Bayesian estimation of the internal structure of proteins from single-molecule measurements

Journal of Chemical Physics

Volumn 134, Issue 8, 2011, Pages

  Miyazaki, Makito ^a   Harada, Takahiro ^b  

^a KYOTO UNIVERSITY   (Japan)

^b UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

BAYESIAN ESTIMATIONS; BAYESIAN INFERENCE; COMPLEX SYSTEMS; CONVENTIONAL METHODS; DEGREES OF FREEDOM; INTERNAL STRUCTURE; NUMERICAL STUDIES; OBSERVATION SYSTEMS; ORDERS OF MAGNITUDE; PHYSICAL NATURE; SINGLE MOLECULE MEASUREMENTS; SINGLE-MOLECULE;

BAYESIAN NETWORKS; INFERENCE ENGINES; MECHANICS; PROTEINS;

NUMERICAL METHODS;

PROTEIN;

ARTICLE; BAYES THEOREM; CHEMISTRY; PROTEIN CONFORMATION;

BAYES THEOREM; PROTEIN CONFORMATION; PROTEINS;

EID: 79952098526     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3516587     Document Type: Article

References (36)

1. T. Nishizaka, K. Oiwa, H. Noji, S. Kimura, E. Muneyuki, M. Yoshida, and K. Kinosita, Jr., Nat. Struct. Mol. Biol. 11, 142 (2004). 10.1038/nsmb721 (Pubitemid 38146517)
2. T. Ishii, Y. Murayama, A. Katano, K. Maki, K. Kuwajima, and M. Sano, Biochem. Biophys. Res. Commun. 375, 586 (2008). 10.1016/j.bbrc.2008.08.073
3. J. P. Junker, F. Ziegler, and M. Rief, Science 323, 633 (2009). 10.1126/science.1166191
4. K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature (London) 365, 721 (1993). 10.1038/365721a0 (Pubitemid 23339876)
5. H. Noji, R. Yasuda, M. Yoshida, and K. Kinosita, Jr., Nature (London) 386, 299 (1997). 10.1038/386299a0 (Pubitemid 27142518)
6. K. Kitamura, M. Tokunaga, A. H. Iwane, and T. Yanagida, Nature (London) 397, 129 (1999). 10.1038/16403 (Pubitemid 29050909)
7. K. Shiroguchi and K. Kinosita, Jr., Science 316, 1208 (2007). 10.1126/science.1140468 (Pubitemid 46877486)
8. K. Hu, L. Ji, K. T. Applegate, G. Danuser, and C. M. Waterman-Storer, Science 315, 111 (2007). 10.1126/science.1135085 (Pubitemid 46196992)
9. I. Golding, J. Paulsson, S. M. Zawilski, and E. C. Cox, Cell 123, 1025 (2005). 10.1016/j.cell.2005.09.031 (Pubitemid 41785418)
10. J. W. J. Kerssemakers, E. L. Munteanu, L. Laan, T. L. Noetzel, M. E. Janson, and M. Dogterom, Nature (London) 442, 709 (2006). 10.1038/nature04928 (Pubitemid 44215328)
11. O. Flomenbom, J. Klafter, and A. Szabo, Biophys. J. 88, 3780 (2005). 10.1529/biophysj.104.055905 (Pubitemid 40991093)
12. A. Baba and T. Komatsuzaki, Proc. Natl. Acad. Sci. U.S.A. 104, 19297 (2007). 10.1073/pnas.0704167104
13. C. B. Li, H. Yang, and T. Komatsuzaki, Proc. Natl. Acad. Sci. U.S.A. 105, 536 (2008). 10.1073/pnas.0707378105 (Pubitemid 351171743)
14. H. Akaike, Likelihood and the Bayes Procedure., in Bayesian Statistics, edited by, J. M. Bernardo, M. H. D. Groot, D. V. Lindley, and, A. F. M. Smith, (University Press, Valencia, 1980), pp. 143-166.
15. C. P. Robert, The Bayesian Choice: A Decision-Theoretic Motivation (Springer-Verlag, New York, 1994).
16. C. M. Bishop, Pattern Recognition and Machine Learning (Springer-Verlag, New York, 2006).
17. We naturally assume that the prior probability distribution of [x] is uniform. In this case, the MAP estimator is identical to a maximum likelihood estimator (MLE).
18. W. Bialek, C. G. Callan, and S. P. Strong, Phys. Rev. Lett. 77, 4693 (1996). 10.1103/PhysRevLett.77.4693
19. R. Yasuda, H. Noji, M. Yoshida, K. Kinosita, Jr., and H. Itoh, Nature (London) 410, 898 (2001). 10.1038/35073513 (Pubitemid 32335828)
20. H. C. Berg, in Random Walks in Biology (Princeton University, Princeton, NJ, 1993), Chap. 4
21. K. Sekimoto, Stochastic Energetics (Springer-Verlag, Berlin Heidelberg, 2010), Chap. 1.
22. L. Onsager and S. Machlup, Phys. Rev. 91, 1505 (1953); 10.1103/PhysRev.91.1505
23. ibid. 91, 1512 (1953). 10.1103/PhysRev.91.1505
24. R. Graham, Z. Physik B 26, 281 (1976). 10.1007/BF01312935
25. R. L. Stratonovich, SIAM J. Control 4, 362 (1966). 10.1137/0304028
26. R. Mortensen, J. Stat. Phys. 1, 271 (1969). 10.1007/BF01007481
27. K. L. C. Hunt and J. Ross, J. Chem. Phys. 75, 976 (1981). 10.1063/1.442098
28. Using the concrete expression for the path probability [Eqs.], Eq. can be explicitly written as a tridiagonal system of linear equations. Therefore, the exact solution of the MAP estimator, [x](y;), can be easily obtained.
29. F. W. Wiegel, Physica 33, 734 (1967). 10.1016/0031-8914(67)90218-2
30. F. W. Wiegel, Physica 37, 105 (1967). 10.1016/0031-8914(67)90109-7
31. See supplementary material at http://dx.doi.org/10.1063/1.3516587 E-JCPSA6-134-046043 for the detailed derivation of the Hamiltonian, the analytical solution of the power spectrum, the time correlation of x(t) and x(t), and the Hamiltonian in the infinite interval limit.
32. D. R. Cox and E. J. Snell, J. R. Stat. Soc. Ser. B (Methodol.) 30, 248 (1968).
33. D. R. Cox and D. V. Hinkley, in Theoretical Statistics (Chapman and Hall, London (1974)), Chap. 8.
34. B. Caroli, C. Caroli, and B. Roulet, J. Stat. Phys. 26, 83 (1981). 10.1007/BF01106788
35. A. Dempster, N. Laird, and D. Rubin, J. R. Stat. Soc. Ser. B 39, 1 (1977).
36. 1-ATPase, the value of is easily changed through controlling viscosity of the solution. h can be controlled by the length of the linker. and k also will be changed by specific ligands such as ADP or ATP analogs, or the mutation.