OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 20 — Sep. 24, 2012
  • pp: 22585–22601

Optimal tracking of a Brownian particle

Alexander P. Fields and Adam E. Cohen  »View Author Affiliations

Optics Express, Vol. 20, Issue 20, pp. 22585-22601 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (3233 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Optical tracking of a fluorescent particle in solution faces fundamental constraints due to Brownian motion, diffraction, and photon shot noise. Background photons and imperfect tracking apparatus further degrade tracking precision. Here we use a model of particle motion to combine information from multiple time-points to improve the localization precision. We derive successive approximations that enable real-time particle tracking with well controlled tradeoffs between precision and computational cost. We present the theory in the context of feedback electrokinetic trapping, though the results apply to optical tracking of any particle subject to diffusion and drift. We use numerical simulations and experimental data to validate the algorithms’ performance.

© 2012 OSA

OCIS Codes
(180.2520) Microscopy : Fluorescence microscopy
(110.3055) Imaging systems : Information theoretical analysis
(110.4155) Imaging systems : Multiframe image processing

ToC Category:

Original Manuscript: August 2, 2012
Revised Manuscript: September 11, 2012
Manuscript Accepted: September 13, 2012
Published: September 18, 2012

Virtual Issues
Vol. 7, Iss. 11 Virtual Journal for Biomedical Optics

Alexander P. Fields and Adam E. Cohen, "Optimal tracking of a Brownian particle," Opt. Express 20, 22585-22601 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. J. Saxton and K. Jacobson, “Single-particle tracking: applications to membrane dynamics,” Annu. Rev. Biophys. Biomol. Struct. 26(1), 373–399 (1997). [CrossRef] [PubMed]
  2. A. D. Douglass and R. D. Vale, “Single-molecule microscopy reveals plasma membrane microdomains created by protein-protein networks that exclude or trap signaling molecules in T cells,” Cell 121(6), 937–950 (2005). [CrossRef] [PubMed]
  3. I. Chung, R. Akita, R. Vandlen, D. Toomre, J. Schlessinger, and I. Mellman, “Spatial control of EGF receptor activation by reversible dimerization on living cells,” Nature 464(7289), 783–787 (2010). [CrossRef] [PubMed]
  4. A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science 300(5628), 2061–2065 (2003). [CrossRef] [PubMed]
  5. M. A. Thompson, J. M. Casolari, M. Badieirostami, P. O. Brown, and W. E. Moerner, “Three-dimensional tracking of single mRNA particles in Saccharomyces cerevisiae using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 107(42), 17864–17871 (2010). [CrossRef] [PubMed]
  6. N. P. Wells, G. A. Lessard, P. M. Goodwin, M. E. Phipps, P. J. Cutler, D. S. Lidke, B. S. Wilson, and J. H. Werner, “Time-resolved three-dimensional molecular tracking in live cells,” Nano Lett. 10(11), 4732–4737 (2010). [CrossRef] [PubMed]
  7. A. P. Fields and A. E. Cohen, “Anti-Brownian traps for studies on single molecules,” Methods Enzymol. 475, 149–174 (2010). [CrossRef] [PubMed]
  8. A. E. Cohen and W. E. Moerner, “Principal-components analysis of shape fluctuations of single DNA molecules,” Proc. Natl. Acad. Sci. U.S.A. 104(31), 12622–12627 (2007). [CrossRef] [PubMed]
  9. Y. Jiang, Q. Wang, A. E. Cohen, N. Douglas, J. Frydman, and W. E. Moerner, “Hardware-based anti-Brownian electrokinetic trap (ABEL trap) for single molecules: control loop simulations and application to ATP binding stoichiometry in multi-subunit enzymes,” Proc. Soc. Photo Opt. Instrum. Eng. 7038, 1–12 (2008). [PubMed]
  10. R. H. Goldsmith and W. E. Moerner, “Watching conformational- and photodynamics of single fluorescent proteins in solution,” Nat. Chem. 2(3), 179–186 (2010). [CrossRef] [PubMed]
  11. H. Cang, D. Montiel, C. S. Xu, and H. Yang, “Observation of spectral anisotropy of gold nanoparticles,” J. Chem. Phys. 129(4), 044503 (2008). [CrossRef] [PubMed]
  12. J. Enderlein, “Tracking of fluorescent molecules diffusing within membranes,” Appl. Phys. B 71(5), 773–777 (2000). [CrossRef]
  13. A. P. Fields and A. E. Cohen, “Electrokinetic trapping at the one nanometer limit,” Proc. Natl. Acad. Sci. U.S.A. 108(22), 8937–8942 (2011). [CrossRef] [PubMed]
  14. A. H. Jazwinski, Stochastic Processes and Filtering Theory (Academic Press, 1970).
  15. K. McHale, A. J. Berglund, and H. Mabuchi, “Bayesian estimation for species identification in single-molecule fluorescence microscopy,” Biophys. J. 86(6), 3409–3422 (2004). [CrossRef] [PubMed]
  16. A. J. Berglund, K. McHale, and H. Mabuchi, “Fluctuations in closed-loop fluorescent particle tracking,” Opt. Express 15(12), 7752–7773 (2007). [CrossRef] [PubMed]
  17. A. J. Berglund and H. Mabuchi, “Performance bounds on single-particle tracking by fluorescence modulation,” Appl. Phys. B 83(1), 127–133 (2006). [CrossRef]
  18. A. J. Berglund and H. Mabuchi, “Tracking-FCS: Fluorescence correlation spectroscopy of individual particles,” Opt. Express 13(20), 8069–8082 (2005). [CrossRef] [PubMed]
  19. A. E. Cohen and W. E. Moerner, “Method for trapping and manipulating nanoscale objects in solution,” Appl. Phys. Lett. 86(9), 093109 (2005). [CrossRef]
  20. Q. Wang and W. E. Moerner, “An adaptive anti-Brownian electrokinetic trap with real-time information on single-molecule diffusivity and mobility,” ACS Nano 5(7), 5792–5799 (2011). [CrossRef] [PubMed]
  21. K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods 7(5), 377–381 (2010). [CrossRef] [PubMed]
  22. B. Zhang, J. Zerubia, and J. C. Olivo-Marin, “Gaussian approximations of fluorescence microscope point-spread function models,” Appl. Opt. 46(10), 1819–1829 (2007). [CrossRef] [PubMed]
  23. M. S. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, “A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking,” IEEE Trans. Signal Process. 50(2), 174–188 (2002). [CrossRef]
  24. T. P. Minka, “A family of algorithms for approximate Bayesian inference,” Ph.D. thesis, Massachusetts Institute of Technology (2001). http://research.microsoft.com/en-us/um/people/minka/papers/ep/minka-thesis.pdf .
  25. P. S. Maybeck, Stochastic models, estimation and control (Academic press, 1979).
  26. H. W. Sorenson and D. L. Alspach, “Recursive Bayesian estimation using Gaussian sums,” Automatica 7(4), 465–479 (1971). [CrossRef]
  27. R. E. Kalman, “A new approach to linear filtering and prediction problems,” J. Basic Eng. Trans. ASME 82(1), 35–45 (1960). [CrossRef]
  28. G. Welch and G. Bishop, “An introduction to the Kalman filter,” University of North Carolina at Chapel Hill technical report TR 95–041 (2006). http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf .
  29. M. Brinkmeier, K. Dörre, J. Stephan, and M. Eigen, “Two-beam cross-correlation: a method to characterize transport phenomena in micrometer-sized structures,” Anal. Chem. 71(3), 609–616 (1999). [CrossRef] [PubMed]
  30. P. Kapusta, “Absolute diffusion coefficients: compilation of reference data for FCS calibration,” http://www.picoquant.com/technotes/appnote_diffusion_coefficients.pdf .

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited