Monomeric kinesin head domains hydrolyze multiple ATP molecules before release from a microtubule.

Transient kinetic analysis of microtubule-stimulated ATP hydrolysis by the monomeric kinesin motor domain DKH357 was performed to investigate the kinetic pattern of a monomer. Both ATP and ADP produced dissociation of the complex, microtubule (MT)·;E, of microtubules with DKH357 at a maximum rate of ∼45 s−1 as determined by decrease in turbidity. The maximum dissociation rate was independent of the KCl concentration between 25 and 200 mM. At subsaturating levels of nucleotide, ATP was more effective than ADP in dissociating DKH357 from MT·;E (1.6 and 0.4 μM−1 s−1 for ATP and ADP, respectively, at 50 mM KCl). Addition of ATP to MT·;E results in a burst of product formation with a maximum initial rate of ∼100 s−1 at saturating levels of ATP. This maximum hydrolysis rate of 100 s−1 is similar to the maximum steady state ATPase rate at saturating microtubules of ∼70 s−1, and thus hydrolysis is at least partially rate-limiting. When the MT lattice was highly occupied with bound DKH357, the amplitude of the burst was ∼2 per DKH357 active site (superstoichiometric). The rate constant for the burst transient was ∼45 s−1, which is the same as the rate for dissociation of DKH357 from the microtubule and this suggests that dissociation and termination of the burst phase are coupled. The size of the burst increased with decreasing initial occupancy of the MT lattice with bound DKH357 and approached the value of ∼4 ATP molecules predicted by previous steady state measurements (Jiang, W., Stock, M., Li, X., and Hackney, D. D., submitted for publication).

Dimers of kinesin head domains are capable of generating processive movement along MTs 1 for extended distances without dissociation (1)(2)(3). The detailed mechanism for generation of processivity and how it is coupled to ATP hydrolysis represents a considerable challenge. Analysis of the bimolecular rates for stimulation by MTs of steady state ATPase and ADP release of dimeric kinesin constructs indicates that Ն100 ATP molecules are hydrolyzed per dimer during each cycle of net binding and release of kinesin from a MT (4). This highly repetitive hydrolysis, without net diffusional dissociation of the kinesin dimer from the MT, is consistent with the hydrolysis of one ATP for each of the many steps of 8 nm (5) that occur during processive movement along the MT. Dimers of kinesin also exhibit half-site ADP release on binding to MTs (6) that provides an attractive mechanism for generation of head-overhead movement along the MT by the alternating attachment of the two head domains of the dimer.
Knowledge of the ATPase kinetics of monomeric constructs is needed to provide a basis for determining how the action of the two heads of a dimer can be coupled. Although the kinetics of dimeric constructs have been investigated extensively (7)(8)(9)(10)(11)(12), relatively little is known of the detailed kinetics of monomer constructs (6,(13)(14). 2 In analogy with the well known kinetic scheme of actomyosin (see Ref. 16), it has been generally assumed that kinesin head domains dissociate from the MT at some stage in their ATPase cycle. Additionally, most models for generation of motility require that kinesin heads dissociate from one site on the MT at some stage in their ATPase cycle and then reattach to a new site further along the MT in the direction of movement. Analysis of the bimolecular rates for stimulation by MTs of steady state ATPase and ADP release, however, indicates that monomers DKH346, DKH357, and DKH365 hydrolyze ϳ4 ATP molecules during each cycle of net binding and release of kinesin from a MT. 2 This is equivalent to saying that the head domain has only a 1 in 4 probability of dissociating from the MT during hydrolysis of each ATP molecule. The value of ϳ4 ATP molecules is significantly less than the value of Ն50 ATP molecules per head for dimers, but is still significantly greater than the value of 1 ATP per head per MT binding cycle that would result if the monomer head always dissociated from the MT at least once during each ATPase cycle.
We now report transient kinetic results that directly demonstrate that hydrolysis of ATP by the MT⅐DKH357 complex is not only faster than dissociation of DKH357 from the MT, but also that dissociation does not even occur during most ATPase cycles. This results in a burst of product formation on addition of ATP to the rigor complex of kinesin with MTs that is larger than the concentration of kinesin active sites (superstoichiometric). The magnitude of this burst is ϳ2 per kinesin head at DKH357:MT ratios close to 1:1, but increases at low initial occupancy of the MT lattice with heads and is consistent with the burst size of ϳ4 per head predicted by the steady state measurements. A preliminary report of these results has been made (17).

MATERIALS AND METHODS
All reactions were performed at 25°C in A25 buffer (25 mM potassium ACES, pH 6.9, 2 mM magnesium acetate, 2 mM potassium EGTA, 0.1 mM potassium EDTA, and 1 mM 2-mercaptoethanol), supplemented with KCl as indicated. Taxol (3 M) was included in reactions containing MTs. Tubulin was prepared and polymerized into MTs as described previously (13) except that unpolymerized tubulin was removed after polymerization by a final centrifugation and gentle resuspension. MT concentrations are reported as the concentration of tubulin het-* This work was supported by Grant NS28562 from the National Institutes of Health. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
‡ To whom correspondence should be addressed: erodimers. The concentration of DKH357 is reported as the concentration of ADP binding sites as determined by equilibration with [␣-32 P]ATP as described previously (18). This level of DKH357 binding sites was 90% of the molar level of total DKH357 determined by Bradford assay (19) using bovine serum albumin as standard. Pyruvate kinase and apyrase were obtained from Sigma.
The MT⅐E complex of DKH357 with MTs was formed in A25 buffer with 50 mM KCl by incubation of DKH357 with an excess of MTs in the presence of a low level of apyrase to hydrolyze the ADP that is released on binding of DKH357 to MTs. Control experiments indicated that aggregation of MTs was more likely with other buffers and salts and when DKH357 was in excess of MTs. Consequently the complex was always formed in this way and then mixed with solutions of different KCl concentration to give the desired final concentration during the reaction.
Stopped flow turbidity measurements were performed with an OLIS stopped flow spectrophotometer at 320 nm and 1.6 cm path length. The MT⅐E complex was dissociated by mixing with an equal volume of buffer containing MgATP or MgADP. Burst measurements were determined by quenched flow methods in a KinTek apparatus using either [␣-32 P]ATP or [␥-32 P]ATP. Typically the MT⅐E complex was mixed with an equal volume of buffer containing [ 32 P]ATP and then quenched by mixing with 2 N HCl to give a final concentration of 0.67 N HCl. The quenched reaction mixture was immediately neutralized by addition of 12 ml of cold 32 mM Tris containing 0.5 mol each of carrier P i , ADP, and ATP. A sample (1 ml) was counted to determine the total counts, and 10 ml was chromatographed on a 1.5-ml column of AG MP-1 (Bio-Rad) generally as described previously (18). For analysis of [ 32 P]P i derived from reaction of [␥-32 P]ATP, the column was washed with water and then P i was eluted with 10 mM HCl (eight fractions of 2 ml). The 10 mM HCl fractions were counted and the area of the peak of [ 32 P]P i was determined. For analysis of [␣-32 P]ADP derived from [␣-32 P]ATP, the columns were washed with water and 15 ml of 10 mM HCl and then ADP was eluted with 20 mM HCl (eight fractions of 2 ml), and the area of the [␣-32 P]ADP peak was determined. In each case the extent of hydrolysis was determined from the fraction of the total counts that were recovered as P i or ADP.
[ 32 P]ATP was purchased from DuPont. In order to reduce the blank levels of counts that coelute with P i and ADP, the [ 32 P]ATP used in reactions was purified on AG MP-1. The [ 32 P]ATP with 0.5 nmol each of carrier P i , ADP, and ATP was adsorbed to 10 l of AG MP-1; washed three times by centrifugation with cold 20 mM HCl; eluted with cold 160 mM HCl and immediately neutralized with Tris base. This typically reduced the blank level to Ͻ 0.5%. To correct for material in the [ 32 P]ATP that is not hydrolyzable to P i and ADP, a sample was exhaustively hydrolyzed by kinesin activated by MTs and the recovery as P i or ADP determined (see Ref. 18 for discussion of this problem).

Formation of MT⅐E Complex-Monomer heads bind to
MTs with a stoichiometry of one head per tubulin heterodimer in the presence of AMP-PNP (13,20). Addition to MTs of head domains with bound ADP results in the release of the ADP (E⅐ADP ϩ MT 7 MT⅐E ϩ ADP), which is essentially complete at low head concentrations (6), but becomes reversible at higher head concentration where the level of released ADP approaches the K d for ADP rebinding. A low level of apyrase can hydrolyze the released ADP, and this allows the binding of heads to the MT to proceed to completion as indicated in Fig.  1A. In the presence of apyrase, addition of DKH357 to MTs produces a linear increase in the turbidity (A 320 ) up to the equivalence point of one head per tubulin heterodimer. The turbidity continues to increase above the equivalence point, but with a lower slope that likely is related to the weaker nonspecific binding observed in the presence of AMP-PNP (13). In the absence of apyrase, the initial increase in turbidity at low concentration of DKH357 is similar to that observed with apyrase, but further binding of DKH357 to the MTs is inhibited due to accumulation of free ADP. Control experiments at an initial ADP concentration of 10 M indicate that the level of apyrase in Fig. 1A results in the hydrolysis of half of the ADP in 60 s. This is sufficient to remove free ADP during the several minutes required to load the drive syringes for stopped or quenched flow experiments, but not so fast as to interfere significantly during the short rapid mixing reactions.
Dissociation of MT⅐E by ATP and ADP-The rate of dissociation of the MT⅐E complex by ATP in 50 mM KCl was determined from the decrease in turbidity as indicated in Fig. 1B. The A 320 decrease for dissociation observed in Fig. 1B is consistent with the turbidity increase observed for association in Fig. 1A, indicating that dissociation is essentially complete on this rapid time scale. The observed rate constant for dissociation is 43 s Ϫ1 at 400 M ATP. The influence of the concentration of ATP on the kinetics of dissociation is indicated in Fig. 1C. The maximum dissociation rate, k d(MT) ATP , is 46 s Ϫ1 at saturating ATP and the K d(MT) ATP value is 29 M for the concentration of ATP required for half-maximum dissociation rate. The k d(MT)

ADP and K d(MT)
ADP values for dissociation of MT⅐E by ADP were also determined and are 52 s Ϫ1 and 129 M. Thus both ATP and ADP have similar maximum rates, but ATP is more effective at low concentration with bimolecular rates for dissociation of the MT⅐E complex of 1.6 and 0.41 M Ϫ1 s Ϫ1 for ATP and ADP, respectively. The kinetics of ATP-induced dissociation were determined over a range of KCl concentrations as indicated in Fig. 1D. The maximum rate at saturating ATP is essentially Burst Kinetics at 50 mM KCl-The transient kinetics of ATP hydrolysis by MT⅐E is indicated in Fig. 2. The initial rate increases with ATP concentration with an approximately hyperbolic dependence as indicated in Fig. 3 with a maximum rate of ϳ100 s Ϫ1 at saturating ATP. This directly demonstrates that the hydrolysis rate is faster than dissociation at 45 s Ϫ1 , even for monomeric kinesin, and is in stark contrast to actomyosin for which the dissociation of the myosin⅐ATP complex from F-actin is much faster than hydrolysis (see Ref. 16). At all 4 ATP concentrations there is a rapid burst followed by transition to a slower phase. At the two lower ATP concentrations of 10 and 25 M in Fig. 2, A and B, detailed modeling was not attempted as the level of free ATP falls significantly during the time course due to conversion to product. At high ATP concentration in Fig. 2, C and D, depletion of free ATP is less significant and they were fit to a model with a rapid initial burst followed by transition to a slower steady state rate. Fitting these curves to a burst model gives burst amplitudes of 1.9 and 1.6 per DKH357 site and burst rates of 40 and 50 s Ϫ1 , respectively, for C and D. Thus the burst is superstoichiometric with more than one molecule of product being formed per active site. This is incompatible with simple burst models in which the burst is due to stoichiometric or substoichiometric accumulation of product before a rate-limiting release step. The rate constant for completion of the burst phase of 40 -50 s Ϫ1 at high ATP is the same as the rate constant of ϳ45 s Ϫ1 for dissociation of DKH357 determined turbidimetrically (Fig. 1C).
Burst Kinetics at 200 mM KCl-In order to better separate the burst and steady state phases, additional experiments were conducted at 200 mM KCl where the steady state rate is reduced, but the maximum rate for dissociation of the head remains constant at ϳ45 s Ϫ1 (Fig. 1D). The burst amplitude is ϳ2.3 per DKH357 (Fig. 4, triangles)  As DKH357 only binds one nucleotide tightly, the superstoichiometric ADP that is generated in the burst phase must either be free, bound to a second site, or not really be stoichiometric due to an error in determination of the absolute concentration of DKH357 sites or the burst amplitude. In order to distinguish bound from free ADP, pyruvate kinase and P-enolpyruvate were included during the burst reaction as a trap for free ADP (Fig. 4, diamonds). The amount of pyruvate kinase used in Fig. 4 gave a t1 ⁄2 for reaction with free ADP of 1 s in control reactions. This level of pyruvate kinase activity is sufficient to reduce the level of free ADP over a period of seconds, but not sufficient to immediately deplete any free ADP generated during the rapid burst phase. The results of Fig. 4 in the presence of pyruvate kinase indicate an overshoot and subsequent recovery back toward the stoichiometric level that is consistent with initial formation of substantial free ADP during the burst, followed by reduction in the free ADP level by pyruvate kinase at longer times. During steady state hydrolysis, DKH357 will be mainly dissociated from the MT, and only a stoichiometric level of bound ADP is expected (18).
The increase in the burst amplitude on increasing the MT level (Fig. 4, circles) could be due to the increased absolute concentration of MTs or to the decrease in the DKH357:MT ratio. This distinction is illustrated by the scheme of Fig. 5. In case I, the MT lattice is close to fully occupied with head domains and interaction between heads may influence the rates of hydrolysis and the rate of dissociation of heads in the presence of ATP. This corresponds approximately to the trian- gles of Fig. 5, A and B. In case II, the increased level of MTs results in a lattice that is only partially occupied, corresponding to the circles of Fig. 5, A and B, in which heads are distributed over an excess of MTs before mixing with ATP. In case III, an initial population of MTs is highly occupied, but an excess of unoccupied MTs is added with the ATP, corresponding to the diamonds of Fig. 5, A and B. The absolute concentration of MTs is the same in cases II and III, but the distribution of heads differs. The results of Fig. 5, A and B, indicate that the burst amplitudes in cases I and III are both similar to each other and considerably smaller than the burst in case II. Thus the fractional occupancy of the MT lattice has an influence on the burst amplitude that is independent of the absolute concentration of MTs. Specifically, the burst amplitude increases with decreasing occupancy of the MT lattice.
Burst Kinetics with DKH340 -Steady state measurements indicate that DKH340 hydrolyzes a significantly greater number of ATP molecules during each productive encounter with a MT in 120 mM potassium acetate (26 versus ϳ4 for other monomer heads). 2 The k bi ATPase and k bi ADP values were determined for DKH340 in 200 mM KCl and are 1.11 and 0.086 M Ϫ1 s Ϫ1 , respectively. Thus the k bi ratio for the average number of ATP molecules hydrolyzed is 12.8. Transient kinetic analysis of ATP hydrolysis by MT⅐DKH340 (Fig. 6) indicates that the burst amplitude is 5.5 per DKH340 even when the MT lattice is largely saturated. This value is significantly higher than that for DKH357, in agreement with the expectation based on the higher k bi ratio value of DKH340.

DISCUSSION
With monomeric DKH346, DKH357, and DKH365, MTs stimulate steady state ATP hydrolysis with a bimolecular rate constant that is ϳ4-fold greater than that for stimulation of the rate of ADP release from E⅐ADP. 2 The most direct explanation of this difference is that kinesin monomers hydrolyze 4 ATP molecules during each productive encounter with a MT, although more complex kinetic explanations are also possible. This is strikingly different from the case of actomyosin in which dissociation is much more rapid than hydrolysis and the corresponding ratio is 1 (Ref. 21 and see Ref. 16). The transient kinetic studies presented here now directly demonstrate that hydrolysis is faster than dissociation even for monomeric DKH357 and that multiple ATP molecules are hydrolyzed before kinesin diffusionally separates from a MT. A burst size of ϳ2 per site is observed with DKH357 at both 50 and 200 mM KCl (Figs. 2 and 4). Inclusion of pyruvate kinase and P-enolpyruvate as a trap for released ADP (Fig. 4) indicates that a significant part of the ADP that is produced during the burst phase is not bound to kinesin. This release of ADP during the burst is consistent with hydrolysis of multiple ATP molecules per kinesin because the ADP that is produced by the first hydrolysis reaction must be released before additional ATP molecules can bind and be hydrolyzed. If the burst were due simply to rate-limiting product release, then the ADP that was produced by the burst would still be bound to kinesin and would not be accessible to pyruvate kinase, as is the case with myosin (22). Thus the usual assumption that the burst and the turbidity transient are due to the steps of a single ATPase cycle is not valid for kinesin monomers and this greatly complicates analysis of the individual steps.
The observed burst stoichiometry of ϳ2 for MT⅐E complexes in which the MTs are largely saturated with DKH357 is lower than the stoichiometry of ϳ4 per site predicted by the steady state measurements, but this disparity is likely due to differences in the DKH357:MT ratio for the two cases. The steady state measurements are performed with the MTs in large excess of DKH357, and most of the lattice of kinesin binding sites on the MT is unoccupied. Because of experimental limitations, the transient kinetic studies must start with a MT lattice with a significant fraction of the sites occupied with kinesin head domains. The MT concentration cannot be further increased without introduction of a large blank absorbance in the turbidity measurements or introduction of a high steady state rate in the burst measurements. Conversely, the DKH357 concentration cannot be reduced greatly without the magnitude of the turbidity change or fractional ATP hydrolysis becoming too close to the blank value in the absence of DKH357. High occupancy of the MT lattice can potentially lead to steric crowding that may accelerate the rate of diffusional separation of DKH357 after addition of ATP, particularly if conformational changes occur that bring a head into closer contact or overlap with heads on neighboring MT sites. Additionally, the rate of ATP hydrolysis may be sensitive to the fractional occupancy of the MT lattice. It is also possible that kinesin head domains transiently dissociate from one MT site and reattach to a new MT site, and thus the occupancy of neighboring sites by other kinesin head domains would prevent rebinding and result in more rapid net diffusional separation. The results of Figs. 4 and 5, A and B, indicate that the stoichiometry of the burst reaction does increase as the occupancy of the MT lattice is reduced, although it is not possible to go to very low DKH357:MT ratios. This increase in burst amplitude at low MT occupancy is consistent with the burst amplitude approaching the value of 4 per site observed by ATPase measurements in the limit of low occupancy of the MT lattice with DKH357. An additional complication that results from the rate constants being sensitive to the occupancy of the MT lattice is that the transients observed here should not be strictly first order, although the deviations from first order behavior would be difficult to detect.
At both 50 and 200 mM KCl the rate constant for termination of the burst phase equals the rate constant for dissociation of DKH357 from the MT as determined turbidimetrically. This indicates that diffusional separation of DKH357 from the MT is responsible for termination of the burst phase or the kinetic equivalent in which a conformational change leads to both termination of further ATP hydrolysis and to rapid dissociation from the MT. The analysis of this process is best illustrated by reference to the scheme of Fig. 7. In the absence of MTs, the lower pathway is followed with ADP release via step 4 being rate-limiting (15). Addition of MTs stimulates the rate of steady state ATP hydrolysis by allowing more rapid ADP release to occur via steps 8 (reverse) and 4 (6,15) to generate the rigor-like complex MT⅐E. Addition of ATP to MT⅐E results in rapid hydrolysis with a rate constant of ϳ100 s Ϫ1 for k 2 at saturating ATP (Figs. 2 and 3) without indication of a lag phase. Subsequent passage through steps 3 and 4 likely occurs at rates comparable with or greater than 100 s Ϫ1 , as there is no indication of a delay between hydrolysis of the first and subsequent ATP molecules during the burst phase (particularly evident for DKH340 in Fig. 6) and because steady state hydrolysis is almost as fast at ϳ70 s Ϫ1 . 2 This suggests that ATP hydrolysis itself is the major rate-determining step. As multiple ATP molecules are hydrolyzed before DKH357 diffusionally separates from the MT, all of the states on the top line of the scheme are more likely to proceed to the right with completion of a cycle of ATP hydrolysis than they are to proceed to the lower line via dissociation of DKH357. Thus k 2 must be greater than k 6 and similarly for k 3 and k 7 and for k 4 and k 8 . All that can be said is that, on average, there are two to four sequential passages through steps 1-4 before dissociation occurs. The rigor binding of DKH357 to MTs is strong, and thus little dissociation is expected via step 5, but it is not known whether the bulk of the dissociation occurs via step 6, 7, or 8.
Most previous transient studies of kinesin have been performed with dimeric species and do not directly relate to the kinetics of individual kinesin head domains. Dimeric species are known to move processively along a MT (1-3) with hydrolysis of many ATP molecules per encounter (4) and to react with alternating head kinetics (6). Thus the observation that initial hydrolysis of ATP by a dimer is faster than dissociation from the MT (9, 11) is expected based on the processive nature of dimeric constructs and does not itself indicate whether hydrolysis is faster than dissociation for individual head domains. One factor complicating analysis of transient kinetic studies with dimers is that the tethered head can have different kinetics from that of the attached head. An additional factor is that tightly bound ADP dissociates from the tethered head in a MT⅐dimer complex in a slow process that is not part of the normal rapid ATPase cycle (6). This altered state would have time to form during the loading of the drive syringes in transient kinetic studies, but in the work to date, the nature of the MT⅐dimer at the start of the reaction has not been determined.
Moyer et al. (14) have also investigated the kinetics of two monomeric kinesin constructs. Their transient kinetic analysis of ATP hydrolysis did detect an initial burst of product formation, but the amplitude was substoichiometric and not supers- FIG. 7. Scheme for stimulation by MTs of ATP hydrolysis by monomeric DKH357. The superscript zero on a rate constant signifies a step in the absence of MTs and DKH357 is designated by E. In the absence of MTs, P i release is fast, and the rate-limiting step is ADP release (15). Thus P i and ADP release are sequential as indicated on the lower line. In the presence of MTs, the relationship of these two steps is not established, but they are indicated on the upper line as sequential with the same order for purposes of discussion only. toichiometric as reported here. This is at least in part due to different experimental conditions. In the work by Moyer et al. (14), the ionic strength and concentration of MTs was such that dissociated heads would rapidly reattach to the MT and continue the MT-stimulated reaction. Thus a larger burst is not observed, because the reaction continues at close to its maximal rate with no sharp transition to a slower steady state phase. In the experiments presented here, initial dissociation of DKH357 terminates its MT-stimulated phase, because conditions were chosen so that rebinding to MTs was slow.
The failure of monomer head domains to dissociate from the MT during each cycle represents partial uncoupling of the ATPase reaction from motility, unless monomer heads have some mechanism to slide along the MT without net diffusional separation during each ATPase cycle. In contrast, the individual head domains of dimers likely do efficiently dissociate and move to a new site during each ATPase cycle, because the ATPase of ϳ40 s Ϫ1 per head equals the dissociation rate of ϳ40 s Ϫ1 per head needed to produce the observed sliding velocities with steps of 8 nm (see Ref. 6 for discussion). One possible mechanism for this interaction in dimers is that the movement of the detached head toward the MT, as it releases ADP, could induce strain in the trailing attached head that accelerates the rate of dissociation of the attached head from the MT.