Autocorrelation topological

Huang, Q.G., Song, W.L. and Wang, L.S. (1997). Quantitative Relationship Between the Physio-chemical Characteristics as well as Genotoxicity of Organic Polluttants and Molecular Autocorrelation Topological Descriptors. Chemosphere, 35,2849-2855. 

In order to transform the information fi om the structural diagram into a representation with a fixed number of components, an autocorrelation function can be used [8], In Eq. (19) a(d) is the component of the autocorrelation vector for the topological distance d. The number of atoms in the molecule is given by N. 

We denote the topological distance between atoms i and j (i.e., the number of bonds for the shortest path in the structure diagram) dy, and the properties for atoms i and j are referred to as pi and pj, respectively. The value of the autocorrelation function a d) for a certain topological distance d results from summation over all products of a property p of atoms i and j having the required distance d. 

A range of physicochemical properties such as partial atomic charges [9] or measures of the polarizabihty [10] can be calculated, for example with the program package PETRA [11]. The topological autocorrelation vector is invariant with respect to translation, rotation, and the conformer of the molecule considered. An alignment of molecules is not necessary for the calculation of their autocorrelation vectors. 

In contrast to the topological autocorrelation vector, it is possible to distinguish between different conformations of a molecule using 3D autocorrelation vectors. 

Topological descriptors and 3D descriptors calculated in distance space", such as 3D autocorrelation, surface autocorrelation, and radial distribution function... 

Through the application of the GA to the topological autocorrelation vector, the descriptor could be reduced from 136 to nine descriptors and the quality of projection was increased by 9.4%. Thus, besides the improvement in efficiency, an improvement in quality could be obtained. 

Figure 8.20. Generation of a ID correlation function, fl (x), by autocorrelation of the ID electron density, Ap (y) for a two-phase topology. Each value of ft (x) is proportional to the overlap integral (total shaded area) of the density and its displaced ghost...

Autocorrelation of Topological Structure Moreau and Broto [24,25] have suggested the autocorrelation vector of a molecular graph as the source for molecular descriptors. This method assumes that each atom i in the graph is uniquely associated with a numeric quantity, qit such as the atomic number, atomic mass, (v)(, (ds), Sv, or electronegativity. The intrinsic atom values of the electrotopological state [26] and the atomic Rd and log Kow parameters [27,28] are other potential atomic descriptors suitable to construct autocorrelation vectors. Generally, the fcth element of the autocorrelation vector is defined as... 

Spatial autocorrelation is a quantitative measure of the probability of finding objects of defined properties within a distance of interest [9, 10]. The concept of autocorrelation is mainly applied in fields such as geography, economics, ecology or meteorology to describe the spatial distribution of features. The idea of a molecular descriptor based on the autocorrelation concept was first introduced into the field of cheminformatics by Moreau and Broto in 1980 [11] with the ATS (autocorrelation of a topological structure) descriptor. For this approach, the atoms of a molecule were represented by properties such as atomic mass or partial charge. The distance between atoms was measured as the number of bonds between the respective atoms (topological distance). 

In 1996, Sheridan et al. [16] were the first to use pharmacophoric atom types for an autocorrelation approach. This technique is suited to characterize ligand-receptor interactions in a general way, allowing for more different but equally interacting molecules to be identified as similar. Sheridan et al. also extended the topological Carhart approach to the 3D case, and this was soon followed up by a binary representation of such a descriptor [17]. In 2003, Stiefl and Baumann [18] reported an autocorrelation approach using surface points representing pharmacophoric features. 

The work of Schneider et al. [6] first focused on the scaffold-hopping ability of autocorrelation descriptors, in this case topological pharmacophores. The general description of the atoms with pharmacophore atom types in combination with the decomposition of molecules into atom pairs was shown to be especially successful in finding new molecules with significant different molecular scaffolds, maintaining the desired biological effect. 

Bauknecht et al. [48] and Sadowski et al. [49] have also developed molecular descriptors that are based on the physicochemical properties of the atoms in a molecule. They calculate several different electronic properties for each atom in a molecule and then use autocorrelation to generate a fixed-length vector that is independent of the size of the molecule. Autocorrelation was first applied to the topology of a molecular structure by Moreau and Broto [50] using the following function ... 

Moreau has proposed the autocorrelation of topological molecular structure (ATS) value. The function is defined in (13). 

DRAGKDN— implementation of about 1400 descriptors of Todeschini and Consonni (114) including constitutional, topological, autocorrelation, geometrical and functional... 

For spatial autocorrelation molecular descriptors calculated on a - molecular graph, lag I is defined as the - topological distance d. 

Moreau-Broto autocorrelation (. Autocorrelation of a Topological Structure, ATS) This is a spatial autocorrelation defined on a molecular graph C as ... 

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