Molecule descriptor

Key Words Biological activity chemical features chemical space cluster analysis compound databases dimension reduction molecular descriptors molecule classification partitioning algorithms partitioning in low-dimensional spaces principal component analysis visualization. 

Hull et al. have developed the Latent Semantic Structure Indexing (LaSSI) approach to perform similarity search in low-dimensional chemical space. To reduce the dimension of initial chemical space, the singular value decomposition method is applied for the descriptor-molecule matrix. Ranking molecules by similarity to a query molecule was performed in the reduced space... 

Figure 2-74. Basic stages for describing a stereoisomer by a permutation descriptor. At the stereocenter, the molecule is separated into the skeleton and its ligands. Both are then numbered independently, with the indices of the skeleton in italics, the indices of the ligands in bold.

The preceding section gave a briefintroduction to the handling of the stereochemistry of molecules by permutation group descriptors. Here we discuss this topic in more detail. The treatment is largely based on ideas introduced in Ref. [100],... 

Determination of the Permutation Descriptor after Rotation of the Molecule... 

The two structures in our example are identical and are rotated by only 1 20 h Clearly, rotation of a molecule docs not change its stereochemistry, Thus, the permutation descriptor of both representations should be (+ I). On this basis, we can define an equation where the number of transpositions is correlated with the permutation descriptors in an exponential term (Eq. (9)). 

Now Ictu.s see how the de.scriptor.s bcltavc under rotation of the entire molecule. 1 f the trans isomer used before is rotated by 1and the descriptors are calculated again, a value of (-1 is obtained two times (right-hand side, bottom line of Figure 2-88). 

However, as the descriptor oFthc eutirc steveoisoraer is obtained by multiplicatiou of the individual descriptors, again a value of (-(-1 is obtained. Thus, as desired, the stereocenter of a double bond does not change through rotation of a molecule. 

Another problem is to determine the optimal number of descriptors for the objects (patterns), such as for the structure of the molecule. A widespread observation is that one has to keep the number of descriptors as low as 20 % of the number of the objects in the dataset. However, this is correct only in case of ordinary Multilinear Regression Analysis. Some more advanced methods, such as Projection of Latent Structures (or. Partial Least Squares, PLS), use so-called latent variables to achieve both modeling and predictions. 

Table 6.3. Sample molecules acetone and isobutene described by atom pair (ap) descriptors.

Mixtures containing up to several thousand distinct chemical entities are often synthesized and tested in mix-and-split combinatorial chemistry. The descriptor representation of a mixture may be approximated as the descriptor average of its individual component molecules, e.g., using atom-pair and topological torsion descriptors. 

To evaluate the performance of the descriptors one needs a database of compoimds for which the biological activities are known, e.g.. either the MDDR or the NCI databases. Queries are selected that are typical of a drug-hke molecule and from therapeutic categories that... 

A structure descriptor is a mathematical representation of a molecule resulting from a procedure transforming the structural information encoded within a symbolic representation of a molecule. This mathematical representation has to be invariant to the molecule s size and number of atoms, to allow model building with statistical methods and artificial neural networks. 

The concept of feature trees as molecular descriptors was introduced by Rarey and Dixon [12]. A similarity value for two molecules can be calculated, based on molecular profiles and a rough mapping. In this section only the basic concepts are described. More detailed information is available in Ref. [12]. 

Steinhauer and Gasteiger [30] developed a new 3D descriptor based on the idea of radial distribution functions (RDFs), which is well known in physics and physico-chemistry in general and in X-ray diffraction in particular [31], The radial distribution function code (RDF code) is closely related to the 3D-MoRSE code. The RDF code is calculated by Eq. (25), where/is a scaling factor, N is the number of atoms in the molecule, p/ and pj are properties of the atoms i and/ B is a smoothing parameter, and Tij is the distance between the atoms i and j g(r) is usually calculated at a number of discrete points within defined intervals [32, 33]. 

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. 

After an alignment of a set of molecules known to bind to the same receptor a comparative molecular field analysis CoMFA) makes it possible to determine and visuahze molecular interaction regions involved in hgand-receptor binding [51]. Further on, statistical methods such as partial least squares regression PLS) are applied to search for a correlation between CoMFA descriptors and biological activity. The CoMFA descriptors have been one of the most widely used set of descriptors. However, their apex has been reached. 

For the calculation of grid-based descriptors it is necessary to align the ligands in the first step. If the molecules have the same skeleton, the alignment step is not critical. Otherwise, the ahgnment may be biased by the user. 

A structure descriptor is a mathematical representation of a molecule resulting from a procedure transforming the structural information encoded within a symbolic representation of a molecule. 

Molecules can be represented by structure descriptors in a hierarchical manner with respect to a) the descriptor data type, and b) the molecular representation of the compound. 

GAs or other methods from evolutionary computation are applied in various fields of chemistry Its tasks include the geometry optimization of conformations of small molecules, the elaboration of models for the prediction of properties or biological activities, the design of molecules de novo, the analysis of the interaction of proteins and their ligands, or the selection of descriptors [18]. The last application is explained briefly in Section 9.7.6. 

Besides these LFER-based models, approaches have been developed using whole-molecule descriptors and learning algorithms other then multiple linear regression (see Section 10.1.2). 

The solubility of a compound is thus affected by many factors the state of the solute, the relative aromatic and aliphatic degree of the molecules, the size and shape of the molecules, the polarity of the molecule, steric effects, and the ability of some groups to participate in hydrogen bonding. In order to predict solubility accurately, all these factors correlated with solubility should be represented numerically by descriptors derived from the structure of the molecule or from experimental observations. 

The compounds were described by a set of 32 radial distribution function (RDF) code values [27] representing the 3D structure of a molecule and eight additional descriptors. The 3D coordinates were obtained using the 3D structure generator GORINA [33]. 

The same structure representation as the one taken in the original study [39] is selected in order to show some possibilities evolving from working with a neural network method. Tabic 10.1-1 gives the ten descriptors chosen lor the representation of the 115 molecules of the data set. 

Finding the adequate descriptor for the representation of chemical structures is one of the basic problems in chemical data analysis. Several methods have been developed in the most recent decades for the description of molecules including their chemical or physicochemical properties [1]. 

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