Random Walk Revisited: Quantification and Comparative Analysis of Drosophila Walking Trajectories

Abstract

Walking trajectory is frequently measured to assess animal behavior. Air-supported spherical treadmills have been developed for real-time monitoring of animal walking trajectories. However, current systems for mice mainly employ computer mouse microcameras (chip-on-board sensors) to monitor ball motion, and these detectors exhibit technical issues with focus and rotation scale. In addition, computational methods to analyze and quantify the "random walk" of organisms are under-developed. In this work, we overcame the hurdle of frame-to-signal translation to develop a treadmill system with camera-based detection. Moreover, we generated a package of mathematical methods to quantify distinct aspects of Drosophila walking trajectories. By extracting and quantifying certain features of walking dynamics with high temporal resolution, we found that depending on their internal state, flies employ different walking strategies to approach environmental cues. This camera-based treadmill system and method package may also be applicable to monitor the walking trajectories of other diverse animal species.

Keywords: Biological Sciences; Biomechanics; Biophysics; Evolutionary Biology.

Graphical abstract

Figure 1

Fly Treadmill System (A) The schematic diagram of the camera-mode fly treadmill system. (B) Lateral view of a tethered fly walking on the ball suspended on the float mount. (C) Bottom view of the ball (left panel). (Middle and right panels) A single frame of infrared video recording of ball motion. Asterisks mark the four air inlets. The arrowhead indicates a mark for positioning the nozzle. (D) (Top) The on and off phases of the solenoid valves of the odor delivery system. (Middle) The dynamics of odor concentration (10⁻¹ dilution of pentanoic acid) detected by photoionization detector (PID). Black dots indicate the average of 29 trials (green lines) and are shown as mean ± SD. Gray zone is the on phase of solenoid valves. Note a 22-s delay between the switching on of solenoid valves and the arrival of odor at a flow rate 17 mL/min. (Bottom) After calibration to the PID signal, the odor history can be divided as pre-odor (off, blue), during odor (on, orange), and post-odor (off, magenta) phases. All experimental data show odor delivery phases after PID signal correction, unless otherwise noted. Scale bars, 2 mm in (B) and 1 mm in (C). See also Figures S1 and S2, and Video S1.

Figure 2

Reconstructing Fly Trajectories from Ball Motion (A) (Top) Time history of starved fly-driven ball motion as displacement along X-dimension (X), displacement along Y-dimension (Y), distance, orientation, rotation center at X, rotation center at Y, and curl at every 10-ms interval (sampling time). The features were derived from the motion of the ball. The speed (mm/10 ms) has the same pattern as walking distance. Odor was a 10⁻¹ dilution of pentanoic acid at 17 mL/min. (B) A reconstructed walking trajectory of a starved fly according to the first two features in (A). Dashed-line contoured area indicates the direction of the nozzle. Color codes of odor phases are the same as (A). (C) Reconstructed walking trajectories of 16 starved flies. (D) The position of the ball rotation center derived from the same fly as in (B). (E) The position of ball rotation centers derived from the same group of flies as in (C). See also Figure S3 and Video S2.

Figure 3

Trajectories Derived from Flies with Different Internal States Show Different Walking Characteristics (A–C) Similar to Figure 2A, the panels show the time history of ball motion features driven by a fed fly in response to food odor (A), by a starved fly in response to food odor (B), and by a starved fly in response to water vapor (C). A 10⁻¹ dilution of pentanoic acid or water vapor was applied at 17 mL/min. (B) The same data as shown in Figure 2A. (D–F) Similar to Figure 2C, the panels show the reconstructed walking trajectories of 15 fed flies in response to food odor (D), 16 starved flies in response to food odor (E), and 17 starved flies in response to water vapor (F). (E) Same data as shown in Figure 2C. (G–I) Similar to Figure 2E, the panels show the reconstructed rotation centers of 15 fed flies in response to food odor (G), 16 starved flies in response to food odor (H), and 17 starved flies in response to water vapor (I). (H) The same data as shown in Figure 2E.

Figure 4

Flies with Different Internal States Oriented toward Environmental Cues with Different Temporal Dynamics (A) Schematic illustrating the calculation of orientation. (Left) A reconstructed walking trajectory. Asterisk indicates the trajectory phase, which is enlarged in the middle panel. (Middle) Orientation is estimated as the counterclockwise angle (black arrow) between the positive x axis (black dashed line) and the vector drawn along the trajectory in a given time interval (gray arrow). (Right) Reconstructed orientation distribution map of a fly during pre-odor (blue), odor (orange), and post-odor (magenta) phases. Radius is the percentage of orientation angles (see Methods). The representative fly tended to orient toward ∼288° during odor and post-odor phases. Orange bracket indicates the positional range of the odor source (∼270°–306°). (B) Reconstructed orientation distribution maps from 15 fed flies in response to food odor (left), 16 starved flies in response to food odor (middle), or 17 starved flies in response to water vapor (right) during pre-odor (blue), odor (orange), and post-odor (magenta) phases. Orange brackets indicate the positional range of the odor source (∼270°–306°). The percentages of orientation angles derived from flies in the same experimental group and in different odor phases were subjected to statistical analysis (see Methods). Mann-Whitney U test was used to compare the unpaired phases. N.S., not significant. *p < 0.05. (C) Orientation distribution of groups of flies with different internal states (n = 15, 16, and 17 for fed/applied odor, starved/applied odor, and starved/applied water vapor groups, respectively). The orientations of flies were calculated in 10-s time bins. The percentages of orientation distributions of flies in the same group in a given time bin were normalized and shown as heatmap. Orange lines indicate the positional range of the odor source (∼270°–306°). (D) Data were analyzed similar to (C), but only the orientation distribution data in the range between 270° and 306° in (C) were extracted. Each dot represents the normalized frequencies between 270° and 306° of the same group in each time bin. See also Figures S4 and S5.

Figure 5

Extracting Walking Features of Flies with Different Internal States (A) A schematic diagram of distance. Distance (black arrow) is the position change along X- and Y-dimensions between two consecutive 10-ms sampling times. (B) The average of distance in a given 5-s time bin is shown. Each line represents the average distance traversed by a fly in three odor phases, with same color codes as Figure 1D. The black dots and lines show mean ± SD in each time bin. (C) A schematic diagram of straightness. Straightness was calculated as the displacement (black arrow)/accumulated distance (gray line) in a 5-s time bin. (D) The dynamics of straightness in three odor phases. The black dots and lines show mean ± SD in each time bin. (E) A schematic diagram of curl is shown from the bottom view of the ball. Curl was calculated as the rotation of a displacement field at pixels between two consecutive frames as indicated by arrows. (F) The curl derived from single flies in each 5-s time bin was averaged. The black dots and lines show mean ± SD in each time bin. (G) Similar to (F) but shows the absolute value of curl, |curl|. (H) The cross-correlation between the distance and |curl| was tested in the three groups of flies. (I) The correlation between average of distance and average of curl in each 5-s time bin derived from three groups of flies. (B, D, E, G, and H) Mann–Whitney U-test was used to assess paired data for time-binned feature distributions during phase switches. *p < 0.05, **p < 0.01, ***p < 0.005; N.S., not significant. See also Figure S6.

Figure 6

Flies with Different Internal States Showed Similar Scale-free Walking Patterns (A) The reconstructed walking trajectories of fed (left panel, n = 15) or starved (right panel, n = 33) flies in the pre-odor phase. The trajectories are coded blue (start) to black (end) as indicated. (B) The features of a single fed (left) or a single starved (right) fly. (C) Accumulated distance, straightness, frequency of normalized distribution of orientation within 270°–306°, and accumulated |curl| of fed and starved flies. The black dots and lines show mean ± SD in each group. Mann-Whitney U test to compare the unpaired phases. N.S., not significant. (D) Principle-component analysis of 28 features derived from the fed and starved fly walking patterns in the pre-odor phase. (E) A representative scale-free analysis of a starved fly walking trajectories in the pre-odor phase. Power-scaling ζ was calculated from least-squares linear fitting of the structure functions showing displacements $\Delta {\text{X}}_T$ in an increased sampling time $T$ on a log-log plot (top). The power-law scaling α was obtained by least-squares linear fitting of the power-scaling ζ against the power q (bottom) (Methods). In this case, the power-law scaling α = 0.73. (F) The power-law scaling for distance, Δorientation, and Δcurl derived from fed and starved flies in the pre-odor phase. (G) Representative trials from three flies with different internal states and encountered different environmental cues. The dynamics of three walking features, curl, orientation, and accumulated displacement are shown throughout the three phases. Representative data from flies in the three groups are shown. The odor-phase is indicated by the gray shadow. The y axis shows the value of curl (positive and negative values represent two opposite rotation directions). Orientation is color coded as shown. Scale bar for curl, 0.1. See also Figures S7 and S8.