Optic Flow

Experiments were performed in the evening Zeitgeber time (Z.T.) and animals were typically imaged 30–60 min following dissection. Fly holders were secured to a raised platform over the spherical treadmill (Supplementary Fig. 3a). The VNC was then located using microscope oculars and positioned in the center of the field-of-view by 2-photon imaging.
The spherical treadmill is an aluminum rod with a ball-shaped hole milled at one end^{22 (link)}. We fabricated 10 mm diameter foam balls (Last-A-Foam FR-7106, General Plastics, Burlington Way, WA USA) and manually spotted them using a Rapidograph pen (Koh-I-Noor, Leeds, MA USA) to provide high-contrast features for optic flow measurements. A 500–600 mL min⁻¹ stream of filtered and humidified air was passed through the holder using a digital flow controller (Sierra Instruments, Monterey, CA USA). Movements of the ball were measured using two optical flow sensors (ADNS3080) outfitted with zoom lenses (Computar MLM3X-MP, Cary, NC USA). The ball and fly were illuminated using a pair of IR LEDs (850-nm peak wavelength) coupled to optic fibers and collimator lenses (ThorLabs, Newton, NJ USA). Optic flow measurements were passed to a microcontroller board (Arduino Mega2560) to be recorded using custom Python code. Simultaneously, video recordings of animals behaving on the ball were made using an IR-sensitive firewire camera (Basler, Ahrensburg, Germany) at approximately 30 fps.
We performed 2-photon microscopy using a Bergamo II microscope (ThorLabs) outfitted with two GaAsP PMT detectors for GCaMP6 and tdTomato imaging and coupled to a Ti:Sapphire laser (MaiTai DeepSee, Newport Spectra-Physics, Santa Clara, CA USA) tuned to 930 nm. We used an Olympus 20× water-immersion objective lens with 1.0 NA (Olympus, Center Valley, PA USA). The microscope was controlled using ThorImage software (ThorLabs). Coronal section imaging experiments were performed in Galvo-Galvo imaging mode at 6–9 Hz. This framerate varied with image size which ranged between 26.58 × 26.58 µm and 53.15 × 53.15 µm. Laser power ranged between 3 mW and 5.7 mW. Volumetric imaging is also possible with appropriate hardware (e.g., Galvo-Resonance scanner and Piezo-driven objective collar).
Occasionally, a puff of air was used to elicit walking behaviors. These puffs were digitally encoded (Honeywell AWM 3300 V, Morris Plains, NJ USA). Custom ROS software interfaced through an analog output device (Phidgets, Calgary, Canada) to ThorSync software (ThorLabs) was used to synchronize optic flow measurements, behavior videography, air puff measurements, and 2-photon image acquisition. For coronal section imaging, a Piezo collar (Physik Instrumente, Karlsruhe, Germany) was used to control rapid z-axis movements of the microscope objective lens.
To compare neural activity between control and Act88F:Rpr animals, we acquired 512 × 512 pixel images at 1.7 fps using a constant laser intensity and PMT gain. Selected imaging regions were empirically chosen as horizontal sections consisting of landmarks observed at ~61–65 µm depth in Supplementary Movie 1.

Integration is assumed to be subject to a “leak” that causes output to decay exponentially to zero in the absence of input. Optic flow integration is modeled in continuous time by the ODE
$$\frac{dY(t)}{dt}=y(t)-Y(t)/{\tau }_f$$
where Y is the output of the integrator and τ_f is the decay time constant. This is equivalent to a low pass IIR filter with time constant and gain both τ_f; for a fixed input y the output Y relaxes exponentially toward asymptotic value yτ_f.
For model simulation the discrete time approximation uses Euler integration with timestep number t and time step duration Δt of 10ms:
$$Y\left[t\right]=Y\left[t-1\right]+\Delta t(y[t]-\frac{Y\left[t-1\right]}{{\tau }_f})$$

We used a free-swimming assay to mimic the natural environment in which larval zebrafish swim against aquatic perturbations. Larvae were put in 300mm long clear acrylic channels with width 10mm and depth 8mm. Eight larvae were tracked simultaneously in parallel channels with visual barriers so that the fish could not see each other. Moving sinusoidal gratings with 100% contrast were presented from below to simulate the optic flow experienced in streams. Height was varied by adjusting the stimulus monitor within the range of 4-60mm. Position of the fish was tracked through processing the 2D image taken from above at 100 frames/s using Basler acA1920-155um USB 3.0 camera with a resolution of 2.3 MP. The setup was illuminated by IR light at a 45 degree angle from above on the side.
Grating speeds were generally kept relatively low to avoid eliciting escape behaviors. The period of the grid was varied in proportion to height for the three height conditions to maintain the same spatial frequency of 0.0156 cycles per degree (cpd) at the center of the channel when refractive effects are ignored, as the frequency eliciting fastest swimming at the intermediate height was found to lie between 0.01 and 0.02 with relatively little variation across that range (S10A Fig). In fact refraction effects increase the perceived spatial frequency to an extent that can vary with height [27 (link)]. However, a further experiment demonstrated that the same grid period scaled in proportion to height was also optimal at both the low and high heights (S10B Fig), suggesting that in these experiments the impact of variations in perceived spatial frequency due to changes in height had a limited effect on the OMR.
Calculating the angle subtended at the eye by rays from a single period of the grid stimulus located directly below the fish indicated that the perceived spatial frequency would have varied from 0.0187 cpd for a fish in the low height condition to 0.0210 cpd in the high height group (S11 Fig). The spatial frequency tuning curve (S10A Fig) suggests that this degree of uncontrolled variation (± 7.7% relative to midpoint of the range) around a point close to the peak of the curve would not have been expected to have much effect on OMR performance, as confirmed by the subsequent experiment. In addition, because refractive effects are at a minimum immediately below the fish but increase markedly toward the periphery, there is some suggestion that the fish may have been responding primarily to optic flow from the region of the ground immediately below, as they do when responding to local edges [14 (link)].
Each experimental session consisted of three traverses at the same height. The initial traverse was to drive the larvae to one end of the channel with the stimulus moving at 5 mm/s for 70s. During the two trial traverses the grating moved first forward for 60s then backward for 60s at the appropriate speed for that session with a resting period of 5s between trials. Experiments were conducted on two consecutive days with larvae aged 6 and 7 dpf respectively. The monitor presenting the stimulus was manually adjusted for the three experimental heights at 4–12, 28–36 and 52–60 mm respectively. We took a mixed design approach: each batch of 32 larvae (total of 96 per experiment) was subjected to only one specific height but all the stimulus speeds. The order of experimental conditions with different combinations of testing height and speed was randomized on the day.

Movement of the fish relative to stimulus below generates an optic flow ω in radians/s:
$$\omega (t)=\frac{1}{h}(s-v(t))$$
where v(t) is the speed of the fish through the water at time t, s the forward speed of the grid stimulus (this corresponds in the natural setting to the speed of the water current sweeping the fish backwards), and h the height of the fish above the water (Fig 1A). Note that height and stimulus speed, although varying between experimental conditions, are fixed for a given trial while the swim speed and resulting optic flow vary. The convention here is that optic flow is positive when the fish is at rest with the stimulus moving and is reduced by swimming. The output of the fish visual system, the sensed optic flow y(t), is assumed to be an accurate estimate of the actual optic flow but with a sensory delay t_delay of 220ms:
$$y(t)=\omega (t-t_{delay})=\frac{1}{h}(s-v(t-t_{delay}))$$