Three-dimensional refinement

Unfortunately, many of the structures that we have described have been determined using two-dimensional X-ray crystal analysis only. Although in favourable cases this method can be extremely powerful, and indeed until about ten years ago was almost the only practicable method, yet its accuracy and reliability are far below what can now be achieved by complete three-dimensional analysis. With the increasing availability of high-speed computational facilities and more accurate means of data collection, three-dimensional refinement of the more important structures could now be undertaken. A great field of interesting and important work therefore awaits the modern crystallographer, and we may soon expect results of an accuracy sufficient to provide critical tests of diverse theoretical treatments. 

K. N. Trueblood, E. Goldish, and J. Donohue. A three-dimensional refinement of the crystal structure of 4-nitroaniline, Acta Crystallogr., Sect. A 14, 1009-1017 (1961). 

Table 2 lists interatomic distances found in X-ray diffraction analyses of mystals of amino-acids, peptides, and compounds of urea. These structure determinations, aU but two of which are based upon three-dimensional refinement of the atomic parameters, are probably the most reliable sources of the distances which characterize the amide group. We are indebted to the authors for permission to present throughout this paper the results of the analyses of ni.-serine. 

Table 2. Bond lengths of the aiode gbottf as debtved from those found IN crystals of AHmO-AdDS, PEPTIDES AND BELATED COMPOUNDS An asterisk indicates three-dimensional refinement of the atomic positions.

A particularly important application of molecular dynamics, often in conjunction with the simulated annealing method, is in the refinement of X-ray and NMR data to determine the three-dimensional structures of large biological molecules such as proteins. The aim of such refinement is to determine the conformation (or conformations) that best explain the experimental data. A modified form of molecular dynamics called restrained moleculai dynarrdcs is usually used in which additional terms, called penalty functions, are added tc the potential energy function. These extra terms have the effect of penalising conformations... 

Step 11. At this point a computer program refines the atomic parameters of the atoms that were assigned labels. The atomic parameters consist of the three position parameters x,j, and for each atom. Also one or six atomic displacement parameters that describe how the atom is "smeared" (due to thermal motion or disorder) are refined for each atom. The atomic parameters are varied so that the calculated reflection intensities are made to be as nearly equal as possible to the observed intensities. During this process, estimated phase angles are obtained for all of the reflections whose intensities were measured. A new three-dimensional electron density map is calculated using these calculated phase angles and the observed intensities. There is less false detail in this map than in the first map. 

The first step for any structure elucidation is the assignment of the frequencies (chemical shifts) of the protons and other NMR-active nuclei ( C, N). Although the frequencies of the nuclei in the magnetic field depend on the local electronic environment produced by the three-dimensional structure, a direct correlation to structure is very complicated. The application of chemical shift in structure calculation has been limited to final structure refinements, using empirical relations [14,15] for proton and chemical shifts and ab initio calculation for chemical shifts of certain residues [16]. 

Figure 17.2 An example of prediction of the conformations of three CDR regions of a monoclonal antibody (top row) compared with the unrefined x-ray structure (bottom row). LI and L2 are CDR regions of the light chain, and HI is from the heavy chain. The amino acid sequences of the loop regions were modeled by comparison with the sequences of loop regions selected from a database of known antibody structures. The three-dimensional structure of two of the loop regions, LI and L2, were in good agreement with the preliminary x-ray structure, whereas HI was not. However, during later refinement of the x-ray structure errors were found in the conformations of HI, and in the refined x-ray structure this loop was found to agree with the predicted conformations. In fact, all six loop conformations were correctly predicted in this case. (From C. Chothia et al.. Science 233 755-758, 1986.)...

X-ray structures are determined at different levels of resolution. At low resolution only the shape of the molecule is obtained, whereas at high resolution most atomic positions can be determined to a high degree of accuracy. At medium resolution the fold of the polypeptide chain is usually correctly revealed as well as the approximate positions of the side chains, including those at the active site. The quality of the final three-dimensional model of the protein depends on the resolution of the x-ray data and on the degree of refinement. In a highly refined structure, with an R value less than 0.20 at a resolution around 2.0 A, the estimated errors in atomic positions are around 0.1 A to 0.2 A, provided the amino acid sequence is known. 

Over the years, this concept was refined in several ways. A scale dependency was modeled by the introduction of scale-dependent quenching of combustion. The first stage of the process was simulated by quasi-laminar flame propagation. In addition, three-dimensional versions of the code were developed (Hjertager 1985 Bakke 1986 Bakke and Hjertager 1987). Satisfactory agreement with experimental data was obtained. 

Three-dimensional structures of Escherichia coli and cat muscle PK had been refined. These studies disclose the essential residues that determine the relative orientations of domains and the precise nature of intersubunit contacts (A3, M15). 

A3. Allen, S., and Muirhead, H Refined three-dimensional structure of cat-muscle (Ml) pyruvate kinase at a resolution of 2.6 A. Acta Crystallogr., Sect. D Biol. Crystallogr. D52, 499-504 (1996). 

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