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What can we say about the dynamics of an animal's behavior from experimental recordings? Excited to announce a preprint from my PhD work on this question https://biorxiv.org/content/10.1101/827535v1 …. I am grateful for the mentorship of @greg_stephens and the collaboration with @antoniocbscosta
We propose a framework based on the concept of “state space” or “phase space” in dynamical systems, which converts variables changing in time to a trajectory, e.g. 4 different “behaviors” of a pendulum become 4 curves.pic.twitter.com/LO9AiNPdi1
Applying our framework to C. elegans behavior, we develop a method to reconstruct a state space from videos of freely moving worms. Our method is based on the idea that good state space reconstructions should allow us to predict the future for as long as possible.pic.twitter.com/oLr2hT0nxU
The low-dimensional reconstructed state space allows us to understand a great deal about worm movement, without knowing the equations of motion! It is globally structured into trajectory bundles corresponding to the canonical behaviors of forward, backward and turning.pic.twitter.com/HuRH85I6WA
At small scales though, the trajectories look messy, and long-term prediction of worm behavior is not possible. A pair of nearby points in state space start close, but go apart after some time. The state space allows us to systematically study behavioral variability in C. eleganspic.twitter.com/sTzwLDhhg1
Analysis of the geometry and topology of these trajectories reveals several hints of deterministic variability coming from chaotic dynamics. These include unstable periodic orbits, exponential divergence of initial conditions and most surprisingly, a symmetric Lyapunov spectrum.
Dynamical systems are well-suited to understand the complexity of C. elegans behavior, characterized by its long term unpredictability, multi scale structure, and paradoxical coexistence of stereotypy & variability. And we believe this is just the start.
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