The structure and timescales of heat perception in larval zebrafish

Abstract

Avoiding temperatures outside the physiological range is critical for animal survival, but how temperature dynamics are transformed into behavioral output is largely not understood. Here, we used an infrared laser to challenge freely swimming larval zebrafish with "white-noise" heat stimuli and built quantitative models relating external sensory information and internal state to behavioral output. These models revealed that larval zebrafish integrate temperature information over a time-window of 400 ms preceding a swimbout and that swimming is suppressed right after the end of a bout. Our results suggest that larval zebrafish compute both an integral and a derivative across heat in time to guide their next movement. Our models put important constraints on the type of computations that occur in the nervous system and reveal principles of how somatosensory temperature information is processed to guide behavioral decisions such as sensitivity to both absolute levels and changes in stimulation.

Figure 1. A setup for heating freely swimming larval zebrafish with high temporal and spatial precision

(A) Schematic of the laser tracking setup. Note that the schematic is not to scale, mirrors were ~47 cm above the dish resulting in scan angles < 7 degrees at all times. Inset depicts a typical larval zebrafish (10 dpf) with the laser spot centered on the centroid (black circle) of the fish. (B) Analysis of heating dynamics. The beam was parked directly on the center of a 4 mm by 840 µm thermistor submerged in the same chamber used for experiments. Top panel shows change in temperature during 4 s long heating steps. Bottom panel indicates the respective cool-down after the laser turned off. Line color indicates laser power at sample. (C) Spatial heating extent at 1000 mW. The beam center was parked at the indicated distances from the thermistor and the temperature 4 s after heating onset was determined. The plot shows the fraction of maximum temperature reached at each distance (red line) and the fraction of fish that displace more than that distance within one camera frame during a movement (black line). Text at dashed line indicates that heating at 0.22 mm distance is 83 % of maximum and only 2 % of swim bouts resulted in a per-frame displacement larger than 0.22 mm. (D) Behavioral response of larval zebrafish to 2 s long steps of the indicated laser power at sample. Traces indicate average swim speed across fish aligned to power onset (red and blue curve) or aligned to random time-points (green curve, control). Shaded regions indicate bootstrap standard error. Dashed black lines mark the on- and off-set of power respectively (N = 40 fish). (E) Average radial distribution in power gradient experiment. Left panel shows the power at sample delivered to larval zebrafish based on their radial position. Right panel shows cumulative distribution of time spent during the experiment at each given radius averaged across fish. Black curve indicates cumulative distribution while the laser is off and red curve indicates cumulative distribution in response to power gradient depicted on the left. Shaded regions indicate bootstrap standard error (N = 25 fish). See also Movie S1 and Figure S1.

Figure 2. White noise heating paradigm

(A) Example traces illustrating laser input and extracted behavioral parameters. A 5 s long example from the middle of one trial of one experiment is shown. Top panel shows the at-sample laser power (dashed red line) and the temperature calculated based on the heating model (solid black line). Middle panel shows instant speed profile of the larval zebrafish and bottom panel reveals changes in heading direction due to turns. Arrows indicate example swim parameters. (B) Histogram of temperature values in each 40 ms timebin across all experiments. (C) Autocorrelation of the temperature stimulus. Autocorrelation time is 960 ms. (D) Cumulative distribution of interbout intervals across all experiments. The dashed black line is the cumulative distribution of inter-bout-intervals during resting, the solid red line depicts the cumulative distribution during laser stimulation. The rightward shift of the curve indicates a shortening of inter-bout-intervals during stimulation and hence an increase in bout frequency. (N = 88,349 bouts during resting and N = 241,433 bouts during stimulation phases). (E) Cross correlation of power at sample and instantaneous speed at different indicated lags. (F) Autocorrelation of bout starts (y-axis clipped at 4×10⁻³). The autocorrelation trace is flat for ~ 80 ms around timepoint 0 because of a hard threshold in allowed minimal bout duration. (E–F) Dotted black lines indicate 0 lag and 0 correlation respectively. Both correlations are derived from all stimulus trials of the same example fish as depicted in panel A. See also Figure S2.

Figure 3. Generalized linear models of bout initiation in response to heat

(A) Schematic of the derivation of the generalized linear model (left panel) and its makeup (right panel). Left: All traces are discretized into 40 ms time-bins. The input to the model consists of the stimulus history over the last second as well as the timing of the previous bout within the past 2 seconds. The bout timing is used as the output in order to derive model coefficients by logistic regression. Time at which a bout occurred is labeled in red. Data shown is a 250 ms slice of one experiment. The panel on the right illustrates how the sensory filter k(t) and the history filter h(t) create a response which is transformed into a bout probability via a logistic nonlinearity. (B) Coefficients of the temperature responsive part k(t) of the generalized linear model (GLM, grey) versus time before a bout. The blue trace indicates coefficients obtained from a control consisting of rotations of the temperature trace relative to the bout start times. Δ indicates filter part sensitive to increases in temperature in time while Σ indicates the 300 ms long main integrative part of the filter. (C) Coefficients of the bout history responsive part h(t) of the GLM (grey) as well as shuffled control (blue) versus time before a bout. R indicates 240 ms refractory period after previous bout initiation. Shaded area in (B) and (C) indicates the bootstrap standard error. (N = 241,513 bouts) (D) Heat map indicating the predicted probability of bout initiation based on the given constant temperature and time since the last bout. (E) Plot of the Fourier transform of the sensory filter depicted in (B). Grey line indicates magnitude in dB of the filter at each frequency (log-log plot). Colored circles indicate frequencies tested behaviorally. (F) Response magnitude across 50 fish that were stimulated with amplitude matched temperature fluctuations at 1 Hz, 3 Hz and 6 Hz. Error bars indicate bootstrap standard error, N = 450 trials each. Dashed black lines indicate predicted response magnitude given the response at 3 Hz based on the filter magnitudes at 1 Hz and 6 Hz respectively. (Average magnitudes: 3.4 × 10⁻³ at 1 Hz, 7.6 × 10⁻³ at 3 Hz, 2.9 × 10⁻³ at 6 Hz. Comparison of value predicted by frequency response to 1Hz, n.s., p = 0.13, comparison of value predicted by frequency response to 6Hz, n.s., p = 0.16, bootstrap hypothesis test). (G)–(I) GLMs for bouts of different displacement (N=27543 bouts in each group). (G) Average speed profiles during “Short”, “Medium” and “Long” bouts. Inset depicts endpoints of different bout categories if the fish were facing left (black circles delineate 2,4 and 8mm of displacement for orientation). (H) Coefficients of the temperature responsive part k(t) of displacement category GLMs versus time before a bout. (I) Coefficients of the bout history responsive part h(t) of displacement category GLMs versus time before a bout. Shaded areas in (H) and (I) indicate bootstrap standard errors. (J) Absolute area of Temperature (yellow) and bout-history (blue) filter for groups of 25,000 bouts with the indicated average displacement relative to the area of filters with the lowest displacement (indicated by dashed grey line). See also Figure S3.

Figure 4. Generalized linear models accurately predict swimming behavior

(A) Comparison of predicted and actual bout probabilities in playback periods. Grey line indicates the response predicted by the generalized linear model given the temperature fluctuations during the playback phase. Brown line indicates actual response probabilities across 50 zebrafish during playback (peri-stimulus-time-histogram). Dashed pink line indicates response predictions for an alternate model with a flat temperature filter but the same history filter as the true model. This “Boxcar” model is constructed such that its response to steady state temperatures is the same as that of the general bout GLM. Inset depicts the temperature stimulus during playback trials. (B) Comparison of expected and empirical quantiles of interbout interval distributions after application of the time rescaling theorem. Rescaling based on the prediction of the full model is shown in grey, a model that is heat responsive but lacks a history component is shown in orange. Dashed line marks the identity, which is the expected fit of a model that perfectly captures observed inter-bout-intervals. (C, D) Comparison of predicted and actual bout probabilities in playback periods. Red and blue lines indicate the response predicted by the long bout and large turn generalized linear models respectively. Black lines indicate actual response probabilities across 50 zebrafish during playback for the respective bout category, filtered with a window size of 125 ms. Shaded area indicates bootstrap standard error. (E) Comparison of correlation of predictions during playback periods versus true response probabilities between the model derived from the given bout-type (y-axis) and a comparison model (x-axis) for 10000 bootstrap samples each. Grey cloud compares the performance of a boxcar model with the general bout model in predicting general bouts. Red cloud compares the performance of the “Long-bout” model and the “Short-bout” model in predicting long bouts. Blue cloud compares the performance of the “Large-turn” model and the “Straight-bout” model in predicting large turns. Crosses indicate the mean correlation with bars depicting bootstrap standard errors. (F) Schematic depiction of how temperature history and self-generated behavior influence bout decisions in larval zebrafish. See also Figure S4.