OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 17 — Aug. 16, 2010
  • pp: 17883–17896

Anomalous behavior in length distributions of 3D random Brownian walks and measured photon count rates within observation volumes of single-molecule trajectories in fluorescence fluctuation microscopy

Gerd Baumann, Ignacy Gryczynski, and Zeno Földes-Papp  »View Author Affiliations


Optics Express, Vol. 18, Issue 17, pp. 17883-17896 (2010)
http://dx.doi.org/10.1364/OE.18.017883


View Full Text Article

Enhanced HTML    Acrobat PDF (893 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Based on classical mean-field approximation using the diffusion equation for ergodic normal motion of single 24-nm and 100-nm nanospheres, we simulated and measured molecule number counting in fluorescence fluctuation microscopy. The 3D-measurement set included a single molecule, or an ensemble average of single molecules, an observation volume ΔV and a local environment, e.g. aqueous solution. For the molecule number N ≪ 1 per ΔV, there was only one molecule at a time inside ΔV or no molecule. The mean rate k of re-entries defined by k = N / τdif was independent of the geometry of ΔV but depended on the size of ΔV and the diffusive properties τdif . The length distribution ℓ of single-molecule trajectories inside ΔV and the measured photon count rates I obeyed power laws with anomalous exponent κ =−1.32 ≈ −4/3.

© 2010 Optical Society of America

OCIS Codes
(170.6280) Medical optics and biotechnology : Spectroscopy, fluorescence and luminescence
(180.1790) Microscopy : Confocal microscopy
(180.2520) Microscopy : Fluorescence microscopy

ToC Category:
Microscopy

History
Original Manuscript: April 27, 2010
Revised Manuscript: July 6, 2010
Manuscript Accepted: July 21, 2010
Published: August 4, 2010

Virtual Issues
Vol. 5, Iss. 13 Virtual Journal for Biomedical Optics

Citation
Gerd Baumann, Ignacy Gryczynski, and Zeno Földes-Papp, "Anomalous behavior in length distributions of 3D random Brownian walks and measured photon count rates within observation volumes of single-molecule trajectories in fluorescence fluctuation microscopy," Opt. Express 18, 17883-17896 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-17-17883


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. Szymanski, and M. Weiss, “Elucidating the origin of anomalous diffusion in crowded fluids,” Phys. Rev. Lett. 103, 038102 (2009). [CrossRef] [PubMed]
  2. I. Golding, and E. C. Cox, “Physical nature of bacterial cytoplasm,” Phys. Rev. Lett. 96, 098102 (2006). [CrossRef] [PubMed]
  3. G. Seisenberger, M. U. Ried, T. Endres, H. Buning, M. Hallek, and C. Brauchle, “Real-time single-molecule imaging of the infection pathway of an adeno-associated virus,” Science 294, 1929–1932 (2001). [CrossRef] [PubMed]
  4. Y. Meroz, I. M. Sokolov, and J. Klafter, “Subdiffusion of mixed origins: when ergodicity and nonergodicity coexist,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 81, 010101 (2010). [CrossRef]
  5. A. Lubelski, I. M. Sokolov, and J. Klafter, “Nonergodicity mimics inhomogeneity in single particle tracking,” Phys. Rev. Lett. 100, 0250602 (2008). [CrossRef]
  6. Z. Földes-Papp, “Ultrasensitive detection and identification of fluorescent molecules by FCS: impact for immunobiology,” Proc. Natl. Acad. Sci. U.S.A. 98, 11509–11514 (2001). [CrossRef] [PubMed]
  7. T. A. Klar, S. Jakobs, M. Dyba, A. Egner, and S. W. Hell, “Fluorescence microscopy with diffraction resolution barrier broken by stimulated emission,” Proc. Natl. Acad. Sci. U.S.A. 97, 8206–8210 (2000). [CrossRef] [PubMed]
  8. S. W. Hell, “Far-field optical nanoscopy,” Science 316, 1153–1158 (2007). [CrossRef] [PubMed]
  9. M. G. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U.S.A. 102, 13081–13086 (2005). [CrossRef] [PubMed]
  10. M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–796 (2006). [CrossRef] [PubMed]
  11. S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006). [CrossRef] [PubMed]
  12. Y. He, S. Burov, R. Metzler, and E. Barkai, “Random time-scale invariant diffusion and transport coefficients,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 101, 058101 (2008).
  13. G. Polya, “Uber eine Aufgabe der Wahrscheinlichkeitsrechnung betreffend der Irrfahrt im Strassennetz,” Math. Ann. 84, 149–160 (1921). [CrossRef]
  14. G. N. Watson, “The triple integrals,” Q. J. Math. 10, 266 (1939). [CrossRef]
  15. B. D. Hughes, Random Walks and Random Environments (Clarendon Press, Oxford, 1995).
  16. R. Niesner, and K.-H. Gericke, “Quantitative determination of the single-molecule detection regime in fluorescence fluctuation microscopy by means of photon counting histogram analysis,” J. Chem. Phys. 124, 134704 (2006). [CrossRef] [PubMed]
  17. G. Baumann, R. F. Place, and Z. Földes-Papp, “Meaningful interpretation of subdiffusive measurements in living cells (crowded environment) by fluorescence fluctuation microscopy,” Curr. Pharm. Biotechnol. 11, 527–543 (2010). [CrossRef] [PubMed]
  18. M. R. Mazo, Brownian motion (Oxford Univ. Press, Oxford, 2009).
  19. F. Spitzer, Principles of random walk (Springer, New York, 2001).
  20. J.-P. Bouchaud, and A. Georges, “Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications,” Phys. Rep. 12, 195 (1990).
  21. P. Levy, Processus stochastiques et mouvement Brownien (Gauthier-Villars, Paris, 1965).
  22. K. J. Falconer, Fractal Geometry (Wiley, Chichester, 2003). [CrossRef]
  23. B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, New York, 1983), pp.237–243 and pp. 326–334.
  24. E. W. Montroll, and G. H. Weiss, “Random walks on lattices,” J. Math. Phys. 6, 364 (1965). [CrossRef]
  25. E. W. Montroll, and M. F. Schlesinger, in Studies in statistical mechanics, edited by J. L. Lebowitz and E. W. Montroll, (Elsevier, New York, 1984), vol.11.
  26. L. Luchowski, Z. Gryczynski, Z. Földes-Papp, A. Chang, J. Borejdo, P. Sarkar, and I. Gryczynski, “Polarized fluorescent nanospheres,” Opt. Express 18, 4289–4299 (2010). [CrossRef] [PubMed]
  27. Z. Földes-Papp, “Fluorescence fluctuation spectroscopic approaches to the study of a single molecule diffusing in solution and a live cell without systemic drift or convection: a theoretical study,” Curr. Pharm. Biotechnol. 8, 261–273 (2007). [CrossRef] [PubMed]
  28. H. Risken, and H. D. Vollmer, “On the application of truncated generalized Fokker-Planck equations,” Z. Physik B 35, 313 (1979). [CrossRef]
  29. I. V. Gopich, “Concentration effects in “single-molecule” spectroscopy,” J. Phys. Chem. B 112, 6214–6220 (2008). [CrossRef]
  30. Y. Chen, J. D. Muller, P. T. C. So, and E. Gratton, “The photon counting histogram in fluorescence fluctuation spectroscopy,” Biophys. J. 77, 553–567 (1999). [CrossRef] [PubMed]
  31. Z. Földes-Papp, “Theory of measuring the selfsame single fluorescent molecule in solution suited for studying individual molecular interactions by SPSM-FCS,” Pteridines 13, 73–82 (2002).
  32. G. Zumofen, J. Hohlbein, and C. G. Huebner, “Recurrence and photon statistics in fluorescence fluctuation spectroscopy,” Phys. Rev. Lett. 93, 260601 (2004). [CrossRef]
  33. Z. Földes-Papp, S.-C. J. Liao, T. You, and B. Barbieri, “Reducing background contributions in fluorescence fluctuation time-traces for single-molecule measurements in solution,” Curr. Pharm. Biotechnol. 10, 532–542 (2009). [CrossRef] [PubMed]
  34. A. C. Beveridge, J. H. Jett, R. A. Keller, L. R. Pratt, and T. M. Yoshida, “Reduction of diffusion broadening in flow by analysis of time-gated single-molecule data,” Analyst (Lond.) (2010), doi:10.1039/b926956h.
  35. Z. Földes-Papp, S.-C. J. Liao, T. You, E. Terpetschnig, and B. Barbieri, “Confocal fluctuation spectroscopy and imaging,” Curr. Pharm. Biotechnol.in press. [CrossRef] [PubMed]

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.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited