Abstract

In fluorescence fluctuation polarization sensitive experiments, the limitations associated with detecting the rotational timescale are usually eliminated by applying fluorescence correlation spectroscopy analysis. In this paper, the variance of the time-averaged fluorescence intensity extracted from the second moment of the measured fluorescence intensity is analyzed in the short time limit, before fluctuations resulting from rotational diffusion average out. Since rotational correlation times of fluorescence molecules are typically much lower than the temporal resolution of the system, independently of the time bins used, averaging over an ensemble of time-averaged trajectories was performed in order to construct the time-averaged intensity distribution, thus improving the signal-to-noise ratio. Rotational correlation times of fluorescein molecules in different viscosities of the medium within the range of the anti-bunching time (1-10 ns) were then extracted using this method.

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    [CrossRef]

2013

L. Turgeman and D. Fixler, “Photon efficiency optimization in time correlated single photon counting technique for fluorescence lifetime imaging systems,” IEEE Trans. Biomed. Eng.PP(99), 1 (2013).
[PubMed]

2012

L. Turgeman and D. Fixler, “Short time behavior of fluorescence intensity fluctuations in single molecule polarization sensitive experiments,” Opt. Express20(8), 9276–9283 (2012).
[CrossRef] [PubMed]

T. A. Nguyen, P. Sarkar, J. V. Veetil, S. V. Koushik, and S. S. Vogel, “Fluorescence polarization and fluctuation analysis monitors subunit proximity, stoichiometry, and protein complex hydrodynamics,” PLoS ONE7(5), e38209 (2012).
[CrossRef] [PubMed]

2011

D. Oh, A. Zidovska, Y. Xu, and D. J. Needleman, “Development of time-integrated multipoint moment analysis for spatially resolved fluctuation spectroscopy with high time resolution,” Biophys. J.101(6), 1546–1554 (2011).
[CrossRef] [PubMed]

2010

G. Hinze and T. Basché, “Statistical analysis of time resolved single molecule fluorescence data without time binning,” J. Chem. Phys.132(4), 044509 (2010).
[CrossRef] [PubMed]

M. Levitus, “Relaxation kinetics by fluorescence correlation spectroscopy: determination of kinetic parameters in the presence of fluorescent impurities,” J. Phys. Chem. Lett.1(9), 1346–1350 (2010).
[CrossRef] [PubMed]

2009

Z. Földes-Papp, S. C. Liao, T. You, and B. Barbieri, “Reducing background contributions in fluorescence fluctuation time-traces for single-molecule measurements in solution,” Curr. Pharm. Biotechnol.10(5), 532–542 (2009).
[CrossRef] [PubMed]

Z. Petrásĕk and P. Schwille, “Fluctuations as a source of information in fluorescence microscopy,” J. R. Soc. Interface6(Suppl_1), S15–S25 (2009).
[CrossRef]

2007

W. E. Moerner, “New directions in single-molecule imaging and analysis,” Proc. Natl. Acad. Sci. U.S.A.104(31), 12596–12602 (2007).
[CrossRef] [PubMed]

S. A. Kim, K. G. Heinze, and P. Schwille, “Fluorescence correlation spectroscopy in living cells,” Nat. Methods4(11), 963–973 (2007).
[CrossRef] [PubMed]

M. R. Foreman, S. S. Sherif, and P. Török, “Photon statistics in single molecule orientational imaging,” Opt. Express15(21), 13597–13606 (2007).
[CrossRef] [PubMed]

2006

D. Fixler, Y. Namer, Y. Yishay, and M. Deutsch, “Influence of fluorescence anisotropy on fluorescence intensity and lifetime measurement: theory, simulations and experiments,” IEEE Trans. Biomed. Eng.53(6), 1141–1152 (2006).
[CrossRef] [PubMed]

K. Bacia, S. A. Kim, and P. Schwille, “Fluorescence cross-correlation spectroscopy in living cells,” Nat. Methods3(2), 83–89 (2006).
[CrossRef] [PubMed]

2005

V. Vukojević, A. Pramanik, T. Yakovleva, R. Rigler, L. Terenius, and G. Bakalkin, “Study of molecular events in cells by fluorescence correlation spectroscopy,” Cell. Mol. Life Sci.62(5), 535–550 (2005).
[CrossRef] [PubMed]

S. Felekyan, R. Kuhnemuth, V. Kudryavtsev, C. Sandhagen, W. Becker, and C. Seidel, “Full correlation from picoseconds to seconds by time-resolved and time-correlated single photon detection,” Rev. Sci. Instrum.76(8), 083104 (2005).
[CrossRef]

B. Wu and J. D. Müller, “Time-integrated fluorescence cumulant analysis in fluorescence fluctuation spectroscopy,” Biophys. J.89(4), 2721–2735 (2005).
[CrossRef] [PubMed]

C.-Y. J. Wei, Y. H. Kim, R. K. Darst, P. J. Rossky, and D. A. Vanden Bout, “Origins of nonexponential decay in single molecule measurements of rotational dynamics,” Phys. Rev. Lett.95(17), 173001 (2005).
[CrossRef] [PubMed]

D. Fixler, R. Tirosh, N. Zurgil, and M. Deutsch, “Tracing apoptosis and stimulation in individual cells by fluorescence intensity and anisotropy decay,” J. Biomed. Opt.10(3), 034007 (2005).
[CrossRef] [PubMed]

2004

K. Suhling, J. Siegel, P. M. P. Lanigan, S. Lévêque-Fort, S. E. Webb, D. Phillips, D. M. Davis, and P. M. French, “Time-resolved fluorescence anisotropy imaging applied to live cells,” Opt. Lett.29(6), 584–586 (2004).
[CrossRef] [PubMed]

G. Hinze, G. Diezemann, and T. Basché, “Rotational correlation functions of single molecules,” Phys. Rev. Lett.93(20), 203001 (2004).
[CrossRef] [PubMed]

A. Schob, F. Cichos, J. Schuster, and C. von Borczyskowski, “Reorientation and translation of individual dye molecules in a polymer matrix,” Eur. Polym. J.40(5), 1019–1026 (2004).
[CrossRef]

J. D. Müller, “Cumulant analysis in fluorescence fluctuation spectroscopy,” Biophys. J.86(6), 3981–3992 (2004).
[CrossRef] [PubMed]

G. Zumofen, J. Hohlbein, and C. G. Hübner, “Recurrence and photon statistics in fluorescence fluctuation spectroscopy,” Phys. Rev. Lett.93(26), 260601 (2004).
[CrossRef] [PubMed]

E. Haustein and P. Schwille, “Single-molecule spectroscopic methods,” Curr. Opin. Struct. Biol.14(5), 531–540 (2004).
[CrossRef] [PubMed]

2003

X. Brokmann, J. P. Hermier, G. Messin, P. Desbiolles, J. P. Bouchaud, and M. Dahan, “Statistical aging and nonergodicity in the fluorescence of single nanocrystals,” Phys. Rev. Lett.90(12), 120601 (2003).
[CrossRef] [PubMed]

L. N. Hillesheim and J. D. Müller, “The photon counting histogram in fluorescence fluctuation spectroscopy with non-ideal photodetectors,” Biophys. J.85(3), 1948–1958 (2003).
[CrossRef] [PubMed]

2002

O. Krichevsky and G. Bonnet, “Fluorescence correlation spectroscopy: the technique and its applications,” Rep. Prog. Phys.65(2), 251–297 (2002).
[CrossRef]

O. Krichevsky and G. Bonnet, “Fluorescence correlation spectroscopy: the technique and its applications,” Rep. Prog. Phys.65(2), 251–297 (2002).
[CrossRef]

M. A. Medina and P. Schwille, “Fluorescence correlation spectroscopy for the detection and study of single molecules in biology,” Bioessays24(8), 758–764 (2002).
[CrossRef] [PubMed]

2001

E. Van Rompaey, Y. Chen, J. D. Müller, E. Gratton, E. Van Craenenbroeck, Y. Engelborghs, S. De Smedt, and J. Demeester, “Fluorescence fluctuation analysis for the study of interactions between oligonucleotides and polycationic polymers,” Biol. Chem.382(3), 379–386 (2001).
[PubMed]

M. Cotlet, J. Hofkens, S. Habuchi, G. Dirix, M. Van Guyse, J. Michiels, J. Vanderleyden, and F. C. De Schryver, “Identification of different emitting species in the red fluorescent protein DsRed by means of ensemble and single-molecule spectroscopy,” Proc. Natl. Acad. Sci. U.S.A.98(25), 14398–14403 (2001).
[CrossRef] [PubMed]

L. A. Deschenes and D. A. Vanden Bout, “Single-molecule studies of heterogeneous dynamics in polymer melts near the glass transition,” Science292(5515), 255–258 (2001).
[CrossRef] [PubMed]

P. G. Debenedetti and F. H. Stillinger, “Supercooled liquids and the glass transition,” Nature410(6825), 259–267 (2001).
[CrossRef] [PubMed]

J. T. Fourkas, “Rapid determination of the three-dimensional orientation of single molecules,” Opt. Lett.26(4), 211–213 (2001).
[CrossRef] [PubMed]

B. Sick, B. Hecht, U. P. Wild, and L. Novotny, “Probing confined fields with single molecules and vice versa,” J. Microsc.202(2), 365–373 (2001).
[CrossRef] [PubMed]

2000

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett.85(21), 4482–4485 (2000).
[CrossRef] [PubMed]

K. Palo, Ü. Mets, S. Jäger, P. Kask, and K. Gall, “Fluorescence intensity multiple distributions analysis: concurrent determination of diffusion times and molecular brightness,” Biophys. J.79(6), 2858–2866 (2000).
[CrossRef] [PubMed]

P. Kask, K. Palo, N. Fay, L. Brand, Ü. Mets, D. Ullmann, J. Jungmann, J. Pschorr, and K. Gall, “Two-dimensional fluorescence intensity distribution analysis: theory and applications,” Biophys. J.78(4), 1703–1713 (2000).
[CrossRef] [PubMed]

1999

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, “Polarization spectroscopy of single fluorescent molecules,” J. Phys. Chem. B103(33), 6839–6850 (1999).
[CrossRef]

J. Widengren, Ü. Mets, and R. Rigler, “Photodynamic properties of green fluorescent proteins investigated by fluorescence correlation spectroscopy,” Chem. Phys.250(2), 171–186 (1999).
[CrossRef]

Y. Chen, J. D. Müller, P. T. C. So, and E. Gratton, “The photon counting histogram in fluorescence fluctuation spectroscopy,” Biophys. J.77(1), 553–567 (1999).
[CrossRef] [PubMed]

E. Van Craenenbroeck and Y. Engelborghs, “Quantitative characterization of the binding of fluorescently labeled colchicine to tubulin in vitro using fluorescence correlation spectroscopy,” Biochemistry38(16), 5082–5088 (1999).
[CrossRef] [PubMed]

1997

P. Kask, R. Günther, and P. Axhausen, “Statistical accuracy in fluorescence fluctuation experiments,” Eur. Biophys. J.25(3), 163–169 (1997).
[CrossRef]

1994

M. Höbel and J. Ricka, “Dead time and afterpulsing correction in multiphoton timing with nonideal detectors,” Rev. Sci. Instrum.65(7), 2326–2336 (1994).
[CrossRef]

1990

H. Qian and E. L. Elson, “Distribution of molecular aggregation by analysis of fluctuation moments,” Proc. Natl. Acad. Sci. U.S.A.87(14), 5479–5483 (1990).
[CrossRef] [PubMed]

1988

I. Iliopoulos, J. Halary, and R. Audebert, “Polymer complexes stabilized through hydrogen bonds. Influence of ‘structure defects’ on complex formation: viscometry and fluorescence polarization measurements,” J. Polym. Sci. A Polym. Chem.26(1), 275–284 (1988).
[CrossRef]

1987

Y. M. Chen and A. J. Pearlstein, “Viscosity temperature correlation for glycerol-water solutions,” Ind. Eng. Chem. Res.26(8), 1670–1672 (1987).
[CrossRef]

P. Kask, P. Piksarv, Ü. Mets, M. Pooga, and E. Lippmaa, “Fluorescence correlation spectroscopy in the nanosecond time range: rotational diffusion of bovine carbonic anhydrase B,” Eur. Biophys. J.14(4), 257–261 (1987).
[CrossRef] [PubMed]

1975

S. R. Aragón and R. Pecora, “Fluorescence correlation spectroscopy and Brownian rotational diffusion,” Biopolymers14(1), 119–137 (1975).
[CrossRef]

1974

D. E. Koppel, “Statistical accuracy in fluorescence correlation spectroscopy,” Phys. Rev. A10(6), 1938–1945 (1974).
[CrossRef]

M. Ehrenberg and R. Rigler, “Rotational brownian motion and fluorescence intensify fluctuations,” Chem. Phys.4(3), 390–401 (1974).
[CrossRef]

1964

L. Szalay and E. Tombácz, “Effect of the solvent on the fluorescence spectrum of trypaflavine and fluorescein,” Acta Physica16(4), 367–371 (1964).
[CrossRef]

1958

L. Mandel, “Fluctuations of photon beams and their correlations,” Proc. Phys. Soc.72(6), 1037–1048 (1958).
[CrossRef]

Aragón, S. R.

S. R. Aragón and R. Pecora, “Fluorescence correlation spectroscopy and Brownian rotational diffusion,” Biopolymers14(1), 119–137 (1975).
[CrossRef]

Audebert, R.

I. Iliopoulos, J. Halary, and R. Audebert, “Polymer complexes stabilized through hydrogen bonds. Influence of ‘structure defects’ on complex formation: viscometry and fluorescence polarization measurements,” J. Polym. Sci. A Polym. Chem.26(1), 275–284 (1988).
[CrossRef]

Axhausen, P.

P. Kask, R. Günther, and P. Axhausen, “Statistical accuracy in fluorescence fluctuation experiments,” Eur. Biophys. J.25(3), 163–169 (1997).
[CrossRef]

Bacia, K.

K. Bacia, S. A. Kim, and P. Schwille, “Fluorescence cross-correlation spectroscopy in living cells,” Nat. Methods3(2), 83–89 (2006).
[CrossRef] [PubMed]

Bakalkin, G.

V. Vukojević, A. Pramanik, T. Yakovleva, R. Rigler, L. Terenius, and G. Bakalkin, “Study of molecular events in cells by fluorescence correlation spectroscopy,” Cell. Mol. Life Sci.62(5), 535–550 (2005).
[CrossRef] [PubMed]

Barbieri, B.

Z. Földes-Papp, S. C. Liao, T. You, and B. Barbieri, “Reducing background contributions in fluorescence fluctuation time-traces for single-molecule measurements in solution,” Curr. Pharm. Biotechnol.10(5), 532–542 (2009).
[CrossRef] [PubMed]

Basché, T.

G. Hinze and T. Basché, “Statistical analysis of time resolved single molecule fluorescence data without time binning,” J. Chem. Phys.132(4), 044509 (2010).
[CrossRef] [PubMed]

G. Hinze, G. Diezemann, and T. Basché, “Rotational correlation functions of single molecules,” Phys. Rev. Lett.93(20), 203001 (2004).
[CrossRef] [PubMed]

Becker, W.

S. Felekyan, R. Kuhnemuth, V. Kudryavtsev, C. Sandhagen, W. Becker, and C. Seidel, “Full correlation from picoseconds to seconds by time-resolved and time-correlated single photon detection,” Rev. Sci. Instrum.76(8), 083104 (2005).
[CrossRef]

Bonnet, G.

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[CrossRef]

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Acta Physica

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Chem. Phys.

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IEEE Trans. Biomed. Eng.

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S. Felekyan, R. Kuhnemuth, V. Kudryavtsev, C. Sandhagen, W. Becker, and C. Seidel, “Full correlation from picoseconds to seconds by time-resolved and time-correlated single photon detection,” Rev. Sci. Instrum.76(8), 083104 (2005).
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J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Springer, 2006).

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Figures (8)

Fig. 1
Fig. 1

A schematic representation of the experimental system. The sample is excited by a laser diode (LD) in 470 nm with a repetition rate of 50 MHz. The polarization of light emitted by the fluorophore depends on the orientation of the transition dipole with respect to the detection system. The orientation of the transition dipole is represented by the angles ϕ and θ . I|| and I are orthogonal polarization components of the fluorescence signal, separated by a polarizing beam splitter (BS). The fluorescence signal is detected at the same time by two separate photomultipliers (HPM hybrid detectors) and delivered to the TCSPC card for processing.

Fig. 2
Fig. 2

(a) The variance of the time averaged signal is compared to the autocorrelation function. The decrease rate of the variance of the time-averaged intensity (blue line) is slower than that of the autocorrelation function (red line). (b) The variance of the time averaged intensity for different τr values (black line – 1ns, red line – 2 ns, blue line – 5ns, green line – 10 ns, purple line – 10 ns, brown line – 20 ns). Differences between the various τr values are significant also in longer time limits (shown in the inset).

Fig. 3
Fig. 3

The variance of the time-averaged intensity for τ r =10ns (solid black line - ideal measurement (δ = 1), dashed black line - t d /T =1/ 100 ) and for τ r =500ns (solid red line - ideal measurement (δ = 1)).

Fig. 4
Fig. 4

Autocorrelation (solid blue- parallel polarization, solid red- perpendicular polarization) and cross-correlation (solid green) data for the fluorescein in 0% glycerol solution (a) and fluorescein in 80% glycerol solution (b). The rotational correlation component of the autocorrelation and cross-correlation traces is completely absent for both solutions.

Fig. 5
Fig. 5

(a) Ω|| and Ω for the different glycerol concentrations (0%- black, 20%- red, 60%- blue, 80%- green). Both Ω|| and Ω are shown to linearly increase. By zooming to shorter acquisition durations, in which fluctuations are shown not to be averaged out, the curves related to different glycerol concentrations become indistinguishable (shown in the inset). (b) Comparison of the photon counting distribution for the different solutions (green triangles- 80% glycerol, blue triangles- 60% glycerol, red triangles- 20% glycerol, black triangles- 0% glycerol) with the Poisson distribution for a mean equal to the corresponding average photon counts of the experimental histogram (solid lines). Lowering the percentage of glycerol, (faster diffusion) results in increased deviation of the histogram from a Poisson distribution. This deviation of the experimental data from the Poisson distribution is much more pronounced in the logarithmic representation as compared to the linear scale (shown in the inset).

Fig. 6
Fig. 6

Typical photon count trajectory for fluorescein in 0% glycerol solution (a) and fluorescein in 80% glycerol solution (b), in the parallel polarization (solid blue) and perpendicular polarization (solid red). The non-normalized time average of Imeasured for each solution is represented by the solid green line.

Fig. 7
Fig. 7

I ¯ (t) 2 I ¯ (t) 2 (a) and I ¯ (t) 2 I ¯ (t) 2 ¯ (b), for various glycerol percentages (0% — black, 20% — red, 60% — blue, 80% — green). Theory (dotted lines) and simulation (thick solid lines) are compared to experimental results (thin solid lines). I ¯ (t) 2 I ¯ (t) 2 decreases in time for all samples. However, fluctuations for the less viscous samples are averaged out faster than fluctuations for the more viscous samples.

Fig. 8
Fig. 8

The rotational correlation time τr measured from the fluorescence fluctuation measurements of 1 nM fluorescein solution (blue rhombus), and from the bulk time-resolved anisotropy decay measurements for 1 µM fluorescein solution (red squares), versus viscosity. The solid straight line fits the fluorescence fluctuation measurements and the dashed line fits to bulk time-resolved anisotropy decay measurements obtained with the same set-up.

Equations (18)

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I || = I e (A+B sin 2 φ+C sin 2 φcos2θ)
I = I e (A+B sin 2 φC sin 2 φcos2θ)
I(t)= I (t)+ I || (t)=2 I e (A+B sin 2 φ(t))
P(n,T) = 0 Ω n n! e Ω P( Ω )dΩ
Ω(t) = 0 Ω(t)P(Ω)dΩ
Ω 2 (t) Ω(t) 2 = 0 t Ω (t) 2 P(Ω)dΩ ( 0 t Ω(t)P(Ω)dΩ ) 2
P( I ¯ ,T)= δ( I ¯ 1 T 0 T I(t)dt )
I ¯ (T) 2 I ¯ (T) 2 = Ω 2 (t) T 2 Ω(t) 2 T 2 = 2 T 2 [ 0 T dt(Tt) δI(t)δI(0) ]
I ¯ (T) 2 I ¯ (T) 2 = 2 T 2 0 T (Tt)F e t/ τ r dt= 2F τ r T + 2F τ r 2 T 2 (1+ e T/ τ r )
I ¯ (T) 2 I ¯ (T) 2 2F τ r T
δ= nλ T
I ¯ (T) 2 I ¯ (T) 2 =δ 2 T 2 0 T (Ttδ)F e tδ/ τ r dt= 2F τ r T 2 { T τ r + e Tδ/ τ r [ τ r +(δ1) ] }
G(τ)= 1 nm [ I A/B I A/B (nm) ] 1 n I A/B 2
G a/b (τ)= 1 nm [ I B I A (nm) ] 1 n [ I B I A ]
I ¯ = { 1 n [ I A + I B ] ¯ } l
Var I ¯ = 1 { I ¯ 2 I ¯ 2 } l ¯ { I ¯ 2 I ¯ 2 } l
P= I A I B I A + I B
D r = K B T 8πη R 3

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