A Plausible Mechanism for Drosophila Larva Intermittent Behavior
291
For the present study recordings longer than 1024 s have been selected.
Instances where larvae contacted the arena borders were excluded. The raw
time series of x, y coordinates have been forward-backward filtered with a firstorder butterworth low-pass filter of cutoff frequency 0.1 Hz before computing the
velocity. The cutoff frequency was selected as to preserve the plateaus of brief stationary periods while suppressing the signal oscillation due to peristaltic-stride
cycles. Velocity values ≥2.5 mm/s have been discarded to account for observed
jumps in single-larva trajectories that are probably due to technical issues during tracking. This arbitrary threshold was selected as an upper limit for larvae
of length up to 5 mm, crawling at a speed of up to 2 strides/sec with a scaled
displacement per stride of up to 0.25.
2.2 Bout Annotation and Distribution
In order to designate periods of rest and activity we need to define a suitable
threshold V θ in the velocity distribution as done for the adult fruitfly in [12].
We used the density estimation algorithm to locate the first minimum V θ =
0.085 mm/s in the velocity histogram of the reference control group. A rest bout
is then defined as a period during which velocity does not exceed V θ . Rest bouts
necessarily alternate with periods termed activity bouts. The bout annotation
method is exemplified for a single larva track in Fig. 2.
To quantify the duration distribution of the rest and activity bouts we used
the maximum likelihood estimation (MLE) method to fit a power-law, an exponential and a log-normal distribution for each group as well as for the reference
control group. Given the tracking framerate of 2 Hz and the minimal tracking
time of 1024 s, we limited our analysis to bouts of duration 2
1 to 2
10 s. The
Kolmogorov-Smirnov distance D KS for each candidate distribution was then
computed over 64 logarithmic bins covering this range. Findings are summarized in Table 2 for the rest bouts and in Table 3 for the activity bouts.
3 Results
The results section is organized as follows. Initially we present a simple conceptual two-state model transitioning autonomously between power-law and nonpower-law regimes. Next we analyse intermittency during larva free exploration
in a freely available dataset [9]. Finally we compare mutant and control larva
phenotypes in the context of intermittency.
3.1 Network Model of Binary Units Reproduces Larval Statistics
of Intermittent Behavior
Previous work on Drosophila adult intermittent behavior reported that restbout durations are power-law distributed while activity-bout durations are
exponentially distributed [12]. Our first contribution is to provide a simple model
displaying how this dual regime might emerge.
291
For the present study recordings longer than 1024 s have been selected.
Instances where larvae contacted the arena borders were excluded. The raw
time series of x, y coordinates have been forward-backward filtered with a firstorder butterworth low-pass filter of cutoff frequency 0.1 Hz before computing the
velocity. The cutoff frequency was selected as to preserve the plateaus of brief stationary periods while suppressing the signal oscillation due to peristaltic-stride
cycles. Velocity values ≥2.5 mm/s have been discarded to account for observed
jumps in single-larva trajectories that are probably due to technical issues during tracking. This arbitrary threshold was selected as an upper limit for larvae
of length up to 5 mm, crawling at a speed of up to 2 strides/sec with a scaled
displacement per stride of up to 0.25.
2.2 Bout Annotation and Distribution
In order to designate periods of rest and activity we need to define a suitable
threshold V θ in the velocity distribution as done for the adult fruitfly in [12].
We used the density estimation algorithm to locate the first minimum V θ =
0.085 mm/s in the velocity histogram of the reference control group. A rest bout
is then defined as a period during which velocity does not exceed V θ . Rest bouts
necessarily alternate with periods termed activity bouts. The bout annotation
method is exemplified for a single larva track in Fig. 2.
To quantify the duration distribution of the rest and activity bouts we used
the maximum likelihood estimation (MLE) method to fit a power-law, an exponential and a log-normal distribution for each group as well as for the reference
control group. Given the tracking framerate of 2 Hz and the minimal tracking
time of 1024 s, we limited our analysis to bouts of duration 2
1 to 2
10 s. The
Kolmogorov-Smirnov distance D KS for each candidate distribution was then
computed over 64 logarithmic bins covering this range. Findings are summarized in Table 2 for the rest bouts and in Table 3 for the activity bouts.
3 Results
The results section is organized as follows. Initially we present a simple conceptual two-state model transitioning autonomously between power-law and nonpower-law regimes. Next we analyse intermittency during larva free exploration
in a freely available dataset [9]. Finally we compare mutant and control larva
phenotypes in the context of intermittency.
3.1 Network Model of Binary Units Reproduces Larval Statistics
of Intermittent Behavior
Previous work on Drosophila adult intermittent behavior reported that restbout durations are power-law distributed while activity-bout durations are
exponentially distributed [12]. Our first contribution is to provide a simple model
displaying how this dual regime might emerge.