3.3 Effect of complex formation
The ESPs of PD-1 and PD-L1 in the isolated condition were calculated to examine the effect of complex formation. In this paper, the ESPs of the isolated PD-1 and PD-L1 are denoted as\(\phi_{\text{iso}}^{PD-1}\left(\mathbf{r}\right)\) and\(\phi_{\text{iso}}^{PD-L1}(\mathbf{r})\), respectively. The values of the \(\phi_{\text{iso}}^{PD-1}\left(\mathbf{r}\right)\) and\(\phi_{\text{iso}}^{PD-L1}(\mathbf{r})\) at the PPI interface are visualized in Figure 2-C and D, respectively. Although they are similar to \(\phi_{\text{com}}^{PD-1}\left(\mathbf{r}\right)\) and\(\phi_{\text{com}}^{PDL-1}(\mathbf{r})\) (Figure 2-A and B), there is noted to be a slight difference. This difference is considered to be caused by charge transfer or polarization due to complex formation.
To clarify the effect of complex formation, the map of the differential ESP between \(\phi_{\text{com}}^{PD-1}\left(\mathbf{r}\right)\) and\(\phi_{\text{iso}}^{PD-1}\left(\mathbf{r}\right)\) or\(\phi_{\text{com}}^{PD-L1}(\mathbf{r})\) and\(\phi_{\text{iso}}^{PD-L1}(\mathbf{r})\) is shown in Figure 2-E or F, where the value range is one-tenth that of the other ESP maps. We note that the amplitude of the change in ESP induced by complex formation is more than 10% of that of the ESP value, indicating that the effect of charge transfer or polarization due to complex formation is not negligible. Additionally, the amplitude of the positive or negative value is enhanced by complex formation. For example, the value of the differential ESP of PD-1 around position P3 is positive (Figure 2-E), and the value of\(\phi_{\text{iso}}^{PD-1}\left(\mathbf{r}\right)\) around positionP3 is also positive (Figure 2-C), suggesting that amplitude of the positive ESP value for PD-1 at this position increases due to complex formation. On the other hand, the amplitude of the negative value of PD-L1 around position P3is also enhanced by complex formation. This indicates that the degree of electrostatic complementarity around positionP 3 increases due to complex formation. A similar situation is observed at the other positions (P4 , P5 ,P6 , and P7 ). These results clearly show that additional electrostatic complementarity is induced by charge transfer or polarization due to complex formation, and that its amplitude is not negligible (more than 10% of the original ESP value). Consequently, we can consider this induced electrostatic complementarity as an important factor for binding between PD-1 and PD-L1. Moreover, this argument is equally valid when using the ESP maps calculated with the neutralized models (see Figure S1-C, D, E, and F). Therefore, our conclusion about the induced electrostatic complementarity is largely independent of the models. As demonstrated by this illustrative example, the method visualizing the pESP is a promising tool for analyzing electrostatic complementarity of PPIs.