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Source The Cell: Problems Book
When analyzed in detail, the rhythmic beating of a cilium is revealed as a series of precisely repeated movements. In Chlamydomonas the flagellar beat cycle is straightforward (Figure1-A). The beat cycle begins with a power stroke, which is initiated by a bend near the base of the flagellum (arrow at base of flagellum 1 in Figure1-A). The power stroke ends when the bent segment of flagellum extends roughly through half the circumference of a circle (flagellum 5 in Figure1-A). The return stroke is formed by the movement of the semicircular segment of the flagellum outward toward the tip, which is accomplished by further bending at the leading edge of the semicircle and relaxation at the trailing edge (flagella 6 to 8 in Figure1-A).
A. How much sliding of microtubule doublets against one another is required to account for the observed bending of the flagellum into a semicircle? Calculate how much farther the doublet on the inside of the semicircle protrudes beyond the doublet on the outside of the semicircle at the tip of the flagellum (Figure2-A). The width of a falgellum is 180 nm.
B. The elastic nexin molecules that link adjacent outer doublets must stretch to accommodate the bending of a flagellum into a semicircle. If the length of an unstretched nexin molecule at the base of a falegellum is 30 nm, what is the length of a stretched nexin molecule at the tip of a flagellum (Figure2-B)? Adjacent dublets are 30 nm apart.
C. Chlamydomonas mutants that are missing radial spokes have paralyzed flagella. The paralysis can be overcome by mutations in a second gene, which encodes a component of the outer dynein arm. Although the flagella now move, their bear pattern is aberrant(Figure1-B) . At the gross level, how does the aberrant beat stroke of the double mutant differ from that of the wild type? What does this gross difference suggest for the function mediated by the radial spokes in Chlamydomonas ?
Figure 1
Figure 2
