Descriptor solvent-accessible surface

The MEP at the molecular surface has been used for many QSAR and QSPR applications. Quantum mechanically calculated MEPs are more detailed and accurate at the important areas of the surface than those derived from net atomic charges and are therefore usually preferable [Ij. However, any of the techniques based on MEPs calculated from net atomic charges can be used for full quantum mechanical calculations, and vice versa. The best-known descriptors based on the statistics of the MEP at the molecular surface are those introduced by Murray and Politzer [44]. These were originally formulated for DFT calculations using an isodensity surface. They have also been used very extensively with semi-empirical MO techniques and solvent-accessible surfaces [1, 2]. The charged polar surface area (CPSA) descriptors proposed by Stanton and Jurs [45] are also based on charges derived from semi-empirical MO calculations. 

The simplest shape for the cavity is a sphere or possibly an ellipsoid. This has the advantage that the electrostatic interaction between M and the dielectric medium may be calculated analytically. More realistic models employ moleculai shaped cavities, generated for example by interlocking spheres located on each nuclei. Taking the atomic radius as a suitable factor (typical value is 1.2) times a van der Waals radius defines a van der Waals surface. Such a surface may have small pockets where no solvent molecules can enter, and a more appropriate descriptor may be defined as the surface traced out by a spherical particle of a given radius rolling on the van der Waals surface. This is denoted the Solvent Accessible Surface (SAS) and illustrated in Figm e 16.7. 

Kaznessis et al. [24] used Monte Carlo simulations on a data set of 85 molecules collected from various sources, to calculate physically significant descriptors such as solvent accessible surface area (SASA), solute dipole, number of hydrogen-bond acceptors (HBAC) and donors (HBDN), molecular volume (MVOL), and the hydrophilic, hydrophobic, and amphiphilic components of SASA and related them with BBB permeability using the MLR method. After removing nine strong outliers, the following relationship was developed (Eq. 37) ... 

Wang et al. [5] reported a set of aqueous solubility models for a larger data set using atom type-classified solvent-accessible surface areas as descriptors. The best model achieved a very encouraging performance (n — 1,708, m — 50, r2 =... 

The Molecular Surface (MS) first introduced by Richards (19) was chosen as the 3D space where the MLP will be calculated. MS specifically refers to a molecular envelope accessible by a solvent molecule. Unlike the solvent accessible surface (20), which is defined by the center of a spherical probe as it is rolled over a molecule, the MS (19), or Connolly surface (21) is traced by the inwardfacing surface of the spherical probe (Fig. 2). The MS consists of three types of faces, namely contact, saddle, and concave reentrant, where the spherical probe touches molecule atoms at one, two, or three points, simultaneously. Calculation of molecular properties on the MS and integration of a function over the MS require a numerical representation of the MS as a manifold S(Mk, nk, dsk), where Mk, nk, dsk are, respectively, the coordinates, the normal vector, and the area of a small element of the MS. Among the published computational methods for a triangulated MS (22,23), the method proposed by Connolly (21,24) was used because it provides a numerical presentation of the MS as a collection of dot coordinates and outward normal vectors. In order to build the 3D-logP descriptor independent from the calculation parameters of the MS, the precision of the MS area computation was first estimated as a function of the point density and the probe radius parameters. When varying... 

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. 

The molecular interaction fields (MIF) obtainable by GRID [1] may be used to define the solvent accessible surface, which resembles the molecular shape. However, MIFs are descriptors that depend on the 3D-location, and usually several thousand are required to describe a shape. In this chapter we present a novel procedure, called PathFinder, which encodes MIF into a compact alignment-free description of molecular shape. 

The nondifferentiability of these surfaces at the seams of interpenetrating spheres as well as the local nondifferentiability of solvent accessible surfaces or union surfaces, are a technical disadvantage. Local nondifferentiability limits the application of the shape group methods in their original form that requires second derivatives for curvature analysis. For example, at every point r of a VDWS where two or more atomic spheres interpenetrate one another, the surface is not smooth and is not differentiable. For such nondifferentiable molecular surfaces, alternative shape descriptors and shape codes have been introduced. 

A set of thirty different descriptors [Stanton and Jurs, 1990] which combine shape and electronic information to characterize molecules and therefore encode features responsible for polar interactions between molecules. The molecule representation used for deriving CPSA descriptors views molecule atoms as hard spheres defined by the - van der Waals radius. The - solvent-accessible surface area SASA is used as the molecular surface area it is calculated using a sphere with a radius of 1.5 A to approximate the contact surface formed when a water molecule interacts with the considered molecule. Moreover, the contact surface where polar interactions can take place is characterized by a specific electronic distribution obtained by mapping atomic partial charges on the solvent-accessible surface. 

Let SAd and SAa be the solvent accessible surface areas of hydrogen-bonding donors (d) and acceptors (a), respectively, and Qa the corresponding partial atomic charges, SASA the molecular solvent-accessible surface area the HB-CPSA descriptors are then defined as follows (note that the two different symbols encountered in the literature for some are considered as synonymous). 

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. 

Solvent-accessible surface area CPSA descriptors Molecular shape analysis Mezey 3D shape analysis... 

The descriptors of the molecular structures that are used in QSAR include physical and electronic properties, fragment compositions, as well as calculated properties of the three-dimensional (3D) structures of the compounds. The 3D properties include scalar parameters like solvent-accessible surface area, or hydro-phobic surface area. They also include field-type reductions of the structure that represent steric interactions, electrostatic potentials, hydrogen-bonding potential, hydrophobic interactions, and so on. 

As a second contribution to the final form of the PP term, we added a part for the solvent-accessible surface area (SASA). Beyond the molecular recognition in terms of preferred distances, the complementarity of shape constitutes an important descriptor for docking. This concept is well defined on considering the surface that is buried between two molecules, after their complexation. For this purpose, we previously developed an efficient way to calculate the SASA of our reduced models [67], and, consequently, of the interface of dimerization. Many articles are concerned with P-P dimers [68] to form stable complexes, the contact surface between two proteins is generally considered to exceed 1200 [69], but additional... 

A group of geometrical descriptors that contain usefirl intuitive meaning is the group based on the molecular volume, solvent accessible surface, and van der Waals radii. The approach for this group is based largely on the... 

In the above formula, D denotes that the summation goes over aU hydrogen donor surfaces, qo is the partial charge on H-bonding donor atoms, Sd is the solvent-accessible surface area of H-bonding donor atoms, and Stot is the total solvent-accessible molecular surface area. The electrostatic descriptors have intuitive interpretations. Their inclusion in QSAR models makes easy and clear analysis of the phenomenon under investigation. 

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