New method to capture the full dynamical complexity of animal movement

For centuries, physicists and mathematicians have strived to model and understand a large variety of complex dynamical patterns: from the way small molecules move, to the movements of planets and stars. Can we apply the same level of mathematical precision to understand how animals move? Tosif Ahamed, Antonio C Costa and Greg J. Stephens of Vrije Universiteit Amsterdam and OIST Graduate University give the answer in Nature Physics.

10/19/2020 | 11:50 AM

The researchers introduced a new method to capture the full dynamical complexity of animal movement, and used it to extract stereotypy and unpredictability in the movement dynamics of the soil-dwelling nematode worm C. elegans, one of the simplest animals.The work is an important step towards a new, quantitative understanding of behavior that can extend to other animals, including humans.

Waving worms
“We take high resolution videos of the worms moving on a two-dimensional surface, and extract the centerline of the body shape for each frame, this is the worm’s posture or pose. As in humans, worms move by changing their pose. We see propagating waves throughout their body, propelling them forward, backward or turning in seemingly random sequences,” says VU Amsterdam physicist Stephens.

To understand these waves requires variables that are maximally predictive of the future. Picture the movement of a pendulum clock. If you look at a still picture of a pendulum, you won’t be able to tell whether it is sitting still or moving towards the left or right. In order to disambiguate and predict the future, you need extra information: watching where the pendulum was a bit before, for example, is enough to be able to accurately predict where it is moving next. Therefore, the new set of variables composed of two adjacent time points of the pendulum is maximally predictive of its future. In mathematical language, we say that this extended set of variables is the state-space of the pendulum.

The researchers used their analysis to find short posture sequences that define the maximally predictive behavioral stateof the worm. As the worm moves, the behavioral state follows cycles which correspond to repeatable movements of forward, backward and turning. However, each cycle is slightly different and closer inspection revealed a striking deterministic variation rather than simply random changes. Deterministic variability is known as chaos and was first observed in simple but nonlinear physical systems. They hypothesized that the worm incorporates chaotic movements to better explore an unknown environment.