Collective Effects in Arrays of Cilia and Rotational Motors - Cell Motility - page 205

A similar method of propulsion is employed by many eukaryotic cells that also
swim by means of flagella. Although prokaryotic and eukaryotic flagella bear the
same name they are quite different. The eukaryotic flagella are not only at least ten
times larger than bacterial flagella in both diameter and length (they can be up to
70 μ m long and 0 . 8 μm wide), they are completely dissimilar in structure, function,
and in the genes that encode their components. The eukaryotic flagellum is built
of microtubules, while the bacterial flagellum is composed of the protein flagellin.
The eukaryotic flagella also do not rotate but actively propagate bending waves [5].
However, propulsion by both kinds of flagella relies on the fluid mechanical fact
that the sideways motion of thin rods encounters greater viscous drag than forward
motion [6].
Other organisms, the ciliates , are covered with cilia, hair-like projections, which
are uniform and aligned in rows [7]. The cilia are used by the cell for swimming
and feeding 1 . Cilia also play an important role in the human body. For example,
thousands of cilia are attached to the bronchioles creating an air current transporting
mucus and small dust particles out of the human lungs. There is also experimental
evidence that during development cilia-generated flow contributes to the placement
of our organs (see Section 8.4).
Most cilia have (similar to eukaryotic flagella) the “9+2” structure [9], where nine
sets of microtubule doublets surround a pair of single microtubules in the center.
Motors (dyneins) cause bending deformations, giving rise to characteristic beating
patterns typically consisting of a power and a recovery stroke [10]. Somewhat special
are monocilia that are primary cilia lacking the central pair of microtubules and thus
have a “9+0” microtubule arrangement [11, 12]. They perform a rapid rotational
motion [13] and very often are tilted giving rise to non-symmetrical velocity fields
(see Section 8.4).
In populations of cilia, beating is very often coordinated. Two types of cooper-
ative motion can be distinguished: i) adjacent cilia beat cooperatively in a synchro-
nized fashion [14]. Here, all cilia oscillate with same frequency and vanishing phase
difference. ii) Cilia maintain a constant phase difference, creating a metachronal
wave [15]. Metachronal waves can propagate in the direction of the effective stroke
(symplectic metachronal waves), in the opposite direction (antiplectic), perpendic-
ular direction (laeoplectic or dexioplecit), or oblique direction [16].
Animals, such as the freshwater protozoa Paramecium , use this collective ciliar
motion to swim. Typically, the cilia beat with a traveling helical wave, where the
direction of the ciliary effective stroke is oblique to the long axis of the body [15].
Thus, Paramecium swims in a spiral course, rotating around its longitudinal axis.
By changing the axis of the helix, a Paramecium can steer and reverse its direction
of motion [17]. This means of motion is extremely ecient: the ∼ 100 μ m long
Paramecium can swim with a velocity of order ∼ 1mm / s.
Cilia-generated flow is also important for feeding of cells. Certain sessile species
of protozoa (such as Stentor and Vorticel la ) use ciliar motion to produce a fluid
current into their mouth region [5, 18].
The main purpose of cilia is to propel fluid over the surface of the cell. How-
ever, there are also other biological macromolecules whose complex shape changes
induce flow in the surrounding fluid. A prominent example is adenosine triphosphate
synthase (ATPsynthase), which exhibits a rotational motion [19, 20]. Although the
1 Cilia can also act a sensors [8]. This aspect is not reviewed here.