3.2 Visualization of electrostatic complementarity
The pESPs of PD-1 and PD-L1 were obtained from FMO calculation of the complex using equation (6) or (7). In this paper, they are denoted as\(\phi_{\text{com}}^{PD-1}\left(\mathbf{r}\right)\) and\(\phi_{\text{com}}^{PD-L1}(\mathbf{r})\), respectively. The subscript “com” is used to explicitly state that they were calculated in the complex condition. The values of\(\phi_{\text{com}}^{PD-1}\left(\mathbf{r}\right)\) and\(\phi_{\text{com}}^{PD-L1}(\mathbf{r})\) at the PPI interface are visualized in Figure 2-A and B, respectively. The positions with positive (blue) and negative (red) values are scattered along the PPI interface, indicating that both PD-1 and PD-L1 form a complicated ESP map at the interface. A more interesting point is that electrostatic complementarity of PD-1 and PD-L1 is clearly shown by comparison between these pESP maps. For example, pESP values for PD-1 and PD-L1 at positionP3 are positive and negative, respectively, indicating that attractive electrostatic interaction exists around this position. Similar observations are made for other positions (P4 , P5 ,P6 , and P7 ). By this analysis, we can understand that a high degree of electrostatic complementarity exists between PD-1 and PD-L1 at the PPI interface.
We also note that the area with a positive value is larger than that with a negative value in the pESP map for PD-1 (Figure 2-A). Conversely, the area with a negative value is larger than that with a positive value for PD-L1 (Figure 2-B). As mentioned above, the net charges of PD-1 and PD-L1 of the structure model used here were +2 and −1, respectively. Therefore, it is assumed that the pESPs shifted to positive or negative in whole. Such an overall shift just depends on the structure modeling. For example, D33−E84 and S93−E146 of PD-1 were included in the complex model, which just depended on the X-ray structure used for the modeling. As a result, the net charge of PD-1 was +2, causing the overall shift in the pESP. To examine the effect of net charges, another complex model was prepared with the net charges neutralized. The pESP maps of the neutralized PD-1 and PD-L1 are given in Figure S1-A and B, respectively. We note that a green area, where the pESP value is around zero, is larger than that of Figure 2-A and B. This result shows that the overall shift in pESP due to the net charge was removed by neutralization. Effect of the net charge is considered to be limited in the overall shift because similar discussion about the electrostatic complementarity is led from both the neutralized and not neutralized models.
In this study, all the FMO calculations were performed under vacuum conditions, i.e., no solvent effect was considered. Recently, the solvent effect on EDN and ESP obtained from FMO calculations was investigated using the polarizable continuum model.34It was reported that solvent made a large contribution to ESP at the molecular surface while the effect on EDN was sufficiently small. The solvent effect on ESP at the PPI interface is expected to be lower than that at the molecular surface, because generally solvent molecules do not directly contact the PPI interface. To evaluate the solvent effect on electrostatic complimentarily, the definition of the pESP given in equations (6) and (7) should be modified to include the solvent molecules as the third part of the system. This is an important and interesting extension of this method, which should be addressed in a future study.