One-dimensional descriptors

FIGURE 5.17 Two-dimensional RDF descriptor of ethene calculated with Cartesian distances in the first and the partial atomic charge as property for the second dimension. Instead of the one-dimensional descriptor with four peaks, the six distances occurring in ethene are clearly divided into the separate property and distance dimensions. 

One-Dimensional Descriptors are calculated on a single property of a molecule. The result is numerically a vector and graphically a one-dimensional function, visualized in two 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. 

One-Dimensional Descriptors Atomic Radial Distribution Functions... 

Usually, the denominator, if present in a similarity measure, is just a normalizet it is the numerator that is indicative of whether similarity or dissimilarity is being estimated, or both. The characteristics chosen for the description of the objects being compared are interchangeably called descriptors, properties, features, attributes, qualities, observations, measurements, calculations, etc. In the formiilations above, the terms matches and mismatches" refer to qualitative characteristics, e.g., binary ones (those which take one of two values 1 (present) or 0 (absent)), while the terms overlap and difference" refer to quantitative characteristics, e.g., those whose values can be arranged in order of magnitude along a one-dimensional axis. 

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. 

As it is essentially impossible to cover a high-dimensional space finely with a modest number of compounds, Lam and co-workers proposed a cell-based method that uniformly covers all low-dimensional subspaces formed by subsets of descriptors (19,20). Typically, they would consider all one-dimensional (ID), 2D, and 3D subspaces. In addition to practical feasibility, this is consistent with Pearlman and Smith s notion of a relevant subspace (21) a particular activity mechanism will likely involve only a few relevant descriptor variables. 

When molecules are represented by low-dimensional descriptors, then the descriptors can be used to define the axes of a chemistry space. Typical descriptors are a small number of physicochemical properties or the principal components generated by the application of principal components analysis to high-dimensional descriptors. Each descriptor then defines one axis and is divided into a series of bins. The combination of all bins over all descriptors defines a set of cells over a chemistry space. Molecules can be mapped onto the cells according to their physicochemical properties. A diverse library is one that occupies a large number of cells in the space, whereas a focused library is one where the molecules occupy a small localized region of the space. 

QSAR methods can be divided into several categories dependent on the nature of descriptors chosen. In classical one-dimensional (ID) and two-dimensional (2D) QSAR analyses, scalar, indicator, or topological variables are examples of descriptors used to explain differences in the dependent variables. 3D-QSAR involves the usage of descriptors dependent on the configuration, conformation, and shape of the molecules under consideration. These descriptors can range from volume or surface descriptors to HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) energy values obtained from quantum mechanics (QM) calculations. 

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-... 

Often, all alignment-based methods and molecular field and potential calculations are classified as pharmacophore perception techniques. We will include most of these methods in this review however, when using the term pharmacophore model, we will be referring mainly to one specific type of perception, namely three-dimensional feature-based pharmacophore models represented by geometry or location constraints, qualitative or quantitative. An extrapolation of the pharmacophore approach to a set of multi-dimensional descriptors (pharmacophore fingerprints) has been developed mostly for library design and focusing purposes [3-8]. 

Figure 1.4. Dimension reduction. The figure illustrates the transformation of an -dimensional descriptor space into an orthogonal three-dimensional space formed by three non-correlated descriptors either selected from the original ones or derived from them as new composite descriptors.

Since SOMs are capable of projecting compound distributions in high-dimensional descriptor spaces on two-dimensional arrays of nodes, this methodology is also useful as a dimension reduction technique, similar to others discussed above. SOM projections and the relationships they establish are usually non-linear, in contrast to, for example, principal component analysis (that, as discussed, generates a smaller number of new composite descriptors as linear combinations of the original ones). 

The substructure list representation can be considered as a one-dimensional representation of a molecule and consists of a list of structured fragments of a molecule the list can only be a partial list of fragments, functional groups, or substituents of interest present in the molecule, thus not requiring a complete knowledge of the molecule structure. The descriptors derived by this representation can be called ID-descriptors and are typically used in - substructural analysis and -> substructure searching. 

Foct, F 2 > AE, and Log P) were used in the cluster analysis. The results are shown in Fig. 3. This is a non-linear map of the descriptors in their four-dimensional space projected into two-dimensions. Nine different clusters can be identified. However, one cluster plus one member of a nearby cluster (the enclosed area within the map) contains all active compounds except for the 3-hydroxy nitroso-piperidine. That is, highly carcinogenic compounds cluster together while the "non-carcinogenic" cyclic nitrosamines are scattered about in the four-dimensional descriptor space. 

---