(266j) Flagellar Bundling

Flagella are long thin appendages of microscopic organisms that can be used for propulsion in low-Reynolds environments. An example is the E. coli bacterium, which has about 6 flagella per cell. For E. coli the flagella are driven by a constant-torque molecular motor, which rotates the flagella in a counter-clockwise motion (CCM). When in a forward swimming motion, all flagella bundle up. At the end of a swimming interval, one or several motors reverses rotation direction, and the flagella attached to these motors unbundle. The cell body then makes a tumbling motion. After a while, all motors turn in the same CC direction again, all flagella bundle up, and the bacterium starts swimming in a straight line again. The bundling and unbundling is poorly understood.

To investigate the bundling, we consider two flexible helices next to each other. Each helix is modeled as several prolate spheroids connected at the tips by springs. On the first spheroid, a constant torque is applied. Torsion springs at the connections provide bending and twisting resistance. Hydrodynamic interactions are incorporated via a modified non-singular Stokeslet. Additionally, there is a repulsive force and torque, based on the Gay-Berne potential to prevent crossing of the flagella.

Our results provide some insights in the details of the bundling process. In the initial stage, rotlet interactions between the rotating helices ensures that both deflect each other. Due to the end point fixation, this deflection combined with the rotlet interaction leads to the flagella rotating around each other. Longer simulations show that the tips of a flagella pair only rotate once around each other, in contrast with a more complicated entwinement suggested before. Flagella closer together bundle faster.

We also show synchronization due to hydrodynamic interactions between flagella out-of-phase. More complicated situations involving three or more flagella, as well as non-aligned pairs are shown as well. Finally, we focus on the unbundling stages.