1 Nature 2001 Vol: 410(6831):898-904. DOI: 10.1038/35073513

Resolution of distinct rotational substeps by submillisecond kinetic analysis of F1-ATPase

The enzyme F1-ATPase has been shown to be a rotary motor in which the central -subunit rotates inside the cylinder made of 33 subunits. At low ATP concentrations, the motor rotates in discrete 120° steps, consistent with sequential ATP hydrolysis on the three -subunits. The mechanism of stepping is unknown. Here we show by high-speed imaging that the 120° step consists of roughly 90° and 30° substeps, each taking only a fraction of a millisecond. ATP binding drives the 90° substep, and the 30° substep is probably driven by release of a hydrolysis product. The two substeps are separated by two reactions of about 1 ms, which together occupy most of the ATP hydrolysis cycle. This scheme probably applies to rotation at full speed (130 revolutions per second at saturating ATP) down to occasional stepping at nanomolar ATP concentrations, and supports the binding-change model for ATP synthesis by reverse rotation of F1-ATPase.

Mentions
Figures
Figure 1: Observation of F1 rotation.a, Atomic structure7 of F1-ATPase viewed from the Fo side (top in b). b, Side view of the observation system. The 40-nm bead gave a large enough optical signal that warranted a submillisecond resolution; but the bead was small enough not to impede the rotation. c, Laser dark-field microscopy for observation of gold beads. Only light scattered by the beads exited the objective and was detected. DFC, dark-field condenser. d, Sequential images of a rotating bead at 2 mM ATP. Images are trimmed in circles (diameter 370 nm) to aid identification of the bead position; centroid positions are shown above the images at 3 magnification. The interval between images is 0.5 ms. Figure 2: Relationship between rate of bead rotation and viscous friction on the bead.Circles, the average rate for a bead calculated over at least 20 consecutive revolutions; squares, the average over different beads (vertical error bars indicate s.d.). ATP at 2 mM and 2 M is indicated by red and blue colours, respectively. The abscissa is the rotational frictional drag coefficient calculated as in Methods. Possible range of for each bead is shown by the size of the squares or associated horizontal error bars. For comparison, rotation rates for an actin filament attached to the -subunit11 are also plotted (triangles). Lines show fits with the rate expected for a motor producing a constant torque11: (1/Vnoload + 2/N)-1 where N = 40 pN nm (assumed torque) and Vnoload = 12.5  1.0 r.p.s. for 2 M ATP and 134  3 r.p.s. for 2 mM ATP (s.e.m.). Figure 3: Comparison of rotation and hydrolysis rates.Red circles, time-averaged rotation rate for individual 40-nm beads. Red squares, rotation rate averaged over different beads. Dark green squares, one-third of the initial rate of ATP hydrolysis. Light green circles, one-third of the rate of ATP hydrolysis in the presence of LDAO. Blue diamonds, rotation rate for an actin filament attached to the -subunit11. Standard deviations greater than the symbol size are shown in bars (n  2). Curves show fits with Michaelis–Menten kinetics, V = Vmax[ATP]/(Km + [ATP]), where Vmax and Km are 129  9 r.p.s. and 15  2 M for bead rotation (red), 4.0  0.3 r.p.s. and 0.7  0.1 M for actin rotation (blue), and 247  9 s-1 and 19  1 M for hydrolysis in the presence of LDAO (light green). Fits with two Km values, V = (Vmax1Km2[ATP] + Vmax2[ATP]2)/([ATP]2 + Km2[ATP] + Km1Km2), are also shown, where Vmax1 = 85  9 s-1, Km1 = 5.2  0.7 M, Vmax2 = 306  22 s-1, and Km2 = 393  147 M for hydrolysis without LDAO (dark green), and Vmax1 = 109  30 r.p.s., Km1 = 12  4 M, Vmax2 = 149  32 r.p.s., and Km2 = 682  2768 M for bead rotation (dashed pink). The latter does not show improvement over the simple fit in red. Values are means s.e.m. Figure 4: Unfiltered time courses of stepping rotation of 40-nm beads at varying [ATP].a, b, 2 mM; c, d, 20 M; e, f, 2 M [ATP]. All curves in a panel are continuous; later curves are shifted, to save space. Grey horizontal lines are placed 30° below black lines. In e, some of the long dwells are cut short. Insets, positions of a bead within 0.25–0.5 ms before (red) and after (green) the main (90° or 120°) steps; runs lasting 0.5 s (2 mM) or 2 s (2 M and 20 M) were analysed. Circles indicate projection of 0° and 90° dwell points on an obliquely situated circular trajectory that best fit the data. Angles in the time courses and in  are those on the oblique circle. Figure 5: Histograms of angular positions over 0.5 s runs.Labels (a–f) are from records of which , a–f are a part. Each time course was passed through a five-point median filter, and its histogram was calculated with 2° bins. The histogram was then averaged over 10° intervals. Green parts (e and f) indicate 2 ms before and after main steps. Crosses indicate peaks identified by eye. To assess the baseline noise in raw data, we also constructed unfiltered, unaveraged histograms at 2 M ATP with 2° bins (not shown). The histograms gave three peaks, of which the half width at 1/e height was estimated by fitting each peak with a gaussian curve; the half widths averaged 18°  7° (mean  s.d. for 15 peaks). Figure 6: Kinetics of substeps.a, b, Eighteen consecutive steps and their average (thick cyan line) in a rotation record at 2 mM (a) or 2 M (b) ATP (see Methods for the averaging procedure). c, Steps in several runs at indicated [ATP], averaged as in a and b. The averaging procedure retained all dwells at 0° position in the ordinate, but some dwells at 120° were converted to a horizontal line at 90° position when the substep from 90° to 120° was contiguous (within 0.25 ms) with the next substep from 120° to 210°. This is why the curves at high [ATP] do not rise much beyond the 90° line. The curves are reproduced on the right; superimposed grey lines represent fits with theoretical curves based on the scheme in a (see Methods). The best fit was obtained with the size of the 30° substep, A30°, of 29.8°  0.3° (mean s.e.m.). Figure 7: Proposed mechanism for F1 rotation.a, Rotation scheme. ATP with asterisk represents ATP or ADP + phosphate; ADP (alone) may be phosphate or ADP + phosphate. b, Stepping time courses expected from a. c, Highly schematic diagram for the potential energy for -subunit rotation. Each coloured line shows in one of the four states in a. The orientation of the -subunit in state A (in a) is taken as 0°. Figure 8: Dwells between main steps.a, Histograms of dwell times between two main (90° or 120°) steps at various [ATP]. Total counts in each histogram are 60, 463, 1,145, 2,862, 631, 2,384, 3,262 and 1,457 in the order of 0.02–6,000 M. Histograms for individual runs are distinguished by colours; they are added to constitute a whole histogram. Pink lines at 0.02 and 0.2 M ATP are single-exponential fits, constantexp(-kt), with k shown in open circles in b. Pink lines at other [ATP] are fits with two rate constants, constant[exp(-kat) - exp(-kbt)], with ka and kb shown (filled black circles in b). Green lines show the result of a global fit to the individual histograms (n = 38; equal weight for each count) with sequential reactions (a) starting with ATP binding at the rate kATPon[ATP] and two ATP-independent reactions with rates k1 and k2: kATPon = (3.0  0.1)  107 M-1 s-1, k1 = 1.64  0.06 ms-1, and k2 = 0.71 0.02 ms-1 (s.e.m.). b, ATP dependence of the rate constants. Blue circles show the total rate, k or kakb/(ka + kb) for the individual fits. Green lines show the rate constants obtained in the global analysis, and the total rate, [k-11 + k-12 + (kATPon[ATP]) -1]-1, is shown by the blue line.
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References
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    • . . . This rotational coupling mechanism was initially proposed by Boyer1, 2, 3, and by others4, 5, 6 . . .
    • . . . Our work is essentially a consolidation and embodiment of the binding-change model1, 2, 3 . . .
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    • . . . The ATP synthase is an enzyme ubiquitous in bacteria, plants and animals, which synthesizes ATP from ADP and inorganic phosphate using proton flow through a membrane1, 2, 3 . . .
    • . . . This rotational coupling mechanism was initially proposed by Boyer1, 2, 3, and by others4, 5, 6 . . .
    • . . . This is the so-called bi-site mechanism2, 3, 17, which is the norm at least at submicromolar [ATP] . . .
    • . . . Our work is essentially a consolidation and embodiment of the binding-change model1, 2, 3 . . .
    • . . . The rotational frictional drag coefficient for the beads was calculated as follows: for a single bead of radius a rotating in water with viscosity (= 10-9 pN nm-2 s), minimal is given by 8a3 when the rotation axis is at the bead centre, and maximal by 8a3 + 6a3 = 14a3 when the axis is at a bead edge; for a bead duplex, minimal is given by 2  8a3 = 16a3 for a vertical duplex rotating around its centre, whereas maximal is 2  8a3 + 6a3 + 6a (3a)2 = 76a3 for a horizontal duplex rotating around an edge. . . .
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    • . . . This rotational coupling mechanism was initially proposed by Boyer1, 2, 3, and by others4, 5, 6 . . .
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    • . . . This rotational coupling mechanism was initially proposed by Boyer1, 2, 3, and by others4, 5, 6 . . .
    • . . . By reciprocity, the affinity of the -subunit for ATP, on the left of the arrow on the central -subunit, must increase as the -subunit rotates6, 16, 17, 28 . . .
    • . . . Affinity for ATP is proportional to exp[(A - B)/kBT], where kBT 4.1 pN nm is the thermal energy at room temperature6, 28 . . .
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    • . . . Later, a crystal structure of F1 showed that a rod-shaped -subunit is surrounded by a cylinder made of three - and three -subunits, arranged alternately7 (Fig. 1a) . . .
    • . . . At nanomolar ATP, the actin filament rotated in discrete 120° steps11, consistent with the pseudo-three-fold symmetrical structure7 of F1 . . .
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    • . . . Rotation of the -subunit in an isolated F1 during ATP hydrolysis has been demonstrated experimentally by various methods8, 9, 10. . . .
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    • . . . Rotation of the -subunit in an isolated F1 during ATP hydrolysis has been demonstrated experimentally by various methods8, 9, 10. . . .
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    • . . . Rotation of the -subunit in an isolated F1 during ATP hydrolysis has been demonstrated experimentally by various methods8, 9, 10. . . .
    • . . . We have visualized the rotation of the -subunit under an optical microscope by fixing F1 on a surface and attaching an actin filament to the -subunit as a marker of its orientation10 . . .
  11. Yasuda, R., Noji, H., Kinosita, K.Jr & Yoshida, M. F1-ATPase is a highly efficient molecular motor that rotates with discrete 120° steps. Cell 93, 1117-1124 , .
    • . . . At nanomolar ATP, the actin filament rotated in discrete 120° steps11, consistent with the pseudo-three-fold symmetrical structure7 of F1 . . .
    • . . . The rotation rate was close to one-third of the rate of ATP hydrolysis in solution, suggesting that one ATP molecule is consumed per 120° step11 . . .
    • . . . On the load-dependent portions in Fig. 2, however, bead rotation was smooth, as was rotation of actin at these ATP concentrations11 . . .
    • . . . The load dependence of actin rotation11 (Fig. 2; triangles) is consistent with the bead assay. . . .
    • . . . This idea is corroborated by observations11, 16, 17 that the torque and its angle dependence, as well as mechanical work done in a 120° step, are independent of [ATP] over the nM–mM range . . .
    • . . . Also, the apparent rate of ATP binding, kATPon, given by 3Vmax/Km of (2.6  0.5)  107 M-1 s-1 agrees with previous estimates based on the analysis of step intervals at nanomolar ATP11, 18. . . .
    • . . . As seen in Fig. 3, the rotation rate was close to one-third of the rate of ATP hydrolysis for bead-free F1 in solution, supporting the contention that one ATP molecule is consumed per 120° rotation11, 16, 17, 18 . . .
    • . . . Global fit to all histograms (green lines) showed kATPon to be (3.0  0.1)  107 M-1 s-1 (consistent with the estimate from Fig. 3 (above) and previous values in actin11 and single-fluorophore18 assays), and the other two rates to be 1.64  0.06 ms-1 and 0.71  0.02 ms-1 . . .
    • . . . Previously we have demonstrated rotation at [ATP] as low as 20 nM, indicating that bi-site hydrolysis accompanies rotation11 and that bi-site is the fundamental mode of rotation17 . . .
    • . . . We have shown that, at least under a high load, F1 does 80–90 pN nm of mechanical work per 120° step11 and that the torque it produces is nearly independent of the rotation angle16, 17 (the potential energy for -subunit rotation is linearly downhill) . . .
    • . . . A flow cell was made of two KOH-cleaned coverslips separated by two spacers with 50 m thickness11 . . .
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    • . . . Bead rotation was imaged by laser dark-field microscopy12 (Fig. 1c), and recorded on a fast-framing charge-coupled-device (CCD) camera at speeds up to 8,000 frames per s . . .
    • . . . We observed 40-nm and 108-nm beads with laser dark-field microscopy12 (Fig. 1c) . . .
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    • . . . Some beads showed rotation (Fig. 1d; movies in Supplementary Information), and motions of these beads were analysed by calculating the centroid of the bead image13 . . .
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    • . . . Diameters up to 60 nm are possible for the height of F1 of 10 nm and the linker lengths of 5 nm for streptavidin14 and 10 nm for BSA15 (Fig. 1b) . . .
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    • . . . Diameters up to 60 nm are possible for the height of F1 of 10 nm and the linker lengths of 5 nm for streptavidin14 and 10 nm for BSA15 (Fig. 1b) . . .
  16. Kinosita, K.Jr, Yasuda, R. & Noji, H. F1-ATPase: a highly efficient rotary ATP machine. Essays Biochem. 35, 3-18 , .
    • . . . This idea is corroborated by observations11, 16, 17 that the torque and its angle dependence, as well as mechanical work done in a 120° step, are independent of [ATP] over the nM–mM range . . .
    • . . . As seen in Fig. 3, the rotation rate was close to one-third of the rate of ATP hydrolysis for bead-free F1 in solution, supporting the contention that one ATP molecule is consumed per 120° rotation11, 16, 17, 18 . . .
    • . . . By reciprocity, the affinity of the -subunit for ATP, on the left of the arrow on the central -subunit, must increase as the -subunit rotates6, 16, 17, 28 . . .
    • . . . We have shown that, at least under a high load, F1 does 80–90 pN nm of mechanical work per 120° step11 and that the torque it produces is nearly independent of the rotation angle16, 17 (the potential energy for -subunit rotation is linearly downhill) . . .
    • . . . One such mechanism (a switch-less model for F1 motor16, 17) is suggested in Fig. 7c, where the minimum in C (after hydrolysis) is placed slightly to the right of the minimum in B (before hydrolysis) . . .
  17. Kinosita, K.Jr, Yasuda, R., Noji, H. & Adachi, K. A rotary molecular motor that can work at near 100% efficiency. Phil. Trans. R. Soc. Lond. B 355, 473-489 , .
    • . . . This idea is corroborated by observations11, 16, 17 that the torque and its angle dependence, as well as mechanical work done in a 120° step, are independent of [ATP] over the nM–mM range . . .
    • . . . As seen in Fig. 3, the rotation rate was close to one-third of the rate of ATP hydrolysis for bead-free F1 in solution, supporting the contention that one ATP molecule is consumed per 120° rotation11, 16, 17, 18 . . .
    • . . . A probable cause is MgADP inhibition: F1 is stochastically inactivated during ATP hydrolysis, when it binds MgADP tightly17, 19, 20 . . .
    • . . . This is the so-called bi-site mechanism2, 3, 17, which is the norm at least at submicromolar [ATP] . . .
    • . . . Previously we have demonstrated rotation at [ATP] as low as 20 nM, indicating that bi-site hydrolysis accompanies rotation11 and that bi-site is the fundamental mode of rotation17 . . .
    • . . . By reciprocity, the affinity of the -subunit for ATP, on the left of the arrow on the central -subunit, must increase as the -subunit rotates6, 16, 17, 28 . . .
    • . . . One such mechanism (a switch-less model for F1 motor16, 17) is suggested in Fig. 7c, where the minimum in C (after hydrolysis) is placed slightly to the right of the minimum in B (before hydrolysis) . . .
    • . . . If so, much of the free-energy drop accompanying ATP hydrolysis occurs in the ATP-binding step17, 29, 30 . . .
  18. Adachi, K. et al. Stepping rotation of F1-ATPase visualized through angle-resolved single-fluorophore imaging. Proc. Natl Acad. Sci. USA 97, 7243-7247 , .
    • . . . Also, the apparent rate of ATP binding, kATPon, given by 3Vmax/Km of (2.6  0.5)  107 M-1 s-1 agrees with previous estimates based on the analysis of step intervals at nanomolar ATP11, 18. . . .
    • . . . As seen in Fig. 3, the rotation rate was close to one-third of the rate of ATP hydrolysis for bead-free F1 in solution, supporting the contention that one ATP molecule is consumed per 120° rotation11, 16, 17, 18 . . .
    • . . . Global fit to all histograms (green lines) showed kATPon to be (3.0  0.1)  107 M-1 s-1 (consistent with the estimate from Fig. 3 (above) and previous values in actin11 and single-fluorophore18 assays), and the other two rates to be 1.64  0.06 ms-1 and 0.71  0.02 ms-1 . . .
    • . . . Nucleotide-depleted F1 was prepared18, and its ATPase activity was determined at 23 °C with an ATP-regenerating system18, 36 containing 1 mM phosphoenolpyruvate, 200 g ml-1 pyruvate kinase, 100 g ml-1 lactate dehydrogenase, 0.15 mM NADH, and indicated MgATP in buffer A (50 mM KCl, 2 mM MgCl2, 10 mM 3-[N-morpholino]propanesulfonic acid-KOH, pH 7.0) . . .
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    • . . . A probable cause is MgADP inhibition: F1 is stochastically inactivated during ATP hydrolysis, when it binds MgADP tightly17, 19, 20 . . .
    • . . . Higher activity at still higher [ATP] is accounted for by binding of ATP to non-catalytic -subunits, which tends to restore the hydrolysis activity19 . . .
    • . . . Lauryldodecylamine oxide (LDAO), a suppressor of the MgADP inhibition19, produced hydrolysis kinetics parallel to the rotation kinetics, although Vmax/3 (82 s-1) was only 60% of Vmax for rotation (Fig. 3). . . .
  20. Matsui, T. et al. Catalytic activity of the 33 complex of F1-ATPase without noncatalytic nucleotide binding site. J. Biol. Chem. 272, 8215-8221 , .
    • . . . A probable cause is MgADP inhibition: F1 is stochastically inactivated during ATP hydrolysis, when it binds MgADP tightly17, 19, 20 . . .
    • . . . Indeed, the rate of inactivation increases with [ATP] and reaches 0.3 s-1 at > 10 M ATP20, the position of the concavity in Fig. 3 . . .
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    • . . . Either interpretation is consistent with the biochemical evidence that the releases of ADP and phosphate occur at similar rates21. . . .
    • . . . Synthesis (or hydrolysis) of ATP on a -subunit does not require much energy, because ATP and ADP + phosphate are in equilibrium on the -subunit21, 26 . . .
  22. Gresser, M. J., Myers, J. A. & Boyer, P. D. Catalytic site cooperativity of beef heart mitochondrial F1 adenosine triphosphatase. Correlations of initial velocity, bound intermediate, and oxygen exchange measurements with an alternating three-site model. J. Biol. Chem. 257, 12030-12038 , .
    • . . . Alternation between two-filled and three-filled states (the tri-site mechanism) has been proposed for hydrolysis at high [ATP], from non-Michaelis–Menten kinetics22, 23 as in Fig. 3, and from quenching of tryptophan fluorescence in the active sites24 . . .
  23. Jault, J.-M. et al. The 33 subcomplex of the F1-ATPase from the thermophilic Bacillus PS3 with the T165S substitution does not entrap inhibitory MgADP in a catalytic site during turnover. J. Biol. Chem. 271, 28818-28824 , .
    • . . . Alternation between two-filled and three-filled states (the tri-site mechanism) has been proposed for hydrolysis at high [ATP], from non-Michaelis–Menten kinetics22, 23 as in Fig. 3, and from quenching of tryptophan fluorescence in the active sites24 . . .
  24. Weber, J., Wilke-Mounts, S., Lee, R. S., Grell, E. & Senior, A. E. Specific placement of tryptophan in the catalytic sites of Escherichia coli F1-ATPase provides a direct probe of nucleotide binding: maximal ATP hydrolysis occurs with three sites occupied. J. Biol. Chem. 268, 20126-20133 , .
    • . . . Alternation between two-filled and three-filled states (the tri-site mechanism) has been proposed for hydrolysis at high [ATP], from non-Michaelis–Menten kinetics22, 23 as in Fig. 3, and from quenching of tryptophan fluorescence in the active sites24 . . .
  25. Milgrom, Y. M., Murataliev, M. B. & Boyer, P. D. Bi-site activation occurs with the native and nucleotide-depleted mitochondrial F1-ATPase. Biochem. J. 330, 1037-1043 , .
    • . . . These results indicating the tri-site mechanism may have been influenced by the MgADP inhibition25 . . .
  26. Zhou, J.-M. & Boyer, P. D. Evidence that energization of the chloroplast ATP synthase favors ATP formation at the tight binding catalytic site and increases the affinity for ADP at another catalytic site. J. Biol. Chem. 268, 1531-1538 , .
    • . . . In contrast, ATP synthesis by ATP synthase is insensitive to the inhibition and seems to proceed by a bi-site mechanism26 . . .
    • . . . Synthesis (or hydrolysis) of ATP on a -subunit does not require much energy, because ATP and ADP + phosphate are in equilibrium on the -subunit21, 26 . . .
    • . . . Indeed, it has been indicated that the equilibrium shifts toward ATP during synthesis26 . . .
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    • . . . A structure27 reported recently indicates that the protruding portion of the -subunit, where the bead was attached, is torsionally flexible, therefore it is possible that the substeps revealed here might be an artefact: intrinsic steps of the -subunit are always 120°, whereas the bead is somehow obstructed at 90° and lags behind for a few ms . . .
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    • . . . By reciprocity, the affinity of the -subunit for ATP, on the left of the arrow on the central -subunit, must increase as the -subunit rotates6, 16, 17, 28 . . .
    • . . . Affinity for ATP is proportional to exp[(A - B)/kBT], where kBT 4.1 pN nm is the thermal energy at room temperature6, 28 . . .
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    • . . . Similar to F1-ATPase, myosin hosts ATP and its hydrolysis product at near equilibrium29, 30 . . .
    • . . . If so, much of the free-energy drop accompanying ATP hydrolysis occurs in the ATP-binding step17, 29, 30 . . .
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    • . . . Similar to F1-ATPase, myosin hosts ATP and its hydrolysis product at near equilibrium29, 30 . . .
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    • . . . Indeed, ATP binding induces large conformational changes in molecules such as myosin31, kinesin32, 33 and chaperonin34. . . .
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    • . . . Indeed, ATP binding induces large conformational changes in molecules such as myosin31, kinesin32, 33 and chaperonin34. . . .
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    • . . . Indeed, ATP binding induces large conformational changes in molecules such as myosin31, kinesin32, 33 and chaperonin34. . . .
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    • . . . Indeed, ATP binding induces large conformational changes in molecules such as myosin31, kinesin32, 33 and chaperonin34. . . .
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    • . . . Two biotin moieties per protein were found in an assay using 4-hydroxyazobenzene-2-carboxylic acid35 . . .
  36. Kato, Y., Sasayama, T., Muneyuki, E. & Yoshida, M. Analysis of time-dependent change of Escherichia coli F1-ATPase activity and its relationship with apparent negative cooperativity. Biochim. Biophys. Acta 1231, 275-281 , .
    • . . . Nucleotide-depleted F1 was prepared18, and its ATPase activity was determined at 23 °C with an ATP-regenerating system18, 36 containing 1 mM phosphoenolpyruvate, 200 g ml-1 pyruvate kinase, 100 g ml-1 lactate dehydrogenase, 0.15 mM NADH, and indicated MgATP in buffer A (50 mM KCl, 2 mM MgCl2, 10 mM 3-[N-morpholino]propanesulfonic acid-KOH, pH 7.0) . . .
  37. Born, M. & Wolf, E. Principles of Optics 7th edn. (Cambridge Univ. Press, Cambridge, 1999) , .
    • . . . Because an object smaller than the wavelength scatters light in proportion to the square of its volume37, these peaks should correspond to single and duplex beads . . .
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