Resolving fluorescent species by their brightness and diffusion using correlated photon-counting histograms

Autoři: Nathan Scales aff001;  Peter S. Swain aff001
Působiště autorů: Department of Physiology, McGill University, 3655 Promenade Sir William Osler, Montreal, Quebec H3G 1Y6, Canada aff001;  School of Biological Sciences, University of Edinburgh, Mayfield Road, Edinburgh EH9 3BF, United Kingdom aff002
Vyšlo v časopise: PLoS ONE 14(12)
Kategorie: Research Article


Fluorescence fluctuation spectroscopy (FFS) refers to techniques that analyze fluctuations in the fluorescence emitted by fluorophores diffusing in a small volume and can be used to distinguish between populations of molecules that exhibit differences in brightness or diffusion. For example, fluorescence correlation spectroscopy (FCS) resolves species through their diffusion by analyzing correlations in the fluorescence over time; photon counting histograms (PCH) and related methods based on moment analysis resolve species through their brightness by analyzing fluctuations in the photon counts. Here we introduce correlated photon counting histograms (cPCH), which uses both types of information to simultaneously resolve fluorescent species by their brightness and diffusion. We define the cPCH distribution by the probability to detect both a particular number of photons at the current time and another number at a later time. FCS and moment analysis are special cases of the moments of the cPCH distribution, and PCH is obtained by summing over the photon counts in either channel. cPCH is inherently a dual channel technique, and the expressions we develop apply to the dual colour case. Using simulations, we demonstrate that two species differing in both their diffusion and brightness can be better resolved with cPCH than with either FCS or PCH. Further, we show that cPCH can be extended both to longer dwell times to improve the signal-to-noise and to the analysis of images. By better exploiting the information available in fluorescence fluctuation spectroscopy, cPCH will be an enabling methodology for quantitative biology.

Klíčová slova:

Dwell time – Fluorescence – Fluorescence spectroscopy – Lasers – Mass diffusivity – Photons – Probability distribution – Generating functions


1. Rosenfeld N, Perkins TJ, Alon U, Elowitz MB, Swain PS. A fluctuation method to quantify in vivo fluorescence data. Biophys J. 2006;91:759–766. doi: 10.1529/biophysj.105.073098 16648159

2. Zamparo L, Perkins TJ. Statistical lower bounds on protein copy number from fluorescence expression images. Bioinformatics. 2009;25:2670–2676. doi: 10.1093/bioinformatics/btp415 19574287

3. Teng SW, Wang Y, Tu KC, Long T, Mehta P, Wingreen NS, et al. Measurement of the copy number of the master quorum-sensing regulator of a bacterial cell. Biophys J. 2010;98:2024–31. doi: 10.1016/j.bpj.2010.01.031 20441767

4. Nayak CR, Rutenberg AD. Quantification of fluorophore copy number from intrinsic fluctuations during fluorescence photobleaching. Biophys J. 2011;101:2284–93. doi: 10.1016/j.bpj.2011.09.032 22067169

5. Finkenstädt B, Woodcock DJ, Komorowski M, Harper CV, Davis JRE, White MRH, et al. Quantifying intrinsic and extrinsic noise in gene transcription using the linear noise approximation: An application to single cell data. Ann Appl Stat. 2013;7:1960–1982. doi: 10.1214/13-AOAS669

6. Bakker E, Swain PS. Estimating numbers of intracellular molecules through analysing fluctuations in photobleaching. Sci Rep. 2019;9:15238. doi: 10.1038/s41598-019-50921-7 31645577

7. Elson EL, Magde D. Fluorescence correlation spectroscopy. I. Conceptual basis and theory. Biopolymers. 1974;13:1–27. doi: 10.1002/bip.1974.360130102

8. Chen Y, Muller JD, So PTC, Gratton E. The photon counting histogram in fluorescence fluctuation spectroscopy. Biophys J. 1999;77:553–567. doi: 10.1016/S0006-3495(99)76912-2 10388780

9. Kask P, Palo K, Ullmann D, Gall K. Fluorescence-intensity distribution analysis and its application in biomolecular detection technology. Proc Nat Acad Sci USA. 1999;96:13756–13761. doi: 10.1073/pnas.96.24.13756 10570145

10. Qian H. On the statistics of fluorescence correlation spectroscopy. Biophys Chem. 1990;38:49–57. doi: 10.1016/0301-4622(90)80039-a 2085652

11. Muller JD. Cumulant analysis in fluorescence fluctuation spectroscopy. Biophys J. 2004;86:3981–3992. doi: 10.1529/biophysj.103.037887 15189894

12. Slaughter BD, Schwartz JW, Li R. Mapping dynamic protein interactions in MAP kinase signaling using live-cell fluorescence fluctuation spectroscopy and imaging. Proc Nat Acad Sci USA. 2007;104:20320–20325. doi: 10.1073/pnas.0710336105 18077328

13. Saffarian S, Li Y, Elson EL, Pike LJ. Oligomerization of the EGF receptor investigated by live cell fluorescence intensity distribution analysis. Biophys J. 2007;93:1021–1031. doi: 10.1529/biophysj.107.105494 17496034

14. Chakraborty M, Kuriata AM, Nathan Henderson J, Salvucci ME, Wachter RM, Levitus M. Protein oligomerization monitored by fluorescence fluctuation spectroscopy: Self-assembly of rubisco activase. Biophys J. 2012;103:949–958. doi: 10.1016/j.bpj.2012.07.034 23009844

15. Palmer AG, Thompson NL. Molecular aggregation characterized by high-order autocorrelation in fluorescence correlation spectroscopy. Biophys J. 1987;52:257–270. doi: 10.1016/S0006-3495(87)83213-7 3663831

16. Melnykov AV, Hall KB. Revival of high-order fluorescence correlation analysis: Generalized theory and biochemical applications. J Phys Chem B. 2009;113:15629–15638. doi: 10.1021/jp906539k 19877707

17. Palo K, Metz U, Jager S, Kask P, Gall K. Fluorescence intensity multiple distributions analysis: Concurrent determination of diffusion times and molecular brightness. Biophys J. 2000;79:2858–2866. doi: 10.1016/S0006-3495(00)76523-4 11106594

18. Wu B, Muller JD. Time-integrated fluorescence cumulant analysis in fluorescence fluctuation spectroscopy. Biophys J. 2005;89:2721–2735. doi: 10.1529/biophysj.105.063685 16055549

19. Perroud TD, Huang B, Zare RN. Effect of bin time on the photon counting histogram for one-photon excitation. ChemPhysChem. 2005;6:905–912. doi: 10.1002/cphc.200400547 15884075

20. Gopich IV, Szabo A. Photon counting histograms for diffusing fluorophores. J Phys Chem B. 2005;109:17683–17688. doi: 10.1021/jp052345f 16853263

21. Laurence TA, Kapanidis AN, Kong XX, Chemla DS, Weiss S. Photon arrival-time interval distribution (PAID): A novel tool for analyzing molecular interactions. J Phys Chem B. 2004;108:3051–3067. doi: 10.1021/jp036499b

22. Palo K, Mets U, Loorits V, Kask P. Calculation of photon-count number distributions via master equations. Biophys J. 2006;90:2179–2191. doi: 10.1529/biophysj.105.066084 16387771

23. Muller BK, Zaychikov E, Brauchle C, Lamb DC. Pulsed interleaved excitation. Biophys J. 2005;89:3508–3522. doi: 10.1529/biophysj.105.064766 16113120

24. Brown CM, Dalal RB, Hebert B, Digman MA, Horwitz AR, Gratton E. Raster image correlation spectroscopy (RICS) for measuring fast protein dynamics and concentrations with a commercial laser scanning confocal microscope. J Microsc. 2008;229:78–91. doi: 10.1111/j.1365-2818.2007.01871.x 18173647

25. Godin AG, Costantino S, Lorenzo LE, Swift JL, Sergeev M, Ribeiro-da Silva A, et al. Revealing protein oligomerization and densities in situ using spatial intensity distribution analysis. Proc Nat Acad Sci USA 2011;108:7010–7015. doi: 10.1073/pnas.1018658108 21482753

26. Chen Y, Tekmen M, Hillesheim L, Skinner J, Wu B, Muller JD. Dual-color photon-counting histogram. Biophys J. 2005;88:2177–2192. doi: 10.1529/biophysj.104.048413 15596506

27. Wu B, Chen Y, Muller JD. Dual-color time-integrated fluorescence cumulant analysis. Biophys J. 2006;91:2687–2698. doi: 10.1529/biophysj.106.086181 16815900

28. Schwille P, MeyerAlmes FJ, Rigler R. Dual-color fluorescence cross-correlation spectroscopy for multicomponent diffusional analysis in solution. Biophys J. 1997;72:1878–1886. doi: 10.1016/S0006-3495(97)78833-7 9083691

29. Meng F, Ma H. A comparison between photon counting histogram and fluorescence intensity distribution analysis. J Phys Chem B. 2006;110:25716–25720. doi: 10.1021/jp063845r 17181211

30. Van Kampen NG. Stochastic processes in physics and chemistry. Amsterdam, The Netherlands: North-Holland; 1981.

31. Huang B, Perroud TD, Zare RN. Photon counting histogram: One-photon excitation. ChemPhysChem. 2004;5:1523–1531. doi: 10.1002/cphc.200400176 15535551

32. Ackermann J, Mathis H, Greiner B. Single molecules in fluorescence fluctuation spectroscopy: effective volume and photon counting histogram. In: Biomedical Optics. BiOS; 2008.

33. Kendall MG, Stuart A. Advanced theory of statistics. vol. I. New York: Macmillan; 1977.

34. Wohland T, Rigler R, Vogel H. The standard deviation in fluorescence correlation spectroscopy. Biophys J. 2001;80:2987–2999. doi: 10.1016/S0006-3495(01)76264-9 11371471

35. Scales N. Resolving fluorescent species by their brightness and diffusion properties using correlated photon counting histograms. Ph.D. Thesis. McGill University; 2013.

36. Digman MA, Brown CM, Sengupta P, Wiseman PW, Horwitz AR, Gratton E. Measuring fast dynamics in solutions and cells with a laser scanning microscope. Biophys J. 2005;89:1317–1327. doi: 10.1529/biophysj.105.062836 15908582

37. Widengren J, Mets U, Rigler R. Fluorescence Correlation Spectroscopy of Triplet-states in Solution - a Theoretical and Experimental Study. J Phys Chem. 1995;99:13368–13379. doi: 10.1021/j100036a009

38. Hillesheim LN, Müller JD. The dual-color photon counting histogram with non-ideal photodetectors. Biophys J. 2005;89:3491–3507. doi: 10.1529/biophysj.105.066951 16126829

39. Hattne J, Fange D, Elf J. Stochastic reaction-diffusion simulation with MesoRD. Bioinformatics. 2005;21:2923–2924. doi: 10.1093/bioinformatics/bti431 15817692

40. Sivia DS, Skilling J. Data analysis: a Bayesian tutorial. Oxford University Press, USA; 2006.

41. Skilling J. Nested sampling for general Bayesian computation. Bayesian Anal. 2006;1:833–860. doi: 10.1214/06-BA127

42. Petersen NO. Scanning fluorescence correlation spectroscopy 1. Theory and simulation of aggregation measurements. Biophys J. 1986;49:809–815. doi: 10.1016/S0006-3495(86)83709-2 3719067

43. Petersen NO, Johnson DC, Schlesinger MJ. Scanning fluorescence correlation spectroscopy 2. Application to virus glycoprotein aggregation. Biophys J. 1986;49:817–820. doi: 10.1016/S0006-3495(86)83710-9 3013328

44. Petrasek Z, Schwille P. Precise measurement of diffusion coefficients using scanning fluorescence correlation spectroscopy. Biophys J. 2008;94:1437–1448. doi: 10.1529/biophysj.107.108811 17933881

45. Chen Y, Muller JD, Tetin SY, Tyner JD, Gratton E. Probing ligand protein binding equilibria with fluorescence fluctuation spectroscopy. Biophys J. 2000;79:1074–1084. doi: 10.1016/S0006-3495(00)76361-2 10920037

46. Kask P, Palo K, Fay N, Brand L, Mets U, Ullmann D, Jungmann J, Pschorr J, Gall K. Two-dimensional fluorescence intensity distribution analysis: Theory and applications. Biophys J. 2000;78:1703–1713. doi: 10.1016/S0006-3495(00)76722-1 10733953

47. Abdollah-Nia F, Gelfand MP, Van Orden A. Artifact-free and detection-profile-independent higher-order fluorescence correlation spectroscopy for microsecond-resolved kinetics 1. multidetector and sub-binning approach. J Phys Chem B. 2017;121:2373–2387. doi: 10.1021/acs.jpcb.7b00407 28230994

48. Abdollah-Nia F, Gelfand MP, Van Orden A. Artifact-free and detection-profile-independent higher-order fluorescence correlation spectroscopy for microsecond-resolved kinetics 2. Mixtures and reactions. J Phys Chem B. 2017;121:2388–2399. doi: 10.1021/acs.jpcb.7b00408 28182427

49. Ishii K, Tahara T. Two-dimensional fluorescence lifetime correlation spectroscopy. 1. Principle. J Phys Chem B. 2013;117:11414–11422. doi: 10.1021/jp406861u 23977832

50. Ishii K, Tahara T. Two-dimensional fluorescence lifetime correlation spectroscopy. 2. Application. J Phys Chem B. 2013;117:11423–11432. doi: 10.1021/jp406864e 23977902

51. Ghosh A, Karedla N, Thiele JC, Gregor I, Enderlein J. Fluorescence lifetime correlation spectroscopy: Basics and applications. Methods. 2018;140:32–39. doi: 10.1016/j.ymeth.2018.02.009 29454862

52. Palo K, Brand L, Eggeling C, Jäger S, Kask P, Gall K. Fluorescence intensity and lifetime distribution analysis: toward higher accuracy in fluorescence fluctuation spectroscopy. Biophys J. 2002;83:605–618. doi: 10.1016/S0006-3495(02)75195-3 12124251

53. Macdonald PJ, Chen Y, Wang X, Chen Y, Mueller JD. Brightness analysis by z-scan fluorescence fluctuation spectroscopy for the study of protein interactions within living cells. Biophys J. 2010;99:979–988. doi: 10.1016/j.bpj.2010.05.017 20682277

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