Atom shape descriptor

With the development of accurate computational methods for generating 3D conformations of chemical structures, QSAR approaches that employ 3D descriptors have been developed to address the problems of 2D QSAR techniques, that is, their inability to distinguish stereoisomers. Examples of 3D QSAR include molecular shape analysis (MSA) [26], distance geometry,and Voronoi techniques [27]. The MSA method utilizes shape descriptors and MLR analysis, whereas the other two approaches apply atomic refractivity as structural descriptor and the solution of mathematical inequalities to obtain the quantitative relationships. These methods have been applied to study structure-activity relationships of many data sets by Hopfinger and Crippen, respectively. Perhaps the most popular example of the 3D QSAR is the com-... 

Geometry-based approach from a geometrical point of view, a cavity is a concave empty space that can be described using 2D (surface) or 3D shape descriptors (19-21). We consider three regions in the protein environment the protein bulk, the bulk solvent and the cavity space. The protein bulk is the space filled by the protein atoms. The bulk solvent is the space outside the protein which differentiates from the space inside the protein which defines the cavity where the drug-like molecule is supposed to bind. The identification of protein pockets by numerical methods suppose the capacity to discriminate first the protein bulk from the rest... 

ADRIANA.code Global physicochemical descriptors, size and shape descriptors, atom property-weighted 2D and 3D autocorrelations and RDF, surface property-weighted autocorrelations 1,244... 

The USR (Ultrafast Shape Recognition) Method. This method was reported by Ballester and Richards (53) for compound database search on the basis of molecular shape similarity. It was reportedly capable of screening billions of compounds for similar shapes on a single computer. The method is based on the notion that the relative position of the atoms in a molecule is completely determined by inter-atomic distances. Instead of using all inter-atomic distances, USR uses a subset of distances, reducing the computational costs. Specifically, the distances between all atoms of a molecule to each of four strategic points are calculated. Each set of distances forms a distribution, and the three moments (mean, variance, and skewness) of the four distributions are calculated. Thus, for each molecule, 12 USR descriptors are calculated. The inverse of the translated and scaled Manhattan distance between two shape descriptors is used to measure the similarity between the two molecules. A value of 1 corresponds to maximum similarity and a value of 0 corresponds to minimum similarity. 

The adenosine A3 receptor antagonistic activity of these compounds have been further analyzed [104] in 3D-QSAR using molecular shape analysis (MSA) and molecular field analysis (MFA) techniques in Cerius2 (version 4.8) software [50]. hi this, Jurs atomic charge descriptors were used for the MSA study and H+ point charges and CH3 derived steric fields were used for the MFA study. In this 3D-QSAR study, MSA resulted in Eqs. 12 and 13 and MFA led to Eq. 14. 

Some research groups have extended the atom-pair descriptors to three-point (triplets) and four-point (quartets) pharmacophore descriptors (35,37,76,81) as described in section 2. These descriptors have a potentially superior descriptive power, and a perceived advantage over atom pairs is the increased "shape" information (intrapharmacophore distance relationships) content of the individual descriptors (37a). The quartet (tetrahedral) four-point descriptors offer further potential 3D content by including information on volume and chirality (37a, 82), compared with the triplets that are components of the quartets and represent planes or "slices" through the 3D shapes. 

The nondifferentiability of these surfaces at the seams of interpenetrating spheres as well as the local nondifferentiability of solvent accessible surfaces or union surfaces, are a technical disadvantage. Local nondifferentiability limits the application of the shape group methods in their original form that requires second derivatives for curvature analysis. For example, at every point r of a VDWS where two or more atomic spheres interpenetrate one another, the surface is not smooth and is not differentiable. For such nondifferentiable molecular surfaces, alternative shape descriptors and shape codes have been introduced. 

In this case, the row siuns of the geometry matrix are obtained by summing only the geometric distance powers of the atoms belonging to the periphery, and the average is found from the number of the contributing atoms only. Each atomic distance sum is considered as a local indicator of molecular shape, and each molecular invariant S is considered a global shape descriptor. 

Proposed as an extension of the - Kier shape descriptors to account for zero order paths, i.e. the atoms A, it is defined as the total information content of the molecule [Kier, 1987b] ... 

The Diverse Property-Derived method (DPD method) is based on the partitioning of six noncorrelated molecular descriptors and physico-chemical properties [Ashton, Jaye et al, 1996]. These are a lipophilicity descriptor (CLOGP), an electrotopological index calculated as normalized sum of the squares of the atomic electrotopological state indices, the number of hydrogen-bond acceptors (HBA), the number of hydrogen-bond donors (HBD), a flexibility index defined as the ratio of the —> Kier shape descriptors over k, and the aromatic density defined as the number of aromatic rings over the molecular volume (Table Cl). 

This is a model for the assessment of log Phased on 363 molecular descriptors derived from the molecular topology and obtained from 6675 diverse chemicals, with r = 0.986 and s = 0.20 [Gombar and Enslein, 1996 Gombar, 1999]. Among the molecular descriptors considered are molecular weight, electrotopological state indices, Kier shape descriptors of order 1-7, and some symmetry descriptors. In particular, several descriptors are defined as the sum of the E-states of the atoms involved in the whole molecule or in predefined molecular fragments. 

Steric fields derived from the CoMFA method [75] were used as 3D shape descriptors, while their major drawback is that a reliable superposition rule for databases is required. Thus, topomeric fields as significant enhancement for comparing the diversity of a set of variable groups attached to a common scaffold have been developed and validated [76], Those fields rely on canonical conformations of aligned compounds from combinatorial libraries using the reaction core. They use a novel way to encode flexibility depending on the shortest bond distance between any atom to the reaction core. 

Earlier work in this area of shape analysis focused on QSAR studies accounting for conformational features of molecules, such as interatomic distances [89], explicit atomic coordinate sets [90], computed intermolecular distances [91], and simpler shape descriptors such as molecular volume [92]. Each of these descriptor types formally requires conformational analysis, and therefore produces, accordingly, a family of solutions for most structures. 

A comparison with the corresponding values of equations (3)-(5) shows that the descriptors D, D, D, in which the atoms in the interior as well as those at the periphery contribute, are superior in describing Chromatographic indices of benzenoids. The superiority of over 5 descriptors becomes even more pronounced if we limit the analysis only to peri-condensed benzenoids for which the descriptors "D and differ. In Table 27 we compare the regressions using the shape descriptors and the full descriptors... 

A Binding Moment Approach to Molecular Orientation. Except for the Kier index, each of the conventional molecular shape descriptors requires a standard orientation of the structure. In the case of the shadow and length/breadth descriptors, this is along principal axes of the molecule. In the case of the MSA descriptors, the structures were aligned by matching the following three atoms ... 

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