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.

Enzyme kinetics is widely used in many biological studies. Most of enzyme kinetic formulae are derived based on the steady state assumption, which is mathematically expressed by a time- differential equation, namely, d(an enzyme state)/dt = 0 in conventional textbooks. In this opinion article, I would like to propose flux method for handling the steady state assumption.In the proposed flux method, a steady state is defined as the condition wherein the flux entering to the state is equal to the flux leaving that state, implying that the traffic of materials passing through the state is nonzero. How the concept of flux, a type of flow rate, is useful for understanding the nature of enzyme reactions and enzyme kinetic studies will be discussed.

In modeling structures with multiple conformers, the one with the higher occupancy is typically used under implicit understanding. Multiple conformers have rarely been studied to determine whether a structure with a higher ligand occupancy conformer is more stable and has stronger protein-ligand binding than the one with the lower occupancy. We performed fragment molecular orbital (FMO) calculations on complexes with high and low ligand occupancies, comparing their energies, such as total energy and ligand binding energy, to investigate this question. The structures for FMO calculation were the SARS-CoV-2 main protease (M^pro) and the covalent inhibitor, GC376. The initial X-ray crystal structure of the complex (PDB ID: 7CB7) possessed stereo isomers of GC376, namely B1S (R form) and K36 (S form), with different occupancies. Our findings showed that for all structural optimization conditions, the total energy of the high ligand occupancy B1S complex was lower than that of the low ligand occupancy K36 complex. In addition, stronger interfragment interaction energy (IFIE) of B1S than of K36 was confirmed for most structural optimization conditions. These differences between B1S and K36 are caused by the presence and absence of a hydrogen bond between the ligand and His41, as revealed by IFIE and structural geometry analyses between the ligand and each amino acid residue of M^pro. The present study, under several structural optimization conditions, would have the potential to model energetically stable structures by efficiently selecting high occupancy conformers from structures with different ones.