Mathematical Biology seminar

Mun Ju Kim
Department of Mathemtics, University of Utah
"Hydrodynamics of Bacterial Flagella"
September 15
3:05pm in LCB 215

Escherichia coli use helical filaments to swim. Due to the small size, the Reynolds number of swimming bacteria is very small (~10^(-5)). At zero Reynolds number, viscous effects dominate inertia and there are significant hydrodynamic interactions. Recent advances in the real-time imaging of fluorescently labeled bacterial filaments [Turner, Ryu, and Berg, J. Bacteriol. 82 (2000)] have made it possible to see details of the bacterial swimming motion. Filaments bundle when the cell swims and disperse when the cell changes swimming direction. In this swimming strategy the hydrodynamics plays a crucial role. We built a macroscopic scale model of bacterial filaments to study the detailed bundling mechanism. Not only did it demonstrate bundling, but it also allowed the study of the roles of parameters such as rotation speed and filament stiffness. To study the hydrodynamics of two rotating helices quantitatively, we also used numerical slender body computations to model the flow induced by two rotating helices. For simplicity, we disregarded the flexibility and focused on the hydrodynamic interactions. Force, torque, and the interaction between the two helices were calculated as functions of geometrical parameters and rotation speeds. Since the helices in these model calculations were rigid, it did not apply to bundling. However, the results captured many features of the initial motion of bundling. We developed a macro-scale particle image velocimetry (PIV) system to measure the full-field velocity distribution for rotating rigid helices and rotating flexible helices. Comparison of the PIV measurements and slender-body calculations agreed well for the case of rigid helices. For the flexible helices, we found that the flow field generated by a bundle in the steady state is well approximated by the flow generated by a single rigid helix with twice thickness. A new model calculation of the filament stiffness was introduced. We used either the slender body theory or the resistive force theory to capture the hydrodynamic forces; the deformation was calculated by the Kirchhoff rod theory and the beam bending equation in terms of stiffness moduli. Using the currently available experimental data, we found that the bending stiffness of bacterial filament is about 10^(-23)Nm^2.