The rigidity of bacterial flagellar filaments and its relation to filament polymorphism

We determined and correlated the rigidity of Salmonella typhimurium, Escherichia coli, and Rhizobium lupini flagellar filaments representing various structural and polymorphic states (plain, complex, straight, superhelical, and right- and left-handed). Persistence length, from which the filament's rigidity and other parameters (Young's modulus, bending force constant, buckling persistence length, flexural deformation, and flexural time) were derived, was determined from electron micrographs of isolated, negatively stained filaments. Outer diameters and radii of strong intersubunit connectivity were determined from three-dimensional image reconstructions and radial mass density profiles from scanning transmission electron microscopy. All filaments appear to be highly rigid with no evident correlation with their helical sense or superhelicity. The complex filament of R. lupini is rigid to the extent that it becomes brittle. The overall flexibility of the flagellum seems to stem mainly from the hook and not from the filament. Polymorphism is probably related to the propelling properties and hydrodynamic shape of the filament rather than to its rigidity.