QSAR—

In order to parameterize a QSAR equation, a quantihed activity for a set of compounds must be known. These are called lead compounds, at least in the pharmaceutical industry. Typically, test results are available for only a small number of compounds. Because of this, it can be difficult to choose a number of descriptors that will give useful results without htting to anomalies in the test set. Three to hve lead compounds per descriptor in the QSAR equation are normally considered an adequate number. If two descriptors are nearly col-linear with one another, then one should be omitted even though it may have a large correlation coefficient. 

In the case of drug design, it may be desirable to use parabolic functions in place of linear functions. The descriptor for an ideal drug candidate often has an optimum value. Drug activity will decrease when the value is either larger or smaller than optimum. This functional form is described by a parabola, not a linear relationship. 

Like QSAR, molecular structures must be available for compounds that 

Once the molecules are aligned, a molecular field is computed on a grid of points in space around the molecule. This field must provide a description of how each molecule will tend to bind in the active site. Field descriptors typically consist of a sum of one or more spatial properties, such as steric factors, van der Waals parameters, or the electrostatic potential. The choice of grid points will also affect the quality of the final results. 

The field points must then be fitted to predict the activity. There are generally far more field points than known compound activities to be fitted. The least-squares algorithms used in QSAR studies do not function for such an underdetermined system. A partial least squares (PLS) algorithm is used for this type of fitting. This method starts with matrices of field data and activity data. These matrices are then used to derive two new matrices containing a description of the system and the residual noise in the data. Earlier studies used a similar technique, called principal component analysis (PCA). PLS is generally considered to be superior. 

Quantitative structure-activity relationships (QSAR) is primarily used for drug design. The underlying principle is that the shape and non-covalent interactions 

For a QSAR analysis, a training set of compounds with known descriptor properties (e.g., pJQ-values, surface area, dipole moment, etc.), including the property of interest, is required. The required dataset can be derived from experimental results or from high-level ab-initio or DFTdata. The Hansch analysis [81] is a statistical method used to analyze and correlate these data in order to determine the magnitude of the target property [Eq. (2.15)] the principal component analysis (PCA) is a more recent alternative [82-84]. 

Recent developments include three-dimensional (3-D) QSAR methods which relate regions of the binding site with complementary properties [85]. The conformation of each molecule then needs be computed and the descriptor property determined. Another interesting development is the electron topological (ET) approach in QSAR methods [86]. Molecular compounds are described by quadratic matrices (n, n number of atoms), where elements close to the diagonal represent electronic parameters while the other elements are related to the structure. 

Because of fhe stereospecifity of biological effects, QSAR (quantitative structure-activity relationships) methods must be capable of taking into account atomic chiralities. Indeed, one of fhe most popular 3D-QSAR methods, CoMFA and other CoMFA-like methods take into account chirality by default, since fhe molecular fields of chiral isomers are different If compounds are highly flexible and no experimental structural information about fhe receptor-ligand complexes is available, CoMFA (and CoMFA-like) methods are not always applicable. Several shortcomings and problems have motivated researchers to consider improvements to these techniques. The first idea for improvement was to modify the conventional 2D descriptors to make them chirahty-sensitive [1]. 

Chiral information is related to symmetry, it must be supplied in addition to geometric data. It is conceivable that a pre-geometric molecular paradigm such as a topological model could incorporate chiral information [1, 2]. 

Several series of novel chirality descriptors of chemical organic molecules were introduced by Golbraikh et al. [5, 6]. These descriptors have been implemented in a QSAR study with a high content of chiral and enantiomeric compounds. It was shown fhat for all data sets 2D-QSAR models that use a combination of chirahty descriptors wifh conventional topological descriptors afford better or similar predictive abihty when compared to models generated wifh 3D-QSAR approaches. 2D-QSAR mefhods enhanced by chirahty descriptors present a powerful alternative to popular 3D-QSAR approaches. 

Uj are fhe vertex degrees of adjacent atoms i andj. The chirahty index y is defined 

The various properties of molecules that can be used in a QSAR are often designed to quantitate the tendency of the molecules to participate in one of the fundamental types of intermolecular interactions electrostatic, hydrogen bonding, dispersion forces, and hydrophobic interactions. In addition, the possibility of steric interference with an interaction is considered. Other methods capitalize on the fact that the 2D structure of a molecule indirectly encodes its properties, instead generate descriptors without an explicit relationship to some physical property. 

RSC Drug Discovery Series No. 13 Drug Design Strategies Quantitative Approaches Edited by David J. Livingstone and Andrew M. Davis Royal Society of Chemistry 2012 

Some of the methods concentrate on the effects of variable substituents on the properties of a constant parent molecule in order to generate a local model. Other methods consider the properties of the whole molecules, often structurally diverse, to generate a global model. Forecasts of biological activity of new molecules from a local model require that the new molecules contain the features common to those used to derive the model. In contrast, forecasts from global models are considered to apply to any new molecule. Usually, predictions from global models are accompanied by some measure of similarity of the new molecules to those used for the model. 

These and other developments now present us with a rich source of molecular descriptors for use with various QSAR technologies. 

Finally, we should point out that while classical QSAR approaches generally result in a single equation with statistical terms, modem 3D-QSAR methods generally produce graphically intensive models that may aid in the interpretation of important features in molecular 3D space and the mapping back of these features onto the molecules of interest. 

Quantitative structure-activity relationships are primarily used for drug design. The underlying principle is that the shape and noncovalent interactions are the main contributors to the selectivity of the binding of substrates to an active center. Therefore, it must be possible to correlate structural properties of substrates with their activity. The assumptions on which QSAR methods are generally based are that all substrates bind to the same site, that structurally related compounds bind with a similar orientation and that dynamic effects can be ignored. 

Second, Completely Revised and Enlarged Edition Peter Comba, Trevor W. Hambley copyright WILEY-VCH Verlag GmbH, 2001 

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This is the domain of establishing Structure-Property or Structure-Activity Relationships (SPR or SAR), or even of finding such relationships in a quantitative manner (QSPR or QSAR). 

The search for structural fragments (substructures) is very important in medicinal chemistry, QSAR, spectroscopy, and many other fields in the process of perception of pharmacophore, chromophore, or other -phores. 

D substructure search is usually known as pharmacophore searching in QSAR. Generally speaking, there are two major approaches to it topological and chemical function queries. These two techniques are based on a slighfly different philosophy and usually provide different results [31]. 

All the techniques described above can be used to calculate molecular structures and energies. Which other properties are important for chemoinformatics Most applications have used semi-empirical theory to calculate properties or descriptors, but ab-initio and DFT are equally applicable. In the following, we describe some typical properties and descriptors that have been used in quantitative structure-activity (QSAR) and structure-property (QSPR) relationships. 

The MEP at the molecular surface has been used for many QSAR and QSPR applications. Quantum mechanically calculated MEPs are more detailed and accurate at the important areas of the surface than those derived from net atomic charges and are therefore usually preferable [Ij. However, any of the techniques based on MEPs calculated from net atomic charges can be used for full quantum mechanical calculations, and vice versa. The best-known descriptors based on the statistics of the MEP at the molecular surface are those introduced by Murray and Politzer [44]. These were originally formulated for DFT calculations using an isodensity surface. They have also been used very extensively with semi-empirical MO techniques and solvent-accessible surfaces [1, 2]. The charged polar surface area (CPSA) descriptors proposed by Stanton and Jurs [45] are also based on charges derived from semi-empirical MO calculations. 

To know what QSAR and QSPR are, and the steps in QSAR/QSPR. 

To understand the recommendations for structure descriptors in order to be able to apply them in QSAR or drug design in conjunction with statistical methods or machine learning techniques. 

A challenging task in material science as well as in pharmaceutical research is to custom tailor a compound s properties. George S. Hammond stated that the most fundamental and lasting objective of synthesis is not production of new compounds, but production of properties (Norris Award Lecture, 1968). The molecular structure of an organic or inorganic compound determines its properties. Nevertheless, methods for the direct prediction of a compound s properties based on its molecular structure are usually not available (Figure 8-1). Therefore, the establishment of Quantitative Structure-Property Relationships (QSPRs) and Quantitative Structure-Activity Relationships (QSARs) uses an indirect approach in order to tackle this problem. In the first step, numerical descriptors encoding information about the molecular structure are calculated for a set of compounds. Secondly, statistical and artificial neural network models are used to predict the property or activity of interest based on these descriptors or a suitable subset. 

The method of building predictive models in QSPR/QSAR can also be applied to the modeling of materials without a unique, clearly defined structure. Instead of the connection table, physicochemical data as well as spectra reflecting the compound s structure can be used as molecular descriptors for model building,... 

Before the comparative molecular field analysis (CoMFA), BCUT descriptors, 4D-QSAR, and HYBOT descriptors arc discussed in more detail, some further descriptors are listed briefly. 

Quantum chemical descriptors such as atomic charges, HOMO and LUMO energies, HOMO and LUMO orbital energy differences, atom-atom polarizabilities, super-delocalizabilities, molecular polarizabilities, dipole moments, and energies sucb as the beat of formation, ionization potential, electron affinity, and energy of protonation are applicable in QSAR/QSPR studies. A review is given by Karelson et al. [45]. 

Besides the aforementioned descriptors, grid-based methods are frequently used in the field of QSAR quantitative structure-activity relationships) [50]. A molecule is placed in a box and for an orthogonal grid of points the interaction energy values between this molecule and another small molecule, such as water, are calculated. The grid map thus obtained characterizes the molecular shape, charge distribution, and hydrophobicity. 

Hopfinger et al. [53, 54] have constructed 3D-QSAR models with the 4D-QSAR analysis formahsm. This formalism allows both conformational flexibility and freedom of alignment by ensemble averaging, i.e., the fourth dimension is the dimension of ensemble sampling. The 4D-QSAR analysis can be seen as the evolution of Molecular Shape Analysis [55, 56]. 

In 4D-QSAR, a grid is used to determine the regions in 3D space responsible for binding. Nevertheless, neither a probe nor interaction energy is used. 

Figure 8-15. Extension of the QSAR method by descriptors not based on structure.

The QSPR/QSAR methodology can also be applied to materials and mixtures where no structural information is available. Instead of descriptors derived from the compound s structure, various physicochemical properties, including spectra, can be used. In particular, spectra are valuable in this context as they reflect the structure in a sensitive way. 

O. A. Raevsky, L. Dolmatova, V. Y. Grigor ev, S. Bondarev, Molecular recognition descriptors in QSAR, in QSAR and Mdecular Modelling Concepts, Cotnpu-... 

This makes PLS an attractive method for QSAR (see Section 10.4). 

Furthermore, QSPR models for the prediction of free-energy based properties that are based on multilinear regression analysis are often referred to as LFER models, especially, in the wide field of quantitative structure-activity relationships (QSAR). 

The fundamental assumption of SAR and QSAR (Structure-Activity Relationships and Quantitative Structure-Activity Relationships) is that the activity of a compound is related to its structural and/or physicochemical properties. In a classic article Corwin Hansch formulated Eq. (15) as a linear frcc-cncrgy related model for the biological activity (e.g.. toxicity) of a group of congeneric chemicals [37, in which the inverse of C, the concentration effect of the toxicant, is related to a hy-drophobidty term, FI, an electronic term, a (the Hammett substituent constant). Stcric terms can be added to this equation (typically Taft s steric parameter, E,). 

Metabolism is still a barrier to be overcome. Some QSAR, pharmacophore, protein, and rule-based models are available to predict substrates and inhibitors of a specific cytochrome P450 isoenzyme [47-55]. 

The first use of QSARs to rationalise biological activity is usually attributed to Hansc [Hansch 1969]. He developed equations which related biological activity to a molecmle electronic characteristics and hydrophobicity. For example ... 

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