Molecules structure, QSAR modeling molecular descriptors

Once a QSAR model is constructed, it must be validated using the external test set. The data points in the test set should not appear in the training set. There are two approaches to improve the prediction accuracy for a given QSAR model. The first approach utilized the concept of "the domain of applicability," which is used to estimate the uncertainty in prediction of a particular molecule based on how similar it is to the compound used to build the model. To make a more accurate prediction for a given molecule in the test set, the structurally similar compounds in the training set are used to construct model and that model is used to make the prediction. In some cases, the domain similarity is measured using molecular descriptor similarity, rather than the structural similarity. The... 

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-... 

Molecular descriptors may provide fundamental and scientific explanations of variations in the activity mechanism due to the structure of molecules. QSAR models can provide insight into kinetic mechanisms of organic compounds, and some of the design uncertainty associated with SCWO kinetics can be reduced. By using appropriate molecular descriptors, then, the results of QSAR models for SCWO could be used to determine the oxidation rate constants of organic compounds of structure similar to the training set chemicals of the QSAR model without experiments. 

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... 

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. 

In our contribution we have focused the discussion on descriptors. The understanding of descriptors is essential for transparency of models and can also lead to mechanistic interpretation of models. Several questions are associated with descriptors. First of all, nowadays thousand of descriptors are defined and can be easily calculated with available software and the first question is how to the select the most relevant descriptors. The topological descriptors are sometimes promising, but there is no clear physicochemical interpretation for them. 3D molecular structure is a problematic quantity as it depends on the media where the molecule is, or on the method of determination. Quantum chemical descriptors, which have a clear physicochemical interpretation, are difficult to calculated. In the cases studies we have addressed some of those questions. We have discussed the sensitivity of the models, and particularly predictions, to descriptors used. According to the critical review of Snyder and Smith [87] on QSAR models for mutagenicity prediction a lot of work still remains to be done. 

Different physical properties and molecular models have been used to define the molecular surface the most common are reported below together with the descriptors proposed as measures of surface areas and molecular volume (- volume descriptors). Molecular surface area and volume are parameters of molecules that are very important in understanding their structure and chemical behaviour such as their ability to bind ligands and other molecules. An analysis of molecular surface shape is also an important tool in QSAR and - drug design-, in particular, both - molecular shape analysis and - Mezey 3D shape analysis were developed to search for similarities among molecules, based on their molecular shape. 

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