Similarity diversity selection

As is the case for structural keys, pharmacophore keys can be readily extended to account for multiple conformations. Additionally, because pharmacophores are two- and three-dimensional objects, they are able to capture information on molecular shape and chirality. Three-point pharmacophore keys also lend themselves well to visualization via three-dimensional scatter plots (see section Visualization without Dimensionality Reduction below). Sheridan s original work has been extended by a number of groups, most notably those at Chemical Design [27], Rhone-Poulenc [30], and Abbott [10]. Davies and Briant [31] have employed pharmacophore keys for similarity/diversity selection using an iterative procedure that takes into account the flexibility of the compounds and the amount of overlap between their respective keys (see section Boolean Logic). 

Hence there are multiple solutions for the final set of 10000 compounds. The final selection can be diversity driven using for example cluster analysis based on multiple fingerprints [63], hole filling strategies by using scaffold/ring analysis (LeadScope [66], SARVision [66]) or pharmacophore analysis [67, 68]. For a review of computational approaches to diversity and similarity-based selections, see the paper of Mason and Hermsmeier [69] and the references therein. 

Two very similar molecules are two different physical objects [40], Hence, chemical/ structural comparison of similarity is a subtle and relative concept that acquires significance in a well-defined reference physical context. In other words, it is necessary to define in what respect and to what extent two different molecules are similar. Molecular series of specific and selective ligands interacting, in vitro and in equilibrium conditions, with a specific receptor constitute a sophisticated example of chemical similarity-diversity classification. This classification is based on the experimental binding affinity (AG°) values that quantify a particular molecular recognition phenomenon, which is, essentially, a noncovalent process [41]. This implies,... 

The quantitative comparison of the optimized 3D structure of a selected set of ligands allows the development of their minimal 3D structural requirements for the recognition and activation of the biological target, that is, the pharmacophore hypothesis, and gives a sound 3D rationale to the available SARs [21]. A more complete and mechanistically relevant approach to the development of the 3D pharmacophore consists in its translation into a numerical molecular descriptor that quantifies the molecular-pharmacophore similarity-diversity for computational QSAR modeling [21,41]. 

Figure 1 SPE maps (see Section 4) showing subset selections using the nearest-neighbor distance metric for a diverse selection (top), and a similar selection (middle). A random selection is shown (bottom) for comparison. AH selections are 100 compounds from a 10,000-member library...

Some basic concepts and definitions of statistics, chemometrics, algebra, graph theory, similarity/diversity, which are fundamental tools in the development and application of molecular descriptors, are also presented in the Handbook in some detail. More attention has been paid to information content, multivariate correlation, model complexity, variable selection, and parameters for model quality estimation, as these are the characteristic components of modern QSAR/QSPR modelling. 

Once the chemical structures are encoded by an appropriate descriptor set, the similarities of descriptors must be calculated. Descriptor similarities are the basis for a selection of compounds according to diversity or similarity [101]. Diversity selection techniques fall into four classes ... 

Fig. 13 Selection of compounds from a virtual combinatorial library, a) First six steps of a maximum dissimilarity selection, b) Selection by excluding similar compounds, c) Maximum diversity selection as a result of clustering, d) Grouping by partitioning of descriptor space.

Due to the large number of descriptors (commonly 15 000-20 000 for each field), multivariate regression analysis is usually performed by partial least squares regression (PLS), with or without —> variable selection. Alternatively to grid-based QSAR models, —> similarity/diversity between molecules can be measured by comparing their interaction fields. 

NMR spectra were also characterized for —> similarity/diversity analysis [Zuperl, Pristovsek et al., 2007] by —> graph invariants obtained using the sequential nearest neighbor method proposed to characterize —> proteomics maps [Randic, Novic et al., 2005]. Moreover, selected chemical shifts were directly used as molecular descriptors for modeling lipophilicity of alcohols [Khadikar, Sharma et al., 2005b]. 

Fligner, M.A., Verducd, J.S. and Blower, P.E. (2002) A modification of the Jaccard—Tanimoto similarity index for diverse selection of chemical compounds using binary strings. Technometrics, 44, 110-119. 

Structure/Response Correlations, data set, chemometrics, statistical indices. Principal Component Analysis, similarity/diversity, validation, variable selection, and variable reduction... 

Given the structural diversity of the ligands that can be attached to polyethylene oligomers, it is not surprising that there is a similar diversity in the sorts of catalysts that have been supported on these materials. Selected examples of catalysts prepared using polyethylene ligands are shown in structures 14-26 in Fig. 4 [32-34,38-40,45-49]. While most of these catalysts contain transition metals, non-transition metal catalysts like poly-ethyldibutyltin chloride 14 or phase-transfer onium catalysts like 24 have also been prepared. 

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