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Undulatory locomotion of {\it C. elegans} on wet surfaces

The physical and bio-mechanical principles that govern undulatory movement on wet surfaces have important applications in physiology, physics, and engineering. The nematode {\it C. elegans}, with its highly stereotypical and functionally distinct sinusoidal locomotory gaits, is an excellent system in which to dissect these properties. Measurements of the main forces governing the {\it C. elegans} crawling gait on lubricated surfaces have been scarce, primarily due to difficulties in estimating the physical features at the nematode-gel interface. Using kinematic data and a hydrodynamic model based on lubrication theory, we calculate both the surface drag forces and the nematode's bending force while crawling on the surface of agar gels. We find that the normal and tangential surface drag force coefficients during crawling are approximately 220 and 22, respectively, and the drag coefficient ratio is approximately 10. During crawling, the calculated internal bending force is time-periodic and spatially complex, exhibiting a phase lag with respect to the nematode's body bending curvature. This phase lag is largely due to viscous drag forces, which are higher during crawling as compared to swimming in an aqueous buffer solution. The spatial patterns of bending force generated during either swimming or crawling correlate well with previously described gait-specific features of calcium signals in muscle. Further, our analysis indicates that changes in the motility gait of {\it C. elegans} is most likely due to the nematode's adaptive response to environments characterized by different drag coefficient ratios.