QSAR/QSPR model

It is interesting to note that various QSAR/QSPR models from an array of methods can be very different in both complexity and predictivity. For example, a simple QSPR equation with three parameters can predict logP within one unit of measured values (43) while a complex hybrid mixture discriminant analysis-random forest model with 31 computed descriptors can only predict the volume of distribution of drugs in humans within about twofolds of experimental values (44). The volume of distribution is a more complex property than partition coefficient. The former is a physiological property and has a much higher uncertainty in its experimental measurements while logP is a much simpler physicochemical property and can be measured more accurately. These and other factors can dictate whether a good predictive model can be built. 

A QSAR/QSPR model can be defined as a mathematical relationship, Y=f(X), between any physical, chemical, or biological property (Y) of a molecule and its chemical structure.6 The main problems here are to define a functional dependence (/), to select a set of pertinent molecular descriptors (X), and to establish a protocol... 

Xu YJ, Gao H (2003) Dimension related distance and its application in QSAR/QSPR model error estimation. QSAR Comb Sci 22 422—429... 

Figure 1.14 General scheme of constructing linear QSAR/QSPR models based on fragment descriptors.

Benchmarking studies on various biological and physicochemical properties 307,312 QSAR/QSPR models for involving fragment descriptors... 

Graph-invariants have been successfully applied in characterizing the structural similarity/dissimilarity of molecules and in QSAR / QSPR modelling. 

Model complexity is an important parameter to compare different QSAR/QSPR models. Moreover, the prediction power of a model is inversely related to its complexity. 

It should be noted that some invariance properties such as invariance to atom numbering and roto-translations are mandatory for molecular descriptors used in QSAR/ QSPR modelling in several cases, chemical invariance is required, particularly when dealing with a series of compounds with different substituents moreover, conformational invariance is closely dependent on the considered problem. 

Quantitative Infonnation Analysis is the term proposed by Kier to denote structure/response correlations, where the word analysis is chosen to avoid any restriction to QSAR/QSPR models, but naturally includes similarity/diversity analysis as well as any explorative analysis or model which refers not only to relationships with the molecular structure. 

Well-known substituent descriptors are the substituent constants which are experimentally determined descriptors among them, - electronic substituent constants, steric substituent descriptors, and lipophilicity substituent descriptors such as - Hansch-Fujita hydrophobic constants are the most commonly used in QSAR/QSPR modelling. 

Some basic concepts and definitions of statistics, chemometrics, algebra, graph theory, similarity/diversity, which are fundamental tools in the development and application of molecular descriptors, are also presented in the Handbook in some detail. More attention has been paid to information content, multivariate correlation, model complexity, variable selection, and parameters for model quality estimation, as these are the characteristic components of modern QSAR/QSPR modelling. 

The concept of the applicability domain concerns the predictive use of QSAR/QSPR models and, then, is closely related to the concept of model validation ( validation techniques). In other vords, the applicability domain is a concept related to the quality of the QSAR/QSPR model predictions and prevention of the potential misuse of model s results. A key component of the prediction quality is indeed to define when a QSAR/QSPR model is suitable to predict a property/activity of a new compound [Tropsha, Gramatica et al, 2003 Jaworska, Nikolova-Jeliazkova et al, 2004 Dimitrov, Dimitrova et al, 2005 Jaworska, Nikolova-Jeliazkova et al, 2005 Netzeva, Worth et al, 2005 Nikolova-Jeliazkova and Jaworska, 2005],... 

A model will yield reliable predictions when model assumptions are fulfilled and unreliable predictions when they are violated. In particular, for QSAR/QSPR models, based on statistical mining techniques, the training set and the model prediction space are the basis for the estimation of space where predictions are reliable. 

The first approach to applicability domain evaluation is the statistical analysis of the training set, trying to define the best conditions for interpolated prediction that is usually more reliable than extrapolation. Extrapolation is not a problem in principle, because extrapolated results from theoretically well-founded models can often be reliable. However, QSAR/QSPR models are usually based on empirical, and limited experimental evidence and/or are only locally valid therefore, extrapolation usually results in high uncertainty and not reliable predictions. 

Note that spectral moments of the distance matrix increase very quickly, thus requiring a proper scaling to be used in QSAR/QSPR modeling. 

Index scale can be used as a measure of hydrophobicity of compounds for QSAR/QSPR modeling studies [Ishihama, Oda et al., 1996 Fatemi, 2003],... 

In general, coefficients, roots, and derivatives of counting polynomials can be used for characterization of molecular graphs and as molecular descriptors in QSAR/QSPR modeling. 

In the Gomparative Spectra Analysis (GoSA), digitalized spectra were used as molecular descriptors for QSAR/QSPR modeling [Bursi, Dao et al., 1999 Bursi, Verwer et al, 2001 Beger... 

Steric effects are among the most relevant in modeling physico-chemical properties and biological activities, thus playing a fundamental role in QSAR/QSPR modeling. 

The development of QSAR/QSPR models is a quite complex process, as outlined in Figure S9. 

Another relevant aspect in structure/response correlations is the ability to obtain information about molecular structure from QSAR/QSPR models. In particular, the term reversible decoding (or inverse QSAR) denotes any procedure capable to reconstruct the molecular structure or fragment starting from molecular descriptor values, that is, once molecular... 

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