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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 GenBank™/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.
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 mmATP. Therefore, under low loads in which the drag force ≪ 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.
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 (
). 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 ≤0.5 steps/ATP (
); these models postulate that ATP hydrolysis rectifies a diffusive motion in such a way that a step only occurs if the diffusion istoward 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 (
). 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.
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 (
); 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 (
); 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 (
), then yields the number of steps/ATP hydrolyzed, i.e. the stoichiometry (n) as shown.
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−1; Ref.
). 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.
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.
Table IKinesin stoichiometry
Speed ± S.E. (v)
ATPase ± S.E. (kcat)
882 ± 14
94 ± 13
9.4 ± 1.3
1.12 ± 0.18
801 ± 18
81 ± 15
9.9 ± 1.9
1.18 ± 0.24
772 ± 29
88 ± 6
8.7 ± 0.7
1.04 ± 0.11
Speed and ATPase rates of single kinesin molecules attached to silica beads at 25 °C. Data from two kinesin preparations with light chains (α2β2) and one preparation without light chains (α2). 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).
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. (
) using native squid kinesin. At the highest kinesin-bead ratio, 5.8, the average run length was greatest (Figs. 2b and3b) 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.
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 (
) kinesin. The mean speed was 882 ± 14 nm/s (mean ± S.E., n = 129) for this preparation at 25 °C.
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 α2β2 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 α2 kinesin (Table I).
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 s−1 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 μmtubulin in the absence of beads was reduced 34% from 10.1 ± 0.4 s−1 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 TableI).
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 (
) 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.
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 (
) 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 (
). 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).
We thank Drs. A. Gordon, W. Hancock, B. Hille, and L. Wordeman for comments on an earlier version of the manuscript.