We have examined the energetics of the interactions of two kinesin constructs with nucleotide and microtubules to develop a structural model of kinesin-dependent motility. Dimerization of the constructs was found to reduce the maximum rate of the microtubule-activated kinesin ATPase 5-fold. Beryllium fluoride and aluminum fluoride also reduce this rate, and they increase the affinity of kinesin for microtubules. By contrast, inorganic phosphate reduces the affinity of a dimeric kinesin

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... for microtubules. These findings are consistent with a model in which the kinesin head can assume one of two conformations, "strong" or "weak" binding, determined by the nature of the nucleotide that occupies the active site. Data for dimeric kinesin are consistent with a model in which kinesin⅐ATP binds to the microtubule in a strong state with positive cooperativity; hydrolysis of ATP to ADP؉P i leads to dissociation of one of the attached heads and converts the second, attached head to a weak state; and dissociation of phosphate allows the second head to reattach. These results also argue that a large free energy change is associated with formation of kinesin⅐ADP⅐P i and that this step is the major pathway for dissociation of kinesin from the microtubule. Molecular motors power a wide variety of physiologically important motile processes. These include movements of intracellular organelles, of chromosomes during mitosis and meiosis, and of cytoskeletal components during the process of ameboid motion (Vallee and Shpetner, 1990; Endow and Titus, 1992) . These enzymes can be broadly classified into two categories: the myosins, which generate movement along actincontaining microfilaments; and a group of microtubule-based motors that include cytoplasmic dynein and the kinesin family of mechanoenzymes (Endow and Titus, 1992) . The myosins remain the best studied group of molecular motors, and much effort has gone into identifying which of the steps in the actomyosin ATPase cycle are responsible for force generation. Studying the nature of these myosin-nucleotide intermediate states has been facilitated by the use of transition metals, which bind to myosin⅐ADP stoichiometrically and with high affinity (Goodno, 1979; Phan and Reisler, 1992; Maruta et al., 1993) . Complexes of these metals with myosin⅐ADP appear to mimic either the myosin⅐ATP or myosin⅐ADP⅐P i structures (Fisher et al., 1994) . Thus, aluminum fluoride appears to induce a prehydrolytic myosin-nucleotide transition state, whereas beryllium induces a myosin⅐ATP structure (Fisher et al., 1994) . The stability of these complexes has allowed their study with spectroscopic, NMR, and crystallographic methods and has provided insight into the structure of the short lived myosin⅐ATP and myosin⅐ADP⅐P i intermediates. The validity of their use in studying myosin-nucleotide intermediates has also been supported by the effects of inorganic phosphate. Phosphate can bind to the active site of myosin⅐ADP to generate a myosin⅐ADP⅐P i state, and it has effects that are physiologically similar to those of vanadate and aluminum fluoride in reducing the affinity of myosin⅐ADP for actin (Dantzig and Goldman, 1985) . Compared with the myosins, the kinesin family of microtubule motors appears to have to comply with a different set of physiologic constraints. Kinesin powers movement of organelles along microtubules and, unlike myosin, appears to operate in isolation (Walker and Sheetz, 1993) . Motility studies in vitro are consistent with this assignment of function, as single kinesin molecules are able to translocate along microtubules for several micrometers at maximal velocity without detaching (Howard et al., 1989). These differences in physiology suggest that the nature of the force-generating transition(s) in the kinesin-microtubule ATPase cycle may likewise be different. Support for this comes from an in vitro motility study (Romberg and Vale, 1993) which demonstrated that ATP␥S, 1 vanadate, and aluminum fluoride prolonged the lifetime of attachment of kinesin to the microtubule; and increasing concentrations of ADP shortened this lifetime. These findings were interpreted to mean that the kinesin⅐ADP⅐P i state (presumably mimicked by aluminum fluoride, vanadate, and ATP␥S) was strongly bound, whereas the kinesin⅐ADP state was weakly bound. However, more recent kinetic studies of the kinesin ATPase cycle could be explained by either of two models. In one, dissociation of the kinesin-microtubule complex occurs in the kinesin⅐ADP⅐P i state, suggesting that this state may be weakly bound, whereas in the other, dissociation occurs in a transition involving a kinesin⅐ADP intermediate state: KMT strong 7 KMDP i ? 7 KMD ? 7 KM strong (Reaction 1) where K is kinesin, M is microtubule, T is ATP, and D is ADP. Determining which of the above models is the most accurate