The millimeter-long soil-dwelling nematode Caenorhabditis elegans propels itself by producing undulations that propagate along its body and turns by assuming highly curved shapes. According to our recent study [PLoS ONE 7, e40121 (2012)] all these postures can be accurately described by a piecewise-harmonic-curvature (PHC) model. We combine this curvature-based description with highly accurate hydrodynamic bead models to evaluate the normalized velocity and turning angles for a worm swimming in an unconfined fluid and in a parallel-wall cell. We find that the worm moves twice as fast and navigates more effectively under a strong confinement, due to the large transverse-to-longitudinal resistance-coefficient ratio resulting from the wallmediated far-field hydrodynamic coupling between body segments. We also note that the optimal swimming gait is similar to the gait observed for nematodes swimming in high-viscosity fluids. Our bead models allow us to determine the effects of confinement and finite thickness of the body of the nematode on its locomotion. These effects are not accounted for by the classical resistive-force and slender-body theories.

Locomotion of the nematode is a key observable used in investigations ranging from behavior to neuroscience to aging. However, while the natural environment of this model organism is 3D, quantitative investigations of its locomotion have been mostly limited to 2D motion. Here, we present a quantitative analysis of how the nematode reorients itself in 3D media. We identify a unique behavioral state of-a roll maneuver-which is an essential component of 3D locomotion in burrowing and swimming. The rolls, associated with nonzero torsion of the nematode body, result in rotation of the plane of dorsoventral body undulations about the symmetry axis of the trajectory. When combined with planar turns in a new undulation plane, the rolls allow the nematode to reorient its body in any direction, thus enabling complete exploration of 3D space. The rolls observed in swimming are much faster than the ones in burrowing; we show that this difference stems from a purely hydrodynamic enhancement mechanism and not from a gait change or an increase in the body torsion. This result demonstrates that hydrodynamic viscous forces can enhance 3D reorientation in undulatory locomotion, in contrast to known hydrodynamic hindrance of both forward motion and planar turns.

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