``Corkscrew'' vs. ``tank-treading'' propulsion of spirochetes.

We consider the potential mechanism of spirochete propulsion driven by twirling of the outer cell surface coupled to counter-rotation of the helical body. We construct a proper slender body theory and use particle-based numerical approach allowing for modeling of locomotion in heterogeneous viscous environment. Depending on the helical pitch angle, two distinct propulsion gaits are identified: corkscrew-like locomotion, similar to propulsion powered by rotating helical flagellum, and surface tank-treading mode relying on hydrodynamic self-interaction of curved helical coils. The latter mechanism is closely related to the considered earlier propulsion of Purcell's toroidal swimmer (Kenneth and Leshansky, Phys. Fluids \textbf{20}, 063104, 2008). Significant augmentation of corkscrew propulsion gait in heterogeneous viscous medium anticipated from the numerical model is in accord with experimental observations of enhanced spirochete propulsion in polymer gels.