Volumes and surface areas: geometries and scaling relationships between coarse- grained and atomic structures

Computing volumes and surface areas of molecular structures is generally considered to be a solved problem, however, comparisons presented in this review show that different ways of computing surface areas and volumes can yield dramatically different values. Volumes and surface areas are the most basic geometric properties of structures, and estimating these becomes especially important for large scale simulations when individual components are being assembled in protein complexes or drugs being fitted into proteins. Good approximations of volumes and surfaces are derived from Delaunay tessellations, but these values can differ significantly from those from the rolling ball approach of Lee and Richards (3V webserver). The origin of these differences lies in the extended parts and the less well packed parts of the proteins, which are ignored in some approaches. Even though surface areas and volumes from the two approaches differ significantly, their correlations are high. Atomic models have been compared, and the poorly packed regions of proteins are found to be most different between the two approaches. The Delaunay complexes have been explored for both fully atomic and for coarse-grained representations of proteins based on only C(α) atoms. The scaling relationships between the fully atomic models and the coarse-grained model representations of proteins are reported, and the lines fit yield simple relationships for the surface areas and volumes as a function of the number of protein residues and the number of heavy atoms. Further, the atomic and coarse-grained values are strongly correlated and simple relationships are reported.