Buckling Instabilities and Complex Dynamics in a Model of Uniflagellar Bacterial Locomotion

Locomotion of microorganisms at low Reynolds number is a long studied problem. Of particular interest are organisms utilizing only a single flagellum to undergo a wide range of motions, such as pushing, pulling, and tumbling or flicking. Recent experiments have called attention to the connection between the stability of the hook protein, connecting cell motor and flagellum, and observed deviations from typical straight swimming trajectories. We thus seek physical explanations to these experimental phenomena by developing a computationally inexpensive, rigid-body dynamic model of a uni-flagellated organism with a flexible body-flagellum connection that captures the most fundamental aspects of locomotion, tracking velocities, forces, torques, and rotational phases. Furthermore, the model addresses the effects of hook bending and twisting on the mechanical stability of the system. Simulations with low hook flexiblity reproduce the classic straight swimming result, but large flexibility produces helical trajectories, subsequently leading to directional changes when coupled with transient stiffening. The model verifies suggested physical mechanisms for swimming in various motilities and highlights the role of flexibility in the biology of real organisms and the engineering of artificial microswimmers.