Proc Natl Acad Sci U S A 103(5): 1278-1282

Reconciling the working strokes of a single head of skeletal muscle myosin estimated from laser-trap experiments and crystal structures

^{Randall Division, King's College London, SE1 1UL London, United Kingdom; and}^{Department of Physiology, Monash University, Clayton, Victoria 3800, Australia}

^{To whom correspondence should be addressed at: Randall Division, New Hunt's House, Guy's Campus, King's College London, London SE1 1UL, United Kingdom. E-mail:}ku.ca.lck@peels.nhoj.

Edited by Edward D. Korn, National Institutes of Health, Bethesda, MD, and approved December 6, 2005

Received 2005 Jul 28

Abstract

Myosin generates force by a rotation of its lever arm. Crystal structures of myosin II indicate an unloaded working stroke of 10–12 nm, a range confirmed by recent x-ray interference experiments. However, when an actin filament, held between two weakly, optically trapped beads is made to interact with a single head of skeletal myosin, the bead displacements have often been reported as having a mean value of 5–6 nm, a value that is commonly interpreted as the working stroke. In general, the observed displacement is not expected to be equal to the working stroke because the kinetics of the stroke is necessarily strain-dependent: this effect biases the frequency of binding events to different actin sites so that displacements smaller than the working stroke are preferentially selected. Our analysis is tailored to current trap experiments, in which the time resolution is insufficient to detect prerigor states. If the preceding transitions are in equilibrium, the mean displacement is zero, contrary to observations in the presence of ATP. However, under ATP-cycling conditions, we find that the mean displacement is deflated to 0.3–0.7 of the true working stroke, depending on the equilibrium constant of the stroke and the rate at which the first myosin product state can detach from actin. The primary working stroke of processive myosin motors as measured by optical trapping is similarly uncertain.

Keywords: optical, tweezers, molecular motor

Abstract

The swinging-lever-arm model for muscle contraction is supported by a great variety of experiments, but there are significant disagreements over the size of the swing. All of the current methods suffer from some ambiguity in interpretation; for example, the estimate derived from crystallography is dependent on structures of myosin heads in the absence of actin (1, 2). However, there is reasonable agreement between this estimate and that derived from x-ray interference experiments (3). For the purposes of this work, attention will be focused on whether the difference between the estimates of 10–12 nm based on these methods and the 5- to 6-nm displacement commonly observed for single-headed interactions in optical trap experiments (4–7) can be explained by a reinterpretation of the latter method.

In optical trap experiments, an actin filament is held taut between two weakly trapped beads and is allowed to interact with a single tethered myosin head (Fig. 1). An obvious possibility is that the small step size commonly reported might be due to the myosin either not being attached in an appropriate manner or alternatively not being oriented correctly relative to the actin filament. As will be made evident in the discussion, these possibilities do not stand up well to serious analysis, and we believe that there is a more fundamental error in current methods of deducing the working stroke from optical trap data. At present, the time resolution of bead detection in the three-bead experiment is not adequate to detect the prestroke bound state, which means that an individual working stroke cannot be characterized and that the size of the working stroke can only be estimated on a statistical basis. Binding events are detected by the reduction in variance of bead position (4), which is facilitated by the use of traps, whose stiffness is low relative to that of myosin. Such weak traps allow substantial movement of the bead–actin–bead dumbbell along the axis of the actin filaments (SD 10–15 nm), and correspondingly four or five actin monomers are accessible at any time. Molloy and coworkers (4) observed that the positions of the dumbbell while bound to myosin could be described by a Gaussian distribution with the same half-width as that describing the positions of the free dumbbell (see Fig. 1), and they proposed that the displacement in the mean position corresponds to the working stroke. This idea represented a major improvement in interpretation and has gained general acceptance. The equality of the observed displacement and the working stroke is valid if the myosin makes a stroke after every actin-binding event. More generally, the displacement equals the working stroke if the probability of an actin-binding event leading to product release and experimental detection is symmetrical about the mean position of the myosin head. There are fundamental reasons for supposing that in general this condition is not satisfied, because the equilibrium constant of the working stroke must be dependent on elastic strain in the myosin and thus on the initial position of the dumbbell at the time of binding to actin. In the muscle fiber, the experimental consequences of this principle were first demonstrated many years ago (8).

An external file that holds a picture, illustration, etc.
Object name is zpq0040609170001.jpg

Fig. 1.

Displacement of actin–bead dumbbell by a single myosin head. (A) Schematic of the three-bead trap experiment with an optically trapped actin filament, showing the myosin free (1), initially bound to actin (2), and after a working stroke (3). (B) The frequency of displacements of the free filament is a Gaussian centered on zero, and the histogram shows a typical distribution of displacements with bound myosin, displaced by the effects of the working stroke.

Acknowledgments

This work was supported by the Medical Research Council (U.K.) and National Institutes of Health Grant AR048776.

Acknowledgments

Notes

Author contributions: J.S., A.L., and D.S. performed research and wrote the paper.

Conflict of interest statement: No conflicts declared.

This paper was submitted directly (Track II) to the PNAS office.

Notes

Author contributions: J.S., A.L., and D.S. performed research and wrote the paper.

Conflict of interest statement: No conflicts declared.

This paper was submitted directly (Track II) to the PNAS office.

References

1. Rayment, I., Holden, H. M., Whittaker, M., Yohn, C. B., Lorenz, M., Holmes, K. C. & Milligan, R. A. (1993) Science261, 58–65. [[PubMed]
2. Houdusse, A., Szent-Gyorgyi, A. G. & Cohen, C. (2000) Proc. Natl. Acad. Sci. USA97, 11238–11243.
3. Reconditi, M., Linari, M., Lucii, L., Stewart, A., Sun, Y. B., Boesecke, P., Narayanan, T., Fischetti, R. F., Irving, T., Piazzesi, G., et al. (2004) Nature428, 578–581. [[PubMed]
4. Molloy, J. E., Burns, J. E., Kendrick-Jones, J., Tregear, R. T. & White, D. C. (1995) Nature378, 209–212. [[PubMed]
5. Ruff, C., Furch, M., Brenner, B., Manstein, D. J. & Meyhofer, E. (2001) Nat. Struct. Biol8, 226–229. [[PubMed]
6. Steffen, W., Smith, D., Simmons, R. & Sleep, J. (2001) Proc. Natl. Acad. Sci. USA98, 14949–14954.
7. Tyska, M. J., Dupuis, D. E., Guilford, W. H., Patlak, J. B., Waller, G. S., Trybus, K. M., Warshaw, D. M. & Lowey, S. (1999) Proc. Natl. Acad. Sci. USA96, 4402–4407.
8. Huxley, A. F. & Simmons, R. M. (1971) Nature233, 533–538. [[PubMed]
9. Lund, J., Webb, M. R. & White, D. C. (1987) J. Biol. Chem.262, 8584–8590. [[PubMed]
10. Lund, J., Webb, M. R. & White, D. C. (1988) J. Biol. Chem.263, 5505–5511. [[PubMed]
11. Kawai, M. & Halvorson, H. R. (1991) Biophys. J.59, 329–342.
12. Dantzig, J. A., Goldman, Y. E., Millar, N. C., Lacktis, J. & Homsher, E. (1992) J. Physiol.451, 247–278.
13. Ranatunga, K. W., Coupland, M. E. & Mutungi, G. (2002) J. Physiol.542, 899–910.
14. Smith, D. A. & Sleep, J. (2004) Biophys. J.87, 442–456.
15. Sleep, J., Irving, M. & Burton, K. (2005) J. Physiol.563, 671–687.
16. Takagi, Y., Shuman, H. & Goldman, Y. E. (2004) Philos. Trans. R. Soc. London Ser. B359, 1913–1920.
17. White, H. D., Belknap, B. & Webb, M. R. (1997) Biochemistry36, 11828–11836. [[PubMed]
18. Kawai, M. & Halvorson, H. R. (1989) Biophys. J.55, 595–603.
19. Kraft, T., Yu, L. C., Kuhn, H. J. & Brenner, B. (1992) Proc. Natl. Acad. Sci. USA89, 11362–11366.
20. Kawai, M(1986) J. Muscle Res. Cell Motil.7, 421–434. [[PubMed][Google Scholar]
21. Tanaka, H., Ishijima, A., Honda, M., Saito, K. & Yanagida, T. (1998) Biophys. J.75, 1886–1894.
22. Iwane, A. H., Kitamura, K., Tokunaga, M. & Yanagida, T. (1997) Biochem. Biophys. Res. Commun.230, 76–80. [[PubMed]
23. Steffen, W., Smith, D. & Sleep, J. (2003) Proc. Natl. Acad. Sci. USA100, 6434–6439.
24. Tyreman, M. (2003) Ph.D. thesis (London University, London).
25. Veigel, C., Coluccio, L. M., Jontes, J. D., Sparrow, J. C., Milligan, R. A. & Molloy, J. E. (1999) Nature398, 530–533. [[PubMed]
26. Whittaker, M., Wilson-Kubalek, E. M., Smith, J. E., Faust, L., Milligan, R. A. & Sweeney, H. L. (1995) Nature378, 748–751. [[PubMed]
27. Smith, D. A. & Geeves, M. A. (1995) Biophys. J.69, 538–552.
28. Mehta, A. D., Rock, R. S., Rief, M., Spudich, J. A., Mooseker, M. S. & Cheney, R. E. (1999) Nature400, 590–593. [[PubMed]
29. Veigel, C., Wang, F., Bartoo, M. L., Sellers, J. R. & Molloy, J. E. (2002) Nat. Cell Biol.4, 59–65. [[PubMed]