Protein-protein interactions (PPIs) are extensively investigated due to
their important roles in numerous biological
processes,1,2 resulting that PPIs are now spotlighted
as a new target of drug discovery.3−8 Additionally, a
detailed understanding of PPIs is essential for the design of antibodies
used for various research purposes and/or therapeutic applications based
on their high affinity and target specificity. Therefore, the importance
of computational approaches to provide physicochemical insight into PPIs
has increased.
Given that electrostatic interactions are among the most essential
components of PPIs, detailed analysis of electrostatic complementarity
between proteins is important. The electrostatic potential (ESP) at the
PPI interface is generally used to obtain information concerning
electrostatic complementarity. Although the ESP of a protein is
routinely calculated using a classical force field, an accurate ESP that
includes the effect of charge transfer or polarization due to complex
formation requires a fully quantum mechanical calculation. However,
because of high computational cost of such calculations, few
studies9−11 have attempted ESP calculation for a large
molecule like a protein using ab initio quantum chemical methods.
Fragment molecular orbital (FMO) method has been applied to reduce the
computational effort of ab initio quantum chemical calculation of
a large molecule.12,13 In this method, a target
molecule is divided into small fragments, and only calculations of
monomers and dimers for each fragment are required in order to reduce
the computational effort while maintaining chemical accuracy. Another
advantage of FMO method is its clear definition of inter-fragment
interaction energy (IFIE),14 which provides detailed
information about intramolecular and/or intermolecular interactions.
Therefore, FMO method is also known to be a powerful tool for analyzing
molecular interactions for large molecules including proteins. This
method has been extended to several electron correlation methods,
including second- and third-order
Møller-Plesset perturbation theories (MP2 and
MP3),15−21 resolution of the identity (RI)
approximation for MP2 and MP3,22−25 local
MP2,26,27 and coupled cluster
theory.28,29Several studies in which a fully quantum mechanical ESP was calculated
using the FMO method were reported.30−34 For example,
ESP obtained by the FMO method was used to improve determination of
atomic charges in classical force fields.30−32Ishikawa reported FMO-based calculations of electrostatic properties,
including electron density (EDN), ESP, and electric field, at
Hartree-Fock and MP2 levels of theory.33 In this
study, a fully quantum mechanical ESP of prion protein (103 amino acid
residues) and human immunodeficiency virus type 1 protease (198 amino
acid residues) were calculated as illustrative examples, which
demonstrated a sufficiently small error associated with fragmentation of
the FMO method. Recently, FMO calculations of EDN and ESP were carried
out in solution condition using the polarizable continuum
model,34 by which the solvent effect on molecular ESP
was detailed investigated. These findings suggest that a fully quantum
mechanical ESP can provide reliable information concerning the
electrostatic properties of proteins, making it potentially useful for
various types of research, including drug discovery. However, to the
best my knowledge, computational analysis of the electrostatic
complementarity of PPIs using a fully quantum mechanical ESP obtained
from the FMO method has not been reported.
In this study, a new method for visualizing the electrostatic
complementarity of a PPI using a fully quantum mechanical EDN and ESP
based on the FMO method is described. To demonstrate the efficacy of
this method, the complex of programmed cell death-1 (PD-1) and its
ligand (PD-L1), which are important proteins in immunotherapy of
cancer,35,36 was selected as an illustrative example.
A recent FMO study by Lim et al.37 analyzed
this complex, as well as the antibodies targeting each respective
protein, with energetics information rather than the EDN and ESP.
The remainder of the paper is presented, as follow. In the next section,
theoretical aspects of the method are provided together with
implementation and computational details. In the third section, results
of the calculations are discussed, and the efficacy of the method is
demonstrated.