the 5 s preceding and following a saccadic event were investigated to classify saccade-related neuronal activity. The STA was calculated from the z score of ΔF/F which was first deconvolved using a calcium impulse response function (CIRF) with τ = 3.1 s47. The tau value was estimated by fitting an exponential decay function to position correlated neurons. The z-score was calculated via Eq. (1), based on baseline fluorescence activity in the entire recording (upper 20% and lower 5% of activity excluded) as

$$\begin{array}{c}z-score=\frac{deconvolved\; DFF-mean\left(baseline\right)}{standard\; deviation\left(baseline\right)} \end{array}$$
(1)

### Tuning curves

In order to calculate tuning curves for conjugate SA neurons (significantly active for “CW-LETN-RENT” and “CCW-LENT-RETN”, see “Results”), all neurons were first identified using the STA. For each saccade, and each neuron, the average saccade-related activation magnitude was then calculated as the sum of the z-score for the saccadic timepoint and two following points divided by three. Saccades were then binned in 4° bins based on saccade size, and the mean peri-saccadic (saccadic time point plus the two following time points) calcium signal z-score for each saccade size bin was calculated for each neuron. The population tuning curves were then generated based on the mean across neurons of all individual neurons’ mean z-scores, and plotted alongside the inter-neuronal standard deviation and standard error of the mean.

### Permutation test for monocular neurons

A permutation test was carried out in order to determine whether the incidence of monocular-classified neurons was above chance level. In order to calculate this, only the 26 recordings with enough LENTmono saccades present in order to classify these neurons were used. In these recordings an average of 7.46 (± 1.8 SD) LENTmono saccades occurred. For each saccade event time, the saccade identity of the saccade event was randomly reassigned to one of the known other saccadic timepoints within the recording, to generate a new file where the total number of each type of saccade remained the same but the saccade magnitudes and timepoints were redistributed (permuted). This was done 1000 times, to create 1000 different versions of each recording. The STA analysis was carried out 1000 times on each of the 26 recordings chosen, each time using a randomly generated saccade timepoint file. The number of neurons which passed the LENTmono rank sum test was calculated and compared with that of the true recordings in order to generate a one-tailed p value.

### Permutation test for anatomical centroid locations

A subset of all identified neurons were pooled into four groups: conjugate, Helmholtz-like, monocular and vergence. The conjugate group contained only CW-LETN-RENT and CCW-LENT-RETN neurons, the Helmholtz-like group contained only RENT, LETN, LENT and RETN neurons, the monocular group contained only RENTmono, LETNmono, LENTmono and RETNmono neurons, and the vergence group contained only “convergent” and “divergent” neurons, other neurons were not used. A permutation test was carried out on the anatomical center-of-masses for each group. For the permutation, we shuffled the neuronal SA type across identified anatomical positions of neurons, but the proportion of occurrence of each SA neuron type corresponded to the proportion in the true recordings. To achieve this, the proportion of each type of neuron (conjugate, Helmholtz-like, monocular, vergence), versus the total number of STA-identified neurons was calculated for each recording (e.g. #mono/#STA-identified neurons), and a matrix of these proportions was generated ([ratioconj rationHelmholtz ratiomono ratioverg]* no. of recordings, 4*146). The proportions were rounded downwards so that the sum of proportions could not be greater than 1. This proportions matrix was then shuffled into 10,000 permutations. A vector containing the shuffled SA neuron proportions was generated for each recording. The identified neurons (anatomical positions) were then randomly reassigned to SA neuron types according to the permuted proportions of SA neuron types in each recording. For example, if the fourth row had the entries [20 50 20 10], then in the 4th recording, 20% of the neurons were randomly assigned conjugate identity, 50% Helmholtz-like, 20% monocular, and 10% vergence identity. This yielded 10,000 populations of each of the four groups of neurons. The center-of-masses of all simulated anatomical neuron positions of each iteration were calculated, and compared to the true center-of-masses of the three experimental groups. The resulting p value was multiplied by 2 to account for the two-tailed test. A Bonferroni post correction was then applied to the results to account for the x, y and z comparisons (factor 3).

### Lateralization index

The lateralization index was calculated as the absolute value of the proportion of neurons on one side (hemisphere) of the hindbrain, versus on the other side of the fish. The index ran from 0 to 1, where a result of 0 corresponds to an even distribution of neurons on either side of the fish, and 1 to complete lateralization of the neuronal population.

### Statistical analysis

During the neuron classification steps, 12 independent saccade categories were defined, and analyzed separately. All statistical tests were performed using Matlab. For the saccade-triggered average testing, rank sum tests were carried out using the Matlab command ranksum; this test was chosen as the data was non-parametric. Significance was determined at α = 0.05, with Bonferroni correction for multiple comparisons applied to all rank sum tests and bootstrapping. Two-sample t tests were carried out on the tuning curves using the Matlab command ttest2.

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## Acknowledgements

This work was funded by the Deutsche Forschungsgemeinschaft (DFG) grants EXC307 (CIN—Werner Reichardt Centre for Integrative Neuroscience) and INST 37/967-1 FUGG.

## Funding

Open Access funding enabled and organized by Projekt DEAL.

## Author information

Authors

### Contributions

CL Designed research, performed research, analyzed data, wrote the paper. CB contributed to the development of stimulation and data analysis tools. ABA Designed research, wrote the paper.

### Corresponding author

Correspondence to Aristides B. Arrenberg.

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Leyden, C., Brysch, C. & Arrenberg, A.B. A distributed saccade-associated network encodes high velocity conjugate and monocular eye movements in the zebrafish hindbrain. Sci Rep 11, 12644 (2021). https://doi.org/10.1038/s41598-021-90315-2

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