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.