Algorithms underlying flexible phototaxis in larval zebrafish

Abstract

To thrive, organisms must maintain physiological and environmental variables in suitable ranges. Given that these variables undergo constant fluctuations over varying time scales, how do biological control systems maintain control over these values? We explored this question in the context of phototactic behavior in larval zebrafish. We demonstrate that larval zebrafish use phototaxis to maintain environmental luminance at a set point, that the value of this set point fluctuates on a time scale of seconds when environmental luminance changes, and that it is determined by calculating the mean input across both sides of the visual field. These results expand on previous studies of flexible phototaxis in larval zebrafish; they suggest that larval zebrafish exert homeostatic control over the luminance of their surroundings, and that feedback from the surroundings drives allostatic changes to the luminance set point. As such, we describe a novel behavioral algorithm with which larval zebrafish exert control over a sensory variable.

Keywords: Allostatic control; Behavioral tracking; Homeostasis; Larval zebrafish; Luminance adaptation; Phototaxis.

Fig. 1.

Larval zebrafish orient towards a set point during luminance-based navigation. (A) Schematic diagram of the experimental setup. Larval zebrafish swim freely while visual stimuli are presented locked to fish reference frames (see Materials and Methods). (B) Experimental design. Each trial consisted of two periods. During the first period (‘pre-adaptation’) fish were held in a dim (L=0.25, n=11 fish) or bright (L=0.75, n=8 fish) environment for at least 10 s. Immediately following pre-adaptation, fish were subjected to a test period for at least 3 s. During the test period, the left and right sides of the environment relative to the fish were held at brightness values (B_L, B_R) selected pseudo-randomly from the set {0, 0.25, 0.50, 0.75, 1.00}. (C) Change in orientation of fish over the last 3 s of pre-adaptation. The color bar reflects equal luminance on the two sides of the fish. Each trace shows the change in orientation in a single trial for a single animal. Orientation values are presented relative to the animal's orientation 3 s before test period onset. Blue traces: condition 1 (n=11 fish, 2200 trials). Red traces: condition 2 (n=8 fish, 720 trials). Thicker traces show the mean of each condition (partial overlap with dashed line). (D) Statistical comparison between pre-adaptation periods in conditions 1 and 2. Top: gray histogram shows bootstrapped distribution of trials shuffled randomly and split with 2200 trials in one group and 720 in another to preserve group size (1000 bootstrapped means). Red and blue ticks show observed means for conditions 1 and 2, respectively (μ₁=0.40 deg, μ₂=−4.72 deg); they fall within the 90% confidence interval (CI) of the shuffled mean [−7.31 deg, 1.26 deg]. Bottom: the bootstrapped null distribution of the difference in means between the two conditions (1000 bootstrapped differences). Trials were shuffled and sorted as described for the histogram above. The purple tick shows the observed difference in means (μ₁−μ₂=5.12 deg), which falls within the 80% CI of the shuffled difference [−7.25 deg, 6.89 deg]. (E) Same as C for the test period. Negative orientation angles were defined to be in the bright direction and positive orientation angles were defined to be in the dim direction, as shown in the color bar. Note the clear separation between the two conditions. (F) Same as D for the test period. Observed means and difference between means fall completely outside bootstrapped distributions for shuffled data (1000 bootstrapped values for each distribution), indicating a difference significant to P<0.001. (G) Analysis of the test period for trials in which one side of the fish was at set point luminance. The luminance of the other side was considered the test luminance. The shaded region denotes the set point luminance. Bias towards the set point side depended significantly on the test luminance (ANOVA, d.f.=4, P<0.05 for both conditions): bias towards the set point luminance was higher when the test luminance deviated from the set point than when the test luminance was equal to the set point luminance (condition 1: test luminance 0.25 versus test luminance 1.0, t-test P<0.01; condition 2: test luminance 0.75 versus test luminance 0.0, t-test P<0.01). Error bars denote standard deviation across fish. (H) Explanation of abbreviations and calculations used to generate I. (I) Percentage of leftward swims plotted as a function of relative distance from the set point: E_R−E_L. Higher E_R−E_L values drive higher leftward swim bias (t-test on slope of linear fit, P<0.001). Error bars denote standard deviation across fish.

Fig. 2.

Larval zebrafish possess a unitary phototactic set point that depends on luminance on both sides of the fish. (A,B) Schematic diagrams of two competing hypotheses for the behavioral algorithm that larval zebrafish use for set point seeking. In A, each eye has its own luminance set point (SP_L and SP_R). B_L and B_R are the brightness experienced by the left and right eye, respectively. In B, there is a unitary set point (SP) that approaches the mean of B_R and B_L. Other computations are identical to those for A except that B_R and B_L are compared with SP instead of SP_L and SP_R. See Materials and Methods for implementation of models. (C) Experimental setup. During pre-adaptation, one side of the fish was bright and the other side was dark. During the test period, the luminance of the bright side was decreased to a final value between the two pre-adaptation values. (D) Simulated turn angle distributions of the two models in A and B during the test period. (E) Cumulative turn angle over the first six bouts predicted by the two models. In all panels, cumulative turn angles were defined to be the cumulative orientation change reached after the first six swim bouts during the first 5 s of the test period or the last 5 s of the pre-adaptation period. Color bar shows luminance; positive angles are defined to be towards higher luminance. (F) Schematic drawing showing that the two models predict opposite behavioral outcomes. (G) Turn angle distribution over all turns made during the first 5 s of the test phase. (H) Cumulative turn angle observed in real fish. (I) Mean cumulative angle change after six swim bouts during pre-adaption and test periods for eight fish. The slight positive phototaxis during pre-adaptation was enhanced during the test period (paired t-test). (J) Schematic diagram of the second experiment, in which the dark side of the pre-adaptation environment was brightened. (K) Mean cumulative angle change after six swim bouts during pre-adaptation and test periods for eight fish. The slight positive phototaxis during pre-adaptation was suppressed during the test (paired t-test).

Fig. 3.

The luminance set point depends on environmental luminance history. (A) Schematic diagram of the experiment to probe temporal evolution of the set point. Fish were subjected to a first pre-adaptation period in either dim (L=0.25, condition 1) or bright (L=0.75, condition 2) luminance. Fish then experienced a second pre-adaptation period of varying length (condition 1: luminance increased to 0.75, condition 2: luminance decreased to 0.25). Finally, fish experienced a split-luminance test period (L=0 on left, L=1 on right). (B) Turn angle probability distribution for both conditions and different pre-adaptation 2 lengths (0, 3, 6, 9 or 12 s, as shown on the right). Low-angle swim bins were truncated (gray slashes) to allow for comparison of changes with larger angle turn distributions. Turn angle distributions were defined over all turns made during the first 5 s of the test phase (n=14 fish). (C) The number of right turns as a fraction of the total number of turns. Angle threshold for turn classification was 15 deg. Note the opposite turning bias for 0 s pre-adaptation 2 and 12 s pre-adaptation 2 in both conditions (t-test, P<0.001 for both conditions). Error bars denote standard deviation across fish.

Fig. 4.

Luminance set point seeking is consistent with previously reported positive phototactic behavior. (A) Schematic diagram of the experiment described in Fig. 1B. (B) Simulated fish results for the experiment shown in A. Different conditions show opposite luminance preferences (exact test on difference between mean orientation after six bouts, P<0.01). (C) Replotted data from Fig. 1E for comparison. (D–F) Simulations of the split-arena phototaxis experiment performed by Brockerhoff et al. (1995). In D, simulated fish swam freely in a brightly lit (L=1) arena; after 500 simulation time steps, the right half of the arena was darkened (L=0). Note that the visual stimuli here were fixed in the lab reference frame, not the fish's reference frame. E shows swim paths and occupancy densities of 100 simulated fish during pre-adaptation and test periods. Arrowheads denote the final positions of the fish. F shows quantification of occupancy density of the left half of the arena during pre-adaptation and test periods for simulated fish and during the test period reported by Brockerhoff et al. (1995). Error bars denote standard deviation of mean occupancy. Pre-adaptation values were not significantly different from chance (t-test, P>0.25); test values were significantly larger than chance (t-test, P<0.001). (G) Simulations of the spotlight phototaxis experiment performed by Burgess et al. (2010). In both conditions, fish were pre-adapted to a dim environment (L=0.1). After 500 simulation time steps, the environment was either completely darkened (L=0, control condition) or darkened (L=0) except for a spotlight (L=1). The arena was 101×101 pixels, and the spotlight had a radius of 11 pixels. During pre-adaptation, fish positions were fixed to the middle of the arena. During the test period, fish were allowed to swim freely, and the visual scene was fixed to the lab reference frame, not the fish reference frame. (H) Swim paths during the test period in the spotlight condition; fish swam towards the spotlight. (I) Fish in the spotlight condition exhibited positive phototaxis if the spotlight luminance was similar to the pre-adaptation luminance and negative phototaxis if the spotlight luminance was too bright, consistent with Burgess et al.’s (2010) findings (pre-adaptation L=0.005). Rate was calculated as the average change in Euclidean distance from the spotlight after 500 time steps, divided by 500.