Abstract

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

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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 .

2011 (2)

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]

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]

2010 (6)

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]

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]

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]

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]

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]

A. P. Fields and A. E. Cohen, “Anti-Brownian traps for studies on single molecules,” Methods Enzymol. 475, 149–174 (2010).
[CrossRef] [PubMed]

2008 (2)

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]

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]

2007 (3)

2006 (1)

A. J. Berglund and H. Mabuchi, “Performance bounds on single-particle tracking by fluorescence modulation,” Appl. Phys. B 83(1), 127–133 (2006).
[CrossRef]

2005 (3)

A. J. Berglund and H. Mabuchi, “Tracking-FCS: Fluorescence correlation spectroscopy of individual particles,” Opt. Express 13(20), 8069–8082 (2005).
[CrossRef] [PubMed]

A. E. Cohen and W. E. Moerner, “Method for trapping and manipulating nanoscale objects in solution,” Appl. Phys. Lett. 86(9), 093109 (2005).
[CrossRef]

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]

2004 (1)

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]

2003 (1)

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]

2002 (1)

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]

2000 (1)

J. Enderlein, “Tracking of fluorescent molecules diffusing within membranes,” Appl. Phys. B 71(5), 773–777 (2000).
[CrossRef]

1999 (1)

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]

1997 (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]

1971 (1)

H. W. Sorenson and D. L. Alspach, “Recursive Bayesian estimation using Gaussian sums,” Automatica 7(4), 465–479 (1971).
[CrossRef]

1960 (1)

R. E. Kalman, “A new approach to linear filtering and prediction problems,” J. Basic Eng. Trans. ASME 82(1), 35–45 (1960).
[CrossRef]

Akita, R.

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]

Alspach, D. L.

H. W. Sorenson and D. L. Alspach, “Recursive Bayesian estimation using Gaussian sums,” Automatica 7(4), 465–479 (1971).
[CrossRef]

Arulampalam, M. S.

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]

Badieirostami, M.

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]

Berglund, A. J.

A. J. Berglund, K. McHale, and H. Mabuchi, “Fluctuations in closed-loop fluorescent particle tracking,” Opt. Express 15(12), 7752–7773 (2007).
[CrossRef] [PubMed]

A. J. Berglund and H. Mabuchi, “Performance bounds on single-particle tracking by fluorescence modulation,” Appl. Phys. B 83(1), 127–133 (2006).
[CrossRef]

A. J. Berglund and H. Mabuchi, “Tracking-FCS: Fluorescence correlation spectroscopy of individual particles,” Opt. Express 13(20), 8069–8082 (2005).
[CrossRef] [PubMed]

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]

Brinkmeier, M.

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]

Brown, P. O.

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]

Cang, H.

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]

Casolari, J. M.

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]

Chung, I.

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]

Churchman, L. S.

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]

Clapp, T.

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]

Cohen, A. E.

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]

A. P. Fields and A. E. Cohen, “Anti-Brownian traps for studies on single molecules,” Methods Enzymol. 475, 149–174 (2010).
[CrossRef] [PubMed]

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]

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]

A. E. Cohen and W. E. Moerner, “Method for trapping and manipulating nanoscale objects in solution,” Appl. Phys. Lett. 86(9), 093109 (2005).
[CrossRef]

Cutler, P. J.

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]

Dörre, K.

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]

Douglas, N.

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]

Douglass, A. D.

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]

Eigen, M.

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]

Enderlein, J.

J. Enderlein, “Tracking of fluorescent molecules diffusing within membranes,” Appl. Phys. B 71(5), 773–777 (2000).
[CrossRef]

Fields, A. P.

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]

A. P. Fields and A. E. Cohen, “Anti-Brownian traps for studies on single molecules,” Methods Enzymol. 475, 149–174 (2010).
[CrossRef] [PubMed]

Flyvbjerg, H.

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]

Forkey, J. N.

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]

Frydman, J.

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]

Goldman, Y. E.

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]

Goldsmith, R. H.

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]

Goodwin, P. M.

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]

Gordon, N.

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]

Ha, T.

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]

Jacobson, K.

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]

Jiang, Y.

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]

Kalman, R. E.

R. E. Kalman, “A new approach to linear filtering and prediction problems,” J. Basic Eng. Trans. ASME 82(1), 35–45 (1960).
[CrossRef]

Lessard, G. A.

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]

Lidke, D. S.

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]

Mabuchi, H.

A. J. Berglund, K. McHale, and H. Mabuchi, “Fluctuations in closed-loop fluorescent particle tracking,” Opt. Express 15(12), 7752–7773 (2007).
[CrossRef] [PubMed]

A. J. Berglund and H. Mabuchi, “Performance bounds on single-particle tracking by fluorescence modulation,” Appl. Phys. B 83(1), 127–133 (2006).
[CrossRef]

A. J. Berglund and H. Mabuchi, “Tracking-FCS: Fluorescence correlation spectroscopy of individual particles,” Opt. Express 13(20), 8069–8082 (2005).
[CrossRef] [PubMed]

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]

Maskell, S.

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]

McHale, K.

A. J. Berglund, K. McHale, and H. Mabuchi, “Fluctuations in closed-loop fluorescent particle tracking,” Opt. Express 15(12), 7752–7773 (2007).
[CrossRef] [PubMed]

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]

McKinney, S. A.

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]

Mellman, I.

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]

Moerner, W. E.

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]

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]

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]

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]

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]

A. E. Cohen and W. E. Moerner, “Method for trapping and manipulating nanoscale objects in solution,” Appl. Phys. Lett. 86(9), 093109 (2005).
[CrossRef]

Montiel, D.

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]

Mortensen, K. I.

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]

Olivo-Marin, J. C.

Phipps, M. E.

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]

Saxton, M. J.

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]

Schlessinger, J.

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]

Selvin, P. R.

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]

Sorenson, H. W.

H. W. Sorenson and D. L. Alspach, “Recursive Bayesian estimation using Gaussian sums,” Automatica 7(4), 465–479 (1971).
[CrossRef]

Spudich, J. A.

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]

Stephan, J.

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]

Thompson, M. A.

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]

Toomre, D.

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]

Vale, R. D.

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]

Vandlen, R.

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]

Wang, Q.

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]

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]

Wells, N. P.

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]

Werner, J. H.

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]

Wilson, B. S.

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]

Xu, C. S.

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]

Yang, H.

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]

Yildiz, A.

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]

Zerubia, J.

Zhang, B.

ACS Nano (1)

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]

Anal. Chem. (1)

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]

Annu. Rev. Biophys. Biomol. Struct. (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]

Appl. Opt. (1)

Appl. Phys. B (2)

J. Enderlein, “Tracking of fluorescent molecules diffusing within membranes,” Appl. Phys. B 71(5), 773–777 (2000).
[CrossRef]

A. J. Berglund and H. Mabuchi, “Performance bounds on single-particle tracking by fluorescence modulation,” Appl. Phys. B 83(1), 127–133 (2006).
[CrossRef]

Appl. Phys. Lett. (1)

A. E. Cohen and W. E. Moerner, “Method for trapping and manipulating nanoscale objects in solution,” Appl. Phys. Lett. 86(9), 093109 (2005).
[CrossRef]

Automatica (1)

H. W. Sorenson and D. L. Alspach, “Recursive Bayesian estimation using Gaussian sums,” Automatica 7(4), 465–479 (1971).
[CrossRef]

Biophys. J. (1)

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]

Cell (1)

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]

IEEE Trans. Signal Process. (1)

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]

J. Basic Eng. Trans. ASME (1)

R. E. Kalman, “A new approach to linear filtering and prediction problems,” J. Basic Eng. Trans. ASME 82(1), 35–45 (1960).
[CrossRef]

J. Chem. Phys. (1)

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]

Methods Enzymol. (1)

A. P. Fields and A. E. Cohen, “Anti-Brownian traps for studies on single molecules,” Methods Enzymol. 475, 149–174 (2010).
[CrossRef] [PubMed]

Nano Lett. (1)

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]

Nat. Chem. (1)

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]

Nat. Methods (1)

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]

Nature (1)

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]

Opt. Express (2)

Proc. Natl. Acad. Sci. U.S.A. (3)

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]

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]

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]

Proc. Soc. Photo Opt. Instrum. Eng. (1)

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]

Science (1)

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]

Other (5)

A. H. Jazwinski, Stochastic Processes and Filtering Theory (Academic Press, 1970).

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 .

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 .

P. S. Maybeck, Stochastic models, estimation and control (Academic press, 1979).

P. Kapusta, “Absolute diffusion coefficients: compilation of reference data for FCS calibration,” http://www.picoquant.com/technotes/appnote_diffusion_coefficients.pdf .

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Tracking and feedback in an anti-Brownian electrokinetic trap. A fluorescent particle diffuses in a quasi-two-dimensional sample chamber at the center of four platinum electrodes. A focused laser is scanned through a set of discrete spots in the sample plane, triggering the particle to emit fluorescence when the laser overlaps with the particle. Detected photons are tallied and assigned to laser spots according to their detection time. A Kalman filter combines this data with a prediction for the location of the particle based on previous data to generate an updated position estimate. The position estimate is used to calculate feedback voltages which are applied to counteract the particle’s motion.

Fig. 2
Fig. 2

Simulated trapping and parameter fitting as a function of diffusion coefficient (left) or electrokinetic mobility (right). Top, fraction of molecules remaining within 3.4 μm of the trap center for the 100 ms simulation. Center, RMS tracking error of the Kalman filter and ADF algorithms. The dashed curve is the analytical prediction for trapping performance [Eq. (24)]. Bottom, maximum likelihood parameter estimation using the ADF algorithm. Parameter estimation using the Kalman filter did not converge for any of these cases. Error bars are ± one standard deviation about the mean of the relative difference between the estimated and true parameter values.

Fig. 3
Fig. 3

Simulated trapping and parameter fitting as a function of photon count rate (not including background photons) and signal-to-background ratio (SBR). Plots are as in Fig. 2, except that the bottom plots all show diffusion coefficient fitting, and fits were attempted using both the ADF algorithm and the Kalman filter. The parameter fitting results for the two algorithms are offset horizontally for clarity.

Fig. 4
Fig. 4

Tracking error as a function of filter parameter mismatch, for three values of signal-to-background ratio (SBR) and both algorithms. Fluorophore photon emission rate is 100 kHz for all plots. The ADF performs best with parameter values matching the true values. For nonzero background count rates, the Kalman filter performs better when its assumed diffusion coefficient is less than the true value.

Fig. 5
Fig. 5

Trapping of Alexa 647 molecules in an anti-Brownian electrokinetic trap. (a) Molecular entry or exit induced large step-like changes in fluorescence intensity. Intensity trace binned to 10 ms. (b) The diffusion coefficient D and electrokinetic mobility μ of each trapped molecule was extracted using the ADF algorithm. The population-average diffusion coefficient was 348 ± 2 μm2/s (s.e.m.); the electrokinetic mobility revealed the presence of two subpopulations, most likely differing in charge.

Equations (31)

Equations on this page are rendered with MathJax. Learn more.

γ( x )=sexp( 1 2 ( xc ) T W 1 ( xc ) )+b,
Pr[ n|x ]= ( γ( x )Δt ) n e γ( x )Δt n! .
g k ( Δx )= exp( | ΔxμΔt E k | 2 4DΔt ) 4πDΔt .
E= x ^ μΔt ,
f k|k = L k 1 Pr[ n k | x k ] f k| k1
f k| k1 = g k1 ( x k x k1 ) f k1| k1 d x k1
f a|b Ν( x ^ a|b , Σ ^ a|b ) ( 2π | Σ ^ a|b | 1 2 ) 1 exp( 1 2 ( x x ^ a|b ) T Σ ^ a|b 1 ( x x ^ a|b ) ).
x ^ k| k1 = x ^ k1|k1 +μΔt E k1 Σ ^ k| k1 = Σ ^ k1| k1 +2DΔtI.
f k|k = L k 1 ( n k ! ) 1 ( Sexp( 1 2 ( xc ) T W 1 ( xc ) )+B ) n k ×exp( ( Sexp( 1 2 ( xc ) T W 1 ( xc ) )+B ) )Ν( x ^ k| k1 , Σ ^ k| k1 ),
f k|k = L k 1 m=0 l m Ν( χ ^ m , Ψ ^ m )
l m e B i=max( n k m,0 ) n k ( 1 ) m+i n k B i S m ( n k i )!i!( m+i n k )! | Ψ ^ m | 1 2 | Σ ^ k| k1 | 1 2 ×exp( 1 2 m ( x ^ k| k1 c k ) T ( m Σ ^ k| k1 +W ) 1 ( x ^ k| k1 c k ) ) χ ^ m Ψ ^ m ( Σ ^ k| k1 1 x ^ k| k1 +m W 1 c k ) Ψ ^ m ( Σ ^ k| k1 1 +m W 1 ) 1 .
L k = m=0 l m .
x ^ k|k = x f k|k dx= L k 1 m=0 l m χ ^ m
Σ ^ k|k =( x x T f k|k dx ) x ^ k|k x ^ k|k T =( L k 1 m=0 l m ( χ ^ m χ ^ m T + Ψ ^ m ) ) x ^ k|k x ^ k|k T .
ln( Λ )= k ln( L k ) .
x ^ k|k = ( Σ ^ k| k1 1 + n k W 1 ) 1 ( Σ ^ k| k1 1 x ^ k| k1 + n k W 1 c k ) Σ ^ k|k = ( Σ ^ k| k1 1 + n k W 1 ) 1 .
L k kal = S n k n k ! | Ψ ^ n k | 1 2 | Σ ^ k| k1 | 1 2 exp( 1 2 n k ( x ^ k| k1 c k ) T ( n k Σ ^ k| k1 +W ) 1 ( x ^ k| k1 c k ) ).
x ^ k|k = w 2 x ^ k|k1 + n k p ^ k| k1 c k w 2 + n k p ^ k| k1 p ^ k|k = w 2 p ^ k| k1 w 2 + n k p ^ k| k1 .
x ^ k| k1 = x ^ k1|k1 +μΔt E k1 p ^ k| k1 = p ^ k1| k1 +2DΔt.
2 ln( L k ) x ( a ) x ( b ) = 2 ln( Pr[ n k | x k ] ) x ( a ) x ( b ) 2 ln( f k| k1 ) x ( a ) x ( b )
F ADF ( a,b ) 2 ln( Pr[ n|x ] ) x ( a ) x ( b ) = 1 Γ( x ) Γ( x ) x ( a ) Γ( x ) x ( b )
F ADF ¯ W 1 ( 1+ B S L i 2 ( S B ) ) Γ S ¯
Σ 1 ¯ F ADF ¯ + ( Σ ¯ +2DΔtI ) 1
Σ ¯ DΔt( ( 2 DΔt F ADF 1 ¯ +I ) 1 2 I )
Σ ^ k|k = ( ( Σ ^ k1| k1 +2DΔtI ) 1 + n k W 1 ) 1 .
Σ ^ k|k ¯ DΔt( ( 2 DΔt W Γ ¯ +I ) 1 2 I )
Σ ¯ 2DW γ s ¯ .
κ= w 2 w 2 + n k p ^ k| k1 .
κ ¯ w 2 w 2 + Γ ¯ DΔt( ( 2 DΔt w 2 Γ ¯ +1 ) 1 2 +1 ) .
κ T ¯ exp( 2D γ ¯ w T ).
τ w 2D γ ¯ .

Metrics