An elasto-hydrodynamical model of friction for the locomotion of Caenorhabditis elegans

Caenorhabditis elegans (C. elegans) is one of the most studied organisms by biologists. Composed of around one thousand cells, easy to culture and to modify genetically, it is a good model system to address fundamental physiological questions and in particular to investigate neuromuscular processes. Many C. elegans mutants can be distinguished by their locomotion phenotype and it then important to understand the biomechanics of their locomotion and in particular the mechanics of their undulating crawling motion on agar aqueous gels where they are commonly grown and observed. In this article, we present a mechanical model of the friction of the worms on their substrate where we have included capillarity (which pins the worm of the gel), the hydrodynamics of the lubrication film (between worm and gel) and the substrate/body elasticity. We determine the ratio of the transverse to longitudinal friction coefficients of the worm body on the culture gel as a function of a control parameter which describes the relative role of the deformation of the gel and the viscous dissipation in the lubrication film. Experimentally this ratio is - for soft gels - larger than the maximal value predicted by our model (this maximum is equal to 2, the value for an infinite cylinder in bulk liquid) and we propose to include the plasticity of the gel (i.e. the dissipation of the deformation of the gel) for a better description of the worm/gel interaction.