X-ray refinement

Traditionally, least-squares methods have been used to refine protein crystal structures. In this method, a set of simultaneous equations is set up whose solutions correspond to a minimum of the R factor with respect to each of the atomic coordinates. Least-squares refinement requires an N x N matrix to be inverted, where N is the number of parameters. It is usually necessary to examine an evolving model visually every few cycles of the refinement to check that the structure looks reasonable. During visual examination it may be necessary to alter a model to give a better fit to the electron density and prevent the refinement falling into an incorrect local minimum. X-ray refinement is time consuming, requires substantial human involvement and is a skill which usually takes several years to acquire. 

The additional penalty function that is added to the empirical potential energy function in restrained dynamics X-ray refinement has the form ... 

Normal Mode Analysis of Biological Molecules A. Normal Mode X-Ray Refinement... 

In the procedure of X-ray refinement, the positions of the atoms and their fluctuations appear as parameters in the structure factor. These parameters are varied to match the experimentally determined strucmre factor. The term pertaining to the fluctuations is the Debye-Waller factor in which the atomic fluctuations are represented by the atomic distribution tensor ... 

The methods discussed in this section extend the original concept of deriving structures from experimental NMR data in two ways. First, during the structure calculation, part of the assignment problem is solved automatically. This allows specification of the NOE data in a fonn closer to the raw data, which makes the refinement similar to X-ray refinement. Second, the quality of the data is assessed. The methods have been recently reviewed in more detail [64,67]. 

Methods for simulating restrained x>ray refinement data from molecular dynamics trajectories. 

Coppens, P., Guru, T.N., Leung, P., Stevens, E.D., Becker, P. and Yang, Y. (1979) Atomic net charges and molecular dipole moments from spherical-atom X-ray refinement and the relation between atomic charge and shape, Acta Cryst. A, 35, 63-72. 

Keywords X-ray crystallography, X-ray refinement, Protein-ligand complexes, Orf2... 

In the next section, we first give a brief overview of the QM (QM/MM) X-ray refinement methodology and implementation, which has been reported previously and then follow this with the case study. 

There are two distinct stereochemical possibilities for the helix which are consistent with the intensity distribution. One of them is a 2-fold single-helix of pitch 19.6A and the other a 4-fold, half-staggered, parallel, double-helix of pitch 39.2A. The doublehelix could be right- or left-handed. In all cases, there is considerable conformational mobility about the (1- 6) linkage of the disaccharide side chain. Preliminary models have been built for each possibility and, due to insufficient diffraction data, detailed x-ray refinements have not been conducted for any of them. 

The electrostatic Hellmann-Feynman theorem states that for an exact electron wave function, and also of the Hartree-Fock wave function, the total quantum-mechanical force on an atomic nucleus is the same as that exerted classically by the electron density and the other nuclei in the system (Feynman 1939, Levine 1983). The theorem thus implies that the forces on the nuclei are fully determined once the charge distribution is known. As the forces on the nuclei must vanish for a nuclear configuration which is in equilibrium, a constraint may be introduced in the X-ray refinement procedure to ensure that the Hellmann-Feynman force balance is obeyed (Schwarzenbach and Lewis 1982). 

If one ignores the X-ray intensities and sets all wto zero in eqn. (xxiv) one, in effect, builds a model to certain sterochemical specifications. This is indeed how initial models for subsequent X-ray refinement can most conveniently be created. 

For example, when the number of reflections is small, pure x-ray refinement may introduce unacceptable stereochemical, features. 

Among the chief disadvantages is the fact that when the calculation of the function is slow, the refinement proceeds slowly. For instance, in x-ray refinement the computation of R" (or R) is lengthy, particularly when the number of reflections and the number of variables are both large. This disadvantage is, however, not serious as the increased demand on computer time is still within reasonable limits established by most computer shops. 

There is continuous progress in molecular dynamics and energy minimization. The main topics are force field improvement [26,53-56], incorporation of effective solvation term [57], b Initio modeling of small protein [49—5155.59], the incorporation of real data for x-ray refinement [60] and NMR structure determination [61], However, much work still has to be done to improve the force fields used for ensr"1 calculations before sn,r but trivial errors be detected... 

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