Dimensionality and Dynamics in the Behavior of C. elegans

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Abstract
A major challenge in analyzing animal behavior is to discover some underlying simplicity in complex motor actions. Here, we show that the space of shapes adopted by the nematode Caenorhabditis elegans is low dimensional, with just four dimensions accounting for 95% of the shape variance. These dimensions provide a quantitative description of worm behavior, and we partially reconstruct “equations of motion” for the dynamics in this space. These dynamics have multiple attractors, and we find that the worm visits these in a rapid and almost completely deterministic response to weak thermal stimuli. Stimulus-dependent correlations among the different modes suggest that one can generate more reliable behaviors by synchronizing stimuli to the state of the worm in shape space. We confirm this prediction, effectively “steering” the worm in real time. A great deal of work has been done in characterizing the genes, proteins, neurons, and circuits that are involved in the biology of behavior, but the techniques used to quantify behavior have lagged behind the advancements made in these areas. Here, we address this imbalance in a domain rich enough to allow complex, natural behavior yet simple enough so that movements can be explored exhaustively: the motions of Caenorhabditis elegans freely crawling on an agar plate. From measurements of the worm's curvature, we show that the space of natural worm postures is low dimensional and can be almost completely described by their projections along four principal “eigenworms.” The dynamics along these eigenworms offer both a quantitative characterization of classical worm movement such as forward crawling, reversals, and Omega-turns, and evidence of more subtle behaviors such as pause states at particular postures. We can partially construct equations of motion for this shape space, and within these dynamics we find a set of attractors that can be used as a rigorous definition of behavioral state. Our observations of C. elegans reveal a precise and complete language of motion and new aspects of worm behavior. We believe this is a lesson with promise for other organisms.

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