Principal component analysis descriptors, chemical structures

The concept of property space, which was coined to quanhtahvely describe the phenomena in social sciences [11, 12], has found many appUcahons in computational chemistry to characterize chemical space, i.e. the range in structure and properhes covered by a large collechon of different compounds [13]. The usual methods to approach a quantitahve descriphon of chemical space is first to calculate a number of molecular descriptors for each compound and then to use multivariate analyses such as principal component analysis (PCA) to build a multidimensional hyperspace where each compound is characterized by a single set of coordinates. 

Recently, Riviere and Brooks (2007) published a method to improve the prediction of dermal absorption of compounds dosed in complex chemical mixtures. The method predicts dermal absorption or penetration of topically applied compounds by developing quantitative structure-property relationship (QSPR) models based on linear free energy relations (LFERs). The QSPR equations are used to describe individual compound penetration based on the molecular descriptors for the compound, and these are modified by a mixture factor (MF), which accounts for the physical-chemical properties of the vehicle and mixture components. Principal components analysis is used to calculate the MF based on percentage composition of the vehicle and mixture components and physical-chemical properties. 

The structural variance of the dataset was analyzed with principal component analysis (PCA) [9] performed on the complete set of ALMOND descriptors calculated for the compounds which comprised the training and test sets. The first two components explained 35% of the stmctural variance of the dataset. Figure 9.1 shows that no structural outliers are present in the dataset and that the training and test sets share similar chemical space. 

Multiple intercorrelations between descriptors of chemical structures are illustrated best using multivariate statistics (section 3.2.2). A principal component analysis of the data set of 18 descriptors (Table 1.6, Figure 1.11) revealed that > 80% of the information content of these descriptors is expressed by four factors that explain 54.7%, 15.8%, 8.1% and 5.6% of the total variance, respectively. 

K. Varmuza and H. Scsibrany. Cluster analysis of chemical structures based on binary molecular descriptors and principal component analysis. Software-Entwicklung in der Chemie, 9 81-90,1995. 

Figure 17 Cluster analysis of 44 isomers with molecular formula C6H3CI3 by principal component analysis (score plot of the first and second principal component containing 41.2% and 18.8% of the total variance, respectively). The chemical structures have been characterized by 20 binary molecular descriptors. The common structural properties within each cluster are characterized by the maximum common substructure (MCS). [Reproduced from Ref. 133 with kind permission of Gesellschaft Deutscher Chemiker]...

Figure 10.3 compares the distributions of a dataset containing the 108 most used existing solvents and a dataset of 239 SOLVSAFE solvent candidates in two principal components which account for the structural diversity of both datasets. One of the defining features of chemical spaces is that molecular structures can be represented as points whose coordinates depend on the values of relevant descriptors or variables. To characterize each molecular structure, SOLVSAFE used 52 structural descriptors. The principal component statistical analysis projects the data contained in the 52-dimensional chemical space into a two-dimensional space (plot in Figure 10.3). This approximation provides an overview of the systematic variation and distribution of the structural information and reveals how significant is the dissimilarity of the SOLVSAFE dataset when compared with the traditional solvents dataset.

Table 1.6 Principal component (PC) analysis of descriptors of chemical structures for a set of diverse organic compounds (a) > 80% of the explained variance is expressed in the first four PCs (b) the loadings of the original descriptor variables in the VARIMAX rotated factor matrix reflect the grouping of the parameters (i.e. high loadings in the same PC indicate high intercorrelations between the descriptors).

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