Connolly’s molecular surface

S. Hofinger and O. Steinhauser, Making use of Connolly s molecular surface program in the isodensity adapted polarizable continuum model, J. Chem. Phys., 115 (2001) 10636-10646. 

Fig. 11.17. View of the Connolly s molecular surface (In dots) of [Ag4U] + (left) and lAgeLe] (right) for rp,obe = I A.

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... 

Connolly (43,44) and Richmond (45) also developed analytical methods for calculating molecular surface area and volume, which provide nearly exact values for the surface area and enclosed volume. Richmond s method provides analytical derivatives for surface area with respect to the cartesian coordinates of the atoms, which may be useful for docking (Section V). Connolly s algorithm also produces spectacular shaded raster graphics images (46), which give a very different feel for a macromolecular surface than conventional space-filling displays. 

The Connolly solvent-excluded volumes (the volume contained within the contact molecular surface) of the probe molecules are 269 A, 392 A, and 515 A for FDM, FDMDG, and FDMTG, respectively. It is clear that increasing the volume of the probe molecule lowers the overall mass transport, thereby decreasing the oxidative current, but increases the selectivity as evidenced by the greater normalized current ratio (AZ/Z s). 

In analyzing surface effects of ultra fine polymer particles, we calculated the surface area and volume using Connolly s contact-reentrant method [231-233]. The contact-reentrant surface (molecular surface) uses a rigid hard sphere with a spherical probe that can trace molecular shape while in contact with the van der Waals surface. The van der Waals surface treats a CH2 bead as a rigid hard sphere equal to the van der Waals radii. The union of the spheres is considered the volume. Connolly s method provides a smooth surface by patching the space between the probe radius and the probed molecule. For our surface area and volume calculations, the van der Waals radius for the PE particles is set at 1.89 C for CH2 beads and the probe radius at 1.4 C to mimic the H2O molecule. Using the molecular surface, we also computed the fractal dimension D to determine roughness of the surface.. The value of D can be calculated by... 

In the literature the Connolly surface and the molecular surface introduced by Lee and Richards are both referred to as solvent accessible surface , a fact which might be confusing. The differences in both surface definitions are shown schematically in Figure 12. Here and in the following, we always refer to Connolly s definition. 

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