Assessment and acceleration of binding energy calculations for protein–ligand complexes by the fragment molecular orbital method

In the field of drug discovery, it is important to accurately predict the binding affinities between target proteins and drug applicant molecules. Many of the computational methods available for evaluating binding affinities have adopted molecular mechanics‐based force fields, although they cannot fully describe protein–ligand interactions. A noteworthy computational method in development involves large‐scale electronic structure calculations. Fragment molecular orbital (FMO) method, which is one of such large‐scale calculation techniques, is applied in this study for calculating the binding energies between proteins and ligands. By testing the effects of specific FMO calculation conditions (including fragmentation size, basis sets, electron correlation, exchange‐correlation functionals, and solvation effects) on the binding energies of the FK506‐binding protein and 10 ligand complex molecule, we have found that the standard FMO calculation condition, FMO2‐MP2/6‐31G(d), is suitable for evaluating the protein–ligand interactions. The correlation coefficient between the binding energies calculated with this FMO calculation condition and experimental values is determined to be R = 0.77. Based on these results, we also propose a practical scheme for predicting binding affinities by combining the FMO method with the quantitative structure–activity relationship (QSAR) model. The results of this combined method can be directly compared with experimental binding affinities. The FMO and QSAR combined scheme shows a higher correlation with experimental data (R = 0.91). Furthermore, we propose an acceleration scheme for the binding energy calculations using a multilayer FMO method focusing on the protein–ligand interaction distance. Our acceleration scheme, which uses FMO2‐HF/STO‐3G:MP2/6‐31G(d) at R_int = 7.0 Å, reduces computational costs, while maintaining accuracy in the evaluation of binding energy. © 2015 Wiley Periodicals, Inc.     

Specific interactions and binding free energies between thermolysin and dipeptides: molecular simulations combined with ab initio molecular orbital and classical vibrational analysis

Thermolysin (TLN) is a metalloprotease widely used as a nonspecific protease for sequencing peptide and synthesizing many useful chemical compounds by the chemical industry. It was experimentally shown that the activity and functions of TLN are inhibited by the binding of many types of amino acid dipeptides. However, the binding mechanisms between TLN and dipeptides have not been clarified at the atomic and electronic levels. In this study, we investigated the binding mechanisms between TLN and four dipeptides. Specific interactions and binding free energies (BFEs) between TLN and the dipeptides were calculated using molecular simulations based on classical molecular dynamics and ab initio fragment molecular orbital (FMO) methods. The molecular systems were embedded in solvating water molecules during calculations. The calculated BFEs were qualitatively consistent with the trend of the experimentally observed inhibition of TLN activity by binding of the dipeptides. In addition, the specific interactions between the dipeptides and each amino acid residue of TLN or solvating water molecules were elucidated by the FMO calculations.     

Ab initio quantum chemical calculation of electron density,electrostatic potential,and electric field of biomolecule based on fragment molecular orbital method

Efficient quantum chemical calculations of electrostatic properties, namely, the electron density (EDN), electrostatic potential (ESP), and electric field (EFL), were performed using the fragment molecular orbital (FMO) method. The numerical errors associated with the FMO scheme were examined at the HF, MP2, and RI‐MP2 levels of theory using 4 small peptides. As a result, the FMO errors in the EDN, ESP, and EFL were significantly smaller than the magnitude of the electron correlation effects, which indicated that the FMO method provides sufficiently accurate values of electrostatic properties. In addition, an attempt to reduce the computational effort was proposed by combining the FMO scheme and a point charge approximation. The error due to this approximation was examined using 2 proteins, prion protein and human immunodeficiency virus type 1 protease. As illustrative examples, the ESP values at the molecular surface of these proteins were calculated at the MP2 level of theory.     

Rapid and accurate assessment of GPCR–ligand interactions Using the fragment molecular orbital‐based density‐functional tight‐binding method

The reliable and precise evaluation of receptor–ligand interactions and pair‐interaction energy is an essential element of rational drug design. While quantum mechanical (QM) methods have been a promising means by which to achieve this, traditional QM is not applicable for large biological systems due to its high computational cost. Here, the fragment molecular orbital (FMO) method has been used to accelerate QM calculations, and by combining FMO with the density‐functional tight‐binding (DFTB) method we are able to decrease computational cost 1000 times, achieving results in seconds, instead of hours. We have applied FMO‐DFTB to three different GPCR–ligand systems. Our results correlate well with site directed mutagenesis data and findings presented in the published literature, demonstrating that FMO‐DFTB is a rapid and accurate means of GPCR–ligand interactions. © 2017 Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Three‐body expansion of the fragment molecular orbital method combined with density‐functional tight‐binding

The three‐body fragment molecular orbital (FMO3) method is formulated for density‐functional tight‐binding (DFTB). The energy, analytic gradient, and Hessian are derived in the gas phase, and the energy and analytic gradient are also derived for polarizable continuum model. The accuracy of FMO3‐DFTB is evaluated for five proteins, sodium cation in explicit solvent, and three isomers of polyalanine. It is shown that FMO3‐DFTB is considerably more accurate than FMO2‐DFTB. Molecular dynamics simulations for sodium cation in water are performed for 100 ps, yielding radial distribution functions and coordination numbers. © 2017 Wiley Periodicals, Inc.     

Roles of K151 and D180 in L‐2‐haloacid dehalogenase from Pseudomonas sp. YL: Analysis by molecular dynamics and ab initio fragment molecular orbital calculations

L ‐2‐haloacid dehalogenase (L ‐DEX) catalyzes the hydrolytic dehalogenation of L ‐2‐haloalkanoic acids to produce the corresponding D ‐2‐hydroxyalkanoic acids. This enzyme is expected to be applicable to the bioremediation of environments contaminated with halogenated organic compounds. We analyzed the reaction mechanism of L ‐DEX from Pseudomonas sp. YL (L ‐DEX YL) by using molecular modeling. The complexes of wild‐type L ‐DEX YL and its K151A and D180A mutants with its typical substrate, L ‐2‐chloropropionate, were constructed by docking simulation. Subsequently, molecular dynamics (MD) and ab initio fragment molecular orbital (FMO) calculations of the complexes were performed. The ab initio FMO method was applied at the MP2/6‐31G level to estimate interfragment interaction energies. K151 and D180, which are experimentally shown to be important for enzyme activity, interact particularly strongly with L ‐2‐chloropropionate, catalytic water, nucleophile (D10), and with each other. Our calculations suggest that K151 stabilizes substrate orientation and balances the charge around the active site, while D180 stabilizes the rotation of the nucleophile D10, fixes catalytic water around D10, and prevents K151 from approaching D10. Further, D180 may activate catalytic water on its own or with K151, S175, and N177. These roles are consistent with the previous results. Thus, MD and ab initio FMO calculations are powerful tools for the elucidation of the mechanism of enzymatic reaction at the molecular level and can be applied to other catalytically important residues. The results obtained here will play an important role in elucidating the reaction mechanism and rational design of L ‐DEX YL with improved enzymatic activity or substrate specificity. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Ab initio quantum mechanical study of the binding energies of human estrogen receptor alpha with its ligands: an application of fragment molecular orbital method

We have theoretically examined the relative binding affinities (RBA) of typical ligands, 17beta-estradiol (EST), 17alpha-estradiol (ESTA), genistein (GEN), raloxifene (RAL), 4-hydroxytamoxifen (OHT), tamoxifen (TAM), clomifene (CLO), 4-hydroxyclomifene (OHC), diethylstilbestrol (DES), bisphenol A (BISA), and bisphenol F (BISF), to the alpha-subtype of the human estrogen receptor ligand-binding domain (hERalpha LBD), by calculating their binding energies. The ab initio fragment molecular orbital (FMO) method, which we have recently proposed for the calculations of macromolecules such as proteins, was applied at the HF/STO-3G level. The receptor protein was primarily modeled by 50 amino acid residues surrounding the ligand. The number of atoms in these model complexes is about 850, including hydrogen atoms. For the complexes with EST, RAL, OHT, and DES, the binding energies were calculated again with the entire ERalphaLBD consisting of 241 residues or about 4000 atoms. No significant difference was found in the calculated binding energies between the model and the real protein complexes. This indicates that the binding between the protein and its ligands is well characterized by the model protein with the 50 residues. The calculated binding energies relative to EST were very well correlated with the experimental RBA (the correlation coefficient r=0.837) for the ligands studied in this work. We also found that the charge transfer between ER and ligands is significant on ER-ligand binding. To our knowledge, this is the first achievement of ab initio quantum mechanical calculations of large molecules such as the entire ERalphaLBD protein.     

Intra- and intermolecular interactions between cyclic-AMP receptor protein and DNA: ab initio fragment molecular orbital study

The ab initio fragment molecular orbital (FMO) calculations were performed for the cAMP receptor protein (CRP) complexed with a cAMP and DNA duplex to elucidate their sequence-specific binding and the stability of the DNA duplex, as determined by analysis of their inter- and intramolecular interactions. Calculations were performed with the AMBER94 force field and at the HF and MP2 levels with several basis sets. The interfragment interaction energies (IFIEs) were analyzed for interactions of CRP-cAMP with each base pair, DNA duplex with each amino acid residue, and each base pair with each residue. In addition, base-base interactions were analyzed including hydrogen bonding and stacking of DNA. In the interaction between DNA and CRP-cAMP, there was a significant charge transfer (CT) from the DNA to CRP, and this CT interaction played an important role as well as the electrostatic interactions. It is necessary to apply a quantum mechanical approach beyond the "classical" force-field approach to describe the sequence specificity. In the DNA intramolecular interaction, the dispersion interactions dominated the stabilization of the base-pair stacking interactions. Strong, attractive 1,2-stacking interactions and weak, repulsive 1,3-stacking interactions were observed. Comparison of the intramolecular interactions of free and complexed DNA revealed that the base-pairing interactions were stronger, and the stacking interactions were weaker, in the complexed structure. Therefore, the DNA duplex stability appears to change due to both the electrostatic and the CT interactions that take place under conditions of DNA-CRP binding.     

CH/pi hydrogen bonds determine the selectivity of the Src homology 2 domain to tyrosine phosphotyrosyl peptides: an ab initio fragment molecular orbital study

The CH/pi hydrogen bond is a weak molecular force occurring between CH groups (soft acids) and pi-systems (soft bases), and has been recognized to be important in the interaction of proteins with their specific ligands. For instance, it is well known that Src homology-2 protein (SH2) recognizes its specific pTyr peptide in two key regions, pTyr-binding region and specificity-determining region, by the use of attractive molecular forces, including the CH/pi hydrogen bond. We hypothesized that the CH/pi hydrogen bond plays a key role in determining the selectivity of SH2 proteins, and studied this issue by the ab initio fragment molecular orbital (FMO) method. The FMO calculations were carried out, at the HF/6-31G* and MP2/6-31G* level, for SH2 domains of Src, Grb2, P85alpha(N), Syk, and SAP, in complex with corresponding pTyr peptides. CH/pi hydrogen bonds have in fact been found to be important in stabilizing the structure of the complexes. We conclude that the CH/pi hydrogen bond plays an indispensable role in the recognition of SH2 domains with their specific pTyr peptides, thus playing a vital role in the signal transduction system.     

Assessing the accuracy of improved force‐matched water models derived from Ab initio molecular dynamics simulations

The accuracy of water models derived from ab initio molecular dynamics simulations by means on an improved force‐matching scheme is assessed for various thermodynamic, transport, and structural properties. It is found that although the resulting force‐matched water models are typically less accurate than fully empirical force fields in predicting thermodynamic properties, they are nevertheless much more accurate than generally appreciated in reproducing the structure of liquid water and in fact superseding most of the commonly used empirical water models. This development demonstrates the feasibility to routinely parametrize computationally efficient yet predictive potential energy functions based on accurate ab initio molecular dynamics simulations for a large variety of different systems. © 2016 Wiley Periodicals, Inc.     

Polarizable empirical force field for nitrogen‐containing heteroaromatic compounds based on the classical Drude oscillator

The polarizable empirical CHARMM force field based on the classical Drude oscillator has been extended to the nitrogen‐containing heteroaromatic compounds pyridine, pyrimidine, pyrrole, imidazole, indole, and purine. Initial parameters for the six‐membered rings were based on benzene with nonbond parameter optimization focused on the nitrogen atoms and adjacent carbons and attached hydrogens. In the case of five‐member rings, parameters were first developed for imidazole and transferred to pyrrole. Optimization of all parameters was performed against an extensive set of quantum mechanical and experimental data. Ab initio data were used for the determination of initial electrostatic parameters, the vibrational analysis, and in the optimization of the relative magnitudes of the Lennard‐Jones (LJ) parameters, through computations of the interactions of dimers of model compounds, model compound‐water interactions, and interactions of rare gases with model compounds. The absolute values of the LJ parameters were determined targeting experimental heats of vaporization, molecular volumes, heats of sublimation, crystal lattice parameters, and free energies of hydration. Final scaling of the polarizabilities from the gas‐phase values by 0.85 was determined by reproduction of the dielectric constants of pyridine and pyrrole. The developed parameter set was extensively validated against additional experimental data such as diffusion constants, heat capacities, and isothermal compressibilities, including data as a function of temperature. © 2008 Wiley Periodicals, Inc. J Comput Chem 2009