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 actin-containing 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 myosinADP stoichiometrically and with high affinity (Goodno, 1979; Phan and Reisler, 1992; Maruta et al., 1993). Complexes of these metals with myosinADP appear to mimic either the myosinATP or myosinADPP structures (Fisher et al., 1994). Thus, aluminum fluoride appears to induce a prehydrolytic myosin-nucleotide transition state, whereas beryllium induces a myosinATP 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 myosinATP and myosinADPP 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 myosinADP to generate a myosinADPP state, and it has effects that are physiologically similar to those of vanadate and aluminum fluoride in reducing the affinity of myosinADP 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 ATPS, ()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 kinesinADPP state (presumably mimicked by aluminum fluoride, vanadate, and ATPS) was strongly bound, whereas the kinesinADP state was weakly bound. However, more recent kinetic studies (Gilbert et al., 1995) of the kinesin ATPase cycle could be explained by either of two models. In one, dissociation of the kinesin-microtubule complex occurs in the kinesinADPP state, suggesting that this state may be weakly bound, whereas in the other, dissociation occurs in a transition involving a kinesinADP intermediate state:

where K is kinesin, M is microtubule, T is ATP, and D is ADP.

Determining which of the above models is the most accurate depiction of the kinesin ATPase cycle requires direct measurements of the binding affinities of the various kinesin-nucleotide intermediate states and the equilibrium constants for the various kinesin-nucleotide transitions. Efforts in this regard have been made by several laboratories, which have examined the steady and pre-steady-state kinetics of these transitions by utilizing bacterially expressed recombinant fragments of kinesin which contain the amino-terminal motor domain and variable amounts of the carboxyl-terminal tail (Huang and Hackney, 1994; Huang et al., 1994; Hackney, 1994a, 1994b; Gilbert and Johnson, 1993, 1994; Gilbert et al., 1995; Ma and Taylor, 1995a, 1995b). These studies have confirmed previous observations using intact kinesin and have extended them by demonstrating that: 1) ATP binding, hydrolysis, and phosphate release are rapid relative to subsequent steps in the hydrolysis cycle; 2) kinesinADP is the predominant species in the system, and release of ADP is the rate-limiting step; 3) microtubules accelerate ADP release several thousandfold; and 4) for dimeric kinesin constructs that contain ADP in the active site, microtubules accelerate release of only one of the two bound ADP molecules. However, these studies have not measured binding affinities of stable kinesinATP and kinesinADPP intermediates and are thus not able to assign microtubule affinities reliably to several of the kinesin-nucleotide states depicted above.

In this study, we have generated two bacterially expressed constructs of human kinesin and examined the effects of ADP, aluminum fluoride, beryllium fluoride, and inorganic phosphate on their binding affinities and steady-state ATPase parameters. These studies indicate that ternary complexes of kinesinADP with salts of aluminum and beryllium mimic the kinesinATP state, which is strong binding; that inorganic phosphate reduces the affinity of dimeric kinesinADP for microtubules; and that the dissociation of the kinesinADPP complex from microtubules represents the major dissociation step in the kinesin-microtubule ATPase mechanism.

EXPERIMENTAL PROCEDURES

Materials

Kinesin Expression in Escherichia coli and Purification of Recombinant Proteins

Sedimentation Velocity Experiments

Preparation of Tubulin and Microtubules

ATPase Assays

Data for K332 ATPase rate versus microtubule concentration were fit to the Michaelis-Menten equation to determine k and K. For K413, rate versus microtubule concentration data had to be corrected for the percentage of K413 which was monomeric, by fitting the ATPase rate, , to

where is the fraction of K413 which is monomeric, 1 - is the fraction which is dimeric, and M is the concentration of tubulin dimer. The value of was determined by equilibrium sedimentation studies of K413 which will be reported elsewhere. ()The values of K and k for monomeric K413 were determined by measuring microtubule-activated ATPase activity at a K413 concentration of 50 nM, where the construct is >95% monomeric.

Mant ADP, Mant AMPPNP Binding Assays

The effect of EDTA treatment on nucleotide binding stoichiometry was measured independently for K413 by the following experiment. Twenty µM K413 in ATPase buffer was incubated with a 30-fold molar excess of mant ADP for 4 h at 4 °C. The sample was dialyzed against 1,000 volumes of ATPase buffer, and the remaining mant ADP was removed followed by gel filtration on Sephadex G-25 (PD-10), which had been equilibrated in ATPase buffer. The concentration of K413 was measured by its absorbance at 280 nm, calculated from its amino acid composition ( = 33,650 M cm; Gilbert and Johnson(1993)), and the concentration of mant ADP was measured by its absorbance at 356 nm ( = 5,800 M cm; Hiratsuka(1983)).

H Labeling of Kinesin

Microtubule Binding Assay

Binding data for K332 could be fit to a binding isotherm of the form

where is the fractional binding, defined as the ratio of sedimented K332 to total K332, is the maximum degree of binding, K is the association constant, and [M] is microtubule concentration. For K413ADP ± beryllium fluoride, fitting required a correction for the fraction of K413 which is dimeric versus monomeric. This was accomplished by utilizing data from equilibrium sedimentation studies. Data were fit to , which assumes: 1) that the fraction of K413 that is monomeric () binds to the microtubule with affinity K, determined by measuring microtubule binding affinity at low K413 concentration, where the construct is monomeric; 2) that the fraction of K413 which is dimeric is 1 - ; 3) that each head of a free dimeric K413 molecule can bind to the microtubule affinity constant K; and 4) that binding of the second head to the microtubule occurs with affinity constant K. , the fractional binding of K413, is defined as the ratio of unsedimented K413 to total K413. Under these conditions, the degree of binding, , is determined by the fractional binding of the monomeric and dimeric species.

Expressing these quantities in terms of the various affinity constants reveals the following (Tanford, 1961).

The validity of using values of in which were derived from equilibrium sedimentation studies was tested by setting as an independent variable in fitting to for the data in Fig. 3A. The value of derived by this method for K413ADP at a concentration of 250 nM ( = 0.62, r = 0.96) was very close to that derived from equilibrium studies ( = 0.60; Footnote 2). Free energies of binding for dimeric K413 were calculated using the microscopic binding constant, K, whose relationship to the individual macroscopic binding constants, K,in is as follows (Tanford, 1961)

Figure 3: Fractional binding versus tubulin dimer concentration for kinesin constructs. Panel A, K413 at 250 nM (closed squares), 50 nM (open triangles), and 250 nM K413 + 1 mM BeSO + 5 mM NaF (closed circles). Data for K413 at 50 nM fit a rectangular hyperbola, which defines a value of K of 7.8 µM and stoichiometry of 0.9. Conditions: 20 mM HEPES, 50 mM potassium acetate, 5 mM MgCl, 1 mM DTT, 1 mM NaN, 1 mM MgADP, pH 7.20, 25 °C. Data for K413ADP ± beryllium fluoride at 250 nM were fit to (see ``Experimental Procedures''), which corrects for the reversible dimerization of this construct. Values of were determined from sedimentation equilibrium studies (Footnote 2). This reveals 1/K = 0.5 µM and 1/K = 7.1 µM for dimeric K413ADP (stoichiometry 0.8) and 1/K = 0.6 µM and 1/K = 0.4 µM for dimeric K413ADP + beryllium fluoride (stoichiometry 0.8). Panel B, 100-200 nM K332 (closed squares), K332 + 1 mM BeSO + 5 mM NaF (closed circles), K332 + 1 mM AlNO + 5 mM NaF (open triangles), K332 + 1 mM AMPPNP (closed diamonds), and K332 + 10 mM sodium phosphate (open squares). Conditions as in panel A. Data for each sample could be adequately fit to a rectangular hyperbola, defining values of dissociation constants as follows: K332ADP, 20.8 µM (stoichiometry 0.9); K332ADPBeF, 5.6 µM (stoichiometry 0.8); K332ADPAlF, 1.4 µM (stoichiometry 0.8); K332AMPPNP, 1.1 µM (stoichiometry 0.8); K332ADPP, 18.2 µM (stoichiometry 0.8).

where n, the number of microtubule binding sites on K413, is equal to 2. Thus, a prediction of the model described by is that the individual values of K are highly correlated with each other. In the presence of cooperativity, K may be larger (positive cooperativity) or smaller (negative cooperativity) than expected from that predicted by the value of K. In the presence of cooperativity, the free energy of binding of the second site to a microtubule would be (Tanford, 1961)

where G is the intrinsic free energy of binding in the absence of cooperativity, and G() is the interaction free energy. The free energy of binding to the second site on K413 was derived by using the value of the microscopic constant, K (derived from K) to determine G and by using the difference between the predicted value of K (determined from K by assuming no interactions) and that determined from .

Effect of Inorganic Phosphate on KinesinADPMicrotubule Affinity

which assumes that only one head of the K413 dimer can attach to the microtubule when phosphate occupies the active site. In this scheme, K is kinesinADP, MK is kinesinADP bound to microtubules, P is inorganic phosphate, and K are association constants for each step. The apparent dissociation constant, K, at a given phosphate concentration, [P], is defined by

which yields the following.

Statistical Methods

RESULTS

Characterization of Human Kinesin Constructs

Titration of the active site of K413 was accomplished by measuring the equilibrium constant for binding of the fluorescent nucleotide derivatives mant ADP and mant AMPPNP, using an equilibrium dialysis technique. Scatchard plot analysis of the data (Fig. 1) demonstrates that K413 binds mant ADP with one class of binding site, characterized by a dissociation constant of 0.67 µM and stoichiometry of 0.80 mol of mant ADP/mol of head. By contrast, the dissociation constant of mant AMPPNP, at 7.1 µM, is approximately 10-fold greater, and the stoichiometry is 1.3 mol/mol of head. The effect of EDTA treatment on K413 was investigated by examining the stoichiometry of mant ADP binding under conditions where it was present in large molar excess over K413 active sites, in the absence of EDTA. This revealed a range of stoichiometries of 0.87-0.95 over five separate measurements (data not shown). Thus, EDTA treatment does appear to reduce the binding stoichiometry by approximately 8-19%. This percentage reduction in the binding stoichiometry after EDTA treatment is very similar to that measured previously, using [H]ATP binding (Ma and Taylor, 1995b).

Figure 1: Binding of mant AMPPNP (closed circles) and mant ADP (closed boxes) to nucleotide-free K413. K413 was made nucleotide-free as described (Sadhu and Taylor, 1992) and mixed with a range of concentration of mant nucleotide. Free nucleotide was measured by an equilibrium dialysis method. Scatchard analysis of the data reveals that binding of mant ADP to K413 is characterized by a dissociation constant of 0.67 µM and a stoichiometry of 0.80; for mant AMPPNP, the corresponding values are 7.1 µM and 1.30.

Steady-state Kinetics of the Kinesin ATPase

As in the case of the Drosophila constructs, the K413 and K332 MgATPase activities are markedly activated by microtubules. At 50 nM K413, the construct is essentially entirely monomeric, and data in Fig. 2A fit conventional Michaelis-Menten kinetics, defining values of K and k of 3.5 µM and 35.1 s, respectively. Increasing the K413 concentration to 300 nM generated data that needed to be fit to . This defined values of K and k for dimeric K413 of 0.54 µM and 8.25 s. Fig. 2B demonstrates the corresponding data for K332, which defines values of K and k of 26.0 µM and 43.6 s.

Figure 2: ATPase rate versus tubulin dimer concentration for kinesin constructs. Panel A, K413 at 300 nM (open squares), 50 nM (open triangles), and 300 nM in the presence of 1 mM BeSO + 5 mM NaF (open circles). Data for K413 at 50 nM fit Michaelis-Menten kinetics with k = 35.1 s and K = 3.5 µM. Data for K413 ± beryllium fluoride at 300 nM were fit to (see ``Experimental Procedures''), which corrects for reversible dimerization of this construct. Values of were determined from sedimentation equilibrium studies (Footnote 2). This reveals k = 8.25 s and K = 0.54 µM for dimeric K413 and k = 0.83 s and K = 0.38 µM for dimeric K413 + beryllium fluoride. Panel B, corresponding data for K332 in the absence (closed diamonds) or presence of 1 mM AlNO + 5 mM NaF (open squares), 1 mM BeSO + 5 mM NaF (open circles), and 0.5 mM sodium vanadate (open triangles). Fitting to Michaelis-Menten kinetics reveals the following: k = 43.6 s and K = 26.0 µM for K332; k = 7.2 s and K = 4.0 µM for K332 + beryllium fluoride; k = 0.08 s and K = 3.7 µM for K332 + aluminum fluoride; and k = 2.9 s and K = 5.8 µM for K332 + sodium vanadate. Panel C, double-reciprocal plot of data from panel B for K332 in the absence (open squares) and presence (open circles) of 1 mM BeSO + 5 mM NaF. This reveals parallel curves, as expected for uncompetitive inhibition, and defines a value of K of 41 µM.

The kinetics of the microtubule-activated ATPase activity showed a marked ionic strength dependence. Raising the ionic strength from 50 mM potassium acetate to 150 mM KCl raised the value of K for K413 to 80 µM and decreased the value of k to 4 s (data not shown). Corresponding data for K332 were 97 µM and 10 s (data not shown).

Dissociation Constant of K413 and K332ADP for Microtubules

Complex Formation with Beryllium Fluoride and Aluminum Fluoride

Beryllium and aluminum fluoride, like vanadate, reduce the affinity of myosinADP for actin, since myosinADPberyllium fluoride and myosinADPaluminum fluoride mimic the weakly bound prehydrolytic myosin states (Fisher et al., 1994). The value of the actin-activated k is reduced in these complexes because of the tight binding of the metals to the active site (Maruta et al., 1993). Thus, if kinesin follows the same behavior, it would be expected that beryllium fluoride and aluminum fluoride should decrease the value of k and increase the value of K for the microtubule-activated kinesin ATPase. As Fig. 2B demonstrates, both transition metals reduce not only k but also K for K332, implying that the kinesin ADPBeF and kinesinADPAlF states are more strongly bound than kinesinADP. Experiments performed in the presence of 0.5 mM sodium vanadate also demonstrate that this transition metal reduces both k and K (Fig. 2B and Table 1). Corresponding data for K413 in the presence of beryllium fluoride are shown in Fig. 2A. A double-reciprocal plot of the microtubule-activated K332 ATPase rate versus microtubule concentration is shown in Fig. 2C for samples in the absence and presence of 1 mM BeSO + 5 mM NaF. This demonstrates essentially parallel curves, as expected for uncompetitive inhibition, and defines a value of K for beryllium fluoride of 41 µM. Corresponding values of K for aluminum fluoride and vanadate are 1.7 and 35 µM, respectively. Thus, at aluminum and beryllium concentrations of 1 mM, essentially all of the active sites of K413ADP and K332ADP have transition metal bound.

The decrease in the value of K implies that the transition metals increase the affinity of kinesinADP for microtubules. This was confirmed by using tritium-labeled K413 and K332 in an Airfuge binding assay. Data are summarized in Fig. 3A for K413 at 250 nM and Fig. 3B for K332 and in Table 1. Dissociation constants for K332ADP are 5.6 µM in the presence of beryllium fluoride and 1.4 µM in the presence of aluminum fluoride, and both values are close to the corresponding values of K (Table 1). Binding data for K332 in the presence of 1 mM AMPPNP are nearly superimposable on those for aluminum fluoride (Fig. 3B and Table 1). Fitting of binding data for K413ADPberyllium fluoride to reveals values of 1/K and 1/K of 0.6 and 0.4 µM, respectively (Table 1).

Effect of Inorganic Phosphate on the Microtubule Affinity of KinesinADP

Figure 4: Effect of phosphate concentration on K413ADP microtubule affinity. Data were fit to (see ``Experimental Procedures'') to determine the dissociation constants of K413ADPP for microtubules (1/K) and of phosphate for K413ADP (1/K), and this reveals 1/K = 17.0 µM and 1/K = 0.8 mM.

DISCUSSION

This study utilized two constructs derived from a human homologue of the Drosophila kinesin heavy chain. K413, containing residues 1-413, is homologous to Drosophila 1-401, a construct that sedimentation equilibrium studies have revealed is largely dimeric (Correia et al., 1995). Similar conclusions have been reached with Drosophila 1-392 (Huang et al., 1994). The sedimentation velocity behavior of K413 is consistent with its capacity to dimerize, although sedimentation equilibrium studies indicate a dimerization dissociation constant that is approximately 10-fold larger. This larger dimerization constant may reflect intrinsic differences between the human and Drosophila sequences or may be due to the steric and/or ionic effects of the hexahistidine sequence at the extreme carboxyl terminus of the human construct, which is used in affinity purification. By contrast, K332 is homologous to the monomeric Drosophila construct containing residues 1-340 (Huang and Hackney, 1994; Correia et al., 1995), and this is consistent with its sedimentation velocity behavior as well as its elution behavior on Sephacryl S-300 and Superose 12 FPLC. Both K332 and K413 possess an intrinsic MgATPase activity that is very low. For both, microtubules enhance this ATPase activity several thousandfold.

A striking feature of the results from microtubule-activated ATPase studies is that the value of k for monomeric K413 is nearly 5-fold larger than that for dimeric K413 and is only 19% less than that for the monomeric construct K332. This finding resolves an apparent discrepancy between the values of k reported for Drosophila constructs that have been presumed to be dimeric. The value of k for dimeric K413 is close to that reported for experiments with Drosophila K401 at a kinesin concentration of 500 nM (10.9 s; Gilbert and Johnson(1993)). Equilibrium sedimentation studies have shown that at this concentration, approximately 90% of the construct is dimeric (Correia et al., 1995). More recent studies from same laboratory reported a value of k of 20 s (Gilbert et al., 1995). However, in this study, the K401 concentration was lower, at 200 nM. At this concentration, approximately 18-20% of the K401 would be monomeric (Correia et al., 1995). predicts that an overall rate of 20 s could be observed if k for dimeric K401 is 10.9 s, and k for monomeric K401 is approximately 55 s, which is consistent with our own results. Other experiments on a Drosophila construct that is 9 residues shorter measured a value of k of 47 s, which is very similar to that for K332 and only 1.3-fold larger than the value of k for monomeric K413 (Hackney, 1994a). In this study, the concentration of the kinesin construct used in the ATPase assay was 8.4 nM. It is reasonable to assume that the association constant for dimerization of this construct should be similar to or perhaps less than that for Drosophila K401, and given this, the published data would indicate that this construct would be >75% monomeric (Correia et al., 1995). Thus, our data clearly indicate that dimerization of kinesin markedly inhibits the degree of microtubule activation.

An increase in enzymatic activity with increasing degrees of truncation has been reported not only for kinesin, but also for other microtubule motors, such as ncd (Stewart et al., 1993; Huang and Hackney, 1994; Huang et al., 1994; Chandra et al., 1993). One possible explanation for this inhibition is that the conformational changes that occur during the power stroke of the kinesin ATPase cycle may be linked to a rate-limiting rotation of one head relative to the other, which would be mediated through the dimerization segment contained within the carboxyl-terminal 81 residues of K413 (Fig. 5). Loss of dimerization, either by dilution of K413 or by truncation of the dimerization segment, would lower the energy barrier for this conformational change and accelerate this rate-limiting step.

Figure 5: Structural model of the kinesin:microtubule mechanochemical cycle. Panel A, model of the K332microtubule interactions. The tubulin dimer is depicted as the arrow-shaped structure, and its binding site for kinesin is depicted as the vertically shaded box. The kinesin monomer is depicted as the comma-shaped structure. In the presence of ADP ± P (MKD/MKDP), kinesin assumes a weak binding conformation, symbolized by the rounded shape of the microtubule-associated end of the molecule. When ATP occupies the active site (MKT), kinesin assumes a strong binding conformation, symbolized by the squared-off shape of the microtubule-associated end of the molecule. Panel B, model of the K413microtubule interactions. In this figure, the two kinesin heads are shaded differently to distinguish them. In addition, the dimerization segment, containing portions of the -helical tail segments of each monomer, is shaded separately. In the absence of nucleotide, or when ATP occupies the active site (MKT, MK), binding to the microtubule demonstrates positive cooperativity, presumably because of a stabilizing of the orientation of the second kinesin head (cross-hatched) by attachment of the first head (dotted) to the microtubule binding site (vertically shaded box). Hydrolysis of ATP to ADP+P (MKDP) leads to a weakening of the affinity of the cross-hatched head of the kinesin dimer. This is postulated to lead to a change in flexibility of the dimerization segment, which allows a rotation of the second (dotted) head and prevents this head from attaching to the microtubule. Dissociation of phosphate (MKD) allows the unattached (dotted) head to reattach weakly to the next available downstream binding site. This is presumed to stabilize the interaction of the other (cross-hatched) head, whose microtubule affinity is thereby enhanced. Dissociation of ADP from the active sites enhances the affinity of the attached heads to that seen in the presence of ATP and regenerates a fully attached state.

Active site titrations with mant ADP and mant AMPPNP give the expected result of one class of binding site with an approximately 1:1 stoichiometry. The affinity of mant ADP for K413, determined in this study by equilibrium methods, is approximately 2 orders of magnitude lower than that measured with the complete heavy chain-light chain complex (Hackney, 1988; Sadhu and Taylor, 1992). The large difference in affinities between intact kinesin and the truncated constructs may reflect the trapping of nucleotide in the active site of intact kinesin when it assumes the folded conformation (see above; Hackney(1992)). In contrast to myosin, which binds AMPPNP with higher affinity than ADP (Trybus and Taylor, 1982), kinesin binds with the reverse order of affinities: the dissociation constant of mant AMPPNP binding to K413 is approximately 10 times larger than that for ADP (Fig. 1). This argues that kinesin interacts with nucleotide in a manner distinct from that for myosin.

The results of microtubule binding studies with the monomeric construct K332 will be discussed first, as their interpretation is more straightforward. Binding studies in the presence of 1 mM MgADP yielded dissociation constants that are close to the corresponding values of K. The relationship between the midpoint of the ATPase titration and the dissociation constant was explicitly developed in a previous study of the actosubfragment 1 ATPase mechanism (Rosenfeld and Taylor, 1984), and the four-state model derived in that study can be applied to the case of kinesin as well. This model, as applied to kinesin, assumes that the kinesinATP and kinesinADPP states are in rapid equilibrium with microtubules, an assumption that is supported by recent studies (Gilbert et al., 1995). According to this model, the relation between steady-state velocity and microtubule concentration is

where k and k are the weighted forward and reverse rate constants, respectively, for the nucleotide hydrolysis step, and K is the association constant of kinesinADPP for the microtubule. For both kinesin and the microtubule-kinesin complex, k k (Ma and Taylor, 1995a, 1995b; Gilbert and Johnson, 1994), which leads to

where K = 1/K. Since the model predicts that the intrinsic affinities of kinesinADP and kinesinADPP are essentially equal, this leads to the prediction that for K332ADP, K K, which is supported by the data in Table 1.

Experiments with K332ADP + beryllium fluoride and aluminum fluoride support the contention that kinesin interacts with nucleotide in a manner distinct from that for myosin. Both transition metals were found to enhance the affinity of K332 for microtubules. In the case of aluminum fluoride, the enhancement in affinity was the same as that seen with AMPPNP. This contrasts markedly with the case of myosins, where these transition metals, as well as inorganic phosphate, reduce the affinity of myosin for actin, as expected with the assignment of the myosinATP and myosinADPP states as weak binding (Goodno and Taylor, 1982; Yamakawa and Goldman, 1991; Phan and Reisler, 1992). Previous studies of kinesin with aluminum fluoride and ATPS in an in vitro motility assay suggested that kinesin has reversed the cycle, that kinesinADP is weak binding and kinesinATP and kinesinADPP are strong binding (Romberg and Vale, 1993). Interpretation of these results and of our own, however, depends on an unambiguous assignment of the conformation for kinesinADPaluminum fluoride and kinesinADPberyllium fluoride. The results of our study indicate that aluminum and beryllium fluoride mimic prehydrolytic kinesin-nucleotide states, which is supported by crystallographic data from myosin (Fisher et al., 1994) and that these states are strongly binding, the opposite of what is seen in myosin.

Binding data for K332 can be interpreted by a relatively simple model, in which monomeric kinesin can attach to the tubulin dimer in one of two conformations: a strong binding state that releases approximately -8.0 kcal/mol of binding free energy, and a weak binding state that releases approximately -6.4 kcal/mol (Fig. 5A). The data in Table 1and Fig. 3B can then be explained by assuming that K332ADP assumes a weak conformation, whereas K332AMPPNP and K332ADP aluminum fluoride assume the strong conformation.

Interpretation of the binding studies with K413 is more complicated because of the reversible dimerization that occurs with this species and the need to account for one-site versus two-site binding of the dimer. The model defined by gave a superior fit to the data ( = 0.011 for K413ADP and K413ADPBeF) than that for a simple hyperbolic isotherm ( = 0.10). However, initial attempts to fit the data to led to large standard errors for 1/K and 1/K because of the high degree of correlation between these parameters. This is consistent with the model described by , since the values of K and K are related to each other (see ``Experimental Procedures''; Tanford(1961)). Improved fitting required use of the Moore-Penrose inverse and led to values of K and K which had acceptable errors. It is proposed that each head of the K413 dimer can assume a strong or a weak conformation. Furthermore, it is presumed that monomeric K413ADP, like K332ADP, attaches to the microtubule via a weak interaction only. We propose that each head of K413ATP, mimicked by K413ADP + beryllium fluoride or aluminum fluoride, is in a strong conformation. If these two heads behave in an identical and independent manner, then K = (K)/4 (Tanford, 1961). Fitting of binding data, however, demonstrates that K = 1.5(K). This implies that binding of the second head of the K413ATP dimer demonstrates positive cooperativity and releases an additional -1.1 kcal/mol of interaction-free energy. Although the structural basis for this cooperative interaction was not determined from this study, one possibility is that the binding of the first head stabilizes the orientation of the second head so that its binding is more favorable. Hydrolysis of ATP to ADP+P is proposed to do two things: it alters the conformation of both heads (to weak binding) as well as their relative orientation, making it sterically impossible for the second head to attach to the microtubule at all. Release of phosphate, to generate a kinesinADP dimer, would allow the second head to reattach. Results of fitting to indicate that for K413ADP, K = (K)/14.2, which is nearly four times smaller than predicted from a noninteracting system. These data can be interpreted to mean that phosphate release has no effect on the intrinsic microtubule affinity of kinesinADP; rather, that weak attachment of the second head (dotted in Fig. 5B) stabilizes the interaction of the first head (cross-hatched in Fig. 5B) with the microtubule and enhances its affinity. This model thus predicts that in the absence of a second head, binding of kinesinADP should be weak and that phosphate should have no effect. The data with K332 and monomeric K413 support this ( Table 1and Fig. 5A). Furthermore, it is proposed that the strong reattachment of one of the K413ADP heads to the microtubule generates force and accelerates release of its bound nucleotide. This is consistent with the finding that K K for K413ADP and explains why microtubules accelerate the release of bound ADP from only one head of dimeric kinesin constructs (Hackney, 1994b).

This model is also consistent with the relative affinities of ADP versus AMPPNP for K413 (Fig. 1). Differences in the energetics of microtubule binding between K413ATP (mimicked by K413AMPPNP or K413ADPberyllium fluoride) and K413ADP should be reflected in reciprocal differences in the energetics of binding of AMPPNP versus ADP if the conformational changes between K413ADP and K413ATP are driven by nucleotide binding. Calculation from the nucleotide binding data reveals a difference of 2.8 kcal/mol, which is close to the value calculated from microtubule affinities, of 2.3 kcal/mol. Finally, the effect of phosphate on K413ADP is not due to a destabilizing of microtubules, as some studies have shown that phosphate enhances microtubule stability, with an apparent dissociation constant of 25 mM (Carlier et al., 1988; Schlistra et al., 1991), whereas others see no effect of inorganic phosphate over this concentration range (Caplow et al., 1989).

These results therefore predict that dissociation of the microtubule-kinesin complex during the ATPase cycle should occur upon formation of the weakly bound kinesinADPP complex, as suggested by one of two models proposed on the basis of kinetic studies (Gilbert et al., 1995). This study provided a kinetic explanation for processivity through the relatively slow rate of dissociation and the rapid rate of rebinding of the weakly bound kinesin intermediate. Our results demonstrate that the most weakly bound K413 intermediate (K413ADPP) has a dissociation constant for microtubules which is still significantly lower than the local concentration of tubulin intracellularly (Gilbert et al., 1995). Thus, our data indicate that at least one head of the kinesin dimer would likely remain attached to the microtubule at all times in the ATPase cycle. It also predicts that there is a large free energy change associated with hydrolysis of ATP in the kinesin-microtubule complex. This free energy change presumably drives the power stroke and if so, should be reflected in a significant conformational change in the kinesin molecule. As a subsequent study will demonstrate, this can be detected through fluorescent anisotropy decay studies on labeled kinesin preparations.

The model presented here is also consistent with several recent structural models of the kinesin-microtubule and ncd-microtubule complex. Hydrolysis of ATP would lead to dissociation of one head and pivoting of the attached head toward the adjacent tubulin subunit. This would enable the unattached head of the kinesin dimer, presumably containing ADP, to attach to the next site along the microtubule protofilament. Since the kinesin head is smaller than the tubulin heterodimer, attachment of the second head could only occur in one direction because of simple steric considerations. This model is similar to those proposed previously (Hirose et al., 1995; Hackney, 1994b), except that it assigns ATP hydrolysis and the production of kinesinADPP as the step that leads to detachment and pivoting of the kinesin molecule. Directionality in this model could be explained by assuming that the more weakly attached of the two kinesinATP heads is the one that detaches after hydrolysis and that for kinesin, this is the head which is closer to the(-) end. Thus, directionality becomes an intrinsic consequence of the polarity of the microtubule lattice. Reversal of directionality, as is seen in ncd, could then simply result from reversing the affinities of the two heads in the ATP-bound state.

FOOTNOTES

*

This work was supported by Grants NS01500 and NS31096 from the NINDS, National Institutes of Health (to S. S. R.), by Grant AR31239 from the NIAMS, National Institutes of Health (to H. C. C.), and by Grant HSF BIR9216150 (to J. J. C.). The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore by hereby marked ``advertisement'' in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

§

To whom correspondence should be addressed: Dept. of Neurology, University of Alabama at Birmingham, UAB Station, 510 Medical Education Bldg., Birmingham, AL 35294-0007.

()

The abbreviations used are: ATPS, adenosine 5`-O-(thiotriphosphate); AMPPNP, adenosine 5`-(,-imidotriphosphate); mant ADP, N-methylanthraniloyl ADP; DTT, dithiothreitol; K332, bacterially expressed human kinesin construct containing residues 1-332; K413, bacterially expressed human kinesin construct containing residues 1-413; PIPES, 1,4-piperazinediethanesulfonic acid.

()

S. S. Rosenfeld, B. Rener, J. J. Correia, M. S. Mayo, and H. C. Cheung, manuscript in preparation.

ACKNOWLEDGEMENTS

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