Correlation calculated descriptor

There are three general classes of descriptors topological, geometrical, and physicochemical. Topological descriptors are derived from the topological representation of the structure, the connection table. The geometrical descriptors are derived from the three dimensional model of the molecule. Physicochemical descriptors may be measured experimentally, calculated using a mathematical model, or represented by linearly correlated calculated descriptors. The descriptors that are currently available in ADAPT are as follows ... 

Osterberg and Norinder [42] further analyzed a subset of the ATPase data published by Litman et al. [39]. The ATPase activity values were correlated by multivariate statistics with calculated descriptors (MolSurf descriptors) related to physicochemical properties suchaslipophilicity, polarity, polarizability and hydrogen bonding. After exclusion of one outlier and large molecules such as valinomycin, gramicidin S and so on, which were not handled by the MolSurf software, only 21 compounds were included in the study. Two models were derived model 1, based on... 

Calculated descriptors have generally fallen into two broad categories those that seek to model an experimentally determined or physical descriptor (such as ClogP or CpKJ and those that are purely mathematical [such as the Kier and Hall connectivity indices (4)]. Not surprisingly, the latter category has been heavily populated over the years, so much so that QSAR/QSPR practitioners have had to rely on model validation procedures (such as leave-k-out cross-validation) to avoid models built upon chance correlation. Of course, such procedures are far less critical when very few descriptors are used (such as with the Hansch, Leo, and Abraham descriptors) it can even be argued that they are unnecessary. 

A major practical issue affecting MP calculations is caused by use of correlated molecular descriptors. During subsequent MP steps, exact halves of values (and molecules) are only generated if the chosen descriptors are uncorrelated (orthogonal), as shown in Fig. 1A. By contrast, the presence of descriptor correlations (and departure from orthogonal reference space) leads to overpopulated and underpopulated, or even empty, partitions (see also Note 5), as illustrated in Fig. ID. For diversity analysis, compounds should be widely distributed over computed partitions and descriptor correlation effects should therefore be limited as much as possible. However, for other applications, the use of correlated descriptors that produce skewed compound distributions may not be problematic or even favorable (see Note 5). 

Because authors present correlation equations in different ways, a uniform pattern of presentation is employed. For each example given, the following information is provided the author(s), the bulk property with its units, the number and types of compounds in the data set, the types of descriptors used, and QM methods employed. Computer programs used in molecular model visualization, QM calculation, descriptor calculation, and statistical calculation will be mentioned. More information on some of the computer programs available for these purposes may be found in two chapters in... 

QSPR - methods correlating calculated structural descriptors with pA ... 

Variables (measured properties and calculated descriptors) that were shown by these models not to correlate with the property of interest (human jejunal permeability) were dismissed as being of low relative importance, based on the method of variable importance (VIP). 

In addition to descriptors calculation, some explorative tools are also available that allow one to calculate descriptor values and their univariate statistics, to project and visualize molecules in the descriptor/response space, to calculate descriptor pair correlations, and to identify the most and the least correlated descriptors with a selected one. 

The acute toxicity of soft electrophiles such as substituted benzenes, phenols, and anilines has been correlated with MNDO-calculated descriptors [118] ... 

Highest descriptor correlations in the co-crystal data set. Only correlations calculated for the same descriptor of both molecules in a co-crystal are given. Descriptors are defined in the text. 

Structure-activity studies have proved instrumental in describing the dependence of inhibitory activity on physicochemical and calculated descriptors. A nearly historical example of a correlation study with phenolic photosynthesis inhibitors is shown in Figure 1 (2). In this equation the only parameters employed were the STERIMOL parameters by Verloop et al. (4). In a more recent analysis of the same set of compounds (it was found that the hydrophobicity parameter k also contributed to inhibitory activity. 

The pool of descriptors that is calculated must be winnowed down to a manageable set before constructing a statistical or neural network model. This operation is called feature selection. The first step of feature selection is to use a battery of objective statistical methods. Descriptors that contain little information, descriptors that have little variation across the data set, or descriptors that are highly correlated with other descriptors are candidates for elimination. Multivariate correlations among descriptor can also be discovered with multiple linear regression analysis, and these relationships can be broken down by elimination of descriptors. 

Inductive methods for establishing a correlation between chemical compounds and their properties are the theme of Chapter 9. In many cases, the structure of chemical compounds has to be pre-processed in order to make it amenable to inductive learning methods. This is usually achieved by means of structure descriptors, methods for the calculation of which are outlined in Chapter 8. 

The molecular electronic polarizability is one of the most important descriptors used in QSPR models. Paradoxically, although it is an electronic property, it is often easier to calculate the polarizability by an additive method (see Section 7.1) than quantum mechanically. Ah-initio and DFT methods need very large basis sets before they give accurate polarizabilities. Accurate molecular polarizabilities are available from semi-empirical MO calculations very easily using a modified version of a simple variational technique proposed by Rivail and co-workers [41]. The molecular electronic polarizability correlates quite strongly with the molecular volume, although there are many cases where both descriptors are useful in QSPR models. 

It is also important to check for correlations between the descriptors. Highly correlated descriptors could lead to the information that they encode being over-represented. A straightforward way to determine the degree of correlation between two properties is to calculate a correlation coefficient. Pearson s correlation coefficient is given by ... 

Intercorrelation coefficients are then computed. These tell when one descriptor is redundant with another. Using redundant descriptors increases the amount of fitting work to be done, does not improve the results, and results in unstable fitting calculations that can fail completely (due to dividing by zero or some other mathematical error). Usually, the descriptor with the lowest correlation coefficient is discarded from a pair of redundant descriptors. 

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