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.

Ever-fluctuating single enzyme molecules: Michaelis-Menten equation revisited

An Erratum to this article was published on 01 March 2006

Abstract

Enzymes are biological catalysts vital to life processes and have attracted century-long investigation. The classic Michaelis-Menten mechanism provides a highly satisfactory description of catalytic activities for large ensembles of enzyme molecules. Here we tested the Michaelis-Menten equation at the single-molecule level. We monitored long time traces of enzymatic turnovers for individual β-galactosidase molecules by detecting one fluorescent product at a time. A molecular memory phenomenon arises at high substrate concentrations, characterized by clusters of turnover events separated by periods of low activity. Such memory lasts for decades of timescales ranging from milliseconds to seconds owing to the presence of interconverting conformers with broadly distributed lifetimes. We proved that the Michaelis-Menten equation still holds even for a fluctuating single enzyme, but bears a different microscopic interpretation.

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

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

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

Figure 1: Single-molecule assay with fluorescent product.
Figure 2: Concentration dependence of waiting time.
Figure 3: Concentration dependence of randomness parameter.
Figure 4: Two-dimensional joint-probability distributions of waiting times.
Figure 5: Fluctuations of turnover rate constants.

Similar content being viewed by others

References

  1. Michaelis, L. & Menten, M.L. Kinetics of invertase action. Biochem. Z. 49, 333–369 (1913).

    CAS  Google Scholar 

  2. Moerner, W.E. & Orrit, M. Illuminating single molecules in condensed matter. Science 283, 1670–1676 (1999).

    CAS  PubMed  Google Scholar 

  3. Xie, X.S. & Trautman, J.K. Optical studies of single molecules at room temperature. Annu. Rev. Phys. Chem. 49, 441–480 (1998).

    CAS  PubMed  Google Scholar 

  4. Ishijima, A. & Yanagida, T. Single molecule nanobioscience. Trends Biochem. Sci. 26, 438–444 (2001).

    CAS  PubMed  Google Scholar 

  5. Weiss, S. Fluorescence spectroscopy of single biomolecules. Science 283, 1676–1683 (1999).

    CAS  PubMed  Google Scholar 

  6. Bustamante, C., Bryant, Z. & Smith, S.B. Ten years of tension: single-molecule DNA mechanics. Nature 421, 423–427 (2003).

    PubMed  Google Scholar 

  7. Lu, H.P., Xun, L. & Xie, X.S. Single-molecule enzymatic dynamics. Science 282, 1877–1882 (1998).

    CAS  PubMed  Google Scholar 

  8. Zhuang, X. et al. Correlating structural dynamics and function in single ribozyme molecules. Science 296, 1473–1476 (2002).

    CAS  PubMed  Google Scholar 

  9. van Oijen, A.M. et al. Single-molecule kinetics of λ exonuclease reveal base dependence and dynamic disorder. Science 301, 1235–1239 (2003).

    CAS  PubMed  Google Scholar 

  10. Velonia, K. et al. Single-enzyme kinetics of CALB-catalyzed hydrolysis. Angew. Chem. Intl. Edn. 44, 560–564 (2005).

    CAS  Google Scholar 

  11. Flomenbom, O. et al. Stretched exponential decay and correlations in the catalytic activity of fluctuating single lipase molecules. Proc. Natl. Acad. Sci. USA 102, 2368–2372 (2005).

    CAS  PubMed  Google Scholar 

  12. Yang, H. et al. Protein conformational dynamics probed by single-molecule electron transfer. Science 302, 262–266 (2003).

    CAS  PubMed  Google Scholar 

  13. Min, W., Luo, G., Cherayil, B.J., Kou, S.C. & Xie, X.S. Observation of a power-law memory kernel for fluctuations within a single protein molecule. Phys. Rev. Lett. 94, 198302/1–198302/4 (2005).

    CAS  Google Scholar 

  14. Segel, I.H. Enzyme Kinetics: Behavior and Analysis of Rapid Equilibrium and Steady State Enzyme Systems (Wiley, New York, 1993).

    Google Scholar 

  15. Xie, X.S. Single-molecule approach to enzymology. Single Molecules 2, 229–236 (2001).

    CAS  Google Scholar 

  16. Qian, H. & Elson, E.L. Single-molecule enzymology: stochastic Michaelis-Menten kinetics. Biophys. Chem. 101–102, 565–576 (2002).

    PubMed  Google Scholar 

  17. Kou, S.C., Cherayil, B.J., Min, W., English, B.P. & Xie, S.X. Single-molecule Michaelis-Menten equations. J. Phys. Chem. B 109, 19068–19081 (2005).

    CAS  PubMed  Google Scholar 

  18. Fersht, A. Structure and Mechanism in Protein Science: A Guide to Enzyme Catalysis and Protein Folding (Freeman, New York, 1999).

    Google Scholar 

  19. Edman, L., Foldes-Papp, Z., Wennmalm, S. & Rigler, R. The fluctuating enzyme: a single molecule approach. Chem. Phys. 247, 11–22 (1999).

    CAS  Google Scholar 

  20. Jacobson, R.H., Zhang, X.J., DuBose, R.F. & Matthews, B.W. Three-dimensional structure of β-galactosidase from E. coli. Nature 369, 761–766 (1994).

    CAS  PubMed  Google Scholar 

  21. Richard, J.P., Huber, R.E., Heo, C., Amyes, T.L. & Lin, S. Structure-reactivity relationships for β-galactosidase (Escherichia coli, lacZ). 4. Mechanism for reaction of nucleophiles with the galactosyl-enzyme intermediates of E461G and E461Q β-galactosidases. Biochemistry 35, 12387–12401 (1996).

    CAS  PubMed  Google Scholar 

  22. Marchesi, S.L., Steers, E., Jr. & Shifrin, S. Purification and characterization of the multiple forms of β-galactosidase of Escherichia coli. Biochim. Biophys. Acta 181, 20–34 (1969).

    CAS  PubMed  Google Scholar 

  23. Seong, G.H., Heo, J. & Crooks, R.M. Measurement of enzyme kinetics using a continuous-flow microfluidic system. Anal. Chem. 75, 3161–3167 (2003).

    CAS  PubMed  Google Scholar 

  24. Hadd, A.G., Raymond, D.E., Halliwell, J.W., Jacobson, S.C. & Ramsey, J.M. Microchip device for performing enzyme assays. Anal. Chem. 69, 3407–3412 (1997).

    CAS  PubMed  Google Scholar 

  25. Matthews, B.W. The structure of E. coli β-galactosidase. C. R. Biol. 328, 549–556 (2005).

    CAS  PubMed  Google Scholar 

  26. Hofmann, J. & Sernetz, M. Immobilized enzyme kinetics analyzed by flow-through microfluorimetry. Resorufin-β-D-galactopyranoside as a new fluorogenic substrate for β-galactosidase. Anal. Chim. Acta 163, 67–72 (1984).

    CAS  Google Scholar 

  27. Ha, T. et al. Initiation and re-initiation of DNA unwinding by the Escherichia coli Rep helicase. Nature 419, 638–641 (2002).

    CAS  PubMed  Google Scholar 

  28. Zwanzig, R. Rate processes with dynamical disorder. Acc. Chem. Res. 23, 148–152 (1990).

    CAS  Google Scholar 

  29. Karplus, M. Aspects of protein reaction dynamics: deviations from simple behavior. J. Phys. Chem. B 104, 11–27 (2000).

    CAS  Google Scholar 

  30. Mesecar, A.D., Stoddard, B.L. & Koshland, D.E., Jr. Orbital steering in the catalytic power of enzymes: small structural changes with large catalytic consequences. Science 277, 202–206 (1997).

    CAS  PubMed  Google Scholar 

  31. Hammes, G.G. Multiple conformational changes in enzyme catalysis. Biochemistry 41, 8221–8228 (2002).

    CAS  PubMed  Google Scholar 

  32. Austin, R.H., Beeson, K.W., Eisenstein, L., Frauenfelder, H. & Gunsalus, I.C. Dynamics of ligand binding to myoglobin. Biochemistry 14, 5355–5373 (1975).

    CAS  PubMed  Google Scholar 

  33. Frauenfelder, H., Sligar, S.G. & Wolynes, P.G. The energy landscapes and motions of proteins. Science 254, 1598–1603 (1991).

    CAS  PubMed  Google Scholar 

  34. Sakmann, B. & Neher, E. Single-Channel Recording 2nd edn. (Plenum, New York and London, 1995).

    Google Scholar 

  35. Benkovic Stephen, J. & Hammes-Schiffer, S. A perspective on enzyme catalysis. Science 301, 1196–1202 (2003).

    CAS  PubMed  Google Scholar 

  36. Kohen, A., Cannio, R., Bartolucci, S. & Klinman, J.P. Enzyme dynamics and hydrogen tunnelling in a thermophilic alcohol dehydrogenase. Nature 399, 496–499 (1999).

    CAS  PubMed  Google Scholar 

  37. Schnitzer, M.J. & Block, S.M. Statistical kinetics of processive enzymes. Cold Spring Harb. Symp. Quant. Biol. 60, 793–802 (1995).

    CAS  PubMed  Google Scholar 

  38. Svoboda, K., Mitra, P.P. & Block, S.M. Fluctuation analysis of motor protein movement and single enzyme kinetics. Proc. Natl. Acad. Sci. USA 91, 11782–11786 (1994).

    CAS  PubMed  Google Scholar 

  39. Yang, S. & Cao, J. Two-event echos in single-molecule kinetics: a signature of conformational fluctuations. J. Phys. Chem. B 105, 6536–6549 (2001).

    CAS  Google Scholar 

  40. Lippitz, M., Kulzer, F. & Orrit, M. Statistical evaluation of single nano-object fluorescence. ChemPhysChem 6, 770–789 (2005).

    CAS  PubMed  Google Scholar 

  41. Lerch, H.-P., Rigler, R. & Mikhailov, A.S. Functional conformational motions in the turnover cycle of cholesterol oxidase. Proc. Natl. Acad. Sci. USA 102, 10807–10812 (2005).

    CAS  PubMed  Google Scholar 

  42. Flomenbom, O., Klafter, J. & Szabo, A. What can one learn from two-state single-molecule trajectories? Biophys. J. 88, 3780–3783 (2005).

    CAS  PubMed  PubMed Central  Google Scholar 

  43. Barsegov, V., Chernyak, V. & Mukamel, S. Multitime correlation functions for single molecule kinetics with fluctuating bottlenecks. J. Chem. Phys. 116, 4240–4251 (2002).

    CAS  Google Scholar 

  44. Magde, D., Elson, E. & Webb, W.W. Thermodynamic fluctations in a reacting system. Measurement by fluorescence correlation spectroscopy. Phys. Rev. Lett. 29, 705–708 (1972).

    CAS  Google Scholar 

  45. Yang, S. & Cao, J. Direct measurements of memory effects in single-molecule kinetics. J. Chem. Phys. 117, 10996–11009 (2002).

    CAS  Google Scholar 

Download references

Acknowledgements

We thank E.J. Sánchez for developing the scanning software and P. Blainey for his help with Matlab simulations. This work was funded by a US National Institutes of Health (NIH) R01 grant and recently by the NIH Director's Pioneer Award to X.S.X. B.P.E. is supported by an NIH Training Grant. K.T.L is supported by the Post-doctoral Fellowship Program of Korea Science & Engineering Foundation. A.M.v.O. acknowledges financial support from the Niels Stensen Foundation. S.C.K. acknowledges support from an NSF grant and an NSF CAREER award.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to X Sunney Xie.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Fig. 1

Effect of surface immobilization on enzymatic activity. (PDF 77 kb)

Supplementary Fig. 2

Loss of enzymatic activity due to tetrameter dissociation. (PDF 78 kb)

Supplementary Fig. 3

Autohydrolysis rate. (PDF 94 kb)

Supplementary Fig. 4

Effectiveness of the bleaching scheme. (PDF 78 kb)

Supplementary Fig. 5

Intensity histogram. (PDF 70 kb)

Supplementary Fig. 6

Autocorrelation of k(t). (PDF 546 kb)

Supplementary Fig. 7

Monte-Carlo simulations. (PDF 120 kb)

Supplementary Methods (PDF 199 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

English, B., Min, W., van Oijen, A. et al. Ever-fluctuating single enzyme molecules: Michaelis-Menten equation revisited. Nat Chem Biol 2, 87–94 (2006). https://doi.org/10.1038/nchembio759

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nchembio759

This article is cited by

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