Skip to main content
NCBI home page
Biophysical Journal logoLink to Biophysical Journal
. 2001 Nov;81(5):2795–2816. doi: 10.1016/S0006-3495(01)75922-X

Hidden-Markov methods for the analysis of single-molecule actomyosin displacement data: the variance-Hidden-Markov method.

D A Smith 1, W Steffen 1, R M Simmons 1, J Sleep 1
PMCID: PMC1301746  PMID: 11606292

Abstract

In single-molecule experiments on the interaction between myosin and actin, mechanical events are embedded in Brownian noise. Methods of detecting events have progressed from simple manual detection of shifts in the position record to threshold-based selection of intermittent periods of reduction in noise. However, none of these methods provides a "best fit" to the data. We have developed a Hidden-Markov algorithm that assumes a simple kinetic model for the actin-myosin interaction and provides automatic, threshold-free, maximum-likelihood detection of events. The method is developed for the case of a weakly trapped actin-bead dumbbell interacting with a stationary myosin molecule (Finer, J. T., R. M. Simmons, and J. A. Spudich. 1994. Nature. 368:113-119). The algorithm operates on the variance of bead position signals in a running window, and is tested using Monte Carlo simulations to formulate ways of determining the optimum window width. The working stroke is derived and corrected for actin-bead link compliance. With experimental data, we find that modulation of myosin binding by the helical structure of the actin filament complicates the determination of the working stroke; however, under conditions that produce a Gaussian distribution of bound levels (cf. Molloy, J. E., J. E. Burns, J. Kendrick-Jones, R. T. Tregear, and D. C. S. White. 1995. Nature. 378:209-212), four experiments gave working strokes in the range 5.4-6.3 nm for rabbit skeletal muscle myosin S1.

Full Text

The Full Text of this article is available as a PDF (685.2 KB).

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Ball F. G., Sansom M. S. Ion-channel gating mechanisms: model identification and parameter estimation from single channel recordings. Proc R Soc Lond B Biol Sci. 1989 May 22;236(1285):385–416. doi: 10.1098/rspb.1989.0029. [DOI] [PubMed] [Google Scholar]
  2. Block S. M., Svoboda K. Analysis of high resolution recordings of motor movement. Biophys J. 1995 Apr;68(4 Suppl):230S–241S. [PMC free article] [PubMed] [Google Scholar]
  3. Chung S. H., Krishnamurthy V., Moore J. B. Adaptive processing techniques based on hidden Markov models for characterizing very small channel currents buried in noise and deterministic interferences. Philos Trans R Soc Lond B Biol Sci. 1991 Dec 30;334(1271):357–384. doi: 10.1098/rstb.1991.0122. [DOI] [PubMed] [Google Scholar]
  4. Chung S. H., Moore J. B., Xia L. G., Premkumar L. S., Gage P. W. Characterization of single channel currents using digital signal processing techniques based on Hidden Markov Models. Philos Trans R Soc Lond B Biol Sci. 1990 Sep 29;329(1254):265–285. doi: 10.1098/rstb.1990.0170. [DOI] [PubMed] [Google Scholar]
  5. Dupuis D. E., Guilford W. H., Wu J., Warshaw D. M. Actin filament mechanics in the laser trap. J Muscle Res Cell Motil. 1997 Feb;18(1):17–30. doi: 10.1023/a:1018672631256. [DOI] [PubMed] [Google Scholar]
  6. Finer J. T., Mehta A. D., Spudich J. A. Characterization of single actin-myosin interactions. Biophys J. 1995 Apr;68(4 Suppl):291S–297S. [PMC free article] [PubMed] [Google Scholar]
  7. Finer J. T., Simmons R. M., Spudich J. A. Single myosin molecule mechanics: piconewton forces and nanometre steps. Nature. 1994 Mar 10;368(6467):113–119. doi: 10.1038/368113a0. [DOI] [PubMed] [Google Scholar]
  8. Fredkin D. R., Rice J. A. Maximum likelihood estimation and identification directly from single-channel recordings. Proc Biol Sci. 1992 Aug 22;249(1325):125–132. doi: 10.1098/rspb.1992.0094. [DOI] [PubMed] [Google Scholar]
  9. Geeves M. A., Holmes K. C. Structural mechanism of muscle contraction. Annu Rev Biochem. 1999;68:687–728. doi: 10.1146/annurev.biochem.68.1.687. [DOI] [PubMed] [Google Scholar]
  10. Guilford W. H., Dupuis D. E., Kennedy G., Wu J., Patlak J. B., Warshaw D. M. Smooth muscle and skeletal muscle myosins produce similar unitary forces and displacements in the laser trap. Biophys J. 1997 Mar;72(3):1006–1021. doi: 10.1016/S0006-3495(97)78753-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. HUXLEY A. F. Muscle structure and theories of contraction. Prog Biophys Biophys Chem. 1957;7:255–318. [PubMed] [Google Scholar]
  12. Horn R., Lange K. Estimating kinetic constants from single channel data. Biophys J. 1983 Aug;43(2):207–223. doi: 10.1016/S0006-3495(83)84341-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. Huxley A. F., Simmons R. M. Proposed mechanism of force generation in striated muscle. Nature. 1971 Oct 22;233(5321):533–538. doi: 10.1038/233533a0. [DOI] [PubMed] [Google Scholar]
  14. Huxley A. F., Tideswell S. Filament compliance and tension transients in muscle. J Muscle Res Cell Motil. 1996 Aug;17(4):507–511. doi: 10.1007/BF00123366. [DOI] [PubMed] [Google Scholar]
  15. Ishijima A., Kojima H., Funatsu T., Tokunaga M., Higuchi H., Tanaka H., Yanagida T. Simultaneous observation of individual ATPase and mechanical events by a single myosin molecule during interaction with actin. Cell. 1998 Jan 23;92(2):161–171. doi: 10.1016/s0092-8674(00)80911-3. [DOI] [PubMed] [Google Scholar]
  16. Kishino A., Yanagida T. Force measurements by micromanipulation of a single actin filament by glass needles. Nature. 1988 Jul 7;334(6177):74–76. doi: 10.1038/334074a0. [DOI] [PubMed] [Google Scholar]
  17. Kojima H., Ishijima A., Yanagida T. Direct measurement of stiffness of single actin filaments with and without tropomyosin by in vitro nanomanipulation. Proc Natl Acad Sci U S A. 1994 Dec 20;91(26):12962–12966. doi: 10.1073/pnas.91.26.12962. [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. Kron S. J., Spudich J. A. Fluorescent actin filaments move on myosin fixed to a glass surface. Proc Natl Acad Sci U S A. 1986 Sep;83(17):6272–6276. doi: 10.1073/pnas.83.17.6272. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. Lorenz M., Poole K. J., Popp D., Rosenbaum G., Holmes K. C. An atomic model of the unregulated thin filament obtained by X-ray fiber diffraction on oriented actin-tropomyosin gels. J Mol Biol. 1995 Feb 10;246(1):108–119. doi: 10.1006/jmbi.1994.0070. [DOI] [PubMed] [Google Scholar]
  20. Lymn R. W., Taylor E. W. Mechanism of adenosine triphosphate hydrolysis by actomyosin. Biochemistry. 1971 Dec 7;10(25):4617–4624. doi: 10.1021/bi00801a004. [DOI] [PubMed] [Google Scholar]
  21. Mehta A. D., Finer J. T., Spudich J. A. Detection of single-molecule interactions using correlated thermal diffusion. Proc Natl Acad Sci U S A. 1997 Jul 22;94(15):7927–7931. doi: 10.1073/pnas.94.15.7927. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Miyata H., Hakozaki H., Yoshikawa H., Suzuki N., Kinosita K., Jr, Nishizaka T., Ishiwata S. Stepwise motion of an actin filament over a small number of heavy meromyosin molecules is revealed in an in vitro motility assay. J Biochem. 1994 Apr;115(4):644–647. doi: 10.1093/oxfordjournals.jbchem.a124389. [DOI] [PubMed] [Google Scholar]
  23. Molloy J. E., Burns J. E., Kendrick-Jones J., Tregear R. T., White D. C. Movement and force produced by a single myosin head. Nature. 1995 Nov 9;378(6553):209–212. doi: 10.1038/378209a0. [DOI] [PubMed] [Google Scholar]
  24. Patlak J. B. Measuring kinetics of complex single ion channel data using mean-variance histograms. Biophys J. 1993 Jul;65(1):29–42. doi: 10.1016/S0006-3495(93)81041-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  25. Rosales R., Stark J. A., Fitzgerald W. J., Hladky S. B. Bayesian restoration of ion channel records using hidden Markov models. Biophys J. 2001 Mar;80(3):1088–1103. doi: 10.1016/S0006-3495(01)76087-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  26. Smith D. A. Direct tests of muscle cross-bridge theories: predictions of a Brownian dumbbell model for position-dependent cross-bridge lifetimes and step sizes with an optically trapped actin filament. Biophys J. 1998 Dec;75(6):2996–3007. doi: 10.1016/S0006-3495(98)77740-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  27. Svensson E. C., Thomas D. D. ATP induces microsecond rotational motions of myosin heads crosslinked to actin. Biophys J. 1986 Nov;50(5):999–1002. doi: 10.1016/S0006-3495(86)83541-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
  28. Svoboda K., Block S. M. Biological applications of optical forces. Annu Rev Biophys Biomol Struct. 1994;23:247–285. doi: 10.1146/annurev.bb.23.060194.001335. [DOI] [PubMed] [Google Scholar]
  29. Tanaka H., Ishijima A., Honda M., Saito K., Yanagida T. Orientation dependence of displacements by a single one-headed myosin relative to the actin filament. Biophys J. 1998 Oct;75(4):1886–1894. doi: 10.1016/S0006-3495(98)77629-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  30. Tskhovrebova L., Trinick J., Sleep J. A., Simmons R. M. Elasticity and unfolding of single molecules of the giant muscle protein titin. Nature. 1997 May 15;387(6630):308–312. doi: 10.1038/387308a0. [DOI] [PubMed] [Google Scholar]
  31. Tyska M. J., Dupuis D. E., Guilford W. H., Patlak J. B., Waller G. S., Trybus K. M., Warshaw D. M., Lowey S. Two heads of myosin are better than one for generating force and motion. Proc Natl Acad Sci U S A. 1999 Apr 13;96(8):4402–4407. doi: 10.1073/pnas.96.8.4402. [DOI] [PMC free article] [PubMed] [Google Scholar]
  32. Veigel C., Bartoo M. L., White D. C., Sparrow J. C., Molloy J. E. The stiffness of rabbit skeletal actomyosin cross-bridges determined with an optical tweezers transducer. Biophys J. 1998 Sep;75(3):1424–1438. doi: 10.1016/S0006-3495(98)74061-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  33. Veigel C., Coluccio L. M., Jontes J. D., Sparrow J. C., Milligan R. A., Molloy J. E. The motor protein myosin-I produces its working stroke in two steps. Nature. 1999 Apr 8;398(6727):530–533. doi: 10.1038/19104. [DOI] [PubMed] [Google Scholar]

Articles from Biophysical Journal are provided here courtesy of The Biophysical Society

RESOURCES