Decomposition of a Protein Solution into Voronoi Shells and Delaunay Layers

A simple formalism is proposed for a quantitative analysis of interatomic voids inside and outside of a molecule in solution. It can be applied for the interpretation of volumetric data, obtained in studies of protein folding in water. The method is based on the Voronoi-Delaunay tessellation of molecular-dynamic models of solutions. It is suggested to select successive Voronoi shells, starting from the interface between the solute molecule and the solvent, and continuing to the outside (into the solvent) as well as into the inner of the molecule. Similarly, successive Delaunay layers, consisting of Delaunay simplexes, can also be calculated. Geometrical properties of the selected shells and layers are discussed. The behavior of inner and outer voids is discussed by the example of a molecular-dynamic model of an aqueous solution of the polypeptide hIAPP.