Abstract
A three-dimensional Voronoi tessellation of folded proteins is used to analyzegeometrical and topological properties of a set of proteins. To each amino acid is associated a centralpoint surrounded by a Voronoi cell. Voronoi cells describe the packing of the amino acids. Specialattention is given to reproduction of the protein surface. Once the Voronoi cells are built, a lot oftools from geometrical analysis can be applied to investigate the protein structure; volume of cells,number of faces per cell, and number of sides per face are the usual signatures of the proteinstructure. A distinct difference between faces related to primary, secondary, and tertiary structures hasbeen observed. Faces threaded by the main-chain have on average more than six edges, whereas thoserelated to helical packing of the amino acid chain have less than five edges. The faces on the proteinsurface have on average five edges within 1% error. The average number of faces on the protein surfacefor a given type of amino acid brings a new point of view in the characterization of the exposition to thesolvent and the classification of amino acid as hydrophilic or hydrophobic. It may be a convenient toolfor model validation.