From the Department of Physiology and Biophysics, University of Washington, Seattle, Washington 98195-7290
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ABSTRACT |
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Conventional kinesin is a motor protein that
moves stepwise along microtubules carrying membrane-bound organelles
toward the periphery of cells. The steps are of amplitude 8.1 nm, the
distance between adjacent tubulin binding sites, and are powered by the hydrolysis of ATP. We have asked: how many steps does kinesin take for
each molecule of ATP that it hydrolyzes? To answer this question, the
motility and ATP hydrolysis of recombinant, heterotetrameric and
homodimeric conventional Drosophila kinesins adsorbed to
200-nm-diameter casein-coated silica beads were assayed under
identical, single-molecule conditions. Division of the speed by the
maximum microtubule-activated ATPase rate gave a stoichiometry of
1.08 ± 0.09 steps for each ATP hydrolyzed at 1 mM
ATP. Therefore, under low loads in which the drag force Conventional kinesin is a protein machine that steps along the
surface of a microtubule as it carries a membrane-bound organelle toward the periphery of a cell (1-3). The size of the steps is ~8 nm
(4, 5). This is the distance between consecutive binding sites along
the microtubule protofilament (6, 7), and a single kinesin molecule can
take hundreds of steps without detaching (8, 9), even against opposing
loads as high as ~6 pN (10-12). The steps are driven by the
hydrolysis of ATP; kinesin is an ATPase (13) whose speed of movement
increases linearly with ATP concentration until it approaches a maximum
of about 800 nm/s (8, 14), and
AMP-PNP,1 a nonhydrolyzable
analog of ATP, arrests movement (15, 16). Despite intensive
biochemical, biophysical, and structural investigations over the last
few years, there remains considerable uncertainty as to the mechanism
by which the stepping is coupled to ATP hydrolysis.
In this work, we address the question: what is the stoichiometry of
kinesin? In other words, how many steps does kinesin take for each ATP
that it hydrolyzes? This question is important because it tests
different models proposed to explain how motor proteins such as kinesin
and myosin work. For example, one class of "thermal ratchet" models
predicts that the stoichiometry is Some clues to the mechanochemical stoichiometry of kinesin have already
been obtained. High resolution tracking experiments show that one ATP
produces no more than one step, because bursts of multiple 8-nm steps
are not observed at limiting, low ATP concentrations (5, 14, 24). On
the other hand, the linear relationship between speed and ATP
concentration (at low ATP concentration) indicates that one ATP is
sufficient to produce a step (8); if two (or more) ATPs were required,
then the speed would depend on the square (or a higher power) of the
ATP concentration. This conclusion is supported by tracking experiments
at low ATP concentration showing that time intervals between steps are
exponentially distributed (5, 14); if two (or more) ATPs were required,
the interval distribution would be peaked rather than monotonically
decreasing. These results are consistent with a stoichiometry of 1 but
do not prove it. For example, the latter results imply that the binding of one ATP molecule can result in a step, but they provide no information about the likelihood that a step will actually occur. Thus
these experiments do not measure the stoichiometry.
In this work, we measure the stoichiometry of kinesin by comparing its
rate of ATP hydrolysis to its rate of stepping. Under conditions in
which a single kinesin molecule is moving along a microtubule, division
of the speed of movement (v) by the maximal, microtubule-stimulated ATPase rate/molecule
(kcat) yields the fuel economy of the
motor (the distance/ATP hydrolyzed). Division of the economy by the
step size, d = 8.1 nm (25), then yields the number of
steps/ATP hydrolyzed, i.e. the stoichiometry (n) as shown.
Preparation of pPK121 and pPK113 Kinesin Constructs--
Two
kinesin expression plasmids were constructed in pET vectors. One
plasmid (pPK113) contained a histidine-tagged conventional kinesin
heavy chain. The second plasmid (pPK121; Fig.
1) was designed for co-expression of the
kinesin heavy chain with histidine-tagged light chains. All enzymes
were purchased from New England BioLabs (Beverly, MA), except T4 DNA
ligase (Life Technologies, Inc.) and T4 gene 32 protein (Boehringer
Mannheim). DNA propagation steps were performed in Escherichia
coli DH5
Plasmids containing a modified Drosophila melanogaster
kinesin heavy chain gene (pET-Kin) and the D. melanogaster
kinesin light chain gene (pBS-13a) were a gift from L. Goldstein. The heavy chain gene was modified by polymerase chain reaction and oligo-directed mutagenesis to restore the wild type N-terminal amino
acid sequence, introduce silent mutations for subsequent handling, and
reduce predicted RNA secondary structure. For the pPK113 plasmid, the
heavy chain gene was additionally modified by polymerase chain reaction
to introduce a C-terminal hexahistidine and thrombin cleavage sequence
(LVPRGS) tag. The genes were cloned into pET20b+ (Novagen, Milwaukee,
WI), and both strands of the final heavy chain constructs were
sequenced to verify the predicted translation products.
The light chain gene was modified by polymerase chain reaction to add a
C-terminal decahistidine tag, and silent mutations were introduced at
the 5' end of the gene to reduce predicted RNA secondary structure and
to avoid low frequency codons. The modified light chain gene and a
heavy chain gene were co-expressed from a pET21a+ plasmid (Novagen).
The complete sequences of our pPK113 and pPK121 expression plasmids
have been deposited in the GenBank data base (accession numbers
AF053733 and AF055298, respectively).
Kinesin Expression--
Both kinesin constructs were expressed
in E. coli BL21(DE3)[pLysS]. Cultures grown in LB at
37 °C to an optical density of 1 at 600 nm (Hewlett-Packard 8452 Diode Array Spectrophotometer, Fullerton, CA) were induced with 0.4 mM isopropyl- Purification of Recombinant, Full-length Kinesin with Light
Chains--
Heterotetrameric kinesin, consisting of both heavy and
light chains, was purified in two steps using nickel-nitrilotriacetic acid agarose and phosphocellulose resins. The tagged light chains and
associated heavy chains were purified from other bacterial proteins by
batch absorption to nickel-nitrilotriacetic acid agarose resin (Qiagen,
Valencia, CA). The resin was poured into a column and washed with wash
buffer (50 mM sodium phosphate, pH 7.0, 1 M
NaCl, 5 mM 2-mercaptoethanol, and 80 mM
imidazole), and eluted with elution buffer (50 mM sodium
phosphate, pH 7.0, 300 mM NaCl, 5 mM
2-mercaptoethanol, and 500 mM imidazole). The eluate
contained a large excess of light chain relative to the amount of heavy chain. To isolate tetrameric kinesin from excess light chains, the
mixture was changed into PC buffer (50 mM sodium phosphate, pH 7.0, 100 mM NaCl, 4 mM MgCl2, 2 mM EDTA, 1 mM 2-mercaptoethanol, 1% glycerol)
by dialysis at 4 °C and passed over a column of P-11 phosphocellulose (Whatman, Hillsboro, OR). The phosphocellulose has low
affinity for light chains; light chains not bound to a heavy chain pass
through the column without being retained. Kinesin was then eluted with
a linear sodium chloride gradient (0.1-1 M) in PC buffer.
The peak fractions were combined, dialyzed into storage buffer (50 mM imidazole, pH 7.0, 100 mM NaCl, 1 mM MgCl2, 2 mM EGTA, 0.1 mM EDTA, 5% (w/v) sucrose, 5 mM
2-mercaptoethanol) with 1.0 µM MgATP, frozen in liquid
nitrogen, and stored at
Coomassie-stained SDS-polyacrylamide gels were scanned (Umax PS-2400X,
Umax Data Systems, Hsinchu, Taiwan) and analyzed with NIH Image version
1.57 for Apple Macintosh. The molar ratio of light chain to heavy
chain, based on relative dye staining, ranged from 1.2 to 1.5 in three
independent preparations. Sucrose density centrifugation in storage
buffer, which has a similar ionic strength to BRB80, was consistent
with a heterotetrameric protein of sedimentation coefficient 8.7 ± 0.3 S ( Preparation of Casein-coated Silica Beads and Kinesin
Adsorption--
A stock solution of 2 nM 0.2-µm-diameter
silica beads (Bangs Laboratories, Carmel, IN) and 2 mg/ml casein was
bath sonicated for 3-4 h to disperse the beads and stored at 4 °C.
The solution was stable over several days. The recombinant kinesin was
adsorbed to the casein-coated beads by mixing the two together rapidly, vortexing, and incubating for 10 min. Adsorption to the beads was
confirmed by Western blot with SUK4 monoclonal antibody (data not shown).
Radiometric Determination of Kinesin Concentration--
The
concentration of active kinesin was determined as half the
concentration of nucleotide binding sites, because there are two ATP
binding sites/molecule. The number of nucleotide binding sites was
measured radiometrically as follows. BA85 nitrocellulose membranes
(Schleicher & Schuell) were prepared by washing in 0.4 N
KOH for 10 min, rinsing in double distilled H2O, and
incubating in cold BRB80 buffer (80 mM potassium PIPES, pH
6.9, 1 mM EGTA, 1 mM MgCl2) for at
least 1 h prior to use. The exchange reactions were run in BRB80
buffer augmented with 1 mg/ml casein, 1 mM
MgCl2, and 250 nM [
The concentration of kinesin was measured for the enzyme in solution in
the absence of beads. Adsorbing kinesin to beads had no significant
effect on the amount of nucleotide that it binds: the nucleotide
binding activity of kinesin on beads was 120 ± 18% that of
kinesin in solution. Therefore, adsorbing kinesin to the casein-coated
silica beads does not cause an appreciable amount of denaturation of
the protein. However, there remains the possibility that some of the
kinesin molecules adsorbed to beads may not be able to access
microtubules, even though they can still bind nucleotide. For example,
suppose that half the motors adsorb "heads-up" (i.e.
able to bind to and move along microtubules) and half adsorb
"heads-down" (i.e. unable to bind to or move along
microtubules but still able to bind nucleotide). Then the
microtubule-stimulated ATPase rate/motile kinesin would be
underestimated by a factor of 2. To rule out this possibility, heterotetrameric kinesin was adsorbed to the casein-coated silica beads
and loaded with [ Microtubules--
Microtubules were polymerized from bovine
brain tubulin at 37 °C in BRB80 with 4 mM
MgCl2, 1 mM GTP and 5% (v/v)
Me2SO. The microtubules were stabilized with 10 µM taxol, airfuged at 28 psi in a Beckman airfuge through
a cushion of 1:1 BRB80:glycerol with 10 µM taxol to
remove excess guanosine nucleotide, resuspended in BRB80 with 10 µM taxol, and thrice sheared through a 30-gauge needle.
The concentration of tubulin was determined by absorbance at 276 nm in
6 M guanidine HCl using an extinction coefficient of 1.03 ml/mg·cm. Microtubule concentrations are expressed in terms of
100-kDa tubulin heterodimers.
In Vitro Motility Assays--
The speed of kinesin adsorbed to
200-nm casein-coated silica beads was measured in motility assays.
Standard flow cells were constructed (30) using coverslips that had
been treated with 3-aminopropyl triethoxysilane (Pierce) to attach
microtubules to the surface. The treatment consisted of washing
coverslips with 2% PCC-54 detergent and rinsing with distilled water.
After drying, the coverslips were soaked in a 20% solution of
3-aminopropyl triethoxysilane in acetone for 5 min followed by short
rinses with acetone and with distilled water. The coverslips were then rinsed for 15 min in slow flowing distilled water and air-dried.
A microtubule solution containing ~3 µM tubulin was
incubated in the flow cell for 15 min. The chamber was then washed with several changes of motility buffer (BRB80 + 10 µM taxol,
20 mM D-glucose, 20 µg/ml glucose oxidase, 8 µg/ml catalase, 0.5% 2-mercaptoethanol, 1 mM MgATP)
after which a solution of kinesin adsorbed to beads diluted in motility
buffer was introduced. Beads and microtubules were visualized by
differential interference contrast microscopy on an inverted microscope
(Zeiss Axiovert), the video images were taken with a Hamamatsu C2400
CCD camera and control unit, and the data were stored on videotape with
a Panasonic AG7350 VCR (Proline, Kirkland, WA) for subsequent analysis.
The speed was determined by dividing the total distance that the bead
moved along a microtubule by the duration of movement.
ATPase Measurements--
Steady-state ATPase rate was measured
in BRB80 with 1 mM MgATP, 10 µM taxol, 1 mg/ml casein, and a variable amount of taxol-stabilized microtubules.
The mixtures were incubated at 25 °C, and the reaction was halted by
adding an equal volume of cold 1 N perchloric acid + 0.2%
Triton X-100. The samples were vortexed and centrifuged (18,000 × g) to remove precipitated proteins. The phosphate
concentration was determined by adding malachite green solution (3 g of
sodium molybdate, 0.25 g of malachite green oxalate, and 0.25 g of Triton X-100/liter 0.7 N HCl) and reacting for 1 min.
The colorimetric reaction was quenched by the addition of 1.4 N sulfuric acid, and the absorbance at 640 nm was read and
compared against a phosphate calibration. In parallel with each sample,
a control was run in which the kinesin was added after the PCA quench.
The difference in phosphate concentration between the sample and
control represents the phosphate liberated by kinesin. This was divided
by the product of the incubation time and one-half the concentration of
nucleotide binding sites (2 ATP binding sites/kinesin molecule); the
turnovers are therefore expressed per kinesin molecule. The enzyme was
stable in our assays for greater than 4 h at room temperature.
Data were fitted to the Michaelis-Menten equation using Igor
(Wavemetrics, Lake Oswego, OR) to obtain the maximal
microtubule-stimulated turnover (kcat) and the
Michaelis constant (Km) defined as the microtubule
concentration necessary for half-maximal activation. The logarithm of
the raw ATP hydrolysis measurements (kinesin + background) was taken
prior to least squares curve fitting; because the relative error in
each of the measurements is approximately the same for each raw data
point, fitting to the logged data ensures that all the points are
weighted according to their uncertainty.
To measure the stoichiometry of kinesin, the motility and ATP
hydrolysis of recombinant, heterotetrameric and homodimeric conventional Drosophila kinesin adsorbed to 200-nm-diameter
casein-coated silica beads were assayed under identical,
single-molecule conditions. Data from three kinesin preparations are
summarized in Table I.
1 pN,
coupling between the chemical and mechanical cycles of kinesin is
tight, consistent with conventional power stroke models. Our results
rule out models that require two or more ATPs/step, such as some
thermal ratchet models, or that propose multiple steps powered by
single ATPs.
INTRODUCTION
Top
Abstract
Introduction
References
0.5 steps/ATP (17, 18); these
models postulate that ATP hydrolysis rectifies a diffusive motion in
such a way that a step only occurs if the diffusion is
toward the next binding site. Because there is an equal
probability that the motor diffuses away from the next binding site
(i.e. in the wrong direction), this model predicts that on average at least two molecules of ATP are hydrolyzed per forward step.
A stoichiometry of less than one could also be due to "futile" hydrolysis cycles, those that fail to produce steps and lead to "slippage" between the mechanical and chemical cycles. Other models postulate a stoichiometry greater than 1 and have been applied to
reconcile the high efficiency of muscle with the mechanical properties
of muscle fibers (19, 20) or to reconcile the large apparent
"interaction distance" between myosin and actin with the smaller
physical size of the myosin head (21, 22). However, there are
alternative explanations of these results that do not require more than
one step/ATP hydrolysis (23). On the middle ground are conventional
"tightly coupled" models in which the mechanical and chemical
cycles are assumed to be strictly coordinated, predicting a
stoichiometry of 1.
Until now, kinesin ATPase assays have been typically done with
molecules in solution, whereas motility assays have been done with the
motors bound to a solid support (e.g. to a glass surface or
bead). This has resulted in apparent stoichiometries varying from as
high as 200 for native, full-length Drosophila kinesin (v = 900 nm/s, kcat = 0.60 s
(Eq. 1)
1; Ref. 26) to as low as 0.008 for a recombinant,
Drosophila kinesin motor domain-glutathione
S-transferase fusion protein (v = 1.5 nm/s,
kcat = 24 s
1; Ref. 27). This
25,000-fold range of stoichiometries, together with an inverse
correlation between speed and ATPase rate, suggests that binding of
kinesin to a solid support may have profound effects on the speed
and/or ATPase. For this reason, we have measured the ATP hydrolysis
rate of kinesin under identical conditions to those used to assay the
motility, namely with kinesin bound to 200-nm-diameter silica beads. At
low kinesin-to-bead ratios where the motility is due to single motors,
the stoichiometry is unity.
EXPERIMENTAL PROCEDURES
or CJ236.
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Fig. 1.
Plasmid diagram of pPK121; co-expression of
heterotetrameric
( 2
2)
conventional Drosophila kinesin from
pET21a+.
-D-thiogalactopyranoside at
20 °C for 3-4 h. Unless otherwise noted, all buffers were augmented with 50-100 µM MgATP. The bacterial cells were harvested
and resuspended in ~30 ml of lysis buffer (50 mM sodium
phosphate, 300 mM NaCl, 40 mM imidazole, 5 mM 2-mercaptoethanol, 10% glycerol, pH 8.0)/liter of
culture, lysed in a French press at ~19,000 psi, sonicated, and
centrifuged (100,000 × g) for 30 min at 4 °C.
80 °C. The homodimeric construct
consisting of only the kinesin heavy chains was purified in a similar manner.
2
2; data not shown), similar to
the sedimentation coefficient of heterotetrameric bovine brain kinesin in its folded conformation (28). Initial characterization of the
recombinant wild type protein in standard microtubule gliding assays
resulted in gliding speeds that were similar to native bovine brain kinesin.
-32P]ATP
(NEN Life Science Products) for 1-2 h at room temperature. A small
aliquot (3 µl) was placed on the 25-mm circular nitrocellulose membrane (held on a filter support under vacuum), and the membrane was
washed with 500 µl of cold BRB80. The membrane was then dried at
60 °C, combined with scintillation mixture, and read in a Beckman scintillation counter. The reading was then compared with a standard curve constructed by diluting the reaction mixture into BRB80 + 1 mg/ml
casein and dotting directly onto the membranes with no wash.
-32P]ATP on ice. The labeled
nucleotide was then chased by diluting the kinesin mixture into buffer
(0 °C) containing 1 mM MgATP in the presence and absence
of 5 µM microtubules polymerized in the presence of
GMP-CPP (to prevent cold-induced depolymerization; Ref. 29). In the
presence of microtubules, 86 ± 4% (S.E.) of the radionucleotide
was released within 1 min, the resolution of the assay. This indicates
that most bead-adsorbed kinesin was accessible to microtubules. We did
not correct the kinesin concentration for these relatively small
effects of the beads on the effective kinesin concentration.
RESULTS
Kinesin stoichiometry
2
2) and one preparation without light chains
(
2). The stoichiometry was calculated by dividing the
distance per ATP by the step size (8.1 nm) and multiplying by 0.97 to
correct for the effect of ADP build-up on the ATPase (see text). The
uncertainties were calculated by adding the variances associated with
the speed, ATPase, concentration (S.E./mean = 0.05), temperature
in motility assay (S.E./mean = 0.04, corresponding to S.E. in the
temperature of 0.5 °C), and temperature in the ATPase assay
(S.E./mean = 0.04).
Bead Motility-- The movement of the kinesin-coated beads along microtubules adsorbed to the silanized surface of the experimental chamber was observed by differential interference contrast microscopy (Fig. 2a). At the resolution of the video images, the motion was smooth with fewer than 1% of the beads stopping or pausing for greater than 0.5 s. The distance traveled during each run of a bead along a microtubule varied greatly from bead to bead, even at the same kinesin-bead ratio (Fig. 2b). At kinesin-bead ratios of less than one, the distances were approximately exponentially distributed, consistent with detachment being a random (Poisson) process. At the lowest kinesin-bead ratio, 0.088 kinesins/bead, fewer than 10% of those beads with motors on them have more than one motor; therefore most of these runs are attributed to a single kinesin molecule. The mean run length of 1.2 µm was similar to that measured by Block et al. (9) using native squid kinesin. At the highest kinesin-bead ratio, 5.8, the average run length was greatest (Figs. 2b and 3b) due to an increase in the frequency of long runs. Presumably these long runs are due to two or more motors powering one bead; for two kinesin molecules to interact with the same microtubule at that density, we estimate that each kinesin must have a "reach" of about 25 nm.
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The rate at which the beads attached to the microtubules increased as the average number of motors/bead increased (Fig. 3a). The attachment rate showed signs of saturation at the highest motor-bead ratio, such that the probability of a bead binding to a microtubule during a diffusive encounter at a kinesin-bead ratio of 4 is roughly half that of a bead saturated with kinesin. This indicates that a high proportion of the adsorbed motors are active, because otherwise there would be no saturation. This supports the radiometric assays described under "Experimental Procedures" showing that almost all the motors adsorbed to beads can bind to microtubules.
The speed at which beads moved along microtubules was independent of the kinesin-bead ratio (Fig. 3c), in agreement with earlier studies on bovine (8) and squid (9) kinesin. The mean speed was 882 ± 14 nm/s (mean ± S.E., n = 129) for this preparation at 25 °C.
ATPase Rate--
The rate of ATP hydrolysis by kinesin bound to
the 200-nm-diameter beads was measured using a modified malachite green
assay. The kinesin-bead ratio was = 0.2, ensuring that greater
than 90% of the beads with kinesin bound to them had only one kinesin
molecule. The hydrolysis rate increased as the microtubule
concentration was increased (Fig. 4), and
the data were fitted with the Michaelis-Menten equation. For the
2
2 preparation whose motility is
characterized in Figs. 2 and 3, the maximal microtubule-stimulated
hydrolysis rate was estimated to be 94 ± 13 s
1/kinesin molecule (mean ± S.E.). The half-maximal
hydrolysis rate occurred at a tubulin concentration of 11 ± 3 µM (mean ± S.E.). Similar results were obtained
with other kinesin preparations including
2 kinesin
(Table I).
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There are two ways that we might have underestimated the ATPase rate.
First, if a bead has two (or more) motors on it, both motors may not be
fully activated. At a kinesin-bead ratio of 0.2, ~10% of
kinesin-beads possess multiple kinesin molecules. To determine whether
multiple molecules on a bead are each activated to the same extent as a
single kinesin molecule bound to single bead, the kinesin-bead ratio
was increased 10-fold and the ATP hydrolysis rate/kinesin molecule was
measured. At a kinesin-bead ratio of 2.0, 86% of kinesin molecules are
bound to beads possessing at least one other kinesin molecule; the ATP
hydrolysis rate/kinesin at 10 µM tubulin of 32 ± 1 s1 was identical to the rate at a kinesin-bead ratio of
0.2, 32 ± 1 s
1, indicating that several kinesin
molecules on a single bead can be fully activated by microtubules.
A second way that the ATPase rate might be underestimated is if, over
the course of an ATP hydrolysis assay, the depletion of ATP and the
accumulation of ADP slow down the hydrolysis reaction. To minimize this
effect, no more than 5% of the ATP was hydrolyzed during the course of
our experiments. To estimate what effect the accumulation of a low
concentration of ADP had on the measured hydrolysis rates, we assayed
microtubule gliding speeds and ATPase rates in the presence of ADP. At
10% ADP ([ATP] = 0.9 mM, [ADP] = 0.1 mM),
the microtubule gliding speed was reduced 13% from 610 ± 10 nm/s
(n = 75) to 530 ± 10 nm/s (n = 75). The corresponding ATP hydrolysis rate at ~8 µM
tubulin in the absence of beads was reduced 34% from 10.1 ± 0.4 s1 to 6.7 ± 0.3 s
1. These results
suggest that the ADP accumulation decreases the instantaneous kinesin
hydrolysis rate in two ways: by decreasing the rate at which kinesin
moves along a microtubule and also by decreasing its apparent affinity
for microtubules. The calculation of kinesin fuel economy and
stoichiometry were corrected for this effect (see the legend to Table
I).
Kinesin Fuel Economy and Stoichiometry-- Dividing the speed of kinesin adsorbed to a silica bead by its maximum microtubule-stimulated hydrolysis rate yields an average fuel economy of 9.4 ± 1.3 and 9.9 ± 1.9 nm/ATP for the two preparations containing light chains and 8.7 ± 0.7 nm/ATP for the preparation lacking light chains (Table I). Based on our controls, we expect the fuel economies to be overestimated by ~3%, due to the build-up of ADP in the ATPase assay but not in the motility assay. Correcting for this overestimate and dividing by the step size of 8.1 nm gives an average stoichiometry of 1.08 ± 0.09 steps/ATP hydrolyzed (data from the three preparations weighted by the reciprocals of their variances). The error is based on the uncertainties in the speed, the ATPase rate, the kinesin concentration measured using the radionucleotide assay, and the uncertainties of temperatures in the motility and ATPase assays (see the legend to Table I).
Our estimate of the stoichiometry depends crucially on the measurement
of the specific activity of the kinesin enzyme. In this study, the
concentration of active kinesin was measured as the number of sites
that can exchange radioactively labeled ATP with unlabeled nucleotide
divided by two because each kinesin molecule has two heads. We showed
that adsorbing kinesin to the silica beads did not affect the
concentration of active enzyme. Furthermore, almost all of the kinesin
adsorbed to the beads with a geometry favorable for binding
microtubules: 86% of the adsorbed motors were stimulated by
microtubules to release their bound nucleotide ("Experimental
Procedures."). Therefore, even though the adsorption of kinesin to
the beads is nonspecific, a large fraction of the enzyme remains active
with respect to nucleotide exchange and microtubule binding. A
potential caveat to using nucleotide exchange to assay activity is that
the time scale of exchange is minutes, whereas the time scale of the
motility assay is seconds, the duration of the runs that the
kinesin-coated beads make along the microtubules. It remains formally
possible, therefore, that kinesin might switch between an active motile
state and a quiescent immotile state on the time scale of tens of
seconds. If this were the case, the quiescent state would be short
lived enough that there would still be full exchange of nucleotide; as
a result the measured ATPase rate would underestimate the true ATPase
rate of the active motile enzyme, and the stoichiometry would be
overestimated. However, a number of arguments show that the fraction of
motors in such a quiescent state is small. First, if the quiescent
state were an attached state, then we would have observed
kinesin-coated beads binding to the microtubules for several seconds
without moving. But this was not seen (less than 1% of beads failed to
move continuously). On the other hand, if the quiescent state were a
detached state, then we would expect that only the nonquiescent
fraction of the motors would be attached to the microtubules even at
very high tubulin concentrations. When the motors are attached to beads
as in our assays, this is difficult to test. However, Hackney (31) used
centrifugation assays on two-headed Drosophila kinesin in
solution to show that the microtubule concentration required for
activating the ATPase is identical to that required for binding. In
other words, at high tubulin concentration all the motors are bound to
the microtubules, ruling out the possibility of significant population
of a quiescent, detached state.
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DISCUSSION |
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By dividing the speed of movement of silica beads moving under the influence of single kinesin molecules by the ATP hydrolysis rate of the same beads under the same experimental conditions, we have shown that kinesin makes on average 1.08 ± 0.09 (mean ± S.E.) 8-nm steps for each molecule of ATP that it hydrolyzes. This is consistent with a stoichiometry of 1. Because our measurements were made on an ensemble of motors, we cannot discern whether kinesin takes one step after hydrolyzing one ATP molecule (1:1 coupling) or whether kinesin takes two consecutive steps after hydrolyzing two ATPs (2:2 coupling). In either case, one 8-nm step is produced per ATP hydrolyzed. However, mechanical measurements of single molecules at rate-limiting ATP concentrations (5, 14, 24) show that there are not clusters of 8-nm steps as would be expected if the coupling were 2:2 or some higher multiple. Therefore, taking our chemical data together with the mechanical recordings, we conclude that the coupling is 1:1, i.e. one ATP hydrolysis cycle results in a single step along a microtubule.
Under the low load conditions used in these experiments, the coupling
between motility and ATP hydrolysis is tight; a stoichiometry of
1.08 ± 0.09 means that at least 90% of the hydrolysis cycles produce a mechanical step (0.90 = 1.08 2 × 0.09 = mean
2 × S.E.). The load in these assays is very small;
the drag force associated with pulling a 200-nm diameter bead at
1 µm/s is only ~0.002 pN (32), which is <0.1% of the maximum
force of ~6 pN that a kinesin molecule can generate (10-12). Whether
the coupling remains tight at high load is not known.
A stoichiometry of 1 is consistent with the power stroke model and
other models that propose a unitary coupling between the chemical and
mechanical cycles of a motor (e.g. Refs. 23, 33, and 34).
Our results rule out any model of chemomechanical transduction that
requires two or more ATP/step (n 0.5), such as the
thermal ratchet models discussed in the Introduction. It also rules out other models mentioned that propose multiple steps powered from by
single ATP (n
2).
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ACKNOWLEDGEMENTS |
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We thank Drs. A. Gordon, W. Hancock, B. Hille, and L. Wordeman for comments on an earlier version of the manuscript.
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FOOTNOTES |
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* This work was supported by National Institutes of Health Grant AR40593 and by a grant from the Human Frontier Science Program (to J. H.).The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
The nucleotide sequence(s) reported in this paper has been submitted to the GenBankTM/EMBL Data Bank with accession number(s) AF053733 and AF055298.
Supported by National Institutes of Health Molecular Biophysics
Training Grant GM08268 and by the Achievement Reward for College Scientists Foundation.
§ To whom correspondence should be addressed: Dept. of Physiology & Biophysics, University of Washington, Box 357290, Seattle, WA 98195-7290. Fax: 206-685-0619; E-mail: johoward{at}u.washington.edu.
The abbreviations used are:
AMP-PNP, adenosine 5'-(,
-imino)triphosphate; GMP-CPP, guanylyl-(
,
)-methylene-diphosphonate; PIPES, 1,4-piperazinediethanesulfonic acid.
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