Molecular similarity spaces

Basak SC, Gute BD, Mills D, Hawkins DM. Quantitative molecular similarity methods in the property/toxicity estimation of chemicals a comparison of arbitrary versus tailored similarity spaces. J Mol Struct (Theochem) 2003 622 127-45. 

Hall, L. H Kier, L. B. The E-state as the basis for molecular strucmre space definition and stmcmre similarity. 

Allan, N.L. and Cooper, D. Momentum-Space Electron Densities and Quantum Molecular Similarity. 173, 85-111 (1995). 

Two objects are similar and have similar properties to the extent that they have similar distributions of charge in real space. Thus chemical similarity should be defined and determined using the atoms of QTAIM whose properties are directly determined by their spatial charge distributions [32]. Current measures of molecular similarity are couched in terms of Carbo s molecular quantum similarity measure (MQSM) [33-35], a procedure that requires maximization of the spatial integration of the overlap of the density distributions of two molecules the similarity of which is to be determined, and where the product of the density distributions can be weighted by some operator [36]. The MQSM method has several difficulties associated with its implementation [31] ... 

Horvath, D. and Jeandenans, C. (2003) Neighborhood behavior of in silico structural spaces with respect to in vitro activity spaces - a novel understanding of the molecular similarity principle in the context of multiple receptor binding... 

Molecular diversity is thus plagued not only with the problems inherent in molecular similarity/dissimilarity [5, 6] but also with those problems associated with molecular populations [7]. One of the foremost problems is that computed molecular similarity values are not invariant to the molecular representation and to the similarity measure used [5]. Nearest-neighbor (NN) relationships, which are employed extensively in many aspects of HTS, are thus problematic, and it is difficult, and in many cases impossible, to obtain consistent subsets [8]. The structure of chemistry space can also be altered significantly in a global sense. As molecular diversity also depends on these factors, it too can be problematic and inconsistencies will no doubt arise. 

Closely allied with the notion of molecular similarity is that of a chemistry space. Chemistry spaces provide a means for conceptualizing and visualizing molecular similarity. A chemistry space consists of a set of molecules and a set of associated relations (e.g., similarities, dissimilarities, distances, and so on) among the molecules, which give the space a structure (8). In most chemistry spaces, which are coordinate-based, molecules are generally depicted as points. This, however, need not always be the case—sometimes only similarities or distances among molecules in the population are known. Nevertheless, this type of pairwise information can be used to construct an appropriate coordinate... 

Molecular similarity analysis has developed substantially over the years, especially as digital computers became faster, more compact, and widely available to scientists. Handling large sets of molecules is generally not a problem. The main problem confronting MSA is the problem of the lack of topological invariance of the chemistry spaces induced by the various similarity measures. Unfortunately, this problem may be fundamentally related to the inherent subjectivity of similarity and thus cannot be addressed in any simple manner. 

Johnson, M. A. (1989) A review and examination of mathematical spaces underlying molecular similarity analysis. J. Math. Chem. 3, 117-145. 

The concepts of molecular similarity (1-3) and molecular diversity (4,5) play important roles in modern approaches to computer-aided molecular design. Molecular similarity provides the simplest, and most widely used, method for virtual screening and underlies the use of clustering methods on chemical databases. Molecular diversity analysis provides a range of tools for exploring the extent to which a set of molecules spans structural space, and underlies many approaches to compound selection and to the design of combinatorial libraries. Many different similarity and diversity methods have been described in the literature, and new methods continue to appear. This raises the question of how one can compare different methods, so as to identify the most appropriate method(s) for some particular application this chapter provides an overview of the ways in which this can be carried out, illustrating such comparisons by,... 

As discussed in Subheading 1., the primary design criterion is often based on either similarity or diversity. Quantifying these measures requires that the compounds are represented by numerical descriptors that enable pairwise molecular similarities or distances to be calculated or that allow the definition of a multidimensional property space in which the molecules can be placed. 

Separability between electronic and nuclear states is fundamental to get a description in terms of a hierarchy of electronic and subsidiary nuclear quantum numbers. Physical quantum states, i.e. wavefiinctions 0(q,Q), are non-separable. On the contrary, there is a special base set of functions Pjt(q,Q) that can be separable in a well defined mode, and used to represent quantum states as linear superpositions over the base of separable molecular states. For the electronic part, the symmetric group offers a way to assign quantum numbers in terms of irreducible representations [17]. Space base functions can hence be either symmetric or anti-symmetric to odd label permutations. The spin part can be treated in a similar fashion [17]. The concept of molecular species can be introduced this is done at a later stage [10]. Molecular states and molecular species are not the same things. The latter belong to classical chemistry, the former are base function in molecular Hilbert space. 

In this chapter, we will give a brief introduction to the basic concepts of chemoinformatics and their relevance to chemical library design. In Section 2, we will describe chemical representation, molecular data, and molecular data mining in computer we will introduce some of the chemoinformatics concepts such as molecular descriptors, chemical space, dimension reduction, similarity and diversity and we will review the most useful methods and applications of chemoinformatics, the quantitative structure-activity relationship (QSAR), the quantitative structure-property relationship (QSPR), multiobjective optimization, and virtual screening. In Section 3, we will outline some of the elements of library design and connect chemoinformatics tools, such as molecular similarity, molecular diversity, and multiple objective optimizations, with designing optimal libraries. Finally, we will put library design into perspective in Section 4. 

The quantification of molecular similarity generally involves three components molecular descriptors to characterize the molecules, weighting factors to differentiate more important characteristics from less important ones, and the similarity coefficient to quantify the degree of similarity between pairs of molecules (20, 21). The first two components are related to the definition of chemical space as discussed in Section 2.4. Therefore, it is natural to assume that structurally similar molecules should cluster together in a chemical space, and to define the similarity coefficient of a pair of molecules to be the distance between them in the chemical space. The shorter the distance is the more similar the pair is. 

Table 13.6 provides a comparison among several leading search methods in terms of their origin, search time, scope and nature of chemical space, format of input query ligand, and molecular similarity measure used. 

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