A protein’s surface is formed from the side-chains of its amino acids, which during the folding process have been positioned at least partially exposed to the extra-molecular environment. As mentioned earlier in Section 1.1.2, two methods were originally proposed for measuring solvent exposure of amino acids in a protein structure. Both methods measure the same quantity, though they are different in how they achieve the measurement. The first method was proposed by Lee and Richards [14] which was shortly followed by Shrake & Rupley [15]. Lee and Richards termed the quantity they were measuring as the solvent accessible surface area of the protein and gave the following definition: “the area mapped out by the centre of a sphere rolling along the surface of a protein, the sphere represents a solvent molecule - usually having a radius of 1.4 Å, that of water, however different radii can be chosen” [14]. Their method is sometimes referred to as the “rolling ball” method. The method is still in use today in the Naccess computer program [4].
The second method proposed by Shrake and Rupley, uses a different method of calculating the accessible surface area. In the same way as Lee and Richards, they defined a probe radius which was added to the van der Waal’s radii of the atoms within the molecule. They then placed 92 points on the resulting sphere and determined which points where accessible to a solvent molecule - and not inside an expanded sphere [15]. Later Connolly [54] developed this further and created a computer software package (called MS) which went through a number of incarnations and is available today as a part of the Chimera package from UCSF. This method of determining the surface area has also been incorporated in the computer program DSSP [55]. The question of how to define the surface of a protein is not necessarily straightforward to answer. Figure 1.2 illustrates the rolling ball method of determining solvent accessible surface area, and includes illustrations for several different interpretations of the protein surface. In the
Figure 1.2: The rolling ball method. The probe with radius r is rolled over the external surface of the amino acids’ atoms. The Solvent Accessible Area is the area traced out by the centre of the probe. Typically a radius of 1.4 Åis chosen for the probe radius, representing the radius of a single water molecule. The molecular surface is the surface area traced out by the edge of the probe closest to the van der Waals surface. The van der Waals surface of the protein is made up of the non-overlapped van der Waals surfaces of the surface atoms.
strictest sense it could be argued that the surface of a protein is defined by the non-overlapped regions of van der Waals surfaces of all atoms on the exterior of the protein, that are exposed to the environment and not the surface of another atom. However, it could also be argued that the surface of the protein consists only of the regions of the van der Waals surface which can come into contact with a solvent molecule, which is referred to as the contact-surface.
Through the application of the rolling ball method, there are other surfaces which can be defined. For example the contact surface is the traced out trajectory of a probes surface coming into contact with the van der Waals surface; or re-entrant surface, which is the trajectory of the probes surface over regions of the surface, such as crevices which may be too narrow for a solvent molecule to penetrate [16, 56], as shown in Figure 1.2. If we combine the re-entrant surface and the contact surface, we get what is referred to as the “molecular surface” [16, 57]. Alternatively, an extended van der Waals surface can be defined, by offsetting the van der Waals surface of the amino acids by the radius of a solvent molecule, which is equivalent to tracing the trajectory of the centre of a probe rolling over the molecular surface of the protein (the volume
enclosed by this surface is referred to as the solvent excluded volume [54, 58]). This is the solvent accessible surface proposed by Lee and Richards, the area which is determined by the following steps:
1. Assign a van der Waals radius to each atom or group of atoms. Note: Hydrogen atoms are not considered separately but are included in a group radius, e.g. a carbon atom has a radius of x-angstroms; but when considering CH3 as a group a radius of y-angstroms is
considered (where y > x ). This is similarly applied to SH, NH, OH, CH2and CH.
2. As the structure is now represented by a set of inter-locking spheres, the continuous struc- ture is sectioned by a set of parallel planes with a predetermined spacing. The resulting cross-sections of the structure shows the inter-locking spheres as circles. The overlap- ping arcs of which are not eliminated. This is because it helps to distinguish one atom from another. It also helps to easily recognise excessive overlap of symmetry related neighbouring molecules. Their method was proposed before the advent of sophisticated computer graphics systems and so relied on the use of outlines on sheets of plastic. 3. The polar atoms (oxygen and nitrogen) are dotted and labelled. The non-polar atoms
(carbon and sulphur) are given solid lines.
4. The sequence number is written at the centre of both the α and β carbons.
5. The skeleton covalent bonds and hydrogen bonds are shown between atom centres to assist in viewing.
Lee and Richards applied their method to investigating the burial of hydrophobic surface area of residues in proteins. To calculate the relevant solvent accessibility, they created two model systems. These were both used to estimate the hydrophilic and the hydrophobic surface area of each amino acid. The models constructed were tri-peptides of Ala-X-Ala and Gly- X-Gly respectively, where X is the residue whose accessibility is being computed. Here a measure of the area accessible to solvent of residue X, in the tri-peptide, is taken as a measure of the residue’s accessibility to solvent in an unfolded state. They then measured the accessible
surface area of each residue in a folded protein. This was compared to the unfolded state and the percentage of the surface area that became buried as a result of folding was then known. They called this the “relative solvent accessibility” of a residue, it is a percentage area of a residue relative to either of the tri-peptide models discussed earlier. This is distinct from the solvent accessible area which is measured in Å2.