Similarity of molecules

Similarity of molecules [40-44] is an important phenomenon serving, for example, by qualitative and quantitative estimation of chemical reactivity or biological activity of chemical species. Distance is a possible way to measure similarity. In the frame of a mathematical model of the logical structure of chemistry, the notion of chemical distance, CD, has been introduced [13], The CD is defined as the sum 

Often, the shape comparisons of local regions of molecules are of interest, which, in many instances, may appear more important than the evaluation of the global similarities of molecules. 

Quantitative similarities of molecules can easily be recognized if it is possible to define quantities for molecular parts which are additive as well as transferable. Such quantities can be derived from transferable molecular orbitals because any one-electron property, such as dipole moment, quadrupole moment, kinetic energy, is a sum of the corresponding contributions from all molecular orbitals in a system, if such orbitals are chosen mutually orthogonal. Thus, for each transferable orthogonal molecular orbital there exists, e.g., a transferable orbital dipole moment. Since chemists appreciate additive decompositions of 

Fig. 4-13. Plot of map luminance versus mean similarity of molecule sets.

Based on this "ID number" approach, the shape similarity of molecules can be evaluated by numerical comparisons of shape codes [2]. The same technique of similarity evaluation, originally developed for complete molecules, can also be applied, in identical form, to the shape codes of functional groups as discussed in earlier parts of this report. 

Scsibrany, H. and Varmuza, K. (1992b) Topological similarity of molecules based on maximum common substructures, in Software Development in Chemistry - Proceedings of the 7th CIC-Workshop Computers in Chemistry", (ed. D. Ziessow) Berlin/Gosen, Germany. 

One very useful approach in rational drug design is the study of the local shapes and local shape similarities of molecules showing similar biochemical activities, and the technique of shape groups offers an algorithmic approach to this problem. 

For applications of the scaled fuzzy Hausdorff-type metric f p(A,B) for assessing the similarity of molecules, the f p(A,B) distance can be used as a dissimilarity measure. 

Pharmacophore fingerprints have also been used to assess the similarity of molecules from an interaction property point of view [49-51]. 

The most usual representation of an organic molecule is the two-dimensional structural formula. Therefore, similarity of molecules is looked at as similarity of the structural formulas. Two molecules are stated to be similar if the structural scaffolds are similar and the substitution patterns are similar. 

Feature trees have been described by Rarey and Dixon [106] as a new way of analyzing the similarity of molecules. This approach is based on building trees that represent molecules. These trees describe the major building blocks of molecules, in addition to their overall arrangement. They are conformation independent. Different types of pairwise comparison algorithms are available to compare trees of different molecules. 

It is necessary to remember that the probability Pa first of all reflects the similarity of molecule under prediction with the structures of molecules that are the most typical in a sub-set of actives in the training set. Therefore, usually, there is no direct correlation between the Pa values and quantitative characteristics of activities. 

Purely numerical methods such as hierarchical clustering or the minimal spanning tree compute the similarity of molecules directly in the high-dimensional descriptor space. The results promise higher accuracy (no mapping errors), but their interpretation is less intuitive. 

Both indices have been applied to other molecular properties, e.g. electrostatic potentials and fields, and to describe the shape similarity of molecules [1068, 1069]. 

Richards et al. [1064, 1065] recently developed a new method to correlate the 3D similarities of molecules in a direct manner with their biological activities. In the first step 3D structures of reasonable conformations of all molecules are generated and aligned in space, as in the CoMFA approach. Then similarity indices between all pairs of molecules are calculated and the resulting N x N similarity matrices are correlated with biological activities. 

In this paper the need for an intelligent support of computational chemistry software packages was stressed and the memory-based classification systems suitable for this task recommended. More experiments with selection of relevant features to determine similarity of molecules and methods from the point of view of calculation of molecular properties are needed. Classification systems, such as the FSM, are ready to handle the data, but the task of collecting large amount of data to create a useful system is quite demanding. 

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