Hybrid Voronoi diagrams, their computation and reduction for applications in computational biochemistry

Geometric models of molecular structures are often described as a set of balls, where balls represent individual atoms. The ability to describe and explore the empty space among these balls is important, e.g., in the analysis of the interaction of enzymes with substrates, ligands and solvent molecules. Voronoi diagrams from the field of computational geometry are often used here, because they provide a mathematical description of how the whole space can be divided into regions assigned to individual atoms. This paper introduces a combination of two different types of Voronoi diagrams into a new hybrid Voronoi diagram - one part of this diagram belongs to the additively weighted (aw-Voronoi) diagram and the other to the power diagram. The boundary between them is controlled by a user-defined constant (the probe radius). Both parts are computed by different algorithms, which are already known. The reduced aw-Voronoi diagram is then obtained by removing the power diagram part from the hybrid diagram. Reduced aw-Voronoi diagrams are perfectly tailored for the analysis of dynamic molecular structures, their computation is faster and storage requirements are lower than in the case of complete aw-Voronoi diagrams. Here, we showed their application to key proteins in cancer research such as p53 and ARID proteins as case study. We identified a biologically relevant cavity in p53 structural ensembles generated by molecular dynamics simulations and analyzed its accessibility, attesting the potential of our approach. This method is relevant for cancer research since it permits to depict a dynamical view of cavities and pockets in proteins that could be affected by mutations in the disease. Our approach opens novel prospects for the study of cancer-related proteins by molecular simulations and the identification of novel targets for drug design.