Chirality Inversions Propagating on Bacterial Flagella

Many experimental investigations have shown that bacterial flagella (the long, whip-like structures that provide thrust during swimming) take on a variety of helical forms under differing mechanical and chemical conditions. During the 1980s a series of experiments examined the response of a single, detached flagellum to simple fluid stresses. In particular, when a flagellum is clamped at one end and placed in an axial external flow, it is observed that regions of the flagellum transform to the opposite chirality and travel as pulses down the length of the filament, the process repeating periodically.

We propose a theory for this phenomenon based on a treatment of the flagellum as an elastic object with multiple stable configurations. This theory is expressed in terms of coupled PDEs for the filament shape and twist configuration, and involves only physical, measurable properties of the flagellum. We generate simulations that quantitatively reproduce key features seen in experiment.

Refreshments will be served at 3:45 p.m. in the Faculty Lounge, Math Annex (Room 1115).