Van der Waals* surface area

Atomic volumes play an important role in relating physicochemical properties to biological effects. Most atoms in molecules are not entirely bounded by interatomic surfaces and an atomic volume is defined as a measure of the space enclosed by the intersection of the atom s zero-flux surfaces with some outer envelope of the density. The envelope with a value of 0.001 au is generally chosen as this has been shown to yield molecular sizes in good agreement with experimentally assigned van der Waals radii [16, 17]. A related property is the van der Waals surface area, which QTAIM determines by integrating an atom s exposed contribution to a molecule s isovalued surface. 

Litman etal. [ 391 analyzed a set of 34 diverse drugs and their effect on the kinetics of the ATPase activity of the microsomal membrane fraction of a P-gp overexpressing CHO cell line. They found a correlation (r=0.75) between the affinity of the modulators and their van der Waals surface area, while the affinity data did not correlate with the lipophilicity of the compounds, expressed as calculated octanol/ water partition coefficients. 

Descriptor vsa base represents van der Waals surface area of basic atoms and indicates the basicity of a compound. Under physiological conditions, a compound with a high vsa base value tends to be protonated and carries positive charges. The positive contribution to log PS indicated that basicity facilitates the compound s permeability across the BBB. This was consistent with their observation that basic compounds have higher log PS values than neutral and acidic compounds. 

The data containing 324 descriptor values of 88 molecules was given as an input to VSMP program, to build models based on three and four descriptors, keeping the interdescriptor correlation below 0.75. The best three-descriptors model, Eq. 80, was based on descriptors 254 (atomic type E-state index), 311 (AlogP98), and 320 (2D Van der Waals surface area) with a correlation coefficient, r, of 0.8425, and the cross-validated correlation coefficient, q, of 0.8239. The correlation coefficients of the other two VSMP models, Eqs. 81 and 82 were 0.8411 and 0.8329, respectively. Significantly, the descriptors 254 and 311 were selected in all the best three-descriptors models of VSMP. The three descriptors, in the models 80, 81, and 82 were 320, 144 (Kappa shape index of order 1), and 30 (topological Xu index), respectively. 

High lipophilicity and van der Waals surface area of basic atoms facilitates a compound s BBB permeability, whereas high polarity and hydrogen-bonding potential have a negative impact on the BBB permeability. 

Narayanan and Gunturi [33] Lipophilicity, E-state indices, Van der Waals surface area, etc. 

Molecular lipophilicity, topological indices, and Van der Waals surface area are the important parameters governing BBB permeability of the compounds. 

The surface area of an atom in a molecule is the amount of surface area of that atom not contained in any other atom of the molecule (see Fig. 1). If we assume that the shape of each atom is a sphere with radius equal to the van der Waals radius, we obtain the van der Waals surface area (VSA) for each atom. The sum of the VSA of each atom gives the molecular VSA. 

Fig. 5. The r2 correlation coefficients for linear models of traditional descriptors as a function of the 32 VSA descriptors. Notes (a) connectivity and kappa shape indices (4) (b) van der Waals surface area, volume, and density ...

Van der Waals Parameter-Kow Relationships Moriguchi et al. [40] have studied the correlation of Kow with either the van der Waals volume, Vvaw, or the van der Waals surface area, Aw, for apolar organic compounds such as inert gases, alkylbenzenes, PAHs, and halogenated alkanes and benzenes. The relationships are... 

A quite different approach to the molecular size of solvents is the estimation of its molecular surface area and volume from the van der Waals radii of the constituent atoms and the manner and geometry of their mutual bonding (Bondi 1964). The necessary calculations are quite involved, and the values shown in Table 3.4 have been taken from a single source (DIPPR 1997), in order to be consistent. The reported molar van der Waals surface areas, Ayiw, are in 104 m2 mol 1 and the molar van der Waals volumes, Fvdw, are in cm3 mol 1, the latter in order to be comparable with the molar volumes (in Table 3.1) and the intrinsic volumes, defined below, also reported in Table 3.4. 

Van der Waals surface area calculated using a connection table approximation Van der Waals volume calculated using a connection table approximation Van der Waals volume calculated using a grid approximation... 

Van der Waals surface area using polyhedral representation... 

Number of nitrogen atoms Number of aromatic atoms Number of rotatable bonds Number of hydrogen bond acceptors Sum of van der Waal surface areas of basic atoms... 

Among further CPSA descriptors are the differences between PPSA and PNSA, and fractional values as ratios of PPSA or PNSA and the total molecular surface area. For the original list of 25 CPSA descriptors as well as for recent extensions, the reader is referred to the literature (Stanton and Jurs, 1990 Aptula et al., 2003 Mattioni et al., 2003 Mosier et al., 2003). It should be further noted that, in contrast to the initially introduced electrostatic molecular surface interaction terms (Grigoras, 1990), the CPSA descriptors were actually defined using solvent accessible surface areas instead of simple van der Waals surface areas (Stanton and Jurs, 1990), a fact that is ignored in the present discussion for the sake of simplicity. 

Figure 4. Relationship of log P and Water Solubility (WS, mmoI/L) with van der Waals Surface Area of A -Alkylated Imidacloprid...

The van der Waals surface area 5Avdw (also known as Total molecular Surface Area, TSA) is then defined as the exterior surface of the union of all such spheres in the molecule, i.e. the area of the van der Waals molecular surface. 

An important parameter that strongly correlates with membrane permeability is polar surface area (PSA) - a sum of van der Waals surface areas of polar atoms (oxygens and nitrogens).Multiple studies " have found an upper PSA threshold value of —140-150 for oral absorption. Similarly, for blood-brain barrier penetration, the upper PSA threshold is —90A (Figure 12.1). Recently, fast algorithms for PSA calculation have been suggested that do not need a... 

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