Direct measurements of the stiffness (elastic bending resistance) of demembranated sea urchin sperm flagella were made in the presence of MgATP 2-and vanadate. Under these conditions, the flagellum is in a relaxed state, with a stiffness of -0 .9 x 10-2 ' N m l, which is -5% of the stiffness obtained in the rigor state in the absence of MgATP2-. MgADP -'does not substitute for MgATP 2 " in producing the relaxed state . A progressive inhibition of movement is observed after addition of MgATP 2-to flagella preincubated with vanadate, in which new bend generation, propagation, and relaxation by straightening are distinguished, depending on the ratio of MgATP 2-and vanadate. At appropriate concentrations of vanadate, increase of the velocity of bend propagation is observed at a very low concentration of MgATP 2-that is not enough to induce spontaneous beating . Vanadate enhances competitive inhibition of beat frequency by MgADP -but not by ADP3-, ATP -, or Pi. These observations, and the uncompetitive inhibition of beat frequency by vanadate, indicate that vanadate can only bind to dyneinnucleotide complexes induced by MgATP 2-and MgADP -. The state accessible by MgATP2-binding must be a state in which the cross-bridges are detached and the flagellum is relaxed . The state accessible by MgADP -binding must be a crossbridged state . Bound vanadate prevents the transition between these two states . Inhibition and relaxation by vanadate in the presence of MgATP2-results from the specific affinity of vanadate for a state in which nucleotide is bound, rather than a specific affinity for the detached state .The sliding microtubule hypothesis for flagellar and ciliary movement has been firmly established by a series of experimental (42, 49, 52) and theoretical works (4,5,31, 40), since the first important observations by P. Satir (43,44) . This hypothesis predicts that the dynein arm plays a vital role in generating the bending wave of flagella, because the dynein arm is involved in the transduction of the chemical energy provided by ATP dephosphorylation into mechanical energy (15, 16) . The conformational change of the dynein arm is assumed to involve the cyclic change of its orientation, including association and dissociation with the adjacent microtubule, as in the actomyosin system (26). This mechanochemical behavior of the dynein arm is thought to be tightly coupled with the cyclic dephosphorylation of ATP, because the rate of ATP hydrolysis is tightly coupled with flagellar movement and beat frequency (7, 10, 11), and because dynein ATPase not only has a latency (I, 21, 32, 47, 48) but also can be increased in activity by microtubular protein (l, 39) and tubulin (25).The dynein microtubule coupling mediated with ATP has also been suggested by some physiologi-J . CELL . BIOLOGY