Skip to main content
SpringerLink
Log in

Information Content of Fluorescence Polarization and Anisotropy

  • Original Paper
  • Published:
Journal of Fluorescence Aims and scope Submit manuscript

Abstract

The equality of information content in fluorescence polarization and emission anisotropy is a common assumption and the two quantities are used according to practical considerations. However, an information-theoretic analysis presented here reveals that their information content is substantially different. A scaling relation exists between polarization and anisotropy, and normalization allows their direct comparison. Various measures of information such as the absolute, relative, differential, and potential entropies all appear larger for anisotropy over part or all of its normalized overlap with the polarization function. The larger information content coincides with the signal range where the emitted light is polarized mostly in the parallel direction. Polarization takes on larger absolute entropy only when the emission is about perpendicular to the incident light and when the differential entropy is considered over the entire physical domain. The additional information locally afforded by polarization appears to be related to its larger signal range whereas the extra information in anisotropy may be attributed to a second perpendicular emission plane in its definition, which is oriented along the axis of propagation of light and takes the contribution of all degrees of rotational freedom into account. Thus anisotropy may be considered as a more accurate and more informative representation of the underlying physical phenomena. Some practical aspects relevant to studies of protein–ligand interactions are also discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. Lakowitz JR (1999) Principles of fluorescence spectroscopy, 2nd edn. Kluwer Academic(Plenum Publishers, New York

  2. Sharma A, Schulman SG (1999) Introduction to fluorescence spectroscopy. Techniques in analytical chemistry series. John Wiley and Sons, Inc, New York

  3. Valeur B (2002) Molecular fluorescence. Principles and applications. Wiley-VCH Verlag GmbH, Weinheim, Germany

  4. Jameson DM, Croney JC, Moens PD (2003) Fluorescence, basic concepts, practical aspects and some anecdotes. Methods Enzymol 360:1–43

    PubMed  CAS  Google Scholar 

  5. Weber G (1952) Polarization of the fluorescence of macromolecules. 1. Theory and experimental method. Biochem J 51:145–155

    PubMed  CAS  Google Scholar 

  6. Weber G (1953) Rotational Brownian motion and polarization of fluorescence of solutions. Adv Protein Chem 8:415–459

    PubMed  CAS  Google Scholar 

  7. Jablonski A (1960) On the notation of emission anisotropy. Bull Acad Polon Sci Ser Sci Math Astr et Phys 6:259–264

    Google Scholar 

  8. Weber G (1966) Polarization of the fluorescence of solutions. In: Hercules D (ed) Fluorescence and phosphorescence. Wiley, New York, pp 217–240

  9. Jameson DM, Sawyer WH (1995) Fluorescence anisotropy applied to biomolecular interactions. Methods Enzymol 246:283– 300

    PubMed  CAS  Google Scholar 

  10. Jameson DM, Croney JC (2003) Fluorescence polarization, past present and future. Comb High Throughput Chem 6:167–173

    CAS  Google Scholar 

  11. Jameson DM, Mocz G (2005) Fluorescence polarization(anisotropy approaches to study protein-ligand interactions, Effects of errors and uncertainties. In: Nienhaus GU (ed) Methods in molecular biology. Protein–ligand interactions: methods and applications, vol 305. Humana Press Inc., Totowa, NJ, pp 301–322

  12. Yguerabide J (1972) Nanosecond fluorescence spectroscopy of macromolecules. Methods Enzymol 26:498–578

    PubMed  CAS  Google Scholar 

  13. Wahl Ph (1975) Fluorescence spectroscopy. In: Chen RF, Edelhoch H (eds) Biochemical fluorescence concepts, vol. 1. Marcel-Dekker, New York, pp 1–41

  14. Shannon CE (1948) A mathematical theory of communication. Bell Syst Technol J 27(379–423):623–656

    Google Scholar 

  15. Shannon CE, Waever W (1949) Mathematical theory of communication. University of Illinois, Urbana

  16. Brillouin L (1956) Science and information theory. Acad Press, New York

  17. Brillouin L (1964) Scientific uncertainty and information. Acad. Press, New York

  18. Kullback S, Leibler RA (1951) On information and sufficiency. Ann Math Stat 22(1):79–86

    Article  Google Scholar 

  19. Kullback S (1959) Information theory and statistics. John Wiley & Sons, Inc., New York

  20. Khinchin AI (1957) Mathematical foundations of information theory. Dover Publications, Inc., New York

  21. Eckschlager K, Stepanek V (1979) Information theory as applied to chemical analysis. John Wiley and Sons, New York

  22. Danzer K, Hopfe V, Marx G (1982) Möglichkeiten der Erhörung der Informationsmenge spectroskopischer Analysenmethode mit Hilfe der Rechentechnik. Z Chem 22:332–338

    CAS  Google Scholar 

  23. Hauser MD (1996) The evolution of communication. The MIT Press, Cambridge, Massachusetts

  24. Bonchev D (1983) Information theoretic indices for characterization of chemical structures. Research Studies Press, Chichester, England

  25. Eckschlager K, Stepanek V (1985) Analytical measurement and information. Advances in the information theoretic approach to chemical analyses. Research Studies Press Ltd. Letchworth, Hertfordshire, England

  26. Eckschlager K, Danzer K (1994) Information theory in analytical chemistry. John-Wiley & Sons, Inc., New York

  27. Magurran A (1988) Ecological diversity and its measurement. Princeton University Press, Princeton, New Jersey

  28. Guiasu S (2001) Quantum mechanics. Nova Science Publishers, Huntington, New York

  29. Alcala JR, Gratton E, Prendegrast FG (1987) Interpretation of fluorescence decays in proteins using continuous lifetime distributions. Biophys J 51:925–936

    PubMed  CAS  Google Scholar 

  30. Lakowicz JR, Gryczynski I, Wiczk W, Johnson ML (1994) Distributions of fluorescence decay times for synthetic melittin in water-methanol mixture and complexed with calmodulin, troponin C, and phospholipids. J Fluoresc 4:169–177

    Article  CAS  Google Scholar 

  31. Bronchon JC (1994) Maximum entropy method of data analysis in time-resolved spectroscopy. Methods Enzymol 240:262–311

    Article  Google Scholar 

  32. van der Heide UA, Hopkins SC, Goldman YE (2000) Maximum entropy analysis of protein orientation using fluorescence polarization data from multiple probes. Biophys J 78:2138–2150

    Article  PubMed  CAS  Google Scholar 

  33. Sengupta P, Garai K, Balaji N, Periasamy N, Maiti S (2003) Measuring size distribution in highly heterogeneous systems with fluorescence correlation spectroscopy. Biophys J 84:1977– 1984

    PubMed  CAS  Google Scholar 

  34. Ash RB (1965) Information theory. Interscience, New York, New York

  35. Levine RD, Tribus M (eds) (1979) The maximum entropy formalism. MIT Press, Cambridge, Massachusetts

  36. Cover TM, Thomas JA (1991) Elements of information theory. John Wiley & Sons, Inc.

  37. O’Neill EL (1963) Introduction to statistical optics. Addison-Wesley, Reading, MA

  38. Smith JDH (2001) Some observations on the concepts of information-theoretic entropy and randomness. Entropy 3:1–11

    Article  Google Scholar 

  39. Perrin F (1926) Polarisation de la lumière de fluorescence. Vie moyenne des molécules dans l‘etat excitè. J de Phys. VIe Sèrie 7:390–401

    CAS  Google Scholar 

  40. Press WH, Flannery BP, Teukolsky AA, Vetterling WT (1989) Numerical recipes in pascal. The art of scientific computing. Cambridge University Press, NY

  41. Renyi A (1965) On the foundations of information theory. Rev Intern Stat 3:1–14

    Article  Google Scholar 

  42. Desper CR, Kimura I (1967) Mathematics of the polarized-fluorescence experiment. J Appl Phys 38:4225–4233

    Article  CAS  Google Scholar 

  43. Badley RA (1976) Fluorescent probing of dynamic and molecular organization of biological membranes. In: Wehry EL (ed) Modern fluorescence spectroscopy. Plenum Press, New York, pp 91– 168

  44. Picozzi A (2004) Entropy and degree of polarization for nonlinear optical waves. Opt Lett 29:1653–1655

    Article  PubMed  Google Scholar 

  45. Wahl Ph (1979) Analysis of fluorescence anisotropy decays by a least squares method. Biophys Chem 10:91– 104

    Article  PubMed  CAS  Google Scholar 

  46. Reflegler P (2005) Polarization degree of optical waves with non-Gaussian probability density functions, Kullback relative entropy-based approach. Opt Lett 30:1090–1092

    Article  Google Scholar 

Download references

Acknowledgements

The author wishes to thank Professor David M. Jameson for his thoughtful comments and valuable discussions. This work was supported, in part, by a grant from the National Institute of Health (NIH/NCRR/RCMI G12-RR03061: Selective Research Excellence in Biomedicine and Health).

Author information

Authors and Affiliations

  1. Pacific Biosciences Research Center, University of Hawaii, Honolulu, Hawaii, 96822, USA

    Gabor Mocz

  2. G. Mocz University of Hawaii, Biotechnology Program, Gilmore Hall 411, 3050 Maile Way, Honolulu, Hawaii, 96822, USA

    Gabor Mocz

Authors
  1. Gabor Mocz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gabor Mocz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mocz, G. Information Content of Fluorescence Polarization and Anisotropy. J Fluoresc 16, 511–524 (2006). https://doi.org/10.1007/s10895-006-0095-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10895-006-0095-7

Keywords

Search

Navigation