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.     

Development of a CD‐MEKC method for investigating the metabolism of tamoxifen by flavin‐containing monooxygenases and the inhibitory effects of methimazole,nicotine and DMXAA

A selective and low‐cost CD‐MEKC method under acidic conditions was developed for investigating the N‐oxygenation of tamoxifen (TAM) by flavin‐containing monooxygenases (FMOs). The inhibitory effects of methimazole (MMI), nicotine and 5,6‐dimethylxanthenone‐4‐acetic acid (DMXAA) on the given FMO reaction were also evaluated; 100 mM phosphate buffer (pH 8.6) was used for performing the enzymatic reaction and the separation of TAM and its metabolite tamoxifen N‐oxide (TNO) was obtained with a BGE consisting of 100 mM phosphoric acid solution adjusted to pH 2.5 with triethanolamine containing 50 mM sodium taurodeoxycholate, 20 mM carboxymethyl β‐CD and 20% ACN. The proposed method was applied for the kinetics study of FMO1 using TAM as a substrate probe. A Michaelis–Menten constant (K_m) of 164.1 μM was estimated from the corrected peak area of the product, TNO. The calculated value of the maximum reaction velocity (V_max) was 3.61 μmol/min/μmol FMO1; 50% inhibitory concentration and inhibition constant (K_i) of MMI, the most common alternate substrate FMO inhibitor, were evaluated and the inhibitory effects of two other important FMO substrates, nicotine and DMXAA, a novel anti‐tumour agent, were investigated.     

Theoretical study of the prion protein based on the fragment molecular orbital method

We performed fragment molecular orbital (FMO) calculations to examine the molecular interactions between the prion protein (PrP) and GN8, which is a potential curative agent for prion diseases. This study has the following novel aspects: we introduced the counterpoise method into the FMO scheme to eliminate the basis set superposition error and examined the influence of geometrical fluctuation on the interaction energies, thereby enabling rigorous analysis of the molecular interaction between PrP and GN8. This analysis could provide information on key amino acid residues of PrP as well as key units of GN8 involved in the molecular interaction between the two molecules. The present FMO calculations were performed using an original program developed in our laboratory, called “Parallelized ab initio calculation system based on FMO (PAICS)”. © 2009 Wiley Periodicals, Inc. J Comput Chem 2009     

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.     

Energy gradients in combined fragment molecular orbital and polarizable continuum model (FMO/PCM) calculation

The analytic energy gradients for the combined fragment molecular orbital and polarizable continuum model (FMO/PCM) method are derived and implemented. Applications of FMO/PCM geometry optimization to polyalanine show that the structures obtained with the FMO/PCM method are very close to those obtained with the corresponding full ab initio PCM methods. FMO/PCM (RHF/6‐31G* level) is used to optimize the solution structure of the 304‐atom Trp‐cage miniprotein and the result is in agreement with NMR experiments. The key factors determining the relative stability of the α‐helix, β‐turn and the extended form in solution are elucidated for polyalanine. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Parallel Fock matrix construction with distributed shared memory model for the FMO‐MO method

A parallel Fock matrix construction program for FMO‐MO method has been developed with the distributed shared memory model. To construct a large‐sized Fock matrix during FMO‐MO calculations, a distributed parallel algorithm was designed to make full use of local memory to reduce communication, and was implemented on the Global Array toolkit. A benchmark calculation for a small system indicates that the parallelization efficiency of the matrix construction portion is as high as 93% at 1,024 processors. A large FMO‐MO application on the epidermal growth factor receptor (EGFR) protein (17,246 atoms and 96,234 basis functions) was also carried out at the HF/6‐31G level of theory, with the frontier orbitals being extracted by a Sakurai‐Sugiura eigensolver. It takes 11.3 h for the FMO calculation, 49.1 h for the Fock matrix construction, and 10 min to extract 94 eigen‐components on a PC cluster system using 256 processors. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

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     

Imidazoline‐N‐oxyl: A DFT Study of Its Protonation Reaction

Imidazoline‐based nitroxides are developed as pH probes. Their pK_a values vary over a wide range (from 1 to 11), depending on the substituents attached to the five‐membered cyclic nitroxide. Density functional calculations using the PBE1PBE method at the 6‐31+G(d,p) level, combined with natural bond orbital (NBO), frontier molecular orbital (FMO), geometry, Mulliken charge, and thermodynamic analyses, are carried out to disclose the effects involved in the changes in pK_a. The studies show that the decrease of seven pK_a units from pyrrolidine ( 11 ) to imidazoline‐N‐oxyl 8 is due to the inductive electron‐withdrawing capacity of the nitroxyl group. On the other hand, by combining both the inductive and mesomeric electron‐withdrawing capacities of the NO₂ group with delocalization of the lone pair on the amino N atom of the π system of the vinyl linker, the pK_a of 4.5 of 8 was increased by around three units to 7.8 for 1 / 2 .     

Importance of CH/π hydrogen bonds in recognition of the core motif in proline-recognition domains: an ab initio fragment molecular orbital study

We examined CH/π hydrogen bonds in protein/ligand complexes involving at least one proline residue using the ab initio fragment molecular orbital (FMO) method and the program CHPI. FMO calculations were carried out at the Hartree–Fock (HF)/6‐31G*, HF/6‐31G**, second‐order Møller–Plesset perturbation (MP2)/6‐31G*, and MP2/6‐31G** levels for three Src homology 3 (SH3) domains and five proline‐recognition domains (PRDs) complexed with their corresponding ligand peptides. PRDs use a conserved set of aromatic residues to recognize proline‐rich sequences of specific ligands. Many CH/π hydrogen bonds were identified in these complexes. CH/π hydrogen bonds occurred, in particular, in the central part of the proline‐rich motifs. Our results suggest that CH/π hydrogen bonds are important in the recognition of SH3 and PRDs by their ligand peptides and play a vital role in the signal transduction system. Combined use of the FMO method and CHPI analysis is a valuable tool for the study of protein/protein and protein/ligand interactions and may be useful in rational drug design. © 2011 Wiley Periodicals, Inc. J Comput Chem 2011     

ONIOM and FMO‐EDA study of metabotropic glutamate receptor 1: Quantum insights into the allosteric binding site

The crystal structure of metabotropic glutamate receptor 1 (mGluR1) complexed with 4‐fluoro‐N‐(4‐(6‐(isopropylamino)pyrimidin‐4‐yl)thiazol‐2‐yl)‐N‐methylbenzamide (FITM, a negative allosteric modulator) and its twelve close structural analogs with a broad spectrum of affinities (2.4 nM < IC₅₀ > 10 000 nM) were investigated using quantum mechanical methods. The our own N‐layered integrated molecular orbital and molecular mechanics (ONIOM) was used to optimize the molecular geometries of the receptor with complexed ligands, which were then used to perform the ab initio calculations using the fragment molecular orbitals method with energy decomposition analysis (FMO‐EDA). The results clearly showed that residues Q660^3.28 and/or Y805^6.55 were the anchoring points for all the studied analogs of FITM, while the H‐bond with T815^7.38 determined only the orientation of very active molecules containing an amino substituent in the pyrimidine moiety (e.g., FITM). The orientation of the other parts of ligands resulted from hydrophobic interactions mainly with L757^5.44, F801^6.51, or W798^6.48. The applied ONIOM/FMO–EDA approach facilitated the study of effects related to very small changes in the ligand structure and led to conclusions regarding the significance of individual interactions in the allosteric binding pocket of mGluR1.     

Accuracy of the three-body fragment molecular orbital method applied to Møller-Plesset perturbation theory

The three‐body energy expansion in the fragment molecular orbital method (FMO) was applied to the 2nd order Møller–Plesset theory (MP2). The accuracy of both the two and three‐body expansions was determined for water clusters, alanine n‐mers (α‐helices and β‐strands) and one synthetic protein, using the 6‐31G* and 6‐311G* basis sets. At the best level of theory (three‐body, two molecules/residues per fragment), the absolute errors in energy relative to ab initio MP2 were at most 1.2 and 5.0 mhartree, for the 6‐31G* and 6‐311G* basis sets, respectively. The relative accuracy was at worst 99.996% and 99.96%, for 6‐31G* and 6‐311G*, respectively. A three‐body approximation was introduced and the optimum threshold value was determined. The protein calculation (6‐31G*) at the production level (FMO2/2) took 3 h on 36 3.2‐GHz Pentium 4 nodes and had the absolute error in the MP2 correlation energy of only 2 kcal/mol. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2007     

Ab initio fragment molecular orbital (FMO) method applied to analysis of the ligand-protein interaction in a pheromone-binding protein

Full quantum computation of the electronic state of proteins has recently become possible by the advent of the ab initio fragment molecular orbital (FMO) method. We applied this method to the analysis of the interaction between the Bombyx mori pheromone-binding protein and its ligand, bombykol. The protein–ligand interaction of this molecular complex was minutely analyzed by the FMO method, and the analysis revealed several important interactions between the ligand and amino acid residues.     

Reactivity and Selectivity of Captodative Olefins as Dienes in Hetero‐Diels–Alder Reactions

The reactivity and selectivity of the the captodative olefins 1‐acylvinyl benzoates 1a – 1f and 3a as heterodienes in hetero‐Diels–Alder reactions in the presence of electron‐rich dienophiles is described. Heterodienes 1 undergo regioselective cycloaddition with the alkyl vinyl etherdienophiles 6a , b and 9 to give the corresponding dihydro‐2H‐pyrans 7, 8 , and 10 under thermal conditions. The reactivity of these cycloadditions depends, to a large extent, on the electronic demand of the substituent in the aroyloxy group of the heterodiene. Frontier‐molecular‐orbital (FMO; ab initio) and density‐functional‐theory (DFT) calculations of the ground and transition states account for the reactivity and regioselectivity observed in these processes.     

Quantum nonlocality in the excitation energy transfer in the Fenna–Matthews–Olson complex

The Fenna–Matthews–Olson (FMO) complex—a pigment protein complex involved in photosynthesis in green sulfur bacteria—is remarkably efficient in transferring excitation energy from light harvesting antenna molecules to a reaction center. Recent experimental and theoretical studies suggest that quantum coherence and entanglement may play a role in this excitation energy transfer (EET). We examine whether bipartite quantum nonlocality, a property that expresses a stronger‐than‐entanglement form of correlation, exists between different pairs of chromophores in the FMO complex when modeling the EET by the hierarchically coupled equations of motion method. We compare the results for nonlocality with the amount of bipartite entanglement in the system. In particular, we analyze in what way these correlation properties are affected by different initial conditions. It is found that bipartite nonlocality only exists when the initial conditions are chosen in an unphysiological manner and probably is absent when considering the EET in the FMO complex in its natural habitat. It is also seen that nonlocality and entanglement behave quite differently in this system. In particular, for localized initial states, nonlocality only exists on a very short time scale and then drops to zero in an abrupt manner. As already known from previous studies, quantum entanglement between chromophore pairs, on the other hand, is oscillating and exponentially decaying and follow thereby a pattern more similar to the chromophore population dynamics. The abrupt disappearance of nonlocality in the presence of nonvanishing entanglement is a phenomenon we call nonlocality sudden death; a striking manifestation of the difference between these two types of correlations in quantum systems.     

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.     

All electron quantum chemical calculation of the entire enzyme system confirms a collective catalytic device in the chorismate mutase reaction

To elucidate the catalytic power of enzymes, we analyzed the reaction profile of Claisen rearrangement of Bacillus subtilis chorismate mutase (BsCM) by all electron quantum chemical calculations using the fragment molecular orbital (FMO) method. To the best of our knowledge, this is the first report of ab initio-based quantum chemical calculations of the entire enzyme system, where we provide a detailed analysis of the catalytic factors that accomplish transition-state stabilization (TSS). FMO calculations deliver an ab initio-level estimate of the intermolecular interaction between the substrate and the amino acid residues of the enzyme. To clarify the catalytic role of Arg90, we calculated the reaction profile of the wild-type BsCM as well as Lys90 and Cit90 mutant BsCMs. Structural refinement and the reaction path determination were performed at the ab initio QM/MM level, and FMO calculations were applied to the QM/MM refined structures. Comparison between three types of reactions established two collective catalytic factors in the BsCM reaction: (1) the hydrogen bonds connecting the Glu78-Arg90-substrate cooperatively control the stability of TS relative to the ES complex and (2) the positive charge on Arg90 polarizes the substrate in the TS region to gain more electrostatic stabilization.