An efficient algorithm calculating common solvent accessible volume.

The solvent accessible surface area and the solvent accessible volume are measurements commonly used in implicit solvent models to include the effect of forces exerted by solvents on the protein surfaces (or the atoms on protein surfaces). The two measurements have limitations in describing interactions between proteins (or proteins' atoms) mediated/bridged by solvents. This is because describing the interactions between proteins should be able to capture the chain of protein-solvent-protein interactions while the solvent accessible surface area or the solvent accessible volume can capture only protein-solvent interactions. If we represent the solvent as a continuous medium, we can consider an atom of a protein can effectively interact with the solvent within a certain distance from its surface (or its own solvent-interacting sphere). In this case, the protein-solvent-protein interactions can be measured by the amount of solvent interacting with two proteins' atoms at the same time (or the volume shared by the two atoms' solvent-interacting spheres excluding the volumes occupied by proteins' atoms). We call the shared volume as the common solvent accessible volume (CSAV); there has been no method developed to determine the CSAV. In this work, we propose a new sweep-line-based method that efficiently calculates the common solvent accessible volume. The performance and accuracy of the proposed sweep-line-based method are compared with those of the naïve voxel-based method. The proposed method takes log-linear time to the number of atoms involved in a CSAV calculation and linear time to the resolution. Our results, tested with 52 protein structures of various sizes, show that the proposed sweep-line-based method is superior to the voxel-based method in both computational efficiency and accuracy.