Multidimensional QSAR

Lill MA, Dobler M, Vedani A. Prediction of small-molecule binding to cytochrome P450 3A4 Flexible docking combined with multidimensional QSAR. ChemMedChem 2006 6 73-81. 

Alternatively, various attempts were made to derive computational models for a large and diverse set of molecules ranging from 2D-QSAR, 3D-QSAR, multidimensional QSAR, to structure-based simulations and combinations of docking and QSAR. 

Lill MA, Winiger F, Vedani A, Ernst B. Impact of induced fit on ligand binding to the androgen receptor A multidimensional QSAR study to predict endocrine-disrupting effects of environmental chemicals. J Med Chem 2005 48 5666-74. 

Vedani A, Zumstein M, Lill MA, Ernst B. Simulating a/p specificity at the thyroid receptor Consensus scoring in multidimensional QSAR. ChemMedChem, 2007 2 78-87. 

Lill, M. A., Vedani, A. Combining 4D pharmacophore generation and multidimensional QSAR modelling hgand binding to the bradykinin B2 receptor. J. Chem. Inform. Model. 2006, 46, 2135-2145. 

Albuquerque, M. G., Araujo de Brito, M., Ferreira da Cunha, E. F., Bicca de Alencastro, R., Antunes, O. A. C., Castro, H. C., Rodrigues, C. R. Multidimensional-QSAR beyond the third-dimension in drug design. Curr. Meth. Med. Chetrc Biol Phys. 2007,1, 91-100. 

Vedani, A. and Dobler, M. (2002) Multidimensional QSAR moving from three- to five-dimensional concepts. Quant. Struct. -Act. Rdat., 21, 382-390. 

Partial least squares (PLS) projections to latent structures [40] is a multivariate data analysis tool that has gained much attention during past decade, especially after introduction of the 3D-QSAR method CoMFA [41]. PLS is a projection technique that uses latent variables (linear combinations of the original variables) to construct multidimensional projections while focusing on explaining as much as possible of the information in the dependent variable (in this case intestinal absorption) and not among the descriptors used to describe the compounds under investigation (the independent variables). PLS differs from MLR in a number of ways (apart from point 1 in Section 16.5.1) ... 

Multidimensional linear regression analysis is the most often employed statistical method for QSARs, This popularity is coupled to the acceptance of the Hansch method for QSAR analyses. The techniques and pitfalls of regression analysis have been well described.(44,45)... 

Odor and taste quality can be mapped by multidimensional scaling (MDS) techniques. Physicochemical parameters can be related to these maps by a variety of mathematical methods including multiple regression, canonical correlation, and partial least squares. These approaches to studying QSAR (quantitative structure-activity relationships) in the chemical senses, along with procedures developed by the pharmaceutical industry, may ultimately be useful in designing flavor compounds by computer. 

A relatively recent technique employed in the generation of QSARs is principal components analysis (PCA), which is viewed by many as a successor to MRA. This alternative approach analyzes the multidimensional variable space of structural descriptors to yield QSAR equations of usually higher statis-... 

In QSAR modeling, the question of molecular representation is central. For the modeling, a molecule is represented as a multidimensional vector, i.e., a molecule is a point in multidimensional representational space. An ideal representation should be unique, uniform, reversible, and invariant on rotation and translation of molecules. Unique means that different structures give different representations, uniform means that the dimension of representation is the same for all structures, reversible means that the structure can be unambiguously reconstructed from the representation vector. Furthermore, invariant means that the representation is not sensitive if a molecule is rotated or translated. It is not expected that we would find a general representation that fulfills all requirements simultaneously [26]. Nowadays, thousands of descriptors and structural representations are in use [26-29]. We will give a short overview, and references about descriptors that often appear in QSAR studies related to mutagenicity of aromatic amines are presented in more detail. 

It is clear that for an unsymmetrical data matrix that contains more variables (the field descriptors at each point of the grid for each probe used for calculation) than observables (the biological activity values), classical correlation analysis as multilinear regression analysis would fail. All 3D QSAR methods benefit from the development of PLS analysis, a statistical technique that aims to find the multidimensional direction in the X space that explains the maximum multidimensional variance direction in the F space. PLS is related to principal component analysis (PCA)." ° However, instead of finding the hyperplanes of maximum variance, it finds a linear model describing some predicted variables in terms of other observable variables and therefore can be used directly for prediction. Complexity reduction and data... 

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