Eighth-Sphere Exposure: A three-dimensional solvent exposure measure

Protein amino acid solvent exposure plays a crucial role in understanding, analyzing and predicting protein structure and function. In this paper, we propose a novel three-dimensional measure of solvent exposure named Eighth-Sphere Exposure based on three-dimensional protein structures. This measure supposes a sphere with a radius of 13Å around a Cα atom, and subdivides its microenvironment into eight quadrants according to a space rectangular coordinate system, constructed by the four backbone amino acid atoms Cα, Cβ, C and N. The number of the neighboring Cα atoms is calculated as the Eighth-Sphere Exposure values. Our analysis is further based on 689 randomly-selected protein chains from a representative and nonredundant data set obtained from PDB-REPRDB database, and histograms are obtained. The performances are analyzed and compared with other solvent exposure measures such as Contact Number and Half-Sphere Exposure. As the eight histograms of Half-Sphere Exposure show very different distributions compared to each other, it indicates that the described division of a residue's spherical neighborhood indeed captures regions with different properties. Our method provides a different view of solvent exposure, and it supplies more characteristic structure information than the Contact Number and Half-Sphere Exposure methods. It is believed that Eighth-Sphere Exposure can be useful in protein structure analysis, prediction, and other areas.