Structural studies of kinesin-nucleotide intermediates.

We have investigated the structural changes that occur in the molecular motor kinesin during its ATPase cycle, utilizing two bacterially expressed constructs. The structure of both constructs has been examined as a function of the nature of the nucleotide intermediate occupying the active site by means of sedimentation velocity, sedimentation equilibrium, fluorescence solute quenching, fluorescence anisotropy decay, and limited proteolysis. While the molecular weight of monomeric and dimeric human kinesin constructs, as measured by sedimentation velocity and sedimentation equilibrium, and the tryptic cleavage pattern are unaffected by the nucleotide intermediate occupying the active site, significant changes in the rotational correlation time of fluorescently labeled kinesin-nucleotide intermediates can be detected. These results suggest that kinesin contains an internal “hinge” whose flexibility varies through the course of the ATPase cycle. In prehydrolytic, “strong” binding states, this hinge is relatively rigid, while in posthydrolytic, “weak” binding states, it is more flexible. Our results, in conjunction with anisotropy decay studies of myosin, suggest that these two molecular motors may share a common structural feature; viz. weak binding states are characterized by segmental flexibility, which is lost upon assumption of a strong binding conformation.

PNP, 1 and in vitro motility studies have suggested that kinesin⅐ADP was a relatively "weak" binding state compared with kinesin⅐ATP (8). Thus, kinesin appears to differ from myosin in several fundamental aspects of its ATPase cycle. In vitro motility studies reveal that unlike myosin, kinesin has the capability of traveling long distances on the microtubule without dissociating (9), a feature termed "processivity." This has been attributed to the slow rate of kinesin dissociation from the microtubule and the rapid rate of its rebinding (6) or to the presence of cooperativity between the two heads of kinesin, preventing the second head of the kinesin dimer from attaching to the microtubule until the first one has detached (10).
In a recent study, we have shown that the binding of two bacterially expressed kinesin constructs to microtubules can be explained by the presence of two classes of binding states, "strong" and "weak" (7). This conclusion is based on the observation that kinesin⅐ADP binds to microtubules with a weaker affinity than kinesin⅐ATP and that it is formation of kinesin⅐ADP⅐P i that leads to microtubule dissociation. Finally, data on the binding of dimeric kinesin⅐ADP could be explained by a model that assumed that cooperative interactions occur between the two heads, which are presumably mediated by the proximal carboxyl-terminal tail segment. Recent image reconstruction results (11) reveal that the orientation of the carboxyl-terminal tail segment of a monomeric kinesin construct is dependent on the nature of the nucleotide occupying the active site. Our results, in conjunction with these studies, thus suggest that significant conformational changes occur during the kinesin ATPase cycle that lead to processive microtubule motility and that these conformations can be studied by examining the structure of kinesin-nucleotide intermediate states.
In the current study, we have examined the nature of these conformational changes by utilizing two bacterially expressed constructs of human kinesin, K413, containing the first Nterminal 413 residues, and K332, containing the first 332 residues. Both constructs have been examined as a function of the nature of the nucleotide intermediate occupying the active site by means of several structurally sensitive techniques. These include sedimentation velocity, sedimentation equilibrium, fluorescence solute quenching, fluorescence anisotropy decay, and limited proteolysis. Results of these studies provide parameters with which to describe structural models of kinesin-based motility; they emphasize the importance of the proximal carboxylterminal tail segment in mediating the nucleotide-driven conformational changes that occur in the kinesin ATPase cycle; and they suggest that myosin and kinesin may share a common structural feature in their chemomechanical transduction mechanism.

EXPERIMENTAL PROCEDURES
Materials-Our recent study (7) details the sources for the materials used here as well as the methodologies for expression and purification of the kinesin constructs K413 and K332, ATPase assays, and the synthesis and purification of mant and 2Ј-deoxy mant nucleotides.
Analytical Ultracentrifugation-All experiments were conducted on a Beckman Optima XLA analytical ultracentrifuge equipped with absorbance optics and an An60Ti rotor as described (13). Sedimentation velocity experiments were all done at 42,000 rpm at 24.6°C in charcoalfilled epon double sector centerpieces. Velocity data were collected at an appropriate wavelength (232-237 nm or 280 nm, depending on the initial concentration) and at a spacing of 0.01 cm with four averages in a continuous scan mode. Velocity data were analyzed using SVED-BERG (14) or DCDT (15)(16)(17). SVEDBERG utilizes Faxen's approximation of the Lamm equation to fit the absorbance profiles from a velocity run to sedimentation and diffusion constants for up to three noninteracting species (14). As described previously, for an interacting system that does not resolve into multiple boundaries, a single species fit with SVEDBERG is found to be an adequate model to extract the boundary position corresponding to the maximum gradient (13). In addition, SVEDBERG is capable of estimating the molecular weight of a single noninteracting species by correcting the ratio of s/D for temperature and buoyancy (14). DCDT generates a distribution of sedimentation coefficients, g(s), by taking the difference of absorbance profiles at successive times, averaged over many differences (15)(16)(17). The g(s) profiles were integrated to give the weight average sedimentation coefficient (͗s͘ ϭ ͐g(s)(s)ds/͐g(s)ds) and plotted versus initial protein concentration (15). This is equivalent to the second moment position. In addition, Stafford (18) has recently described a modification of the DCDT method where g(s) can be fit to a gaussian distribution to estimate the diffusion coefficient from the gaussian half-width. As with SVEDBERG, molecular weight can then be estimated by correcting s/D for solution conditions. Sedimentation coefficients were corrected to standard conditions, s 20,w , where indicated (19). Equilibrium experiments at 24.6 and at 4°C were performed at 16,000 and 20,000 rpm for K413 and 20,000 rpm for K332 in charcoal-filled epon six-channel centerpieces. Equilibrium data were collected at 280 nm at a spacing of 0.001 cm with 16 averages in a step scan mode. Equilibrium was checked by comparing scans at various times up to 30 h. Data sets were edited with REEDIT (13) to extract the three channels of data and fit individually or jointly with NONLIN (20) to an appropriate association scheme. NONLIN fits to an effective reduced molecular weight, where M is the molecular weight, v is the partial specific volume, is the solvent density, ϭ (2 rpm/60), R is the gas constant, and T is the temperature in degrees Kelvin (21). Data from different speeds and from different wavelengths can be combined for global fitting. Fits to a single species give a z-average and thus a z-average molecular weight, M z (22). The sequence-derived molecular weights included the contribution of one bound nucleotide and correspond to the monomer M 1 in an association scheme. This was calculated to be 47,832 for K413 and 38,365 for K332. For fits to an association scheme, 1 was held at the correct value. Equilibrium constants were fit as ln K to constrain them to positive values and were converted from absorbance units to molar units by the appropriate extinction coefficients, corrected for the 1.2-cm path length of the centerpieces and the degree of polymerization, In NONLIN, K n is defined as the overall association of n monomers to an n-mer. Solute Quenching-Solute accessibility of mant ADP and 2Ј-deoxymant ADP bound to kinesin constructs was measured using acrylamide, as described previously (12). Data were fit to the Stern-Volmer equation (24,25) using a least squares curve-fitting program (DeltaGraph 3.5).
Fluorescence Methodologies-Steady state fluorescence measurements were made on an SLM/Aminco 8000C fluorescence spectrophotometer with sample holder thermostated at 20°C. Fluorescence lifetimes and anisotropy decays of mant nucleotide-labeled kinesin constructs were performed as described previously (12). Studies in the presence of aluminum fluoride or beryllium fluoride were performed within 2-3 h of the addition of these transition metals to K413 or K332. Previous studies had demonstrated that complex formation with these metals is complete within 30 min (7). Anisotropy decay of the tryptophan residues of K413 was measured at 20.0°C on a PRA 3000 single photon-counting system equipped with a rhodamine 6G dye laser synchronously pumped by a mode-locked Spectra-Physics 171 argon laser, operating at 41 MHz. The cavity-dumped dye laser was set at 4 MHz and provided a train of light pulses with a half-width of 15 ps. The output of the dye laser was frequency-doubled to 295 nm by an angletuned KDP crystal to generate 1-ps pulses. A DCM dye laser was used, and its output was frequency-doubled to 325 nm as the excitation source for mant ADP. The general procedures used to measure anisotropy decay and analyze the decay data have been described (26). The decay data from the tryptophan residues or mant nucleotide were analyzed by a biexponential model. The recovered short rotational correlation times in both cases were on the order of 2 ns or less. The long correlation times reflect global motions of the protein or of functional domains (27).
Limited Proteolysis and Sequencing-Kinesin constructs K332 and K413 in 20 mM HEPES, 50 mM potassium acetate, 5 mM MgCl 2 , 0.1 mM ADP, 0.1 mM EGTA, 1.0 mM dithiothreitol, pH 7.20, were treated with 1:300 (w/w) L-1-tosylamido-2-phenylethyl chloromethyl ketone-treated trypsin (Worthington) at room temperature. Digestion was stopped at defined intervals by the addition of phenylmethylsulfonyl fluoride to 1.0 mM. Samples were run on SDS-polyacrylamide gel electrophoresis, as described. Experiments were repeated in the presence 1 mM BeSO 4 plus 5 mM NaF. For examining the effect of proteolysis on microtubule binding and ATPase kinetics, kinesin digests were dialyzed against the appropriate buffers overnight to remove residual phenylmethylsulfonyl fluoride.
Digestion mixtures of K413⅐ADP, containing 20 -40 g of total protein, were subjected to SDS-polyacrylamide gel electrophoresis and electrotransferred to nitrocellulose. Separated bands were visualized on the nitrocellulose membrane by staining with Ponceau S (Sigma), and individual bands were excised and submitted for amino-terminal sequence analysis by Edman degradation. Fig. 1 presents corrected weight average sedimentation coefficients (͗s 20,w ͘) for K332 plotted as a function of K332 concentration. The sedimentation coefficient distributions for these data are presented in Fig. 2A. The average weight average sedimentation coefficient (͗s 20,w ͘), derived from these distributions is 3.30 Ϯ 0.03, with a linear fit of the data extrapolating to an s 20,w 0 of 3.32 S. Single species fits of the same data with SVEDBERG give an average sedimentation coefficient (s 20,w ) of 3.37 Ϯ 0.02 with a linear fit extrapolating to an s 20,w 0 of 3.34 S. Single species SVEDBERG fits are the best fits for these data, and combined with the identity of these results with weight average sedimentation coefficients, we conclude that K332 samples are composed of a single species, most likely corresponding to a monomer. The sedimentation coefficient for K332 is slightly larger than the values previously reported for K336 (3.25 S) and K341 (2.9 S) (13). This is despite the fact that K332 and K341 are nearly identical in molecular weight (ADP complexes of 38,365 and 38,274, respectively), and K366 is larger than K332 (ADP complex of 41,404). Sedimentation velocity data for K332 are consistent with a prolate ellipsoid model with a degree of hydration of 0.4 g/g and an axial ratio of 2.98 (Fig. 7A). This is more compact than the earlier estimates for K341 and K366 (13) and explains the larger sedimentation coefficient for K332. The difference may be due to the fact that K332 is derived from a human placental sequence, while K341 and K366 are from Drosophila. Alternatively, this deviation may be due to the presence of the carboxyl-terminal polyhistidine tag added to K332 to facilitate purification. To verify the conclusion that K332 is in a monomeric state, sedimentation equilibrium experiments were performed.

Sedimentation Velocity Studies of K332-
Sedimentation Equilibrium Studies of K332-Equilibrium experiments were conducted on six initial concentrations of K332 from 3.5 to 18 M at 24,000 rpm and at 24.6°C. Early in the run (10 -12 h) all channels could be globally fit to a single species (root meant square fit of 0.0047) with an average molecular weight of 39,452 (range 38,761-40,142). This is within 2.8% of the expected molecular weight of 38,365. However, with increasing sedimentation time beyond 12 h, the molecular weight of each channel increased to a value larger than monomer, and single species fitting of even individual channels was not possible. Attempts to fit the data to a self-association mechanism also failed. The data were analyzed with a PC version of Biospin to extract model-independent molecular weight data (13). Plots of the z-average molecular weight as a function of protein concentration revealed a significant nonsuperposition of M z derived from different channels. This is consistent with irreversible aggregation of the protein. Given the sedimentation velocity result that K332 is monomeric and that at early sedimentation times in the equilibrium run the molecular weight data are also consistent with K332 being monomeric, it must be concluded that K332 is simply unstable at room temperature. That K332 is monomeric at early times after thawing (Ͻ12 h) is further substantiated by the SVEDBERG molecular weight estimates derived from the ratio of s/D, e.g. 35,340 Ϯ 2370. In addition, Stafford (18) has reported a new method for estimating molecular weight from g(s) analysis. When this method was applied to the sedimentation velocity data for K332, a value of 35,508 Ϯ 1803 was obtained. While both these estimates are low, they are further evidence that K332 is monomeric.
Sedimentation Velocity Studies of K413- Fig. 1 presents corrected weight average sedimentation coefficients for K413 plotted as a function of K413 concentration. The sedimentation coefficient increases slightly with increasing protein concentra- der these various conditions are presented in Fig. 2B. The sedimentation coefficient distributions are nearly symmetric, consistent with previous observations on kinesin head domain constructs, and this probably represents an interacting system (13). Fits with SVEDBERG in general were best described by a single species, and when plotted against K413 concentration they extrapolated linearly to 4.90 S, in excellent agreement with the weight average data. These data extrapolate to a smaller s 20,w value and exhibit less concentration dependence than K401, a Drosophila construct previously studied by similar methods (13). Since K413 is larger than K401 by 2300 daltons, this difference in sedimentation behavior could be due to more asymmetry in the K413 molecule or to less intrinsic association of the K413 monomer. In order to determine the molecular weight of the 4.86 S species and the nature of its self-association, sedimentation equilibrium studies were conducted.
Sedimentation Equilibrium Studies of K413-Equilibrium experiments were conducted on initial concentrations of K413 between 4.9 and 10.9 M at 16,000 and 20,000 rpm at 24.6°C. All channels could be fit equally well to a 1-2-4 (monomerdimer-tetramer) and to a 1-2-3 (monomer-dimer-trimer) model. The results of the 1-2-4 model are presented in Table I. Experiments were also conducted in the presence of aluminum fluoride, beryllium fluoride, and 20 mM sodium phosphate over similar concentration ranges. Both the aluminum fluoride and beryllium fluoride data at 24.6°C exhibited a very slow, continuous change in distribution during the course of these experiments, indicating a slow, irreversible aggregation event. Equilibrium distributions were finally obtained after 30 h and were consistent with much larger polymers in solution than dimers and tetramers. The results are consistent with a timedependent denaturation of the K413 construct in the presence of 1 mM AlF 4 or BeF 3 . The agreement of the velocity data at 24.6°C suggests that the solutions begin in a native state but are unstable during the time required for equilibrium to be obtained (Ͼ12 h). In an attempt to avoid this apparently irreversible aggregation, equilibrium experiments at 16,000 and 20,000 rpm were conducted at 4°C. Data for K413⅐ADP at 4°C are summarized in Table I, while corresponding data for K413⅐ADP⅐BeF, K413⅐ADP⅐AlF, and K413⅐ADP⅐P i are summarized in Table II. The control experiments with K413 plus ADP were again equally well fit by a 1-2-4 (monomer-dimer-tetramer) or 1-2-3 (monomer-dimer-trimer) model for both the 16,000 and 20,000 rpm (Table I). For samples in the presence of AlF 4 plus ADP, data sets at 16,000 rpm exhibited a continuously changing distribution and gave a poor fit to a 1-2-4 mechanism. Either larger species were spun out at 20,000 rpm, allowing a reasonable fit to a 1-2-4 mechanism, or in the presence of AlF 4 , the equilibrium was achieved more slowly. By contrast, samples in the presence of BeF 3 plus ADP could be fit to a 1-2-4 mechanism at both 20,000 and 16,000 rpm A species distribution plot, based on the global fit of the ADP data (Table I) is presented in Fig. 3 over the range of 1 nM to 100 M K413. At 25°C, the weight fraction of dimer becomes predominant above the K d for dimerization and peaks near 10 M total K413. Above this concentration, tetramer becomes significant but does not exceed the weight fraction of dimer. Based upon the sedimentation velocity (Figs. 1 and 2) and sedimentation equilibrium results (Tables I and II), these distributions reflect the species in solution for all conditions studied.
Limited Proteolysis of Kinesin Constructs-Incubation of K413 or K332 with trypsin produced a cleavage pattern consistent with a single site of cleavage near the carboxyl terminus (Fig. 4). The pattern of cleavage was unaffected by beryllium fluoride (data not shown). Cleavage of both K332 and K413 generated a larger peptide with M r 28,000, which presumably represents the amino-terminal half. For K332, the smaller peptide migrated as a broad band with M r ϳ8000, while for  K413 it appeared as a band with M r 17,000. Amino-terminal sequencing of the M r 17,000 band revealed a sequence of NINKSLSALGNV, establishing that cleavage occurs at lysine 252 (28). Attempts to separate the two halves of trypsincleaved K413 or K332 utilizing gel filtration, ion exchange chromatography, or affinity chromatography on nickel-agarose were unsuccessful (data not shown), which indicates that the two halves remain associated together. In order to assay the effect of tryptic cleavage on the enzymatic properties of kinesin, K332 was digested with trypsin. The digest, containing a residual 10% of undigested K332, was mixed with a large excess of microtubules, and the ATPase activity was measured as a function of tubulin dimer concentration. A small degree of ATPase activity was detected in this assay, which could be completely explained by the presence of the residual, undigested K332. These results thus indicate that cleavage of K332 at position 252 abolishes microtubule activation of the ATPase activity. Qualitatively similar results were obtained with a tryptic digest of K413. A sample of this K332 digest was labeled with [ 3 H]succinimidyl propionate, and binding to microtubules was measured in an Airfuge assay, as described (7). This reveals that while 10% of the sample binds with a dissociation constant essentially identical to that for uncleaved K332 ( (24), where F o and F are the fluorescence intensities in the absence and presence of quencher, f i is the fractional emission of each component, K i is the Stern-Volmer quenching constant, and V i is the static quenching parameter. In general, the lower the value of K i , the less exposed the fluorophor is to solute. The presence of multiple components causes downward curvature in a plot of F o /F versus [Q], while static quenching causes upward curvature. Fig. 5 shows such a plot for complexes of K413 and K332 with the fluorescent nucleotide analogue 2Јdeoxy-mant ADP. This probe was used instead of mant ADP, since the latter is a mixture of the 2Ј-and 3Ј-mant isomers. As Fig. 5 demonstrates, solute quenching of both K332⅐2Ј-deoxymant ADP and K413⅐2Ј-deoxy-mant ADP reveals a single component, whose Stern-Volmer quenching constants are 2.97 M Ϫ1 and 3.08 M Ϫ1 , respectively. These represent an approximately 26% reduction in the Stern-Volmer constant when compared with free nucleotide (3.80 M Ϫ1 , Fig. 5). The addition of beryllium sulfate to 1 mM and NaF to 5 mM had little effect on these quenching constants for either K332 or K413, reducing them to 2.70 M Ϫ1 and 2.50 M Ϫ1 , respectively. By comparison, the Stern-Volmer quenching constant for mant ADP is reduced 3.5-fold  (Table I)  . The addition of beryllium fluoride reduces this further, to 0.77 M Ϫ1 (Fig. 5). Previous studies of complexes of mant ADP with skeletal muscle myosin subfragment 1 have shown that binding of nucleotide reduces the Stern-Volmer constant by 12-fold, from 2.43 to 0.2 M Ϫ1 (29). Thus, our results indicate that by comparison with HMM or subfragment 1, the nucleotide binding site of kinesin is significantly more exposed to aqueous medium.
Fluorescence Lifetime and Lifetime Solute Quenching Studies-The fluorescent nucleotide mant ADP consists of a mixture of the 2Ј-hydroxyl-and 3Ј-hydroxyl-modified species, in a 0.35:0.65 molar ratio (29). In aqueous solution, however, the fluorescence decay of free mant ADP can be described by a single lifetime of 4.0 ns (29). Likewise, when complexed with smooth muscle myosin, the fluorescence decay remains as a single exponential with a lifetime of 9.2 ns (12), suggesting that the environments around the 2Ј-hydroxyl and 3Ј-hydroxyl fluorophors when bound to myosin are identical. By contrast, the fluorescence decay of complexes of mant ADP with K413 can be described by two lifetimes, with values of 9.1 Ϯ 0.1 and 3.2 Ϯ 0.2 ns and with relative contents of 0.35 and 0.65, respectively. Given the finding that the relative contents of these two lifetime decays are identical to the relative molar ratios of the two mant isomers, it seems most likely that these lifetime components correspond to decays from the 2Ј-mant and 3Ј-mant species, respectively. This was confirmed by examining the transient fluorescent decay of K413 complexed to 2Ј-deoxy-mant ADP, whose fluorophor is exclusively located at the 3Ј-hydroxyl. This revealed a single component with a lifetime  (Fig. 6). Thus, fluorophors located at the 2Ј-and 3Ј-ribose hydroxyl positions detect different solute accessibilities that presumably reflect different environments. Anisotropy Decay Studies of Fluorescently Labeled K413 and K332-K413 and K332 were labeled in the catalytic site with mant ADP by incubation with a 20-fold molar excess of mant ADP, followed by dialysis and gel filtration on Sephadex G-25 to remove unbound nucleotide. Anisotropy decay measurements of mant ADP-labeled K413 and K332 were performed on these preparations at a concentration of 10 M and in the presence and absence of beryllium fluoride. This concentration was chosen to maximize the amount of K413 that is dimeric, which under these conditions constitutes 76 -84% of the total (Fig. 3). For K332⅐mant ADP, two rotational correlation times were measured that were unaffected by beryllium fluoride (Table III). The longer correlation time for K332⅐mant ADP, at 26 ns, was essentially unaffected by the addition of beryllium fluoride (Table III). The values of limiting anisotropies of 0.24 -0.26 for K332 are smaller than the corresponding values of 0.34 -0.35 for myosin subfragment 1 (12).
The anisotropy decay of K413⅐mant ADP at a concentration of 10 M could be described by two rotational correlation times (Table III). The shorter correlation time, at 0.75 ns, presumably reflects local probe motion. In a previous study, we demonstrated that phosphate binds to the active site of K413⅐ADP with a dissociation constant of 0.83 mM and reduces the apparent affinity of microtubule binding by nearly 6-fold (7). Anisotropy measurements demonstrate no significant effect of 20 mM sodium phosphate addition to the rotational correlation time of Binding of 2Ј-deoxy-mant ADP to K413 or K332 reduces the Stern-Volmer quenching constant by approximately 26%, compared with free nucleotide. The addition of beryllium fluoride produces a modest reduction in solute accessibility. By contrast, complex formation of smooth muscle HMM with 2Ј-deoxy-mant ADP reduces solute accessibility 3.5fold, compared with free nucleotide, and the addition of beryllium fluoride causes a further 30% reduction in solute accessibility. K413⅐mant ADP. By contrast, the addition of beryllium fluoride increased the long correlation time by 47%, to 134 ns.
Transient fluorescence decay measurements were also made on 10 M K413⅐ADP Ϯ beryllium fluoride or sodium phosphate, as well as on K413⅐AMPPNP by monitoring the time-dependent fluorescence emission from the three tryptophan residues of K413. These residues, at positions 340, 360, and 368, are located within the presumed ␣-helical dimerization segment of K413 and are absent in K332. Anisotropy decay measurements reveal a long rotational correlation time of 36 ns for K413⅐ADP. Binding of AMPPNP or of ADP plus beryllium fluoride to the active site generates a strong binding state (7) and increases the rotational correlation times to 49 and 60 ns, respectively. By contrast, the addition of sodium phosphate to 20 mM had no significant effect.
These results are compared with those from a previous study (12) of smooth muscle HMM and subfragment 1 complexed with mant nucleotides and are included in Table III for comparison. DISCUSSION We have utilized sedimentation velocity, sedimentation equilibrium, limited proteolysis, and spectroscopic measurements in order to develop a structural model of the kinesin ATPase cycle that is consistent with our previous enzymatic and microtubule binding studies (7). These studies have utilized two bacterially expressed constructs, K413 and K332, derived from a human homologue of the Drosophila kinesin heavy chain. K413 contains the first 413 amino-terminal residues and corresponds to Drosophila K401, whose sedimentation behavior has been previously described (13). K332 contains the first 332 amino-terminal residues and corresponds to Drosophila residues 1-340. Our previous study (12) revealed that these two constructs differ markedly in their enzymatic behavior and that this difference was due to a nearly 5-fold reduction in the value of k cat with dimerization (k cat ϭ 43.6 s Ϫ1 for K332, 35.1 s Ϫ1 for monomeric K413, and 8.3 s Ϫ1 for dimeric K413). Such a difference in enzymatic properties had been previously noted between monomeric and dimeric kinesin constructs (13) and led to our examination of the sedimentation behavior of K413 and K332.
The sedimentation behavior of these two constructs demonstrates both similarities and differences when compared with previous studies on the corresponding Drosophila constructs (13). Like Drosophila K366 and K341, human K332 behaves as a monomeric species at relatively early times during the sedimentation equilibrium measurement. However, K332 also demonstrates some capability to form oligomers, which appear to represent irreversible aggregation after long sedimentation times (Ͼ Ͼ12 h). This may reflect an effect of the carboxylterminal polyhistidine tail that was present in the K332 and K413 constructs. Sedimentation velocity studies of K332 are also consistent with a monomeric species of 35.3-35.5 kDa at early sedimentation times (Ͻ12 h). The larger value of s 20,w 0 for K332 compared with Drosophila K341 suggests that the human construct may be less asymetric than that from Drosophila.
By contrast, interpretation of the sedimentation behavior of K413 is more complex and requires accounting for the capacity of this construct to reversibly oligomerize. As in the case of K332, sedimentation velocity studies demonstrated a single, stable component during early times (Ͻ12 h) that is consistent with a predominantly dimeric species (Fig. 1). Sedimentation equilibrium studies at low temperature and over relatively early times revealed behavior that is consistent with a 1-2-4 self-association scheme, results that are qualitatively similar to that for Drosophila K401 (13). An interacting boundary involving pseudodimerization (e.g. dimer to tetramer) is not expected to resolve into multiple zones but will reflect instead the weight average concentration of dimer and tetramer, as has been documented for interacting systems obeying Gilbert theory (30,31). An important difference between our results and those reported earlier for Drosophila K401 is that K 2 , the association constant for dimerization, is nearly 1 order of magnitude smaller for K413.
Our previous study demonstrated that ternary complexes of kinesin with ADP and beryllium fluoride or aluminum fluoride produced a strong binding state (7). Over the time course of the sedimentation velocity experiments (3-4 h), no significant effect of these transition metals on the s 20,w 0 value could be seen. Furthermore, the sedimentation velocity data over this time course demonstrated no evidence of aggregation. By contrast, equilibrium sedimentation studies over a prolonged period at room temperature (Ͼ12 h) demonstrated evidence of a slow, irreversible aggregation induced by these transition metals. This was reduced by lowering the temperature to 4°C, allowing modeling of the data according to a 1-2-4 equilibrium (Table II). This demonstrated values of K 2 and, consequently, distributions of monomer, dimer, and tetramer that are very similar to Samples labeled with mant ADP were incubated with a 20-fold molar excess of mant ADP, and free nucleotide was removed by gel filtration on Sephadex G25 (PD10, Pharmacia). For samples examined in the presence of beryllium fluoride, the above buffer was supplemented with 1 mM BeSO 4 and 5 mM NaF. Anisotropy measurements using tryptophan as a fluorophor were performed in the above buffer supplemented with 0.5 mM ADP. Samples in the presence of ADP plus inorganic phosphate were performed in the 10 mM potassium acetate, 20 mM potassium phosphate, 25 mM HEPES, 5 mM MgCl 2 , 1 mM dithiothreitol, 1 mM NaN 3 , pH 7.20. A 1 limiting anisotropy; , rotational correlation time (in ns). those for K413⅐ADP (Fig. 3, Tables I and II). Therefore, in order to avoid the confounding effects of any aggregation, all spectroscopic studies on kinesin constructs were performed within 2-3 h of thawing and the addition of transition metals. The sedimentation equilbrium results described in this study are consistent with the dimeric kinesin construct K413 undergoing a 1-2-4 mechanism of self-association, e.g. one involving dimerization and subsequent dimerization of dimers.  (Table II). Based upon sedimentation velocity studies, the K d for dimer dissociation is unaffected by changes in nucleotide or nucleotide analogue binding (Tables I and II). Nucleotide independence was also observed in the previous study on K401 self-association (13), although the K d for dimer dissociation was much smaller, at 37 nM. This we ascribe to the presence of the hexahistidine tag at the carboxyl terminus. It is generally assumed that dimer dissociation is an artifact of the use of truncation mutants and that the native molecule probably never dissociates. In addition, higher order aggregates are also assumed to be artefactual. However, there is a recent report of a bimodal kinesin-like motor, KRP 130 , a homotetrameric Bim C-related kinesin, that associates by antiparallel alignment of the coiled-coil domain into a motor that can slide microtubules relative to each other (32). Thus, at higher concentrations, full-length kinesin might form tetramers or higher order oligomers. Alternatively, tetramer formation may be inhibited by the carboxyl-terminal "cargo" domain of typical kinesin. Smaller constructs may gain oligomerization capability by removal of this carboxyl-terminal domain.
The sedimentation velocity and equilibrium studies indicate that the transition from strong to weak binding is not associated with large scale changes in shape or oligomerization of the kinesin dimer. In order to probe for the nature of the structural changes that underlie this transition, we examined K413 and K332 with limited proteolysis and with several spectroscopic techniques. Limited proteolysis of both K413 and K332 with trypsin demonstrated that cleavage occurs only at lysine 252. This residue is located at the apex of a segment of random coil in the kinesin and Ncd crystal structures, referred to as L11 in the crystallographic model, which is in close proximity to at least one of the putative microtubule binding sites (33,34). It has been suggested that movements in this random coil and in its flanking ␣-helix (␣4) occur in response to ATP hydrolysis and affect the orientation of the microtubule binding domain (34). Thus, this loop may be envisioned to function as a transducer, transmitting the structural changes induced by nucleotide hydrolysis in the catalytic domain to the microtubule binding domain. Cleavage at this site would thus be expected to prevent communication between these two domains and would be predicted to abolish microtubule-stimulated activation of the kinesin ATPase, as was seen. This loop may also be responsible for the proper orientation of the microtubule binding domain, which would explain why cleavage also inhibits microtubule binding. The addition of beryllium fluoride to K413⅐ADP or K332⅐ADP produced no change in the cleavage pattern or in the kinetics of cleavage at lysine 252, which suggests that this loop remains solvent-exposed throughout the ATPase cycle.
Solute quenching studies of mant ADP (Figs. 5 and 6) likewise demonstrated no significant change in solute accessibility produced by the addition of beryllium. However, they did reveal that the catalytic site of kinesin does interact with nucleotide in a manner distinct from myosin. When bound to the active site of kinesin, the mant fluorophor of 2Ј-deoxy-mant ADP is significantly more solvent-exposed than when bound to myosin. This is consistent with recent crystallographic models of myosin and kinesin, which demonstrate that while the ribose moiety of kinesin-bound ADP makes no direct protein contacts and is solvent-exposed, that for myosin-bound ADP sits within a narrow tunnel that is much less solvent-exposed (33). Lifetime quenching of mant ADP bound to the active site of kinesin reveals one additional difference. mant ADP consists of a mixture of the 2Ј-and 3Ј-isomers. In the case of myosin, both isomers give a single lifetime of 9.2 ns when bound to the active site of smooth muscle myosin (12). By contrast, the lifetime of the 2Ј-isomer increases to to 9.1 ns, while that for the 3Ј-isomer decreases slightly to 3.2 ns. The relative lack of change in the lifetime of the 3Ј-isomer is consistent with the observation that binding of 2Ј-deoxy-mant ADP to kinesin produces no fluorescence change (data not shown). These results thus suggest that the environments around the 2Ј-and 3Ј-hydroxyl groups of the ribose moiety in kinesin⅐ADP are different, a conclusion supported as well by the differences in solute accessibilities measured for these two isomers (Fig. 6). This is also supported by the smaller limiting anisotropy for kinesin⅐mant ADP compared with myosin⅐mant ADP, which suggests that the ribose moiety of mant ADP-bound kinesin is less constrained than that of myosin.
Thus, sedimentation velocity, sedimentation equilibrium, limited proteolysis, and solute quenching studies fail to demonstrate any significant differences between pre-and posthydrolytic kinesin states, even though these two states differ significantly in their microtubule affinities. We therefore utilized one additional structurally sensitive technique, fluorescence anisotropy decay, to examine the conformational changes associated with the strong 3 weak transition. The anisotropy decays of K413 and K332 are biexponential, with two rotational correlation times. The short correlation times are on the order of 1-2 ns. If these constructs are approximated by a prolate ellipsoid of revolution, the two rotational correlation times ( a and b ) can be calculated from the Perrin equation with appropriate frictional coefficients (35) for different values of axial ratio (a/b) at several assumed values of hydration (0.1-0.4 g of H 2 O/g of protein). These calculations show that the predicted short correlation times ( b ) are at least 1 order of magnitude larger than those that were observed from the anisotropy decay data. These results rule out the possibility that the observed short correlation time corresponds to rotation of the short axis of the protein and strongly suggest that it reflects motions of the fluorophors. The observed long correlation time can then be assumed to represent the harmonic mean of a and b . This comparison shows that the observed long correlation time of 26 ns for K332 is compatible with an axial ratio of approximately 2.5-3 if the hydration is taken as 0.4. This is remarkably close to that calculated from sedimentation velocity data, and is consistent with the relative unit cell dimensions of the motor domains of Ncd and kinesin of 1:2:2 (33,34). Similarly, the long correlation time of 91 ns for K413 would correspond to an axial ratio of about 5 for the same degree of hydration as K332. This would be consistent with the anisotropy data for K332 if it were assumed that 1) the two heads of K413 are rigidly attached to each other, 2) they are oriented with their long axes colinear, and 3) the "hinge" separating the motor domains in the K413⅐ADP state is sufficiently flexible such that the motion of the motor domain containing bound mant ADP is not strongly coupled to the motion of the carboxyl-terminal coiled-coil tail.
If the putative hinge were located within the residues immediately carboxyl-terminal to K332 and were flexible in the K413⅐ADP state, this would produce a segment of 162 carboxyl-terminal residues in dimeric K413 that would have appreciable motional freedom. This model was tested by taking advantage of the fact that the three tryptophan residues in K413 are located within approximately 20 residues of each other, within the carboxyl-terminal tail. The long correlation observed with the anisotropy decay of the tryptophans is 36 ns, a factor of 2-3 smaller than that obtained from bound mant ADP. This correlation time would be consistent with an extended coiled-coil that has significant motional freedom.
Finally, unlike the other structurally sensitive techniques used in this study, fluorescence anisotropy decay measurements did detect significant changes in K413 that correlated with the strong 3 weak transition. In particular, the rotational correlation time of K413 with fluorescent probes in both the catalytic site and the dimerization segment increased 40 -50% with the assumption of the strong conformation. By contrast, although beryllium fluoride also enhances the microtubule affinity for K332⅐ADP, it has essentially no effect on the corresponding rotational correlation times. That this prolongation in correlation time corresponds to the weak 3 strong transition is supported by data with AMPPNP, which also prolongs the correlation time for the tryptophan residues in the dimerization segment (Table III).
Fitting of the anisotropy data to a biexponential decay did not reveal a systematic deviation at prolonged times, as would be expected if the calculated rotational correlation time included a major contribution from tetramer or octamer. The data from Fig. 3 suggest that at a K413 concentration of 10 M, approximately 9% is monomeric and 5% is tetrameric. Estimates of the major correlation time for monomer and tetramer can be made from similar measurements of K332 and heavy meromyosin, respectively, and are in the range of 30 -35 ns and 200 -250 ns, respectively. Consequently, the measured correlation time of 91 ns for K413⅐mant ADP could be viewed as a harmonic mean of that for monomer (30 -35 ns), tetramer (200 -250 ns), and dimer (82-85 ns). The presence of small amounts of monomer or tetramer in a 10 M preparation of K413⅐mant ADP thus would not significantly distort the relationship between the measured correlation time and that for dimeric K413. Thus, we conclude that the nearly 50% increase seen in rotational correlation time produced by the addition of beryllium fluoride to K413⅐ADP reflects an intrinsic difference in the conformations of the strong and weak binding states. An increase in rotational correlation time could indicate one of three possibilities, that the kinesin motor domain becomes elongated, less bent, or internally rigid as it assumes the strong conformation. Several lines of evidence presented in this study suggest that the last possibility is correct. First, an increase in axial ratio to approximately 9 could explain the increase in rotational correlation time seen with beryllium fluoride. However, this would predict that s 20,w decrease by 23%, which was not seen. Second, the angle between the catalytic domains and the tail segment of the K413 dimer might change in response to the transition strong 3 weak. An analogous mechanism has been proposed for the strong 3 weak transition in myosin (36). Hydrodynamic calculations for myosin subfragment 1 demonstrate that a bend between the catalytic and regulatory domains by as much as 45°would produce less than a 1% change in the value of s 20,w (37), which underscores the relative insensitivity of sedimentation velocity measurements to rotational frictional coefficients (27). Thus, the lack of change of s 20,w for K413 between strong and weak states might suggest a similar mechanism. However, this is not supported by results of anisotropy decay measurements using intrinsic tryptophan probes in the dimerization segment (Table III, schematically depicted in Fig. 7B). These measurements demonstrate that the K413 dimer has significant segmental flexibility in the weak state that is partially lost upon assumption of the strong state. The sedimentation velocity and anisotropy data, however, are con- FIG. 7. Schematic of kinesin weak and strong binding states. A, K332 is drawn schematically, based on the crystallographic models of kinesin and Ncd, as a bilobed structure (33,34). Sedimentation and anisotropy data are fit to a model that approximates the structure of K332 to a prolate ellipsoid (dashed line), with long and short axes of a and b, respectively. The locations of lysine 252 and of the nucleotidebinding site are indicated. B, K413 is depicted as consisting of two heads, analogous in structure to that of K332. These are proposed to be rigidly connected to each other via the proximal dimerization segment, which is separated from the distal dimerization segment by a variably flexible hinge. It is proposed that this hinge can be flexible in the weak state and rigid in the strong state. The ␣-helical tail contains three tryptophan residues (symbolized by the ball and stick figure) at positions 340, 360, and 368. Anisotropy and sedimentation data suggest that the two motor domains can be approximated together as a prolate ellipsoid (dashed line) with long and short axes of aЈ and b, respectively, where aЈ Ϸ 2a. In the weak state, rotational motions of the conjoined motor domains are proposed to be relatively independent of those of the carboxyl-terminal tail segment, while in the strong state, they are proposed to be linked. This figure has been drawn to illustrate the spatial relationships between the putative hinge and the other major structural features of the dimer, and it depicts the heads in a parallel orientation. sistent with a model in which the dimerization segment is separated from the catalytic domains by an internal hinge, which is flexible in the K413⅐ADP state and rigid in the K413⅐ATP state. This would be expected to increase the rotational correlation time for a probe attached at either the catalytic site (mant ADP) or in the dimerization segment (tryptophan residues 340, 360, and 368). Furthermore, in this case, s 20,w would not be expected to change significantly. That no change in the correlation time for K332⅐ADP versus K332⅐ADP⅐beryllium fluoride was seen suggests that the conformational changes within the motor domain that occur with the strong 3 weak transition are subtle and must be amplified by regions on the carboxyl-terminal side of this domain, as has been suggested (33). Furthermore, they argue that the hinge must be distal to the carboxyl terminus of this construct. The value of the correlation time for the tryptophan residues in K413⅐ADP suggests that location of this putative hinge must be near the amino terminus of the dimerization segment. Thus, in the model depicted in Fig. 7B, we have placed the hinge at the junction of the motor domain and the dimerization segment. Finally, this model of the kinesin dimer provides a structural basis for understanding how cooperativity may occur in this molecular motor (7,10). The value of the long correlation time for mant ADP-labeled K413 is nearly 4-fold longer than that for K332⅐mant ADP, as would be expected if the two heads of the K413 dimer were rigidly attached to each other (Fig. 7B). Such a rigid attachment could be envisioned to be due to multiple intersubunit contacts that could transmit structural information from one head of the K413 dimer to the other.
The structural model illustrated in Fig. 7B is based on studies in which both heads are in the same state. In fact, there is mounting evidence that cooperative interactions allow the ATPase cycles of the two heads to be out of phase, e.g. one head is in a strong state while the other is in a weak one (10,40). Processivity could then be envisioned to occur if the flexibility of the hinge were linked to the state of the leading, attached head. For example, the addition of microtubules to a K413⅐ADP dimer would presumably lead to binding of one of the two heads to the microtubule lattice with subsequent rapid release of the bound nucleotide from this bound head (10). We propose that in this state, with one head strongly bound to the microtubule lattice, the hinge would be rigid and would thus prevent the second head from orienting itself so as to make contact with the microtubule. Binding of ATP to the attached head would be rapidly followed by hydrolysis, generating a weak state (7). We propose that this would increase the flexibility of the hinge and allow the second ADP-containing head to attach to the microtubule one subunit downstream. Release of ADP from this new, leading head would produce a strong state in this head, stiffen the hinge, and thereby load the system with enough strain to induce dissociation of the trailing, weak head. This would complete the cycle with the net effect of movement along the microtubule lattice by one subunit.
The anisotropy data depicted in Table III suggest that, like kinesin, myosin may also utilize a variably flexible hinge in its ATPase mechanism. The addition of beryllium fluoride to HMM⅐ADP or subfragment 1⅐ADP (both of which are strong binding states) produces weak binding states that are characterized by shorter rotational correlation times. Thus, for both kinesin and myosin, strong binding states are characterized by longer rotational correlation times than weak binding states, and the data for both molecular motors is consistent with a model in which a variably flexible hinge is rigid in strong binding states and flexible in weak binding ones. The relationship between binding affinity and conformational flexibility was not determined in this study. However, one possible expla-nation is that the strong 3 weak transition may represent an equilibrium that occurs independently of nucleotide or microtubules. Nucleotide could then be viewed as an allosteric modifier, shifting the equilibrium toward a strong or weak state, as has been previously proposed for myosin (38,39).