Electron density maps 250 INDEX

The difference electron density map following the last cycle of least squares refinement did not show evidence for a simple disorder model to explain the anomalously high B for the hydroxyl oxygen. Attempts to refine residual peaks with partial oxygen occupancies did not significantly improve the agreement index. 

Fig. 15. Intensity profiles along the equator of the bony fish muscle low angle X-ray diffraction pattern from muscles at rest (A), fully active (B), and in rigor (C). The indexing in (A) is based on the hexagonal A-band lattice, and the arrows indicate peaks that come from the Z-band. (C) to (F) are computed electron density maps based on the amplitudes of the A-band peaks in (A) to (A), respectively. The simple lattice unit cell is outlined in (D). (From Harford and Squire, 1997.)...

In Sect. 5.2.1 the structural properties of the two columnar phases Coli and C0I2 formed by mixtures of C50 and water or formamide are discussed. In this appendix details on the indexation of their X-ray diffraction patterns as weU as on the calculation of the electron density map of the Coli phase are given. 

Fig. 9.31 (a) Intensity profile of SR SAXS reflections with the Lorentz correction red circle) observed for the powder X3 sample. The numbers given on the figure are the (hkO) indexes. In (b), most probable reconstitution of the electron density map for the X3 phase by the nine, reflections with the phase differences. The map indicates that the cylindrical rods packed into the hexagonal lattice are constructed of two concentric cylinders as illustrated in (c). The cylindrical association is also supported by AFM topography image of (d) observed on the surface of the fan-shaped domain in the X3 phase... 

The final result of structure determination is a coordinate, or protein database (pdb) file, that describes the model that was built from the scattering data/electron density map. This file contains the Cartesian coordinates for the protein, any bound ligands, numerous water molecules, as well as any other atoms/ molecules whose positions are relatively fixed in the crystal. The accuracy of this model can be assessed using a number of parameters, including (i) a comparison of the R-factor to the free R-factor, (ii) the temperature (or B) factor, and (iii) the number of Ramachandran outliers. Although these factors can be combined to form a single quality index (Brown and Ramaswamy, 2007), it is useful to discuss the individual parameters since these parameters can often be directly obtained from the downloaded coordinate file. 

Graphical Models are introduced and illustrated in Chapter 4. Among other quantities, these include models for presentation and interpretation of electron distributions and electrostatic potentials as well as for the molecular orbitals themselves. Property maps, which typically combine the electron density (representing overall molecular size and shape) with the electrostatic potential, the local ionization potential, the spin density, or with the value of a particular molecular orbital (representing a property or a reactivity index where it can be accessed) are introduced and illustrated. 

The crude molecular image seen in the F0 map, which is obtained from the original indexed intensity data (IFobsI) and the first phase estimates (a calc), serves now as a model of the desired structure. A crude electron density function is devised to describe the unit-cell contents as well as they can be observed in the first map. Then the function is modified to make it more realistic in the light of known properties of proteins and water in crystals. This process is called, depending on the exact details of procedure, density modification, solvent leveling, or solvent flattening. 

A particular mapping -> is determined by the Kohn-Sham construction (KSC) minimize the kinetic energy orbital functional T = JT(j t i) for specified spin-indexed electron density p. This applies Hohenberg-Kohn logic to a... 

For both types of FIDCO surfaces, the usual Shape Group method [2] of electron density shape analysis is applicable. The additional formal domain boundaries AD i(Ga b(3)) and AD i(GA(B)(a)) introduce one additional index -1, which can be treated the same way as relative curvature indices. The one-dimensional homology groups obtained by truncations using all possible index combinations are the shape groups of FIDCO surfaces. The (a,b)-parameter maps and shape codes are generated the same way as for complete molecules [2],... 

In many instances, the relaxation terms, <]>, can be ignored, and the frontier molecular orbital theory as first put forth by Fukui - is recovered. For particular molecules, the identification reactive sites using f(t) has been successful.A convenient way to visualize the reactive sites in a molecule using the above reactivity index is to first display an isosurface of the electron density that just encloses the van der JKials volumes of the individual atoms in the molecule. Typically, the value of this isosurface is between 0.002 and 0.005. Next, the values of the reactivity index are mapped upon this surface and color coded from blue (zero) to ted (most positive). 

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