Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Thermally activated transitions in a bistable three-dimensional optical trap

Nature volume 402, pages 785–787 (1999)Cite this article

Abstract

Activated escape from a metastable state underlies many physical, chemical and biological processes: examples include diffusion in solids, switching in superconducting junctions1,2, chemical reactions3,4 and protein folding5,6. Kramers presented the first quantitative calculation7 of thermally driven transition rates in 1940. Despite widespread acceptance of Kramers’ theory8, there have been few opportunities to test it quantitatively as a comprehensive knowledge of the system dynamics is required. A trapped brownian particle (relevant to our understanding of the kinetics, transport and mechanics of biological matter9,10) represents an ideal test system. Here we report a detailed experimental analysis of the brownian dynamics of a sub-micrometre sized dielectric particle confined in a double-well optical trap. We show how these dynamics can be used to directly measure the full three-dimensional confining potential—a technique that can also be applied to other optically trapped objects11,12. Excellent agreement is obtained between the predictions of Kramers’ theory and the measured transition rates, with no adjustable or free parameters over a substantial range of barrier heights.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Interwell transitions in a dual optical trap.
Figure 2: Experimentally determined potential energy of the particle in a double-well optical trap.
Figure 3: Experimental and theoretical transition rates.

Similar content being viewed by others

References

  1. Han,S., Lapoint,J. & Lukens,J. E. Effect of a two-dimensional potential on the rate of thermally induced escape over the potential barrier. Phys. Rev. B 46, 6338–6345 ( 1992).

    Article  ADS  CAS  Google Scholar 

  2. Devoret,M. H., Esteve,D., Martinis,J. M., Cleland,A. & Clarke,J. Resonant activation of a brownian particle out of a well: microwave-enhanced escape from the zero-voltage state of a Josephson junction. Phys. Rev. B 36, 58–73 (1987).

    Article  ADS  CAS  Google Scholar 

  3. van Kampen,N. G. Stochastic Processes in Physics and Chemistry (Elsevier, Amsterdam, 1992).

    MATH  Google Scholar 

  4. Gillespie,D. T. Exact stochastic simulation of coupled chemical reactions. J. Chem. Phys. 81, 2340–2361 ( 1977).

    Article  CAS  Google Scholar 

  5. Sali,A., Shakhnovich,E. & Karplus, M. How does a protein fold? Nature 369, 248–251 (1994).

    Article  ADS  CAS  Google Scholar 

  6. White,S. H. & Wimley,W. C. Membrane protein folding and stability: Physical principles. Annu. Rev. Biophys. Biomol. Struct. 28, 319–365 (1999).

    Article  CAS  Google Scholar 

  7. Kramers,H. A. Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7, 284–304 (1940).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  8. Melnikov,V. I. The Kramers problem: fifty years of development. Phys. Rep. 209, 2–71 (1991).

    ADS  MathSciNet  Google Scholar 

  9. Mehta,A. D., Reif,M., Spudich,J. A., Smith,D. A. & Simmons, R. M. Single molecule biomechanics with optical methods. Science 283, 1689–1695 (1999).

    Article  ADS  CAS  Google Scholar 

  10. Smith,D. E., Babcock,H. P. & Chu,S. Single-polymer dynamics in steady shear flow. Science 283, 1724–1727 ( 1999).

    Article  ADS  CAS  Google Scholar 

  11. Svoboda,K., Schmidt,C. F., Schnapp,B. J. & Block,S. M. Direct observation of kinesin stepping by optical trapping interferometry. Nature 365, 721–727 (1993).

    Article  ADS  CAS  Google Scholar 

  12. Tskhovrebova,L., Trinick,J., Sleep,J. A. & Simmons,R. M. Elasticity and unfolding of single molecules of the giant muscle protein titin. Nature 387, 308–312 ( 1997).

    Article  ADS  CAS  Google Scholar 

  13. Simon,A. & Libchaber,A. Escape and synchronization of a brownian particle. Phys. Rev. Lett. 68, 3375–3378 (1992).

    Article  ADS  CAS  Google Scholar 

  14. Ghislain,L. P., Switz,N. A. & Webb,W. W. Measurement of small forces using an optical trap. Rev. Sci. Instrum. 65, 2762–2768 (1994).

    Article  ADS  CAS  Google Scholar 

  15. Landauer,R. & Swanson,J. A. Frequency factors in the thermally activated process. Phys. Rev. 121, 1668– 1674 (1961).

    Article  ADS  Google Scholar 

  16. Risken,H. The Fokker-Planck Equation (Springer, Berlin, 1989).

    Book  Google Scholar 

  17. Hänggi,P., Talkner,P. & Borkovec, M. Reaction-rate theory: fifty years after Kramers. Rev. Mod. Phys. 62, 251–341 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  18. Linkwitz,S., Grabert,H., Turlot,E., Esteve,D. & Devoret,M. H. Escape rates in the region between the Kramers limits. Phys. Rev. A 45, R3369– R3372 (1992).

    Article  ADS  CAS  Google Scholar 

  19. Luchinsky,D. G. & McClintock,P. V. E. Irreversibility of classical fluctuations studied in analogue electrical circuits. Nature 389, 463–466 ( 1997).

    Article  ADS  CAS  Google Scholar 

  20. Smelyanskiy,V., Dykman,M. I. & Golding, B. Time oscillations of escape rates in periodically driven systems. Phys. Rev. Lett. 82, 3193– 3197 (1999).

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

We thank R. Kruse for his assistance with the experiment and graphics. Support from the Center for Fundamental Materials Research at Michigan State University and from the NSF Division of Physics, and Division of Materials Research is gratefully acknowledged.

Author information

Author notes

  1. Lowell I. McCann

    Present address: Department of Physics, University of Wisconsin-River Falls, River Falls, Wisconsin, 54022, USA

  2. Brage Golding: Correspondence and requests for materials should be addressed to B.G.

Authors and Affiliations

  1. Department of Physics and Astronomy, Michigan State University East Lansing, 48824-1116, Michigan, USA

    Lowell I. McCann, Mark Dykman & Brage Golding

Authors
  1. Lowell I. McCann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mark Dykman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Brage Golding
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Brage Golding.

Rights and permissions

Reprints and permissions

About this article

Cite this article

McCann, L., Dykman, M. & Golding, B. Thermally activated transitions in a bistable three-dimensional optical trap. Nature 402, 785–787 (1999). https://doi.org/10.1038/45492

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/45492

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing