Figure 1.
The top part shows a side view of two left-handed flagella, with average distance , helix radius
, and pitch
. The bottom part shows a top view with the external forces
generating a torque and the phase angles
.
Figure 2.
Single flagellum rotation frequency and swimming speed.
Mean values of the rotation frequencies (squares) and mean induced fluid velocities (bullets) of a single helix for various applied torques. The lines indicate the linear dependence on the torque.
Figure 3.
(a) Phase angle difference as a function of time for various applied torques on helix
and the distance
. The torque
is changed from 200 (top) to 920 (bottom) with an increment of 40; the constant torque is
. (b) Average phase lag
as a function of the torque
. The red line indicates the fit
, where
. The blue line is the tangent at
. The inset provides an approximate measure of the number of occurring slips during the time interval
as a function of the applied moment
.
Figure 4.
Phase diagram of bundle integrity.
Phase diagram indicating stable bundles (shaded), intermittent slippage (squares), and drift states (bullets) for various flagella distances and torques on helix 2. The torques on helices 1 and 3 are .
Figure 5.
Bead distance distributions and mean distances.
(a) Normalized bead-distance distribution functions between helices at
,
is the helical pitch (cf. Fig. 1), for the torque
(black), 500 (red), 600 (green), 700 (blue), and 800 (magenta) with
. The distance between anchored helix ends is fixed at
. The inset shows the distribution functions for
(black), 300 (red), and 200 (blue). (b) Average bead distances between the helices at
(black),
(red), and
(blue) (
) as a function of the torque
.
Figure 6.
Snapshots of helices for various torque differences.
Snapshots of side (top) and top (bottom) views for the torque , 400, 600, and 800 (from left to right) at
. See also videos S1 8 and S2 8 for
and 800, respectively.
Figure 7.
Average forces on bacteria body.
Average forces per monomer on the anchoring plane of three helices as a function of the torque for
at
. The bullets indicated the forces by helix two and the solid squares those by helix one and three. The circles and open squares are the contributions by the corresponding hydrodynamics forces for unbundled helices.
Figure 8.
Illustration of the forces and torques on a bacterium and the estimated change in orientation .
and
are the excess forces after the mean driving force has been subtracted. The induced torque rotates the whole structure, which gives rise to the drag forces
on the cell body and
on the tail.