Skip to main content
PMC home page
Biophysical Journal logoLink to Biophysical Journal
. 2000 Apr;78(4):2138–2150. doi: 10.1016/S0006-3495(00)76760-9

A maximum entropy analysis of protein orientations using fluorescence polarization data from multiple probes.

U A van der Heide 1, S C Hopkins 1, Y E Goldman 1
PMCID: PMC1300805  PMID: 10733991

Abstract

Techniques have recently become available to label protein subunits with fluorescent probes at predetermined orientation relative to the protein coordinates. The known local orientation enables quantitative interpretation of fluorescence polarization experiments in terms of orientation and motions of the protein within a larger macromolecular assembly. Combining data obtained from probes placed at several distinct orientations relative to the protein structure reveals functionally relevant information about the axial and azimuthal orientation of the labeled protein segment relative to its surroundings. Here we present an analytical method to determine the protein orientational distribution from such data. The method produces the broadest distribution compatible with the data by maximizing its informational entropy. The key advantages of this approach are that no a priori assumptions are required about the shape of the distribution and that a unique, exact fit to the data is obtained. The relative orientations of the probes used for the experiments have great influence on information content of the maximum entropy distribution. Therefore, the choice of probe orientations is crucial. In particular, the probes must access independent aspects of the protein orientation, and two-fold rotational symmetries must be avoided. For a set of probes, a "figure of merit" is proposed, based on the independence among the probe orientations. With simulated fluorescence polarization data, we tested the capacity of maximum entropy analysis to recover specific protein orientational distributions and found that it is capable of recovering orientational distributions with one and two peaks. The similarity between the maximum entropy distribution and the test distribution improves gradually as the number of independent probe orientations increases. As a practical example, ME distributions were determined with experimental data from muscle fibers labeled with bifunctional rhodamine at known orientations with respect to the myosin regulatory light chain (RLC). These distributions show a complex relationship between the axial orientation of the RLC relative to the fiber axis and the azimuthal orientation of the RLC about its own axis. Maximum entropy analysis reveals limitations in available experimental data and supports the design of further probe angles to resolve details of the orientational distribution.

Full Text

The Full Text of this article is available as a PDF (176.8 KB).

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Ajtai K., Ringler A., Burghardt T. P. Probing cross-bridge angular transitions using multiple extrinsic reporter groups. Biochemistry. 1992 Jan 14;31(1):207–217. doi: 10.1021/bi00116a030. [DOI] [PubMed] [Google Scholar]
  2. Ajtai K., Toft D. J., Burghardt T. P. Path and extent of cross-bridge rotation during muscle contraction. Biochemistry. 1994 May 10;33(18):5382–5391. doi: 10.1021/bi00184a005. [DOI] [PubMed] [Google Scholar]
  3. Berger C. L., Craik J. S., Trentham D. R., Corrie J. E., Goldman Y. E. Fluorescence polarization of skeletal muscle fibers labeled with rhodamine isomers on the myosin heavy chain. Biophys J. 1996 Dec;71(6):3330–3343. doi: 10.1016/S0006-3495(96)79526-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Biophysical Society 41st annual meeting. New Orleans, Louisiana, 2-6 March 1997. Abstracts. Biophys J. 1997 Feb;72(2 Pt 2):A1–476. [PMC free article] [PubMed] [Google Scholar]
  5. Burghardt T. P., Ajtai K. Following the rotational trajectory of the principal hydrodynamic frame of a protein using multiple probes. Biochemistry. 1994 May 10;33(18):5376–5381. doi: 10.1021/bi00184a004. [DOI] [PubMed] [Google Scholar]
  6. Burghardt T. P., Ajtai K. Mapping global angular transitions of proteins in assemblies using multiple extrinsic reporter groups. Biochemistry. 1992 Jan 14;31(1):200–206. doi: 10.1021/bi00116a029. [DOI] [PubMed] [Google Scholar]
  7. CHEN R. F., BOWMAN R. L. FLUORESCENCE POLARIZATION: MEASUREMENT WITH ULTRAVIOLET-POLARIZING FILTERS IN A SPECTROPHOTOFLUOROMETER. Science. 1965 Feb 12;147(3659):729–732. doi: 10.1126/science.147.3659.729. [DOI] [PubMed] [Google Scholar]
  8. Corrie J. E., Brandmeier B. D., Ferguson R. E., Trentham D. R., Kendrick-Jones J., Hopkins S. C., van der Heide U. A., Goldman Y. E., Sabido-David C., Dale R. E. Dynamic measurement of myosin light-chain-domain tilt and twist in muscle contraction. Nature. 1999 Jul 29;400(6743):425–430. doi: 10.1038/22704. [DOI] [PubMed] [Google Scholar]
  9. Corrie J. E., Craik J. S., Munasinghe V. R. A homobifunctional rhodamine for labeling proteins with defined orientations of a fluorophore. Bioconjug Chem. 1998 Mar-Apr;9(2):160–167. doi: 10.1021/bc970174e. [DOI] [PubMed] [Google Scholar]
  10. Dale R. E., Hopkins S. C., an der Heide U. A., Marszałek T., Irving M., Goldman Y. E. Model-independent analysis of the orientation of fluorescent probes with restricted mobility in muscle fibers. Biophys J. 1999 Mar;76(3):1606–1618. doi: 10.1016/S0006-3495(99)77320-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Dominguez R., Freyzon Y., Trybus K. M., Cohen C. Crystal structure of a vertebrate smooth muscle myosin motor domain and its complex with the essential light chain: visualization of the pre-power stroke state. Cell. 1998 Sep 4;94(5):559–571. doi: 10.1016/s0092-8674(00)81598-6. [DOI] [PubMed] [Google Scholar]
  12. Fajer P. G. Determination of spin-label orientation within the myosin head. Proc Natl Acad Sci U S A. 1994 Feb 1;91(3):937–941. doi: 10.1073/pnas.91.3.937. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. Griffin B. A., Adams S. R., Tsien R. Y. Specific covalent labeling of recombinant protein molecules inside live cells. Science. 1998 Jul 10;281(5374):269–272. doi: 10.1126/science.281.5374.269. [DOI] [PubMed] [Google Scholar]
  14. Hopkins S. C., Sabido-David C., Corrie J. E., Irving M., Goldman Y. E. Fluorescence polarization transients from rhodamine isomers on the myosin regulatory light chain in skeletal muscle fibers. Biophys J. 1998 Jun;74(6):3093–3110. doi: 10.1016/S0006-3495(98)78016-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Irving M., St Claire Allen T., Sabido-David C., Craik J. S., Brandmeier B., Kendrick-Jones J., Corrie J. E., Trentham D. R., Goldman Y. E. Tilting of the light-chain region of myosin during step length changes and active force generation in skeletal muscle. Nature. 1995 Jun 22;375(6533):688–691. doi: 10.1038/375688a0. [DOI] [PubMed] [Google Scholar]
  16. Kinosita K., Jr, Kawato S., Ikegami A. A theory of fluorescence polarization decay in membranes. Biophys J. 1977 Dec;20(3):289–305. doi: 10.1016/S0006-3495(77)85550-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Mchaourab H. S., Lietzow M. A., Hideg K., Hubbell W. L. Motion of spin-labeled side chains in T4 lysozyme. Correlation with protein structure and dynamics. Biochemistry. 1996 Jun 18;35(24):7692–7704. doi: 10.1021/bi960482k. [DOI] [PubMed] [Google Scholar]
  18. Polekhina G., Thirup S., Kjeldgaard M., Nissen P., Lippmann C., Nyborg J. Helix unwinding in the effector region of elongation factor EF-Tu-GDP. Structure. 1996 Oct 15;4(10):1141–1151. doi: 10.1016/s0969-2126(96)00122-0. [DOI] [PubMed] [Google Scholar]
  19. VanderMeulen D. L., Nealon D. G., Gratton E., Jameson D. M. Excitation wavelength dependent fluorescence anisotropy of eosin-myosin adducts. Evidence for anisotropic rotations. Biophys Chem. 1990 Jul;36(2):177–184. doi: 10.1016/0301-4622(90)85021-w. [DOI] [PubMed] [Google Scholar]
  20. WEBER G. Polarization of the fluorescence of macromolecules. I. Theory and experimental method. Biochem J. 1952 May;51(2):145–155. doi: 10.1042/bj0510145. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Wilson M. G., Mendelson R. A. A comparison of order and orientation of crossbridges in rigor and relaxed muscle fibres using fluorescence polarization. J Muscle Res Cell Motil. 1983 Dec;4(6):671–693. doi: 10.1007/BF00712160. [DOI] [PubMed] [Google Scholar]
  22. Yasuda R., Noji H., Kinosita K., Jr, Yoshida M. F1-ATPase is a highly efficient molecular motor that rotates with discrete 120 degree steps. Cell. 1998 Jun 26;93(7):1117–1124. doi: 10.1016/s0092-8674(00)81456-7. [DOI] [PubMed] [Google Scholar]
  23. Zhang Z., Huang L., Shulmeister V. M., Chi Y. I., Kim K. K., Hung L. W., Crofts A. R., Berry E. A., Kim S. H. Electron transfer by domain movement in cytochrome bc1. Nature. 1998 Apr 16;392(6677):677–684. doi: 10.1038/33612. [DOI] [PubMed] [Google Scholar]
  24. van der Heide U. A., Orbons B., Gerritsen H. C., Levine Y. K. The orientation of transition moments of dye molecules used in fluorescence studies of muscle systems. Eur Biophys J. 1992;21(4):263–272. doi: 10.1007/BF00185121. [DOI] [PubMed] [Google Scholar]
  25. van der Heide U. A., Rem O. E., Gerritsen H. C., de Beer E. L., Schiereck P., Trayer I. P., Levine Y. K. A fluorescence depolarization study of the orientational distribution of crossbridges in muscle fibres. Eur Biophys J. 1994;23(5):369–378. doi: 10.1007/BF00188661. [DOI] [PubMed] [Google Scholar]

Articles from Biophysical Journal are provided here courtesy of The Biophysical Society

RESOURCES