Fragment-based similarity measures

Closely related to weighting is standardization, which involves a rescaling of the variables in a multivariate analysis to ensure that all of them are measured on the same scale and that one, or a few, of them do not dominate the overall similarities. Many different approaches to standardization have been discussed in the literature.Bath et al. ° evaluated the use of seven of these with fragment-based similarity measures but concluded that their application did little to improve performance in simulated property prediction experiments. 

Chen, X., Reynolds, . H. (2002) Performance of similarity measures in 2D fragment-based similarity searching comparison of... 

ADMA = adjustable density matrix assembler AFDF = additive fiizzy density fragmentation GSTE = geometrical similarity as topological equivalence MEDLA = molecular electron density loge assembler MEP = molecular electrostatic potential RBSM = resolution-based similarity measures SGM = shape group methods VDWS = van der Waals surface ID, 2D, 3D = one, two, and three dimensions. 

Figure 8.3 Example of a 2D similarity search, showing a query molecule and five of its nearest neighbors. The similarity measure for the search is based on 2D fragment bit-strings and the Tanimoto coefficient.

Although such a fragment-based measure clearly provides a very simple picture of the similarity relationships between pairs of structures, it is both efficient (because it involves just the application of logical operations to pairs of bit-strings) and effective (in that it is able to bring together molecules that are judged by chemists to be structurally similar to each other) in operation. 

The D-score is computed using the maximum dissimilarity algorithm of Lajiness (20). This method utilizes a Tanimoto-like similarity measure defined on a 360-bit fragment descriptor used in conjunction with the Cousin/ChemLink system (21). The important feature of this method is that it starts with the selection of a seed compound with subsequent compounds selected based on the maximum diversity relative to all compounds already selected. Thus, the most obvious seed to use in the current scenario is the compound that has the best profile based on the already computed scores. Thus, one needs to compute a preliminary consensus score based on the Q-score and the B-score using weights as defined previously. To summarize this, one needs to... 

Separating methods which use molecular parts into two categories, atom-based or fragment-based/ seems to make a distinction without a significant difference. In atom-based methods, each atom of the molecule is examined in respect to its connectivity index, and to the oxidation and hybridization state of all those atoms directly attached to it (Viswa-nadhan, 1989) or to some similar measure of atomic state (Broto, 1984). 

Many different structural descriptors have been developed for similarity searching in chemical databases [4] including 2D fragment based descriptors, 3D descriptors, and descriptors that are based on the physical properties of molecules. More recently, attention has focused on diversity studies and many of the descriptors applied in similarity searching are now being applied in diversity studies. Structural descriptors are basically numerical representations of structures that allow pairwise (dis)similarities between structures to be measured through the use of similarity coefficients. Many diversity metrics have been devised that are based on calculating structural (dis)similarities, some of these are described below. 

One of the most commonly used structural descriptors in similarity and diversity studies is that of the 2D fragment bitstring where a molecule is represented by a vector of binary values that indicate the presence or absence of structural features, or fragments, within the molecule. Many different similarity measures or coefficients have been developed to quantify the degree of similarity between such vector based descriptors [5-7]. Usually, the values that can be taken by a coefficient lie in the range 0..1, or they can be normalised to be within this range. A similarity coefficient of 1 indicates that the two molecules are identical with respect to the structural descriptors and a value of 0 indicates that the two molecules are maximally different... 

Bath, P.A., Poirrette, A.R., Willett, P. and Allen, EH. (1994). Similarity Searching in Files of Three-Dimensional Chemical Structures Comparison of Fragment-Based Measures of Shape Similarity. J.Chem.InfComput.ScL, 34,141-147. 

Bath, P.A., Morris, C.A. and Willett, P. (1993) Effects of standardization on fragment-based measures of structural similarity. /. Chemom, 7, 543-550. 

Bath PA, Morris CA, Willet P (1993) Effects of Standardization on Fragment-Based Measures of Structural Similarity. J Chemom 7 543-550... 

Bath PA, Poirette AR, Willett P. Similarity searching in files of three-dimensional chemical structures comparison of fragment-based measures of shape similarity. J Chem Inf Comput Sci 1994 34 141-147. 

Interesting and surprising results were obtained " from a comparison of molecular similarity measurements based on topological indices, " or on the occurrence of common structural fragments. These two measures agree in some cases and disagree in other ones. 

---