3.1. Protonation state of Glu177 and N- and C-terminals of APR + APRin
As Glu177 exists near the Zn ion of APR and has a significant effect on APR activity, its protonation state had to be determined in an appropriate manner. Thus, we considered the different protonation states (Figure S3 in the SI) of Glu177 and optimized the structure of the solvated APR + APRin complex using the MM method. The obtained structures were compared with the PDB structure, and the most appropriate protonation state of Glu177 that did the best job reproducing the PDB structure of the APR + APRin complex was determined.
In the PDB structure  of the APR + APRin complex, the Glu177 of APR, the catalytic base of the HEXXH motif, forms a hydrogen bond with the Ser2 of APRin. In our optimized complex structures, there is no hydrogen bond between Glu177 and Ser2 when Glu177 has a Glu− or Glh-2 protonation state, as shown in Fig. 2a and c, respectively. At the same time, the oxygen atom of the Glu177 sidechain is separated from the oxygen atom of the OH group of the Ser2 sidechain. Notably, a crystal water molecule bridging the Ser2 and Thr173 of APR plays an important role in determining the direction of the OH group. In contrast, Fig. 2b reveals that the OH group of the Glu177 sidechain forms a hydrogen bond with the oxygen atom of Ser2 when Glu177 is in the Glh-1 protonation state. This hydrogen bond (Fig. 2b) is comparable to that in the PDB structure . Consequently, Fig. 2 demonstrates that Glh-1 is the most preferable protonation state for the Glu177 of APR in the X-ray structure.
In the PDB structure  of the APR + APRin complex, the OH group of the Ser1 sidechain as well as the backbone N atom of the Ser1 located at the N-terminal of APRin are directly coordinated with the Zn ion of APR, as shown in Fig. 3a. Therefore, the structures of the N- and C-terminals of APRin as well as APR are likely to have a significant influence on the interaction between APR and APRin. Thus, we considered different types of terminal structures for both the APR and APRin peptides to determine the most preferable structure.
At first, we assigned the NH3+ and COO− structures to the N- and C-terminals, respectively, and the APR + APRin complex structure was optimized using the MM method. As shown in Fig. 3b, the structure around the Zn ion was altered significantly from the PDB structure due to the repulsive electrostatic interaction between the NH3+ group of APRin and the Zn ion. Accordingly, it was revealed that the altered NH3+ and COO− structures are not suitable for reproducing the PDB structure  of the APR + APRin complex.
Next, we assigned the Ace and Nme structures to the N- and C-terminals, respectively, as shown in Figure S4c in the SI. The optimized structure around the Zn ion is shown in Fig. 3c. The oxygen atom of the Ace group coordinated directly to the Zn ion at 1.84 Å distance, and the distance between the N atom of the Ser1 main chain and the Zn ion was elongated to 3.6 Å, resulting in significant deformation from the PDB structure (Fig. 3a). Therefore, the Ace group was found to be unsuitable for the N-terminal structure of APPin.
The results indicated that the NH2 group remained as the only choice for the N-terminal structure of APRin. However, a force field for the NH2 terminal was not prepared among the AMBER force fields. Therefore, we added hydrogen atoms and solvating water molecules to the PDB structure of the APR + APRin complex and optimized only the positions of the hydrogen atoms and the water molecules using the AMBER18-MM method, under the assumption that the N- and C-terminal structures were the NH3+ and COO− groups, respectively. In the optimized structure, the NH3+ and the COO− of APR and APRin were changed into NH2 and COOH, respectively. The specific interactions between APR and APRin for this structure were investigated at an electronic level using the ab initio FMO method.
3.2. Specific interactions between APR and APRin
To determine the residues of APRin that are the main contribution to the specific binding between APRin and APR, we first investigated the total IFIEs of each APRin residue with all APR residues. As shown in Fig. 4, the Ser1 and Ser2 at the N-terminal of APRin as well as the charged Arg83 and Arg90 residues have large attractive total IFIEs. In particular, Ser1 strongly interacts with the APR residues.
In the present FMO calculations, we considered crystal water molecules explicitly and evaluated the electronic properties of the APR + APRin complex in a vacuum. As a result, the electrostatic interactions between the APR and APRin residues were overestimated, as indicated in Fig. 4. It is expected that this overestimation would be improved by considering a continuum solvation model. However, the trend of the IFIEs is likely to not change even when the continuum solvation model is employed.
The previous experiments [5, 7] revealed that the Ser1 backbone carbonyl of APRin interacts with the catalytic Zn, while the Ser2 side chain of APRin forms a hydrogen bond to the carboxyl end of the catalytic Glu177 of APR. Our present FMO results (Fig. 4), which indicate the significant contribution of the Ser1 and Ser2 residues to the binding to APR, are comparable to these experimental results.
To elucidate the reason for the high attractive interaction energy between Ser1 and the APR residues, we investigated the IFIEs between Ser1 and each of the APR residues. As shown in Fig. 5a, Ser1 interacts very strongly with the Zn group of APR and has no significant interaction with the other APR residues. In fact, as indicated in Fig. 5b, the OH group of the Ser1 sidechain interacts electrostatically with the imidazole ring of APR Hid186, and the N atom of the NH2 group at the N-terminal of Ser1 is directly coordinated at 2.33 Å to the Zn ion of APR. In addition, one of the H atoms of the terminal NH2 group of Ser1 forms a hydrogen bond with the imidazole ring of Hid180, whereas the other H atom interacts electrostatically with the imidazole ring of Hid176. Accordingly, Fig. 5b indicates that the N-terminal part of APRin is important for the strong binding between APRin and the Zn group of APR.
Further, the Ser2 of APRin interacts with the APR residues in a similar way to Ser1. As shown in Fig. 6a, it interacts strongly with the Zn group. However, the size of IFIE for Ser2 is approximately one-fifth of that for Ser1. This difference in the IFIEs results in a larger total IFIE for Ser1 than for Ser2, as shown in Fig. 4. The oxygen atom of the main chain between Ser2 and Ser1 is strongly coordinated to the Zn ion, as shown in Fig. 6b, whereas no other interaction was found between Ser2 and the APR residues. As a result, the interaction between Ser2 and APR is significantly weaker than that of Ser1.
Figure 4 also elucidated that the Arg83 and Arg90 residues, which exist far from the N-terminal of APRin, interact strongly with the APR residues. These APRin residues are positively charged and can interact electrostatically with the charged residues of APR. To explain their strong interactions, we investigated the IFIEs among Arg83/Arg90 and each of the APR residues. As shown in Fig. 7a, Arg83 interacts with many APR residues in an attractive or repulsive manner. These interactions are mainly caused by the electrostatic interactions between the charged Arg83 and the charged residues of APR. In particular, Arg83 interacts strongly with the negatively charged Asp196 and Glu218 residues of APR. In fact, the NH2+ group of the Arg83 sidechain forms a hydrogen bond (2.55 Å) with the COO− group of the Asp196 sidechain, as shown in Fig. 7b. In addition, Arg83 interacts electrostatically with the COO− group of the Glu218 sidechain at a 5.26-Å distance.
The Arg90 of APRin also interacts with many APR residues, as shown in Fig. 8a. Among the APR residues, negatively charged Asp196, Asp201, and Glu218 interact strongly with the positively charged Arg90 of APRin. Although these residues exist a significant distance from Arg90, as shown in Fig. 8b, long-range electrostatic interactions occur via the charged groups of these charged residues. Accordingly, our present ab initio FMO calculations elucidate that the charged residues of APR contribute significantly to the specific interactions between APR and the charged Arg83 and Arg90 residues of APRin, as indicated in Figs. 7 and 8.
It was elucidated from the present FMO study that the Ser1, Ser2, Arg83, and Arg90 of APRin are the main contributors to the interactions between APRin and APR. In particular, Fig. 4 indicates that the Ser1 at the N-terminal of APRin interacts strongly with the Zn group of APR, playing an important role in the interaction. In a previous experiment , the six residues at the N-terminal of APRin were found to be necessary to the inhibitory effect of APRin against APR. Our present FMO calculations highlight that among the six residues, Ser1 and Ser2 are particularly important for strong binding to APR. In addition, the charged Arg83 and Arg90 residues of APRin were found to contribute to the binding between APRin and APR. These facts became evident after investigating the electronic properties of the APR + APRin complex using the ab initio FMO method.
The main aim of our work is to obtain small molecular inhibitors of APR, and the present FMO results are important guidelines for that. Based on the total IFIEs for each of the APRin residues shown in Fig. 4, it is possible to suggest a number of small peptides as putative inhibitors. A dipeptide consisting of Ser1 and Ser2 would be the smallest possible peptide inhibitor. However, a previous structural and mutational study  revealed that a peptide consisting of the first five N-terminal residues (Ser1-Ser2-Lue3-Ile4-Leu5) of APRin did not inhibit the APR activity, indicating that the peptide did not obtain a proper orientation at the APR active site for inhibiting the enzyme. This result indicates the importance of the APRin main body for guiding the N-terminus to the active-site cleft of APR. In the present study, the positively charged Arg83 and Arg90 residues of APRin were found to interact strongly with many charged residues of APR, as shown in Figs. 7 and 8. Therefore, there is a possibility that these residues may act as anchor sites for proper orientation of the N-terminal residues within the APR active site. Studies are now underway to optimize the structures of our proposed molecules and investigate their binding properties to APR. The results will be published elsewhere.