Swimming Hydrodynamics of a Run-And-Tumble Bacterium with Helical Flagella

Abstract

To study the swimming of a peritrichous bacterium such as Escherichia coli, which is able to change its swimming direction actively, we simulate the “run-and-tumble” motion using a bead-spring model to account for the hydrodynamic and the mechanical interactions between the cell body and multiple flagella, the reversal of the rotation of a flagellum in a tumble and the associated polymorphic transformations of the flagellum. The cell body and each flagellum are connected by a flexible hook, so that the flagella can take independent orientations with respect to the cell body. This simulation reproduces the experimentally observed behaviors of E. coli, namely, a three-dimensional random-walk trajectory in run-and-tumble motion and steady clockwise swimming near a wall. We show that the polymorphic transformation of a flagellum in a tumble facilitates the reorientation of the cell, and that the time-averaged flow field near a cell in a run has double-layered helical streamlines, with a time-dependent flow magnitude large enough to affect the transport of surrounding chemoattractants. This new model, which can be refined by using more beads if more quantitative predictions are desired, strikes a balance between accuracy and simplicity that will permit it to be used to determine the migration behavior of particles near a swimming cell, cell-cell hydrodynamic interactions, the effect of the number and geometric distribution of flagella on migration, the mechanism of circular swimming near a wall, details of the tumbling motion, and the effect of the Brownian motion on swimming. We also develop minimal models, inspired by the simple model of Najafi and Golestanian, that contain only 3-5 beads, and can simulate simple “pusher” and “puller” micro-swimmers, and are also able to include helical flow typically produced by rotary flagellar motion.