Tables for
Volume F
Crystallography of biological macromolecules
Edited by E. Arnold, D. M. Himmel and M. G. Rossmann

International Tables for Crystallography (2012). Vol. F, ch. 18.6, p. 517   | 1 | 2 |

Section 18.6.9. Example: combined maximum-likelihood and simulated-annealing refinement

A. T. Brunger,a* P. D. Adams,b W. L. DeLano,c P. Gros,d R. W. Grosse-Kunstleve,b J.-S. Jiang,e N. S. Pannu,f R. J. Read,g L. M. Riceh and T. Simonsoni

aHoward Hughes Medical Institute, and Departments of Molecular and Cellular Physiology, Neurology and Neurological Sciences, and Stanford Synchrotron Radiation Laboratory (SSRL), Stanford University, 1201 Welch Road, MSLS P210, Stanford, CA 94305, USA,bThe Howard Hughes Medical Institute and Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, CT 06511, USA,cGraduate Group in Biophysics, Box 0448, University of California, San Francisco, CA 94143, USA,dCrystal and Structural Chemistry, Bijvoet Center for Biomolecular Research, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands,eProtein Data Bank, Biology Department, Brookhaven National Laboratory, Upton, NY 11973–5000, USA,fDepartment of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1,gDepartment of Haematology, University of Cambridge, Wellcome Trust Centre for Molecular Mechanisms in Disease, CIMR, Wellcome Trust/MRC Building, Hills Road, Cambridge CB2 2XY, England,hDepartment of Molecular Biophysics and Biochemistry, Yale University, New Haven, CT 06511, USA, and iLaboratoire de Biologie Structurale (CNRS), IGBMC, 1 rue Laurent Fries, 67404 Illkirch (CU de Strasbourg), France
Correspondence e-mail:

18.6.9. Example: combined maximum-likelihood and simulated-annealing refinement

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CNS has a comprehensive task file for simulated-annealing refinement of crystal structures using Cartesian (Brünger et al., 1987[link]; Brünger, 1988[link]) or torsion-angle molecular dynamics (Rice & Brünger, 1994[link]). This task file automatically computes cross-validated [\sigma_{A}] estimates, determines the weighting scheme between the X-ray refinement target function and the geometric energy function (Brünger et al., 1989[link]), refines a flat bulk solvent model (Jiang & Brünger, 1994[link]) and an overall anisotropic B value for the model by least-squares minimization, and subsequently refines the atomic positions by simulated annealing. Options are available for specification of alternate conformations, multiple conformers (Burling & Brünger, 1994[link]), noncrystallographic symmetry constraints and restraints (Weis et al., 1990[link]), and `flat' solvent models (Jiang & Brünger, 1994[link]). Available target functions include the maximum-likelihood functions MLF, MLI and MLHL (Pannu & Read, 1996[link]; Adams et al., 1997[link]; Pannu et al., 1998[link]). The user can choose between slow cooling (Brünger et al., 1990[link]) and constant-temperature simulated annealing, and the respective rate of cooling and length of the annealing scheme. For a review of simulated annealing in X-ray crystallography, see Brünger et al. (1997)[link].

During simulated-annealing refinement, the model can be significantly improved. Therefore, it becomes important to recalculate the cross-validated [\sigma_{A}] error estimates (Kleywegt & Brunger, 1996[link]; Read, 1997[link]) and the weight between the X-ray diffraction target function and the geometric energy function in the course of the refinement (Adams et al., 1997[link]). This is important for the maximum-likelihood target functions that depend on the cross-validated [\sigma_{A}] error estimates. In the simulated-annealing task file, the recalculation of [\sigma_{A}] values and subsequently the weight for the crystallographic energy term are carried out after initial energy minimization, and also after molecular-dynamics simulated annealing.


Adams, P. D., Pannu, N. S., Read, R. J. & Brünger, A. T. (1997). Cross-validated maximum likelihood enhances crystallographic simulated annealing refinement. Proc. Natl Acad. Sci. USA, 94, 5018–5023.
Brünger, A. T. (1988). Crystallographic refinement by simulated annealing: application to a 2.8 Å resolution structure of aspartate aminotransferase. J. Mol. Biol. 203, 803–816.
Brünger, A. T., Adams, P. D. & Rice, L. M. (1997). New applications of simulated annealing in X-ray crystallography and solution NMR. Structure, 5, 325–336.
Brünger, A. T., Karplus, M. & Petsko, G. A. (1989). Crystallographic refinement by simulated annealing: application to crambin. Acta Cryst. A45, 50–61.
Brünger, A. T., Krukowski, A. & Erickson, J. W. (1990). Slow-cooling protocols for crystallographic refinement by simulated annealing. Acta Cryst. A46, 585–593.
Brünger, A. T., Kuriyan, J. & Karplus, M. (1987). Crystallographic R factor refinement by molecular dynamics. Science, 235, 458–460.
Burling, F. T. & Brünger, A. T. (1994). Thermal motion and conformational dis­order in protein crystal structures: comparison of multi-conformer and time-averaging models. Isr. J. Chem. 34, 165–175.
Jiang, J.-S. & Brünger, A. T. (1994). Protein hydration observed by X-ray diffraction: solvation properties of penicillopepsin and neuraminidase crystal structures. J. Mol. Biol. 243, 100–115.
Kleywegt, G. J. & Brünger, A. T. (1996). Checking your imagination: applications of the free R value. Structure, 4, 897–904.
Pannu, N. S., Murshudov, G. N., Dodson, E. J. & Read, R. J. (1998). Incorporation of prior phase information strengthens maximum-likelihood structure refinement. Acta Cryst. D54, 1285–1294.
Pannu, N. S. & Read, R. J. (1996). Improved structure refinement through maximum likelihood. Acta Cryst. A52, 659–668.
Read, R. J. (1997). Model phases: probabilities and bias. Methods Enzymol. 277, 110–128.
Rice, L. M. & Brünger, A. T. (1994). Torsion angle dynamics: reduced variable conformational sampling enhances crystallographic structure refinement. Proteins Struct. Funct. Genet. 19, 277–290.
Weis, W. I., Brünger, A. T., Skehel, J. J. & Wiley, D. C. (1990). Refinement of the influenza virus haemagglutinin by simulated annealing. J. Mol. Biol. 212, 737–761.

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