Log in

Extracting intracellular diffusive states and transition rates from single-molecule tracking data

  • Article
  • Published:

From Nature Methods

View current issue Submit your manuscript

Abstract

We provide an analytical tool based on a variational Bayesian treatment of hidden Markov models to combine the information from thousands of short single-molecule trajectories of intracellularly diffusing proteins. The method identifies the number of diffusive states and the state transition rates. Using this method we have created an objective interaction map for Hfq, a protein that mediates interactions between small regulatory RNAs and their mRNA targets.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figure 1: A test of the vbSPT approach using simulated data.
Figure 2: Convergence properties for the model presented in Figure 1 with localization error (σ) of 20 nm.
Figure 3: Test of vbSPT on synthetic data with a spatially varying diffusion constant in a cell geometry.
Figure 4: vbSPT analysis of experimental tracking data on Hfq.

Similar content being viewed by others

Accession codes

Accessions

Swiss-Prot

References

  1. Manley, S. et al. High-density map** of single-molecule trajectories with photoactivated localization microscopy. Nat. Methods 5, 155–157 (2008).

    Article  CAS  Google Scholar 

  2. Niu, L. & Yu, J. Investigating intracellular dynamics of FtsZ cytoskeleton with photoactivation single-molecule tracking. Biophys. J. 95, 2009–2016 (2008).

    Article  CAS  Google Scholar 

  3. English, B.P. et al. Single-molecule investigations of the stringent response machinery in living bacterial cells. Proc. Natl. Acad. Sci. USA 108, E365–E373 (2011).

    Article  CAS  Google Scholar 

  4. Bakshi, S., Siryaporn, A., Goulian, M. & Weisshaar, J.C. Superresolution imaging of ribosomes and RNA polymerase in live Escherichia coli cells. Mol. Microbiol. 85, 21–38 (2012).

    Article  CAS  Google Scholar 

  5. Bronson, J.E., Fei, J., Hofman, J.M., Gonzalez, R.L. Jr. & Wiggins, C.H. Learning rates and states from biophysical time series: a Bayesian approach to model selection and single-molecule FRET data. Biophys. J. 97, 3196–3205 (2009).

    Article  CAS  Google Scholar 

  6. Bishop, C.M. Pattern Recognition and Machine Learning (Springer, 2006).

  7. Das, R., Cairo, C.W. & Coombs, D. A hidden Markov model for single particle tracks quantifies dynamic interactions between LFA-1 and the actin cytoskeleton. PLoS Comput. Biol. 5, e1000556 (2009).

    Article  Google Scholar 

  8. Chung, I. et al. Spatial control of EGF receptor activation by reversible dimerization on living cells. Nature 464, 783–787 (2010).

    Article  CAS  Google Scholar 

  9. Beausang, J.F. et al. DNA loo** kinetics analyzed using diffusive hidden Markov model. Biophys. J. 92, L64–L66 (2007).

    Article  CAS  Google Scholar 

  10. Mahmutovic, A., Fange, D., Berg, O.G. & Elf, J. Lost in presumption: stochastic reactions in spatial models. Nat. Methods 9, 1163–1166 (2012).

    Article  CAS  Google Scholar 

  11. Vogel, J. & Luisi, B.F. Hfq and its constellation of RNA. Nat. Rev. Microbiol. 9, 578–589 (2011).

    Article  CAS  Google Scholar 

  12. Waters, L.S. & Storz, G. Regulatory RNAs in bacteria. Cell 136, 615–628 (2009).

    Article  CAS  Google Scholar 

  13. Efron, B. Bootstrap methods: another look at the jackknife. Ann. Stat. 7, 1–26 (1979).

    Article  Google Scholar 

  14. Link, T.M., Valentin-Hansen, P. & Brennan, R.G. Structure of Escherichia coli Hfq bound to polyriboadenylate RNA. Proc. Natl. Acad. Sci. USA 106, 19292–19297 (2009).

    Article  CAS  Google Scholar 

  15. Fender, A., Elf, J., Hampel, K., Zimmermann, B. & Wagner, E.G. RNAs actively cycle on the Sm-like protein Hfq. Genes Dev. 24, 2621–2626 (2010).

    Article  CAS  Google Scholar 

  16. MacKay, D.J.C. Information Theory, Inference, and Learning Algorithms (Cambridge University Press, 2003).

  17. Bronson, J.E., Hofman, J.M., Fei, J., Gonzalez, R.L. Jr. & Wiggins, C.H. Graphical models for inferring single molecule dynamics. BMC Bioinformatics 11 (suppl. 8), S2 (2010).

    Article  Google Scholar 

  18. MacKay, D.J.C. Ensemble learning for hidden Markov models. 〈http://www.inference.phy.cam.ac.uk/mackay/abstracts/ensemblePaper.html〉 (1997).

  19. Ghahramani, Z. An introduction to hidden Markov models and Bayesian networks. in Hidden Markov Models: Applications in Computer Vision (eds. Bunke, H. & Caelli, T.) 9–42 (World Scientific, River Edge, New Jersey, USA, 2001).

  20. Beal, M.J. Variational Algorithms for Approximate Bayesian Inference. PhD thesis, Univ. College London (2003).

  21. Okamoto, K. & Sako, Y. Variational Bayes analysis of a photon-based hidden Markov model for single-molecule FRET trajectories. Biophys. J. 103, 1315–1324 (2012).

    Article  CAS  Google Scholar 

  22. Eddy, S.R. What is Bayesian statistics? Nat. Biotechnol. 22, 1177–1178 (2004).

    Article  CAS  Google Scholar 

  23. Green, P.J. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82, 711–732 (1995).

    Article  Google Scholar 

  24. Robert, C.P., Rydén, T. & Titterington, D.M. Bayesian inference in hidden Markov models through the reversible jump Markov chain Monte Carlo method. J. R. Stat. Soc., B 62, 57–75 (2000).

    Article  Google Scholar 

Download references

Acknowledgements

We thank I. Barkefors for her careful and critical reading of the manuscript. M.L. is grateful to C.H. Wiggins and J.-W. van de Meent for insightful discussions. This work was supported by the European Research Council (J.E.), the Knut and Alice Wallenberg Foundation (J.E.), Vetenskapsrådet (J.E.), the Göran Gustafsson Foundation (J.E.), the Wenner-Gren Foundations (M.L.) and the Center for Biomembrane Research (M.L.).

Author information

Authors and Affiliations

Authors

Contributions

J.E. and M.L. conceived the method, M.L. designed the vbSPT algorithm, M.L. and F.P. implemented and tested the algorithm, F.P. designed and implemented the image analysis and particle-tracking algorithms, and C.U. cloned and characterized the bacterial strains. F.P. and J.E. built the optical setup. F.P., C.U. and J.E. designed the experiments, and C.U. and F.P. performed the experiments. F.P., M.L., C.U. and J.E. wrote the manuscript.

Corresponding author

Correspondence to Johan Elf.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Text and Figures

Supplementary Tables 1–7 and Supplementary Notes 1–5 (PDF 1053 kb)

Supplementary Software

vbSPT (variational Bayes single-particle tracking) software (ZIP 6389 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Persson, F., Lindén, M., Unoson, C. et al. Extracting intracellular diffusive states and transition rates from single-molecule tracking data. Nat Methods 10, 265–269 (2013). https://doi.org/10.1038/nmeth.2367

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nmeth.2367

  • Springer Nature America, Inc.

Navigation