Computational modeling crystallographic data

From the regularities mentioned here de Rango et al.I45) designed two general models for helicenes, viz. the triple helical model and the stair case model. In the triple helical model all C-atoms are located on one of three helices an inner helix with (n +1) C-atoms (n = number of benzene rings), a medium helix with (n +1) C-atoms and an outer helix with 2n C-atoms. In general, atoms of helicenes coincide very well with the best helices, obtained by computation from crystallographic data. 

The comparison with experiment can be made at several levels. The first, and most common, is in the comparison of derived quantities that are not directly measurable, for example, a set of average crystal coordinates or a diffusion constant. A comparison at this level is convenient in that the quantities involved describe directly the structure and dynamics of the system. However, the obtainment of these quantities, from experiment and/or simulation, may require approximation and model-dependent data analysis. For example, to obtain experimentally a set of average crystallographic coordinates, a physical model to interpret an electron density map must be imposed. To avoid these problems the comparison can be made at the level of the measured quantities themselves, such as diffraction intensities or dynamic structure factors. A comparison at this level still involves some approximation. For example, background corrections have to made in the experimental data reduction. However, fewer approximations are necessary for the structure and dynamics of the sample itself, and comparison with experiment is normally more direct. This approach requires a little more work on the part of the computer simulation team, because methods for calculating experimental intensities from simulation configurations must be developed. The comparisons made here are of experimentally measurable quantities. 

A topic of actuality is the study of receptor proteins and enzymes for which data bases with crystallographic information are now made available. Computer modelling of the active sites of receptors and enzymes are important tools in rational drug design. Principal components and cluster analysis can be applied to the primary... 

The dispersion and repulsion contributions have been modelled and computed with a variety of approaches [3,8], The most diffused PCM version adopts the procedure developed by Floris and Tomasi [10], based on atom-atom interaction parameters, proposed by Caillet and Claverie from crystallographic data [11] ... 

Computational studies have been of paramount importance in order to integrate the results of the experimental studies indicated above with the electron crystallographic data known. According to Snyder and co-workers, a satisfactory and experimentally verifiable model of the tubulin-binding site and of the conformation of paclitaxel has been obtained by computational methods on the first electron crystallographic model. In this context, a new paclitaxel conformer, T-Taxol (Fig. 10c), was proposed [59, 81, 82],... 

Based on the accumulated crystallographic and adsorption data of PCPs, computational modeling studies of small-molecule adsorption have been performed (an... 

This new family of oxazolidinones was described and shown to effectively displace compounds that bind the ribosomal 50S A-site (linezolid site), including chloramphenicol and Puromycin [80]. The structures of several family members (16-20) are depicted in Scheme 3. The reader is referred to the primary citations for tables of antibacterial activity data (as is the case for all case studies). Compounds such as 17 and 19 were compounds predicted to have good oral bioavailability in the QSAR model [79]. Compounds such as 16 were predicted to have good Haemophilus influenzae activity in that QSAR activity model [79]. The computational and crystallographically inspired design of novel oxazolidinones eventually led to Rib-X Pharmaceuticals clinical candidate, Radezolid (20), currently in Phase II clinical trials [31]. 

When the application of Eq. (11) to a least squares analysis of x-ray structure factors has been completed, it is usual to calculate a Fourier synthesis of the difference between observed and calculated structure factors. The map is constructed by computation of Eq. (9), but now IFhid I is replaced by Fhki - F/f /, where the phase of the calculated structure factor is assumed in the observed structure factor. In this case the series termination error is virtually too small to be observed. If the experimental errors are small and atomic parameters are accurate, the residual density map is a molecular bond density convoluted onto the motion of the nuclear frame. A molecular bond density is the difference between the true electron density and that of the isolated Hartree-Fock atoms placed at the mean nuclear positions. An extensive study of such residual density maps was reported in 1966.7 From published crystallographic data of that period, the authors showed that peaking of electron density in the aromatic C-C bonds of five organic molecular crystals was systematic. The random error in the electron density maps was reduced by averaging over chemically equivalent bonds. The atomic parameters from the model Eq. (11), however, will refine by least squares to minimize residual densities in the unit cell. 

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