Capturing the Continuous Complexity of Behavior inC. elegans

Abstract

Animal behavior is often quantified through subjective, incomplete variables that may mask essential dynamics. Here, we develop a behavioral state space in which the full instantaneous state is smoothly unfolded as a combination of short-time posture dynamics. Our technique is tailored to multivariate observations and extends previous reconstructions through the use of maximal prediction. Applied to high-resolution video recordings of the roundworm C. elegans, we discover a lowdimensional state space dominated by three sets of cyclic trajectories corresponding to the worm's basic stereotyped motifs: forward, backward, and turning locomotion. In contrast to this broad stereotypy, we find variability in the presence of locally-unstable dynamics, and this unpredictability shows signatures of deterministic chaos: a collection of unstable periodic orbits together with a positive maximal Lyapunov exponent. The full Lyapunov spectrum is symmetric with positive, chaotic exponents driving variability balanced by negative, dissipative exponents driving stereotypy. The symmetry is indicative of damped, driven Hamiltonian dynamics underlying the worm's movement control.

Tracking changes in behavioural dynamics using prediction error

“…Within each type of worm, the shape of the error as a function of the parameters shows strong consistency between individuals. Generally, the optimal parameter settings occur at > 1, and the wildtype shows evidence of nonlinearity, i.e., the optimal value of > 0, which is consistent with previous observations (Ahamed et al, 2019;Costa et al, 2019). The mutant worms on the other hand generally do not show clear evidence of nonlinearity on average, though the sensitivity to is very weak over the parameter range explored.…”

“…Non-categorical distinctions of behaviour must necessarily confront the problem of measuring distances between time series -a highly non-trivial problem. The recent success of dynamic embedding representations of worm motion (Ahamed et al, 2019;Brennan and Proekt, 2019), suggests that this problem could be addressed within the framework of empirical dynamic modeling (EDM) (Sugihara and May, 1990).…”

“…This highlights a challenge in the measurement of worm motion behaviour: in most dynamic representations (e.g. Ahamed et al, 2019;Brown et al, 2013) rate and shape are coupled.…”

“…Brennan and Proekt, 2019) or using body motion alone (e.g. Ahamed et al, 2019). Costa et al (2019) used a hybrid approach in which eigenworm time series were dynamically partitioned and approximated locally with a sequence of linear models, revealing larger variation within behavioural types than previously thought.…”

WormPose: Image synthesis and convolutional networks for pose estimation inC. elegans

“…All animals, including humans, reveal important and subtle information about their internal dynamics in their outward configurations of body posture, whether these internal dynamics originate from gene expression [1], neural activity [2], or motor control strategies [3]. Estimating and analyzing posture and posture sequences from high-resolution video data is thus a general and important problem, and the basis of a new quantitative approach to movement behavior (for reviews see e.g.…”