How worms move in 3D

Animals that live in the sky, underwater or underground display unique three dimensional behaviours made possible by their ability to generate movement in all directions. As animals explore their environment, they constantly adapt their locomotion strategies to balance factors such as distance travelled, speed, and energy expenditure. While exploration strategies have been widely studied across a variety of species, how animals explore 3D space remains an open problem. The nematode Caenorhabditis elegans presents an ideal candidate for the study of 3D exploration as it is naturally found in complex fluid and granular environments and is well sized (~1mm long) for the simultaneous capture of individual postures and long term trajectories using a fixed imaging setup. However, until recently C. elegans has been studied almost exclusively in planar environments and in 3D neither its modes of locomotion nor its exploration strategies are known. Here we present methods for reconstructing microscopic postures and tracking macroscopic trajectories from a large corpus of triaxial recordings of worms freely exploring complex gelatinous fluids. To account for the constantly changing optical properties of these gels we develop a novel differentiable renderer to construct images from 3D postures for direct comparison with the recorded images. The method is robust to interference such as air bubbles and dirt trapped in the gel, stays consistent through complex sequences of postures and recovers reliable estimates from low-resolution, blurry images. Using this approach we generate a large dataset of 3D exploratory trajectories (over 6 hours) and midline postures (over 4 hours). We find that C. elegans explore 3D space through the composition of quasi-planar regions separated by turns and variable-length runs. To achieve this, C. elegans use locomotion gaits and complex manoeuvres that differ from those previously observed on an agar surface. We show that the associated costs of locomotion increase with non-planarity and we develop a mathematical model to probe the implications of this connection. We find that quasi-planar strategies (such as we find in the data) yield the largest volumes explored as they provide a balance between 3D coverage and trajectory distance. Taken together, our results link locomotion primitives with exploration strategies in the context of short term volumetric foraging to provide a first integrated study into how worms move in 3D.