Quantification of protein surfaces, volumes and atom-atom contacts using a constrained Voronoi procedure

Motivation: Geometric representations of proteins and ligands, including atom volumes, atom-atom contacts and solvent accessible surfaces, can be used to characterize interactions between and within proteins, ligands and solvent. Voronoi algorithms permit quantification of these properties by dividing structures into cells with a one-to-one correspondence with constituent atoms. As there is no generally accepted measure of atom-atom contacts, a continuous analytical representation of inter-atomic contacts will be useful. Improved geometric algorithms will also be helpful in increasing the speed and accuracy of iterative modeling algorithms. Results: We present computational methods based on the Voronoi procedure that provide rapid and exact solutions to solvent accessible surfaces, volumes, and atom contacts within macromolecules. Furthermore, we define a measure of atom-atom contact that is consistent with the calculation of solvent accessible surfaces, allowing the integration of solvent accessibility and inter-atomic contacts into a continuous measure. The speed and accuracy of the algorithm is compared to existing methods for calculating solvent accessible surfaces and volumes. The presented algorithm has a reduced execution time and greater accuracy compared to numerical and approximate analytical surface calculation algorithms, and a reduced execution time and similar accuracy to existing Voronoi procedures for calculating atomic surfaces and volumes.