Shape properties

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]. 

Labeled Various substrates in amorphous as well as fibrous forms loaded for each experiment Form/shape/properties... 

In this chapter, we extend the discussion of the previous chapter to nonspherical shapes. Only solid particles are considered and the discussion is limited to low Reynolds number flows. The flow pattern and heat and mass transfer for a nonspherical particle depend on its orientation. This introduces complications not present for spherical particles. For example, the net drag force is parallel to the direction of motion only if the particle has special shape properties or is aligned in specific orientations. 

A drawback to additive property models of molecular structure is that 3-dimensional molecular properties cannot be determined. However, it is clear that conformation, or more generally, molecular shape, can be an important factor in expression of biological activity. Thus, there is a need to be able to determine conformational/shape properties of molecules and to use these properties to develop a QSAR. 

The unproven, but reasonable, assumption implicit to SAR-directed conformational studies, both experimental and theoretical, is that one of the stable intramolecular conformers is the "active conformation, A difficulty to applying conformational data in quantitative drug design is selection of conformational features for QSAR development. Moreover, molecular shape properties are preferable features to have available in design studies. Conformation is a component of shape. The properties of the atoms, most notably their "sizes," comprise an additional set of factors needed to specify molecular shape. 

Molecular shape properties, derived from conformational investigations, have also been used to rationalize commonality and diversity in biological action. These shape properties include ... 

Alkanes and cycloalkanes IUPAC, shapes, properties, reactions 11.6-11.11... 

Figure 13.2 Multiple property-based library shaping. Property distributions are shown for the raw collection (gray bars) and for the selected library members (black bars). The drug-likeness score corresponds to the output value of an artificial neural network, where a value of 1 indicates maximal drug-likeness (for details, see the text). The rule-of-5 violations are counted per molecule.

Chirality, an important shape property of molecules, can be regarded as the lack of certain symmetry elements. Chirality measures are in fact measures of symmetry deficiency. These principles, originally used for crisp sets, also apply for fuzzy sets. Considering the case of three-dimensional chirality, the lacking point symmetry elements are reflection planes a and rotation-reflections 82 of even indices. Whereas the lacking symmetry elements can be of different nature in different dimensions, nevertheless, all the concepts, definitions, and procedures discussed in this section have straightforward generalizations for any finite dimension n. 

Dynamic Shape Properties Conformational Freedom and Electronic Excitation... 

For a continuous function, such as the electronic density p(r), all points r fulfilling equation (2.3) do form a continuous surface. Consequently, the terms contour surface and isodensity surface are appropriate for G(a). For the study of the 3D shape properties of molecular bodies, represented by level sets F(a) of electronic charge densities, it is sufficient to study the shape of their boundaries these boundaries are the MIDCO s G(a). 

Molecules are three-dimensional objects and they do occupy some space. When considering the space requirements of molecules, it is natural to associate with them a formal molecular body and a formal molecular surface [84-88]. In a simplistic model, this surface is a formal molecular boundary, a closed surface that separates the 3D space into two parts the molecular body enclosed by the surface that is supposed to represent the entire molecule, and the rest of the 3D space that falls on the outside of the surface, hence on the outside of the molecule. The above, intuitive concepts of molecular body and molecular surface are very useful for the interpretation of molecular size and shape properties within approximate models. 

The actual sign ("phase") of the molecular orbital at any given point r of the 3D space has no direct physical significance in fact, any unitary transformation of the MO s of an LCAO (linear combination of atomic orbitals) wavefunction leads to an equivalent description. Consequently, in order to provide a valid basis for comparisons, additonal constraints and conventions are often used when comparing MO s. The orbitals are often selected according to some extremum condition, for example, by taking the most localized [256-260] or the most delocalized [259,260] orbitals. Localized orbitals are often used for the interpretation of local molecular properties and processes [256-260]. The shapes of contour surfaces of localized orbitals are often correlated with local molecular shape properties. On the other hand, the shapes of the contour surfaces of the most delocalized orbitals may provide information on reactivity and on various decomposition reaction channels of molecules [259,260]. 

We can formulate the above ideas more precisely by considering the dynamic shape properties of molecules within a nuclear configuration space M. 

It is natural to imagine molecular shape properties as they would appear to an observer moving about a sphere enclosing the molecule. If the observer is able to characterize all possible views, this characterization can provide a detailed shape description. 

A practical implementation of the above approach is the following a global shape property of the molecule is assigned to each point of the sphere S, followed by the determination of those domains of S where this shape property is invariant. A pair of examples is shown in Figure 5.9, where the shape globe invariance domains of a MIDCO surface for two relative convexity shape domain partitionings (P) with respect to two reference curvatures, b = 0, and b < 0, are given. As... 

One should note that within each shape globe map an entire family of topological descriptors Fj(s) = I(i), i=l,...k is assigned to each point s of the sphere S, providing information on a global shape property of the enclosed molecule. 

The three-dimensional RBSM method relies on the shape properties of interior filling polycubes Pj(G(a),n) inscribed in molecular contour surfaces G(a) when assessing the similarity of the G(a) contours and the formal molecular bodies B(a) enclosed by them. In order to define levels of resolution scaled relative to the molecular size, the absolute size parameter s is not used directly. One obtains more comparable shape characterizations of both small and large objects when using the same number of cubes. Consequently, each level of resolution is defined by the number n of cubes of interior filling polycubes Pi(G(a),n), which depends on the relative size of the object G(a) as compared to the cube size s. 

In many chemical problems the comparisons of local molecular regions are more important than global comparisons. The presence of functional groups or other molecular moieties with specified shape properties often imply similar chemical behavior even if the molecules compared have very different global shapes. For this reason, local molecular shape descriptors and local shape codes are of major importance. 

In nearly all chemically important problems, shape complementarity refers to local shape properties. Most of the typical molecular interactions where shape complementarity is relevant involve only some local moieties of the molecules. Global shape complementarity is more difficult to achieve and seldom plays a role. 

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