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Refinement of Macromolecular Structures by the Maximum-Likelihood Method

Garib N. Murshudov; A. A. Vagin; E. J. Dodson · Acta Crystallographica Section D Biological Crystallography · 1997

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Author / responsible party
Garib N. Murshudov; A. A. Vagin; E. J. Dodson
Publisher
Acta Crystallographica Section D Biological Crystallography
Year
1997
Language
English

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This paper reviews the mathematical basis of maximum likelihood. The likelihood function for macromolecular structures is extended to include prior phase information and experimental standard uncertainties. The assumption that different parts of a structure might have different errors is considered. A method for estimating sigma(A) using 'free' reflections is described and its effects analysed. The derived equations have been implemented in the program REFMAC. This has been tested on several proteins at different stages of refinement (bacterial alpha-amylase, cytochrome c', cross-linked insulin and oligopeptide binding protein). The results derived using the maximum-likelihood residual are consistently better than those obtained from least-squares refinement.

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APA 7

Murshudov, G. N, Vagin, A. A, & Dodson, E. J. (1997). Refinement of Macromolecular Structures by the Maximum-Likelihood Method. https://doi.org/10.1107/s0907444996012255

MLA

Murshudov, Garib N, et al. "Refinement of Macromolecular Structures by the Maximum-Likelihood Method." 1997. https://doi.org/10.1107/s0907444996012255.

Chicago

Murshudov, Garib N, A. A. Vagin, and E. J. Dodson. 1997. "Refinement of Macromolecular Structures by the Maximum-Likelihood Method.". https://doi.org/10.1107/s0907444996012255.

Harvard

Murshudov, G. N, Vagin, A. A. and Dodson, E. J. 1997, Refinement of Macromolecular Structures by the Maximum-Likelihood Method, Acta Crystallographica Section D Biological Crystallography, available at: https://doi.org/10.1107/s0907444996012255 [Accessed 7 Aug. 2026].

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Title
Refinement of Macromolecular Structures by the Maximum-Likelihood Method
Author / contributors
Garib N. Murshudov; A. A. Vagin; E. J. Dodson
Publisher
Acta Crystallographica Section D Biological Crystallography
Publication year
1997
Language
English

Subjects

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Maximum likelihood; Likelihood function; Function (biology); Mathematics; Basis (linear algebra); Least-squares function approximation; Residual; Applied mathematics; Macromolecule; Statistics; Computer science; Algorithm
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