Enz Methods 2000

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Kinetics: A Tool to Study Molecular Motors

Susan P. Gi lber t 1 and Andrew T. Mackey

Department of Biological Sciences, 518 Langley Hall, University of Pittsburgh,Pi t t sburgh, Pennsylvania 15260

Molecular motors are enzymes that couple the energy from

nucleoside triphosphate hydrolysis to movement along a la-

ment lattice. The three cytoskeletal motor superfamilies in-

clude myosin, dynein, and kinesin. However, in the last decadet has become apparent that the nucleic acid-based enzymesDNA and RNA polymerases as well as the DNA helicases)

share a number of mechanistic features in common with the

microtubule and actin motors despite the fact that their cellu-ar functions are so different. This review addresses the mech-

anistic approaches that have been used to study molecularmotors. We discuss the basic biochemical techniques used to

characterize a protein preparation, including active site deter-mination and steady-state kinetics. In addition, we present the

ransient-state kinetic approaches used to dene a mechano-

chemical cycle. We attempt to integrate the information ob-ained from kinetic studies within the context of motility re-

sults to provide a better understanding of the contribution ofeach approach for dissecting unidirectional force generation.© 2000 Academic Press

P re-stea dy-sta te kinetic approa ches de ne th e squence of rea ctions occurring a t the a ctive site ofenzyme fol lowing substrate binding and leadingproduct relea se. It is t hese reaction st eps th a t d ri

the stru ctura l tra nsitions tha t a ccount for the movment of molecula r m otors, t heir processivity (or lathereof), and their directionality of force generatiIn this article we describe the methods and expements used to dene a mechanochemical crossbridcycle, s ta r t ing a t the beginning when the pur imotor protein is rst in hand to the later s tageswhich one probes for cooperativity between modomains. The methods and experiments can be anhave been a ppl ied to many enzymes , bu t in ta rticle w e focus predomina ntly on the microtububased motors, kinesin and non-claret disjunction(Ncd), for our examples. Also, this review ta rgthose who are interested in molecular motors awa nt to learn about mechan ist ic approaches. Fomore deta iled present at ion of tra nsient sta te kinetheory and methods, we refer you to several exclent reviews (1–3) an d the 1999 edition of the texbook by Fersht (4).

MEASUREMENT OF MOTORCONCENTRATION

Most invest igators begin the character izat ionthe motor preparation by measuring protein concetration using a simple colorimetric method such the Bradford assay (5) or by opt ical absorbance280 nm using B eer–Lambert law where

A 28 0 / l concent ra t ion.

K401, D rosophi l a kinesin construct containing the N-terminal401 amino acids; MC1, Ncd construct consist ing of amino acidesidues Leu 209 -Lys 700 ; MC6, Ncd construct consist ing of amino

acid residues Met 333 -Lys 700 ; Mt N, Microtubule Ncd complex;Mt K, microtubule kinesin; E ATP , enzyme ATP intermediat e;E S, enzyme substrate complex; NC, Nitrocellulose; TLC, thinayer chromatography; BSA, bovine serum albumin; mantADP,

2 (3 )-O -( N -methyla nt hra niloyl)a denosine 5 -diphosphate; mant-ATP , 2 (3 )-O -( N -methylanthraniloyl)adenosine 5 -triphosphate;2 -dATP , 2 -deoxyadenosine 5 -triphosphate; P i , inorganic phos-phate ; MDCC-PB P, uorescent ly modied phosphat e-bindingprotein.

1 To whom correspondence should be addressed. Fax: (412)624-4759. E-mail: spg1 @pitt.edu.

METHODS 2 2 , 337–354 (2000)

doi:10.1006/meth.2000.1086, available online at http://www.idealibrary.com on

31046-2023/00 $35.00Copyright © 2000 by Academic PressAll rights of reproduction in any form reserved.

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The length ( l ) of th e light path through th e sam ple isypically 1 cm. The extinction coefcent ( ) for a motor

protein can be calculated (6) based on constituentamino acids that absorb at 280 nm (tryptophan, ty-rosine, a nd cyst ine),

t ot a t rp b t yr c cy s, [2]

where Trp , Tyr , Cy s are the molar extinction coefcientsn 6 M guan idinium hydrochloride of tryptopha n

( tr p 5690 M 1 cm 1), t yrosine ( ty r 1280 M

1 cm 1),and cystine ( cys 120 M

1 cm 1), and a , b , and c a rehe numbers of residues per molecule of protein. Typ-cally, the protein is denatured with either 6 M gua-

nidium hy drochloride or 6 M u rea beca use a bsorba nceat 280 nm can be affected by light-scattering artifacts,oligomerization, and the local environment of the ab-sorbing species. For many proteins, no difference is

observed in the spectra for the native protein in com-parison to denatured protein. For example, we see thesame spectra for dimeric kinesin construct K401 ( Dro- sophila kinesin construct conta ining the N-terminal401 amino acids), monomeric MC6 (Ncd construct con-sis t ing of amino acid residues Met 333 –Lys 700 ), anddimeric MC1 (Ncd construct consisting of amino acidresidues Leu 209 –Lys 700 ). Note tha t for cysteine resi-dues, it is cystine (S–S) that absorbs at 280 nm ratherhan cysteine (6); yet the researcher usually does not

know the number of cystines in the native protein,only the total number of cysteine residues. Two ap-proaches can be used to calculate the extinction coef- cient of the motor protein. B ecause the extinctioncoefcent for cystine is quite low a t 120 M 1 cm 1, thecont ribution to tot can be ignored especially when theotal number of cysteine residues is small. The alter-

na tive approach is t o assume t ha t all or some propor-ion of the cysteine residues exist as disuldes; there-

fore, each two cysteines would contribute one cystineo t he calcula tion of tot . It is also advisable to scan the

UV spectrum of the puried protein to determine ifnucleotide is bound at the active site (broad peak atA 259 ) (7, 8) and if th ere a re other contributions to t heoptical a bsorbance tha t ma y introduce art ifa cts in thespectrophotometric determination of protein concen-ration.

DETERMINATION OF ACTIVE SITECONCENTRATION

For ma ny experiments, especially motility a ssay s,t is not necessary to know the absolute concentra-

tion of active protein. Yet, for steady-state kineta nd ligan d binding experiments, t he a ctive site ccent ra t ion i s cr it i ca l to the inte rpre ta t ion of tda ta . The four assays d iscussed here can be pformed without specialized instrumentation. The knesin superfamily members t ha t ha ve been charate r ized b iochemica l ly a re a l l pur ied wi th At ight ly bound a t the ac t ive s i te. This t igh t Abinding ca n be exploited t o determ ine the concentrtion of ATP binding sites in the protein preparatioby using nitrocellulose lter binding (7), gel ltt ion cent rifu ga tion (9), an d/or a phosph ocrea t ine kna se coupled a ssa y (10, 11). Convent iona l a ctive st i t ra t ion can be used for motor prote ins such myos in and dynein tha t a re pur i ed wi th the ir tive sites free of nucleotide (12).

Nitrocellulose Binding Assay

Nit rocellulose (NC , 0.2- m pore size; SchleicherSchuell, Inc., Keene, NH) is cut to t the size ofdot-blot a ppara tus a nd pretrea ted t o reduce nonspcic binding. The NC is added to dis t i l led (dHH 2O at 100°C for 3 min fo l lowed by a co ld dHw a sh. The NC is then incubat ed in 0.5 M KOH fomin follow ed by extensive wa shing in ddH 2O priorequilibra tion in th e rea ction buffer plus 0.1 mg/mbovine serum albumin (BSA). The dot-blot appartus is assembled with the pretreated NC and asrated. The thumbscrews are tightened again to prvent spreading of the sample, and each well toused is checked with buffer to ensure an even arap id ow. I t i s impor tan t tha t the NC not dry prior to a pplica tion of t he r eaction sa mple.

Motor (0–5 M) is in cuba t ed w it h 8 [ -32 P ]ATP (30- L reaction mix) in buffer plus 0mg/mL BS A a t 25° C for 60–90 min . Dur ing tincubat ion, ADP t ight ly bound at the act ive s i tereleased fol lowed by the subsequent b inding [ -32 P]ATP. The samples (10 L in duplicate)

then applied to NC in a dot-blot apparatus and pirated. Free nucleotides ([ -32 P]ATP, [ -32 P]ADADP ) w ill pa s s t h rough the NC, yet nucleottightly bound at the active site will become adsorbonto the NC w ith t he motor protein. Two- a nd th remicroliter aliquots (in duplicate) of the 30- L retion mix ar e spott ed onto the NC w ithout a spiratito determine tota l counts. The NC membr a ne is thair-dried and imaged by direct emission usingP hosphor imaging system to qua nti ta te the ra diobeled nucleotides a dsorbed to t he NC at each mo

concentr a tion. The adva nta ge of this a ssa y is tharequires a very small amount of protein to det

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mine the concentration of active sites. Note thoughhat the assay is based on the s low release of ADP

from the act ive s i te of the motor in the absence ofmicrotubules. Therefore, as the rate of nucleotidedissociation increases or if the afnity of the nucle-ot ide for t he act i ve s it e is weakened , t h is a s saybecomes less effective t o qua ntify a ctive sites.

Gel Filtration Assay

For th i s assay, ge l l t ra t ion i s used to separa tenucleotide that is free in solution from nucleotideha t i s bound to t he a ct ive s ite of the motor. The

concentrat ion of protein and the concentrat ion ofnucleotide t ha t part it ions to t he excluded volume ishen determined, with the concentration of nucleo-ide representing the concentration of active enzyme

sites.The biospin columns (B io-G el P -30, B io-Ra d La b-

oratories , Hercules , CA) are prepared by washinghe column initially with 500 L buffer containing

0.25 mg/mL IgG or ovalbumin, followed by thr eewashes (500 L each) with buffer to equilibrate thecolumn a nd remove residual protein tha t is a dded todecrease t he nonspeci c binding of t he motor t o theP -30 resin. In a ddit ion, th e centr ifuga tion conditionsmust be determined such tha t the volume added t ohe column (80 L) is recovered as the void volume

(79–82 L).A 300 L r eaction m ixture conta ining 20 M pro-

ein s i tes (est imated by Bradford) is incubated atroom t empera ture w ith 20 M [ -32 P]ATP for 60–90min t o allow for ADP release, follow ed by [ -32 P ]ATPbinding and hydrolys is to label the ac t ive motorsites. An 80- L al iquot is a pplied to the prewa shedbiospin column (performed in duplicate) and centri-fuged a t 1000 g fo r 5 min a t 20°C in a benchtopswinging bucket centrifuge (2450 rpm, Sorvall RT6000B tabletop centrifuge). Aliquots of 5, 7, and 10

L a re used to determine tota l counts for t he calcu-at ion of nucleotide concentra tion, a nd a liquots of 10an d 15 L a re used t o determine protein concentr a-ion. Approximately 80 L (79– 82 L) is recovered

as t he vo id vo lume fo r ana lys i s by the Brad fo rdassay for protein concentration and liquid scintilla-ion counting for nucleotide concentration determi-

nation. Parallel experiments are included in whicheither n o protein is used in th e reaction or sta nda rdprot ein s such a s immunog lobulin G (IgG) andovalbumin are subst ituted for the motor protein.

These cont rol experiments a ssess t he degr ee of non-speci c binding of th e motor protein to th e gel ltra -

t ion res in , whether f ree nucleot ide par t i t ionw ithin the bead pores, and w hether th ere w ere othinconsistencies in the a ssa y procedure.

Phosphocreatine Kinase Coupled AssayThis active site assay incorporates an ATP rege

erat ion syst em in w hich phosphocreat ine kina se caalyzes the t ransfer of the phosphoryl group frophosphocreat ine to ADP to genera te ATP . The motois incubat ed with ra diolabeled [ -32 P]ATP for 60–min. During t he incubat ion, ADP a t t he active sitreleased followed by [ -32 P ]ATP binding a nd hydlysis. B eca use the [ -32 P ]ADP a t t he active site ofenzyme is inaccessible to phosphocreatine, the inacessible [ -32 P]ADP can be quantied as the conctrat ion of motor s i tes . The react ion volume of tinitial st ep is 50 L w ith a t ra ce amount of radibeled nucleotide present (5 L) and motor conctra t ion a t 40 M based on a Bradford estimate. Treaction mixture is incuba ted for a time suf cientconvert all ATP to ADP (60–90 min for conventionkinesin and Ncd). The reaction volume is then icreased to 200 L by the add it i on of 150 LATPase buffer (Reaction Mix A) to yield a nal cocentration of 10 M motor. React ion Mix A is vided into tw o 100 L a l iquots to perform t he a sin the presence and absence of the ATP chase. Raction Mix B contains phosphocreatine kinase (0

mg /mL ), 4 mM phophocreat ine, a nd 5 mM MgAin ATP a se buffer. F ive microliters of Rea ction M ixis pipetted rapidly with 5 L of Reaction Mix B incubat ed for t imes va ryin g from 5 s to 20 min. Afmixing, the nal concentration of reactants is 5 motor, 0.15 mg/mL phosphocreat ine kina se, 2 m Mphosphocreat ine, a nd 2.5 mM MgATP. The reation is terminat ed by th e addit ion of 10 L 2 N Hfollowed by 20 L chloroform t o degrad e th e proteThe react ion mixtures a re neut ra l ized wi th 2 Tris/3 M Na OH ( 5 L) to s epa ra t e ADP and

from ATP using thin-layer chromatography (TLCAn aliquot (1.5 l) of the aqueous phase is spottonto a polyethyleneimine (PEI)-cellulose TLC pla(EM Science of Merck, 20 20 cm. plast ic-ba ckand developed wi th 0.6 M potass ium phosphabuffer, pH 3.4, with phosphoric acid. Radiolabelnucleotide is qu a nti ed by direct emission u sinP hosphor imaging sys tem. The concent ra t ion ADP for ea ch t ime point is t hen calculat ed from counts in the ADP spot (cts AD P) rela tive t o countsthe ATP spot (cts ATP ),

ADP AXP 0 ct s ADP / ct s ADP ct s ATP ,

3KINETIC ANALYSIS OF MOLECU LAR MOTORS

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where [AXP] 0 is the concentration of ADP originallypresent a t t he active site a nd is assumed t o be equa lo the protein concentration (E ADP), ct s AD P repre-

sents the counts in t he spot m igrat ing a s ADP , an dct s ATP represents t he counts in t he spot migra ting a sATP. Therefore, cts AD P ct s ATP represents the t ota lcounts for each time point. One advantage of usingTLC to separa te ADP and P i from ATP is tha t bothhe substrat e and t he product a re quant ied; there-

fore, small differences in volume spotted onto theTLC plate do not introduce error in calculating theconcentration of the product produced. The data are t to the equat ion

ADP A exp k 1 t C , [4]

w here the a ctive site concentra tion is t he sum of the

amplitude ( A ) and the consta nt t erm ( C ) to extrap-olat e to zero time; time (t ) is in seconds. The excessnonradioactive MgATP (2.5 mM) provides a chase;herefore, k 1 is the rst-order ra te consta nt for ADP

release in the absence of microtubules (Fig. 1). Theactive site concentration ( A C ) determined in th epresence of the ATP chase should be equivalent tohe act ive s ite concentrat ion determined in t he a b-

sence of MgATP . To ensure t he coupled a ssa y is fa st

enough to regenerat e ATP , cont rol experiments a rperformed w ith double (0.3 mg/mL na l concentrtion a fter mixing) an d t riple (0.45 mg/mL) a mounof the phosphocrea tine kin a se. The phosphocrea tinkina se concentrat ion can be increased i f there evidence that the regenerat ion system is not suciently fast to regenerate the ATP.

This assa y a ssumes tha t t he active site concentrtion is equa l to or less t ha n t he t ota l protein conctration; therefore, if the protein concentration is uderestimated by the colorimeteric protein assay, inaccurate active site concentration will be obtainTo avoid this type of error, we routinely assume ththe tota l protein concentr a tion is 25%higher thwe measure by the Bradford assay. For examplethe protein determinat ion is estima ted a t 20 M,assume a 25 M stock motor concentration for tphosphocreatine kinase assay. After the active sdeterminat ion is performed, th e a ccura te a ctive sconcentr a tion can be calculat ed.

The phosphocreatine kinase coupled assay for at ive s i te determinat ion can be used for motor prteins that do not bind nucleotide as tightly or whthere is concern that the nitrocellulose or biospassays may not be accurate because of faster nucotide release or weaker binding of nucleotide. Tphosphocreat ine kinase coupled a ssay also ha s tadvantage tha t the ra te cons tan t for ADP re lecan be determined by the same experiment.

Conventional Active Site Titration

This a ssay is based on th e premise that the cocent ra t ion of ac t ive s i tes i s re la ted to the in i tburst of product formed a t t he active site during trs t tu rnover. For many enzymes , the s low, ralimiting st ep of th e pat hw a y occurs a fter nu cleothydrolysis; therefore , the E ADP P i intermediwi l l accumula te and can be quant ied as the ccentrat ion of act ive s i tes of the enzyme. This aproach is valuable for motor proteins that are pued free of nucleotide, and it is usually consideone aspect of a pre-stea dy-sta te kinetic an a lysis (dcu ss ed in m or e d et a il u nd er R a pid C h em icQuench-Flow Methods). However, the assay hbeen adapted to require very small amounts of ptein and has been used successfully for myosin (1wh ose ATP ase pa thw ay is shown in Scheme 1.

M ATP º M TP º M D P P i º M ADP P

SCHEME 1. Myosin ATPase mechanism.

FIG. 1. Active site determina tion for monomeric Ncd, MC6, inhe absence of microtubules. The MC6 [ -32 P ]ADP complex (5 M

MC6) wa s ra pidly mixed wit h 0.30 mg/ml creat ine kinase, 4 mMphosphocreatine in th e absence ( E ) or in t he presence ( F ) of 5 m MMgATP at 25°C. All concentrations reported are nal concentra-ions af ter mixing. The da ta were t to E q. [4], [ADP ] A

exp( k 1 t ) C , where the sum of the ampl i tude ( A ) a n d t h econstant te rm ( C ) is equal to the ADP concentration at t ime 0.Th i s sum rep resen t s t he t ot a l MC6 enzyme s i t es t ha t b ind

-32 P]ADP tightly to form the MC6 ADP intermediate and pro-vides t he a ctive site concentra tion at 4.1 M. In the presence ofunla beled MgATP ( F ) , the ra te of [ -32 P]ADP release (k 1 ) w a sdetermined to be 0.003 s 1 . Repr in ted wi th permiss ion f rom

Mackey and Gilbert (11). Copyright © 2000 American ChemicalSociety.


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Five micrograms of puried myosin ( 200 nM sites)was mixed wi th 400 nM [ -32 P ]ATP in a 100- Lreact ion volume. The react ion mixture wa s incu-bated for 20 s at 25°C, followed by the addition of 1mM unlabeled MgATP and incubation for an addi-ional 10 min t o chase the [ -32 P]ATP bound at the

act ive s i te . The react ion was quenched with acid,and the l ibera ted P i was quant ied fo l lowing or-ga nic extra ction (13, 14). Alterna tively, r a diola beledATP can be separa ted from the products ADP [ -32 P ]P i by TLC, and [ -32 P ]P i quantied direct ly.The 20 s incubat ion w a s suf ciently long t o a llow forone ATP turnover but not two turnovers. Therefore,he assay provides a quanti tat ive determinat ion ofhe M ADP P i intermediate.

This a pproach ha s been modi ed t o measure a c-ive s i tes for an enzyme in w hich ADP is t igh t ly

bound; th e exa mple we present is dimeric Ncd, MC1.Five m icromolar MC1 (N ADP) i s incubated wi thra ce am ounts of [ -32 P]ATP for times ranging from

30 s to 60 min. The react ions are quenched withacid, a nd the products [ -32 P]ADP and P i are sepa-ra ted f rom [ -32 P ]ATP by TLC an d qua nti ed. AsADP is re leased f rom the ac t ive s i te, [ -32 P ]ATPbinds to the act ive s i te and is hydrolyzed. BecauseADP product release is so s low (0.003 s 1), eachactive site under the conditions of the assay retains[ -32 P ]ADP (Fig. 2). An importa nt a ssum ption of th isassay i s tha t [ -32 P ]ATP binding an d hy drolysis a resignicantly faster than ADP product release suchha t once ADP is r elea sed f rom the ac t ive s it e,

[ -32 P ]ATP wi ll immedia te ly b ind and be hydro-yzed. It is importa nt t o note tha t t his assa y w ill not

report an act ive s i te concentrat ion tha t is higherhan the 5 M motor concentration. The reaction is

assumed to contain 5 M Ncd si tes as well as 5 ADP with a trace amount of [ -32 P ]ATP equilibra twi th N ADP . The concentra tion of [ -32 P]ADP bouat the a ct ive is determined by the equa t ion

ADP* ADP 0 ct sADP / ct s ADP ct s ATP ,

w here [ADP *] represents ra diolabeled ADP forma t t he active site, [ADP ]0 in the equat ion is assumto be 5 M, cts AD P represents the counts in the spmigra t ing a s ADP , and ct sATP represents the counin th e spot migrat ing a s ATP . The da ta are plot tas a funct ion of t ime and t to a s ingle exponenfunction (Fig. 2). This a ssa y detects the concentrt ion of s i tes tha t a re 5 M, determines the t irequired to exchan ge ADP at the a ct ive s ite for diolabeled ATP for subsequent experiments, and etima tes th e rat e consta nt for ADP product releasethe absence of microtubules.

STEADY-STATE ATPase MEASUREMENTS

Steady-State Kinetic ParametersThe rst goal of a steady-state kinetic analysis

a molecular motor is to “get to know” the molecumotor to compare i ts character is t ics with thoseother molecular motors. These experiments requironly trace amounts of enzyme ( g); therefore, thexper iments a re among the rs t per formed af tpuricat ion of the protein. Because th e steady -stakinet ic para meters a re ba sed on the ent ire popultion of molecules, it is critical that the concentratiof active sites be d etermin ed. For microtubule-ba smolecular motors , ve s tea dy-sta te para meters cbe determined: k ca t, K m ,ATP , K 0.5,Mts , k ca t/K m ,ATP , ak ca t/K 0.5,Mts .

k ca t is dened as the turnover number (micromol

product produced per second per active site of tenzyme) and is expressed in units of reciprocal seonds . I t i s impor tan t to remember tha t k ca t repsents the maximum rate constant of product formt ion a t s a tu ra t ing subst r a t e . For a microtububased motor, sat urat ing substrate implies th at bothe microtubules and MgATP are at sufciently hiconcentrations for maximal microtubule activatiof ATP turn over. Therefore, t he stea dy-sta te kineics must rs t be determined as a funct ion of microtubule concentration with MgATP saturatin

(typically 1–2 mM nal concentration is used), flow ed by determina tion of the kinetics at sa tura ti

FIG. 2. MC1 active si te determination by nucleotide binding.MC1 (N AD P ) a t 5 M w a s r ea ct ed w i t h t r a ce a m ou n ts of

-32 P]ATP, and the r eac t ion was quenched a t va r ious t ime

points. The dat a were t t o a single exponentia l function (Eq . [4])which provides an active site concentration of 4.9 M.


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microtubule concentr a tion w ith the MgATP var yingfrom low to high concentrations. For Ncd, saturatingmicrotubules could not be obtained for the assa ybecause of the h igh v iscos ity associa ted wi th therequ ired microtu bule concentr a tion ( 100 M tubu-in) (11, 15). Because only 50 M microtubules could

be used for the ATP concentration dependence, thek ca t determined was lower at 1 .6 s 1 t han tha t ob -ained by the microtubule concentration dependence

a t 2.1 s 1 (11). These da ta do not re ect inconsist en-cies in the experiments. Rather, the results empha-s ize the meaning of k ca t, i. e. , t he max imum ra t econs tan t of ATP turnover a t sa tura t ing microtu-bules and sat urat ing ATP .

The K m (K m ,ATP or K 0.5,Mt ) is an apparent dissocia-ion constant that represents the overal l dissocia-ion constant of all enzyme-bound species. The key

n understanding K m is the real izat ion that i t rep-resents al l th e substrat e a nd product intermediatesbound to t he enzyme a nd is therefore a funct ion ofal l the ra te consta nts in t he pathw ay. Although i t isnot the t rue substra te dissociat ion consta nt for theE S complex, the K m provides important informationfor chara cterizing a m olecular motor by de ning th esubs t r a t e concen t r a t i on a t wh ich the r a t e of t hereact ion is equal to 12 k ca t. The K m ,ATP determined bysteady-state kinetics can also be compared with theK m ,ATP obtained from m oti l ity assa ys. Leibler a nd

Huse (16) proposed that the rat io of the moti l i tyK m ,ATP and the solut ion kinet ics K m ,ATP is approxi-mat ely equal t o the n umber of motors required forsustained movement . This rat io then can providenforma tion about processivity a nd t he dut y cycle atni t ia l s tages of character izat ion prior to the more

complex opt ica l t rap mot i li ty exper iments. Fordimeric kinesin, this ratio reveals tight coupling (7,17–20) in w hich a sing le, dimeric kinesin molecule isrequired for continuous movement along a microtu-bule. Yet for dimeric Ncd, the ratio is much higher(235 M/23– 40 M), suggesting that several dimericNcd molecules are required for sustained microtu-bule movement (11, 15, 21, 22).

The k ca t/K m parameter is dened as the apparentsecond-order ra te consta nt for productive substra tebinding, and it sets a low er limit on th e true second-order rate constant for the substrate binding. Thesimilarity between the true second-order rate con-s tan t for subs t ra te b inding a nd t he k ca t/K m s teady-sta te para meter is determined by the kinet ic part i -

ioning of the E S complex eith er t o dissocia te t o E S or to go forwa rd for ca ta lysis. In th e ca se of dimeric

kinesin, K401, kinetic partit ioning of the K Aintermediat e (Scheme 2)

M K ATP L | ;k 1

k 1

M K ATP L | ;k 2

M K ADP P M K ADP L | ;k 6

M K

k 3 . . k 5

K ADP P L | ;k 4

K ADP P

SCHEME 2. Mt K401 ATPase mechanism.

wa s detected such tha t th e k ca t/K m was s ignicanless tha n the t rue second-order ra te consta nt fATP binding (23, 24). The magnitude of k ca t/K m be u sed to eva lua t e enzyme speci city for ss tra tes; therefore, it can be a very valuable paraeter to determine early in the analysis especiallymore than one nucleotide can be hydrolyzed by tmolecular motor of interest (23, 25).

The k ca t/K 0.5,Mt parameter (also referred to as (26)) is dened as the apparent second-order raconstant for productive motor association with tmicrotubule. The principles discussed a bove a lhold for this constant . However, i t is importantremember t hat k ca t/K 0.5,Mt may or may not be equalent to the true second-order rate constant for mcrotu bule binding. One mu st consider pa rt itioningthe Mt E nucleot ide intermediate as well a s the netic mecha nism.

Microtubule Preparation

As experimenta lists, w e ta ke great strides to ptect our enzyme’s nat ive s ta te t o ensure the a ct it i es we measure a re representa t ive of the ac t imolecular motor. Yet , i t i s equal ly impor tan t think a bout the lament pa rtner, especial ly for tmicrotubule-based motors because microtubules ar

more la bile tha n either F-actin or DNA and ma nythe measurements are dependent on the concentrtion of microtubules present in the assay. On the dof our experiments, the microtubules are assemblefrom soluble tubulin (cold depolymerized and claed by centr i fugat ion) and stabi l ized with 20 taxol (7). This procedure yields microtubules thare competent for polymerization with essentially soluble tubulin remaining. The tubulin concentrtion for this preparation is determined prior to eperimenta tion by the Lowry method (27). Althou

20 M ta xol is rout inely included in t he microtu bubuffers, the taxol concentration can be increased


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be stoichiometric for experiments at high microtu-bule concentr a tions or high sa lt concentra tions.

Radiolabeled ATPase Assays

The advantage of using a radiolabeled substrateo determine s teady-sta te turnover is t he high sen-

si t ivity of the assa y. A complete substrate concen-ra tion series of experiments ca n be performed w ith

a few micrograms of enzyme. Because we separateADP P i from ATP using TLC, either [

32 P ]ATPor [ 32 P]ATP can be used. Our assay is describedusing formic acid rat her tha n H Cl, a recent modi -ca t i on s ug ges t ed b y D r. S m it a P a t el (U M D NJRWJ Medical School). B eca use formic a cid is vola-ile, the a cid-qu enched reaction mixtur e ca n be spot-ed directly onto the TLC plate for elution withouthe r equ ir emen t t o neu t r a lize t he r eac t ion wi th

base. The formic acid quench procedure decreaseshe t ime required for t he assa y; however, steps must

be taken to avoid acid hydrolysis of the ATP. Ourquenched reac t ions a re s tab le on ice for 60 minwi thout increased format ion of ADP a l though weroutinely spot immediat ely a fter q uenching ea ch re-a ction mixture.

For the ATP a se measurements, t w o tubes a re pre-pared each containing 50 L for a tota l react ionvolume of 100 L. E nzyme tube A conta ins the mo-ecular motor, microtubules, ATPase buffer, and 40M t a xol. S u bs tr a t e t ube B con t a in s 1 L of

[ -32 P ]ATP , unlabeled MgATP , a nd ATP a se buffer.The reactions are initiated by the addition of 5 L ofube A to 5 L of tube B and incubated at 25°C for

various times (eight time points per 100 L). The10- L reaction for each time point is terminated byhe addit ion of 10 L of 5 N formic acid. The zeroime points are determined by denaturing the en-

zyme (5 L tube A) with 10 L formic acid prior tohe addi t ion of 5 L o f t h e [ -32 P ]ATP substra te

mixtu re (t ube B). An a l iquot (1.5 L ) of t hequenched react ion mixture for each t ime point isspotted onto a PEI-cellulose F TLC plate (20 20cm, plastic-backed, EM Science) and developed in0.6 M potass ium phosphate buffer, pH 3.4, wi thphosphoric a cid. R a diolabeled nucleotide is qua nti-ed d i rec t ly us ing a Phosphor imager. [ -32 P ]ATP(or [ -32 P]ATP) a s purchased con ta in s a sma lla mount of ADP P i (1–2%) w hich is evid ent a t th ezero time reactions. The concentration of productobta ined a t ea ch time point is t herefore corrected for

he contaminat ing [ -32

P ]ADP determined in ea chreact ion by the zero t ime points . The data are ini-

tially plotted as the concentration of product formas a funct ion of t ime and t to a s t raight l ine. Tslope provides the ra te of the reaction (micromolsubstrate converted to product per micromolar ezyme sites per second) for each ATP concentratioThe rates (s 1) of th ese reactions a re th en plott eda function of ATP concentr at ion, a nd t he dat a a reto a hyperbola t o determine the st eady-sta te kineconstants, k ca t a nd K m ,ATP . For th e substra te conctra t ion dependence experiments , the lament cocentra tion must be high enough t o provide the maimum ra te of ATP hydrolys is a t sa tura t ing Aconcentrat ions. Similar ly, to determine the K 0and the k ca t from the microtubule concentration dpendence experiments, the concentr a tion of ATmust be sufcient ly high to provide the maximura te of ATP turn over.

Coupled NADH Oxidation System

ATP ase assays can be successful ly per formwithout using radiolabeled substrate, and one poular coupled assay is based on quantifying the crease in uorescence of NADH as it is oxidizedNAD (Fig. 3). This approach is routinely used fthe microtubule kinesin (M K) ATP a se (28, 29). ThM K complex (100–200 nM kinesin, 0–8 M t ulin, 20 M taxol) is mixed with 0.5 mM MgATP athe coupled NADH system (1.5 mM KCl, 0.2 mNADH , 0.5 mM ph osphoenol pyruva te (P E P ), 0.01pyruva te kinase, a nd 0.03 U lacta te dehydrogena sconcentrations reported are nal concentrations ter mixing. The decrease in uorescence is montored a t 340 nm, a nd t he t ime-dependent quenchinof uorescence is t to a l ine to obtain the s teastate rate of ATP turnover. The advantages of t

FIG. 3. Coupled NADH oxidation assay to determine steastate ATPase. ATP turnover by a molecular motor (K) is linkedthe oxidation of NADH to NAD to observe the time-depend

decrease in uorescence a t 340 nm. P EP , phosphoenolpyruvaPK, pyruvate kinase; LDH, lactate dehydrogenase.


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assay are tha t i t i s re la t ive ly s imple and does notrequire ra dioa ctive nucleotide. However, contr olsmust be done to ensure th a t t he coupled a ssa y is fastenough to recycle the ATP and prevent ADP accu-mulat ion. In a ddition, a s t he concentr a tion of micro-ubules is increased, th e light -sca tt ering ar tifact in-

creases such t ha t the NADH optical signa l becomesunreliable for rate determination.

Malachite Green Assay to Detect Inorganic Phosphate

The adva nta ges of using this a ssa y (30) a re tha t i ts relat ively simple to perform, does not require ra -

dioactive nucleotide, and can be used to assess theATP a se activity of ATP a na logs such a s 2 (3 )-O -( N -methylanthraniloyl) ATP (mantATP) where radiola-beled ATP a na logs a re not commercia lly a vailable(8, 24, 31, 32).

The reagents include 0.045%malachite green hy-drochloride in water (45 mg per 100 mL H 2O), 4.2%a mmonium molybda te in 4 N H Cl (4.2 g per 100 mL4 N H Cl), 34%sodium citra te (34 g per 100 mL H 2O),and 5 mM KH 2P O 4 a s the s t anda rd phosphate solu-ion. The color reagent (0.8 mL per sample) is pre-

pared directly before the ATPase assay is performedby mixing 3 vol of the 0.045%malachite green solu-ion with 1 vol of th e 4.2% amm onium molybdat e

solution for 20 min . The color rea gent is th en lter edusing Whatm a n (Clifton, N J ) No. 5 lter pa per.

The ATPase assay is performed (25 L reaction),quenched with 25 L of 2 N HCl , a nd neut ra l izedwi th 2 M Tr i s–3 M NaOH ( 4 L) as describedpreviously (32). For each 54 L ATPase reaction,800 L of the color reagent is added and vortexedmmediately. The mixture is incubat ed for 1 min a t

room temperature, followed by addition of 100 L ofhe 34%sodium citrat e solution a nd immedia te vor-exing. Color development is a l lowed to occur at

room t empera ture for 30 min, a nd t he a bsorba nce at

660 nm is read immediat ely aga inst a buffer reagentblank. For the phosphate s tandards (20–500 M),he stock solution is diluted to obtain nal concen-r a t ion s in 25 L. The P i s t a nd a rd s a r e a ls o

quenched with HCl and neutral ized comparable tohe ATPase reactions. For our kinesin experiments,

we used microtubules as high as 16 M tubulin toreach full activation of the steady-state ATPase (24,32). However, for Ncd, a much higher concentrationof microtubules was required to approach ATPasesaturation (50 M). As the microtubule concentr a-

ion increased, the background concentration of P increased such that there was a loss of sensitivity for

detection of the P i generated by ATP turnover. Thlimitation of the malachite green assay for studymicrotubule-based motor proteins is th a t i t m a y nhave the sensi t ivi ty required to quantify P i gena ted dur ing nucleotide tur nover a t high microtubuconcentrations.

PRE-STEADY-STATE KINETICS

The stea dy-sta te kinetic a na lysis provides impota nt basic informa tion a bout a molecular motor, bthe resul ts cannot address the events at the act isite following substrate binding and prior to produrelea se. Furth ermore, the st eady-sta te kinetics canot provide an understanding of the cooperat ivibetween motor doma ins tha t is essential t o unidirt ional movement . In contrast , pre-steady-state knetics ca n provide this informa tion. Tra nsient-stakinet ic methods can be used to measure the rata nd dissociat ion consta nts of individua l steps in tpathway of a molecular motor in the presence aabsence of the lament partner. The constants dtermined from these experiments represent indiviua l pieces to a jigsaw puzzle. The goal a t the endthe a na lysis is to be able to t together the piecedene the pathway and understand the couplingATP turn over t o energy t ra nsduction for unidiretional m ovement.

However, th e experiments typica lly r equire ra pmixing instrumentation (chemical quench-ow astopped- ow instruments), mill igram amounts protein, a nd a s ignicant t ime investment to estlish a pat hw a y. Our goal in this section is to provthe reader with an understanding of the experimetal design, what can be learned from each expement , and the l imi ta t ions in in te rpre ta t ion of tdata . We refer the reader to several excel lent rview s on tra nsient-sta te kinetic theory an d methoology for a more complete presentation (1–4).

Rapid Chemical Quench-Flow Methods

This method involves the rapid mixing (1–2 ms) the enzyme wi th the subs t ra te t o ini t ia te the retion, followed by termination of the reaction at desired time with a quenching agent (hydrochloacid, formic acid, triuoroacetic acid). Because quench denatures the enzyme, the subs t ra te aproduct(s) bound at the act ive s i te are released

the solution. The product formed at each time inteva l can be quant i ed; therefore, th i s exper im


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measur es the time course of product format ion. In apre-steady-sta te kinet ic experiment , the enzymeconcent ra t ion i s typ ica l ly much h igher than therace a mount used for s teady s ta te k inet ics . The

enzyme concentrat ion must be high to provide t hesignal necessary to observe and quantify react ionsa t t he active site during th e r st t urnover. Althoughhese experiments do provide informa tion a bout the

ra te of th e reaction, the da ta a lso de ne the kineticsn a bsolute concent ra tion un its w hich can be rela tedo enzyme active sites. This amplitude informations cr i t ical to dening a pathway.

Acid Quench

We have used the rapid quench approach to de-ermine the ra te cons tan t of ATP hydrolys is for

dimeric Ncd, MC1 (Fig. 4) (33), and dimeric kinesin,

K401 (Fig . 5) (23). These molecula r motors a re u sedo describe the experimental protocol and also tol lustrate what can be learned about a motor fromhis type of analysis . The Mt Ncd complex (20 Mubulin, 5 M MC1, 20 M ta xol) wa s ra pidly mixedn the quench-ow instrument with increasing con-

cent ra t ions of [ -32 P ]ATP . (All concentr a tions re-ported are nal concentrat ions af ter mixing 1:1.)Each reaction was quenched with acid and expelledfrom the instrument . An al iquot (1.5 L) of eachreact ion mixture was spot ted onto a PEI-cel lulose

TLC pla te and developed wi th 0.6 M potass iumphosphate buffer, pH 3.4, with phosphoric acid tosepara te [ -32 P]ATP from [ -32 P]ADP P i. The ra-diolabeled nucleot ide was quantied direct ly, andhe concentrat ion of ADP for each t ime point wa shen ca lcu la ted f rom the counts in the ADP spot

(cts AD P) rela tive t o counts in t he ATP spot (cts ATP ) a sdescribed by

ADP ATP 0 ct s ADP / ct s ADP ct s ATP , [6]

where [ADP] represents radiolabeled ADP productforma tion, a nd [ATP ] 0 is the concentration of ATPused in the react ion. All t ime points must be cor-rected using t he zero time point becau se of th e 1– 4%contaminat ing [ -32 P ]ADP present wi th the rad io-nucleot ide. The da ta were t to the burst equa t ion

ADP A 1 exp k bt k 2 t , [7]

where A is the amplitude of the burst representing

he format ion of [ -32

P]ADP P i a t t he a ct i ve s it eduring the rst turnover, k b is the rate constant of

the pre-steady-state burst phase, k 2 is the rate cstant of the linear phase and corresponds to steadstate turnover, and t is t he t ime in seconds.

Figure 4A shows t he acid quench da ta for MC1four different ATP concentrations (33). There is ainitial, rapid, exponential phase of product formt ion tha t occurs a t the ac t ive s i te dur ing the turnover. The ini t ia l burst phase is fol lowed byslower, l inear phase of product formation that cresponds to subsequent turnovers of ATP by tenzyme. The observation of a burst of product f

FIG. 4. P re-steady-sta te ATP hydrolysis by MC1. The pformed Mt N complex (5 M MC1, 20 M tubulin) was rapmixed in t he chemical q uench ow instrument with varying cent ra tions of [ -32 P]MgATP and allowed to react for 0.01–2 s. concentrations reported are nal after mixing. (A) Transients ATP hydrolysis in the presence of 10 M (F ), 25 M ( ), 50

(} ), a nd 100 M (Œ) [ -32

P]MgATP. The data were t to the buequa tion (Eq . [7]). Only t he initia l 0.8 s of each tr an sient is shoto expand the t ime domain of t he in i t ia l burs t phase. (B) Psteady-sta te kinetic burst ra te consta nt calculated for each t rs ient and plo t ted as a funct ion of [ -32 P ]MgATP concentra tiThe dat a were t to a hyperbola w hich yields k 2 23.4 s 1

K d,ATP 16.4 M (Scheme 3). The [ -32 P ]MgATP concentra tiused were sufciently high such t ha t ATP binding ( k 1 ) no lonlimits the rate of the rst turnover. Therefore, the maximum rconstant for the burs t predicts the ma ximum ra te constant ATP hydrolysis ( k 2 ). (C) Amplitude of t he pre-stea dy-sta te buplotted as a function of [ -32 P ]MgATP concentra tion. The dwere t to a hyperbola (maximum burst amplitude 5.7

M). Reprinted with permission from Foster and G ilbert (3Copyright © 2000 American Chemical Society.


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mation in this experiment indicates that ATP bind-ng and hydrolysis are s ignicantly faster than the

rat e-l imit ing s t ep th at occurs af ter cat alysis . Thedata for each ATP concentration were t to Eq. [7]which provides the burs t ra te ( k b) , the ampli tude( A ), and t he rat e consta nt of the linear pha se (k 2 ) inunits of micromolar product per second. To convertk 2 to a rst-order ra te consta nt (s 1), k 2 is divided byhe enzyme ac t ive s ite concent ra t ion used in the

react ion. One an t icipat es tha t the ra te consta nt , k 2 ,wil l be consistent with the s teady-sta te kinet ic rateconsta nt once enzyme, m icrotubule, an d ATP con-centra tions a re considered.

Figure 4B shows the burst ra tes obta ined from exponent ial pha se (E q. [7]) a nd plotted a s a functiof ATP concentrat ion. Note that the burst rate icreases as a function of ATP concentration. At hiATP concentra tions, ATP binding no longer limithe ra te of the rs t tu rnover ; t herefore, the mamum ra te consta nt of the burst pha se obta ined frothe t of the da ta to a hyperbola provides the rconstant for ATP hydrolysis (Scheme 3).

M K ATP L | ;k 1

k 1

M N ATP L | ;k 2

M N ADP P M N ADP L | ;k 6

M N

k 3 . . k 5

N ADP P L | ;k 4

N ADP P

SCHEME 3. Mt Ncd ATP a se m echa nism.

The t of the da ta a lso provides th e K d for substrbinding because this experiment measures directthe format ion of product a t t he active site during trst turnover.

Figure 4C shows the burst ampli tudes obtainfrom Eq. [7] and plotted as a function of ATP cocentration. The burst amplitude represents the foma t ion o f t he N ADP P i intermediate (Scheme and can be re la ted to the concent ra t ion of ac ts i tes of the enzyme. Note that the maximum buampli tude determined at 300 M ATP is 4.5 suggest ing approach to a ful l burst ampli tude o

M. The fact that the burst ampli tude saturatesthe enzyme concentration used in the experiment

M) is indicat ive of relat ively t ight ATP bindisuggesting that there is l i t t le, if any, partit ioningthe N ATP intermediate. The burst amplitude datfrom this type of experiment are frequently useddetermine the concentration of active sites (34–36In contra st , t he sa me experiment at s imilar mictubule and nucleotide concentrations for dimeric k

nes in , K401 (F ig . 5), sugges t s pa r t i t ion ing Mt K ATP intermediate between the forward patwa y towa rd ATP hydrolys is and the reverse paway to ATP dissociation (Scheme 2). In the casekinesin, the maximum ampli tude of the burst wsignicant ly less tha n the concentrat ion of enzyactive sites in the experiment.

The bur s t amplit ude da t a can a l so be u sed obtain mechan ist ic informa tion about t he pat hwaFor monomeric kinesin, a super-stoichiometric bursampli tude w as inte rpreted a s indica t ive t ha t t

monomeric kinesin remained t ight ly bound to tmicrotubule for multiple t urnovers of ATP a nd th

FIG.5. Kin etics of ATP h ydr olysis for the Mt K401 ATP a se. TheMt K401 complex (10 M K401,12 M tubulin) was preformedand reacted with [ -32 P ]MgATP for 5–200 ms, follow ed by t he a cidquench. (A) Tra nsients for ATP hydrolysis in th e presence of 25

M (F ), 50 M ( ), 100 M (Œ ), 200 M (E ), 600 M ( ), 800 M‚ ) [ -32 P]MgATP. The curves were calculated by numerical in-

egration with the following rate constants: k 1 1. 8 M1

s1

,k 1 200 s 1, k 2 100 s 1 , k 4 200 s 1. (B) Pre-steady-statekinetic burst rate constant determined for each transient usingEq. [7] and plotted as a function of [ -32 P ]MgATP concentra tion.The da t a were t t o a hyperbola wh ich y ields k 2 93 s 1

Scheme 2). The [ -32 P ]MgATP concentra tions used were suf-ciently high such t ha t ATP binding ( k 1 ) no longer l imi ts theat e of the rst turnover. Therefore, the ma ximum rat e consta ntor the burst predicts the maximum rate constant for ATP hydro-ysis (k 2 ). (C) Amplitude of the pre-steady-state burst (Eq. [7])

plotted as a function of [ -32 P ]MgATP concentra tion. The da tawere t to a h yperbola (maximum burst amplitude 5.5 M andapparent K d,ATP 87 M). Reprinted with permission from Gil-

bert and J ohnson (23). Copyright © 1994 American ChemicalSociety.


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ATP hydrolysis was uncoupled from movement (24,37). For dimeric Ncd, the observat ion of a burstamplitude approxima tely equal to t he enzyme con-cent ra tion (1:1 stoichiometry) wa s interpret ed as ev-dence that dimeric Ncd was not processive for ATP

hy dr olysis (22, 33).

Pu l se–Ch ase

To measure the kinet ics of ATP binding or tonvestigate possible par tit ioning of t he E ATP inter-

mediate, a pulse– cha se experimenta l design is used.The pulse–chase experimental results for dimerickinesin, K401 (Fig. 6), provided evidence that kine-sin binds ATP w eakly (23). The Mt K401 complexwas r ap id ly mixed wi th [ -32 P ]ATP for 5–200 ms(5–8 half-lives of the hydrolysis reaction), followedby a 5 mM MgATP chase. The react ion was then

termina ted by th e addition of acid, and t he produwere separated by TLC for analysis.

The concentration of MgATP for the chase must in la r ge excess t o pr even t t h e [ -32 P ]ATP [ -32 P ]ADP from binding the act ive s ite during time of the chase and prior to the acid quench. Tpulse– cha se experiment is designed to a llow all net ical ly s table [ -32 P]ATP at the act ive s i te to conver t ed t o [ -32 P ]ADP (Scheme 2). Howevweakly bound [ -32 P]ATP or [ -32 P ]ATP in s olutiwill not partit ion toward ATP hydrolysis. The daa re qua nti ed from t he TLC a s described by Eq s.and [7].

The amount of ADP formed in the ac id quenexper imen t r epre sen t s K AD P P i K AD PAD P. H ow e ver , in t h e pu ls e– ch a se expem en t , t h e a m ou n t of AD P f or m ed r epr es enX1 K ATP K AD P P i ADP , w i th X1 represei ng t h e p a r t it i on in g f a ct or, t h e f r a ct i on of K ATP in t ermed ia t e t ha t p roceeds t oward AThydrolysis (Scheme 2):

X1 k 2/ k 2 k 1 .

The partit ioning factor can be determined from tATP hydrolysis rate constant ( k 2 ) determined frthe a cid quench experiment an d by using the K ISI M comput er modeling progra m (38) to a na lyze tpulse–chase da ta to dete rmine k 1 (23). The raconstant for ATP dissociation ( k 1 ) can not be msured directly because of the difculty in obtainins tab le Mt K ATP interm ediat e. Therefore, k 1 wdetermined by computer simulation (23).

Stopped-Flow MethodsThe s topped-ow ins t rumen t , like t he r ap

quench, ra pidly mixes reacta nts on a mill isecot ime scale , but for this method a n opt ical s ignaobta ined. The optical signa l can be light scat terinabsorbance, turbidity, or uorescence, but the goin a stopped- ow experiment is tha t the optica l sna l cor re la te wi th a d is t inc t s tep in the reac t iSt opped- ow experiments a re essentia l beca use t happroach can measure the nucleot ide-dependenconformat iona l cha nges th a t occur a s t he motor ptein interacts w ith i ts lament part ner. The l imit ion of the method i s in the in te rpre ta t ion of tstopped-ow kinetic data (discussed below).

Subst ra te Bin din g

The kinetics of ATP binding can be measured uing an intrinsic uorescence change that occurs

FIG. 6. Kinetics of ATP binding for the Mt K401 ATPase. The

Mt K401 complex (10 M K401,12 M tubulin) was preformedand reacted wi th [ -32 P ]MgATP for 5–200 ms, followed by th e 5mM MgATP chase. (A) The tra nsients for ATP binding in thepresence of 25 M (F ), 50 M ( ), 100 M (Œ ), 200 M (E ), 600

M ( ) [ -32 P]MgATP. The curves were calculated by numericalntegration with the following ra te consta nts: k 1 1. 8 M 1 s 1,

k 1 200 s 1 , k 2 100 s 1 , k 4 200 s 1 (Scheme 2). (B)Presteady-state kinetic burst rate constant determined for eachra nsient using E q. [7] an d plott ed as a function of [ -32 P ]MgATP

concentration. (C) Amplitude of the pre-steady-state burst (Eq.7]) plott ed a s a funct ion of [ -32 P]MgATP concentration. The data

were t to a h yperbola (maximum burst amplitude 7.3 M andapparent K d,ATP 69 M). Reprinted with permission from Gil-

bert and J ohnson (23). Copyright © 1994 American ChemicalSociety.


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ATP binding at the active site (excitation at 290 nmw ith uorescence emission a t 340 nm ). B eca use ofhe locat ion of t ryptophans present in the cat alyt ic

motor domain, the ATP binding kinetics for actomy-osin w ere den ed by using t he intrinsic uorescencesignal (39, 40) . However, when this approach wasa pplied to kinesin, there wa s no detecta ble chan ge inntr insic u orescence (9). In retr ospect, th is result is

not su rpr is ing based on the f ac t t ha t w i th in t heca ta lytic motor domain of kinesin, there ar e no tryp-ophan residues and only a few tyrosines that could

serve as r eporters of conforma tiona l cha nges. Sa dhua nd Ta ylor (9) investigat ed a number of the uores-cent ATP analogs that were used in studies for my-osin and reported that only mantATP gave a uo-rescence enha ncement of high enough ma gnitude t obe usa ble for kinet ic stu dies for kinesin. This a na loghas also proved to be very valuable for studies withkinesin superfamily members including Ncd, Eg5,and Kar3 (11 , 22 , 24 , 32 , 33 , 41–45) as wel l asmyosin superfamily members (36, 46–49).

One a nt icipat es tha t a uorescent n ucleot ide an-alog may have different kinetic parameters in com-parison t o the na tura l substrat e; therefore, i t is im-porta nt to measure t he s tea dy-sta te kinet ics of t hea na log to determine the k ca t and the K m . For dimerickinesin, K401, and monomeric kinesin, K341, thek ca t for mantATP was comparable to the k ca t usingATP (24, 32). H owever, th e K m ,mantATP w as e leva t eda pproxima tely t hreefold. Although the K m is ele-va ted somewhat , mantATP is cons idered to be agood a na log beca use of its uorescence enha ncementand the a b il ity to detect s teps in t he pa thwa y t ha tma y n ot be accessible using t he nonu orescent, na t-ura l subs t ra te . F ur thermore, mantADP has beenextremely valuable in resolving the coopera t ivitybetween the motor domains of dimeric kinesin andNcd as discussed below.

To measure the kinetics of mantATP binding, a

Mt motor complex was preformed and rapidly mixedw ith m a ntATP in th e stopped- ow. For dimeric a ndmonomeric kinesin as well as dimeric and mono-meric Ncd, th e uorescence tr a nsient s show a bipha -sic signal with a rapid increase in uorescence fol-ow ed by a s ig ni ca n t ly s low er d ecr ea s e in

uorescence (Fig. 7A). The in terpret a tion of t he in i-ial , fast exponential phase is s t raightforward and

can be correlat ed w ith m ant ATP binding to t he a c-ive site. However, the interpretation of the second

phase, t he s low decrease in uorescence, is more

difcult to interpret. Does it represent a conforma-ional change af ter mantATP binding and prior to

ma ntATP hydrolysis? Does it represent ma ntAThydrolysis? Does i t represent a conformat ioncha nge a fter ma nt ATP hydrolysis? This exam ple lustra tes a limita tion of the st opped- ow methodtha t a rat e associated w ith a n opt ical s ignal canalw ays be interpreted accurat ely. Therefore, i t importa nt to explore an d consider al l reasonabinterpretat ions of a stopped- ow signal.

The subst ra te binding experiment is t ypically rpea ted a s a function of man tATP concentr a tion, athe rat e consta nt of ea ch init ia l , exponential phais plotted a s a fun ction of ma nt ATP concentr a tionshown in Fig. 7B. The data are t to

k obs k on mantATP k off,

FIG. 7. 3 Mant-2 -dATP binding t o the Mt MC6 complex. T

preformed Mt MC6 complex (8 M MC6, 20 M tubul in) ra pidly mixed in the stopped- ow instrum ent w ith t he uorescATP an alog 3 mant-2 dATP . (A) A tra nsient is shown a t 1003 mant-2 dATP . The uorescence signa l (jagged curve) repsents an average of ve traces, and the smooth l ine is the t oda ta to a double exponentia l function (Eq . 11). The ra te constof the initial observed uorescence enhancement is 150 s 1 ,lowed by a slower phase in which the relative uorescencecreased ( k ob s 11 s 1) . (B) Apparent rate constants for thecrease (F ) and decrease (E ) in uorescence enhancement afunction of 3 mant-2 dATP. The data from the init ial , rapid crease in uorescence ( F ) were t to Eq. [9], providing the secorder rate constant for substrate binding at 2.03 M 1 s 1 and

y intercept, k of f 28 s1

. The maximum ra te constant of second phase ( E ), the decrease in uorescence, was 13.7 s 1.


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where k o bs i s the ra te cons tan t ob ta ined f rom theexponential phase of the uorescence change, k o ndenes the second-order rate constant for mantATPbinding, a nd k of f represent s dissociat ion of ma nt ATPby either t he reverse rea ction, the forw a rd rea ction,or a combina t ion of bo th . In F igs . 7A and 7B, weshow substrate binding for the man tATP isomer,3 mant-2 dATP . The da ta for the slow, second pha seare plotted as a function of 3 mant-2 dATP concen-ration. The data did not reveal a substrate concen-rat ion dependence as expected i f 3 mant-2 dATP

binding were l imit ing 3 mant-2 dATP hyd rolysis.Also, the m a ximum r a te consta nt a t 13.7 s 1 wa s tooslow to account for 3 mant-2 dATP hydrolysis. Theslow phase was assumed to represent a conforma-iona l change in the pro te in a f te r in i t ia l 3 man t -

2 dATP bind ing a nd /or hyd rolysis.The advantage of measuring the kinetics of ATP

binding by us ing a uorescence s igna l i s tha t thestopped- ow can accurat ely measure s ignicant lyfaster rates more accurately than the rapid quenchnstrument . In addit ion, the s topped- ow experi-

ments are much less t ime consuming and less de-manding physically in comparison to rapid quenchexperiments. However, t he pulse– cha se experiments the better experiment to determine partitioning ofhe E ATP intermediate because it provides ampli-ude informa tion in concentrat ion uni ts . When a

uorescent ATP ana log i s used , the invest iga tormust alw ays consider w hether the conta cts tha t oc-cur with amino acids of the act ive s i te are al teredbeca use of the uorescent fun ctiona l group added t ohe nucleotide. Typically, investigators use both the

pulse– cha se ra pid quench experiment an d st opped- ow kinet ics t o evaluat e substrat e binding.

Kinetics of Phosphate Release The kinetics of phosphate release from a molecu-

ar motor can be measured directly using a uores-

cently modi ed phosphat e-binding protein (MDCC-PBP) coupled assay (22, 24, 32, 36, 50, 51). Thismethod was developed by Webb and collaborators(50) a nd is extremely powerful in detecting a point inhe ATPase cycle that has been difcult to measure

di rec t ly. In the coupled assay, the lament motorcomplex is rapidly mixed in the stopped-ow instru-ment w ith ATP in th e presence of MDC C-P B P . Themotor binds and hydrolyzes ATP. When inorganicphosphate i s re leased f rom the ac t ive s i te of themotor, the phosphate-binding protein binds the free

P i ra pidly a nd t ightly, exhibiting a vefold cha nge inuorescence tha t is due t o t he con forma t iona l

change in the phosphate binding protein (50). Thkinetics a re recorded a s r elat ive uorescence (voltbut t he da ta ca n be converted to concentr a tion (ba sed on cont rol experiment s in w hich 2 M MDCPBP is rapidly mixed with known concentrationsKH 2P O 4. Therefore, t he amplitude of the kinesigna l can be evalua ted relat ive to the enzyme sconcentr a tion used in the experiment. This a ssay technically more difcult than traditional stoppow kinetic experiments. However, the MDCC-Pcoupled assa y provides mecha nist ic informa tithat historically has been very difcult to obtainwa s th i s assay t ha t wa s inst rumenta l in our undstanding the mechanistic basis of kinesin’s procsivity (32).

K in eti cs of AD P Rel ease

Probab ly t he ea s ies t method to measu re ADproduct release from the Mt motor ADP intermeate is to use the uorescence signal from mantAD(11, 22, 24, 32, 33, 41–45). In this experiment (oulined in Fig. 8A), motor ADP complex is incubawith mantADP in excess. As ADP is released, mtADP binds the ac t ive s ite . The motor mantAcomplex is then rapidly mixed with microtubules the s topped-ow wi th exci ta t ion a t 360 nm aemission monitored a t 450 nm. Mant ADP uorecence is q uenched by the aq ueous buffer; t herefo

FIG. 8. Experimental designs to determine the mant ADP lease kinetics from the Mt kinesin complex.


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here is a decrease in uorescence as mantADP isrelea sed from t he a ctive site of th e enzyme. For t hisexperiment, ATP is typically included in the micro-ubule syringe to a ct a s a cold cha se and ensure th a t

ma nt ADP once releas ed does not rebind to the activesite.

K i neti cs of M otor A ssoci ati on and Di ssoci ati on w i th t he F i l amen t For actomyosin (52) and for axonemal dynein (53),

hese kinetics w ere measur ed by stopped- ow lightsca tt ering (295 nm). H ow ever, for kinesin a nd Ncd,we monitored turbidity at 340 nm because t he tur-bidity signa l provided great er sensitivity a t low ATPconcentr a tions t o measu re t he dissocia tion kineticsfor Mt kines in and Mt Ncd complexes. The tra di-iona l exper iment to measure motor deta chment

f rom it s cy toske let a l pa r tne r was dened by thea ctomyosin kinetic experiments (52) in w hich thea ctomyosin complex wa s ra pidly mixed wit h MgATPn the stopped-ow. There was a decrease in light-

scat ter ing intensity, an d the dat a w ere t by a s ingleexponential function. The rate constant for dissoci-at ion increased l inearly a s a funct ion of ATP an dapproached 2000 s 1. Because dissociation was sig-ni cant ly faster th a n ATP hydrolysis ( 10-fold), t henterpre ta t ion made by Lymn and Taylor wa s tha t

A M binds ATP , follow ed by ra pid deta chment fromF-a ctin for ATP hydrolysis. When the sa me t ype ofexper imen t wa s per formed for Mt k ines in andMt Ncd complexes, th e kinetics for deta chment w eresignicantly slower at 12–14 s 1 and slower tha n thekinetics for ATP hyd rolysis. However, a dditiona l ex-periments were performed to show denitively thatkinesin a nd Ncd rema in on th e microtubule for ATPhydrolysis (15, 17, 22, 32, 33).

An importa nt point about s t opped-ow dat a isreemphasized by the presentation of the dissociationkinetic experiment. Stopped-ow kinetics are based

on optical signals; therefore, the investigator mustma ke the interpreta tion of wheth er the kinetics rep-r esen t motor det achmen t f rom the lament andwh ether m otor detachment occurs before or af terATP hydrolysis. Although it ma y appear unlikely,one must also consider that the stopped-ow kinet-cs ma y not be measuring detachment but ma y rep-

resent a n ATP -dependent conforma tiona l cha nge oc-cu rr in g w h ile t h e m ot or is s t ill b ou nd t o t h elament. For the monomeric Ncd motor MC6 (11),we observed tha t the a mpli tude associated w ith t he

dissociation kinetics was quite small relative to thesa me experiment for dimeric MC1 at th e same a ctive

site concentration (Fig. 9). We pursued a series experiments as a funct ion of sal t concentrat ion determine wheth er the stopped- ow signal w a s reresenting an ATP-dependent conformational changof the motor bound to the microtubule, or wheththe signal represented a few MC6 motors detachifrom the microtubule. The dra ma tic increase in thamplitude as a function of salt concentration (F9C) indica tes t ha t the stopped- ow signal in Fig. represented a few MC6 molecules deta ching froth e microtubule. Therefore, the interpret a tion of thkinetics was that MC6 does not readily detach frthe microtubule a s proposed for dimeric MC1 athat ATP hydrolysis was uncoupled from moveme(11). However, if the da ta from Figs. 9A a nd 9B wconsidered without t he da ta in Fig. 9C, th e interpta tion of th e dissociat ion kinet ics for monomeric Nwould be quite different. This example with monmeric MC6 emphasizes the importance of carefevalua tion of st opped- ow signals.

The kinetics of motor a ssocia tion a re st ra ightfward for the kinesin superfamily members becauthe motor is puri ed with ADP t ight ly bound a t act ive s i te . The assumption can be made that i tthe kinesin ADP intermediate that binds the mictubule, fol lowed by subsequent ADP release frthe Mt K ADP intermediat e (Scheme 2). For t he asociat ion kinet ics, one expects a n increa se in tu rbiity as the motor binds the microtubule.

The a ssociat ion kinet ics eva lua te productive bining of t he motor to t he microtubule as does tlanding ra te a ssay used to evaluat e molecular momotility (18, 21, 54, 55). In the motility assay, tcoversl ip is coat ed w ith motor a t a known densMicrotubules a re a dded, a nd t he number tha t moare scored. Landing rates (Mt s 1 mm 2) a re plotas a function of motor density. Thus, the kinetic amotility experiments are probing the same point the crossbridge cycle, productive motor associatiwi th the lament .

Motor Domain Cooperativity

For the kinet ic experiments , the rate constanare reported as k ob s to emphas ize tha t the da ta port the stopped- ow signals from both motor mains for d imer ic motors a nd as many as s ix suni ts for many DNA hel icases and the F 1-ATP a sThe challenge is to design experiments that probone motor domain sepa ra te from the other(s) to d

ne a mecha nism tha t explains the reaction stepseach act ive s i te throughout the crossbridge cyc


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Furthermore, an invest igator at tempts to ident ithe specic s teps at which intermolecular interat ions occur and to understand the contr ibut ion motor domain cooperativity to unidirectional movment. A series of experiments have been developfor kinesin to explore domain cooperat ivi ty thshould be applicable to other molecular motors.

Dimeric Kinesin: Head 1 versus Head 2

B y using the uorescence s ignal from ma ntADinvestigators have been able to dissect the interation of each kinesin motor domain with the mictubule (Fig. 8). Figure 8A shows the experimeoriginal ly used to measure mantADP release froboth motor domains of dimeric kinesin (17, 32). the experiment, ADP tight ly bound a t t he active si s exchanged wi th mantADP to labe l both modomains w i th t he uorescen t ADP ana log . Tkinesin mantADP complex is then rapidly mixedthe s topped-ow instrument with microtubulesMgATP . In the initia l experiment s, ATP w a s a ddas a cha se to prevent ma ntADP from rebinding active site. However, in the absence of nucleotidein the presence of ADP , the kinet ics for man tADrelease were b iphas ic, wi th the rs t exponentphase fast and the second quite slow (44, 56, 5The in t erpret a t i on of t he da t a wa s t ha t t he motor domain binds the microtubule with rapid rlease of mantADP , and rap id release of mantAfrom th e second motor domain r equired ATP bindina t head 1. Therefore, to measure the k inet ics mantADP release from both motor domains of tdimer required ATP.

These init ia l experiments revealed a s t ra tegy measur e the kinetics of ma ntADP relea se from he1 separ a t e from t he h ea d 2 kinet ics (22, 44, 57). ATbinding to head 1 is required for microtubule assciat ion of hea d 2 and t he ra pid relea se of ma ntADTherefore, to measure the kinetics of mantADP r

FIG. 9. ATP -induced dissociat ion kinetics of the Mt MC6 com-plex. (A) MgATP (15 M 100 mM KCl nal concentra tion) wa s

apidly mixed with the preformed Mt MC6 complex (2 M MC6,2 M t ubulin nal) and monitored in a stopped-ow instrumento mea sure t he kinetics of MC6 dissociation from t he microtubule.

The smooth l ine i s the t of t he dat a to a s ingle exponent ia l ,providing k ob s 6.5 s 1 a t 15 M ATP. (B) The observed expo-nentia l ra te is plott ed as a function of MgATP concentra tion. Thedata were t t o a hyperbola wi th k diss 14.0 s 1 . Inset : Da ta for0–250 M MgATP. (C) The ATP-induced dissociation kinetics ofdimeric MC1 were measured at the same time as the dissociationkinetics for monomeric MC6. Both Mt Ncd complexes were pre-ormed with either 4 M MC6 or 4 M MC 1 (a ctive site concen-rations) with microtubules at 6 M tubulin , and the react ions

were initia ted w ith 1 mM MgATP plus KCl. All react ions w ere in

ATPase buffer which contains 50 mM potassium acetate in addi-ion to any KC l added to the reaction. The data were t to either

one or t wo exponential terms. For MC1 in the a bsence of a dKCl, k ob s 14.4 s 1, relative amplitude 0.32. For MC6, k o11.4 s 1, relative amplitude 0.02. Note that there is a progsive increase in the amplitude a ssociat ed w ith MC6 dissociatkinetics as t he a dded salt wa s increased from 0 to 500 mM KThere wa s no a ppreciable turbid i ty s ignal associa ted wi th reaction in which microtubules (6 M t ubulin) in t he a bsencmotor were rea cted wit h 1 mM MgATP 500 mM K Cl. Reprin

wit h permission from Ma ckey a nd G ilbert (11). Copyright © 2American Chemical Society.


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ea se from hea d 1, ATP w a s not a dded to th e micro-ubule syringe or al ternat ively, MgADP was added

w ith t he microtubules to dela y t he kinetics of mant -ADP release for head 2 (Fig. 8B). Thus, the kineticsof man tADP relea se for head 1 were measured wit h-out the contr ibuting signal of ma ntADP relea se fromhead 2.

Figur e 8C show s an experiment , int roduced by Maan d Taylor (57), to m easure t he man tADP releasekinetics from hea d 2, without t he contr ibuting ma nt-ADP s igna l f rom head 1. In th i s exper iment , anequilibrium Mt K ma ntADP complex is preformedby incubat ing t he dimeric motor, microtubules, a ndone-ha lf the concentr at ion of man tADP a s th e activesite concentration (one mantADP bound per kinesindimer). The presence of microtubules establishes ahigh-a f nity site for man tADP a nd a low a f nity sitefor man tADP , and the exper imen t a s sumes tha tmantADP wi ll on ly accumula t e a t the h igh a fni tysite. Subsequently, the Mt K mantADP complex wasrapidly mixed with MgATP, and the kinetics of man-ADP release from head 2 were measured. There-

fore, these three experiments dened critical inter-molecular interactions between the kinesin motordomains required for unidirect ional force genera-ion.

One Head or Tw o for M ovement

Another a pproa ch to explore cooperativity is t ostudy the monomeric motor in direct compar ison tohe dimeric motor (10, 11, 24, 37, 41, 55, 58–62).

This approach with kinesin, Ncd, and cytoplasmicdynein revealed tha t t he partner motor domain wa srequired to weaken the a fnity of the a djacent headw ith t he microtubule, leading t he a uthors t o proposehat both motor domains were required for move-

ment (11, 24, 59, 62).

Ki neti c Dat a to E valuat e Processivi ty

Kinetic processivity has been dened as the aver-age number of ATPase cycles before dissociation ofhe motor from i ts lament partner, and invest iga-ors have turned to s teady-s ta te and pre-s teady-

sta te kin etics to correla te processive ATP hyd rolysisw ith processive movement . Three criteria ha ve beenpresented a s tests for kinetic processivity.

Hackney in t roduced the rs t t es t based on theresults with kinesin (26). The steady-state kineticparameter, k ca t/K 0.5,Mt 10

8 M 1 s 1 indicated that

mult iple ATP tu rnovers occurred per encount er w ithhe microtubule. The second test for processivity is

tha t the s teady-s ta te k ca t divided by th e pre-steasta te ra te consta nt for dissociat ion be 1 for procsive motors. This a pproach has been accurat e predicting processivity based on the results for nesin (processive), Ncd (nonprocessive), and myosII (nonprocessive) (22, 32, 33, 57, 63). The third tesof processivi ty is the s ize of the pre-steady-staburst in t he ra pid qu ench experiments. A burst a mpli tude greater than the concentrat ion of enzymsites indica tes t ha t multiple ATP hydrolysis evenoccur per encount er w ith t he la men t (22, 24, 32, 337, 60).

Although each of these tests can be used to evua te processivity, t he kinetics can not subst itute fa direct experiment to evaluate processive movment. However, the single-molecule motility expeiments t o determine processivity can quite dif cua nd it ma y ta ke years before the technical problea re resolved. Therefore, invest iga tors w ill use a ll tmechanis t ic and mot i l i ty da ta ava i lab le in an tempt to determine processivity. For the kinet icone must always be caut ious in the interpretat ibecause the condit ions of the assay impact the netics a nd consta nts de ned by th e experiments. Fexample, the sal t concentrat ion in an experimecan grea t ly a l ter t he a f nity of a motor for i t s ment partner which wil l be reected in the kineconsta nts ( k a nd K ). From our perspective, the beexperimenta l indicator of a motor ’s processivitythe observat ion t hat the K m,ATP in the moti li ty a sis comparable to the K m ,ATP determined by steastate kinetics (16). These experiments require mcrogram amounts of protein and are performed the rst months to cha racter ize a new motor. Deitive proof of processivity requires single-molecumotility experiments and determination of step siz

Data Analysis

Kinetic data are t ypical ly t to equat ions by nl inear regression methods tha t describe t he t imdependence of t he r eaction (single exponent ial, d oble exponent ial fun ctions) such t ha t t he single expnential equat ion

Y A exp k 1 t C [

or the double exponentia l equa tion

Y A 1exp k 1 t A 2exp k 2 t C [

provides t he a mplitude ( A ), the rate of the react


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(k ), and t he endpoint ( C ) of t he rea ction. Although itmay appear obvious to use a double exponent ia lfunct ion t o t dat a represent ing tw o phases (man t-ATP binding) or data for the same reaction but forw o motor domains, in reality it ca n be quite dif culto ex t ract the in t r ins ic ra te cons tan ts us ing th is

approach. Problems can resul t because the differ-ence in th e rat es associat ed with tw o phases is smallor because the signals representing each componentare not well separ at ed (man tADP release kinet icsfor dimeric kinesin). Although one always begins by t t ing k inet ic da t a to exponent ia l equat ions , thenal s tage of dening a mechanism involves com-puter s imulat ion of the data to a model (1–3, 38) .Global t t ing of the da ta by numer ica l in tegra t ionusing either KI NS IM/FI TSI M (38, 64) or Scientist(Micromat h Inc.) wil l model the dat a to a kinet icscheme, predicting the observed concentration de-pendence of the r a tes a nd a mplitudes of each phase.Computer s imulat ion should be considered as anadditional experiment, performed to eliminate otherpossible mecha nisms a nd t o test one or m ore modelsproposed ba sed on the kinetic results.

CLOSING COMMENTS

In this a r t icle, w e ha ve presented the kinet ic ex-periments used to establish an ATPase crossbridgecycle, using kinesin and Ncd as our examples, tollustrate the basic principles. We encourage inter-

ested readers to exa mine the original research pub-icat ions for these microtubule-based motors an d

also to watch closely the developing stories for my-osin V (36, 49, 65, 66) a nd myosin VI (67). Thea pplica tion of pre-stea dy-sta te kinetic methods t ostudy molecular motors has increased dramaticallybecause of advances in inst rumenta t ion and theoverexpression an d puri cat ion of the motor pro-eins. Transient-state kinetics can now be used rou-inely in combination with biophysical, structural,

and genetic techniques to unlock the secrets of en-ergy t ra nsduction for unidirectional m ovement.

ACKNOWLEDGMENTS

We tha nk Smita S . P ate l a nd Roger D. S loboda for carefullyeading this ma nuscript a nd ma king insightful comments. S.P .G.

s supported by G ran t G M 54141 from t he Nat iona l Insti tut es ofHea lth . S .P.G . was the r ecipi en t of a Ba s il O’Connor S t a r t e r

Scholar Research Award (5-FY95-1136) from the March of DimB irth D efects Foundat ion a nd a n American Ca ncer Society J uFaculty Research Award (J FRA-618).

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