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.