Understanding the hydrodynamic interaction among flagella of E. coli using the immersed boundary method combined with the Kirchhoff rod theory

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A new mathematical model is developed to understand the swimming mechanism of bacteria such as Escherichia coli. The bacterium E. coli is a single-celled organism which swims in a viscous fluid by rotating its helical flagellar filaments. Two successive motions are involved in the cell motility: Runs (straight swimming propelled by flagellar bundling) and tumbles (random reorientation by interspersing flagella). This project will focus on the study of the hydrodynamic interaction among flagella and flagellar filament shapes that arise through polymorphic transformations?local changes in helical wavelength, helical diameter, and handedness?during swimming. A generalized version of the immersed boundary method combined with the unconstrained Kirchhoff rod theory is used to study biological fluid mechanics in the bacterium. A new feature of this method is that the interaction of the immersed boundary with the fluid now involves not only translation of the immersed boundary points at the local fluid velocity, but also rotation of the associated triads at the local fluid angular velocity. This method will find numerous applications in biological fluid dynamics, where filamentous structures interact with a viscous fluid. Examples include the supercoiling of DNA during transcription and replication and protein folding. In addition, one of the challenges in nanotechnology is to develop machines at the nanoscale which can be used in the treatment of disease. Understanding swimming mechanism by means of rotary motors will help to create a nanomachine, operated by self-propelled biomolecular nano motors, that could be used for drug delivery inside the body. Furthermore, such interdisciplinary projects give rise to problems and activities that can be used to attract students to science through the investigator's work with the Women in Science and Engineering program (WISE) at her university.