2.6. Computational details
To show a potential of this method, the interaction of PD-1 and PD-L1, which is one of the most important PPIs in immunotherapy of cancer,35,36 was selected as an illustrative example. In this study, the X-ray structure of the PD-1/PD-L1 complex was downloaded from the PDB (PDB-ID: 4ZQK).41 The structure contains the amino acid residues ranging from D33 to E84 and from S93 to E146 for PD-1 and from A18 to A132 for PD-L1. Missing hydrogen atoms were added to the structure, and N- and C-terminals of these peptide chains were capped with −COCH3 and −NHCH3, respectively. Energy minimization was performed with the AMBER99SB42 force field using the AMBER 10 package.43 As a result, the net charges of PD-1 and PD-L1 of the model used here were +2 and −1, respectively. To examine the effect of net charge, a neutralized model of the complex was prepared by adding two chloride ions near the positively charged residues of PD-1 (R112 and R143) as counter ions and one sodium ion near the negatively charged residue of PD-L1 (D90). These residues were sufficiently distant from the PPI interface. After adding these ions, energy minimization was then performed.
As mentioned above, pEDN and pESP were calculated as grid data in the current implementation. Here, the grid with a separation of 0.3 Å which covered the interface between PD-1 and PD-L1 was used (total number of grid points: 712,659). The pEDN and pESP at the grid points were calculated at the MP2 level of theory using RI approximation, where cc-pVDZ basis sets44 and the auxiliary basis sets produced by Weigend et al.45 were used. For the FMO calculations, each amino acid residue was treated as a single fragment, except for cysteines involved in a disulfide bond, which were merged into one fragment. In addition to calculations for the complex, FMO calculations for isolated PD-1 and PD-L1 were performed using the same atomic coordinates. By comparison of ESPs calculated in the isolated condition with those calculated in the complex condition, the effect of charge transfer or polarization due to complex formation can be evaluated.