A mechanistic model for Ncd directionality.

Ncd is a kinesin-related protein that drives movement to the minus-end of microtubules. Pre-steady-state kinetic experiments have been employed to investigate the cooperative interactions between the motor domains of the MC1 dimer and to establish the ATPase mechanism. Our results indicate that the active sites of dimeric Ncd free in solution are not equivalent; ADP is held more tightly at one site than at the other. Upon microtubule binding, fast release of ADP from the first motor domain is stimulated at 18 s(-1), yet rate-limiting ADP release from the second motor domain occurs at 1.4 s(-1). We propose that the head with the low affinity for ADP binds the microtubule first to establish the directional bias of the microtubule.Ncd intermediate where one motor domain is bound to the microtubule with the second head detached and directed toward the minus-end of the microtubule. The force generating cycle is initiated as ATP binds to the empty site of the microtubule-bound head. ATP hydrolysis at head 1 is required for head 2 to bind to the microtubule. The kinetics indicate that two ATP molecules are required for a single step and force generation for minus-end directed movement generated by this non-processive dimeric motor.

similarity, there are striking differences in their motor behavior that are important for biological function in vivo. First, Ncd translocates to the minus-end of microtubules, while kinesin moves to the plus-end (2,4,11). Additionally, kinesin is a highly processive motor, taking several steps per encounter with the microtubule, while Ncd has been shown to be nonprocessive, both mechanically and chemically (12)(13)(14)(15). Ncd and kinesin also differ in their motility and ATPase rates; Ncd is a much slower motor.
Comparison of the kinesin and Ncd crystal structures suggests that despite the structural similarity of the individual catalytic motor domains, there is a different overall orientation of the heads within the Ncd dimer in comparison to those of the kinesin dimer, both in solution and when bound to the microtubule (16 -21). The neck linker, a sequence of ϳ15 amino acids directly adjacent to the catalytic core, has been implicated in specifying the direction of movement for kinesin superfamily members and to be important for force generation (17,(22)(23)(24). For Ncd, the neck linker includes 13 amino acids N-terminal to the catalytic core. There is high sequence homology among minus-end directed kinesin motors, yet this neck linker sequence is different from that of the plus-end directed kinesins. Furthermore, analysis of kinesin-Ncd chimeric motors showed that the amino acid sequence of the neck linker did indeed determine the polarity of microtubule movements (22)(23)(24).
Recently published structural and spectroscopy studies by Rice et al. (25) using monomeric kinesin K349 revealed a dramatic plus-end directed conformational change in the neck linker upon ATP binding. The neck linker became immobile and extended toward the microtubule plus-end, yet the catalytic core did not shift its orientation on the microtubule significantly. Furthermore, in the presence of ADP, the neck linker returned to a state of high mobility comparable to solution conditions in the absence of microtubules (K⅐ADP). These results with monomeric kinesin K349 viewed within the context of the alternating site mechanism of ATP hydrolysis (26 -29) provide a plausible model for kinesin plus-end directed motility and force generation.
Electron microscopy reconstructions have revealed that dimeric Ncd binds the microtubule with its detached head pointed toward the microtubule minus-end (17)(18)(19)(20)(21). This image is quite different from the Mt⅐kinesin EM reconstructions and has been cited as a structural intermediate important for Ncd minus-end directed movement. Our experimental approach has been to explore the mechanistic features of the Mt⅐Ncd ATPase that establish this intermediate and to account for the structural transitions during the ATPase cycle to explain the direction of Ncd motion and its non-processive motility.
Previous studies have defined a minimal kinetic mechanism for the Mt⅐Ncd complex (14, 15, 30 -34). It has been determined that ADP release is the rate-limiting step in the mechanism. However, it is still unclear how the mechanism of ATP hydrolysis for Ncd may relate to its reversed directionality. Here we report that the two heads of dimeric Ncd are not identical. Gel filtration and stopped-flow kinetics reveal that the two heads within the dimer are different in solution in the absence of microtubules, with one head binding ADP weakly and one head binding ADP tightly. Stopped-flow experiments indicate that the two heads of the dimer release ADP at different rates after interacting with the microtubule. We propose that the head with the low affinity for ADP binds the microtubule first to establish the intermediate captured by cryo-EM with the detached head directed toward the minus-end of the microtubule. The kinetics reveal cooperative interactions within the dimer that account for the orientation of this directionally biased Mt⅐Ncd intermediate. The kinetics also establish a distinctive ATPase mechanism for Ncd and provide insight into the mechanochemistry variability among kinesin superfamily members.
Protein Purification-The dimeric Ncd construct (MC1) was expressed in the Escherichia coli cell line BL21(DE3) from a clone generously provided by Dr. Sharyn Endow, Duke University Medical Center (36). This MC1 construct was expressed as a nonfusion protein and contains amino acid residues Leu 209 -Lys 700 ; therefore, the N-terminal ATP-independent microtubule-binding site is absent. MC1 was purified and characterized as described previously (15,33,36). Four different MC1 preparations were used for the pre-steady-state experiments reported, and the steady-state parameters were comparable to those reported previously: k cat ϭ 2 s Ϫ1 , K m,ATP ϭ 23 M, and K 1/2,Mt ϭ 20 M. MC1 is dimeric under the conditions of the experiments reported here based on the K d for dimerization for MC1 at Ͻ5 nM (33). For the pre-steady-state experiments reported, we did not pretreat the Mt⅐N complex with apyrase to remove bound ADP. This approach was chosen due to concern that the Ncd protein behavior may be altered by the treatment, leading to a significant fraction of inactive protein associated with removal of the nucleotide (14,32,37). In addition, one goal of the study was to understand cooperative interactions between the two motor domains within the Ncd dimer. Removal of nucleotide from the active sites of the dimer would render the motor domains equivalent; therefore, the initial Ncd intermediate in the experiments may not be representative of the Ncd motor at the same point in the ATPase cycle in vivo.
On the day of each experiment the microtubules were assembled from soluble tubulin (cold depolymerized and clarified by centrifugation) and stabilized with 20 M taxol as described previously (38). This procedure yielded microtubules that were competent for polymerization with essentially no soluble tubulin remaining. All concentrations reported in the figure legends and manuscript represent the final concentrations of the reactants after mixing.
Stopped-flow Kinetics-The kinetics of mant-ATP binding and mant-ADP release were measured using a KinTek Stopped-Flow Instrument (Model SF-2001, KinTek Corp., Austin, TX) equipped with mercury arc lamp at 25°C in ATPase buffer. Each trace shown is an average of 4 -8 traces. For experiments with the nucleotide analogs mant-ATP and mant-ADP, the fluorescence emission at 450 nm was monitored using a 400-nm cut-off long-wave pass filter with excitation at 360 nm. The ATP-promoted dissociation kinetics of the Mt⅐MC1 complex were determined by turbidity measurements at 340 nm. The kinetic transients were fit to the appropriate exponential functions (presented in figure legends) using KinTek software (version 6.00).
The stopped-flow transients in Fig. 3 were each fit to a single exponential function plus a linear term to obtain the rate and the amplitude of the observed process of mant-ADP release. The amplitudes were plotted as a function of ATP concentration, and the data were fit to a hyperbolic function (Fig. 3B). ATP␥S (Fig. 3C), AMP-PNP (Fig. 3D), and AMP-PCP (data not shown) were evaluated as competitive inhibitors of ATP. The fit of the data to a hyperbola provided the K 1/2,ATP in the presence of either 50 M ATP␥S (Fig. 3C) or 1 mM AMP-PNP (Fig. 3D). The apparent K d,ATP␥S , and K d,AMP-PNP were obtained from Equation 1.
Acid Quench Experiments-The rate constant of ATP hydrolysis was measured using a rapid chemical quench-flow instrument (KinTek Corp.) at 25°C in ATPase buffer. ATP hydrolysis was measured by rapidly mixing the preformed Mt⅐N complex (1 M MC1, 20 M tubulin, 20 M taxol, final after mixing) with increasing concentrations of [␣-32 P]ATP. The reaction was quenched with 2 N HCl and expelled from the instrument. Chloroform (100 l) was immediately added and vortexed to denature the protein. The reaction was then neutralized with 2 M Tris, 3 N NaOH to pH 7.2-8.0. An aliquot (1.5 l) of each reaction mixture was spotted onto a polyethyleneimine-cellulose TLC plate and subsequently developed with 0.6 M potassium phosphate buffer, pH 3.4, with phosphoric acid. Radiolabeled nucleotide was quantified using a FUJI Bas-2000 PhosphorImager (Fuji Photo Film Co., Ltd). The acid quench released bound nucleotide and products from the active site of MC1. Thus, the product formed at each time point represents the sum of N⅐ADP⅐P i , N⅐ADP, and ADP released from the active site of the enzyme and free in solution. In Scheme 1, we designate the radiolabeled molecules by an asterisk (*). The data were analyzed by nonlinear regression using KaleidaGraph software (Synergy Software, Reading, PA).
Each time course of ATP hydrolysis was fit to the biphasic burst equation, where A is the amplitude of the burst representing the formation of [␣-32 P]ADP⅐P i at the active site; k b is the rate constant of the pre-steadystate burst phase; k ss is the rate constant of the linear phase and corresponds to steady-state turnover; and t is the time in seconds. The ATP concentration dependence of the burst rate ( Fig. 5B) and burst amplitude ( Fig. 5C) were fit to quadratic Equations 3 and 4, respectively, where k b is the rate of the exponential burst; k 4 , the rate constant for ATP hydrolysis; N 0 , the concentration of MC1 sites (1 M); A, amplitude of the pre-steady-state burst; A max , maximum burst amplitude. Gel Filtration to Determine Fraction ADP High Affinity Sites-MC1 is purified with ADP bound at the active site (33,37); therefore, the strategy of the assay is to use gel filtration to quantify the concentration of [␣Ϫ 32 P]ADP that partitions with MC1 protein. The centrifuge columns (Bio-Spin P-30 columns, 50 -100-l sample size, Bio-Rad Laboratories) were prepared by washing the column initially with 500 l of ATPase buffer containing 0.25 mg/ml ␥-globulin (Bio-Rad protein standard), followed by 3 washes (500 l each) with ATPase buffer to equilibrate the column and remove residual ␥-globulin that was added to decrease the nonspecific binding of MC1 to the P-30 resin. A 300-l reaction mixture containing 20 M MC1 sites (estimated by Bradford) was incubated at room temperature with 20 M [␣ 32 -P]ATP for 60 -90 min to allow for ADP release, followed by [␣ 32 -P]ATP binding and hydrolysis to label the active motor sites. An 80-l aliquot was applied SCHEME 1. Microtubule-Ncd ATPase to the pre-washed centrifuge column (performed in duplicate) and centrifuged at ϳ1000 ϫ g for 5 min at 22°C in a bench-top swinging bucket centrifuge (2450 rpm, Sorvall RT 6000B Refrigerated Tabletop Centrifuge). Approximately 80 l (79 -81.5 l) was recovered as the void volume for analysis by the Bradford Assay for protein concentration and liquid scintillation counting for nucleotide concentration determination. Aliquots of 5, 7, and 10 l were used to determine total counts for the calculation of nucleotide concentration, and aliquots of 10 and 15 l were used to determine protein concentration. Parallel experiments were included as controls in which either no protein was used in the reaction or dimeric kinesin K401 or ovalbumin was used. These control experiments assessed the degree of nonspecific binding of the MC1 to the gel filtration resin, whether all free nucleotide partitioned within the bead pores, and whether there were other inconsistencies in the assay procedure. Kinetic modeling and simulations were performed using Scheme 1 with Scientist software (MicroMath Scientific Software, Salt Lake City, UT).

ADP Release from Head 2-
The rate of mant-ADP release from the Mt⅐MC1 complex was measured previously by rapidly mixing the preformed MC1⅐mant-ADP complex with microtubules in the presence of MgATP in the stopped-flow (15). A maximum observed rate of 3.7 s Ϫ1 was obtained, and the kinetics represent mant-ADP dissociation from both motor domains. We then pursued experiments to measure directly the kinetics of mant-ADP release from each motor domain of the Ncd dimer. Cryo-EM studies have revealed a stable Mt⅐Ncd intermediate in which one motor domain is bound to the microtubule, yet the second motor domain is detached and directed toward the minus-end of the microtubule (17)(18)(19)(20)(21). For our experiments, we assumed that the detached motor domain would bind mant-ADP more tightly than the motor domain bound to the microtubule (experimental design shown in Fig.  1B) because microtubules activate ADP release from 0.005 s Ϫ1 in the absence of microtubules to ϳ2 s Ϫ1 at high microtubule concentrations (14, 15, 30 -34, 37). To determine the rate of mant-ADP release from the detached motor domain (head 2), microtubules, MC1, and mant-ADP were preincubated to form the Mt⅐MC1⅐mant-ADP complex (1 mant-ADP per MC1 dimer). This complex was rapidly mixed with MgATP to initiate mant-ADP release from head 2. Fig. 1 shows the time dependence of the fluorescence change as mant-ADP is released from the more hydrophobic active site of the motor domain to the solution where the fluorescence is quenched. Both the rate and the amplitude associated with the fluorescence exponential phase increases as a function of ATP concentration. The rate of mant-ADP release from head 2 is ATP concentration dependent with the maximum rate constant at 1.4 s Ϫ1 (K 1/2 ϭ 0.6 M ATP). These results suggest that ADP release from head 2 is rate-limiting for steady-state turnover because all other steps in the pathway have been determined to be significantly faster than the k cat at 2 s Ϫ1 (14,15). This experiment also implies that ATP binding at the first head is necessary for the second head to bind the microtubule and release its mant-ADP. Fig. 2 presents the same experiment but with mant-ADP release from head 2 initiated by MgADP. The maximum rate constant observed was 1.3 s Ϫ1 (K 1/2 ϭ 0.5 M ADP). Note that the ADP-promoted kinetics of mant-ADP release were comparable to those observed for ATP (Fig. 1), both for the observed rate of mant-ADP dissociation as well as the K 1/2 . These data suggest that the conformation required for mant-ADP release from head 2 can be achieved either by ATP binding and hydrolysis at head 1 or by ADP binding directly to head 1 to induce the structural transition.
Is ATP Hydrolysis Required for Head 2 Mant-ADP Release?-This experiment was performed using several nucleotides and nucleotide analogs to determine whether the post-ATP hydrolysis state at head 1 is required for the second head to bind the microtubule and release its mant-ADP (Fig. 3). The Mt⅐N⅐mant-ADP complex (1 mant-ADP per MC1 dimer) was rapidly mixed with buffer, ATP, ADP, the non-hydrolyzable ATP analogs, AMP-PNP and AMP-PCP, or the slowly hydrolyzable ATP analog, ATP␥S. In the presence of 1 mM ATP and ADP, mant-ADP is released and the amplitude associated with the kinetics is significantly larger than the amplitude associated with the kinetics at the other experimental conditions. In the buffer control and thus in the absence of added nucleotide, the amplitude of mant-ADP release is Ͻ5% of the amplitude change associated with ATP or ADP. Although the amplitude of the AMP-PCP kinetics is also quite low, subsequent experiments revealed that AMP-PCP does not compete with ATP for binding MC1 active sites. In the presence of 1 mM AMP-PNP and ATP␥S, the amplitude of the fluorescence change is less than 24% of the amplitude change observed in the presence of 1 mM ATP or ADP. Yet, both AMP-PNP and ATP␥S bind to the active site as effectively as either ADP or ATP at 1 mM analog concentration (apparent K d,AMP-PNP ϭ 199 M and K d,ATP␥S ϭ 1.1 M). These data indicate that ATP binding at head 1 is not sufficient for dissociation of the second high affinity mant-ADP, and either the ADP⅐P i or ADP state is required for the second motor domain to bind the microtubule and release its mant-ADP. We attribute the fluorescence change in the presence of AMP-PNP and ATP␥S to the fact that the analogs cannot exactly form the Mt⅐N⅐ATP intermediate conformation, and AMP-PNP and ATP␥S may in fact resemble an ADP⅐P i intermediate to a limited extent. The small amplitude associated with the AMP-PNP and ATP␥S promoted kinetics of mant-ADP dissociation is consistent with the interpretation that a post-ATP hydrolysis intermediate (either the ADP⅐P i or ADP state) at head 1 is necessary for the second head to bind the microtubule and release its tightly bound mant-ADP.
ADP Release from Head 1-In order to determine the kinetics of mant-ADP dissociation from the first motor domain, MC1 was incubated with mant-ADP to replace ADP bound at the active sites of the dimer (2 mant-ADP per MC1 site, 4 mant-ADP per dimer). The MC1⅐mant-ADP complex was then rapidly mixed with microtubules in the absence of added nucleotide in the stopped-flow. In the absence of added ATP or ADP, microtubule-activated mant-ADP release from head 1 only is observed (Fig. 3). Fig. 4 shows the time dependence of the fluorescence change at eight different microtubule concentrations. The rate of the initial exponential phase increased as a function of microtubule concentration, and the fit of the data to a hyperbola yielded the maximum rate of mant-ADP release from the first head at 18 s Ϫ1 . This rate is significantly faster than the rate of mant-ADP release observed for the second motor domain at 1.4 s Ϫ1 (Fig. 1). These data are consistent with the model shown in Scheme 1 in which rapid ADP release from head 1 is followed by ATP binding and hydrolysis at this site, causing the second motor domain to bind the microtubule and release its mant-ADP in the rate-limiting step of the cycle.
Tight Binding of ATP by One Head-The kinetics of mant-ADP release activated by either ATP or ADP revealed a K 1/2 of 0.5-0.6 M (Figs. 1 and 2). These results showed that mant-ADP release from head 2 was activated at very low ATP concentrations which appeared surprising based on the K m,ATP at 23 M determined by steady-state kinetics and the K d,ATP at 16 M determined by the rapid quench experiments (15,33). However, the head 2 mant-ADP release kinetics reflect ATP binding and hydrolysis to head 1 only while the steady-state and acid quench kinetics evaluate ATP turnover at both motor domains. Furthermore, because the sensitivity of the fluorescence signal is so high, very low concentrations of ATP could be used to evaluate mant-ADP release (Fig. 1). The mant-ADP release kinetics revealed a tight site for ATP binding that was not evident in our earlier experiments because their experimental design evaluated the composite behavior of both ATP-binding sites of the Ncd dimer, a tight site and a weak site.
We pursued acid quench experiments with MC1 to examine ATP binding and hydrolysis by head 1 at very low ATP concentrations, and these results are presented in Fig. 5. The time course for ATP hydrolysis was measured at 1 M MC1 to examine the kinetics at significantly lower ATP concentrations than performed previously (15). Fig. 5A shows transients at four different ATP concentrations (2, 5, 10, and 100 M ATP). There was an initial exponential burst of product formation corresponding to the formation of the N⅐ADP⅐P i intermediate during the first turnover, followed by a slower linear phase which represents subsequent ATP turnovers. The rate constants determined for the linear phase of each transient were consistent with those determined by steady-state kinetics at 20 M microtubules (k cat ϭ 1.1 Ϯ 0.03 s Ϫ1 ; K m,ATP ϭ 16.9 Ϯ 2.3 M).
The rate of the initial exponential phase increased as a function of ATP concentration (Fig. 5B), and the data were fit to Equation 3. The maximum rate of ATP hydrolysis was 35 s Ϫ1 and the K d,ATP was 3.4 M. The burst amplitude at 40 M ATP (Fig. 5C) was 0.5 M (ϳ50% of the enzyme site concentration), indicating that the data obtained at these lower ATP concentrations represents only one head. The maximum burst amplitude obtained from the fit of the data was 0.8 M and thus representing ATP hydrolysis at both motor domains of the dimer. The K d,ATP at 17.8 M determined from the burst amplitude data (Fig. 5C) is similar to the K d,ATP reported previously at 15 M (15). These results indicate that the rate constants for ATP hydrolysis at head 1 (Scheme 1, k 4 ) and head 2 (k 8 ) are similar, yet the ATP binding affinities at each site differ. The K d,ATP obtained from panel B represents the K d,ATP for head 1 and suggests this site binds ATP tightly. The K d,ATP determined from the burst amplitude data (Fig. 5C) represents both sites of the dimer, implying that the second ATP molecule binds more weakly than the first. The burst amplitude at 0.8 M rather than 1 M is attributed to the loss of signal at very high ATP concentrations in rapid quench-flow experiments. We reported previously that the maximum burst amplitude was approximately equal to the site concentration used in the experiment (15).
Asymmetry within the Ncd Dimer-Early experiments suggested that the two sites of MC1 free in solution bound ADP with different affinities. We tested this hypothesis directly by rapidly mixing mant-ATP with dimeric MC1 in the stoppedflow in the absence of microtubules (Fig. 6). The kinetics of mant-ATP binding revealed a rapid exponential burst of fluorescence enhancement associated with mant-ATP binding to the active site, followed by a significantly slower linear phase at 0.005 s Ϫ1 . The rate of the exponential phase increased as a function of mant-ATP concentration, and the fit of the data to a hyperbola provided the maximum rate at 7 s Ϫ1 . The observation of the exponential burst in this experiment is indicative that there were MC1 sites unoccupied and available to bind mant-ATP immediately. If ADP were tightly bound at all MC1 active sites, the kinetics of mant-ATP binding would appear linear and reflect the slow release of ADP at Ͻ0.01 s Ϫ1 as observed in the linear phase of the transient in Fig. 6 and reported previously for MC1 (15).
Although this stopped-flow experiment revealed unoccupied active sites, the amplitude of the fluorescence signal is relative and cannot be directly correlated with the concentration of MC1 active sites used in the experiment. Gel filtration experiments were performed to quantify the concentration of [␣Ϫ 32 P]ADP that partitions with MC1 protein. In this experiment, MC1 was incubated with [␣Ϫ 32 P]ATP for sufficient time to allow ADP to be released from the active site and radiolabeled ATP to bind and be hydrolyzed. The samples were then applied to a gel filtration column and centrifuged. The concentrations of MC1 and [␣Ϫ 32 P]ADP were determined for the excluded volume. The results in Table I show that the concentration of radiolabeled ADP that partitioned with MC1 was approximately half the concentration of MC1 protein (0.6:1). In contrast, the concentration of radiolabeled ADP that partitioned with dimeric kinesin K401 was 0.9:1 and for ovalbumin, 0.035:1. These results suggest that within the Ncd dimer, the active sites bind ADP with different affinities with one site binding ADP tightly and the other site binding ADP more weakly. The alternative interpretation that 50% of the MC1 protein is inactive appears unlikely. The protein concentration determined by the Bio-Rad protein assay was comparable to the concentration of active sites determined by acid-quench burst experiments and the creatine kinase active site titration (15,34). These results indicate that one motor domain binds ADP tightly while the other head binds ADP more weakly, resulting in a rapid equilibrium at this weak site. These data suggest that upon dimerization, an asymmetry is established between the motor domains, and this asymmetry is intrinsic to the dimer before it interacts with the microtubule. Note that this asymmetry was not observed in conventional kinesin K401.
ATP-promoted Dissociation Kinetics-As we began to evaluate different models for the Mt⅐Ncd ATPase mechanism, the need to understand the point in the cycle in which the Ncd dimer completely detaches from the microtubule became critical. Previously, the rate constant for dissociation was reported at 13 s Ϫ1 (15), yet it was unclear whether detachment of head 1 occurred at 13 s Ϫ1 or whether the 13 s Ϫ1 represented the dissociation of the dimer from the microtubule. As the dissociation kinetics were re-evaluated, it was apparent that the kinetics were biphasic with a rapid exponential phase, followed by a second, significantly slower exponential phase (Fig. 7). We tested the hypothesis that the initial fast exponential phase represented detachment of head 1, and the second, slow exponential phase of the turbidity kinetics represented dissociation of head 2. The experiments were repeated to analyze both exponential phases as a function of ATP (Fig. 7). As observed previously, the rate of the initial exponential phase increased as a function of ATP and was fast with the maximum observed rate constant at 12 s Ϫ1 . The rate of the second exponential phase also increased as a function of ATP concentration with the maximum observed rate of dissociation at 1.4 s Ϫ1 . These results are consistent with sequential detachment of the motor domains (Scheme 1). Although the dissociation kinetics in the second phase were observed at 1.4 s Ϫ1 , this rate constant does not necessarily represent the intrinsic rate constant. The mant-ADP release kinetics in Fig. 1 indicated that ADP release occurred at 1.4 s Ϫ1 and was rate-limiting for the pathway; therefore, any step that occurs after this slow step (k 6 ) will be  Table I) clearly indicate two sites exhibiting different affinities for ADP, one binding ADP weakly while the other binds ADP tightly. These results were really surprising because the two polypeptides are equivalent in amino acid sequence, length, and presumably state of post-translational modification because the protein is expressed in an E. coli expression system from a single gene. Furthermore, this behavior was never seen with the kinesin dimer, K401 either in the control experiments presented here or in the nitrocellulose binding assays published previously (38). These data for MC1 suggest that upon dimerization, an asymmetry is established between the motor domains, and this asymmetry is intrinsic to the dimer before it interacts with the microtubule.
The kinetic and gel filtration data presented here would appear to be in direct conflict with the Ncd dimeric crystal structure showing both active sites occupied by ADP (17). However, the crystallization conditions included 2 mM MgADP to stabilize the protein. Our results are completely consistent with the structural studies because the addition of 2 mM MgADP is expected to drive the equilibrium toward dimeric Ncd with both the weak and tight sites occupied by ADP. The mechanistic experiments presented here (Fig. 6, Table I) have revealed a structural intermediate that has not been detected previously and may not be detectable by conventional imaging and crystallography approaches because Ncd is labile and de-grades in the absence of ADP.
The ATPase Pathway-Scheme 1 shows our model for the Mt⅐Ncd ATPase based on the equilibrium binding studies (33), the pre-steady-state kinetics (14,15,34), the motility (13,17,24), and structural results for Ncd (16 -21, 39, 40). The cycle begins at the star (૽) intermediate, and the experimentally determined rate constants are designated. We propose that the motor domain that holds ADP more weakly (designated head 1) binds the microtubule first and stimulates fast release of ADP. The asymmetry in the Ncd dimer establishes the Mt⅐Ncd intermediate observed in the cryo-electron micrographs in which one motor domain is bound to the microtubule with the second motor domain detached and pointed toward the minus-end of the microtubule (upper right, intermediate 3). ATP then binds to the empty site (head 1), followed by rapid ATP hydrolysis which is required for head 2 to bind to the microtubule. (Rapid quench radiolabeled species are indicated by the asterisk.) Head 1 detaches from the microtubule as the N⅐ADP⅐P i intermediate with the second head poised for rate-limiting ADP product release at 1.4 s Ϫ1 . A second round of ATP binding and hydrolysis is required to release head 2 and therefore release the dimer from the microtubule. This model is consistent for a non-processive dimeric motor and provides a mechanism for directional bias intrinsic to the Ncd dimer. Furthermore, this model predicts that dimeric Ncd takes a single step to the next microtubule binding site, yet 2 ATP molecules are required for this step and the force-generating structural transitions for

minus-end directed movement.
There were several key experiments that excluded other potential models. The experiment presented in Fig. 1 was designed to begin as intermediate 3 with mant-ADP bound at the high affinity site. The slow rate of mant-ADP release at 1.4 s Ϫ1 (k 6 ) is the slowest step measured in the pathway and is therefore rate-limiting for steady-state turnover. Furthermore, the results presented in Fig. 3 established that ATP hydrolysis at head 1 (k 4 ) to reach the ADP⅐P i or ADP state was required for mant-ADP release from head 2 (k 6 ). Thus, the results in Figs. 1-3 revealed the intermolecular cooperativity that was required for rate-limiting mant-ADP release.
The equilibrium binding experiments published previously (33) indicated that the only conditions that led to Ncd partitioning off the microtubule were ADP ϩ P i , indicating that the N⅐ADP⅐P i intermediate was the nucleotide intermediate that detached from the microtubule. Furthermore, these data were sigmoidal, and the fit to the Hill equation indicated that two sites were cooperative. These results as well as the rapid quench burst amplitude data presented here (Fig. 5) and in Ref. 15 are indicative that both sites must hydrolyze ATP before the Ncd dimer is released from the microtubule (k 9 ). Therefore, these experiments suggest an ATPase cycle in which both motor domains of the dimer must participate directly.
Our interpretation of the biphasic dissociation kinetics presented in Fig. 7 requires the assumption that the turbidity signal associated with intermediate 3 is greater than intermediate 6, and both are greater than the turbidity signal of the microtubule with Ncd detached and free in solution. Although at first glance this assumption may seem naive, there are several lines of evidence that support the interpretation that the second phase of the turbidity kinetics represents a true step on the pathway. Experimentally, we cannot determine a rate constant for head 2 detachment any faster than 1.4 s Ϫ1 because this step is limited by ADP release at k 6 ϭ 1.4 s Ϫ1 . The fact that the second phase of the dissociation kinetics is ATP-dependent is indicative that this exponential phase represents a true step on the pathway rather than a nonspecific, slow linear phase seen at the end of stopped-flow transients. These are typically very slow and not ATP dependent. Furthermore, the rapid quench burst experiments show that both motor domains hydrolyze ATP during the exponential burst phase and prior to steady-state (Fig. 5). Last, the ATP-promoted dissociation kinetics for monomeric Ncd, MC6, reveal that the monomer does not detach from the microtubule. ATP-promoted dissociation requires a dimeric Ncd motor (34).   A very careful mechanistic study on dimeric Ncd was published by Pechatnikova and Taylor (14), and our kinetics are very similar to theirs. However, we have excluded their model based on our previously published dissociation kinetics (33). In the Pechatnikova and Taylor model, ATP binding at the vacant site of intermediate 3 (our Scheme 1) leads to detachment of Ncd as the ATP⅐N⅐ADP intermediate. This intermediate subsequently rebinds to the microtubule by the ADP-containing head, followed by ATP hydrolysis, and ADP release as the rate-limiting step. We propose that Ncd cannot detach as the ATP⅐N⅐ADP intermediate because ATP hydrolysis is required for dissociation (33). We performed a dissociation experiment as shown in Fig. 7, but dissociation was initiated by either ATP or the nonhydrolyzable ATP analog, AMP-PNP. In the presence of AMP-PNP, there was no change in the turbidity signal indicating that ATP binding is not sufficient to stimulate dissociation. These kinetics show that ATP binding and ATP hydrolysis must both occur for Ncd to detach from the microtubule (33).
The model presented in Scheme 1 is consistent with the mechanistic, motility, and structural results for dimeric Ncd. This model accounts for the minus-end direction of motion and reveals cooperative interactions that are important for force generation for a non-processive dimeric motor. This model is attractive because it provides a mechanism to account for the directional bias of intermediate 3 and minus-end directed Ncd motility. The determinants for minus-end directionality have been localized to the neck linker sequence, and these results evaluated in the context of the kinetics presented here lead to the testable hypothesis that the neck linker sequence establishes the asymmetry within the Ncd dimer. The sequential ATPase mechanism for Ncd is quite different from conventional kinesin's ATPase mechanism. This study with dimeric Ncd illustrates the mechanistic diversity for energy transduction that is utilized by two kinesin superfamily members.