Shape superposition-free

Methods for molecular shape similarity can be roughly divided into two categories those that require finding the optimal superposition of the molecules being compared (superposition-based) and those that, by contrast, are independent of molecular orientation and position (superposition-free). Here we are restricting our focused review to those techniques that have demonstrated to perform shape similarity and its suitability to bioisosteric replacement in small molecules. 

In the superposition-free category, techniques are typically based on exploiting interatomic distances in a way that is independent of molecular orientation and position. One group of superposition-free methods measuring molecular shape was based on atom triplet distances. Bemis and Kuntz [16] devised a method that considered each molecule as the set of its atom triplets. Molecular shape histograms were calculated with the perimeters of the triangle formed by each atom triplet and... 

We note that line shape calculations may be reduced to near trivial proportions if the basic line profile is approximated by one of the better model profiles mentioned in Chapters 5 and 6. This is generally possible, even advantageous, if the van der Waals bound-bound and bound-free transitions do not shape the spectra significantly. In such a case, the spectra are constructed by a simple superposition of the model line profiles, which is done in seconds even if small (desktop type) computers are used. The simplified line shape calculation has been used successfully on many occasions. Early examples are shown in Figs. 3.11, 3.13, and 3.33, but many more are known [58],... 

Results (fig.2) show that the parent material is almost stress free. In the weld pool tensile bulk (around 60 MPa) stresses were found, whereas the opposite occurs in the heat-affected zones (HAZ). Curve shapes are consistent with theoretical and experimental behaviours reported in literature [6,7], and suggest the presence of structure change stresses , according to Macherauch s definition [7], This means that a superposition of the shrinkage stress due to different cooling rates inside and at the borders of the weld, and structural change stresses due to the presence of different phases can be outlined. 

Without subtracting the residual sharp spectral components of spin-labeled ASYN in the presence of SUVs, a multi-component spectral simulation strategy is required in order to describe the experimental data (Fig. 9b, c). Three different contributions featuring different isotropic rotational mobilities can be allocated to free spin labels, labeled residues not bound to SUVs, and residues bound to SUVs by the following approach. The spectra of ASYN in the absence of liposomes are well described by a superposition of two components. Si and S2, where Si corresponds to the spectrum of the free spin label MTSSL measured independently. In the presence of SUVs, an additional component S3 is needed, corresponding to the broadened part of the spectra. The shape of component S3 and the prefactors... 

The temperature dependence of ionic reactions at constant pressure in near-and supercritical water shows a typical non-Arrhenius behavior. If free-radical reactions are important for the global rate, the Arrhenius plot may even become more comphcated by the superposition and interaction of the two mechanisms. Figure 7.8 shows the Arrhenius plot of the glycerol degradation in near- and supercritical water at 45 MPa. Here, the overlay of ionic and free-radical reactions is responsible for such an unusual shape. (For details see [128].)... 

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