5.6 Crawling and Swimming
79
Fig. 5.17 Left: Demonstration of the reversibility of Stokes flow. Right: A reversible change of
configuration
a cross-linked actin network. It is pushed ahead as actin monomer units squeeze in
to join growing filaments at their barbed ends attached to the bacterium (Mogilner
and Oster, 1996), in the same way as filaments attached to the plasma membrane
grow within a cell (Sect. 5.4).
Swimming is the most natural form of locomotion for microbes. As they are
small, inertia plays no role in their motion. Its effect is measured by the Reynolds
number: size times velocity divided by kinematic viscosity. With a size of about 10
microns, a microbe would have to swim as fast as a torpedo to bring the Reynolds
number close to unity. Viscous (Stokes) flow at low Reynolds number is more
amenable to mathematical analysis; the classic book on swimming organisms by
James Lighthill (1975) has not aged, but quite a lot has been added since then
(Lauga, 2016).
Stokes flow is dissipative but, paradoxically, it is reversible in some respects. A
narrow colored strip in a narrow gap between two cylinders spreads out into a formless cloud when the inner cylinder slowly rotates, but gathers back almost precisely
(just a bit blurred by diffusion) when the direction of rotation is reversed (Fig. 5.17,
three panels on the left). Therefore a swimmer changing its configuration in a reversible way, as a clam would do (Fig. 5.17, right), cannot advance, by the scallop
theorem due to Purcell (1977).
Microscopic swimmers avoid this injunction by deforming their bodies and attached utensils in a variety of fancy ways. The most common propulsion aid is a
flagellum (“whip” in Latin), a thin helical hollow tube. Bacteria developed a real
motor, with stators driving it, using energy from either sodium or hydrogen ion flux
through the membrane (Fig. 5.18, left). Rotation of the helix is balanced by the body
rotation in the opposite direction. Eukaryotic flagella do not rotate, but they can beat
in various fashions (Fig. 5.18, right). Sperm propels itself in this way.
Some organisms have several flagella, and some have their entire body covered
with shorter hair-like cilia and propel themselves by waving them in a coordinated
way. It is possible to swim even without external appendages, and even without
79
Fig. 5.17 Left: Demonstration of the reversibility of Stokes flow. Right: A reversible change of
configuration
a cross-linked actin network. It is pushed ahead as actin monomer units squeeze in
to join growing filaments at their barbed ends attached to the bacterium (Mogilner
and Oster, 1996), in the same way as filaments attached to the plasma membrane
grow within a cell (Sect. 5.4).
Swimming is the most natural form of locomotion for microbes. As they are
small, inertia plays no role in their motion. Its effect is measured by the Reynolds
number: size times velocity divided by kinematic viscosity. With a size of about 10
microns, a microbe would have to swim as fast as a torpedo to bring the Reynolds
number close to unity. Viscous (Stokes) flow at low Reynolds number is more
amenable to mathematical analysis; the classic book on swimming organisms by
James Lighthill (1975) has not aged, but quite a lot has been added since then
(Lauga, 2016).
Stokes flow is dissipative but, paradoxically, it is reversible in some respects. A
narrow colored strip in a narrow gap between two cylinders spreads out into a formless cloud when the inner cylinder slowly rotates, but gathers back almost precisely
(just a bit blurred by diffusion) when the direction of rotation is reversed (Fig. 5.17,
three panels on the left). Therefore a swimmer changing its configuration in a reversible way, as a clam would do (Fig. 5.17, right), cannot advance, by the scallop
theorem due to Purcell (1977).
Microscopic swimmers avoid this injunction by deforming their bodies and attached utensils in a variety of fancy ways. The most common propulsion aid is a
flagellum (“whip” in Latin), a thin helical hollow tube. Bacteria developed a real
motor, with stators driving it, using energy from either sodium or hydrogen ion flux
through the membrane (Fig. 5.18, left). Rotation of the helix is balanced by the body
rotation in the opposite direction. Eukaryotic flagella do not rotate, but they can beat
in various fashions (Fig. 5.18, right). Sperm propels itself in this way.
Some organisms have several flagella, and some have their entire body covered
with shorter hair-like cilia and propel themselves by waving them in a coordinated
way. It is possible to swim even without external appendages, and even without