New applications of maximum likelihood and Bayesian statistics in macromolecular crystallography

Current Opinion in Structural Biology

Volumn 12, Issue 5, 2002, Pages 670-673

  McCoy, Airlie J ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ACCURACY; BAYES THEOREM; CALCULATION; CHEMICAL STRUCTURE; CRYSTALLOGRAPHY; DENSITY; HISTOGRAM; MACROMOLECULE; MODEL; NORMAL DISTRIBUTION; PRIORITY JOURNAL; REVIEW;

EID: 0036816461     PISSN: 0959440X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0959-440X(02)00373-1     Document Type: Review

References (41)

1. Molina E.C. Two Papers by Bayes with Commentaries. 1963;Hafner Publishing Company, New York.
2. Bricogne G. Bayesian statistical viewpoint on structure determination: basic concepts and examples. Methods Enzymol. 276:1996;361-423.
3. La Fortelle E., Bricogne G. Maximum-likelihood heavy-atom parameter refinement for multiple isomorphous replacement and multiwavelength anomalous diffraction methods. Methods Enzymol. 276:1997;472-494.
4. Pannu N., Murshudov G., Dodson E., Read R. Incorporation of prior phase information strengthens maximum-likelihood structure refinement. Acta Crystallogr. D54:1998;1285-1294.
5. Pannu N., Read R. Improved structure refinement through maximum likelihood. Acta Crystallogr. A52:1996;659-668.
6. Murshudov G., Vagin A., Dodson E. Refinement of macromolecular structures by the maximum-likelihood method. Acta Crystallogr. D53:1997;240-255.
7. Bricogne G., Irwin J. Macromolecular refinement. Dodson E.M., Ralf A., Bailey S. Proceedings of the CCP4 Study Weekend. 1996;85-92 Daresbury Laboratory, Daresbury, UK.
8. Read R. Pushing the boundaries of molecular replacement with maximum likelihood. Acta Crystallogr. D57:2001;1373-1382. This paper describes the maximum likelihood rotation and translation functions, including how to introduce information about partial models.
9. Terwilliger T. Reciprocal-space solvent flattening. Acta Crystallogr. D55:1999;1863-1871.
10. Terwilliger T. Maximum-likelihood density modification. Acta Crystallogr. D56:2000;965-972. This paper builds on the map probability function described in [9] (which introduces the Bayesian theory of the map probability function for solvent flattening and derives the derivatives of the map probability function with respect to the structure factors). The map probability function is extended to include histogram matching.
11. Terwilliger T. Maximum-likelihood density modification using pattern recognition of structural motifs. Acta Crystallogr. D57:2001;1755-1762. This paper describes a map probability function for solvent flattening, histogram matching and pattern recognition of helices.
12. Terwilliger T. Map-likelihood phasing. Acta Crystallogr. D57:2001;1763-1775. This paper describes the use of map probability functions for the removal of model bias ('prime-and-switch' phasing).
13. Cowtan K. General quadratic functions in real and reciprocal space and their application to likelihood phasing. Acta Crystallogr. D56:2000;1612-1621. This paper describes the general principle of converting Gaussian probability distributions in one space (real or reciprocal) to Gaussian probability distributions in the other space using the Fourier transform.
14. Read R.J., Fujinaga M. Experiences with a new translation-function program. Acta Crystallogr. D20:1987;517-521.
15. Vagin A., Teplyakov A. MOLREP: an automated program for molecular replacement. J Appl Crystallogr. 30:1997;1022-1025.
16. Grosse-Kunstleve R., Adams P. Patterson correlation methods: a review of molecular replacement with CNS. Acta Crystallogr. D57:2001;1390-1396.
17. Navaza J. Implementation of molecular replacement in AmoRe. Acta Crystallogr. D57:2001;1367-1372.
18. Kissinger C., Gehlhaar D., Smith B., Bouzida D. Molecular replacement by evolutionary search. Acta Crystallogr. D57:2001;1474-1479.
19. Glykos N., Kokkinidis M. Multidimensional molecular replacement. Acta Crystallogr. D57:2001;1462-1473.
20. Sim G. The distribution of phase angles for structures containing heavy atoms. II. A modification of the normal heavy-atom method for non-centrosymmetrical structures. Acta Crystallogr. 12:1959;813-815.
21. Wilson A. The probability distribution of X-ray intensities. Acta Crystallogr. 2:1949;318-321.
22. Hendrickson W.A., Ward K.B. A packing function for delimiting the allowable locations of crystallized macromolecules. Acta Crystallogr. A32:1976;778-780.
23. Harada Y., Lifchitz A., Jolles P. A translation function combining packing and diffraction information: an application to lysozyme (high-temperature form). Acta Crystallogr. A37:1981;398-406.
24. Stubbs M.T., Huber R. An analytical packing function employing Fourier transforms. Acta Crystallogr. A47:1991;521-526.
25. Xiang S., Carter C.J., Bricogne G., Gilmore C. Entropy maximization constrained by solvent flatness: a new method for macromolecular phase extension and map improvement. Acta Crystallogr. D49:1993;193-212.
26. Zhang K. K.C.P.M: Combining constraints for electron-density modification. Methods Enzymol. 277:1997;53-64.
27. Abrahams J., Leslie A. Methods used in the structure determination of bovine mitochondrial F1 ATPase. Acta Crystallogr. D52:1996;30-42.
28. Abrahams J. Bias reduction in phase refinement by modified interference functions: introducing the γ-correction. Acta Crystallogr. D53:1997;371-376.
29. Bricogne G. Maximum entropy and the foundations of direct methods. Acta Crystallogr. A40:1984;410-445.
30. Bèran P., Szöke A. Simulated annealing for phasing using spatial constraints. Acta Crystallogr. A51:1995;20-27.
31. Bricogne G. A Bayesian statistical theory of the phase problem. I. A multichannel maximum-entropy formalism for constructing generalized joint probability distributions of structure factors. Acta Crystallogr. A44:1988;57-68.
32. Cowtan K., Main P. Improvement of macromolecular electron-density maps by the simultaneous application of real and reciprocal space constraints. Acta Crystallogr. D49:1993;148-157.
33. Cowtan K., Main P. Phase combination and cross validation in iterated density-modification calculations. Acta Crystallogr. D52:1996;43-48.
34. Lunin V. Electron-density histograms and the phase problem. Acta Crystallogr. D49:1993;90-99.
35. Roberts A., Brünger A. Phase improvement by cross-validated density modification. Acta Crystallogr. D51:1995;990-1002.
36. Wang B.-C. Resolution of phase ambiguity in macromolecular crystallography. Methods Enzymol. 115:1985;90-112.
37. Misra S., Puertollano R., Kato Y., Bonifacino J.S., Hurley J.H. Structural basis for acidic-cluster-dileucine sorting-signal recognition by VHS domains. Nature. 415:2002;933-937.
38. Buckler D.R., Zhou Y.C., Stock A.M. Evidence of intradomain and interdomain flexibility in OmpR/PhoB homolog from Thermotoga maritima. Structure. 10:2002;153-164.
39. Davies D.R., Interthal H., Champoux J.J., Hol W.G.J. The crystal structure of human tyrosyl-DNA phosphodiesterase, Tdp1. Structure. 10:2002;237-248.
40. Qiu C., Sawada K., Zhang X., Cheng X.D. The PWWP domain of mammalian DNA methyltransferase Dnmt3b defines a new family of DNA-binding folds. Nat Struct Biol. 9:2002;217-224.
41. + revealed by the atomic resolution structure of FprA, a Mycobacterium tuberculosis oxidoreductase. Biochemistry. 41:2002;8807-8818.