Drosophila Ncd reveals an evolutionarily conservedpowerstroke mechanism for homodimeric andheterodimeric kinesin-14sPengwei Zhanga,1, Wei Daib,1, Juergen Hahnb,c,2, and Susan P. Gilberta,2

aDepartment of Biological Sciences, bDepartment of Chemical & Biological Engineering, and cDepartment of Biomedical Engineering, Center forBiotechnology and Interdisciplinary Studies, Rensselaer Polytechnic Institute, Troy, NY 12180

Edited by Thomas D. Pollard, Yale University, New Haven, CT, and approved April 14, 2015 (received for review March 21, 2015)

Drosophila melanogaster kinesin-14 Ncd cross-links parallel microtu-bules at the spindle poles and antiparallel microtubules within thespindle midzone to play roles in bipolar spindle assembly and properchromosome distribution. As observed for Saccharomyces cerevisiaekinesin-14 Kar3Vik1 and Kar3Cik1, Ncd binds adjacent microtubuleprotofilaments in a novel microtubule binding configuration anduses an ATP-promoted powerstroke mechanism. The hypothesistested here is that Kar3Vik1 and Kar3Cik1, as well as Ncd, use acommon ATPase mechanism for force generation even though themicrotubule interactions for both Ncd heads are modulated by nu-cleotide state. The presteady-state kinetics and computational mod-eling establish an ATPase mechanism for a powerstroke model ofNcd that is very similar to those determined for Kar3Vik1 and Kar3-Cik1, although these heterodimers have one Kar3 catalytic motordomain and a Vik1/Cik1 partner motor homology domain whoseinteractions with microtubules are not modulated by nucleotidestate but by strain. The results indicate that both Ncd motor headsbind the microtubule lattice; two ATP binding and hydrolysis eventsare required for each powerstroke; and a slow step occurs aftermicrotubule collision and before the ATP-promoted powerstroke.Note that unlike conventional myosin-II or other processive molecu-lar motors, Ncd requires two ATP turnovers rather than one for asingle powerstroke-driven displacement or step. These results aresignificant because all metazoan kinesin-14s are homodimers, andthe results presented show that despite their structural and func-tional differences, the heterodimeric and homodimeric kinesin-14sshare a common evolutionary structural and mechanochemicalmechanism for force generation.

presteady-state kinetics | dynamic modeling | microtubules

In the early stages of mitosis and meiosis, the bipolar metaphasespindle must be established, and kinesin-14 molecular motors

play key roles in this process (1–4). In contrast to the microtu-bule (MT) plus-end directed processive kinesins, kinesin-14s arenot processive as single molecules; they promote MT minus-end-directed force and use an ATP-promoted powerstroke to cross-link and slide one MT relative to another (5–17). Sequenceanalysis indicates that all members of the kinesin-14 subfamily aredimeric, yet the structural organization of kinesin-14 motors differsfrom the N-terminal processive kinesins. The kinesin-14s exhibitC-terminal motor domains connected by an N-terminal continu-ous coiled-coil stalk with an N-terminal ATP-independent MTbinding site (7, 18–22). And although most of the kinesin-14sare homodimeric, some yeast species, including Saccharomycescerevisiae and Candida glabrata, contain heterodimeric kinesin-14s(13, 14, 19). The conventional hypothesis for homodimerickinesin-14 force generation proposed that only one motor headinteracts with the MT and only one ATP turnover is required tocomplete the powerstroke (Fig. S1A) (10, 12). In contrast, our pre-steady-state kinetics (9, 23, 24) and the results of Kocik et al. (25)concluded that both Ncd heads were required for Ncd forcegeneration and also documented cooperative interactions be-tween the Ncd heads during ATP-promoted MT interactions.

The scheme in Fig. S1B accounted for these results and proposedthat both Ncd heads interact with the microtubule, and two ATPturnovers are required (24).Through our recent studies on S. cerevisiae Kar3Vik1 and

Kar3Cik1, we discovered novel properties of these yeast kinesin-14s that challenged the earlier models of how kinesin-14s gen-erate force for their cellular functions (13, 15, 26–28). TheC-terminal globular domain of Vik1 exhibits the structure of akinesin motor domain (MD), yet Vik1 as well as Cik1 lack anucleotide-binding site (13, 26). Because the C-terminal domainof Vik1 binds MTs independently of Kar3 and with high affin-ity (26), it was designated the Vik1 motor homology domain(MHD). A series of site-directed cross-links at the base of thecoiled coil near the motor heads of Kar3Vik1 were introduced,and motility assays indicated that both the Kar3MD andVik1MHD must interact with the MT lattice to generate sustainedMT gliding, yet significant unwinding of the coiled coil was notrequired (>10 Å but <20 Å) (13). This series of experiments led tothe proposal that Kar3Vik1 binds the MT lattice on adjacent MTprotofilaments rather than a single protofilament in a head-to-tailfashion because such a small degree of unwinding of the coiled coilwould not allow the 8-nm separation required for the two-headbound state. Indeed, high-resolution unidirectional metal shad-owing, which strongly emphasizes the surface features whenviewed by EM, also captured this mode of MT binding in thepresence of ADP. The unidirectional metal shadowing experi-ments were repeated for Kar3Cik1 and Ncd, and both exhibitedthis noncanonical MT binding configuration, suggesting thatthe adjacent MT protofilament binding configuration may be

Significance

Kinesin molecular motors couple ATP turnover to force productionto generate microtubule-based movement and microtubule dy-namics. Kinesin-14s are unique in that they are nonprocessive,bind to adjacent microtubule protofilaments rather than stepalong a single protofilament as observed for processive kinesins,and use a powerstroke mechanism to slide microtubules. Earlierstudies proposed that only one head of the Ncd dimer interactswith the microtubule to drive the ATP-promoted powerstroke andtherefore only one ATP turnover was required. The results pre-sented here challenge the one head/one ATP turnover hypothesisand define a common pathway for Kar3Vik1, Kar3Cik1, and Ncd.These findings are significant because they reveal that the keyprinciples for force generation by kinesin-14s are conserved fromyeast to higher eukaryotes.

Author contributions: P.Z., W.D., J.H., and S.P.G. designed research; P.Z. and W.D. per-formed research; P.Z., W.D., J.H., and S.P.G. analyzed data; and P.Z., W.D., J.H., and S.P.G.wrote the paper.

This article is a PNAS Direct Submission.1P.Z. and W.D. contributed equally to this work.2To whom correspondence may be addressed. Email: sgilbert@rpi.edu or hahnj@rpi.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1505531112/-/DCSupplemental.

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characteristic of kinesin-14s in general and not specific to Kar3Vik1and/or Kar3Cik1 (15).CryoEM and subsequent helical reconstruction of the MT

complexes of Kar3Vik1 and Kar3Cik1 at different nucleotidestates captured the same nucleotide-dependent powerstroke in-termediates as reported for Ncd (10–13, 15). Apyrase was usedto generate the nucleotide-free prepowerstroke state (Fig. 1,E4), and AMPPNP, the nonhydrolyzable ATP analog, revealed apostpowerstroke intermediate in which the coiled-coil stalk wasrotated ∼70 degrees toward the MT minus end (Fig. 1, E5).Because Kar3Vik1, Kar3Cik1, and Ncd share common structuralsimilarities at distinct nucleotide states, we hypothesized thatNcd must use the same series of structural transitions for forceproduction even though both Ncd motor heads are catalytic.Therefore, a series of experiments were pursued to test the

proposed scheme presented in Fig. 1 and to validate or rule outtwo earlier models (Fig. S1). The following assumptions weremade based on earlier studies (9, 13, 23, 24, 26–28): (i) In so-lution, homodimeric Ncd exhibits an asymmetry in which onehead holds ADP tightly bound while the partner head holdsADP weakly (E0) (24). (ii) MT collision is followed by rapidADP release (E0–E1) (24). (iii) By analogy to Kar3Vik1, thehead that initially collides with the MT (E1) binds α-tubulin in anoncanonical MT binding configuration and is rotated relative toits partner head that binds β-tubulin (E4) (13, 26). (iv) ATPbinding at the first head (E2) promotes MT binding of thepartner head followed by ADP release to generate the pre-powerstroke intermediate (E2–E4) (24) (v) ATP binding at head2 generates the postpowerstroke intermediate with the coiled-coil stalk rotated ∼70° (E5) (10, 12). (vi) Motor detachment fromthe MT occurs after the ATP-promoted powerstroke and afterATP hydrolysis (E5–E6) (23). (vii) There are two ATP bind-ing and hydrolysis events to generate one powerstroke (9, 24).(viii) The powerstroke occurs later in the scheme and can onlyoccur upon ATP binding to the Ncd head bound to β-tubulin(10, 12). (ix) Ncd•ADP•Pi rather than Ncd•ADP may be theweakest MT binding state for at least one of the Ncd heads basedon earlier MT•Ncd cosedimentation studies (E3 and/or E6) (23).

ResultsTwo ATP Turnover Events Are Required Per Powerstroke. Beforepursuing new experiments to test the mechanism in Fig. 1, thepulse-chase and acid-quench presteady-state kinetics experi-ments were repeated to evaluate whether two ATP binding andhydrolysis events were required before Ncd detachment from theMT as proposed previously (9, 24). For these experiments, thepreviously characterized N-terminal truncation of Ncd MC1 wasused (9, 23, 24, 29).The results presented in Figs. S2 and S3 and Table S1 show

conclusively that two ATP turnovers occurred before Ncd de-tachment from the MT with the interpretation that there was oneATP turnover per Ncd head. These results rule out the model inFig. S1A, in which only one Ncd head interacts with the MT andone ATP binding event drives the rotation for the powerstroke(10, 12). However, these results are consistent with the earlierscheme proposed by Foster et al. (24) (Fig. S1B).

The Foster et al. model (24) (Fig. S1B) was based on the as-sumption that the Ncd would have an ATPase mechanochemicalcycle more similar to that of kinesin-1 in that there was a MT two-head bound state with one true step, and the second ATP turnoverwas required to detach Ncd from the MT. Note that this modelwas proposed before the publications that supported the Ncd le-ver-arm rotation model (10–12). With the more recent insightsfrom studies on Kar3Cik1 and Kar3Vik1, a fresh perspective wasneeded to test these models, and the next series of experimentswere designed to reveal transient intermediates that were notcaptured previously by mechanistic or structural studies.

A Slow Structural Transition Is Required Before ATP Binding. A newexperiment was designed to mimic the reaction condition at thebeginning of the cycle where Ncd collides with the MT followedby ADP release and subsequent ATP binding at head 1 (Fig. 1,E0–E2). For Kar3Cik1 and Kar3Vik1, this strategy was necessaryto capture the transient E1 state in which the MHD collided withthe MT first (27, 28). For these experiments, 10 μM Ncd•ADPwas rapidly mixed in the stopped-flow instrument with 40 μMMTs plus the fluorescent ATP analog 2′-(3′)-O-(N-methylan-thraniloyl) ATP (mantATP). At these concentrations (final:5 μM Ncd•ADP, 20 μM MTs), Ncd MT association is fast andoccurs before mantATP binding (Table S1). Fig. 2A shows rep-resentative transients at 0.5–5 μM mantATP, and Fig. 2B pre-sents the observed rates of mantATP binding as a function ofmantATP concentration. A hyperbolic function plus a y-interceptwas fit to the data and provided the maximum rate constant of4.4 s−1. Previous experiments at similar conditions measured therate constant of mantATP binding to the preformed MT•Ncdcomplex at 2.3 μM−1·s−1, or for example 35 s−1 at 15 μMmantATP (9). Furthermore, mantADP release from the activesite of the first Ncd head upon MT collision was 17.8 s−1 (24)(Table S1). Therefore, these results are consistent with a slowconformational change that occurs after MT collision followedby fast ADP release and before ATP binding. We propose thatthe experimental design in Fig. 2 has captured the slow con-formational change that occurs after MT collision to form thetransient E1 intermediate that is poised to bind ATP.If a slow conformational change were required to form the E1

intermediate poised for ATP binding, then this step can bebypassed by preforming the MT•Ncd intermediate. This strategywas used to measure the kinetics of ATP binding and ATP hy-drolysis revealing that both were fast events (Figs. S2 and S3)and to measure the kinetics for phosphate release (Fig. 3 A–C).

The Intrinsic Rate Constant of Phosphate Release Is Fast. To measurethe kinetics of phosphate release, the Martin Webb fluorescentlylabeled phosphate binding protein (MDCC-PBP) assay was used(30, 31). The MT•Ncd complex was preformed, MDCC-PBP wasadded (final concentrations: 2.5 μM Ncd•ADP, 20 μM MTs, 10μM MDCC-PBP), and then the reactants were rapidly mixedwith ATP plus KCl. The additional salt in the ATP syringe doesnot affect the first ATP turnover but limits additional ATPturnovers by weakening the binding of the second motor headto the MT (31). ATP binding and hydrolysis occur rapidly atthe active site, followed by phosphate release. The phosphate

Fig. 1. Proposed Ncd powerstroke mechanism. Homodimeric Ncd in solution is asymmetric with one head holding ADP tightly bound and the other head withADP weakly bound. The cycle begins with MT collision of head 1 (low ADP affinity, yellow) followed by rapid ADP release to form intermediate E1. ATP binds tohead 1, promoting the association of head 2 (blue head) to the adjacent MT protofilament to form the E2 transient intermediate. ATP hydrolysis is required athead 1 for release of ADP from head 2. This transition results in the prepowerstroke E4 intermediate with head 2 tightly bound and nucleotide-free, and head 1detached from the MT. ATP binding at head 2 drives the ∼70° rotation of the coiled-coil stalk toward the MT minus end forming the E5, postpowerstroke state.ATP hydrolysis at head 2 leads to Ncd detachment from the MT (E6), followed by its rapid transition to the E0 intermediate poised for MT binding.

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released to solution was bound rapidly and tightly by MDCC-PBP, eliciting an increase in fluorescence that can be quantified(Fig. 3). Fig. 3A shows representative transients at varying ATPconcentrations. These transients are biphasic and display a lag,attributed to ATP binding and ATP hydrolysis. The observedrate of the initial exponential phase of each transient was plottedas a function of ATP concentration (Fig. 3B), and the hyperbolicfit to the data provides the maximum rate constant of phosphaterelease at 14.3 s−1.A phosphate standard curve (Fig. 3C, Inset) was used for each

transient to convert the exponential amplitude associated withphosphate release in units of relative fluorescence to units of phos-phate concentration. The hyperbolic fit to the data (Fig. 3C)revealed a maximum amplitude of 1.1 μM phosphate for 2.5-μM Ncd sites, indicating that the phosphate release data rep-resent 44% of the sites. These results are consistent with theinterpretation that the experimental design for Fig. 3 A–Ccaptured the intrinsic rate constant of phosphate release fromhead 1 that occurs after step E3 due to the additional salt addedin the ATP syringe for this experiment.

The Slow Structural Transition After MT Collision Can Also Be Capturedby Phosphate Release Kinetics. If a slow conformational change wererequired for ATP binding, then the rate constant of phosphaterelease would also be slow because phosphate release occurs afterATP binding and ATP hydrolysis. Fig. 3 D–F shows the results inwhich the kinetics of phosphate release were measured from head1 and head 2. This experimental design mimicked the start of thecycle as in Fig. 2 where 10 μMNcd•ADP plus 15 μMMDCC-PBPwere rapidly mixed in the stopped-flow instrument with 40 μMMTs with varying ATP (final: 5 μM Ncd•ADP, 7.5 μM MDCC-

PBP, 20 μM MTs). Note that no additional KCl was added to theATP syringe, and at the conditions of this experiment, Ncd•ADPcollision with the MT occurs before ATP binding. Once ATPbinding and hydrolysis occur, phosphate is released from the ac-tive site. MDCC-PBP rapidly binds the free phosphate released tothe solution resulting in an increase in fluorescence. Fig. 3D showsrepresentative transients, and the observed rate of the initial ex-ponential phase associated with phosphate release was plotted as afunction of ATP concentration (Fig. 3E). The hyperbolic fit to thedata provided a maximum rate constant for phosphate release at2.9 s−1, consistent with the interpretation that a slow conforma-tional change must occur before ATP binding to limit the rate ofphosphate release.The phosphate standard curve in Fig. 3F was used to convert

the exponential amplitude associated with phosphate release inunits of relative fluorescence to units of phosphate concentration,and these data were plotted as a function of ATP concentration.The amplitude data can be correlated with the concentration ofNcd sites (5 μM Ncd•ADP) that bind and hydrolyze ATP, fol-lowed by phosphate release. The maximum amplitude at 5.7 μM(1.1 Pi/Ncd site) is consistent with the interpretation that two ATPturnover events were required before Ncd detachment from theMT (Fig. 1, E0–E6).The phosphate release kinetics (Fig. 3), in combination with

the results from Fig. 2, place a slow step early in the scheme afterMT collision and before ATP binding. The experimental designfor Fig. 3 A–C captured phosphate release after one ATP turn-over from head 1 and revealed that phosphate release is in-trinsically a fast step at 14.3 s−1.

Computational Modeling of the Proposed Mechanism. To test thevalidity of the proposed mechanism in Fig. 1, we performed com-putational modeling. The transients in Fig. 2A were fit to a singleexponential equation. However, from a modeling perspective, thistype of model is the analytical solution of a certain class of dynamicsystems described by a set of linear ordinary differential equations(ODEs). Though the exponential equation fits the experimentaldata with a very good degree of accuracy, it has to be refit fordifferent experimental conditions potentially due to the existence ofnonlinearity in the powerstroke process, which makes the estimatedparameter values inconsistent and difficult to interpret. Therefore, afirst principles-based model represented by nonlinear ODEs (32)was developed with the goal to capture the dynamics of the Ncdpowerstroke process (shown in Fig. 1) for a variety of differentinitial concentrations of mantATP (Fig. 2). The model is describedin more detail below and summarized in Fig. 4.E0 → E1. The start of the Ncd powerstroke consists of three sep-arate steps: (i) Ncd in solution with ADP on both heads,Ncd•ADP•ADP (denoted as X1 here) collides with a MT andforms the MT•Ncd•ADP•ADP collision complex (denoted asN1): X1 ⇌N1. Because this step is fast and reversible, the reactionwill quickly reach an equilibrium where the ratio of [N1] to [X1],where [ ] represents the concentration, is a constant denoted byK1. (ii) After MT collision, ADP on the first Ncd head is releasedto form the MT•Ncd•Ø•ADP intermediate (denoted as N2).Here, Ø represents an empty active site: N1 ⇌N2. This step isfast and reversible, i.e., it will quickly reach equilibrium, thusthe ratio of [N2] and [N1] is a constant denoted by K2. (iii) TheMT•Ncd•Ø•ADP intermediate undergoes a conformational changeand forms the MT•Ncd*•Ø•ADP intermediate (denoted as X2).Here, * represents the complex after the conformational change hastaken place: N2 ⇌X2. When writing the rate expression, the con-stants K1 and K2 can be combined as part of the overall reaction rateto yield the following expression:

X1�k1

k−1X2, [1]

where k1 and k-1 represent the reaction rates where the informa-tion from the three steps above are combined. Eq. 1 describes

Fig. 2. MantATP binding following MT•Ncd association. Ncd•ADP was rap-idly mixed in the stopped-flow instrument with MTs plus increasing concentra-tions of mantATP. Final concentrations: 5 μM Ncd•ADP sites, 20 μM MTs, and0.5–15 μMmantATP. (A) Transients are shown from low to high concentrations:0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, and 5 μM mantATP, and a single exponentialfunction was fit to each. (B) The observed rates of the exponential phase ofmantATP binding were plotted as a function of mantATP concentration. Ahyperbolic function plus a y-intercept was fit to the data, which provided themaximum rate constant of 4.4 ± 0.2 s−1, koff of 1.8 ± 0.1 s−1, and K1/2,mantATP of9.4 ± 1.4 μM. (Inset) Illustration of experimental design.

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the process before the binding of mantATP to the first headof Ncd.E1→ E2.MantATP (denoted asM) binds the first head and formsMT•Ncd*•mantATP•ADP (denoted as X3). A fluorescencesignal is released during this step. The model describing this stepis given by

X2 +M�k2k−2

X3, [2]

where k2 is the binding rate of mantATP to the first head and k-2is the mantATP dissociation rate constant.E2 → E3. MantATP hydrolysis at the first head is fast andnonreversible.E3 → E4. MantATP binding at the first head signals the secondNcd head to bind to the MT and release ADP. MantATPhydrolysis forms the MT•Ncd*•mantADP•Pi•Ø intermediate(denoted as X4) in this process. The Ncd*•mantADP•Pi headmay detach from the MT followed by rapid phosphate release orphosphate release may occur first followed by detachment asNcd*•mantADP. This coupled event is slow and weakly re-versible. Therefore, the steps from E2 to E4 can be combinedand modeled as follows:

X3 →k3 X4, [3]

where k3 is a reaction rate incorporating the entire process afterthe binding of mantATP to the first head and before mantATPbinding to the second head. It should be noted that the

fluorescence signal still exists when mantADP is bound tothe first head; however, the intensity may potentially change.E4 → E5. MantATP binds to the second head (denoted as M)to form the MT•Ncd*•mantADP•mantATP intermediate.MantATP binding to the second head promotes the rotationof the coiled-coil stalk, i.e., the powerstroke, and these coupledreactions are fast.E5 → E6. MantATP on the second head is hydrolyzed, and thenPi is released to form the MT•Ncd*•mantADP•mantADP in-termediate (denoted as X5). This process is fast and non-reversible. Because the fluorescence signal still exists aftermantATP hydrolysis, although the change of intensity is un-known, the processes from E4 to E6 are combined and mod-eled as follows:

X4 +M→k4 X5, [4]

where k4 represents the reaction rate, including the process ofmantATP binding to the second head and the subsequenthydrolysis.

Parameter Estimation. The initial concentration of mantATP isdifferent in each of the nine experiments (Fig. 2A). Dataobtained from experiments 1, 3, 5, 7, and 9 were used for modelfitting via parameter estimation, and data obtained from exper-iments 2, 4, 6, and 8 were used to further validate model pre-diction accuracy (Fig. 4). The method used for estimation isexplained in detail in SI Materials and Methods. The estimatedparameters are listed in Fig. 4C, and the simulation results usingthe estimated parameters are shown in Fig. 4D. It can be seen

Fig. 3. Phosphate release. (A–C) Phosphate releasefrom the MT•Ncd complex. The MT•Ncd complexwas preformed, and subsequently the MT•Ncdcomplex plus MDCC-PBP were rapidly mixed in thestopped-flow instrument with the increasing con-centrations of MgATP plus 200 mM KCl (syringeconcentration). The fluorescence enhancement ofMDCC-PBP upon binding inorganic phosphate(Pi) was monitored. Final concentrations: 2.5 μMNcd•ADP sites, 20 μM MTs, 10 μM MDCC-PBP, 0.025U/mL PNPase, 75 μM MEG, and 1.25–500 μM MgATP.(A) Representative transients of Pi product releasefrom Ncd following ATP hydrolysis are shown fromlow to high concentrations: 0, 1.25, 2.5, 5, 10, 25,and 100 μM of MgATP. (B) The observed exponentialrate of Pi release from each transient was plotted asa function of MgATP concentration, and the hy-perbolic fit to the data provided kmax = 14.3 ± 0.3 s−1

and K1/2,ATP = 23.3 ± 2.3 μM. (Inset) Experimentaldesign. (C) The amplitude (A0) of the initial expo-nential phase of each transient was plotted as afunction of MgATP concentration, and the hyper-bolic fit to the data provided the maximum ampli-tude A0,max = 1.1 ± 0.01 μM (∼44% Ncd sites). (Inset)Phosphate standard curve used to convert the rela-tive fluorescence in volts to micromolar Pi. (D–F)Phosphate release following MT•Ncd association.Ncd•ADP plus MDCC-PBP were rapidly mixed withMTs in the presence of increasing concentrations ofMgATP, and the fluorescence enhancement wasmonitored. Final concentrations: 5 μM Ncd•ADP,20 μM MTs, 7.5 μM MDCC-PBP, 0.025 U/mL PNPase,75 μM MEG, and 0.5–500 μM MgATP. (D) Represen-tative transients of Pi product release from Ncd fol-lowing ATP hydrolysis. (E) The observed exponentialrate of Pi release was plotted as a function ofMgATP concentration, and the hyperbolic fit to the data provided the maximum rate constant for Pi release at 2.9 ± 0.1 s−1 with K1/2,ATP = 16 ± 0.97 μM. (Inset)Illustration of the experimental design. (F) The amplitude of the initial exponential phase of each transient was plotted as a function of MgATP concentration,and the hyperbolic fit to the data provided A0,max = 5.7 ± 0.25 μM (∼1.1 Pi/Ncd site). (Inset) Phosphate standard curve used to convert the relative fluorescencein volts to micromolar Pi.

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that the results obtained for both the training and, more im-portantly, the validation sets are in good agreement with theexperimental data.Several conclusions can be drawn from the estimated param-

eters. First, parameter k1 has a value of 4.70 s−1, which is con-sistent with the assumption that the conformational change atthe start of the cycle is a slow step. Second, parameter k2 has avalue of 2.31 μM−1·s−1, which is within the commonly assumedrange of the ATP binding rate of 2–3 μM−1·s−1 and which wasexperimentally measured at 2.3 μM−1·s−1 (Table S1). Third, theparameter k3 has a value of 1.36 s−1, which is consistent with theexperimentally determined rate constant of mantADP releasefrom the second head at 1.4 s−1 and the steady-state ATPase kcatmeasured at 2.1 s−1 (Table S1). Fourth, parameter k4 has a valueof 2.52 μM−1·s−1, which is within the commonly assumed rangeof ATP binding rates of 2–3 μM−1·s−1.

DiscussionEarlier studies suggested that only one head of Ncd interactedwith the MT at a time (Fig. S1A), and the data were based oncryoEM studies that failed to capture a stable intermediate withboth Ncd heads bound to the MT (10, 12). MT gliding experi-ments were performed in which Ncd heterodimers with only onemotor head promoted wild-type rates of gliding, and the steady-state ATPase scaled with the concentration of motor heads (12).These results appeared at the time to provide definitive evidenceto support the one head/one ATP turnover powerstroke model.However, these studies can now be interpreted in the context ofmultiple single Ncd heads driving normal MT gliding.The studies with Kar3Vik1 and Kar3Cik1 provided insights for

another potential model for Ncd not previously considered be-cause the assumption at the time was that an Ncd homodimerwould bind to the MT in a head-to-tail fashion on a single MTprotofilament (Fig. S1B). The publications documenting thatKar3Vik1, Kar3Cik1, and Ncd bind to adjacent protofilamentson the MT lattice (13, 15) in combination with similarity in theirprepowerstroke and postpowerstroke intermediates resulted inthe experiments reported here to ask if homodimeric Ncd withtwo ATP binding sites can modulate MT interactions much likeKar3Vik1 and Kar3Cik1. The scheme in Fig. 1 guided the ex-periments and led to new insights.

The Initial Steps from E0 to E4 to Form the Prepowerstroke Intermediate.For Ncd, one head holds ADP tightly and the partner head holdsADP weakly (24); therefore, there is an asymmetry in Ncd remi-niscent of Kar3Vik1 and Kar3Cik1. We propose based on earlier

work that the initial collision with the MT occurs by the head thatholds ADP weakly resulting in rapid ADP release at 17.8 s−1 (Fig. 1,E0–E1; Table S1) (24). The results in Fig. 2 and Fig. 3 D–F indicatethat a slow conformational change at 4.4 s−1 must occur after MTcollision to generate the transient E1 intermediate poised for ATPbinding. ATP binding occurs rapidly at 2.3 μM−1·s−1 (Table S1) (9),and ATP binding at head 1 is required for head 2 to bind to theMT to form the E3 intermediate (24). However, in experimentsdesigned to look at mantADP release from head 2 specifically(E3–E4), ATP binding at head 1 was not sufficient for head 2 torelease mantADP upon MT association (24). Rather, ATP hydro-lysis was also required to generate the E4 prepowerstroke in-termediate (figure 3 in ref. 24). In other experiments designed tomeasure mantADP release from both heads upon MT collision byinclusion of ATP in the MT syringe (Fig. 1, E0–E4), the transientswere biphasic with an initial fast rate of mantADP at 14.2 s−1, fol-lowed by a second slow phase of mantADP release at 1.85 s−1 (Fig.S4; Table S1). These results are consistent with earlier studies aswell as the parameters obtained from the computational modeling(Fig. 4).

The Steps from E4 to E6 to Complete the Powerstroke. The experi-ments to measure the steps from E4 to E6 were performedpreviously (9, 23, 24), and we propose that head 2 is boundto β-tubulin and nucleotide-free. The pulse-chase experiments(Fig. S2) revealed a rapid ATP-promoted isomerization at 81 s−1,which has been interpreted to represent the structural transitionsrequired to form the intermediate poised for ATP hydrolysis (27,28). This postpowerstroke intermediate was captured by cryoEMusing the nonhydrolyzable ATP analog, AMPPNP (10, 12). Acid-quench experiments show that ATP hydrolysis was rapid at 26 s−1

(Fig. S3; Table S1) (9, 24) and was required for Ncd to detachfrom the MT (E6) (24). Interestingly, ATP hydrolysis for Kar3-Cik1 and Kar3Vik1 were also measured at 26 s−1 (27, 28),reflecting the similarity of residues at the pivot point for thecoiled-coil stalk rotation and the active site residue configurationfor ATP hydrolysis. The presteady-state kinetics performedpreviously measured the dissociation step at 12–14 s−1 (Table S1)(23, 24), and it is proposed that after detachment from the MT,the Ncd E6 intermediate returns to the E0 state, poised to rebindto the MT.

The Ncd•ADP•Pi State. For kinesins, the data suggest that the ADPstate is the weakest MT bound state. In fact, most kinesins,including Ncd, are purified with ADP bound at the activesites. However, when the equilibrium MT Ncd cosedimentation

Fig. 4. Modeling of the proposed mechanism.(A) Model components and the corresponding sym-bols. (B) The developed first principles-based modeldescribing the steps given in Eqs. 1–4 is written as aset of ODEs. (C) Unknown parameters are estimatedfor the model using data obtained from experiments1, 3, 5, 7, and 9 (Fig. 2A). (D) Model predictions usingestimated parameters. Circles are experimental dataunder different initial concentrations of mantATP(Fig. 2A). Solid lines are model predictions for thecases where experimental data were used for train-ing. Dashed lines are the model predictions where theexperimental data were not used for training but forvalidation.

Zhang et al. PNAS | May 19, 2015 | vol. 112 | no. 20 | 6363

BIOPH

YSICSAND

COMPU

TATIONALBIOLO

GY

experiments were performed, ADP generated an Ncd intermediatethat remained bound to the MT (23). The interpretation was thatbecause of the cooperativity, ADP remained bound to the headdetached from the MT with the MT-bound Ncd head, nucleotide-free. In fact, the only state that was weakly bound to the MT wasgenerated by the addition of 2 mM ADP plus potassium phosphate.These data were plotted as the fraction of Ncd partitioning to thesupernatant as a function of potassium phosphate concentration.Rather than showing a hyperbolic binding curve, a sigmoidalbinding curve was observed, indicating cooperativity between thetwo Ncd sites (23). Although it is not known whether detachmentof head 1 occurs as an ADP•Pi intermediate or whether phos-phate release occurs first at 14.3 s−1 followed by detachment asthe ADP state (E3–E4), it is reasonable to propose, based on thecosedimentation results and the noncanonical MT binding con-figuration, that head 1 detaches from the MT directly after ATPhydrolysis as the ADP•Pi state. In contrast, Ncd at E6 may de-tach as the Ncd•ADP state because the MT•Ncd E5 intermediateis bound to β-tubulin rather than α-tubulin. Regardless, the dataindicate that Ncd dissociation from the MT and phosphate releaseare coupled reactions with one occurring rapidly and the otheroccurring more slowly, and experimentally only the slow stepcan be observed.

The Computational Model. The results in Fig. 4 provide furtherevidence to support the proposed mechanism in Fig. 1. The twomost important parameters from the modeling were the predictionof a 4.7 s−1 structural transition that occurs after MT collision andbefore ATP binding, and a slow step of 1.37 s−1 associated withmantADP release and similar to the experimentally determinedrate constant of mantADP release at 1.4 s−1 from the second headand steady-state ATP turnover at 2.1 s−1 (Table S1). In fact, it isremarkable that the computational model fit the mantATP bind-ing experimental data so well.

The computational model was also used to test the validity ofthe Foster et al. (24) scheme in Fig. S1B, which lacks the slowconformational change at 4.7 s−1 early in the cycle. The modelpredictions for the Foster et al. (24) scheme do not fit the datawell, because almost all of the transients and several of thesteady states for intermediate mantATP concentrations arepoorly predicted by the model. Also, the fits lack the initial lagphase revealed by the experiments in Fig. 2 and captured by thecomputational model presented in this work in Fig. 4.In conclusion, the studies with S. cerevisiae Kar3Vik1 and

Kar3Cik1 provided new insights and challenged us to ask ex-perimentally whether homodimeric Ncd behaves more likeKar3Vik1 and Kar3Cik1 than the processive kinesins. The sig-nificance of the findings reported here is the conclusion that thekey principles for force generation by kinesin-14s are evolu-tionarily conserved from yeast to higher eukaryotes. In addition,the results show conclusively that for Ncd, two ATP turnoversare required to generate a single powerstroke displacement orstep in contrast to conventional myosin II (33) and the processivemyosins and kinesins, which require only a single ATP turnoverfor each step (34, 35). Therefore, this study implicates thehomodimeric kinesin-14s as a novel class of molecular motorswhere two ATP turnover events are required for each power-stroke-driven microtubule displacement or step.

Materials and MethodsErrors are reported as ±SEM. A complete description of the plasmids, pro-teins, and methods used is provided in SI Materials and Methods.

ACKNOWLEDGMENTS. This work was supported by NIH Grant 2R37GM54141(to S.P.G.), National Science Foundation Chemical, Bioengineering, Environ-mental, and Transport Systems Grant 0941313, and American Chemical SocietyPetroleum Research Fund Grant 50978-ND9 (to J.H.).

1. Endow SA, Henikoff S, Soler-Niedziela L (1990) Mediation of meiotic and early mitoticchromosome segregation in Drosophila by a protein related to kinesin. Nature345(6270):81–83.

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7. Sablin EP, et al. (1998) Direction determination in the minus-end-directed kinesinmotor Ncd. Nature 395(6704):813–816.

8. Pechatnikova E, Taylor EW (1999) Kinetics processivity and the direction of motion ofNcd. Biophys J 77(2):1003–1016.

9. Foster KA, Gilbert SP (2000) Kinetic studies of dimeric Ncd: Evidence that Ncd is notprocessive. Biochemistry 39(7):1784–1791.

10. Wendt TG, et al. (2002) Microscopic evidence for a minus-end-directed power strokein the kinesin motor Ncd. EMBO J 21(22):5969–5978.

11. Yun M, et al. (2003) Rotation of the stalk/neck and one head in a new crystal structureof the kinesin motor protein, Ncd. EMBO J 22(20):5382–5389.

12. Endres NF, Yoshioka C, Milligan RA, Vale RD (2006) A lever-arm rotation drives mo-tility of the minus-end-directed kinesin Ncd. Nature 439(7078):875–878.

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23. Foster KA, Correia JJ, Gilbert SP (1998) Equilibrium binding studies of non-claretdisjunctional protein (Ncd) reveal cooperative interactions between the motor do-mains. J Biol Chem 273(52):35307–35318.

24. Foster KA, Mackey AT, Gilbert SP (2001) A mechanistic model for Ncd directionality.J Biol Chem 276(22):19259–19266.

25. Kocik E, Skowronek KJ, Kasprzak AA (2009) Interactions between subunits in heter-odimeric Ncd molecules. J Biol Chem 284(51):35735–35745.

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28. Chen CJ, Rayment I, Gilbert SP (2011) Kinesin Kar3Cik1 ATPase pathway for micro-tubule cross-linking. J Biol Chem 286(33):29261–29272.

29. Chandra R, Endow SA, Salmon ED (1993) An N-terminal truncation of the ncd motorprotein supports diffusional movement of microtubules in motility assays. J Cell Sci104(Pt 3):899–906.

30. Brune M, Hunter JL, Corrie JET, Webb MR (1994) Direct, real-time measurement ofrapid inorganic phosphate release using a novel fluorescent probe and its applicationto actomyosin subfragment 1 ATPase. Biochemistry 33(27):8262–8271.

31. Klumpp LM, Hoenger A, Gilbert SP (2004) Kinesin’s second step. Proc Natl Acad SciUSA 101(10):3444–3449.

32. Singh A, Jayaraman A, Hahn J (2006) Modeling regulatory mechanisms in IL-6 signaltransduction in hepatocytes. Biotechnol Bioeng 95(5):850–862.

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34. Sun Y, Goldman YE (2011) Lever-arm mechanics of processive myosins. Biophys J101(1):1–11.

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6364 | www.pnas.org/cgi/doi/10.1073/pnas.1505531112 Zhang et al.

Supporting InformationZhang et al. 10.1073/pnas.1505531112SI Materials and MethodsNcd Protein Expression and Purification. The Ncd pET/MC1 plas-mid (1, 2) was a generous gift of Sharyn A. Endow (Duke Uni-versity Medical Center, Durham, NC) and was expressed inE. coli BL21-CodonPlus (DE3)-RIL cell line (Stratagene) forpurification as described previously (2, 3). Cells were grown in ly-sogeny broth (LB) with antibiotics (75 μg/mL ampicillin, 10 μg/mLchloramphenicol) at 37 °C until A600 was ∼0.4, and then thecells were cooled on ice to 16 °C, followed by induction with75 μM isopropyl β-D-1-thiogalactopyranoside. Protein expres-sion was continued for 16 h at 16 °C with shaking, followedby centrifugation. The cell pellets were resuspended in lysisbuffer (10 mM sodium phosphate buffer, pH 7.2, 30 mM NaCl,5 mM MgCl2, 1 mM EGTA, 1 mM EDTA, 10 mM phenyl-methylsulfonyl fluoride, 1 mM DTT, and 0.02 mM ATP) at10 mL/g wet weight, and adjusted to 0.1 mg/mL lysozyme. The cellswere incubated for 45 min at 4 °C with gentle stirring. Followingthree cycles of freezing (liquid N2) and thawing (37 °C), the lysateswere clarified by ultracentrifugation. The supernatant was loadedonto a SP Sepharose column (HiTrap SP FF; GE Healthcare LifeSciences) that was preequilibrated in SP Sepharose binding buffer(10 mM sodium phosphate buffer, pH 7.2, 30 mM NaCl, 5 mMMgCl2, 0.1 mM EGTA, 0.1 mM EDTA, 1 mM DTT, 0.02 mMATP). After washing with the binding buffer, the proteins wereeluted from the column with a linear gradient of 30–600 mM NaClin Sepharose binding buffer. Fractions containing Ncd MC1 wereidentified by SDS/PAGE, pooled, and dialyzed against dieth-ylaminoethyl (DEAE) column binding buffer (10 mM sodiumphosphate buffer, pH 7.2, 30 mM NaCl, 2 mM MgCl2, 0.1 mMEGTA, 0.1 mM EDTA, 1 mM DTT, 0.02 mM ATP). The dialyzedproteins were loaded onto a preequilibrated DEAE column (Hi-Trap DEAE FF; GE Healthcare) and the column was washed withDEAE column binding buffer, followed by protein elution with alinear gradient of 30–400 mM NaCl in the DEAE column bindingbuffer. Fractions enriched in Ncd MC1 were identified by SDS/PAGE, pooled, and dialyzed in 20 mM Hepes, pH 7.2, with KOH,0.1 mM EDTA, 0.1 mM EGTA, 5 mMmagnesium acetate, 50 mMpotassium acetate, 1 mM DTT, and 100 mM NaCl. The dialyzedprotein was clarified and then concentrated by ultrafiltration,followed by loading onto an HPLC gel filtration column (Su-perose 10/300 GL; GE Healthcare) using a Beckman CoulterSystem Gold HPLC. The eluted homodimeric Ncd was collectedand dialyzed against ATPase buffer: 20 mM Hepes, pH 7.2 withKOH, 0.1 mM EDTA, 0.1 mM EGTA, 5 mM magnesium ace-tate, 50 mM potassium acetate, 1 mM DTT, plus 5% sucrose.The dialyzed protein was clarified by ultracentrifugation, frozenas aliquots in liquid N2, and stored at −80 °C. A single Ncd MC1polypeptide contains the N-terminal 11 amino acid residues ofbacteriophage T7 S10 protein (MASMTGGQQMG), two linkerresidues (RD), and the C-terminal 492 residues of Ncd, corre-sponding to amino acid sequence Leu209–Lys700. The predictedmolecular weight based on amino acid sequence is 57,363 perpolypeptide chain and 114,726 for the MC1 homodimer. Beforeeach experiment, Ncd was clarified for 10 min at 4 °C (BeckmanCoulter TLX ultracentrifuge, TLA-100 rotor, 313,000 × g), andthe protein concentration was determined using the Bio-Radprotein assay with IgG as a protein standard. MT concentrationsare reported as paclitaxel-stabilized tubulin polymer.

Pulse-Chase Kinetics of ATP Binding. To measure the kinetics ofATP binding (Fig. S2), the MT•Ncd complex (10 μMNcd•ADP/30 μM MTs or 16 μM Ncd•ADP/30 μM MTs, syringe concen-

trations) was preformed and rapidly mixed in a chemical quench-flow instrument (RQF-3; KinTek Corp.) with MgATP plus trace[α-32P]ATP and 200 mM KCl (syringe concentrations) from 5 to400 ms (4–6). The reaction mixture was subsequently chased with30 mM nonradiolabeled MgATP (syringe concentration) for 6 s(>10 ATP turnovers) and expelled from the instrument into a1.5-mL tube containing 100 μL of 22 N formic acid. The acidterminated the reaction and released any nucleotide at the activesite. The time of the chase allowed stably bound [α-32P]ATP tobe converted to [α-32P]ADP•Pi, yet any [α-32P]ATP unbound orbound loosely to the active site was diluted by the high con-centration of nonradiolabeled ATP. One microliter of each re-action mixture was spotted onto a PEI-cellulose TLC plate(EMD Millipore) and developed with 0.6 M potassium phos-phate buffer, pH 3.4, to separate [α-32P]ATP from [α-32P]ADP + Pi.The radiolabeled nucleotide was quantified using Image Gaugev4 software (FUJIFILM Science Laboratory). The concentra-tion of [α-32P]ADP product was plotted as a function of time,and the pre-steady-state burst equation (Eq. S1) was fit to eachtransient:

½ADP�=A0½1� expð−kbtÞ�+ kslowt, [S1]

where A0 is the amplitude of the exponential burst phase, rep-resenting the stable formation of [α-32P]ATP•motor complexthat proceeded through ATP hydrolysis during the first ATPturnover, kb is the observed rate of the exponential burst phase,and t is the time in seconds. The kslow is the rate constant of thelinear phase (μM·s−1) and, when divided by the Ncd site concen-tration, corresponds to steady-state turnover. The observed ex-ponential rates of each transient were plotted as a function ofMgATP concentration, and Eq. S2 was fit to the data:

kobs = ½K1k+1′ ½ATP�=ðK1½ATP�+ 1Þ�, [S2]

where K1 represents the equilibrium association constant forformation of the collision complex (Kd = 1/K1), and k+1′ repre-sents the first-order rate constant for the ATP-promoted isom-erization to form the intermediate poised for ATP hydrolysis.The amplitude of each transient was plotted as a function ofMgATP concentration, and the hyperbolic fit to the data pro-vided the maximum amplitude, which can be related to the Ncdactive sites in the experiment.

Acid-Quench Kinetics of ATP Hydrolysis.The pre-steady-state kineticexperiments to determine the time course of ATP hydrolysis wereperformed with a KinTek chemical quench-flow instrument.The MT•Ncd complex (10 μM Ncd•ADP/30 μM MTs, 16 μMNcd•ADP/30 μM MTs, or 20 μM Ncd•ADP/30 μM MTs, syringeconcentrations) was rapidly mixed with MgATP plus trace[α-32P]ATP and 200 mM KCl (syringe concentrations) for timesranging from 5 to 400 ms. The reaction mixture was quenchedwith 22 N formic acid (syringe concentration), which terminatedthe reaction and released any nucleotide at the active site. Theradiolabeled products [α-32P]ADP and Pi were separated from[α-32P]ATP by TLC and quantified using Image Gauge v4 soft-ware (FUJIFILM Science Laboratory). The concentration ofproduct was plotted as a function of time, and Eq. S1 was fit tothe data, where A0 is the amplitude of the exponential burstphase, representing the formation of [α-32P]ADP•Pi at the activesite during the first ATP turnover, kb is the rate of the expo-nential burst phase, and t is the time in seconds. The constant

Zhang et al. www.pnas.org/cgi/content/short/1505531112 1 of 8

kslow is the rate of the linear phase and, when divided by the Ncdsite concentration, corresponds to steady-state turnover. Theobserved rate and amplitude of the exponential burst phase ofeach transient were plotted as a function of MgATP concen-tration, and a hyperbolic function was fit to each data set, pro-viding the rate constant of ATP hydrolysis and the maximumamplitude of the exponential phase.

MT•Ncd Cosedimentation Assays. To determine the concentrationof Ncd bound to the MTs in the preformed MT•Ncd complex forthe pulse-chase (Fig. S2) and acid-quench (Fig. S3) experiments,equilibrium cosedimentation experiments were performed (3, 7).Reactions of 200 μL with MTs were formed at 8 μM Ncd•ADP/15 μM MTs or 16 μM Ncd•ADP/30 μM MTs in ATPase bufferplus 40 μM paclitaxel and incubated at room temperature for 30min followed by centrifugation at 25 °C (Beckman Coulter TLXultracentrifuge, TLA-100 rotor, 313,000 × g, 30 min). For eachreaction, the supernatant was collected (top 100 μL of 200 μLwith remaining 100 μL discarded). The MT pellet was re-suspended in 100 μL of 5 mM CaCl2 in buffer and incubated at4 °C for 10 min. This step was repeated, and the two 100 μLCaCl2 aliquots were combined. Laemmli 2× sample buffer wasadded to the supernatant (100 μL + 100 μL sample buffer) andresuspended pellet (200 μL + 200 μL sample buffer) for eachreaction pair, followed by analysis by SDS/PAGE, in which thesupernatant and pellet samples were loaded as equal volumes.The 8% acrylamide/2 M urea Coomassie Brilliant Blue R-250stained gels were analyzed and quantified by Image Gauge v4software.

MantATP Binding Following MT•Ncd Association. To mimic the re-action condition at the beginning of the cycle, 10 μM Ncd•ADPwas rapidly mixed with 40 μM MTs plus varying concentrationsof mantATP in the SF-2003 KinTek stopped-flow instrument(Fig. 2). Final concentrations: 5 μMNcd•ADP sites, 20 μMMTs,and 0–15 μMmantATP (Invitrogen). The change in fluorescenceof mantATP was monitored by excitation at 360 nm with de-tection at 450 nm using a 409-nm long-pass filter (Semrock,Inc.). The fluorescence of mantATP as well as mantADP isenhanced by the hydrophobic environment of the active site. Asingle exponential function was fit to each transient, and theobserved rates obtained were plotted as a function of mantATPconcentration. A hyperbolic function plus a y-intercept was fit tothe data, providing the maximum rate constant of mantATPbinding.

MantADP Release Kinetics from Head 1 and 2. The Ncd•mantADPcomplex (4 μM Ncd sites/8 μM mantADP) was rapidly mixed inthe stopped-flow instrument with varying MT concentrationsplus 1 mM MgATP. Final concentrations: 2 μM Ncd sites, 4 μMmantADP, 2–20 μM MTs, and 500 μM MgATP. The data werecollected at a 2-s time domain to optimize capturing both theinitial fast phase as well as the subsequent slow phase. Eachtransient (Fig. S4A) was fit to a double-exponential function.The observed rates for both the initial fast exponential phase andsubsequent slow phase were each plotted as a function of ATPconcentration (Fig. S4B). The hyperbolic fit to each provided themaximum rate constant of mantADP release from the first Ncdhead to collide with the MT and the maximum rate constantassociated with the second head’s MT collision event and sub-sequent mantADP release.

Pre-Steady-State Kinetics of Phosphate Release. The kinetics of Pirelease were determined using the E. coli phosphate-binding pro-tein (PBP) that was developed as a Pi biosensor by introduction of asingle cysteine into PBP at position 197 (A197C) and selectively

labeled with the fluorophore MDCC (8, 9). The probe was ex-cited at 436 nm with fluorescence emission at 474 nm detectedvia a 450-nm long-pass filter (Semrock, Inc.) in the stopped-flowinstrument. MDCC-PBP binds phosphate rapidly (∼136 μM−1·s−1)and tightly (Kd ∼0.1 μM), resulting in a fluorescence enhancementof approximately sevenfold that can be quantified (8–11). To re-move free phosphate from the solutions and stopped-flow chamber,a “Pi mop” containing bacterial purine nucleoside phosphorylase(PNPase) and 7-methylguanosine (MEG) was used to sequestercontaminating free phosphate as ribose-1-phosphate. The concen-trations of MEG and PNPase were adjusted to 75 μM MEG and0.025 U/mL PNPase in each syringe to achieve a rate of phosphateremoval at 0.002 s−1 to prevent the Mop reaction from competingwith MDCC-PBP.To convert the MDCC-PBP fluorescence amplitude of each

transient in volts into units of Pi concentration, a phosphatestandard curve was used. MDCC-PBP in ATPase buffer withadded 0.02 U/mL PNPase and 150 μM MEG (syringe concen-trations) was rapidly mixed in the stopped-flow instrument withvarying concentrations of KH2PO4. The initial exponential am-plitude of each KH2PO4 transient in volts was plotted as afunction of phosphate concentration to obtain a linear fit of thedata. The phosphate-calibration curve was then used to convertthe amplitude of each transient in Fig. 3 to units of concentrationto relate to the total number of ATP hydrolysis and phosphaterelease events per Ncd site concentration in the experiment. Thephosphate standard curve is performed with each experiment atthe concentration of MDCC-PBP used to measure phosphaterelease from the MT•motor complex.

Parameter Estimation Method. The parameter estimation problemfor the dynamic model of the Ncd powerstroke process (Fig. 4)can be mathematically formulated as follows:

minP

X

i

X

k

�Fik − F̂ik

�2

_X1 =−k1X1 + k-1X2

_X2 = k1X1 − k−1X2 − k2X2M + k−2X3

_X3 = k2X2M− k−2X3 − k3X3

s.t. _X4 = k3X3 − k4X4M_X5 = k4X4M_M=− k2X2M + k−2X3 − k4X4MF= λ1X3 + λ2X4 + λ3X5

P= ½k1, k-1, k2, k-2, k3, k4, λ1, λ2, λ3�T, pj ≥ 0  ∀  j= 1,2, . . . , 9.

Here, Fik and F̂ik are the simulated and measured fluorescence atthe kth sampling time under the ith experimental condition.Parameters p include k1, k−1, k2, k−2, k3, k4, λ1, λ2, and λ3. Thesampling times tk are at 0.3, 0.5, 0.7, 0.9, 1.1, 1.3, 1.5, 1.6, 1.7, 1.8,1.9, and 2.0 s. Data used for estimation were obtained from themantATP binding experiments (Fig. 2), which were conducted atdifferent initial concentrations of mantATP in the range of 0.5,1.5, 2.5, 3.5, and 4.5 μM.The parameter estimation problem is solved by applying an

optimization algorithm that requires repeated evaluation of theobjective function and its gradients by numerical integration ofthe ordinary differential equations (ODEs). In this work, fmincon(a MATLAB function) is used as the nonlinear programming(NLP) solver, and ode45 (a MATLAB function) is used as theODE solver.

Zhang et al. www.pnas.org/cgi/content/short/1505531112 2 of 8

1. Chandra R, Endow SA, Salmon ED (1993) An N-terminal truncation of the Ncd motorprotein supports diffusional movement of microtubules in motility assays. J Cell Sci104(Pt 3):899–906.

2. Chandra R, Salmon ED, Erickson HP, Lockhart A, Endow SA (1993) Structural andfunctional domains of the Drosophila Ncd microtubule motor protein. J Biol Chem268(12):9005–9013.

3. Foster KA, Correia JJ, Gilbert SP (1998) Equilibrium binding studies of non-claretdisjunctional protein (Ncd) reveal cooperative interactions between the motor do-mains. J Biol Chem 273(52):35307–35318.

4. Foster KA, Gilbert SP (2000) Kinetic studies of dimeric Ncd: Evidence that Ncd is notprocessive. Biochemistry 39(7):1784–1791.

5. Foster KA, Mackey AT, Gilbert SP (2001) A mechanistic model for Ncd directionality. JBiol Chem 276(22):19259–19266.

6. Gilbert SP, Mackey AT (2000) Kinetics: A tool to study molecular motors. Methods22(4):337–354.

7. Chen CJ, Rayment I, Gilbert SP (2011) Kinesin Kar3Cik1 ATPase pathway for micro-tubule cross-linking. J Biol Chem 286(33):29261–29272.

8. Brune M, Hunter JL, Corrie JE, Webb MR (1994) Direct, real-time measurement ofrapid inorganic phosphate release using a novel fluorescent probe and its applicationto actomyosin subfragment 1 ATPase. Biochemistry 33(27):8262–8271.

9. Brune M, et al. (1998) Mechanism of inorganic phosphate interaction with phosphatebinding protein from Escherichia coli. Biochemistry 37(29):10370–10380.

10. Gilbert SP, Webb MR, Brune M, Johnson KA (1995) Pathway of processive ATP hy-drolysis by kinesin. Nature 373(6516):671–676.

11. Klumpp LM, Hoenger A, Gilbert SP (2004) Kinesin’s second step. Proc Natl Acad SciUSA 101(10):3444–3449.

Zhang et al. www.pnas.org/cgi/content/short/1505531112 3 of 8

Fig. S1. Alternative Ncd ATPase schemes. (A) TheWendt et al. (1) and Endres et al. (2) model proposes that only one Ncd head interacts with a microtubule with oneATP turnover event per powerstroke. The cycle is initiated when one head of dimeric Ncd collides with the MT, followed by ADP release (E0–E1). ATP binding to thenucleotide-free head triggers the ∼70° rotation of the coiled-coil stalk toward the MT minus end (E1–E2). ATP hydrolysis occurs followed by phosphate release andNcd dissociation fromMT (E2–E3). (B) The scheme proposed by Foster et al. (3) was based on the assumption that both Ncd heads interact with the MT and both bindand hydrolyze ATP. The cycle begins with MT collision followed by ADP release (E0–E2). ATP binding followed by ATP hydrolysis triggers the second head to bind tothe MT (E3–E4). This model predicts that rearward head detachment occurs as the ADP•Pi state, triggering tight MT binding of the leading head followed by ADPrelease (E5–E6). Another ATP turnover is required for detachment of Ncd from the MT (E7–E9). This model differs from theWendt et al. (1) and Endres et al. (2) modelin that both heads of the Ncd dimer interact with the MT with two ATP turnover events per powerstroke.

1. Wendt TG, et al. (2002) Microscopic evidence for a minus-end-directed power stroke in the kinesin motor Ncd. EMBO J 21(22):5969–5978.2. Endres NF, Yoshioka C, Milligan RA, Vale RD (2006) A lever-arm rotation drives motility of the minus-end-directed kinesin Ncd. Nature 439(7078):875–878.3. Foster KA, Mackey AT, Gilbert SP (2001) A mechanistic model for Ncd directionality. J Biol Chem 276(22):19259–19266.

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Fig. S2. Pulse-chase kinetics of ATP binding. The MT•Ncd complex was rapidly mixed in the chemical quench-flow instrument with increasing concentrationsof MgATP + trace [α-32P]ATP and 200 mM KCl, followed by a chase with 30 mM unlabeled MgATP (syringe concentrations). Final concentrations: 5 μMNcd•ADP/15 μM MTs or 8 μM Ncd•ADP/15 μM MTs, 0–300 μM [α-32P]ATP, and 100 mM KCl. (A) Representative transients for ATP binding show an initialexponential formation of [α-32P]ADP•Pi during the first ATP turnover followed by a linear phase of product formation representing subsequent ATP turnovers.Final MT•Ncd complex concentrations: 8 μM Ncd•ADP/15 μM MTs. (B) The observed rates of the pre-steady-state exponential phase determined for individualtransients were plotted as a function of MgATP concentration, and the Eq. S2 fit provided the maximum kb = 81.3 ± 2.6 s−1 and Kd,ATP = 7.1 ± 0.03 μM. (C) Theamplitude of each exponential phase was normalized to the concentration of Ncd sites and plotted as a function of MgATP concentration. A hyperbolic fit tothe data provided the maximum burst amplitude of 0.84 ± 0.03 μM ADP•Pi per site and Kd,ATP = 47 ± 5.2 μM. The data in B and C represent multiple ex-periments. (D) The MT•Ncd complex used in the pulse-chase experiments was evaluated by cosedimentation assays. The supernatant (S) and pellet (P) for eachreaction are shown with the concentration of MTs indicated above each pair. Approximately 80% of the total Ncd pelleted with MTs at the conditions of thepulse-chase experiments, indicating that all MT-associated Ncd motor heads did bind and hydrolyze ATP during the first ATP turnover.

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Fig. S3. Acid-quench kinetics of ATP hydrolysis. The preformed MT•Ncd complex was rapidly mixed in the chemical quench-flow instrument with increasingconcentrations of MgATP + trace [α-32P]ATP and 200 mM KCl (syringe concentrations). Final concentrations: 5 μM Ncd•ADP/15 μM MTs, 8 μM Ncd•ADP/15 μMMTs, or 10 μM Ncd•ADP/15 μM MTs, 0–300 μM [α-32P]ATP, and 100 mM KCl. (A) Representative transients show an initial exponential phase of [α-32P]ADP•Piduring the first ATP turnover followed by a linear phase of product formation representing subsequent ATP turnovers. Final MT•Ncd complex concentrations:8 μM Ncd•ADP/15 μM MTs. (B) The observed rates of the presteady-state exponential phase determined for individual transients were plotted as a function ofMgATP concentration, and the hyperbolic fit to the data provided the maximum kb = 26 ± 0.6 s−1 and Kd,ATP = 7.2 ± 0.9 μM. At high ATP concentrations, ATPhydrolysis becomes rate-limiting; therefore, the maximum kb represents the rate constant for ATP hydrolysis. (C) The amplitude of the exponential phase foreach transient was normalized to the concentration of Ncd sites and plotted as a function of MgATP concentration. The hyperbolic fit to the data providedAmax = 1.09 ± 0.04 μM ADP•Pi per site and Kd,ATP = 63.7 ± 6 μM. The acid-quench amplitude data also support the argument that all MT-associated Ncd motorheads did bind and hydrolyze ATP during the first ATP turnover.

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Fig. S4. MantADP release kinetics from Ncd heads 1 and 2. The Ncd•mantADP complex (4 μM Ncd sites/8 μM mantADP) was rapidly mixed in the stopped-flowinstrument with increasing concentrations of MTs plus 1 mM MgATP. Final concentrations: 2 μM Ncd sites/4 μM mantADP, 2–20 μM MTs, and 500 μM MgATP.(A) Representative transients are biphasic with an initial rapid phase of fluorescence quenching followed by a slow phase. Each transient was fit to a double-exponential function, which provided the observed rates of mantADP release from each exponential phase. (B) The observed rates for the initial fast phase ofmantADP release associated with the first head that collides with the MT and the subsequent slow phase of mantADP release associated with the second headthat collides with the MT were plotted as a function of MT concentration. The hyperbolic fit of each data set provided a maximum rate constant for the fastphase at 14.2 ± 0.7 s−1 and the slow phase at 1.85 ± 0.1 s−1. The amplitudes associated with each phase were not equivalent with only ∼25% of the totalamplitude associated with the fast phase. The decrease in the amplitude associated with the initial fast phase results because of the relatively weak ADPaffinity for one of the Ncd heads in solution and previously proposed to be the head that initially collides with the MT (1) as well as the time domain used tocapture both the fast and slow exponential phases. These results are consistent with rates reported previously for mantADP release upon MT collision and ATP-promoted head 2 mantADP release (Table S1) (1).

1. Foster KA, Mackey AT, Gilbert SP (2001) A mechanistic model for Ncd directionality. J Biol Chem 276(22):19259–19266.

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Table S1. Experimentally determined constants for the MT•Ncd ATPase

Reaction step Constants

mantATP binding following MT•Ncd association kmax = 4.4 ± 0.2 s−1

koff = 1.8 ± 0.1 s−1

K1/2,mantATP = 9.4 ± 1.4 μMmantATP binding to the MT•Ncd complex

(from ref. 1)kmax = 2.3 ± 0.1 μM−1·s−1

k−1 not observedATP binding (pulse-chase) K1 = 0.14 ± 0.03 μM−1

k+1′ = 81.3 ± 2.6 s−1

K1k+1′ = 11.4 ± 0.08 μM−1·s−1

Kd,ATP = 7.1 μMA0 = 0.84 ± 0.03 μM ADP•Pi per Ncd site

Kd,ATP = 47 ± 5.2 μMATP hydrolysis (acid quench) kmax = 26 ± 0.6 s−1

Kd,ATP = 7.2 ± 0.9 μMA0 = 1.09 ± 0.04 μM ADP•Pi per Ncd site

Kd,ATP = 63.7 ± 6 μMMT•Ncd association (from ref. 1) kmax = 0.7 ± 0.1 μM−1·s−1

k−1 = 2.7 ± 0.6 s−1

mantADP release from head 1 (from ref. 2) kmax = 17.8 ± 1.6 s−1

K1/2,MT = 2.2 ± 2.0 μMmantADP release from head 2 (from ref. 2) kmax = 1.4 ± 0.02 s−1

K1/2,ATP = 0.64 ± 0.06 μMPhosphate release following MT•Ncd association kmax = 2.9 ± 0.1 s−1

K1/2,ATP = 16 ± 1 μMA0,max = 5.7 ± 0.25 μM Pi (∼1.1 Pi/Ncd site)

Phosphate release from the MT•Ncd complex kmax = 14.3 ± 0.3 s−1

K1/2,ATP = 23.3 ± 2.3 μMA0,max = 1.1 ± 0.01 μM Pi (∼0.44 Pi/Ncd site)

ATP-promoted MT•Ncd dissociation (from ref. 1) kmax = 13.1 ± 0.6 s−1

K1/2,ATP = 18.7 ± 4.1 μMSteady-state parameters (from ref. 3) kcat = 2.1 ± 0.2 s−1

Km,ATP = 23.1 ± 1.5 μMK1/2,MT = 18.3 ± 5.1 μM

Errors are ±SEM.

1. Foster KA, Gilbert SP (2000) Kinetic studies of dimeric Ncd: Evidence that Ncd is not processive. Biochemistry 39(7):1784–1791.2. Foster KA, Mackey AT, Gilbert SP (2001) A mechanistic model for Ncd directionality. J Biol Chem 276(22):19259–19266.3. Foster KA, Correia JJ, Gilbert SP (1998) Equilibrium binding studies of non-claret disjunctional protein (Ncd) reveal cooperative interactions between the motor domains. J Biol Chem

273(52):35307–35318.

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