Calculated Size Descriptors

MW is often taken as the size descriptor of choice, while it is easy to calculate and is in the chemist s mind. However, other size and shape properties are equally simple to calculate, and may offer a better guide to estimate potential for permeability. Thus far no systematic work has been reported investigating this in detail. Cross-sectional area Ad obtained from surface activity measurements have been reported as a useful size descriptor to discriminate compounds which can access the brain (Ad 80A ) of those that are too large to cross the blood-brain barrier (BBB) [55]. Similar studies have been performed to define a cut-off for oral absorption [56]. 

Molecular weight is often taken as the size descriptor of choice, while it is easy to calculate and is in the chemist s mind. However, other size and shape properties are equally simple to calculate and may offer a better guide to estimate potential for 

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Some properties, such as the molecular size, can be computed directly from the molecular geometry. This is particularly important, because these properties are accessible from molecular mechanics calculations. Many descriptors for quantitative structure activity or property relationship calculations can be computed from the geometry only. 

Descriptor median values naturally depend on the composition and size of compound databases. Whenever source databases are changed, reduced, or extended in size, descriptor medians need to be re-calculated to ensure accurate MP analysis. Relatively small changes in median values can significantly alter partitioning results. 

From the geometry matrix, the usual -> graph invariants can be calculated such as -t characteristic polynomial, -> eigenvalue-based descriptors, -> path counts, - ID numbers, -> 3D-Balaban index, -> 3D-Schultz index and so forth [Randic, 1988b Nikolic et al, 1991]. It is noteworthy that all these indices are sensitive to molecular geometry. Moreover, the geometry matrix is used for the calculation of size descriptors and - 3D-MoRSE descriptors. 

Among the size descriptors, this is the simplest and most used molecular - OD-descriptor, calculated as the sum of the atomic weights. It is related to molecular size and is atom-type sensitive. It is defined as ... 

Molecular descriptors related to the dimensions of the molecule and often calculated from the - molecular geometry. Combined with molecular shape information, they are closely related to - steric descriptors. The simplest size descriptors are atom count, -> bond count, -> molecular weight, and some among the -> volume descriptors such as van der Waals volume. Other size descriptors are - Sterimol parameters and - WHIM size descriptors. 

A substituent size descriptor defined as the volume V of the portion of the substituent within a sphere centred at the link atom [Meyer, 1986b], Tlie radius of the sphere was chosen equal to 0.3 nm to comprise the substituent portion responsible for the steric effect of the substituent. It was used, together with the - ovality index calculated on the substituent, to estimate substituent steric effects for substituents with equal volume V , much larger steric effects are observed for globular substituents. 

Steric descriptors and/or -> size descriptors representing the volume of a molecule. The volume of a molecule can be derived from experimental observation such as the volume of the unit cell in crystals or the molar volume of a solution or from theoretical calculations. In fact, analytical and numerical approaches have been proposed for the calculation of molecular volume where the measure depends directly on the definition of - molecular surface-, -> van der Waals volume and -> solvent-excluded volume are two volume descriptors based on van der Waals surface and solvent-accessible surface, respectively. 

The ideal descriptor can be decoded to obtain the original chemical structure or the properties that have been used to calculate the descriptor. Although this is definitely desired, the real world shows that the information used to calculate the descriptor is usually too complex to use it at its full size. A descriptor shall have a reasonable size for effective computation, and this is mostly achieved by reducing information to the facts that are of major importance for the task. The need for a fixed descriptor dimension also contradicts this requirement. 

The size of a virtual library can be reduced by applying filters to eliminate reagents that are known to be undesirable [67]. However, in some cases, the virtual library may still be too large to allow full enumeration, and thus full product-based design is infeasible. (Although the need for full enumeration may not be necessary in the future, for example, Barnard et al. [82] have recently developed a method for the rapid calculation of descriptors for the products in a virtual combinatorial library that avoids the need for enumeration.)... 

The more subtle, but potentially more exciting, consequence of such multidimensional data analysis is the superposition of biological annotations onto a collection of measurements, allowing connections between the biological coordinates to be made independently of the measurements themselves. As we have seen in this chapter, there are specific relationships between various calculated molecular descriptors, based on the theory of their construction or on their relationships to molecular properties such as size and shape. Similarly, there are implicit encodable relationships between the different assays that comprise any multidimensional fingerprint of assay outcomes, such as combinations of cell states and cellular assays (Fig. 13.1-7(c)). Exploiting such relationships across diverse collections of small molecules indeed may uncover new relationships between the biological states themselves. 

The size descriptor molar volume V can be calculated. Thus the polarity factor A is obtained indirectly from log P measurements, where A = 0 for nonpolar compounds. A appears to reflect the H-bonding capacity of a compound. 

The possibility of rotation of some groups of atoms around some chanical bonds is intuitively associated with molecular flexibility. Consequently, the number of rotatable bonds and the percentage of rotatable bonds are the simplest descriptors that measure the molecular flexibility. More complicated formulas calculate flexibility descriptors by weighting some topological descriptors therefore, they consider the shape and size of the molecules, the number of atoms, and the sum of bond orders (Tarko 2004c). 

The number of aromatic bonds minimum, average, and maximum value of the aromaticity of the aromatic bonds percentage of aromatic bonds number of aromatic molecular zones or aromaticity of the peripheral topological path can be calculated as descriptors. Some descriptors simultaneously reflect the aromaticity and size of the molecule. Other descriptors reflect the concentration of aromaticity in small areas of the molecule. 

Following are some examples of calculation of descriptors for organometallic complexes in which the ligand has low molecular weight. Descriptors were chosen whose values seem to be more sensitive to the presence and type of metal atom, as well as to the number, shape, and size of ligands. Some of the analyzed complexes have been synthesized and have various practical applications. 

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