3D-MoRSE Code

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]. 

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. 

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. 

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 ... 

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... 

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. 

In the three-dimensional (3D) approach the 3D structure (see Structure Generators) of a molecule is transformed into a structure code. This is performed by regarding every atom pair in the molecule as a point scatterer and calculating the center symmetric diffraction pattern of the molecule as it would be obtained from an electron diffraction experiment. Based on these equations the 3D molecular representation of structures based on electron diffraction (3D-MoRSE) code has been developed. The 3D-MoRSE code is calculated using the equation... 

Figure 6 shows the 3D-MoRSE codes for cyclohexane, benzene, and s-triazine. A careful analysis of the code patterns shows some similarities of code regions corresponding to partial similarities of the structures (e.g., ring systems). 

Figure 7 Experimental IR spectrum of cholesterol and the spectrum simulated using the 3D-MoRSE code and a CPG network...

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