Recent advances in microscopy techniques has uncovered unique aspects of flagella-driven motility in bacteria. A remarkable example is the discovery of flagellar wrapping, a phenomenon whereby a bacterium wraps its flagellum (or flagellar bundle) around its cell body and propels itself like a corkscrew, enabling locomotion in highly viscous or confined environments. For certain bacterial species, this flagellar-wrapping mode is crucial for establishing selective symbiotic relationships with their hosts. The transformation of a flagellum from an extended to a folded (wrapped) state is triggered by a buckling instability driven by the motor-generated torque that unwinds the helical filament. This study investigated this biologically inspired, novel buckling mechanism through a combination of macroscale physical experiments, numerical simulations, and scaling theory to reveal its underlying physical principles. Excellent quantitative agreement between experiments and numerical results showed that long-range hydrodynamic interactions are essential for accurate quantitative descriptions of the geometrically nonlinear deformation of the helical filament during wrapping. By systematically analyzing extensive experimental and numerical data, we constructed a stability diagram that rationalized the stability boundary through an elastohydrodynamic scaling analysis. Leveraging the scaling nature of this study, we compared our physical results with available biological data and propose that bacteria exploit motor-induced buckling instability to initiate their flagellar wrapping. Our findings indicate that this mechanically driven process is essential to bacterial-wrapping motility and, consequently, plays a critical role in symbiosis and infection.

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• Biological fluid dynamics
• Elasticity
• Bacteria
• Flagella