Coordinate refinement

A molecular dynamics simulation nsnally starts with a molecular structure refined by geometry optimization, but wnthont atomic velocities. To completely describe the dynamics of a classical system con lain in g X atom s, yon m nsl define 6N variables. These correspond to ilX geometric coordinates (x, y, and /) and iSX variables for the velocities of each atom in the x, y, and /. directions. 

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. 

Page 1176 (Figure 28 11) is adapted from crystallographic coordinates deposited with the Protein Data Bank PDB ID 6TNA Sussman J L Holbrook S R Warrant R W Church G M Kim S H Crystal Structure of Yeast Phenylalanine tRNA I Crystallographic Refinement / Mol Biol 1978 126 607 (1978)... 

The atoms of a protein s structure are usually defined by four parameters, three coordinates that give their position in space and one quantity, B, which is called the temperature factor. For well refined, correct structures these B-values are of the order of 20 or less. High B-values, 40 or above, in a local region can be due to flexibility or slight disorder, but also serve as a warning that the model of this region may be incorrect. 

More recently, Grubbs et al. obtained a refined mechanistic picture of the initiating step by conducting a 31P NMR spectroscopic study of the phosphine exchange in precatalysts 12-A. These investigations revealed that substitution of the phosphine proceeds via a dissociative-associative mechanism, i.e., a 14-electron species 12-B is involved that coordinates the alkene to give a 16-electron species 12-C (Scheme 12) [26a]. Increased initiation rates are observed if the substituents R and the phosphine ligands PR3 in precatalysts... 

X-Ray diffraction from single crystals is the most direct and powerful experimental tool available to determine molecular structures and intermolecular interactions at atomic resolution. Monochromatic CuKa radiation of wavelength (X) 1.5418 A is commonly used to collect the X-ray intensities diffracted by the electrons in the crystal. The structure amplitudes, whose squares are the intensities of the reflections, coupled with their appropriate phases, are the basic ingredients to locate atomic positions. Because phases cannot be experimentally recorded, the phase problem has to be resolved by one of the well-known techniques the heavy-atom method, the direct method, anomalous dispersion, and isomorphous replacement.1 Once approximate phases of some strong reflections are obtained, the electron-density maps computed by Fourier summation, which requires both amplitudes and phases, lead to a partial solution of the crystal structure. Phases based on this initial structure can be used to include previously omitted reflections so that in a couple of trials, the entire structure is traced at a high resolution. Difference Fourier maps at this stage are helpful to locate ions and solvent molecules. Subsequent refinement of the crystal structure by well-known least-squares methods ensures reliable atomic coordinates and thermal parameters. 

CNs, the Fe ion is postulated to be coordinated by one SO and a mixture of CO and CNs. The interpretation is based on the temperature factor refinement and pyrolytic analysis of oxidized sulfur species (33). In addition, the bridging ligand is postulated to be an inorganic sulfur ion (instead of an oxo ligand, as proposed for the D. gigas). This... 

There are therefore four adjustable parameters per atom in the refinement (xy, yy, Zj, By). In the computer experiments we have carried out to test the assumptions of the nucleic acid refinement model we have generated sets of observed structure factors F (Q), from the Z-DNA molecular dynamics trajectories. The thermal averaging implicit in Equation III.3 is accomplished by averaging the atomic structure factors obtained from coordinate sets sampled along the molecular dynamics trajectories at each temperature ... 

Structure factors corresponding to 3,195 reflections between lOA and 1.7A were calculated for each of 50 coordinate sets at each temperature. Only the 246 heavy atoms of the hexamer were included in the structure factor calculations hydrogen atoms were not included in the refinement. 

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