Abstract

The rapid bundling and unbundling of helical flagellar filaments is an essential component to the run-and-tumble motion of multi-flagellated bacteria, but the physical mechanism behind it is not yet fully understood. What makes this problem difficult to solve is not only the coupling of elastic and hydrodynamic effects, but also the way in which the helical structures manage to fit together. During a `run’, all flagella rotate counterclockwise and they wrap around each other in a right-handed sense to form a tight helical bundle. This is possible despite the intrinsic left-handedness of normal shape flagella, which indicates that geometry plays an important role in this process. During a `tumble’, at least one of the flagella changes its rotation direction, and the associated flagellum separates from the rest of the bundle under the combined action of hydrodynamic and elastic forces. To add to this complexity, the flagellum is known to transition between different polymorphic shapes. The combination of geometry and mechanics will once again be crucial if we want to understand how all these different polymorphic shapes interact. In this talk we will present some ongoing work on the geometric constraints that govern the wrapping of helical structures around each other. We will also discuss the relevance of our results to the helical flagella of Salmonella typhimurium and Escherichia coli, two of the most commonly studied species of bacteria.