Descriptor values

Values calculated based on original and interpolated Abraham descriptors. Values in brackets are calculated based on Abraham parameters regressed from COSMO a-moments [65]. 

Korany et al. [28] used Fourier descriptors for the spectrophotometric identification of miconazole and 11 different benzenoid compounds. Fourier descriptor values computed from spectrophotometric measurements were used to compute a purity index. The Fourier descriptors calculated for a set of absorbencies are independent of concentration and is sensitive to the presence of interferents. Such condition was proven by calculating the Fourier descriptor for pure and degraded benzylpenicillin. Absorbance data were measured and recorded for miconazole and for all the 11 compounds. The calculated Fourier descriptor value for these compounds showed significant discrimination between them. Moreover, the reproducibility of the Fourier descriptors was tested by measurement over several successive days and the relative standard deviation obtained was less than 2%. 

One of the simplest and most common ways to evaluate a molecule for ADME properties is a qualitative examination of its basic descriptor values such as molecular weight (MW), ClogP for lipophilicity, polar surface area (PSA), counts of hydrogen bond donors and acceptors (HBD, HBA), and count of rotatable bonds (RB). This type of approach popularized by Lipinski s famous Rule of 5 was published a decade ago [6]. Lipinski et al. established cutoffs for MW (500), ClogP (5), HBA (10), and HBD (5). These cutoffs were based on the 90th percentile of distributions of molecules in the World Drug Index having USAN or INN names. The Rule of 5 considers a violation of any two of these cutoffs to be an alert for poor absorption or permeability. 

The data containing 324 descriptor values of 88 molecules was given as an input to VSMP program, to build models based on three and four descriptors, keeping the interdescriptor correlation below 0.75. The best three-descriptors model, Eq. 80, was based on descriptors 254 (atomic type E-state index), 311 (AlogP98), and 320 (2D Van der Waals surface area) with a correlation coefficient, r, of 0.8425, and the cross-validated correlation coefficient, q, of 0.8239. The correlation coefficients of the other two VSMP models, Eqs. 81 and 82 were 0.8411 and 0.8329, respectively. Significantly, the descriptors 254 and 311 were selected in all the best three-descriptors models of VSMP. The three descriptors, in the models 80, 81, and 82 were 320, 144 (Kappa shape index of order 1), and 30 (topological Xu index), respectively. 

Target = Ideal descriptor values Ql Acceptable compounds Q Rejected compounds... 

Several different approaches have been used to generate druglikeness prediction tools. The simplest approach is to identify a range of descriptor values for druglike compounds. The best known example of this approach is the Lipinski rules [16], which predict poor... 

Descriptor frequence values (cm )] are claimed to be helpful in predicting the direction of these rearrangements (96ZOK1742). These values were developed for oxazoles, 1,2,4-oxadiazoles, and furazanes. The calculated descriptor values [v sr(cm )] for the E- and Z-isomers of 4-aminofurazan 3-carboxamidoximes [E-I and Z-I, = (CH2)4, (013)2] and their rearranged 3-(substituted amino)furazan 4-carboxamidoximes [II,... 

Fig. 7. Artificial neural network model. Bioactivities and descriptor values are the input and a final model is the output. Numerical values enter through the input layer, pass through the neurons, and are transformed into output values the connections (arrows) are the numerical weights. As the model is trained on the Training Set, the system-dependent variables of the neurons and the weights are determined.

Once -dimensional chemical reference space has been defined, the descriptors values are calculated for all compounds in a dataset, thereby assigning a coordinate vector to each molecule. In principle, partitioning analysis could proceed in -dimensional space, but it is often attempted to reduce its dimensionality in order to generate a low-dimensional representa-... 

Because principal component analysis attempts to account for all of the variance within a molecular dataset, it can be negatively affected by outliers, i.e., compounds having at least some descriptor values that are very different from others. Therefore, it is advisable to scale principal component axes or, alternatively, pre-process compound collections using statistical filters to identify and remove such outliers prior to the calculation of principal components. 

Figure 1. Simplified three-dimensional representation of the multi dimensional spaces containing the catalysts, the descriptor values, and the figures of merit.

By dividing the problem this way, we translate it from an abstract problem in catalysis to one of relating one multi dimensional space to another. This is still an abstract problem, but the advantage is that we can now quantify the relationship between spaces B and C using QSAR and QSPR models. Note that space B contains molecular descriptor values, rather than structures. These values, however, are directly related to the structures (8). 

Any QSAR method can be generally defined as an application of mathematical and statistical methods to the problem of finding empirical relationships (QSAR models) of the form ,- = k(D, D2,..., D ), where ,- are biological activities (or other properties of interest) of molecules, D, P>2,- ,Dn are calculated (or, sometimes, experimentally measured) structural properties (molecular descriptors) of compounds, and k is some empirically established mathematical transformation that should be applied to descriptors to calculate the property values for all molecules (Fig. 6.1). The goal of QSAR modeling is to establish a trend in the descriptor values, which parallels the trend in biological activity. In essence, all QSAR approaches imply, directly or indi-... 

The multiple linear regression (MLR) method was historically the first and, until now, the most popular method used for building QSPR models. In MLR, a property is represented as a weighted linear combination of descriptor values F=ATX, where F is a column vector of property to be predicted, X is a matrix of descriptor values, and A is a column vector of adjustable coefficients calculated as A = (XTX) XTY. The latter equation can be applied only if the matrix XTX can be inverted, which requires linear independence of the descriptors ( multicollinearity problem ). If this is not the case, special techniques (e.g., singular value decomposition (SVD)26) should be applied. 

Table 2.5 defines the 40 molecular descriptors and provides their values. Figure 2.1 provides further definition of the different types of molecular fragments used while Figure 2.2 provides further definition of the hydrogen bonding and biphenyl ring corrections. Simamora and Yalkowsky (1994) consider the values in parentheses in Table 2.5 insignificant, based on the statistical analysis used to derive the molecular descriptor values. 

Figure 6.19 Graphic representation of the distances in a simplified three-dimensional descriptor space (space B). Catalysts with descriptor values within the model are good candidates for optimization. Those outside the model space may lead to new discoveries.

A point that is often not fully realized is that the chemical descriptors, as typically obtained with commercial software, are quite ambiguous because the exact mathematic equation used to get the descriptor value is not available, and different software or even different versions of the same software may produce different values for, apparently, the same descriptor. 

Chemical descriptors are in most of the cases obtained with equations that are not known. Even if the references to certain general equations are given, in practice, it is difficult to replicate the results obtained with chemical descriptors. As we have discussed, chemical descriptors based on tridimensional structures are subject to manual optimization, and this may change the descriptor values. But even in the case of other simpler descriptors, we found that using software from two different commercial sources, the results may be different. Even the use of two different versions of the same software may provide different results for the same descriptor. Even descriptors, which seem simple, such as number of double bonds, or of aromatic rings, are critical because they depend on how tautomers and aromaticity are considered in the different software, or are sensitive to the structure format that is used. 

For each molecule, calculation of n descriptor values produces an TV-dimensional coordinate vector in descriptor space that determines its position ... 

Thus, calculation of these descriptor values for a molecule involves the separate calculation of atomic charges and SAAs. 

Here n, and //, are the number of descriptor values for molecules i and /, respectively, and ny is the number of common values. />.,. is the distance between molecules i and j, D the average distance, and n the total number of molecules. 

Here dL is the descriptor value of molecule i, dav the average (or mean) value of the entire data set, the a standard deviation, and d( the scaled value of descriptor d for molecule i. This procedure ensures that all chosen descriptors have similar value ranges (i.e., that descriptor axes have comparable length) and thus prevents space distortions. 

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