In structure-based drug design, the fragment molecular orbital (FMO) method, which can quantitatively evaluate interaction energy with high accuracy, helps identify critical amino acid residues and types of inter- and intramolecular interactions for molecular recognition of ligands, peptides, and antigens. In this study, we performed FMO calculations using 679 apoprotein structures, classified them according to their characteristic amino acid residue pair groups (e.g., charged, polar, hydrophobic, and aromatic residues), and statistically analyzed the characteristics of their intramolecular interactions by using inter-fragment interaction energy (IFIE). The average total IFIE between amino acid residues was stronger in the order of pairs of oppositely charged residues, pairs of charged and neutral polar residues, pairs of neutral polar residues, and pairs of hydrophobic residues. Focusing on the dispersion interaction energy obtained using energy decomposition, except for the pairs of both charged residues, pairs of amino acid residues that consisted of aromatic rings had the largest attractive interaction energy compared to other residue pair groups. Furthermore, we compared the intramolecular interaction energy between the FMO and the classic molecular mechanics (MM) methods. The latter tended to estimate the attractive and repulsive interaction energies were weaker than those using the FMO method. As for the dispersion force, the van der Waals interaction energy obtained by the MM method tended to be partially repulsive of amino acid residue pairs with relatively short distances. Such statistical energy interaction analyses of amino acid residue pairs not only depend on understanding the intramolecular interactions of proteins, but is also expected to act as the indicators of IFIEs in molecular recognition (e.g., antigen–antibody and peptide drugs). Furthermore, analysis of critical amino acid residues and their interactions will help understand proteins' molecular bonding and structural stability.
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