A novel mechanism for volitional locomotion in larval zebrafish

To locomote stably, animals must coordinate volitional actions that change posture with opposing reflexes that hold posture constant [1–8]. These conflicting actions are thought to necessitate integrated control, in which reflexes are modulated to permit or even produce volitional movements [9–14]. Here we report that larval zebrafish (Danio rerio) utilize a simpler control scheme featuring independent volitional and reflexive movements. We present behavioral evidence that larvae swim in depth by appending destabilizing trunk rotations to steer with independent rotations to balance. When we manipulated buoyancy to deflect fish up or down, they redirected steering without coordinated changes to their balance reflex. As balance developed and increasingly opposed destabilization-mediated steering, larvae acquired compensatory use of their pectoral fins to steer. Removing the pectoral fins from older larvae impaired steering but preserved the strong balance reflex. Consequentially, older larvae without fins were strikingly less maneuverable — unable to revert to destabilization-mediated steering — revealing a rigidity inherent within the framework of independent volitional and reflexive control. Larval zebrafish therefore produce effective but inflexible locomotion by sequencing independent volitional and reflexive movements. These results reveal a simple control scheme, applicable for robotic design, that solves the general problem of coordinating volitional movements with the vital reflexes that oppose them.

To locomote stably, animals must coordinate volitional actions that change posture with opposing reflexes that hold posture constant [1][2][3][4][5][6][7][8]. These conflicting actions are thought to necessitate integrated control, in which reflexes are modulated to permit or even produce volitional movements [9][10][11][12][13][14]. Here we report that larval zebrafish (Danio rerio) utilize a simpler control scheme featuring independent volitional and reflexive movements. We present behavioral evidence that larvae swim in depth by appending destabilizing trunk rotations to steer with independent rotations to balance. When we manipulated buoyancy to deflect fish up or down, they redirected steering without coordinated changes to their balance reflex. As balance developed and increasingly opposed destabilizationmediated steering, larvae acquired compensatory use of their pectoral fins to steer. Removing the pectoral fins from older larvae impaired steering but preserved the strong balance reflex. Consequentially, older larvae without fins were strikingly less maneuverableunable to revert to destabilization-mediated steering -revealing a rigidity inherent within the framework of independent volitional and reflexive control. Larval zebrafish therefore produce effective but inflexible locomotion by sequencing independent volitional and reflexive movements. These results reveal a simple control scheme, applicable for robotic design, that solves the general problem of coordinating volitional movements with the vital reflexes that oppose them.
Animals destabilize their bodies to move, complicating the challenge of maintaining balance []. For example, humans walk in "controlled falls," toppling forward with each step before regaining stability []. The conict between movement and stability is pervasive, but a simple body plan constrains the problem for young zebrash. During the rst days of swimming, zebrash larvae possess largely inefectual ns and simply propel where they point [, ]. Larvae must therefore rotate away from horizontal to climb or dive for a number of vital behaviors, including prey capture, predator evasion, buoyancy control, and circadian migration [-]. However, larvae also exhibit a righting reex, a tendency to reorient towards a preferred posture near horizontal [, ] ( Figure A). Larvae are therefore a simpler model system faced with a universal challenge: to integrate reexes into locomotion so as to permit mobility but maintain stability.
Due to their small size, larvae swim intermittently, alternat-ing between passive periods when they are rotated and pushed by external forces, and active bouts when they swim and adjust their posture [-]. Accordingly, freely-swimming larvae spontaneously vary their posture and depth, but tend to remain near horizontal ( Figure B) []. Therefore, to dene how larvae controlled their bodies to achieve both mobility and stability, we examined their posture during spontaneous swim bouts at week post-fertilization (wpf). First, we examined when larvae made spontaneous trunk rotations that permitted changes to depth -volitional control of posture we termed "steering." Second, we determined when larvae exhibited their righting reex -responses to instability in which they reoriented towards their preferred posture. We found that larvae changed their elevation by steering up or down while they accelerated during bouts. Specically, we examined whether rotations during a bout impacted its trajectory, or if larvae propelled where they pointed when a bout began (the null trajectory). Deviations from the null trajectory were positively correlated with trunk rotations during bouts, particularly those during the msec before speed peaked (r=.; Figure C , D). This window corresponds to the greatest acceleration each bout (Supplemental Figure S) and includes rotations that precede trunk rotation (Supplemental Figure S). Therefore, larvae steer by rotating their trunks at the start of a bout.
Larvae temporally ofset steering and their righting reex, rotating towards their preferred posture while decelerating. In control theoretic terms, the reex provides negative feedback to reduce postural error, the extent posture deviates from its "set point." Postural error at the start of a bout was negatively correlated with rotations during the bout, indicating that bouts acutely stabilize posture ( Figure E). In particular, the best correlated rotations occurred for msec afer speed peaked (r=-.; Figure F), corresponding to the greatest deceleration (Supplemental Figure S). Larvae rotated towards an empirical set point, the posture at which no balance feedback was expected (intercept of the best-t line to pre-bout posture and righting rotation), just nose-up to horizontal (. ± .°). Larvae therefore counteract destabilization, including volitional rotations away from horizontal, while they decelerate. We tested whether the temporally dissociable rotations for steering and righting might be independent. Surprisingly, we found that steering and righting were not correlated (r=-.; Figure G). These data indicate that larvae locomote by sequencing nose-up/down rotations that steer with indepen-dent rotations that balance ( Figure H). Accordingly, righting rotations did not correlate with trajectory changes (r=-.; Supplemental Figure SA), suggesting larvae balance without directly impacting translation. Furthermore, steering rotations were not correlated with postural error before a bout (r=-.; Supplemental Figure SB), such that movement is not constrained by stability. We therefore conclude that steering and righting are both sequential and independent. We next tested whether steering and righting were under independent control. We measured how larvae maintain elevation when challenged -a problem that could be solved by modulating either steering or balance. To climb, for instance, a larva could steer upwards, away from its posture set point ( Figure A, le); alternatively, a larva could reorient nose-up using its righting reex, by biasing the set point upwards (Figure A, right) [, ]. Complementarily, larvae could facilitate steering by weakening their reex, permitting greater deviations from horizontal. Can larvae efectively control their swims while steering and righting independently? To challenge larvae to climb and dive, we leveraged their propensity to actively maintain position [, ]. During passive periods between bouts, larvae are moved by gravity and buoyancy (Supplemental Figure S) []. They tend to be denser than water [-] and, consequently, tended to sink between bouts ( Figure B) []. Under typical conditions larvae counteracted sinking by weakly biasing their bouts upwards, consistent with their natural nose-up bias to posture ( Figure C).
If we displaced larvae vertically by manipulating their buoyancy, they biased swims to climb or dive. To exacerbate sinking we altered the swim bladder, a sac larvae typically inate with air from the surface ⇠ days post-fertilization []. Larvae instead inate their swim bladders with denser paran oil if raised with oil on the water's surface [] (Figure D, top). Larvae with oil-lled swim bladders sank more between bouts and biased those bouts systematically upwards, compared to siblings with air-lled swim bladders ( Figure E, top). In contrast, when we increased the force of buoyancy by placing larvae acutely in a low concentration (.%) of glycerol, larvae tended to rise between bouts and bias those bouts downwards ( Figure D, E, bottom).
Larvae could maintain elevation when challenged by modulating either their steering and/or their righting reex. Denser larvae climbed by steering upwards ( Figure F; paired ttest with Bonferroni correction: t =., p<.), while more buoyant larvae dove by steering downwards (t =-., p<.). In addition, denser larvae modulated their posture set point, using their righting reex to skew posture, and therefore trajectory, upwards (p<., t =.; Figure G, top). However, larvae with elevated buoyancy did not adjust their set point (p>., t =-.; Figure G, bottom), meaning set point modulation was selective.
If steering and righting are independent, larvae ought bias the former up or down without coordinating the reex set point. Crucially, we found that individual changes to steering and set point were uncorrelated, whether larvae were climbing ( Figure  H; Spearman's ρ = .) or diving (ρ = .). Furthermore, larvae did not aid steering by suppressing reex strength, as measured by its gain -the proportion of postural error canceled by the average bout (Table S; Oil vs. Air: t =-., p>.; .% vs. % glycerol: t =., p>.). Together, these data show that when challenged, zebrash larvae control elevation by independently modulating the volitional and reexive components of locomotion.
Independent control of steering and righting poses a potential problem as sh mature. Young larvae make destabilizing rotations to steer, meaning developmental improvements to stability [] will impair steering unless larvae compensate. However, if steering and righting mature independently, larvae would be unable to preserve mobility by ensuring that balance does not come to dominate. Evidence that larvae are unable to check their righting reex to maintain mobility would support the hypothesis of independent control. Therefore, we investigated and manipulated how steering and righting change throughout early development. We found that improvements to balance permit greater stability as sh develop. We measured locomotion in siblings from to wpf (n= groups of sh), and found that older larvae prolonged the balance phase of their bouts ( Figure A). With age, each bout came to reduce a greater proportion of postural error, equating to larger reex gain ( Figure B; main efect of age: F (,) =., p<.; main efect of clutch: F (,) =., p>.). When pooling all bouts, the gain doubled from . at wpf ( bouts) to . at wpf ( bouts). Reex gain was inversely correlated with posture variation, such that older larvae better constrained their trunks about their preferred posture ( Figure C; Spearman's ρ = -., p<.). Maturation of the righting reex therefore afords greater stability while swimming. As stability increased, larvae maintained maneuverability through parallel improvements to steering. At one wpf, larvae propelled where they pointed, such that steering rotations provided a proportional change to swim trajectory -corresponding to steering gains near (Figure D,E; Theil-Sen estimated slope of trajectory vs. posture; Supplemental Figure S). Older larvae could efectively climb or dive while remaining closer to horizontal, having gained additional control over their movements. They did not simply propel where they pointed, but skewed trajectories to amplify steering rotations, giving a steering gain much larger than (Figure D,E; two-way ANOVA, main efect of age: F (,) =., p<.; main efect of clutch: F (,) =., p>.). Therefore, developing larvae came to swim with less trunk destabilization, much as human toddlers walk more stably by learning to swing their arms [], and gymnasts learn to prioritize trunk stability in their movements [].
We found that steering improvements reect emergent n use. Mature sh use their pectoral ns, homologues of amniote forelimbs, to steer in depth [, -], but week-old zebrash possess minimally functional pectoral ns []. After surgical removal of the pectoral ns, all larvae propelled precisely where they pointed, with steering gains reduced to ( Figure F; two-way ANOVA, main efect of n removal: F (,) =., p<.; main efect of age: F (,) =., p<.; interaction efect: F (,) =., p<.; n= clutches). Fin removal also abolished the acquired agility to make large trajectory changes from one bout to the next (Supplemental Figure S). While the efect of n removal was large at wpf, cutting steering gain nearly in half (paired ttest with Bonferroni correction, t =., p<.), larvae at wpf also exhibited signicant impairment (t =., p<.). For n use to increase steering gain, larvae must skew movements upwards when their trunks are oriented up, and downwards when oriented down, suggesting larvae actively coordinate their trunks and ns to steer. Together, these data suggest larvae increasingly use pectoral ns to amplify the efects of trunk rotation on their swimming movements.
We found that n development selectively impacted steering. Aside from efects on the direction of locomotion, larvae swam comparably afer loss of the ns. Fin removal had no impact on their rate of swimming or the speed and displacement of their bouts (Supplemental Table S). Furthermore, larvae produced comparable trunk rotations afer loss of the ns (Supplemental Table S; main efect of n removal on angular speed: F (,) =., p>.). The pectoral ns therefore complement trunk-based steering but are not necessary to rotate the trunk. Importantly, n-derived improvements to steering progressed distinctly from the maturation of the righting reex, as changes to steering and reex gains were uncorrelated throughout development ( Figure G; Spearman's ρ = ). Across clutches, larvae improved steering and righting to diferent extents and at diferent rates ( Figure B,E). Thus steering and righting develop complementarily, even as their control remains independent.
Independent control made larvae inexible, unable to adapt steering when challenged. Specically, older larvae could not modulate their reex to restore efective trunk-based steering when their ns were removed. Forced once more to propel where they point, nless larvae at wpf must deviate from horizontal to climb or dive. However, they failed to reduce their reex gains afer n removal (Figure H, Supplemental Figure  SA; main efect of n removal: F (,) =., p>.; main effect of age: F (,) =., p<.) and therefore continued to tightly restrict trunk posture afer n removal (Supplemental Figure SB; two-way ANOVA of posture variance by clutch, main efect of age: F (,) =., p<.; main efect of n removal: F (,) =., p>.). Greater stability at wpf therefore equated to less maneuverability without the ns, evident in reduced variation of swim trajectory ( Figure I; main efect of n removal: F (,) =., p<.; paired t-test with Bonferroni correction at wpf: t =., p<.; at wpf: t =., p>.). By reverting larvae to undeveloped steering, we discovered a limitation of their locomotion -age-expected volitional and reexive control are necessary for proper swimming, as the two are age-matched to achieve stability and maneuverability.
By producing efective locomotion across a range of parameters for steering and righting, independent control allowed larvae to modify existing movement patterns, a prerequisite for locomotor development [-]. However, independent control lef larvae unable to manage the trade-of between stability and maneuverability, to compensate for n loss by reverting to the trunk-based steering of younger larvae. Temporal dissociation thus provides a simple but limited means for new swimmers to avoid conict between steering and stabilizing movements.
Temporary suppression of righting reexes may be a useful and conserved mechanism to sequence volitional and reexive control. Cycles of de-and re-stabilization are also apparent in human gait []. Vestibular stimulation impacts stepping late but not early in the gait cycle [], when reexes may be suppressed to avoid interference with volitional control of walking. A neural means to inactivate vestibular reexes has been described during voluntary movements of the eyes [-], and an analogous circuit may exist to inactivate descending vestibular commands during locomotion. Modulation of sensory signals according to gait cycle phase is a general mechanism to appropriately adjust locomotion to reect ongoing sensation [].
In summary, our experiments show that efective locomotion, in this case stable maneuvering under water, can emerge from an unexpectedly straightforward control scheme with independent volitional and reexive movements. All animals that move themselves must permit instability in some form []; the larval zebrash provides a natural proof-of-principle for one of the simplest possible solutions to this general problem -destabilize oneself to move, then re-stabilize when nished. Larvae also reveal one shortcoming of such rudimentary control, lacking the exibility to revert to earlier modes of locomotion as they develop. Requiring no coordination beyond that which sequences volitional and reexive components, independent control is likely simpler to neurally implement than the integrated control of more advanced locomotion [, ], and thus well-suited for robotic control. Animals that move and then balance may be a developmental and evolutionary intermediary between those that move without balance and those that move and balance in concert.

Fish Care
All procedures involving zebrash larvae (Danio rerio) were approved by the Institutional Animal Care and Use Committee of New York University. Fertilized eggs were collected from in-crosses of a breeding population of Schoppik lab wildtype zebrash maintained at .°C on a standard / hour light/dark cycle. Before dpf, larvae were maintained at densities of -larvae per petri dish of cm diameter, lled with -mL E with . ppm methylene blue. Subsequently, larvae were maintained on system water in -L tanks at densities of -per tank and fed twice daily. Larvae received powdered food (Otohime A, Reed Mariculture, Campbell, CA) until dpf and brine shrimp thereafer. Larvae were checked visually for swim bladder ination before all behavioral measurements.

Physical manipulations
To generate larvae with swim bladders lled with paran oil, dpf larvae were visually checked for the absence of swim bladders and transferred to mL conical tubes (Falcon, Thermo Fisher Scientic) at a density of larvae per tube, as previously []. The tubes were lled with mL E containing methylene blue (as above), then topped with mL paran oil (VWR, Radnor, PA) and incubated until dpf for experimentation. Control siblings were maintained similarly in mL E in conical tubes without an oil surface.
Pectoral ns were removed surgically from larvae anesthetized in .% ethyl--aminobenzoic acid ethyl ester (MESAB, Sigma-Aldrich E, St. Louis, MO). Pairs of anesthetized, length-matched siblings were immobilized dorsal-up in % low-melting temperature agar (Thermo Fisher Scientic ), and both pectoral ns of one larva were removed by pulling the base laterally with forceps. Then, the altered larva and its control sibling were freed from the agar with a scalpel and allowed to recover in E for -hours prior to behavioral measurement.

Swimming measurement
Data were analyzed from a previous study of larvae from each of clutches at wpf, and from larvae with oil-lled swim bladders and control siblings at days post-fertilization []. For measuring efects of pectoral n removal, new data were captured identically from -larvae per condition per clutch (n=) at and wpf. For comparing swimming in and .% glycerol solutions, larvae per condition per clutch (n=). Siblings were transferred to a glass tank (/G/ xx mm, Starna Cells, Inc., Atascadero, CA) lled with -mL E and recorded for hours unless otherwise noted. The thin tank ( mm) maximized the time the sh spent swimming in the imaging plane. The enclosure containing the tank was kept on the same / hour light/dark cycle as the aquaculture facility using overhead LEDs, which maintained water temperature at °C. Video was captured using a digital camera (BFLY-PGE-SM, Point Grey Research, Richmond, BC, Canada) equipped with a close-focusing, manual zoom lens (-mm Macro Zoom Lens, Navitar, Inc., Rochester, NY, USA) with f-stop set to to maximize depth of focus. The eld-ofview, approximately x cm, was aligned concentrically with the tank face. A W nm infrared LED backlight (eBay) was transmitted through an aspheric condenser lens with a difuser (ACL-DG-B, ThorLabs, NJ), and an infrared lter (-, Edmund Optics, NJ) was placed in the light path before the imaging lens.
Larvae with visually-conrmed paran oil-lled swimbladders and control siblings were tested in parallel as above, larvae per clutch per condition (n=), for hours starting the day of dpf. When imaging larvae with oil-lled swim bladders, E in the tanks was topped with a thin layer of paran oil, outside the eld of view, to prevent supplementary ination with air over the course of testing. To increase the density of the swimming medium, larvae were acutely imaged in solutions of glycerol (Sigma-Aldrich, St. Louis, MO). Three sets of siblings from each clutch (n= clutches) were measured in parallel at dpf, in three concentrations of glycerol dissolved in E (, ., and % by volume). Data were collected for only hours in glycerol solution to minimize physical buoyancy adaptation.

Video acquisition and detection
Video acquisition was performed as previously []. Digital video was recorded at Hz with an exposure time of ms, and kinematic data were extracted online using the NI-IMAQ vision acquisition environment of LabVIEW (National Instruments Corporation, Austin, TX, USA). Background images were subtracted from live video, intensity thresholding and particle detection were applied, and age-specic exclusion criteria for particle maximum Feret diameter (the greatest distance between two parallel planes restricting the particle) were used to identify larvae in each image. The position of the visual center of mass and the trunk posture (orientation of the trunk in the pitch, or nose-up/down, axis) were collected each frame. Trunk posture was dened as the orientation, relative to horizontal, of the line passing through the visual centroid that minimizes the visual moment of inertia, such that a larva with trunk posture zero has its longitudinal axis approximately horizontal.

Behavior analysis
Data analysis and modeling were performed using Matlab (MathWorks, Natick, MA, USA). Epochs of consecutively saved frames lasting at least . sec were incorporated in subsequent analyses if () they contained only one larva and () were captured during the last hours of the light phase of the lightdark cycle, to minimize efects of light onset. Instantaneous diferences of body particle centroid position were used to calculate swim speed. Consecutively detected bouts faster than Hz were merged into single bouts. Larvae with paran oil-lled swimbladders infrequently sank at speeds exceeding mm/sec. For these larvae and control siblings with air-lled swimbladders, bouts were excluded if the movement vector was pointed vertically down (below -°to horizontal; about % of bouts).
Bouts were excluded if initiated from a vertical orientation (>°or <-°, constituting of , total bouts) due to ambiguous detection of vertical up and down postures. The posture set-point was calculated as the y-intercept of the bestt line to pre-bout posture vs. late change in posture. The gain of the righting reex was computed as the opposite of the slope of the best t line of posture change (from the time of maximal bout speed to msec later) to the pre-bout posture ( msec prior to maximal speed). Developmental trajectories were analyzed by Two-way ANOVA treating clutch as a categorical factor and age as a continuous factor. Trajectory of a swim bout was dened as the direction of the translation vector from msec before to msec afer max speed was reached. The change in trajectory was the diference between this trajectory and the pre-bout posture, such that a change in trajectory of zero described a larvae that swam directly where it pointed at the start of a bout. Changes in trajectory between successive bouts were compared based on ts to the mean cumulative probability distributions for clutches at a given age. Scale factors of the best-t Weibull distributions were analyzed with two-way ANOVA and pairwise t-tests with Bonferroni correction.

Data sharing
All raw data and analysis code are available online at http://www.schoppiklab.com/  The relationship (Pearson's correlation coecient) between instantaneous trunk rotations throughout the bouts with deviations from null trajectories. Bouts were aligned by peak swim speed (top). The red "steering" window contains the largest positive correlation between changes to trajectory and posture. Data are plotted for individual clutches (sibling groups, thin lines, n=) and their mean (thick line). (D) Deviation from the null trajectory is plotted versus trunk rotation across the steering window (red in C), for each of observed bouts. The line conveys means for bins of bouts. (E) The relationship (Pearson's correlation coecient) between instantaneous trunk rotations with the pre-bout posture ( msec before peak swim speed) for bouts aligned by peak swim speed (top). The tan "righting" window contains the largest negative correlation. (F) Trunk rotation across the righting window (tan in E) is plotted as a function of pre-bout posture for bouts in (D). The empirical posture set point, computed as the best-t line intercept, is indicated with a vertical dashed line. (G) Balancing rotations are plotted as a function of steering rotations for the bouts in (D). (H) Schematic depicting how larvae swim in depth -by rst making steering rotations independent from initial posture, then attaining speed, and nally with righting rotations that are independent from how they steered.