Two-dimensional descriptors

Moreau has proposed the autocorrelation of topological molecular structure (ATS) value. The function is defined in (13). 

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At the low end of the hierarchy are the TS descriptors. This is the simplest of the four classes molecular structure is viewed only in terms of atom connectivity, not as a chemical entity, and thus no chemical information is encoded. Examples include path length descriptors [13], path or cluster connectivity indices [13,14], and number of circuits. The TC descriptors are more complex in that they encode chemical information, such as atom and bond type, in addition to encoding information about how the atoms are connected within the molecule. Examples of TC descriptors include neighborhood complexity indices [23], valence path connectivity indices [13], and electrotopological state indices [17]. The TS and TC are two-dimensional descriptors which are collectively referred to as TIs (Section 31.2.1). They are straightforward in their derivation, uncomplicated by conformational assumptions, and can be calculated very quickly and inexpensively. The 3-D descriptors encode 3-D aspects of molecular structure. At the upper end of the hierarchy are the QC descriptors, which encode electronic aspects of chemical structure. As was mentioned previously, QC descriptors may be obtained using either semiempirical or ab initio calculation methods. The latter can be prohibitive in terms of the time required for calculation, especially for large molecules. 

In an effort to understand if HAMs are, in any way, different from LAMs (low activity molecules), we extended this survey to compounds published between 1991 and 2002, as indexed in WOMBAT [26]. This database [27] contains 4927 unique structures with at least one measured activity better than 1 nM (HAMs), and 34028 unique structures with at least one activity less than 1 XM (LAMs). Between HAMs and LAMs, 1080 molecules are common, that is, they have at least one activity above 1 nM and at least one activity below 1 XM. This is not uncommon for, for example, highly selective molecules. We did not exclude these from either set since we monitor trends, not exact figures. We studied these trends using 2-D-(two-dimensional) descriptors, that is, descriptors that do not use information related to the three-dimensional characteristics of model compounds. These descriptors can be classified as follows ... 

Engkvist, O. and Wrede, P. High throughput, in silico prediction of aqueous solubility based on one- and two-dimensional descriptors./. Chem. Inf Comput. Sci. 2002, 42, 1247-1249. 

Figure 2 illustrates the generation of cells and the UCC criterion with a very simple example involving the choice of four molecules from 20 in a two-dimensional descriptor space formed by variables xx and x2. The space is divided into four bins for each ID descriptor (solid or dashed lines) and into four cells in a 2 x 2 arrangement in two dimensions (solid lines). Solid circles represent the four selected molecules, while open circles are unselected. 

Schneider et al. (245) used 333 one and two-dimensional descriptors to create a virtual screening filter for CYP 3A4 inhibition. After the application of a space-... 

Two-Dimensional Descriptors derived from two-dimensional structure representa-Similarity-Based tions of a molecule are popular in ligand-based screening owing to... 

Another simple approach to finding new inhibitors based on SAR data is to search for compounds that are similar to existing inhibitors. Either two-or three-dimensional molecular descriptors can be calculated for each molecule, and a search is performed on a database to find compounds whose descriptors are most similar to the known inhibitors. Two-dimensional descriptors can be calculated very rapidly, allowing hundreds of thousands of structures to be processed in an hour. Three-dimensional descriptors are more challenging, since they require a time-consuming three-dimensional... 

Two-dimensional descriptors are normally represented by linear bit strings indicating the presence or the absence of some properties in the molecule Examples include structural fragments (structural keys, 40, 41, 36), specific atom paths with predefined... 

D (two-dimensional) descriptors derived from algorithms applied to a topological representation (molecular graph). 

Fig. 12 Regions of a two-dimensional descriptor space defined by different similarity computation methods. The small circles show positions of a predefined set of molecules (e.g., cluster of active compounds). Similar compounds are found in the marked regions. The dissimilarities are calculated as a) Euclidean distances to the cluster center b) Mahalanobis distances to each molecule of the predefined set and c) sum of all nonlineariy scaled Euclidean distances.

Figure 5.18 shows a 2D RDF descriptor of a complex molecule. A direct interpretation wonld be more sophisticated however, the valne of separating distance and property becomes more obvious. 2D RDF descriptors of the distance dimension n and the property dimension m can be treated like a one-dimensional vector containing m descriptors of length n. This makes it easy to compare two-dimensional descriptors using the same algorithms as for one-dimensional vectors. 

Two-Dimensional Descriptors are calculated on two different properties of a molecule, each of which is represented in a single mathematical dimension. The result is numerically a matrix and graphically a two-dimensional function, visualized in three dimensions. 

For any pD-model p 3), we can develop descriptors of variable dimensionality d. Examples of zero-dimensional descriptors are single numbers such as the radius of gyrationio (used for OD, ID, and 2D models) or the molecular volume 1 (used for 2D models). One-dimensional descriptors such as radial distribution functions or knot polynomials are used in OD and ID models, respectively. Two-dimensional descriptors include distance maps and Rama-chandran torsional-angle maps for some OD and ID models. Similarly, molecular graphs (2D descriptors) can be associated with ID models (contour lines), 2D models (molecular surfaces), or 3D models (e.g., the entire electron density function). Shape descriptors of higher dimensionality can also be constructed. 

Two-Dimensional Descriptors Distance Maps and Related Descriptions... 

Use of other molecular descriptors (alone or in combination) for deriving QSAR models is also common in environmental chemistiy. However, it is interesting to note that only two-dimensional descriptors are employed (Figure 4). Indeed, the number of QSAR models designed with three-dimensional descriptors is very scarce in environmental sciences. Thus, for example, in the whole environmental QSAR literature, fewer than 10 publications deal with CoMFA (e.g., Briens and co-workers, Dearden and Stott ) while this approach is now widely used in drug design (see Comparative Molecular Field Aiuilysis (CoMFA)). 

Figure 1.14 Suggested looping technique for the exploration of a two-dimensional descriptor space.

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