Biological Physics: Energy, Information, Life

5.3. Biological applications[[Student version, December 8, 2002]] 157

Figure 5.9:(Schematic; photomicrograph.) (a)The bacterial flagellar motor, showing elements analogous to those
of a macroscopic rotary motor. The inner part of the motor assembly develops a torque relative to the outer part,
which is anchored to the polymer network (the “peptidoglycan layer”), turning the flagellum. The peptidoglycan
layer provides the rigid framework for the cell wall; it is located in the periplasmic space between the cell’s two
membranes. (b)Composite electron micrograph of the actual structure of the motor assembly. Top to bottom,
about 75nm.[Digital image kindly supplied by D. Derosier; see (Derosier, 1998).] [Copyrighted figure; permission
pending.]

ω

v

df

v

df

z

x

y

Figure 5.10:(Schematic.) Principle of flagllar propulsion in bacteria. A thin, rigid, helical rod is cranked about its
helix axis at angular speedω.For better visualization a phantom cylinder has been sketched, with the rod lying on
its surface. Two short segments of the rod have been singled out for study, both lying on the near side of the helix
and separated by one turn. The rod is attached (black circle) to a disk and the disk is rotated, cranking the helix
about its axis. The two short segments then move downward, in the plane of the page. Thus dflies in the plane of
the page, but tipped slightly to the left as shown (see Figure 5.8). Thus a net force with a negativez-component is
required to keep the helix spinning in place.

to spin the flagellum in place (in addition to a torque about the axis).
Suppose the flagellum is not anchored, but instead is attached to a bacterium at its rightmost
end. Then there is nothing to supply a net leftward force; cranking the flagellum will therefore
pull the bacterium to theright.This is the propulsion mechanism we sought. Interestingly, mutant
bacteria have been found with straight flagella. They spin and spin, but never go anywhere.
T 2 Section 5.3.1′on page 168 discusses the ratio of parallel and perpendicular friction constants
in greater detail.