The relaxation (straightening) of flagellar rigor waves, which is known to be induced by micromolar ATP concentrations was investigated with respect to its dependence on the binding and hydrolysis of ATP. Flagellar rigor waves were formed by the dilution of demembranated, reactivated sea urchin (Lytechinus pictus) spermatozoa into ATP-free buffer. Relaxation in response to nucleotide was quantitated by measuring theta, the mean flagellar bend angle per sperm; this novel assay permitted determination of the rate of relaxation. It was found that (a) the rate of flagellar relaxation induced by 4 X 10(-6) M ATP was inhibited 80% by vanadate concentrations of 3 X 10(-6) M and above; (b) of 16 hydrolyzable and nonhydrolyzable nucleotide di-, tri-, and tetraphosphates tested, only three, each of which was hydrolyzed by the flagellar axonemal ATPase activity (ATP, dATP, and epsilon-ATP) were also capable of effecting relaxation; (c) several hundred ATP molecules were estimated to be hydrolyzed by each dynein of ATP hydrolysis, which defines the efficiency of ATP utilization, increased 30-fold as the ATP relaxation depends on ATP hydrolysis; (b) because it depends on ATP hydrolysis, flagellar relaxation is an inappropriate model system for investigating the role of ATP binding in the mechanochemical cycle of dynein; and (c) the efficiency of mechanochemical coupling in flagellar motility is an ATP-dependent phenomenon. A general model of relaxation is proposed based on active microtubule sliding.

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