Calculation of the volumetric characteristics of biomacromolecules in solution by the Voronoi-Delaunay technique

Recently a simple formalism was proposed for a quantitative analysis of interatomic voids inside a solute molecule and in the surrounding solvent. It is based on the Voronoi-Delaunay tessellation of structures, obtained in molecular simulations: successive Voronoi shells are constructed, starting from the interface between the solute molecule and the solvent, and continuing to the outside (into the solvent) as well as into the interior of the molecule. Similarly, successive Delaunay shells, consisting of Delaunay simplexes, can also be constructed. This technique can be applied to interpret volumetric data, obtained, for example, in studies of proteins in aqueous solution. In particular, it allows replacing qualitatively and descriptively introduced properties by strictly defined quantities, such as the thermal volume, by the boundary voids. The extension and the temperature behavior of the boundary region, its structure and composition are discussed in detail, using the example of a molecular dynamics model of an aqueous solution of the human amyloid polypeptide, hIAPP. We show that the impact of the solute on the local density of the solvent is short ranged, limited to the first Delaunay and the first Voronoi shell around the solute. The extra void volume, created in the boundary region between solute and solvent, determines the magnitude and the temperature dependence of the apparent volume of the solute molecule.