Section 22.1.2.1.2. Molecular, solvent-accessible and occluded surface areas

The concept of molecular surface derives from the behaviour of non-bonded atoms as they approach each other. As indicated by the Lennard–Jones potential, strong unfavourable interactions of overlapping non-bonding electron orbitals increase sharply according to , and atoms behave almost as if they were hard spheres with van der Waals radii that are characteristic for each atom type and nearly independent of chemical context. Of course, when orbitals combine in a covalent bond, atoms approach much more closely. Lower-energy attractions between atoms, such as hydrogen bonds or aromatic ring stacking, lead to modest reductions in the distance of closest approach. The van der Waals surface is the area of a volume formed by placing van der Waals spheres at the centre of each atom in a molecule.

Non-bonded atoms of the same molecule contact each other over (at most) a very small proportion of their van der Waals surface. The surface is complicated with gaps and crevices. Much of this surface is inaccessible to other atoms or molecules, because there is insufficient space to place an atom without resulting in forbidden overlap of non-bonded van der Waals spheres (Fig. 22.1.2.1). These crevices are excluded in the molecular surface area. The molecular surface area, also known as the solvent-excluding surface, is the outer surface of the volume from which solvent molecules are excluded. Strictly, this would depend on the orientation of non-spherically symmetric solvents such as water. However, since hydrogen atoms are smaller than oxygen atoms, for current purposes it is sufficient to consider water as a sphere with a radius of 1.4 to 1.7 Å, approximating the `average' distance from the centre of the oxygen atom to the van der Waals surface of water. The practical definition of the molecular surface is, then, the area of the volume excluded to a spherical probe of 1.4 to 1.7 Å radius.

Figure 22.1.2.1 | top | pdf | Surfaces in a plane cut through a hypothetical molecule. The molecular surface consists of the sum of the atomic surfaces that can be contacted by solvent molecules and the surface of the space between atoms from which solvent molecules are excluded. The solvent-accessible surface is the surface formed by the set of the centres of spheres that are in closest contact with the molecular surface.

As an aside, it is important to note that surface-area calculations depend on inexact parameterization. For example, there is no radius of any hard-sphere model that can give a realistic representation of the solvent. Furthermore, the choice of van der Waals radii can depend on whether the distance of zero or minimum potential energy is estimated and the potential-energy function or experimental data used. (Tables of common values are given by Gerstein & Richards in Section 22.1.1.) Thus, calculations of molecular and accessible surfaces are approximate. However, when the errors are averaged over large areas of a macromolecule, the numbers can be precise enough to give important insights into function.

Fig. 22.1.2.1 shows that the molecular surface consists of two components. The contact surface is part of the van der Waals surface. The re-entrant surface encloses the interstitial volume and has components that are the exterior surfaces of atoms (contact surface) and parts of the surfaces of probes placed in positions where they are in contact with van der Waals surfaces of two or more atoms (re-entrant surface).

The occluded molecular surface is an approximate complement to the solvent-accessible surface. It is the part of the surface that would be inaccessible to solvent because of steric conflict with neighbouring macromolecular atoms. It is an approximation in that current calculations use van der Waals surfaces, ignoring the differences between atomic and re-entrant surfaces (see below), and the volume of the probe is not fully accounted for (Pattabiraman et al., 1995). Occluded area is defined as the atomic area whose normals cannot be extended 2.8 Å (the presumptive diameter of a water molecule) without intersecting the van der Waals volume of another atom. This crude approximation to the surface that is inaccessible to water not only increases the speed of calculation, but enables surface areas to be partitioned between the atoms. It is used primarily to evaluate model protein structures by comparing the fraction of each amino acid's surface area that is occluded with that calculated for the same residue types in a database of accurate structures.