3D-MoRSE

D MoRSE desaiptor, radial distribution function (RDF code), WHIM descriptors, GETAWAY descriptors,... 

D Molecule Representation of Structures Based on Electron Diffraction Code (3D MoRSE Code)... 

The 3D MoRSE code is closely related to the molecular transform. The molecular transform is a generalized scattering function. It can be used to predict the intensity of the scattered radiation i for a known molecular structure in X-ray and electron diffraction experiments. The general molecular transform is given by Eq. (22), where i(s) is the intensity of the scattered radiation caused by a collection of N atoms located at points r. ... 

Steinhauer and Gasteiger [30] developed a new 3D descriptor based on the idea of radial distribution functions (RDFs), which is well known in physics and physico-chemistry in general and in X-ray diffraction in particular [31], The radial distribution function code (RDF code) is closely related to the 3D-MoRSE code. The RDF code is calculated by Eq. (25), where/is a scaling factor, N is the number of atoms in the molecule, p/ and pj are properties of the atoms i and/ B is a smoothing parameter, and Tij is the distance between the atoms i and j g(r) is usually calculated at a number of discrete points within defined intervals [32, 33]. 

Beside the descriptors, further attempts have been made to encode the 3D molecular structures with functions. Such are 3D-MoRSE code [54] spectrum-like representations [55] and radial distribution functions [56]. Also, experimentally determined infrared, mass, or NMR spectra can be taken to represent a molecule [57]. Another example is comparative molecular field analysis (CoMFA) where the molecular 3D structures are optimized together with the receptor [58]. This approach is often applied in drug design or in specific toxicology studies where the receptor is known. The field of molecular descriptors and molecular representations has exploded in the recent decades. Over 200 programs for calculating descriptors and different QSAR applications are listed on web page [59]. 

Examples of geometrical descriptors are the - quantum-chemical descriptors, -> moment of inertia, - length-to-breadth ratio, -> surface areas, - volume descriptors, - CPSA descriptors, -> EVA descriptors, -> WHIM descriptors, 3D-MoRSE descriptors, -> interaction energy values, spectrum-like descriptors. 

From the geometry matrix, the usual -> graph invariants can be calculated such as -t characteristic polynomial, -> eigenvalue-based descriptors, -> path counts, - ID numbers, -> 3D-Balaban index, -> 3D-Schultz index and so forth [Randic, 1988b Nikolic et al, 1991]. It is noteworthy that all these indices are sensitive to molecular geometry. Moreover, the geometry matrix is used for the calculation of size descriptors and - 3D-MoRSE descriptors. 

These descriptors are based on the distance distribution in the - geometrical representation of a molecule and constitute a radial distribution function code (RDF code) that shows certain characteristics in common with the - 3D-MoRSE code. 

Attention to the combination of the molecular geometry with chemical atomic information has led to the development of spectral molecular representations given, for example, by -> 3D-MoRSE descriptors [Schuur and Gasteiger, 1996], - RDF descriptors [Hemmer et al, 1999], - spectrum-like descriptors [Novic and Zupan, 1996], -+ EVA descriptors [Ferguson et al, 1997], -> SWM signals [Todeschini et al, 1999], and - Blurock spectral descriptors [Blurock, 1998]. 

Examples of applications of the rules to obtain uniform length descriptors are - EVA descriptors, - topological charge indices, atomic walk count sequence, -+ SE-vectors, - molecular profiles, -> 3D-MoRSE descriptors, - autocorrelation descriptors. 

D-molecule representation of structures based on electron diffraction 3D-MoRSE descriptors... 

D-MoRSE descriptors ( 3D-M0lecule Representation of Structures based on Electron diffraction, MoRSE descriptors)... 

Soltzberg Wilkins introduced a number of simplifications in order to obtain a binary code. Only the zero crossing of the I s) curve, i.e. the values at which I(s) = 0 in the range 1 - 31 A-i are considered. The s range is then divided into 100 equal intervals, each described by a binary variable equal to 1 if the interval contains a zero crossing, 0 otherwise. Thus, a 3D-MoRSE code consisting of a 100-dimensional binary vector is obtained. 

RDF descriptors have recently been proposed based on a radial distribution function with some characteristics in common with the I s) function used to obtain the 3D-MoRSE descriptors. 

Description WebSite Calculation of several sets of molecular descriptors from molecular geometries (topological, geometrical, WHIM, 3D-MoRSE, molecular profiles, etc.). http //www.disat.unimib.it/chm/... 

Schuur, J. and Gasteiger, J. (1996). 3D-MoRSE Code - A New Method for Coding the 3D Structure of Molecules. In Software Development in Chemistry - Vol. 10 (Gasteiger, J., ed.), Fach-gruppe Chemie-Information-Computer (CIC), Frankfurt am Main (Germany), pp. 67-80. 

D autocorrelation, 3D MoRSE code, and radial distribution function code... 

The radial distribution function code (RDF code) is closely related to the 3D-MoRSE code and it is calculated by equation (10.3) ... 

Another code for representation of the 3D structure of a molecule with a fixed number of variables irrespective of the number of atoms in the molecule (3D MoRSE code) has been proposed by Soltzberg and Wilkins. This molecular description is based on methods used in the interpretation of electron diffraction data. The approach has been used successfully for both the simulation of infrared spectra... 

Many years later, it was found that this characteristic of the descriptor could be used for the correlation of biological activity and three-dimensional structure of molecules. The activity of a compound also depends on the distances between atoms (such as H-bond donors or acceptors) in the molecular structure [91]. Adaptation of the RBF function to biological activity led to the so-called 3D-MoRSE code (3D-Molecule Representation of Structures based on Electron diffraction) [92]. The method of RBF calculation can be simplified in order to derive a descriptor that includes significant information and that can be calculated rapidly ... 

Gasteiger et al. returned to the initial I s) curve and maintained the explicit form of the curve [36]. For A they substituted various physicochemical properties such as atomic mass, partial atomic charges, and atomic polarizability. To obtain uniform length descriptors, the intensity distribution I s) is made discrete, calculating its value at a sequence of evenly distributed values of, for example, 32 or 64 values in the range of 0 - 3lA. The resolution of the molecule representation increases with higher number of values. The resulting descriptor is the 3D MoRSE (Molecular Representation of Structures based on Electron diffraction) Code. 

D MoRSE codes are valuable for conserving molecular features, but it is not possible to interpret them directly. This drawback leads to investigations of related types of descriptors. Steinhauer and Gasteiger picked up the idea of radial distribution... 

RDFs have certain characteristics in common with the 3D Molecular Representation of Strnctnres Based on Electron Diffraction (MoRSE) code. In fact, the theory of RDF is related to the theoretical basis of 3D MoRSE functions. In 1937, Degard nsed the exponential term in the RDE to account for the experimental angular limitations in electron diffraction experiments [2]. 

In electron diffraction experiments, the intensity is the Eourier transform of dnr j gif) and is related to the electron distribution in the molecule [3]. The Eourier transform of a 3D MoRSE code leads to a frequency pattern, but lacks a most important feature of RDF descriptors the frequency distribution. In contrast to the corresponding RDF descriptors 3D MoRSE codes can be hardly interpreted directly. Nevertheless, 3D MoRSE codes lead to similar results when they are used with methods where direct interpretability is not required. 

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