Topological structural descriptors

KRose, L.H. Hall, L. Hall and L.B. Kier, Modeling Blood-Brain Barrier Partitioning Using Topological Structure Descriptors, MDL-Whitepaper, 2003. 

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). 

Clerc, J.T and Terkovics, A.L. (1990) Versatile topological structure descriptor for quantitative stmcture/property studies. Anal. Chim. Acta, 235, 93-102. 

These pharmacophore techniques are different in format from the traditional pharmacophore definitions. They can not be easily visualized and mapped to the molecular structures rather, they are encoded as keys or topological/topographical descriptors. Nonetheless, they capture the same idea as the classic pharmacophore concept. Furthermore, this formalism is quite useful in building quantitative predictive models that can be used to classify and predict biological activities. 

Ivanduc, O., Ivanduc, T. Matrices and structural descriptors computed from molecular graph distances. In Topological Indices and Related Descriptors in QSAR and QSPR, Devillers, J. Balahan, A. T. (eds.), Gordon Breach, Amsterdam, 1999, pp. 221-277. 

Ivanciuc, 0. Design of topological indices. Part 25. Burden molecular matrices and derived structural descriptors for glycine antagonists QSAR models. Rev. Roum. Chim. 2001, 46, 1047-1055. 

Voelkel, A. Structural descriptors in organic chemistry - new topological parameter based on electrotopological state of graph vertices. Comput. Chem. 1994, 18, 1. ... 

In addition to looking for data trends in physical property space using PCA and PLS, trends in chemical structure space can be delineated by viewing nonlinear maps (NLM) of two-dimensional structure descriptors such as Unity Fingerprints or topological atom pairs using tools such as Benchware DataMiner [42]. Two-dimensional NLM plots provide an overview of chemical structure space and biological activity/molecular properties are mapped in a 3rd and/or 4th dimension to look for trends in the dataset. 

The second variant of QSAR is the use of actual structural descriptors, such as molecular orbital indices or topological codes, to define numerically the structure of a molecule and to find linear relationships with numerical biological data (Kier and Hall, 1976, 1992). 

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... 

Quantitative structure-activity relationships represent an attempt to correlate activities with structural descriptors of compounds. These physicochemical descriptors, which include hydrophobicity, topology, electronic properties, and steric effects, are determined empirically or, more recently, by computational methods. The success of a QSAR method depends on two factors the training dataset obtained by testing a group of chemicals and the descriptors obtained from some easily measurable or calculable property of the chemicals. 

Carhart et al. [15] described a generalized structural descriptor called an atom pair which is defined in terms of the atomic environments of, and shortest path separation between, all pairs of atoms in the topological representation of a chemical structure. A similar descriptor has been suggested by Klopman [16]. More recently, Judson [20] described a more sophisticated approach to analyze structural feature of molecules for structure-activity studies. 

Quantitative structure-activity relationship (QSAR) (Hansch and Klein, 1986 Hansch and Leo, 1995) represents an attempt to correlate structural descriptors of compounds with activities. The physicochemical descriptors include numerical parameters to account for electronic properties, steric effect, topology, and hydrophobicity of analogous compounds. In its simplest form, the biochemical activities are correlated to the numerical substituent descriptors of analogous compounds tested by a linear equation such as... 

TSARBatch for Windows Accelrys Inc. www.accelrys.com Log K, various topological, structural, 3D and molecular orbital descriptors... 

The structure of a chemical is responsible for the presence and magnitude of its properties. The properties can be energy levels and their derivatives, as well as physicochemical, or biological, properties. To avoid discrimination between the different properties (which are the subject of detailed consideration in Chapters 3, 4, and 6) in the context of quantitative relationships between structural descriptors (i.e., topological indices [TIs]) and various properties, we will use the broader abbreviation QSPR (Quantitative Structure-Property Relationship). 

The aims of this chapter are to illustrate to the reader (1) the calculation of some commonly used TIs and structural descriptors, (2) the current status of the interpretation of topological indices, and (3) to make some recommendations regarding the application of the structural descriptors in QSPR studies. 

Finally, some authors (Lu et al., 2000 Sabljic, 2001) suggest that due to the significant correlation between the topological indices and physicochemical properties, such as log Kow the former alone or in principal components can replace the latter in the QSPR models. The strongest support of this point of view is probably the fact that the TIs do not bring experimental or calculation error into the models. For the successful replacement of physicochemical properties such as log Kow, more than one structural descriptor is often required, which reflects the stability and interpretability of the resulting models. 

Although various computational approaches for the prediction of intestinal drug permeability and solubility have been reported [219], recent computer-based absorption models utilize a large number of topological, electronic, and geometric descriptors in an effort to take both aqueous drug solubility and permeability into account. Thus, descriptors of partitioned total surface areas [168], Abraham molecular descriptors [220,221], and a variety of structural descriptors in combination with neural networks [222] have been shown to be determinants of oral drug absorption. 

---