Molecular descriptor constitutional descriptors

As we have seen, molecular descriptors constitute information about steric and electronic constraints conferred by chemical structure [104, 105]. Molecular descriptors underlie both pharmacophore models [106, 107] and analyses of similarity or diversity among compound collections [108,109]. The calculation of descriptors therefore serves as a starting point in the analyses of small-molecule relationships assessed prior to compound synthesis, before selecting compounds for HTS, and in the interpretation of biological measurements of small-molecule perturbation. 

CODESSA can compute or import over 500 molecular descriptors. These can be categorized into constitutional, topological, geometric, electrostatic, quantum chemical, and thermodynamic descriptors. There are automated procedures that will omit missing or bad descriptors. Alternatively, the user can manually define any subset of structures or descriptors to be used. 

A common feature of the various methods that we have developed for the calculation of electronic effects in organic molecules is that they start from fundamental atomic data such as atomic ionization potentials and electron affinities, or atomic polarizability parameters. These atomic data are combined according to specific physical models, to calculate molecular descriptors which take account of the network of bonds. In other words, the constitution of a molecule (the topology) determines the way the procedures (algorithms) walk through the molecule. Again, as previously mentioned, the calculations are performed on the entire molecule. 

Table 1 Calculation of some molecular-based descriptors for BOA, DIMBOA and MBOA. Physicochemical descriptor like logP (partition coefficient between octanol and water) constitutional descriptors like the number of a specified atoms or bonds (number of carbons, hydrogens, oxygens, nitrogens, single and aromatic bonds, the total number of atoms and bonds) and molecular weight quantum-mechanical descriptors like HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital).

Each of these columns of this symmetrical matrix may be seen as representing a molecule in the subspace formed by the density functions of the N molecules that constitute the set. Such a vector may also be seen as a molecular descriptor, where the infinite dimensionality of the electron density has been reduced to just N scalars that are real and positive definite. Furthermore, once chosen a certain operator in the MQSM, the descriptor is unbiased. A different way of looking at Z is to consider it as an iV-dimensional representation of the operator within a set of density functions. Every molecule then corresponds to a point in this /V-dimensional space. For the collection of all points, one can construct the so-called point clouds, which allow one to graphically represent the similarity between molecules and to investigate possible relations between molecules and their properties [23-28]. 

In our study we compare two diversity-driven design methods (uniform cell coverage and clustering), two analysis methods motivated by similarity (cell-based analysis and cluster-classification), and two descriptor sets (BCUT and constitutional). Thus, our study addresses some of the many questions arising in a sequential screen how to choose the initial screen, how to analyze the structure-activity data, and what molecular descriptor set to use. The study is limited to one assay and thus cannot be definitive, but it at least provides preliminary insights and reveals some trends. 

Following a similar approach but using a smaller data set of 369 compounds, Ivanciuc et al. correlated their liquid viscosity (10 Pa s) at 298 K with a mixed set of descriptors to obtain Eq. [48]. This involves three QM descriptors, one topological, and one constitutional descriptor. The QM descriptors were calculated with the AMI Hamiltonian in AMPAC, and CODESSA was used to calculate the descriptors and perform the statistical analyses. The HDCA2 parameter is the same HBD charged surface area used in Eq. [46]. The maximum electrophilic reactivity index, Ep, for a carbon atom is defined by X/ lumo,/A lumo+ 10), with the summation over the valence AOs on a carbon atom in the LUMO. The maximum AO electronic population, Y, models the molecular nucleophilicity and is defined by... 

In - grid-based QSAR techniques, the energy value at each grid point p constitutes a molecular descriptor. For the selected -> molecular interaction fields (steric, hydrophobic, coulombic, etc.), the calculated value at each grid point p depends on the relative orientation of the compound with respect to the grid. As a consequence, the use of... 

Connoiiy surface area - molecular surface (O solvent-accessible molecular surface) constant interval reciprocal indices -> distance matrix constant and near-constant variables variable reduction constitutional descriptors... 

Electric polarization, dipole moments and other related physical quantities, such as multipole moments and polarizabilities, constitute another group of both local and molecular descriptors, which can be defined either in terms of classical physics or quantum mechanics. They encode information about the charge distribution in molecules [Bbttcher et al, 1973]. They are particularly important in modelling solvation properties of compounds which depend on solute/solvent interactions and in fact are frequently used to represent the -> dipolarity/polarizability term in - linear solvation energy relationships. Moreover, they can be used to model the polar interactions which contribute to the determination of the -> lipophilicity of compounds. 

Physico-chemical properties constitute the most important class of experimental measurements, also playing a fundamental role as - molecular descriptors both for their availability as well as their interpretability. Examples of physico-chemical measurable quantities are refractive indices, molar refractivities, parachors, densities, solubilities, partition coefficients, dipole moments, chemical shifts, retention times, spectroscopic signals, rate constants, equilibrium constants, vapor pressures, boiling and melting points, acid dissociation constants, etc. [Lyman et al, 1982 Reid et al, 1988 Horvath, 1992 Baum, 1998]. 

In any case, experimental values or their estimated values are commonly used as molecular descriptors (i.e. as predictors in X block) or constitute the response (i.e. in Y block) which has to be modelled by other descriptors, i.e. reproduced by theoretical models. 

The meaning of the G-WHIM descriptors is that previously defined for WHIM descriptors, but now the descriptors refer to the interaction molecular field instead of the molecule. For example, the eigenvalues X,i, Xz and >,3, relate to the interaction field size the eigenvalue proportions i9i and i>2 relate to the interaction field shape the group of descriptors constituted by the inverse function of the kurtosis (k), i.e., = 1/k ... 

MODEL Molecular Descriptor Lab (MODEL) (http //jing.cz3.nus.edu.sg/ cgi-bin/model/model.cgi) is a free Web-based server for computing a comprehensive set of 3778 molecular descriptors, which can be divided into 6 classes constitutional descriptors, electronic descriptors, physical chemistry properties, topological indexes, geometrical molecular descriptors, and quantum chemistry descriptors [73], Compounds can be provided to the server in various molecular formats such as PDB, MDL, MOL2, and COR, and the computed molecular descriptors are displayed in a few seconds or less. Cross-links to the relevant sections of the reference manual page are also provided for some of the descriptors and descriptor classes. 

Constitutional Descriptor is a type of molecular descriptor that represents the chemical composition of a molecule in a generic way. It is independent from molecular connectivity and geometry. 

Since infrared spectroscopy monitors the vibrations of atoms in a molecule in 3D space, information on the 3D arrangement of the atoms should somehow be contained in an infrared spectrum. An infrared spectrum itself, as well as other spectra, constitutes a molecular descriptor. The relationships between the 3D structure and the infrared spectrum are rather complex so that no attempts have yet been successful in deriving the 3D structure of a molecule directly from the infrared spectrum. 

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