Flow-Induced Deformations and Bending Stiffness of Tethered Salmonella Flagella*

The mechanical properties of the bacterial flagellum are essential for understanding bacterial locomotion. We analyze an experiment where a Salmonella flagellum, attached to the bottom of a microfluidic channel, is stretched due to the hydrodynamic forces. We reconstruct the 3D geometry of the flagellum from microscopic images. Using the method of regularized Stokeslets, we determine hydrodynamic forces acting on the flagellum. Coupling the forces to a Kirchhoff rod model allows us to predict the deformed shape of the flagellum, taking as inputs the background flow, the undeformed geometry of the flagellum, and its bending stiffness. Previous studies suggest that flagella can take 12 different polymorphic forms, distinguished by the pitch and radius of their helical shapes. However, in absence of any flow, we observed flagella with a different pitch and radius not comparable to any known form. Furthermore, we found that if the undeformed shape is assumed to be that of a known polymorphic form, predicted deformed shapes are unlike those that are observed in the presence of flow. On the other hand, if the undeformed shape is assumed to be that observed in the absence of flow, bending stiffness of 2-2.5 pN.μm² predicts the observed deformed shapes.