Mapping the continuum of gait strategies and limb-coupling dynamics in mouse and fly locomotion

Locomotion is a fundamental aspect of the behavior of most animals, yet it is regulated by a complex network of control structures and pathways that are not yet fully understood. Research on mice and flies has revealed distinct control mechanisms in four- and six-legged animals. However, these studies have primarily relied on coarse quantifications, such as footfall timings, support structures, and stance durations, which do not allow for detailed characterization at a sub-cycle level. The use of machine learning paradigms has enabled high-throughput analyses and pattern abstraction, allowing us to examine locomotion in unprecedented detail. We specifically leverage this technology in three key ways: first, we employ SLEAP to continuously track high-resolution trajectories of body parts in over 10,000 naturally occurring locomotion bouts of mice and flies. Second, we adapt DeepPhase, a periodic autoencoder, to extract a continuous phase variable from sawtooth-like trajectories. Finally, we apply sparse Bayesian learning to identify neuromuscular coupling dynamics. Using the high-resolution coordinate and phase data, we create detailed maps of the gaits exhibited by flies and mice, enabling us to identify instantaneous gaits and gait transitions. We then model and compare the associated limb dynamics in different regions of the locomotion manifolds using a Kuramoto system of phase-coupled oscillators. This approach quantifies internal control parameters, such as the strength of limb-limb coupling and generator phase offsets, based on external kinematic data. Our findings reveal controller symmetries that align with patterns observed from direct neural measurements, and we demonstrate that coupling parameters depend on gait and speed. Lastly, we compare the locomotor strategies of mice and flies and discuss their implications for the development and conservation of kinematic and control paradigms.