Molecules structure, QSAR modeling statistical methods

Any QSAR method can be generally defined as an application of mathematical and statistical methods to the problem of finding empirical relationships (QSAR models) of the form ,- = k(D, D2,..., D ), where ,- are biological activities (or other properties of interest) of molecules, D, P>2,- ,Dn are calculated (or, sometimes, experimentally measured) structural properties (molecular descriptors) of compounds, and k is some empirically established mathematical transformation that should be applied to descriptors to calculate the property values for all molecules (Fig. 6.1). The goal of QSAR modeling is to establish a trend in the descriptor values, which parallels the trend in biological activity. In essence, all QSAR approaches imply, directly or indi-... 

For deriving a QSAR model, three different types of elements are required (Figure 23.1). First, a measured endpoint for a set of molecules has to be available. Second, chemicals must be described by means of their physicochemical properties or structurally derived parameters. Last, a statistical method must be used for linking the first two elements. These three critical ingredients of the general methodology in the derivation of a QSAR model are briefly discussed in the next sections. 

Three-dimensional quantitative structure-aaivity relationships (3D-QSARs) are quantitative models that relate the biological activity of small molecules with their properties calculated in 3D space.All 3D-QSAR methods combine molecular modeling and statistical analysis of the relative biological potency within a set of compounds. In this chapter, we provide... 

We have seen that 3D-QSAR techniques use mathematical tools to compare three-dimensional representations of molecules with their biological properties. Most of the methods, except those relying on the 3D structure of the ligand-macromolecule complex, require that the molecules be aligned. Sometimes the alignment and the choice of the conformation are automated by the method, but usually these crucial details are left to the scientist. Because the methods are quantitative, they all rely on statistical validation of the model. Usually this is done by leave-one-out cross-validation, but data scrambling and true predictions are also used by many workers. 

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