1. INTRODUCTION
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.