Motor-Driven Bacterial Flagella and Buckling Instabilities

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 sophisticated 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.Comment: 15 pages, 11 figure

Over sterk samendrukbare schroefveren en rubberstaven en over hun toepassing bij trillingsvrije opstellingen

Mechanical, Maritime and Materials Engineerin

A Hybrid Thermopneumatic and Electrostatic Microvalve with Integrated Position Sensing

This paper presents a low-power hybrid thermopneumatic microvalve with an electrostatic hold and integrated valve plate position sensing. This combination of actuators in a single structure enables a high throw and force actuator with low energy consumption, a combination that is difficult to otherwise achieve. The completed 7.5 mm × 10.3 mm × 1.5 mm valve has an open flow rate of 8 sccm at 600 Pa, a leak rate of 2.2 × 10<sup>−3</sup> sccm at 115 kPa, a open-to-closed fluidic conductance ratio of nearly one million, an actuation time of 430 ms at 250 mW, and a required power of 90 mW while closed. It additionally requires no power to open, and has a built-in capacitive position sensor with a sensitivity of 9.8 fF/kPa. The paper additionally presents analytical models of the valve components, design tradeoffs, and guidelines for achieving an optimized device