Carbo similarity index

Once the protein interaction pattern is translated from Cartesian coordinates into distances from the reactive center of the enzyme and the structure of the ligand has been described with similar fingerprints, both sets of descriptors can be compared [25]. The hydrophobic complementarity, the complementarity of charges and H-bonds for the protein and the substrates are all computed using Carbo similarity indices [26]. The prediction of the site of metabolism (either in CYP or in UGT) is based on the hypothesis that the distance between the reactive center on the protein (iron atom in the heme group or the phosphorous atom in UDP) and the interaction points in the protein cavity (GRID-MIF) should correlate to the distance between the reactive center of the molecule (i.e. positions of hydrogen atoms and heteroatoms) and the position of the different atom types in the molecule [27]. 

Carbo Similarity Indices Over Condensed TDQSH.307... 

TRANSFORMATION OF THE TDQS HYPER VECTORS GENERALIZED CARBO SIMILARITY INDICES... 

CARBO SIMILARITY INDICES OVER CONDENSED TDQSH... 

Finally, in the last chapter (Chapter 12) of Part II of this book, Ramon has studied the molecular quantum similarity (QS) measures involving three density functions. The necessary algorithms have been described here. General theory and computational feasibility of a h3q)ermatricial or tensorial representation of molecular structures associated to any molecular quantum object set (MQOS) have been nicely explained in this chapter. Secondly, generalized Carbo similarity indices (CSI) have also been studied. The theoretical and computational approaches have been supported by various suitable applicative examples. 

The most prevalent among the similarity coefficients is the so-called cosine similarity index or correlation coefficient. For the field functions discussed in Subheading 2.4. it is usually called the Carbo similarity index, and this nomenclature will be used here as well,... 

Field-based similarities are usually evaluated by the cosine or correlation function similarity measure employed initially by Carbo and co-workers (67) to compute molecular similarities based upon quantum mechanical wavefunctions. Such a measure, which is usually called a Carbo similarity index, is given by... 

A modified version of the Carbo similarity index [Meyer and Richards, 1991], defined as ... 

The final vector comprising of the seven invariant moments represents the distribution of the property P on the bidimensional map. This representation was used to compare bidimensional molecule projections by Carbo similarity index and Hodgkin similarity index. 

This cosine-like index has, for any pair of compared systems, a value between 0 (total dissimilarity) and 1 (complete similarity) depending on the similarity associated to the two molecules. Some authors refer to this index as Carbo Similarity Index. 

Figure 11 Dendrogram obtained with the Carbo similarity index for the set of 31 steroids. Figure reprinted with permission from Bultinck and Carbo-Dorca/ Copyright 2003 American Chemical Society.

The well-known cosine similarity coefficient, also called the Carbo similarity index [10], provides a measure of the cosine of the angle between two vectors... 

Once known the TDQSH Z) = (P2i ) as defined in Eq. (11) and in the previous paragraph discussion example, one can envisage to transform it in an equivalent way as DDQS matrices can be manipulated for example, defining a transformation leading to a TD Carbo similarity index... 

For every element of the TDQSH and using the TDSS vector Eq. (17) elements, there can be also defined a TD Carbo similarity index (TDCSI) as follows ... 

Mcmahon, A.J. and King, P.M. Optimization of carbo molecular similarity index using gradient methods. /. Comput. Chem. 1997, 38, 151-158. 

More recently the idea of quantitative comparison of electron structure of the molecules was revived by Carbo [28] who proposed for this purpose the similarity index rAB, expressing the desired similarity of two molecules A and B in terms of density matrices (Eq. 2)... 

Carbo et al. introduced the concept of similarity index (SI) for measuring the similarity of two molecular electron density functions [99, 100]. The Carbo SI... 

Lobato, M., Amat, L., Besalu, E. and Carbo-Dorca, R. (1997) Structure-activity relationships of a steroid family using quantum similarity measures and topological quantum similarity indexes. Quant. Struct. -Act. Relat., 16, 465—472. 

The Carbo index Rab was originally proposed as a method of comparing molecules in terms of their electron density q [1066]. In a more general version (eq. 212) this similarity index can be applied to compare any structural properties and Pb of two molecules A and B. 

The basic requirement for a successful molecular (dis)similarity index is a function able to describe the produa or difference of a property for two overlaid molecules over all (relevant) property space. Perhaps the most widely applied index for the calculation ctf 3D molecular similarity was pioneered by Carbo et al. ... 

Similarity measures are involved in several well-known similarity index formulae [2, 38, 40] such as the Carbo (also known as Cosine) index ... 

Cosine similarity coefficient Also known as the Carbo index c. EllWiB s... 

Many applications of QSM use not the MQSM values as such but similarity indices. There exist many such indices and for a review, the reader is referred to Willett et al. [54]. One example that was touched upon above is the Carbo index. The Carbo index is one of the so-called C-class descriptors giving a value between 0 and 1 where a higher value indicates higher similarity. Although originally defined for overlap MQSM, it can be generalized to different operators f so that the Carbo index becomes... 

According to some authors, the similarity between shape functions might give more interesting information than using the electron density [63]. In this context, it should be mentioned that the Carbo index retains the same value. Moreover, it has... 

The value of SI(II) also varies in the range 0 to 1. When pA = npB (n is constant and 0) is substituted into Eq. (15), the Carbo index will be unity, which means that the Carbo index represents the similarity of the shapes of electron density distributions but not of the magnitudes. When pA = npB is substituted into Eq. (16), the result will be SI(H) = 2n/(l + n2), which means that the Hodgkin index characterizes the similarity in the shape as well as in the magnitude of the electron density functions [104],... 

Fig. 4. Projection of the point-molecule representation of the nine molecules using the Carbo index obtained from a gravitational-like similarity measure. The studied property is the boiling point...

Several measures of the shape and electronic similarity between pairs of molecules have been devised. The Carbo index was developed to enable the electron density of two molecules in some relative orientation to be compared [Carbo et ah 1980]. It is essentially the Cosine... 

The current version of this approach uses N x N matrices (N being the number of molecules included in the data set), in which the 3D similarity indices of each molecule as compared to every other molecule of the whole set are the non-diagonal elements of the similarity matrix [1064, 1065]. In an application to the affinities of 31 steroids to corticosteroid- and testosterone-binding globulins (same data as used in CoMFA studies, e.g. [36]), Carbo index similarity matrices were calculated for the shape and the electrostatic potentials of all molecules. Using the similarity... 

In a more detailed study of technique validation and of the comparison of different similarity evaluation methods [1065], several Carbo indices (also using Gaussian function approximations), the Hodgkin index (eq. 213),... 

---