Electron density maps, validity

Below we briefly describe the crystallographic software pipelines using AutoRickshaw as an example, with its flexibility and the ability to decide on the path to be taken dependent on the outcome of a previous step. On one hand, AutoRickshaw has features and general steps, which are also shared by many other pipelines. On the other hand, AutoRickshaw is perhaps the first software pipeline which aims not at the delivery of a fully built, refined, and validated model but rather at fast evaluation of the quality of the X-ray data in terms of interpretability of the obtained electron density map. 

If, on the other hand, the electron density map calculated at some resolution r is somehow improved in quality in real space, then if it is transformed to produce structure factors, phases at somewhat higher resolution, r + Ar, can be computed that do have some measure of validity. Improvement of an electron density map thus allows gradual extension of phases in reciprocal space to higher resolution, and ultimately to an electron density map of sufficient quality and detail that a model can be constructed. This is another example of those bootstrap, incremental procedures so common to X-ray crystallography. 

On Output, a refinement job will produce a res-file (which is a valid ins-file for the next round of refinement) containing the new description of the model, a pdb-file containing the coordinates of the refined model, an Ist-file containing logging information, and an fcf-file containing stmcture factor moduli and phases for the calculation of electron density maps. The fcf-file can be read directly by Xfit (McRee, 1999) and Coot (Emsley and Cowtan, 2004) or converted into other formats with SHELXPRO. 

Thus, if it is assumed that the local virial theorem is valid for the model electron densities fitted to the experimental structure factors, the kinetic, g(r), and potential, v(r), energy densities may be mapped, as well as the energy characteristics of the (3,-1) bond critical points evaluated [38]. 

There are a number of ways of monitoring the distribution of electron density in any molecular entity. The total density can be computed at a number of points in space and presented as a contour map or some three-dimensional representation. Shifts are easily examined by density difference maps which plot the difference in density between two different configurations. For example, the density shifts caused by H-bond formation can be taken as the difference between the complex on one hand, and the sum of the densities of the two non interacting subunits on the other, with the two species placed in identical positions in either case. Comparisons with x-ray diffraction data have verified the validity of this ap-proach. Also, the total density of the complex itself can be examined for the presence of critical points that indicate H-bonding interactions . 

To show the validity of using Eq. (1) to compute the total electronic energy of a many-electron system, Hohenberg and Kohn, in their famous 1964 paper, presented two proofs that provided the foundation for DFT. In the first, they proved that an external potential (such as classical nuclei distributed in space) is a unique functional of the electron density (apart from a trivial additive constant). For most practical purposes, the converse is true, and the electron density of N electrons in an external potential is considered to result uniquely from that potential. Parr and Yang (1989) give an in-depth discussion of these issues, in addition to providing the staple text on DFT. We also remind the reader that a functional maps a set of functions to a set of numbers, in contrast to a function, which maps one set of numbers to another set of numbers. 

Figure 4. Pictorial representation of 3D-QSAR models. The color code is as follows sterically favourable and unfavourable interactions, green and red regions, respectively favourable and unfavourable influence of high electron density, cyan and yellow zones respectively. To aid interpretation the template 26, idazoxan compounds 35 and 40 have been added to the electrostatic map, whereas clonidine, compounds 5, 8 and 34 are shown in the steric map. n, number of data points q and r, cross-validated and non-cross-validated correlation coefficient, respectively s, standard deviation one, optimal number of components.

Voigt-Martin et al. [13] have used MICE to solve the stmcture of 4-(4 -(N,N-dimethyl)aminobenzylidene)-pyrazolidine-3,5-dione at 1.4A in projection using 42 reflections. The potential maps do not resolve atoms with these data and models have to be fitted to the map density in a way reminiscent of macromolecular crystallography. This can pose problems in structure validation which were overcome in this case by simulation calculations. There is an excellent agreement between the solution and independent model building and high resolution electron microscopy studies. 

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