Topological autocorrelation vectors

Topological autocorrelation vectors are calculated from the two-dimensional structure of a molecule that can be expressed as molecular graph. One of the original 

The properties p of the atoms i and j are considered for a particular topological distance d. Sjj is a Kronecker delta that represents additional constraints or conditions. The topological distance may also be replaced by the Euclidean distance, thus accounting for two- or three-dimensional arrangement of atoms. Three-dimensional spatial autocorrelation of physicochemical properties has been used to model the biological activity of compound classes [24]. In this case, a set of randomly distributed points is selected on the molecular surface, and all distances between the surface points are calculated and sorted into preset intervals. These points are used to calculate the spatial autocorrelation coefficient for particular molecular properties, such as the molecular electrostatic potential (MEP). The resulting descriptor is a condensed representation of the distribution of the property on the molecular surface. 

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. 

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

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. 

Bauknecht, H., Zell, A., Bayer, H., Levi, P, Wagener, M., Sadowski, J. and Gasteiger, J. (1996). Locating Biologically Active Compounds in Medium-Sized Heterogeneous Datasets by Topological Autocorrelation Vectors Dopamine and Benzodiazepine Agonists. J.Chem.Inf.Com-putScL, 36,1205-1213. 

In contrast to the topological autocorrelation vectors in the 3D autocorrelation vector, the spatial distance between atoms is used for calculation. Flence, using 3D autocorrelation vectors, it is possible to distinguish between different conformations of a molecule. The calculation of autocorrelation vectors of surface properties is similar to equation (10.2) ... 

Autocorrelation Vectors (topological autocorrelation vectors, autocorrelation of a topological Structure, ATS) are molecular descriptors for a property distribution along the topological structure. 

H Bauknecht, A Zell, H Bayer, et al. Locating biologically active compounds in medium-sized heterogeneous datasets by topological autocorrelation vectors dopamine and benzodiazepine agonists. J Chem Inf Comput Sci 36 1205-1213, 1996. 

The topological autocorrelation vector is invariant with respect to translation, rotation and the confotmer of the molecule considered. An alignment of molecules is not necessary for the calculation of their autocorrelation vectors. 

Topological autocorrelation vectors were also used by Gasteiger [21] as input to a Kohonen network which successfully separated dopamine from benzodiazepine receptor agonists, even when these compounds were embedded in a large and diverse set of chemicals extracted from a commercial supplier catalog. Gasteiger [22] has also extended the concept to... 

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