Multi-animal two-dimensional closed-loop OMR

The design of the two-dimensional closed-loop OMR assay was inspired by work in a previous study¹¹. We used the following transformation to update the velocity of the stimulus:

The stimulus velocity (V_s) at time t was calculated as the base velocity (V_B) minus the tail beat frequency (F) multiplied by a constant gain factor. The velocity of the OMR stimulus along a single dimension was directly proportional to the online calculated tail beat frequency. A moving average (box car filter) was applied to the tail beat frequency. This was used to simulate the effects of bursting and gliding during swimming. The velocity of the stimulus also depended on the orientation of the stimulus (θ) relative to the heading direction, where θ ∈ [-180°, 180°). This term reaches a maximum value of 1 when the stimulus is perfectly aligned with the heading angle at 0°. We calculated the orientation of the stimulus using the following equation:

The angular velocity of the OMR stimulus (V_θ) was a function of the mean tail curvature (TC) along all calculated tail segments (s) at a given time t weighted by the inverse of time since the onset of the swimming bout (t₀). The equation for angular velocity weighs the amplitude of the mean tail curvature with the relative length of the swimming bout, such that the initial amplitudes of the swimming bout produced larger changes to the angular velocity compared to subsequent amplitudes.

On a 10 cm petri dish, we mounted one fish at a time (4 total) in a 2 × 2 grid with all fish facing the same direction. Once the agarose was set for all fish, filtered system water was added. We inserted a laser-cut IR-transmitting black acrylic piece shaped like a cross to separate fish into quadrants. This was to ensure that fish could not see neighboring stimuli. We tested the four fish simultaneously, each presented with its own two-dimensional closed-loop OMR stimulus. We used a sinusoidal grating with a spatial frequency of 10 mm. We used a gain value of 1 for all trials. In a single test session, larvae were randomly presented with one of 8 grating orientations that were equally positioned around the unit circle [-180° to 135°]. After an initial 1-min period with static gratings, the gratings moved at a velocity of 10 mm/s for 30 s, after which both stimulus velocity and stimulus orientation were updated based on the fish’s behavior. Each initial starting orientation was presented to the fish four times for a total of 32 trials.

For calculating the probability density of stimulus orientations over time, we included all of the trials across all fish. The distribution of values for each time bin were determined by taking a snapshot of values at the point in time when the time bin started. The distribution of stimulus orientations at each point in time was normalized across trials. Stimulus orientations were binned into 45° samples. To compare the effects of stimulus orientation on bout kinematics, we used the stimulus orientation at the start of each bout. We grouped bouts based on their stimulus orientation into bins of 45° and performed a one-way ANOVA on the binned bouts. Finally, we used a polynomial regression to model the relationship between kinematics and stimulus orientation. A range of models were tested with degrees ranging from 1 to 10, and the model with the greatest change in explained variance was taken as the best model.