Russian version English version
Volume 1   Issue 1   Year 2006
Lunin V.Y., Afonine P.V., Urzhumtsev A.G.

Statistical Modelling and Likelihood-based Choice in Macromolecular Crystallography

Mathematical Biology & Bioinformatics. 2006;1(1):17-26.

doi: 10.17537/2006.1.17.


  1. Bricogne G. Maximum Entropy and the Foundations of Direct Methods. Acta Cryst. 1984;A40:410-455. doi: 10.1107/S0108767384000866
  2. Bricogne G, Gilmore CJ. A multisolution method of phase determination by combined maximization of entropy and likelihood. I. Theory, algorithms and strategy. Acta Cryst. 1990;A46:284-297. doi: 10.1107/S0108767389012882
  3. Bricogne G, Irwin J. Maximum-Likelihood Refinement of incomplete models with BUSTER + TNT. In: Proceedings of the CCP4 Study Weekend. Daresbury Laboratory. Warrington, England; 1996. P. 85-92.
  4. CochranW. Relations between the phases of structure factors. Acta Cryst. 1955;5:473–478. doi: 10.1107/S0365110X55001485
  5. Giacovazzo C. Direct Phasing in Crystallography. Oxford: Oxford University Press.; 1999.
  6. Hauptman H, Karle J. Solution of the phase problem. I. The centrosymmetric crystal: American Crystallographic Association Monograph, 3. Wilmington: The Letter Shop; 1953.
  7. Lunin VYu, Urzhumtsev AG. Improvement of Protein Phases by Coarse Model Modification. Acta Cryst. 1984;A40:269-277. doi: 10.1107/S0108767384000544
  8. Lunin VYu, Skovoroda TP. R-free Likelihood-Based Estimates of Errors for Phases Calculated from Atomic Models. Acta Cryst. 1995;A51:880-887. doi: 10.1107/S010876739500688X
  9. Lunin VYu, Lunina NL, Petrova TE, Urzhumtsev AG, Podjarny AD. On the Ab initio solution of the Phase Problem for Macromolecules at Very Low Resolution. II. Generalized Likelihood Based Approach to Cluster Discrimination. Acta Cryst. 1998;D54:726-734.
  10. Lunin VY. The likelihood based choice of priors in statistical approaches to the phase problem. In: Direct Methods for Solving Macromolecular Structures. Ed. S.Fortie. The Netherlands: Kluwer Academic Publishers; 1997. V. 507. P. 451-454 (NATO ASI Series C).
  11. Lunin VY, Lunina NL, Petrova TE, Skovoroda TP, Urzhumtsev AG, Podjarny AD. Low-resolution ab initio phasing: problems and advances. Acta Cryst. 2000;D56:1223-1232.
  12. Lunin VY, Urzhumtsev AG. Maximal Likelihood Refinement. It works, but why? CCP4 Newsletter on Protein Crystallography. 1999;37:14-28.
  13. Lunin VY, Afonine PV, Urzhumtsev AG. Likelihood-based refinement. I. Irremovable model errors. Acta Cryst. 2002;A58:270-282. doi: 10.1107/S0108767302001046
  14. Luzzati V. Traitement Statistique des Erreurs dans la Determination des Structures Cristallines. Acta Cryst. 1952;5:802-810. doi: 10.1107/S0365110X52002161
  15. Murshudov GN, Vagin AA, Dodson EJ. Refinement of Macromolecular Structures by the Maximum-Likelihood Method. Acta Cryst. 1997;D53:240-255.
  16. Pannu NS, Read RJ. Improved Structure Refinement Through Maximum Likelihood. Acta Cryst. 1996;A52:659-668. doi: 10.1107/S0108767396004370
  17. Petrova TE, Lunin VY, Podjarny AD. A likelihood-based search for the macromolecular position in the crystalline unit cell. Acta Cryst. 1999;A55:739-745. doi: 10.1107/S0108767399001890
  18. Petrova TE, Lunin VY, Podjarny AD. Ab initio low-resolution phasing in crystallography of macromolecules by maximization of likelihood. Acta Cryst. 2000;D56:1245-1252.
  19. Read RJ. Improved Fourier Coefficients for Maps Using Phases from Partial Structures with Errors. Acta Cryst. 1986;A42:140-149. doi: 10.1107/S0108767386099622
  20. Read RJ. Structure-Factor Probabilities for Related Structures. Acta Cryst. 1990;A46:900-912. doi: 10.1107/S0108767390005529
  21. Sheldrick GM, Hauptman HA, Weeks CM, Miller R, Usón I. Direct methods. In: International Tables for Crystallography, Vol. F. Eds. Rossmann M, Arnold E. Dordrecht Boston London: Kluwer Academic Publishers; 2001. P. 333-345. doi: 10.1107/97809553602060000689
  22. Srinivasan R, Parthasarathy S. Some Statistical Applications in X-ray Crystallography. Oxford: Pergamon Press; 1976.
  23. Wilson AJC. The Probability Distribution of X-ray Intensities. Acta Cryst. 1949;2:318-321. doi: 10.1107/S0365110X49000813
  24. Woolfson MM. The statistical theory of sign relationship. Acta Cryst. 1954;7:61-64. doi: 10.1107/S0365110X54000102
Table of Contents Original Article
Math. Biol. Bioinf.
doi: 10.17537/2006.1.17
published in Russian

Abstract (rus.)
Abstract (eng.)
Full text (rus., pdf)
References Translation into English
Math. Biol. Bioinf.
doi: 10.17537/2006.1.t12

Full text (eng., pdf)


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