Simulated annealing refinement

Adams PD et al (1997) Cross-validated maximum likelihood enhances crystallographic simulated annealing refinement. Proc Natl Acad Sci USA 94(10) 5018-5023... 

One possibility is to run simulated annealing refinement in torsion angle space as implemented in CNS (Briinger et ah, 1998). As this is one of the most powerful programs in terms of radius of convergence, it is especially useful to look for the decrease of the free-R-factor (Adams et al., 1999), but this is a rather cpu-intensive task if several possible solutions are to be tested. 

FIGURE 10.12. Diagram of a local and global minimum during refinement. Not that the ordinates are the R vale in the least-squares refinement, or the energy in the simulated annealing refinement. This emphasizes that the R value is not the only indicator of the correctness of a structure that can be used. 

Figure 3. The segment consisting of residues Cys-192 and His-193 of the 2.8 A resolution structure of a single site mutant of aspartate aminotransferase [23]. Superimposed are the initial structure (dotted lines) obtained by fitting the atomic model to a multiple isomorphous replacement map, the structure obtained after several cycles of rebuilding and restrained least-squares refinement (thick lines), the structure obtained after simulated annealing refinement (thin lines), and the structure obtained after conjugate gradient minimization (dashed lines).

Simulated annealing refinement is most useful when the initial model is relatively crude. Given a well-refined model, it offers little advantage over conventional methods, with the possible exception of providing information about the accuracy and conformational variability of the refined structure [63]. However, when only a crude model is available, simulated annealing refinement is able to greatly reduce the amount of human intervention required. The initial model can be as crude as one that is obtained by automatic building based on positions alone [64]. 

Simulated annealing refinement can produce R values in the twenties for partially incorrect structures. For example, after refinement of the protease from human immunodeficiency virus HIV-1 a partially incorrect structure [65] produced an R value of 0.25 whereas the correct structure produced a R value of 0.184 [66] with comparable geometry. 

The goal of any optimization problem is to find the global minimum of a target function. In the case of crystallographic refinement, one searches for the conformation or conformations of the molecule that best fit the diffraction data at the same time that they maintain reasonable covalent and non-covalent interactions. As the above examples have shown, simulated annealing refinement has a much larger radius of convergence than... 

Simulated annealing refinement is usually unable to correct very large errors in the atomic model or to correct for missing parts of the structure. The atomic model needs to be corrected by inspection of a difference Fourier map. In order to improve the quality and resolution of the difference map, the observed phases are often replaced or combined with calculated phases, as soon as an initial atomic model has been built. These combined electron density maps are then used to improve and to refine the atomic model. The inclusion of calculated phase information brings with it the danger of biasing the refinement process towards the current atomic model. This model bias can obscure the detection of errors in atomic models if sufficient experimental phase information is unavailable. In fact during the past decade several cases of incorrect or partly incorrect atomic models have been reported where model bias may have played a role [67]. 

Difference maps phased with simulated annealing refined structures often show more details of the correct chain trace [23]. However, the omission of some atoms from the computation of a difference map does not fully remove phase bias towards those atoms if... 

In general, the improvement of the electron density map achieved in simulated annealing refinement is a consequence of conformational changes distributed throughout the molecule. This is a reflection of the fact that the first derivatives of the crystallographic residual (Eq. 1) with respect to the coordinates of a particular atom depend not only on the coordinates of that atom and its neighbors but also on the coordinates of all other atoms including solvent atoms in the crystal structure. 

Korostelev, A., Laurberg, M., Noller, H.F. Multistart simulated annealing refinement of the crystal structure of the 70s ribosome. Proc. Natl. Acad. Sci. USA 2009,106(43), 18195. 

Figure 4 Dials plots for selected residues from one of the test cases used by Stein et al. (a) Conformational sampling over the course of a torsion angle dynamics refinement, (b) Conformational sampling over the course of a Cartesian molecular dynamics simulated annealing refinement...

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