Protein is considered as polypeptide chains linked together. A polypeptide chain is a chain of amino acids (amino acid residues) linked together by peptide bonds. An amino acid consists of a central carbon atom (usually alpha Carbon Cα) and an amino group (NH2), a hydrogen atom (H), a Carboxy group (COOH) and a side chain (R) bound to the Cα. The backbone of the polypeptide is given by the repeated sequence of three atoms of each residue in the chain: the amide N, the alpha Carbon Cα and the Carbonyl C.
PDB is Protein Database Bank which contains the structure of the proteins. From protein data structure in the PDB, we determined coordinates of each atom Calpha on the C chain polypeptide and use graph model to represent protein structure [9]. In this model, each vertex is an amino acid. We selected Calpha atom to represent amino acid. Two vertices have an edge when their Calpha atom are neighbors of each other, in other words, the distance between Calpha atoms of two amino acids is smaller than a given threshold δ, the threshold is usually selected in range 6.5-8.5°A. Figure 3 shows the protein structure and the graph representing this protein structure.
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9. Vishveshwara, S., et al.: Protein structure insights from graph theory. Journal of Theoretical and Computational Chemistry 1(1) (2002)