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Kinetic and Mechanistic Basis of the Nonprocessive Kinesin-3 Motor NcKin3*

Kinesin-3 motors have been shown to transport cellular cargo along microtubules and to function according to mechanisms that differ from the conventional hand-over-hand mechanism. To find out whether the mechanisms described for Kif1A and CeUnc104 cover the full spectrum of Kinesin-3 motors, we characterize here NcKin3, a novel member of the Kinesin-3 family that localizes to mitochondria of ascomycetes. We show that NcKin3 does not move in a K-loop-dependent way as Kif1A or in a cluster-dependent way as CeUnc104. Its in vitro gliding velocity ranges between 0.30 and 0.64 μm/s and correlates positively with motor density. The processivity index (kbi,ratio) of ∼3 reveals that not more than three ATP molecules are hydrolyzed per productive microtubule encounter. The NcKin3 duty ratio of 0.03 indicates that the motor spends only a minute fraction of the ATPase cycle attached to the filament. Unlike other Kinesin-3 family members, NcKin3 forms stable dimers, but only one subunit releases ADP in a microtubule-dependent fashion. Together, these data exclude a processive hand-over-hand mechanism of movement and suggest a power-stroke mechanism where nucleotide-dependent structural changes in a single motor domain lead to displacement of the motor along the filament. Thus, NcKin3 is the first plus end-directed kinesin motor that is dimeric but moves in a nonprocessive fashion to its destination.

The kinesin superfamily of proteins contains molecular motors that move along microtubules. Members of the founding class, Kinesin-1 (conventional), move according to the socalled hand-over-hand mechanism that leads to processive motility (1). This mechanism involves two motor heads that alternately bind to the microtubule and produce a stepwise progression of the motor. It implies that the catalytic cycles of the motor heads alternate because the nucleotide state of the catalytic domain determines the microtubule affinity (2). This mechanism is referred to as alternating site catalysis, and has been proven by measuring the consecutive release of ADP from head 1 and 2 of the kinesin dimer (3)(4)(5). ADP release experi-ments show that half of the enzyme-bound ADP is liberated upon interaction with the microtubule and the other half upon addition of ATP. Afterward, the motor continues to perform processive catalytic cycles because of the interlaced interaction of both motor heads. In agreement, the rate of the second ADP release is at least as fast as the stepping rate. The kinetic model of alternating site catalysis is consistent with the hand-overhand mechanism that predicts shifted phases of the kinetic cycles of both motor heads. All Kinesin-1 motors investigated so far conform to this model.
Conversely, the nonprocessive Kinesin-14 motor Ncd does not show the ADP release pattern typical for alternating site catalysis. Ncd is a homodimeric kinesin from Drosophila melanogaster and is involved in mitosis and meiosis (6 -8). It moves to the microtubule minus end, and it most likely generates motility because of a molecular power stroke (9 -15). ADP release also occurs in two steps, one that is triggered by microtubule binding, and one that is induced by nucleotide binding. By contrast to conventional kinesin, however, Ncd dissociates from the microtubule at a rate in the range of k cat , implying that the motor dissociates after one kinetic cycle. The ADP release behavior of Kinesin-1 and Ncd therefore reveals two opposing motility mechanisms, namely processive hand-over-hand motility and nonprocessive power stroke motility. These types of motility, however, do not cover the entire spectrum of kinesin mechanisms. The Kinesin-3-type motor KIF1A has been reported to move continuously along microtubules in a quasiprocessive manner, although the constructs used were monomeric (16 -20). These truncated motor constructs also change their microtubule affinity in a nucleotide-dependent fashion but do not dissociate from the filament in their weak microtubule-binding state. They do not avoid dissociation by alternating microtubule interactions but by the action of a positively charged, lysine-rich region (K-loop). This loop binds to the negatively charged, glutamate-rich C terminus of tubulin, the E-hook. This interaction allows lateral sliding of Kinesin-3 proteins to the next binding site and prevents detachment from the microtubule.
It is controversial whether all Kinesin-3 motors work as described for KIF1A. Dictyostelium discoideum DdUnc104, for example, is constitutively dimeric, and thus could move in principle by a hand-over-hand mechanism (21). On the other hand, Caenorhabditis elegans CeUnc104 has been reported to move nonprocessively (22,23). Interestingly, CeUnc104 becomes a processive motor if dimerization is enforced either by high local motor concentrations or by insertion of an artificial dimerization domain (23). In vivo the switch between the monomeric and the dimeric state might regulate cargo transport (24). Remarkably, C. elegans or D. discoideum Unc104 have not been investigated in stoichiometric or kinetic ADP release assays that might support or disprove half-site catalysis. All KIF1A and KIF1C constructs that have been characterized previously were monomeric (25). Therefore, half-site catalysis cannot occur.
Given the fundamental functional differences among different Kinesin-3 motors, it is interesting to know whether this class of kinesins is based on a common underlying mechanism. If not, it is interesting why phylogenetically related proteins developed divergent mechanisms. To address these questions, we cloned a novel Kinesin-3 member, NcKin-3 from Neurospora crassa, which is involved in transporting and shaping mitochondria (26). We show that NcKin3 is a dimeric, plus end-directed microtubule motor whose gliding velocity correlates positively with the motor density on the coverslip. Comparison of K m,ATP values in gliding and ATPase assays indicates a low duty ratio. This, together with a low processivity index (k bi,ratio ), suggests that NcKin3 is not processive. In agreement, the motor detaches at a rate comparable with the steady-state ATP turnover rate from the filament. Remarkably, only one of the motor heads releases ADP in a microtubule-dependent fashion. The second head loses ADP at a constant microtubuleindependent rate. Together, our study presents the first description of a nonprocessive, plus end-directed kinesin vesicle motor.

EXPERIMENTAL PROCEDURES
Cloning, Protein Expression, and Purification-The DNA encoding NcKin3 was isolated from a mycelial cDNA library of N. crassa (27) (NCU03715.2 in N. crassa genome release 7). For recombinant expression NcKin3 was cloned into a pT7.7 vector (28). A C-terminal truncated version of NcKin3, consisting only of 558 amino acids (NcKin3-558), was generated from pT7.7-NcKin3 by PCR. A short peptide sequence was added to NcKin3-558 that adds a reactive cysteine to the protein. This allows labeling with maleimide compounds (PSIVHRKCF (29)). At the C terminus of NcKin3-558, an NgoMIV restriction site was inserted for the addition of amino acids 432-546 of human kinesin tail (hTail). 3 The hTail DNA was transferred from an NcKin hTail pT7-based plasmid (30) and inserted into pT7.7-NcKin3-558 via the NgoMIV and HindIII restriction sites.
Proteins were purified by ion exchange chromatography on a High Trap SP-Sepharose column as described (Fig. 1B) (31).
Peak fractions were supplied with 10% glycerol, frozen in liquid nitrogen, and stored at Ϫ70°C. Protein concentration was estimated by a Bradford assay (Bio-Rad) and via the absorption at a wavelength of 280 nm.
Determination of the Oligomerization State-To characterize the oligomerization state of NcKin3, the Svedberg coefficient and the Stokes radius were determined by density gradient centrifugation and gel filtration (32). The molecular weight was calculated according to Equation 1 (33), where n A is Avogadro's number; is viscosity (10 Ϫ3 N ms Ϫ2 ); is specific volume of the sample (0.725 cm 3 /g), and is the density of the medium (1.0 g/cm 3 ).
Gliding Assays and Polarity Marked Microtubules-For gliding assays at high NcKin3 concentrations, NcKin3-558cys was labeled with biotin-maleimide (32). The protein was incubated with a 4-fold excess of maleimide conjugate on ice for 60 min. The reaction was stopped by addition of 10 mM dithiothreitol. Active motors were selected in a microtubule binding and release step (34).
To measure the concentration dependence of the velocity, the hTail-tagged version of NcKin3-558 was used. Fluorescently labeled microtubules were observed in a total internal reflection microscope, and their velocity was measured using software from Olympus Biosystems (Planegg, Germany). For statistical analysis Kaleidagraph 3.6 (Synergy Software, Reading, PA) and Prism 4.0 (GraphPad Software Inc., San Diego) were used.
Basal ATPase Activity-Slow steady-state ATPase rates in the absence of polymerized tubulin were measured using [␥-32 P]ATP (35). NcKin3 (5 M) was incubated in 12A25ϩ buffer (12.5 mM Aces-KOH, 25 mM potassium acetate, 5 mM MgCl 2 , 0.5 M EGTA, pH 6.8) with 1 mM [␥-32 P]ATP at 22°C. After various time points, the reaction was quenched in 0.3 M perchloric acid. A suspension of charcoal in 1 mM NaH 2 PO 4 was added, mixed, and centrifuged to separate the charcoal. After determination of the specific activity of the [␥-32 P]ATP solution, ␥-32 P-labeled inorganic phosphate in the supernatant was quantified by scintillation counting. The ATPase rates were calculated from the hyperbolic fits of the time traces.
Steady-state ATPase-Microtubule activated steady-state ATPase rates were determined in a coupled enzymatic assay (36). The assay was performed in 12A25ϩ buffer at 22°C. K 0.5,MT was determined at an ATP concentration of 1 mM. The microtubule concentration was maintained at ϳ10 M for titra-tions with ATP. NcKin3 concentrations were typically 1 M. Tubulin was purified from pig brain as described (37). Microtubules were obtained by spinning a freshly thawed tubulin aliquot at 120,000 ϫ g and 4°C, supplementing the supernatant with 1 mM GTP and 20 M paclitaxel, and removing excess nucleotides by centrifugation through a sucrose cushion. Finally, the microtubule pellet was suspended in 12A25ϩ, 20 M paclitaxel, and the protein concentration determined at 280 nm (3).
Stochiometry of Mant-ADP Release-NcKin3 was incubated with equimolar amounts of mant-ATP for 30 min on ice. The final kinesin concentration in the assay was 0.9 M. The fluorescence decrease caused by mant-ADP release was observed in an Aminco Bowman spectrofluorometer (32). The fluorescence was excited at 356 nm and the emission detected at 445 nm. All experiments were performed at 22°C in 12A25ϩ buffer. Microtubules were treated with apyrase prior to the centrifugation through a sucrose cushion. Microtubule concentrations ranged between 1 and 11 M. To release mant-ADP from the second head, an excess of unlabeled ATP (1 mM) was added subsequently.
Pre-steady-state Mant-ADP Release-NcKin3 was incubated with a 4-fold excess of mant-ATP for 30 min on ice. Excess nucleotide was removed by gel filtration in Sephadex G-25 spin columns. The labeling ratio was calculated from the extinctions at 280 nm (⑀ ϭ 38,000 M Ϫ1 cm Ϫ1 ) and 356 nm (⑀ ϭ 5,800 M Ϫ1 cm Ϫ1 ). Pre-steady-state mant-ADP release was measured in a BioLogic stopped-flow apparatus (SFM-3; BioLogic Inc., Grenoble, France) at 22°C in 12A25ϩ buffer. Fluorescence was excited at 365 nm, and emission was detected at 442 nm using a band pass interference filter of Ϯ10 nm width (Chroma Technology Corp., Rockingham, VT). A final concentration of 400 nM mant-ADP-labeled NcKin3 was rapidly mixed with 0 -12 M microtubules in the presence of 1 mM ATP (final concentrations). The traces shown are averages of at least five stoppedflow traces. All traces obeyed single exponential behavior and were fitted using either the software BioKine (BioLogic Inc., Grenoble, France) or TableCurve2D (Systat Software Inc., Point Richmond, CA). The rates showed a hyperbolic dependence on the microtubule concentration and were fitted according to Equation 2, The constants presented in this work are averages from three independent experiments.
Cosedimentation Assay-Increasing amounts of NcKin3-558 (1-25 M) in BRB80ϩ buffer were mixed with 2 M microtubules in the presence of 1 mM ADP or 1 mM AMP-PNP. The samples were mixed and then centrifuged in a Beckman Optima 100 ultracentrifuge (100,000 rpm, 10 min, 4°C). The supernatants were carefully removed and mixed with SDS sample buffer. The pellets were resuspended in BRB80ϩ and stopped in PAGE sample buffer. Pellet and supernatant samples were separated on 12% SDS-PAGE and stained with Colloidal Blue staining (Invitrogen). Gel photos were taken with the EagleEye CCD camera system (Stratagene Inc., La Jolla, CA) and quantified using the ImageJ software. The concentrations of motors in pellet and supernatant were analyzed with SigmaPlot Software (Systat Software, Inc., Point Richmond, CA). Binding parameters were calculated from a hyperbolic curve fit.
Detachment Rates-The microtubule detachment kinetics of NcKin3 was determined by the change of light scattering in two assays. (i) For stopped-flow assays, the NcKin3 microtubule complex was formed by incubating NcKin3-558 with a 1.5-fold excess of microtubules in the presence of 0.01 unit/ml apyrase (Sigma). Subsequently, 0.4 M of the complex (final concentration) was mixed with ATP (0 -64 M) in a stopped-flow apparatus (BioLogic Inc., Grenoble, France). The sample was illuminated at a wavelength of 436 nm, and the light scattering signal was observed through a 440 Ϯ 10 nm band-pass filter. At least five traces of each ATP concentration were used for averaging. Averaged traces were analyzed by single exponential curve fitting using the TableCurve2D software (Systat Software Inc.). The observed rates were plotted against the ATP concentration and fitted according to Equation 3, Detachment of NcKin3 from the microtubule was also (ii) measured via the light scattering signal in a flash-photolysis apparatus, described in detail in the Supplemental Material.

RESULTS
Unusual Structural Features of NcKin3-NcKin3 was found at mitochondria of the ascomycete N. crassa, suggesting that it is an organelle motor and responsible for the transport and shaping of mitochondria (26). To study the mechanistic basis of this motor, we isolated the DNA from a mycelial cDNA library and cloned it into a bacterial expression vector (27,38). The coding sequence includes 1947 bp that code for a protein of 647 amino acids and a predicted molecular mass of 72 kDa. Noteworthy, the cDNA sequence consists of a 5Ј extension that codes for 37 N-terminal amino acids that are not part of the conserved motor domain (Fig. 1). The NcKin3 motor domain sequence reveals a clear membership in the Kinesin-3 subfamily (39). However, the molecule shows several unusual features. For example, BLAST searches with the N-terminal extension in the GenBank TM data base fail to detect any similarities outside fungal Kinesin-3s. The functional role is unclear because a truncated mutant (amino acids 38 -558) of NcKin3 lacking the extension shows the same microtubule-activated steady-state ATPase rate and half-maximal activation constant for microtubules as the construct with the extension (amino acid 1-558; data not shown). As another distinctive feature, NcKin3 and other short fungal Kinesin-3 motors possess a much shorter and less charged K-loop region (typically 1 Arg and 1 Lys residue, separated by 2-3 residues; Fig. 1A). Finally, the C-terminal nonmotor part is unusually short (about 200 amino acids), does not contain forkhead-associated or pleckstrin homology domains, and does not show homology to other Kinesin-3 clades. Curiously, the last 90 residues form a cluster that contains 21 Asp and 7 Glu residues that result in a highly negative net charge of the tail.
The recombinant full-length protein was active in ATPase and gliding assays but poorly expressed. Also, the preparation contained significant degradation products. Therefore, we cloned truncated versions lacking parts of the C terminus (Fig.  1B). The longest truncation, NcKin3-558 was used in most experiments described here, and a reactive cysteine was added at the C terminus, allowing modifications with maleimide labels (29,30). The truncated, biotin-tagged NcKin3-558 kinesin was equally fast in gliding assays as the recombinant fulllength NcKin3 protein.
NcKin3 Is a Dimer-Automatic and manual analysis of the NcKin3 stalk sequence predicts the formation of a twostranded coiled coil between residues 437 and 513, although some heptads deviate significantly from the ideal repeat pattern, and the start of the helix is uncertain (Fig. 1A). Coiled coils contain characteristic periodic repeats of seven amino acid residues numbered a-g, where positions a and d are mostly hydrophobic, and e and g are often charged or hydrophilic (40 -42). In the case of NcKin3, the start of the coiled coil can be predicted as early as at residue 427, but then a change of the coil phase would occur after residue 441 (shift from a to f position).
In agreement with the prediction, gel filtration and sucrose density gradient centrifugation assays revealed that NcKin3 is dimeric (Fig. 2) (43). The two longest constructs, NcKin3-558 and -513 are stable dimers, suggesting that the full-length protein is also dimeric. Shorter constructs (NcKin3-415, -434, -457, -470, and -488) are monomeric, implying that the last three predicted coil heptads are crucial for dimer stability (Fig.  1). Conversely, the first seven predicted heptads are not sufficient for dimerization in truncated constructs but, as shown below, are still functionally important. With the exception of D. discoideum Unc104, all other Kinesin-3 motors have been reported to be primarily monomeric (21-23, 44, 45). As NcKin3 does not show similarity to DdUnc104 outside the motor domain, it contains a so far unknown dimerization domain.
Features of NcKin3 Motility-To find out whether NcKin3 is a microtubule motor, we performed multiple motor gliding NcKin3 has a subgroup-specific N-terminal extension of 36 amino acids (absent in mouse KIF1A, C. elegans Unc104, and D. discoideum Unc104), followed by the conserved core motor domain. The motor domain contains an unusual K-loop with fewer lysines than in other Kinesin-3 motors, interspersed with Ser, Gly, and Pro residues. A short stretch corresponding to the neck linker of Kinesin-1 motors follows before a presumable coiled coil region starts (for comparison the human kinesin (HsKIF5B) neck coiled coil is boxed in the sequence alignment (49)). The predicted coil phase is indicated by letters a-g above the sequence and clearly dissimilar to the human kinesin coiled coil. The C-terminal 134 residues (tail) do not show any recognizable sequence motifs and are highly Asp-rich between position 558 and 647. B, the SDS gel below the scheme shows bacterially expressed, purified truncation mutants used in the study (the number indicates the last NcKin3 residue). DECEMBER 8, 2006 • VOLUME 281 • NUMBER 49 assays. At saturating motor densities on the surface of the flow chamber, microtubules were transported with a maximum velocity of 0.59 Ϯ 0.09 m/s (average Ϯ S.E., n ϭ 65 microtubules), which is slow compared with gliding velocities of other Unc104 motors (v ϭ 1.2 to 2.5 m/s (19,21,23)). 45 of 50 polarity-labeled microtubules were transported to the dim region, showing that NcKin3 is a plus end-directed motor (Fig. 3A).

Nonprocessive Kinesin-3 Motility
NcKin3 gliding velocities depended on the motor concentration in the sample (Fig. 3). At saturating concentrations of more than 2 M, NcKin3 in a flow cell of ϳ3 ϫ 18 mm 2 , the maximum gliding velocity was 0.52 Ϯ 0.04 m/s (n ϭ 179). At lower motor concentrations, the gliding velocity gradually decreased to a minimum velocity of 0.30 Ϯ 0.08 m/s (n ϭ 74) at an NcKin3 concentration of 0.06 M, which is significantly different from the highest density in a t test (p Ͻ 0.0001; Fig. 3). The mean gliding velocities at the tested motor concentrations differ significantly with p Ͻ 0.0001 in an unpaired analysis of variance test, and they show a positive linear trend (p Ͻ 0.0001).
Below a threshold of 0.06 M, no microtubule binding was observed, even with very high microtubule concentrations. Assuming that the motors are distributed evenly on the two surfaces of the flow chamber, this corresponds to a motor density of 4.5 ϫ 10 9 molecules/m 2 . Obviously, a high motor den-sity is required to keep NcKin3 and microtubules in contact, indicating that NcKin3 is a cooperative, nonprocessive motor. To exclude that NcKin3 proteins clustered by streptavidin are responsible for microtubule transport at low NcKin3 concentration, residues 432-546 of human kinesin tail were appended to the C terminus of NcKin3-558 (30). The resulting protein, NcKin3-558hTail, adhered unspecifically to the coverslip but behaved like the original NcKin3-558cys protein in ATPase assays. Its gliding properties were indistinguishable from the biotinylated construct.
To ensure that motor properties of NcKin3-558 proteins were not altered by the absence of the lacking 89 C-terminal wild-type amino acids, we determined the gliding velocity of the full-length protein NcKin3-647. This construct turned out to adhere unspecifically to the coverslip and displayed a gliding velocity of 0.64 Ϯ 0.06 m/s at saturating motor concentration, equal to the maximum gliding velocity of the NcKin3-558 construct. Therefore, the mechanisms of full-length and truncated motors are likely to be identical.
Enzymatic Properties-Processivity describes the ability of motor protein to perform several catalytic cycles on a polymeric substrate without detachment. Processive movement according to the hand-over-hand mechanism leads to distinctive kinetic features, specifically (i) an unusually high apparent binding rate in the steady-state ATPase, (ii) a large ratio between the apparent and the real binding rate measured in pre-steady-state ADP release experiments, and (iii) a duty ratio of Ն50%. To test whether NcKin3 shows these characteristics of processive motors, we performed kinetic steady-state and pre-steady-state assays and characterized the motility in microscopic assays.
Stoichometry of Mant-ADP Release-Kinesin-1 motors show a strictly coordinated action of their two motor domains. To discern the action of the two heads of the NcKin3 dimer, mant-ADP-loaded kinesin was first mixed with a 10-fold excess of microtubules and then chased with 1 mM nonfluorescent ATP (Fig. 4). The initial fluorescence signal of the mant-ADP NcKin3 complex decreased fast upon microtubule addition, and dropped further when ATP was added. The amplitude of the second phase was essentially identical to the first phase, indicating that the ADP of one head was released upon microtubule binding, whereas the ADP of the other head was only released after ATP binding of the kinesin microtubule complex. Importantly, the rate of the ATP-dependent fluorescence decrease was 10 3 -10 4 -fold slower (ϳ0.02 s Ϫ1 ) than expected for a hand-over-hand mechanism. If the gliding velocity of 0.53 m/s of NcKin3 was caused by alternating heads that step 8 nm for each ATP, a release rate of 530 nm/(8 nm⅐s) ϭ 66 s Ϫ1 would be expected.
We examined the ADP release at microtubule concentrations ranging from 1 to 10 M at an NcKin3 concentration of 0.9 M (Fig. 4) to decide whether the second rate describes a microtubule-dependent process. The rate of the second phase was unaffected by the microtubule concentration, as expected for a motility model where release and microtubule re-binding occurs.
In the presence of AMP-PNP, a nonhydrolysable ATP analogue, the rate of the second ADP release also remained unaffected (data not shown), indicating that neither detachment of the motor from the microtubule is necessary for the second mant-ADP release nor ATP hydrolysis. In a control experiment we analyzed the ADP release of the monomeric NcKin3-434. Here, ADP release occurred in a single step upon addition of the microtubules (Fig. 4). Addition of ATP had no further effect on the fluorescence signal, excluding the existence of a secondary ATP-binding site in the NcKin3 motor head. The rate of ADP release from the monomer was faster than can be resolved manually in the spectrofluorimeter (the fastest rates we are able to measure manually are ϳ0.1-0.25 s Ϫ1 ). Therefore, it is faster than the slow rate of the dimeric construct (0.02 s Ϫ1 ). In the absence of microtubules the monomeric motor still released ADP at a slow rate of 0.02 s Ϫ1 , comparable with the ADP release rate of the second head of dimeric NcKin3.
As a further control, a construct containing NcKin3 motor heads (amino acids 1-434) and a partial human kinesin tail coiled coil (termed NcKin3-434hTail) was tested. Although this construct is dimeric (supplemental Fig. S1), it behaved like the NcKin3-434 monomer in mant-ADP release assays, and it lost its ADP ligand in a single fast step. This observation implies that the dimerization domain of the NcKin3 wild-type protein, located between residues 435 and 513, confers the characteristic ADP release feature of the second NcKin3 head.
To exclude that the two-step ADP release behavior was because of properties of the methylanthraniloyl derivative of ADP, the stoichiometry of released [␣-32 P]ADP was determined (Supplemental Material). The isolated kinesin ([␣-32 P]ADP) microtubule complex contained 0.84 ADP ligands per NcKin3-558 dimer, indicating the release of one ADP per motor dimer (supplemental Fig. S2). The same exper-  DECEMBER 8, 2006 • VOLUME 281 • NUMBER 49 iment performed in the presence of ATP, or without ATP but with the monomeric NcKin434 protein, resulted in the absence of radioactive ADP in the kinesin microtubule complex, indicating the complete release of all kinesin-bound ADP. These data are consistent with the observations in mant-ADP release assays and suggest that the mant-ADP release mimics the ADP release behavior.

Nonprocessive Kinesin-3 Motility
In summary, these data indicate that NcKin3 contains one head with microtubule-stimulated ATPase activity, and another one with an activity that is unaffected by microtubules.
This means that the ADP release from NcKin3-558 is an asymmetric two-step process and involves two heads of NcKin3 that possess different affinities for ADP. Binding of head 1 to microtubules induces ADP release from the low affinity site rapidly. The second head binds ADP tightly and turns over ATP independent from microtubule interactions at a low basal level. This observation is incompatible with a hand-over-hand mechanism for movement of NcKin3. To support these implications we compared the microtubule-induced mant-ADP release with the steady-state ATPase activity, and we estimated the degree of biochemical processivity (46).
Steady-state ATPase Kinetics-NcKin3 has an ATPase activity that is accelerated from 0.012 Ϯ 0.001⅐s Ϫ1 per motor head (n ϭ 3 independent preparations) without microtubules to 11.6 Ϯ 4.0 s Ϫ1 (n ϭ 5) under saturating microtubule concentrations (Table 1 and Fig. 5). This ATP turnover number (k cat ) was calculated assuming that both NcKin3 heads contribute equally to the total microtubule-activated ATP turnover. If, as indicated by the above mant-ADP release experiments, one head cannot be stimulated by microtubules, this value has to be corrected by a factor of 2, leading to a k cat of 23.2 s Ϫ1 per active head. We note that this number is still small in comparison to the gliding velocity observed in multimotor assays. From a structural point of view, a reasonable estimate for the stroke size is 6 -10 nm at maximum, which would lead to a velocity of 0.14 -0.23 m/s at 23.2 ATP⅐s Ϫ1 (observed ϳ0.6 m/s) for a processive motor (47).
The microtubule concentration required for half-maximal activation (K 0.5,MT ) was 1.0 Ϯ 1.2 M (n ϭ 4), and the ATP concentration for half-maximal ATPase activity (K 0.5,ATP ) was 4.0 Ϯ 0.9 M (n ϭ 2). Accordingly, the ratio between k cat and K 0.5,MT , the k bi,ATP value, which reflects the apparent binding rate between NcKin3 and microtubule, is 11.6 M Ϫ1 s Ϫ1 (23.2 if only one head contributes). This constant contains implicit information on the processivity of the enzyme (3). An enzyme that performs several catalytic cycles upon a single encounter with a substrate will show a k cat /K 0.5,MT that is much larger (typically much more than 100 M Ϫ1 s Ϫ1 ) than the actual bimolecular binding rate that can be measured in pre-steady-state assays.
To compare apparent and actual bimolecular NcKin3 microtubule binding rate, we measured the transient rate of ADP release in a stopped-flow experiment (Fig. 5). Mant-ADP was  used to monitor the dissociation of ADP from NcKin3 upon binding to the microtubule. At saturating microtubule concentrations, ADP release of NcKin3 occurred at a rate of k max (ADP release) ϭ 7.1 Ϯ 2.0 s Ϫ1 with a K 0.5,MT of 0.94 Ϯ 0.04 M (n ϭ 3) (Fig. 5). These values are comparable with k cat and K 0.5,MT val-ues measured in steady-state assays, suggesting that (as for other kinesins) ADP release is rate-limiting in the catalytic cycle of NcKin3. From these parameters, the physical bimolecular rate, k biADP , can be calculated as k biADP ϭ k max (ADP release)/K 0.5,MT ϭ 7.55 M Ϫ1 s Ϫ1 . This rate constant is 1.5-or 2.9-fold larger than the apparent rate constant determined in steady-state assays and the ratio k bi,ratio ϭ k bi (ATP)/k bi (ADP) ϭ 1.5 or 2.9, depending on the model. According to Ref. 3, this number is an estimate for the numbers of ATP molecules hydrolyzed per encounter between NcKin3 and the microtubule, indicating that NcKin3 is a motor protein that performs one or few catalytic cycles per microtubule encounter.
Microtubule Detachment-To test whether the release rate of NcKin3 from microtubules agrees with a low degree of processivity, we measured the ATP-induced dissociation of the NcKin3-558 microtubule complex (Fig. 6). A kinesin that detaches after a single step or chemical cycle is expected to show a detachment rate as fast as its k cat or faster.
We measured detachment rates in a stopped-flow apparatus, where the dissociation of kinesin and microtubules is observed by the change of light scattering. As this assay is only interpretable if the weak microtubule-binding nucleotide state is known, we tested the affinities of monomeric and dimeric NcKin3 constructs in the presence of ADP and the nonhydrolysable ATP analogue AMP-PNP in microtubule co-sedimentation assays (supplemental Fig. S4). As observed for all other kinesins tested so far, both mutants display a roughly 7-fold lower K D value in the ADP state compared with the AMP-PNP state (0.20 Ϯ 0.16 M), suggesting that NcKin3 dissociates from the filament in the ADP-bound state (1.4 Ϯ 0.8 M).
Microtubule detachment rates were measured in dependence of ATP concentrations from 0 to 64 M. The light scattering signals showed a single exponential time course. The absence of a scattering signal change in control experiments FIGURE 5. Chemical processivity of the NcKin3 protein. A, the steady-state ATPase rate of NcKin3 was measured at variable microtubule concentrations. Based on the concentrations of polypeptide chains, the k cat was 11.6 s Ϫ1 . Considering that only one of two heads participates in the microtubule-dependent ATPase reaction, the k cat is 23.2 s Ϫ1 . The K 0.5,MT was 1.0 M, and the k cat /K 0.5,MT was 11.6 or 23.2 M Ϫ1 s Ϫ1 . B, to determine the ADP release rate, mant-ADP loaded NcKin3 was mixed with microtubules in a stopped-flow apparatus. The rates of the single exponential decays were plotted against the microtubule concentration. Each data point is an average of at least five individual stopped-flow traces. The data points were fitted to a hyperbolic function (solid line), which was the best fit for the given data. The k obs was 7.55 s Ϫ1 ; the K 0.5,MT was 0.94 M, and the k obs /K 0.5,MT was 8.03 M Ϫ1 s Ϫ1 . The ratio between the steady-state and the pre-steady-state binding rates (k bi ratio (46)) is thus 1.5 or 2.9. DECEMBER 8, 2006 • VOLUME 281 • NUMBER 49 without microtubules and without ATP showed that the traces represented dissociation events. The rates showed a hyperbolic dependence on the ATP concentration with a maximum detachment rate of k max ϭ 22.19 Ϯ 7.64 s Ϫ1 and a half-maximal activation constant of K1 ⁄ 2 ϭ 2.22 Ϯ 2.75 M ATP (Fig. 6). Thus, k max was similar to the steady-state turnover rate (k cat ϳ23 s Ϫ1 ), the K1 ⁄ 2 similar to the K m,ATP value of steady-state ATP hydrolysis (K m,ATP ϭ 4.0 Ϯ 0.9 M).

Nonprocessive Kinesin-3 Motility
To rule out that the observed scattering signal results from mixing artifacts in stopped-flow experiments, detachment rates were also measured in a flash-photolysis apparatus. Here, light-induced liberation of ATP from caged ATP induces the dissociation of the NcKin3 microtubule complex (supplemental Fig. S3). These assays showed single exponential release kinetics, excluding the existence of fast rates invisible in stopped-flow assays. They also support that the traces observed in stopped-flow scattering assays represent dissociation events. The slower rates observed in flash photolysis experiments were most likely because of the inhibitory effect of caged ATP (48).
Duty Ratio-To support the hypothesis that NcKin3 is a dimeric, nonprocessive motor, we estimated its duty ratio from comparisons of K 0.5,ATP in gliding and enzymatic assays (Fig. 7) (47). The duty ratio, r, is defined as the time fraction of the catalytic cycle a motor spends in the strongly filament-bound state. The ratio of K 0.5,ATP measured in the steady-state ATPase assay and K 0.5,ATP measured in the multiple motor gliding assays is a reasonable estimate for this value because the K 0.5,ATP in the gliding assay reflects the situation where half of the molecules "wait" for ATP in the microtubule-bound state, whereas the K 0.5,ATP in the steady-state ATPase results from intermediates of the entire cycle, including the unattached states (47). For NcKin3 the values for K 0.5,ATP in gliding and ATPase assays strongly deviate. In the steady-state ATPase, we measured K 0.5,ATP ϭ 4.0 Ϯ 0.9 M in the multiple motor gliding assays K 0.5,ATP ϭ 138.0 Ϯ 49.5 M (Fig. 6). This results in a duty ratio of r ϭ 0.03, which means that NcKin3 spends only 3% of the catalytic cycle attached to the filament. This ratio is typical for nonprocessive enzymes that work in ensembles. Motors that move processively based on a hand-over-hand mechanism of two motor heads require duty ratios of at least 0.5.
Knowledge of the duty ratio, k cat value, and gliding velocity (v gld ) allows estimation of working distances (⌬) of molecular FIGURE 6. Microtubule detachment of Nckin3. The dissociation of the preformed NcKin3 microtubule complex was induced by ATP in a stopped-flow apparatus and followed by the change of the light scattering signal. A shows a representative average from 5 traces. The gray curve is a mono-exponential fit to the data that was used to derive the rates, k obs . B, plots k obs against the ATP concentration, and B shows a hyperbolic dependence with a k max of 22.2 s Ϫ1 and a K1 ⁄2 of 2.2 M, comparable with the steady-state parameters k cat and K 0.5,ATP . FIGURE 7. Duty ratio. A and B show example measurements of the gliding velocity and the ATPase rate of NcKin3-558 in dependence of the ATP concentration. The ratio of K m,ATP in these assays served to estimate the duty ratio (47). The average K m,ATP in ATPase assays was 4.0 Ϯ 0.9 and 138.0 Ϯ 49.5 M in gliding assays, suggesting a duty ratio of 0.03. motors (47): ⌬ ϭ (v gld ϫ r)/k cat . Accordingly, NcKin3-558 is calculated to have a working distance of (0.59 m s Ϫ1 ⅐0.03)/ 23.2 s Ϫ1 ϭ 0.8 nm (Fig. 8). In comparison to processive kinesins, or the distance between two tubulin dimers in the microtubule (8.1 nm), this is a very short distance and hardly compatible with a hand-over-hand mechanism.

DISCUSSION
Our data indicate that NcKin3 is a dimeric and nonprocessive kinesin motor with unique mechanistic properties (Fig. 8) as follows. 1) The velocity for microtubule gliding depends on the NcKin3 coating density of the flow chamber and is faster than predicted from ATP turnover and reasonable stroke size dimensions. This indicates a cooperative action of several motors at a single microtubule. 2) The ADP release from the two heads is not coupled, and only one head interacts with the microtubule. Microtubule-induced mant-ADP release is a twostep process with a fast and a slow rate. The slow rate, presumably resulting from the free microtubule unbound head, is 2 orders of magnitude slower than the k cat value and independent of the microtubule concentration. This excludes a hand-overhand mechanism.
3) The chemical processivity of NcKin3 is low. The ratio of apparent bimolecular binding in steady-state ATPase assays and mant-ADP release experiments of 1.5-3 suggests only few catalytic cycles per microtubule encounter, after which NcKin3 detaches from the microtubule. This is supported by microtubule detachment rates that resemble the k cat value. 4) NcKin3 has a low duty ratio (r ϳ0.03), implying that it cannot use a hand-over-hand type mechanism. If the motor is bound only 3% of its chemical cycle time to the filament, even a dimer is not sufficient to support a continuous microtubule association. These arguments suggest that NcKin3 also acts cooperatively in the cellular environment. In vivo, the protein is found on mitochondria, which are likely to harbor a large number of motors. Coating density fluctuations or local clustering might be a means of regulating mitochondria shape and transport speed.
The comparison of NcKin3 with other kinesin motors shows important features that have not been observed in other kinesins so far. As our data are incompatible with a hand-over-hand mechanism, NcKin3, it clearly differs from processive Kinesin-1, -2, and -5 motors. NcKin3 also differs from other Kinesin-3 motors, although some of its kinetic features may hold true for other Kinesin-3 members as well. KIF1A has been extensively used as a model for Kinesin-3 motors. It can function as a monomeric, quasi-processive motor (19,45). In this motility mode, it presumably proceeds by a combination of ATP-dependent microtubule affinity changes and the action of the K-loop that tethers the motor at the microtubule during phases of weak affinity (18,20). It was shown that the average displacement was coupled to a single ATP hydrolysis, although fluctuations in the velocity and directionality indicate a stochastic, diffusive nature of movement. An asymmetric binding potential might impose the bias to the microtubule plus end. In contrast to KIF1A, NcKin3 does not have the structural prerequisites to move in this manner because it does not contain a fully developed K-loop (Fig. 1).
Another member of the Kinesin-3 family has been studied in detail, the Unc104 motor from C. elegans. The bacterially expressed CeUnc104 motor is monomeric and does not support processive movement in single molecule assays (22). Only CeUnc104 mutants that were dimerized artificially by a synthetic coiled coil domain showed processive runs (23). Transport of associated cargo was only observed when two protein chains were artificially connected or forced to dimerize by very high local motor concentrations (24). It is unclear whether the same mechanism applies to KIF1A because the constructs used for the studies are not comparable. Mouse KIF1C and D. discoideum Unc104, however, were found as a dimers in vivo, leaving the possibility that KIF1A behaves aberrantly (44,50).
The observations on CeUnc104 indicate that Kinesin-3 activity might be regulated by dimerization in vivo. This is clearly not the case for NcKin3 that is constitutively dimeric but not processive, excluding that regulation by dimerization is a general feature of Kinesin-3 motors. Whether the mechanistic basis of dimerized CeUnc104 constructs differs fundamentally from NcKin3 is unclear because CeUnc104 has not been investigated in biochemical assays for processivity. It may be interesting to investigate other Kinesin-3 motors in kinetic assays and to test their head-head coordination.
In its kinetic properties, NcKin3 most closely resembles Ncd, a nonprocessive minus end-directed Kinesin-14 from D. melanogaster (9 -13, 51-54). Like NcKin3, Ncd consists of two identical polypeptide chains that show different affinities to ADP. However, unlike NcKin3 both Ncd motor domains are able to interact with the microtubule (11,55,56). First, the motor head with the lower affinity for ADP binds to the microtubule, whereas the second head is detached and points toward the microtubule minus end (15,51). According to Ref. 13, the motor detaches from the microtubule after binding a new ATP and is then competent to re-bind with either of its heads. Alternatively, ATP hydrolysis of the first head may allow binding of the partner head to the next ␤-tubulin subunit in the minus end direction (52). Subsequently, the other FIGURE 8. Model of NcKin3 function. NcKin3 is a homodimeric motor (gray) that interacts with one head with the microtubule, whereas the second head (white) is not activated by microtubules. ATP binding to the nucleotide-free, microtubule-bound head and subsequent catalytic events induce a power stroke that leads to a working distance of a calculated size of 0.8 nm (see text and Ref. 47). Afterward, the motor dissociates from the microtubule (probably in the ADP-state) and has to be converted into the pre-power-stroke conformation to allow the next catalytic round.
head would hydrolyze a second ATP before it entered a state where the motor dissociated from the microtubule. According to this model, one step of Ncd requires the hydrolysis of two ATP molecules.
Either mechanism is unlikely for NcKin3 because the mant-ADP release from the high affinity site was much slower than k cat and equal to the basal activity. It was also independent of the microtubule concentration up to a 10-fold excess of tubulin over motor heads. Hence, there is no sign of microtubule interaction of the second head. However, like Ncd NcKin3 probably uses a power-stroke mechanism for generation of motility (15,55), but because Ncd is a minus end motor, the stroke has to be oriented toward the opposite direction.
In summary, these comparisons show that NcKin3 moves by a mechanism so far unknown for kinesins. Possibly, the motor is adapted to special requirements of mitochondria shaping. A high local motor accumulation may allow microtubule interaction and local expansion of the mitochondrion. Filamentous fungi are known to possess networks of elongated mitochondria, whose shape depends on intact microtubules (57)(58)(59). Alternatively, the motor serves additional cellular functions, which require a nonprocessive motor.
An interesting future question is the functional role of the second motor head. The truncated constructs used in this study provide only limited insight because the lack of large protein portions is likely to induce major structural defects. More sophisticated chimeric constructs are required to overcome these limitations. Possibly, one of the two heads contacts the microtubule in a similar way as the K-loop of Kif1A and acts as a passive tether. Alternatively, the second head might influence the catalytic cycle of the microtubule-bound head by an allosteric effect. It will be interesting to study artificial singleheaded heterodimeric motors to elucidate the function of the second head. This and other studies show that the hand-overhand mechanism may not be a general principle for kinesin motors. It will therefore be interesting to track down the elementary process of generation of motility.