Regensburg 2010 – wissenschaftliches Programm

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BP: Fachverband Biologische Physik

BP 32: Posters: Physics of Cells

BP 32.31: Poster

Donnerstag, 25. März 2010, 17:15–20:00, Poster B1

Hopf Bifurcation in Rotating Bacterial Flagella — •Reinhard Vogel and Holger Stark — TU Berlin

Many types of bacteria swim by rotating a bundle of helical filaments also called flagella. Each filament is driven by a rotatory motor. When its sense of rotation is reversed, the flagellum leaves the bundle and undergoes a sequence of configurations characterized by their pitch, radius and helicity (polymorphism). Finally the flagellum assumes its original form and returns into the bundle.

The flagellum of bacteria such as E. coli and Salmonella consists of three parts; the rotary motor embedded in the cell membrane, a short proximal hook that couples the motor to the third part, the long helical filament. The hook has a well regulated length of 0.055µ m and a diameter of around 0.02µ m. The filament is up to 20 µ m long and like the hook about 0.02µ m in diameter. It is relatively stiff but can switch between distinct polymorphic forms.

In this contribution, we demonstrate how the hook transmitting the torque of the motor to the filament can be modeled. We then investigate the shape of the flexibel helical filament when the motor torque is applied. For small torques acting such that the cell body is pushed forward, the helix axis is approximatly parallel to the torque and the filament is only slightly deformed. The thrust force assumes a stationary value. However, when the torque is increased, the filament starts to bend which is visible through a Hopf bifurcation in the thrust force. We discuss the importance of this bifurcation for the bundle formation and for the transitions between different polymorphic configurations.