Analysis of protein three-dimension structure using amino acids depths

The issue of amino acid depth in proteins gives important insights to our understanding of protein's three-dimensional structure. There has already been much research done in mathematical and statistical sciences regarding the general definitions, properties and algorithms describing the particle depth of spatially extended systems. We constructed a method of calculating the amino acids depths and applied it to a set of 527 protein structures. We propose the introduction of amino acid depth tendency factors for three-dimensional structures of proteins. The depth tendency factors relate not only to the hydrophobicity indices but also to the electrostatic charge. We found a relationship between the protein size and the number of residues using the distance between the deepest residue and surface residues. We made a prediction regarding the number of residues on the surface of a protein, the deepest amino acid, and the average depth, all of which are fitted well to a linear functional relationship with the length of the protein. Finally, we have predicted the depths of multiple peptides in protein's three-dimension structure.