Local descriptors

However, the behavior of the local descriptors of reachvity is somewhat different. The local quantities are calculated using the Lowdin-based method of population analysis [47], It was observed that when the electric held is applied toward the more electronegative atom of the systems HF and HCN, the value of its nucleophilicity (CFF for electrophilic attack) decreases with increasing held strength (Figure 25.2c). The variation of FF can be well supported with the variation in the induced dipole moment, given in Table 25.1, of the species in... 

Chemical Information, Irvine CA Tripos, Inc. St. Louis MO), similarity searching can be carried out around a well-defined compound class using local descriptors such as atom pairs [46, 47] or topomeric shape [48, 49]. Also, ligand-based pharmacophore searches are able to identify follow-up compounds that are less obvious and more diverse than similarity searches [30, 50-54]. The problem with the latter methods is defining the molecular shape or pharmacophore specifically enough to be useful when there are few hits within a compound class and they cannot be reliably aligned (as is often the case for NMR hits in the absence of detailed structural information). 

This model can subsequently be used to predict the activity estimates for new structures. In addition, it can provide information concerning the influence on activity for each local descriptor in different positions of the structure, which can be useful for the lead optimization, the analysis of action mechanism, and the detection of relevant 3D alignment anchors. 

As an example, let us consider the MFTA model of the HIV-1 reverse transcriptase inhibition by the tetrahydroimidazobenzodiazepinone (TIBO) derivatives. The model is based on the atomic charge Q, atomic van der Waals radius R and group lipophilicity Lg as the local descriptors (V=73, Np=5, i = 0.887, g = 0.686). Figure 5.5 shows the molecular supergraph with the superimposed structure of one training set compound. 

Figure 5.7 shows the major contributions of the local descriptors to activity and selectivity. As can be seen, the activity and selectivity maps are quite similar but also differ. Such fine distinctions are difficult to take into account to design new promising structures intuitively (especially if selectivity with respect to other receptor subtypes is also required). Thus, the automated virtual screening approach is preferred. 

Figure 5.7 Major local descriptor contributions to the MFTA models of activity a) and selectivity b) for the A3 adenosine receptor agonists.

After predicting the activity and selectivity values by means of the MFTA models, the compounds with unreliable predictions were filtered from the virtual screening set using the outlier rating values (Section 5.2.2.6) for two predictions (the threshold value was 30). As a result, a set of 50 structures was obtained. Figure 5.8 shows the distribution of the predicted values. Only one compound is predicted to provide better selectivity than the training set structures as well as reasonable activity. The local descriptor values for this adenosine derivative indeed match the descriptor impacts identified by the MFTA-based selectivity model. 

The calculated retention is compared with the experimental value in Table 1. From a statistical point of view, the improvement when using the rotamer with better fit is insignificant (Fg g = 1.26 and 1.07) and the assumption could be considered as disputable. This can be explained by the small number of compounds that are able to rotate around the cr-bond in the total matrix. Independent of the reliability of the assumption, a beneficial conclusion can be drawn from Eqs. (l)-(3). They demonstrate that the retentions of the studied benzene derivatives are governed in the studied cases only by local descriptors and predominately by the local descriptors for the — O — atom in the hydroxyl group. The connectivity index used in many studies (e.g.. Ref. 5) showed, in the studied case, a correlation coefficient of only 0.285. 

Another conclusion from Eq. (4) is that benzodiazepine s retention, again, is governed by local descriptors (about 65% contribution of DD[5])... 

The maximum value entry in the ith row is a local descriptor called the geometric eccentricity representing the longest geometric distance from the ith vertex to any other vertex in the molecule ... 

Because of the discontinuity of this derivative, a backward Fukui function f"(r) and a forward Fukui function f (r) are defined, corresponding to local descriptors for electrophilic and nucleophilic attack, respectively. In terms of the finite difference approximation, both functions can be written as ... 

As opposed to the global reactivity descriptors described above, the analysis of site selectivity in a molecule demands the local descriptors like the Fukui function defined as [35,36],... 

The resulting descriptor can be regarded as isolated from the molecular RDF that contains the sum of N possible descriptors. Thus, every Af-atomic molecule can have N local RDF descriptors. However, local descriptors can cover the entire molecule, depending on the predehned maximum distance of the function their center is just localized on a single atom. 

The Cartesian RDF seems to represent the biological activity of the Ruthenium complex. In any case, the descriptor is qnite complex and cannot be compared easily with other molecnles of similar ligand arrangement and with similar biologic potency. Another approach is based on a local descriptor that specifies the chemical environment of the reaction center the Rntheninm atom. 

Local, or atomic, RDF descriptors are snitable to characterize an individual atom in its chemical environment. They are nsnally not appropriate for investigations of diverse data sets, since each A-atomic molecnle can have N local descriptors. A typical application of local descriptors is the characterization of steric hindrance at reaction centers. This can be performed nsing a conseqnent numbering of the atoms of the reactants. In the following experiment, the Rnthenium atom of each conformer shown in Figure 5.8 was the first atom in the data file, and the local RDF descriptors for atom 1 (Ru) were calculated. Figures 5.10a through 5.10c show the results for the Cartesian RDF descriptors. 

The discussions in this section briefly described the use of local descriptors. Another application of local descriptors is the characterization of atoms in nuclear magnetic resonance (NMR) spectroscopy. This is described later with an application for the prediction of chemical shifts in H-NMR spectroscopy, where protons were represented by their local RDF descriptors. 

Local Descriptors (atomic descriptors) run over all pairs of a predefined atom with every other atom. 

Local Descriptors for Nuclear Magnetic Resonance Spectroscopy... 

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