Motor-driven bacterial flagella and buckling instabilities |
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Authors: | R Vogel H Stark |
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Institution: | (1) Institute for Theoretical Physics, TU Berlin, Berlin, Germany |
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Abstract: | Many types of bacteria swim by rotating a bundle of helical filaments also called flagella. Each filament is driven by a rotary
motor and a very flexible hook transmits the motor torque to the filament. We model it by discretizing Kirchhoff’s elastic-rod
theory and develop a coarse-grained approach for driving the helical filament by a motor torque. A rotating flagellum generates
a thrust force, which pushes the cell body forward and which increases with the motor torque. We fix the rotating flagellum
in space and show that it buckles under the thrust force at a critical motor torque. Buckling becomes visible as a supercritical
Hopf bifurcation in the thrust force. A second buckling transition occurs at an even higher motor torque. We attach the flagellum
to a spherical cell body and also observe the first buckling transition during locomotion. By changing the size of the cell
body, we vary the necessary thrust force and thereby obtain a characteristic relation between the critical thrust force and
motor torque. We present a elaborate analytical model for the buckling transition based on a helical rod which quantitatively
reproduces the critical force-torque relation. Real values for motor torque, cell body size, and the geometry of the helical
filament suggest that buckling should occur in single bacterial flagella. We also find that the orientation of pulling flagella
along the driving torque is not stable and comment on the biological relevance for marine bacteria. |
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