Tanimoto function

The SQL statement above computes the Tanimoto similarity between all pairs of compounds using fingerprint bitstrings stored in the column gfp. The tanimoto function is described in Chapter 8 and shown in the Appendix. This SQL statement uses the Case conditional clause. This is done in order to avoid computing elements unnecessarily. The matrix of similarities is symmetric and the diagonal elements are exactly 1. The sqlQuery R function reads the rows of the similarity matrix into an R data.frame named tani. This is coerced into a matrix of the correct number of rows and columns using the matrix function and further coerced into a distance R object. The R distance object is the lower half of a symmetric distance matrix. Since the tanimoto similarity is used, the distance (or dissimilarity) is represented by 1.0 minus the tanimoto... 

The tanimoto function is used to compute the Tanimoto similarity of two bitstrings. The input bit strings would have been computed with the publicl66keys function or another equivalent fragment key or fingerprint function. 

As is well known, the Tanimoto similarity coefficient, which is the most widely used similarity measure, exhibits size-dependent behavior [5, 92-95] that can significantly influence the results of similarity searches. A significant part of the problem can be traced to the terms in the denominator of the Tanimoto function that counts the number of elements that are common to both molecular fingerprints. Thus, when molecules of widely varying sizes are treated, the number of elements in fingerprint... 

The author is grateful to Mr. H. Horiuchi for the preparation of photoelectrochemical cells. Professor S. Yamada for discussion, and Professor Y. Tanimoto and Associate Professor Y. Fujiwara for using the superconducting magnets. The author also thanks The Center of Advanced Instrumental Analysis, Kyushu University, for H-NMR measurements. This study was financially supported by the Grant-in-Aids for Scientific Research Priority Areas (Area 767, No. 15085203) and (Area 432, No. 17034051), Scientific Research (C) (No. 17550131), and twenty first century COE Program Function Innovation of Molecular Informatics from M EXTof the Japan. 

The Jaccard similarity coefficient is then computed with eq. (30.13), where m is now the number of attributes for which one of the two objects has a value of 1. This similarity measure is sometimes called the Tanimoto similarity. The Tanimoto similarity has been used in combinatorial chemistry to describe the similarity of compounds, e.g. based on the functional groups they have in common [9]. Unfortunately, the names of similarity coefficients are not standard, so that it can happen that the same name is given to different similarity measures or more than one name is given to a certain similarity measure. This is the case for the Tanimoto coefficient (see further). 

Kojima K, Kaneda K, Yoshida C, Dansako H, Fuji N, Yano T, Shinagawa K, Yasukawa M, Fujita S, Tanimoto M (2003) A novel fusion variant of the MORF and CBP genes detected in therapy-related myelodysplastic syndrome with t(10 16)(q22 p 13). Br J Haematol 120 271—273 Koken MH, Saib A, de The H (1995) A C4HC3 zinc finger motif. C R Acad Sci 111 318 733-739 Korzus E, Torchia J, Rose DW, Xu L, Kurokawa R, Mclnemey EM, Mullen TM, Glass CK, Rosenfeld MG(1.9 98) Transcription factor-specific requirements for coactivators and their acetyltransferase functions. Science 279 703—707... 

When molecules are represented by high-dimensional descriptors such as 2D fingerprints or several hundred topological indices, then the diversity of a library of compounds is usually calculated using a function based on the pairwise (dis)similarities of the molecules. Pairwise similarity can be quantified using a similarity or distance coefficient. The Tanimoto coefficient is most often used with binary fingerprints and is given by the formula below ... 

In order to apply the SA protocol, one of the keys is to design a mathematical function that adequately measures the diversity of a subset of selected molecules. Because each molecule is represented by molecular descriptors, geometrically it is mapped to a point in a multidimensional space. The distance between two points, such as Euclidean distance, Tanimoto distance, and Mahalanobis distance, then measures the dissimilarity between any two molecules. Thus, the diversity function to be designed should be based on all pairwise distances between molecules in the subset. One of the functions is as follows ... 

It is now universally acceptable to measure the similarity of two molecules using the Tanimoto Index of their database keys or fingerprints. There is no standard fingerprint and the similarity measures consequently can vary. Most fingerprints are dependent upon which functional groups are... 

For binary descriptors, the most commonly used distance function is the Tanimoto (or Jaccard) coefficient given in (5). Here x and y are two binary sets (encoded molecules). AND is the bitwise and operation (a bit in the result is set if both corresponding bits in the two operands are set), and lOR the bitwise inclusive or operation (a bit in the result is set if either corresponding bits in the two operands is set). The result, T, is a measure of the number of features shared by the two molecules relative to the ones they could have in common. 

Create Function tanimoto(bit, bit) Returns Real As Select nbits set( 1 2) real /... 

Yokota and Tanimoto (39) have worked out the expected fluorescence decay when both quenching and diffusion are active and the diffusion is not fast enough to maintain the initial distribution of excitation. In such a case the decay function of the excited sensitizers is given by (39)... 

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