Substituents cluster analysis

Fig. 37.2. Principal components loading plot of 7 physicochemical substituent parameters, as obtained from the correlations in Table 37.5 [39,40]. The horizontal and vertical axes account for 46 and 31%, respectively, of the correlations. Most of the residual correlation is along the perpendicular to the plane of the diagram. The line segments define clusters of parameters that have been computed by means of cluster analysis.

Cluster analysis is simply a method to group entities, for which a number of properties or parameters exist, by similarity [292, 308-313]. Various distance measurements are used, and the analysis is performed in a sequential manner, reducing the number of clusters at each step. Such a procedure has been described for use in drug design and environmental engineering research as a way to group substituents that have the most similarity when various combinations of the electronic, steric, and statistically derived parameters are considered. 

Hansch and Leo have used cluster analysis to define sets of aliphatic and aromatic substituents useful in the design of compounds, such that various aspects of the substituents are taken into account in a balanced way. ... 

In the literature, a large number of substituent descriptors have been reported. In order to use this information for substituent selection, appropriate statistical methods may be used. Pattern recognition or data reduction techniques, such as principal component analysis (PCA) or cluster analysis (CA) are good choices. As explained in Section V in more detail, PCA consists of condensing the information in a data table into a few new descriptors made of linear combinations of the original ones. These new descriptors are called principal components or latent variables. This technique has been applied to define new descriptors for amino acids, as well as for aromatic or aliphatic substituents, which are called principal properties (PPs). The principal properties can be used in factorial design methods or as variables in QSAR analysis. 

Fig. 22.17 Comparison of (a) principal components analysis, (b) non-linear mapping, (c) Ward s cluster analysis and (d) Kohonen mapping to display similarity of 15 substituents characterized by five para substituent constants (tt, F, R, MR and /.).

Cluster analysis was used by Hansch et. al. C100D as an aid in the selection of substituents in drug design. 

So, the two main problems in compound selection are the choice of analogues to sample effectively a multi-parameter space and the avoidance of collinearity between physicochemical descriptors. A number of methods have been proposed to deal with these two problems. An attractive approach was published by Hansch and co-workers (Hansch et al. 1973) which made use of cluster analysis (Chapter 5) to group 90 substituents described by five physicochemical parameters. Briefly, cluster analysis operates by the use of measurements of the distances between pairs of... 

Another approach which makes use of the distance between points in a multidimensional space was published by Wootton and co-workers (Wootton et al. 1975). In this method the distances between each pair of substituents is calculated, as described for cluster analysis, and substituents are chosen in a stepwise fashion such that they exceed a certain preset minimum distance. The procedure requires the choice of a particular starting compound, probably but not necessarily the unsubstituted parent,... 

This program contains substituent constant data and also calculates physicochemical properties. Analysis facilities include PCA, PLS, regression (MLR), cluster analysis, NLM. 

Cluster analysis is thus very successful as a tool to design a set of substituents well spread in parameter space. Its greatest weakness, its failure to guarantee complete orthogonality, leads to a trial-and-error search for a set that meets this criterion. An alternative approach to series design has been suggested by Wootten and his co-workers. These authors address the issue... 

A set of compounds substituted in the 5 -position was designed to explore the physiochemical parameter space represented by 7C, F, R and MR. This initial compound set was restricted to cover these minimum parameters in the interest of efficiency. Later, if the level of activity warranted it, the initial set could be expanded to more fully explore parameter space. In order to adequately cover the chosen parameter space, a 2 factorial design was utilized. ( 5) The 16 required compounds were selected via cluster analysis from our substituent physical-chemical database. ( ) Marker points which represented the factorial design were included in the data set prior to clustering. (2) In this way substituents which best represented the factorial design were those that were... 

Since we wished to optimize this series with a minimal expenditure of our synthetic resources, the sequential simplex technique (SSO) was selected (11,12). This strategy is very resource efficient, requiring only n + 1 compounds to start the optimization, where n is the number of physiochemical parameters used to describe the characteristics of a substituent. We selected pi to account for lipophilicity and field (F) and resonance (R) were used to describe the electronic effects of each substituent (14). Verloop s Sterimol parameters (H), minimum van der Waals radius (B] ) and length (L) were selected to describe the size of the substituent. Using cluster analysis, we selected a set of six substituents that cover physiochemical parameter space well (15). These are-listed in Figure 6. 

Substituted pyridazinones can be categorized into five groups by cluster analysis, of which one is of analogues which inhibit phytoene desaturase. A comparison of seven different phenylpyridazinones found that an m-trifluoro substituent at the phenyl ring and a methyl-... 

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