Eric Blanc

Real-space molecular-dynamics structure refinement.

Real-space targets and molecular-dynamics search protocols have been combined to improve the convergence of macromolecular atomic refinement. This was accomplished by providing a local real-space target function for the molecular-dynamics program X-PLOR. With poor isomorphous replacement experimental phases, molecular dynamics does not improve real-space refinement. However, with high-quality anomalous diffraction phases convergence is improved at the start of refinement, and torsion-angle real-space molecular dynamics performs better than other available least-squares or maximum-likelihood methods in real or reciprocal space. It is shown that the improvements result from an optimization method that can escape local minima and from a reduction of overfitting through the implicit use of phases and through use of a local refinement in which errors in remote parts of the structure cannot be mutually compensating.

Potential use of real-space refinement in protein structure determination

Through testing refinement protocols using free R-factor estimates of model quality, it is shown that real-space refinement can be a useful addition to conventional reciprocal-space refinement, even for protein structures with poor electron-density maps derived from multiple isomorphous replacement. By alternating real- and reciprocal-space refinements, starting with an experimental map, then calculating 2F(o) - F(c) maps, it is demonstrated with the structure of HMG-CoA reductase, that quick automatic refinement can yield a model with a free R factor 1.5% better than exhaustive reciprocal-space refinement, and within 1% of a model that was interactively rebuilt and refined repeatedly.

DETERMINATION OF THE RELATIVE PRECISION OF ATOMS IN A MACROMOLECULAR STRUCTURE

Several real-space indices and temperature factors are compared with respect to their correlation with atomic positional error and their ability to indicate atoms and residues with the worst of subtle errors. The best index, rED, is a correlation coefficient between model and map electron densities, similar to one proposed earlier, but incorporating two improvements. Firstly, resolution is accounted for explicitly by calculating the model electron density by Fourier transformation of resolution-truncated scattering factors. Secondly, the deviation between model and map electron densities is assigned to neighboring atoms according to their contribution to the electron density of each grid point. With maps of various qualities, rED is the single index with best correlation to atomic error with grouped or individual atoms, and it is the most reliable indicator of poor residues. With poorer omit maps, imprecision of individual atoms is best diagnosed by a combination of low rED or high B factor. With the improved methods, 60-70% of the least precise atoms can detected in a fully refined structure. Similarly, 40-80% of the least precise atoms of an unrefined model can be detected by comparison with an isomorphous replacement map. This is useful in assessing and improving the quality of a model, but not sufficient to confidently validate all atoms of a structure at sub-atomic resolution.

Improved free R factors for cross-validation of macromolecular structure – importance for ­real-­space refinement

Improvements in free R cross-validation are based on changed scaling procedures and the use, in map calculation, of estimates of the validation amplitudes which are independent of the actual observed values. The deleterious effects of the omitted test data are mitigated by reduction of the test-set size, which is made possible by constraining test and working sets to share the same scaling coefficients, thereby reducing the degrees of freedom and the dependence of free R on data selection. Further improvements come with use of a modified free R factor, R freeTA. Instead of omitting the validation reflections from map calculation, their amplitudes are replaced by the average of resolution peers that is (nearly) independent of the actual cross-validation amplitudes. The improvements are relevant to model building, phase refinement by density modification and especially to real-space refinement. Although for real data at about 3 A resolution, free R factors of about 0.25 are affected little, the precision of the structure is improved by about 0.1 A. Tests with simulated data show that with good agreement between observed and calculated amplitudes (as in very high resolution studies or simulated refinement tests), free R factors can be improved by factors greater than two.

RSREF: interactive real-space refinement with stereochemical restraints for use during model-building

Method of solution: All symmetryequivalent atom positions for the full unit cell are generated using the symmetry operators of the given space group. A loop then generates all reflections hk/for the specified range [-hmax, +hrnax], [-kmax, +krnax], [-/max, +/max]For the precession method, however, only one reciprocal lattice layer is generated. Since XRDIFF is primarily designed for the single-crystal methods, no multiplicities are used for the powder methods. All overlapping reflections are correspondingly summed up before the diffractogram or Debye-Scherrer ring pattern is displayed. The latter may correspond to the symmetric or asymmetric film geometry. Various profile shape functions may be used for the calculation of the diffractogram profile. For the calculation of the diffraction intensities, the LPG factors are considered as well as the atomic temperature factors (if given).

On planarity and similarity restraints

Planarity and similarity restraints are described using a unified framework for the computation layout. In both cases, the gradient and Hessian of the restraint residual with respect to atomic coordinates are derived. All computed quantities (residual, gradient, Hessian, normal and distance to the plane for planarity restraints, rotation and translation in the case of similarity) can be obtained directly, without iterative procedure.

Use of Non-Crystallographic Symmetry for Ab Initio Phasing of Virus Structures

Several virus structures have now been determined through ab initio phasing at very low (~20A) resolution followed by extension to high resolution using their non-crystallographic symmetry (NCS). The methods are described, and post-mortem investigations of phase determination are analyzed, particularly for relevance to the more challenging general case of ab initio determination of protein structure.

Real-Space Refinement Using RSRef

Real-space methods for the refinement of macromolecular structures are briefly presented with regard to their most common application, when “experimental” phases are accurate. Recent improvements extend their use to initial stages of protein refinements, when phases are poor. RSRef can also be used interactively to hasten model (re)building and improve the starting point for conventional refinement.