Solubility topological descriptors

Several research groups have built models using theoretical desaiptors calculated only from the molecular structure. This approach has been proven to be particularly successful for the prediction of solubility without the need for descriptors of experimental data. Thus, it is also suitable for virtual data screening and library design. The descriptors include 2D (two-dimensional, or topological) descriptors, and 3D (three-dimensional, or geometric) descriptors, as well as electronic descriptors. 

Tutorial Developing Models for Solubility Prediction with 18 Topological Descriptors... 

Figure 10.1-3. Predicted versus experimental solubility values of 552 compounds in the test set by a back-propagation neural network with 18 topological descriptors.

T. Petrova et al., Modeling of fullerene C60 solubility in organic solvents The use of quantum-chemical and topological descriptors in QSPR study. J. Nanopart. Res., 2009 (submitted)... 

Votano JR, Parham M, Hall LH, Kier LB. New predictors for several ADME/Tox properties Aqueous solubility, human oral absorption, and Ames genotoxicity using topological descriptors. Mol Divers 2004 8 379-91. 

Figure 9.2 The root mean squared error (RMSE) of models for prediction of aqueous solubility of chemical compounds shown as a function of the number of molecules, n, used for model development and validation. The results of methods developed using quantum chemical (3D), topological descriptors (2D/1D), and methods based on other physicochemical descriptors (PhysChem) are shown.

Yan AX, Gasteiger J. Prediction of aqueous solubility of organic compounds by topological descriptors. QSAR Combin Sci 2003 22 821-9. 

By considering QSAR orthogonal descriptors with associate min-max prescription in chemical reactivity (as exposed for the consecrated chemical reactivity descriptors, to which other may be added, as related to solubility, topology, etc.) ... 

In this approach, connectivity indices were used as the principle descriptor of the topology of the repeat unit of a polymer. The connectivity indices of various polymers were first correlated directly with the experimental data for six different physical properties. The six properties were Van der Waals volume (Vw), molar volume (V), heat capacity (Cp), solubility parameter (5), glass transition temperature Tfj, and cohesive energies ( coh) for the 45 different polymers. Available data were used to establish the dependence of these properties on the topological indices. All the experimental data for these properties were trained simultaneously in the proposed neural network model in order to develop an overall cause-effect relationship for all six properties. 

It is to be noted that in fact the optimal descriptors examined in the present study are topological characteristics. In other words, no information, except the topology of solvent molecules and experimental values of the fullerene C60 solubility, has been used. 

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. 

Yalkowsky and Banerjee have pubhshed an extensive review of methods for estimating aqueous water solubility of organic compounds. Many methods have been developed based on measured properties such as partition coefficients, chromatographic parameters, and activity coefficients. " Purely in silico methods are based on LFER, and a variety of geometric, electronic, and topological molecular descriptors. ... 

Log P can be used as an additional parameter, in combination with other descriptors. For example, neural network models developed by Liu and So and Goller et al use log P in combination with topological and quantum-chemical descriptors. Many methods do not use log R as a descriptor. These methods have been described in several reviews. However, there is a clear relationship between these two physicochemical properties, namely log P and aqueous solubility. 

Methods Using 2D and ID Descriptors A good number of articles on aqueous solubility used a nonlinear method of data analysis, in particular, for methods developed with ID and 2D descriptors. Huuskonen [16] used E-state indexes [52,53] and several other topological indexes, with a total of 30 indexes, to develop his models. The predicted results for the 413 test set, SE = 0.71, calculated with MLRA were improved with a neural network, resulting in SE = 0.6. Tetko [17] noticed that E-state indexes represent a complete system of descriptors for molecules, and thus only these descriptors are sufficient to develop the aqueous solubility model. Indeed the model developed by the authors using exclusively E-state indexes provides similar results when compared to the model of Huuskonen [16]. Later on, the model was redeveloped using the Associative Neural Network (ASNN) method [54],... 

In view of these studies Balakin et al. [22] concluded that there is no statistical support for the idea that 3D descriptors are more appropriate for prediction of aqueous solubility of chemicals compared to 2D or ID methods. Because of the difficulties in generating and finding conformational minimum for 3D structures, one should initially try more simple indexes based on molecular topology. The big advantage of the later method is their speed 2D methods can typically process tens of thousands of molecules per second, and that makes them very useful for screening of virtual libraries of compounds. 

Figure 9.2 represents a plot of errors in the methods reviewed above as well as in those of several other works [22,44,59]. As the figure demonstrates, there is no apparent difference in the performance of methods developed with any particular group of descriptors, that is, quantum-chemical (median RMSE = 0.47) and topological (median RMSE = 0.53), or using physicochemical descriptors (median RMSE = 0.50). The median error of all methods (RMSE = 0.51) approximately corresponds to the experimental error of solubility measurements. 

Goller AH, Hennemann M, Keldenich J, Clark T. In sihco prediction of buffer solubility based on quantum-mechanical and HQSAR- and topology-based descriptors. J Chem Inf Model 2006 46 648-58. 

Ivanciuc, O. (2001g) Design of topological indices. Part 26. Structural descriptors computed from the Laplacian matrix of weighted molecular graphs modeling the aqueous solubility of aliphatic alcohols. Rev. Roum. Chim., 46, 1331-1347. 

Similar relationships have also been derived with other descriptors that are generally collinear with log for non-polar non-specific toxicants for example, water solubility (Konemann, 1981b Zaroogian et al., 1985), topological indices (Basak and Magnuson, 1983 Koch, 1983 Sabljic, 1983), or with substructure indicators (Hall, Maynard and Kier, 1989), which may be applied if the log P of the test compounds cannot be estimated, and also to cross-check the predictions obtained, especially when there is reasonable doubt about the correctness of the respective log P values. 

In actual applications of MSA, many different types of representations are utilized to compute molecular similarities [41, 52-54]. Johnson [55] has provided a detailed discussion of the manifold types of mathematical spaces and their associated representations. The information contained in the representations is usually in the form of molecular or chemical features called descriptors that are derived from the structural and chemical properties of molecules. Descriptors ate nominally classified as ID (one-dimensional), 2D, or 3D. ID descriptors are usually associated with whole molecule properties such as molecular weight, logP, solubility, number of hydrogen bond donors, nnmber of rotatable bonds, and so on. 2D descriptors are associated with the topological strnctnre of molecules as typically depicted in chemists drawings. Such depictions show the atoms, the bonds connecting them, and in some cases include stereochemical features, but they do not explicitly depict the 3D structures of molecules. 3D descriptors, as their name implies, are associated with the 3D structures of molecules. Todeschini and Consonni [56] have compiled an extensive reference containing many of the descriptors used in chemical informatics applications. 

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