Quantum mechanics/molecular mechanics strategies for docking pose refinement: distinguishing between binders and decoys in cytochrome C peroxidase

We investigate the effect of systematically applying molecular dynamics (MD) and quantum mechanics/molecular mechanics (QM/MM) to docked poses in an attempt to improve the correspondence between theoretical prediction and experimental observation. The proposed scheme involves running a short time scale MD simulation on a docked ligand pose (and any known structurally important crystal structure waters in the active site), followed by QM/MM minimization. Both of these steps are relatively fast for moderately sized ligands; longer time scale MD involving the protein is not found to improve the results. The final binding energy is given in terms of the QM/MM total energy, a van der Waals correction, and a term to account for desolvation effects. This methodology is first tested with a trypsin inhibitor, for which we establish the importance of running MD before reoptimizing with QM/MM. The method is then applied to cytochrome c peroxidase using a set of binders and decoys. In this example, the proposed methodology affords much better discrimination between binders and decoys than the traditional docking approach used. For both systems presented, application of this protocol results in a significantly better energetic ranking and a smaller root mean squared deviation from known crystallographic ligand poses. This work highlights the importance of including polarization effects through QM/MM and of sampling with MD to refine a set of initial docked poses.     

Inclusion of the ligand field contribution in a polarizable molecular mechanics: SIBFA-LF

To account for the distortion of the coordination sphere that takes place in complexes containing open-shell metal cations such as Cu(II), we implemented, in sum of interactions between fragments ab initio computed (SIBFA) molecular mechanics, an additional contribution to take into account the ligand field splitting of the metal d orbitals. This term, based on the angular overlap model, has been parameterized for Cu(II) coordinated to oxygen and nitrogen ligands. The comparison of the results obtained from density functional theory computations on the one hand and SIBFA or SIBFA-LF on the other shows that SIBFA-LF gives geometric arrangements similar to those obtained from quantum mechanical computations. Moreover, the geometric improvement takes place without downgrading the energetic agreement obtained from SIBFA. The systems considered are Cu(II) interacting with six water molecules, four ammonia or four imidazoles, and four water plus two formate anions.     

Dimer asymmetry in superoxide dismutase studied by molecular dynamics simulation

Summary Molecular dynamics (MD) simulations of 100 ps have been carried out to study the active-site behaviour of the Cu,Zn superoxide dismutase dimer (SOD) in water. The active site of each subunit was monitored during the whole simulation by calculating the distances between functional residues and the catalytic copper. The results indicate that charge orientation is maintained at each active site but the solvent accessibility varies. Analysis of the MD simulation, carried out by using the atomic displacement covariance matrix, has shown a different intra-subunit correlation pattern for the two monomers and the presence of inter-subunit correlations. The MD simulation presented here indicates an asymmetry in the two active sites and different dynamic behaviour of the two SOD subunits.     

Increasing the time step with mass scaling in Born‐Oppenheimer ab initio QM/MM molecular dynamics simulations

Born‐Oppenheimer ab initio QM/MM molecular dynamics simulation with umbrella sampling is a state‐of‐the‐art approach to calculate free energy profiles of chemical reactions in complex systems. To further improve its computational efficiency, a mass‐scaling method with the increased time step in MD simulations has been explored and tested. It is found that by increasing the hydrogen mass to 10 amu, a time step of 3 fs can be employed in ab initio QM/MM MD simulations. In all our three test cases, including two solution reactions and one enzyme reaction, the resulted reaction free energy profiles with 3 fs time step and mass scaling are found to be in excellent agreement with the corresponding simulation results using 1 fs time step and the normal mass. These results indicate that for Born‐Oppenheimer ab initio QM/MM molecular dynamics simulations with umbrella sampling, the mass‐scaling method can significantly reduce its computational cost while has little effect on the calculated free energy profiles. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Stabilization of a transition-state analogue at the active site of yeast cytosine deaminase: importance of proton transfers

It is believed that the binding of pyrimidin-2-one to cytosine deaminase (CD) leads to the formation of 4-[R]-hydroxyl-3,4-dihydropyrimidine (DHP). Here the formation of transition-state analogue (TSA) at the active site of yeast cytosine deaminase (yCD) is investigated by quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) and free energy simulations. It is shown that DHP may in fact be unstable in the active site and a proton transfer from the Zn hydroxide group to Glu-64 may occur during the nucleophilic attack, leading to an alkoxide-like TSA complex instead. The free energy simulations for the nucleophilic attack process show that the proton transfer from the Zn hydroxide to Glu-64 may play an important role in stabilizing the TSA complex.     

Development of massive multilevel molecular dynamics simulation program,platypus (PLATform for dYnamic protein unified simulation), for the elucidation of protein functions

A massively parallel program for quantum mechanical‐molecular mechanical (QM/MM) molecular dynamics simulation, called Platypus (PLATform for dYnamic Protein Unified Simulation), was developed to elucidate protein functions. The speedup and the parallelization ratio of Platypus in the QM and QM/MM calculations were assessed for a bacteriochlorophyll dimer in the photosynthetic reaction center (DIMER) on the K computer, a massively parallel computer achieving 10 PetaFLOPs with 705,024 cores. Platypus exhibited the increase in speedup up to 20,000 core processors at the HF/cc‐pVDZ and B3LYP/cc‐pVDZ, and up to 10,000 core processors by the CASCI(16,16)/6‐31G** calculations. We also performed excited QM/MM‐MD simulations on the chromophore of Sirius (SIRIUS) in water. Sirius is a pH‐insensitive and photo‐stable ultramarine fluorescent protein. Platypus accelerated on‐the‐fly excited‐state QM/MM‐MD simulations for SIRIUS in water, using over 4000 core processors. In addition, it also succeeded in 50‐ps (200,000‐step) on‐the‐fly excited‐state QM/MM‐MD simulations for the SIRIUS in water. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

An extensible interface for QM/MM molecular dynamics simulations with AMBER

We present an extensible interface between the AMBER molecular dynamics (MD) software package and electronic structure software packages for quantum mechanical (QM) and mixed QM and classical molecular mechanical (MM) MD simulations within both mechanical and electronic embedding schemes. With this interface, ab initio wave function theory and density functional theory methods, as available in the supported electronic structure software packages, become available for QM/MM MD simulations with AMBER. The interface has been written in a modular fashion that allows straight forward extensions to support additional QM software packages and can easily be ported to other MD software. Data exchange between the MD and QM software is implemented by means of files and system calls or the message passing interface standard. Based on extensive tests, default settings for the supported QM packages are provided such that energy is conserved for typical QM/MM MD simulations in the microcanonical ensemble. Results for the free energy of binding of calcium ions to aspartate in aqueous solution comparing semiempirical and density functional Hamiltonians are shown to demonstrate features of this interface. © 2013 Wiley Periodicals, Inc.     

Design parameters for tuning the type 1 Cu multicopper oxidase redox potential: insight from a combination of first principles and empirical molecular dynamics simulations

The redox potentials and reorganization energies of the type 1 (T1) Cu site in four multicopper oxidases were calculated by combining first principles density functional theory (QM) and QM/MM molecular dynamics (MD) simulations. The model enzymes selected included the laccase from Trametes versicolor, the laccase-like enzyme isolated from Bacillus subtilis, CueO required for copper homeostasis in Escherichia coli, and the small laccase (SLAC) from Streptomyces coelicolor. The results demonstrated good agreement with experimental data and provided insight into the parameters that influence the T1 redox potential. Effects of the immediate T1 Cu site environment, including the His(N(δ))-Cys(S)-His(N(δ)) and the axial coordinating amino acid, as well as the proximate H(N)(backbone)-S(Cys) hydrogen bond, were discerned. Furthermore, effects of the protein backbone and side-chains, as well as of the aqueous solvent, were studied by QM/MM molecular dynamics (MD) simulations, providing an understanding of influences beyond the T1 Cu coordination sphere. Suggestions were made regarding an increase of the T1 redox potential in SLAC, i.e., of Met198 and Thr232 in addition to the axial amino acid Met298. Finally, the results of this work presented a framework for understanding parameters that influence the Type 1 Cu MCO redox potential, useful for an ever-growing range of laccase-based applications.     

Representation of Zn(II) complexes in polarizable molecular mechanics. Further refinements of the electrostatic and short-range contributions. Comparisons with parallel ab initio computations

We present refinements of the SIBFA molecular mechanics procedure to represent the intermolecular interaction energies of Zn(II). The two first-order contributions, electrostatic (E(MTP)), and short-range repulsion (E(rep)), are refined following the recent developments due to Piquemal et al. (Piquemal et al. J Phys Chem A 2003, 107, 9800; and Piquemal et al., submitted). Thus, E(MTP) is augmented with a penetration component, E(pen), which accounts for the effects of reduction in electronic density of a given molecular fragment sensed by another interacting fragment upon mutual overlap. E(pen) is fit in a limited number of selected Zn(II)-mono-ligated complexes so that the sum of E(MTP) and E(pen) reproduces the Coulomb contribution E(c) from an ab initio Hartree-Fock energy decomposition procedure. Denoting by S, the overlap matrix between localized orbitals on the interacting monomers, and by R, the distance between their centroids, E(rep) is expressed by a S(2)/R term now augmented with an S(2)/R(2) one. It is calibrated in selected monoligated Zn(II) complexes to fit the corresponding exchange repulsion E(exch) from ab initio energy decomposition, and no longer as previously the difference between (E(c) + E(exch)) and E(MTP). Along with the reformulation of the first-order contributions, a limited recalibration of the second-order contributions was carried out. As in our original formulation (Gresh, J Comput Chem 1995, 16, 856), the Zn(II) parameters for each energy contribution were calibrated to reproduce the radial behavior of its ab initio HF counterpart in monoligated complexes with N, O, and S ligands. The SIBFA procedure was subsequently validated by comparisons with parallel ab initio computations on several Zn(II) polyligated complexes, including binuclear Zn(II) complexes as in models for the Gal4 and beta-lactamase metalloproteins. The largest relative error with respect to the RVS computations is 3%, and the ordering in relative energies of competing structures reproduced even though the absolute numerical values of the ab initio interaction energies can be as large as 1220 kcal/mol. A term-to-term identification of the SIBFA contributions to their ab initio counterparts remained possible even for the largest sized complexes.     

Towards the Accurate Thermodynamic Characterization of Enzyme Reaction Mechanisms

We employed QM/MM molecular dynamics (MD) simulations to characterize the rate-limiting step of the glycosylation reaction of pancreatic α-amylase with combined DFT/molecular dynamics methods (PBE/def2-SVP : AMBER). Upon careful choice of four starting active site conformations based on thorough reactivity criteria, Gibbs energy profiles were calculated with umbrella sampling simulations within a statistical convergence of 1–2 kcal ⋅ mol⁻¹. Nevertheless, Gibbs activation barriers and reaction energies still varied from 11.0 to 16.8 kcal ⋅ mol⁻¹ and −6.3 to +3.8 kcal ⋅ mol⁻¹ depending on the starting conformations, showing that despite significant state-of-the-art QM/MM MD sampling (0.5 ns/profile) the result still depends on the starting structure. The results supported the one step dissociative mechanism of Asp197 glycosylation preceded by an acid-base reaction by the Glu233, which are qualitatively similar to those from multi-PES QM/MM studies, and thus support the use of the latter to determine enzyme reaction mechanisms.     

The Jahn-Teller effect of the Cr(2+) ion in aqueous solution: Ab initio QM/MM molecular dynamics simulations

The hydration structure of Cr(2+) has been studied using molecular dynamics (MD) simulations including three-body corrections and combined ab initio quantum mechanical/molecular mechanical (QM/MM) MD simulations at the Hartree-Fock level. The structural properties are determined in terms of radial distribution functions, coordination numbers, and several angle distributions. The mean residence time was evaluated for describing ligand exchange processes in the second hydration shell. The Jahn-Teller distorted octahedral [Cr(H(2)O)(6)](2+) complex was pronounced in the QM/MM MD simulation. The first-shell distances of Cr(2+) are in the range of 1.9-2.8 A, which are slightly larger than those observed in the cases of Cu(2+) and Ti(3+). No first-shell water exchange occurred during the simulation time of 35 ps. Several water-exchange processes were observed in the second hydration shell with a mean residence time of 7.3 ps.     

A valence bond model for aqueous Cu(II) and Zn(II) ions in the AMOEBA polarizable force field

A general molecular mechanics (MM) model for treating aqueous Cu²⁺ and Zn²⁺ ions was developed based on valence bond (VB) theory and incorporated into the atomic multipole optimized energetics for biomolecular applications (AMOEBA) polarizable force field. Parameters were obtained by fitting MM energies to that computed by ab initio methods for gas‐phase tetra‐ and hexa‐aqua metal complexes. Molecular dynamics (MD) simulations using the proposed AMOEBA‐VB model were performed for each transition metal ion in aqueous solution, and solvent coordination was evaluated. Results show that the AMOEBA‐VB model generates the correct square‐planar geometry for gas‐phase tetra‐aqua Cu²⁺ complex and improves the accuracy of MM model energetics for a number of ligation geometries when compared to quantum mechanical (QM) computations. On the other hand, both AMOEBA and AMOEBA‐VB generate results for Zn²⁺–water complexes in good agreement with QM calculations. Analyses of the MD trajectories revealed a six‐coordination first solvation shell for both Cu²⁺ and Zn²⁺ ions in aqueous solution, with ligation geometries falling in the range reported by previous studies. © 2012 Wiley Periodicals, Inc.     

The influence of the Jahn-Teller effect and of heteroligands on the reactivity of Cu2+

Experimentally hardly accessible Jahn-Teller inversions and the influence of heteroligands on the reactivity of Cu2+ are characterized by ab initio QM/MM MD simulations of Cu2+ ion and its amino complexes in water.     

The importance of dynamics in substrate-assisted catalysis and specificity

The QM/MM MD and free energy simulations show that the dynamics involving a His residue at the P1 site of the substrate may play an important role in substrate-assisted catalysis and specificity for a serine-carboxyl peptidase.     

Anisotropic, Polarizable Molecular Mechanics Studies of Inter- and Intramolecular Interactions and Ligand-Macromolecule Complexes. A Bottom-Up Strategy

We present an overview of the SIBFA polarizable molecular mechanics procedure, which is formulated and calibrated on the basis of quantum chemistry (QC). It embodies nonclassical effects such as electrostatic penetration, exchange-polarization, and charge transfer. We address the issues of anisotropy, nonadditivity, and transferability by performing parallel QC computations on multimolecular complexes. These encompass multiply H-bonded complexes and polycoordinated complexes of divalent cations. Recent applications to the docking of inhibitors to Zn-metalloproteins are presented next, namely metallo-beta-lactamase, phosphomannoisomerase, and the nucleocapsid of the HIV-1 retrovirus. Finally, toward third-generation intermolecular potentials based on density fitting, we present the development of a novel methodology, the Gaussian electrostatic model (GEM), which relies on ab initio-derived fragment electron densities to compute the components of the total interaction energy. As GEM offers the possibility of a continuous electrostatic model going from distributed multipoles to densities, it allows an inclusion of short-range quantum effects in the molecular mechanics energies. The perspectives of an integrated SIBFA/GEM/QM procedure are discussed.     

Evidence for sevenfold coordination in the first solvation shell of Hg(II) aqua ion

A quite unexpected sevenfold coordination of the hydrated Hg(II) complex in aqueous solution is revealed by an extensive study combining X-ray absorption spectroscopy (XAS) and quantum mechanics/molecular dynamics (QM/MD) calculations. As a matter of fact, the generally accepted octahedral solvation of Hg(II) ion cannot be reconciled with XAS results. Next, refined QM computations point out the remarkable stability of a heptacoordinated structure with C2 symmetry, and long-time MD simulations by new interaction potentials including many-body effects reveal that the hydrated complex has a quite flexible structure, corresponding for most of the time to heptacoordinated species. This picture is fully consistent with X-ray absorption near-edge structure experimental data which unambiguously show the preference for a sevenfold instead of a sixfold coordination.     

Complexes of a Zn‐metalloenzyme binding site with hydroxamate‐containing ligands. A case for detailed benchmarkings of polarizable molecular mechanics/dynamics potentials when the experimental binding structure is unknown

Zn‐metalloproteins are a major class of targets for drug design. They constitute a demanding testing ground for polarizable molecular mechanics/dynamics aimed at extending the realm of quantum chemistry (QC) to very long‐duration molecular dynamics (MD). The reliability of such procedures needs to be demonstrated upon comparing the relative stabilities of competing candidate complexes of inhibitors with the recognition site stabilized in the course of MD. This could be necessary when no information is available regarding the experimental structure of the inhibitor–protein complex. Thus, this study bears on the phosphomannose isomerase (PMI) enzyme, considered as a potential therapeutic target for the treatment of several bacterial and parasitic diseases. We consider its complexes with 5‐phospho‐d ‐arabinonohydroxamate and three analog ligands differing by the number and location of their hydroxyl groups. We evaluate the energy accuracy expectable from a polarizable molecular mechanics procedure, SIBFA. This is done by comparisons with ab initio quantum‐chemistry (QC) calculations in the following cases: (a) the complexes of the four ligands in three distinct structures extracted from the entire PMI‐ligand energy‐minimized structures, and totaling up to 264 atoms; (b) the solvation energies of several energy‐minimized complexes of each ligand with a shell of 64 water molecules; (c) the conformational energy differences of each ligand in different conformations characterized in the course of energy‐minimizations; and (d) the continuum solvation energies of the ligands in different conformations. The agreements with the QC results appear convincing. On these bases, we discuss the prospects of applying the procedure to ligand‐macromolecule recognition problems. © 2016 Wiley Periodicals, Inc.     

Complexes of thiomandelate and captopril mercaptocarboxylate inhibitors to metallo-beta-lactamase by polarizable molecular mechanics. Validation on model binding sites by quantum chemistry

Using the polarizable molecular mechanics method SIBFA, we have performed a search for the most stable binding modes of D- and L-thiomandelate to a 104-residue model of the metallo-beta-lactamase from B. fragilis, an enzyme involved in the acquired resistance of bacteria to antibiotics. Energy balances taking into account solvation effects computed with a continuum reaction field procedure indicated the D-isomer to be more stably bound than the L-one, conform to the experimental result. The most stably bound complex has the S(-) ligand bridging monodentately the two Zn(II) cations and one carboxylate O(-) H-bonded to the Asn193 side chain. We have validated the SIBFA energy results by performing additional SIBFA as well as quantum chemical (QC) calculations on small (88 atoms) model complexes extracted from the 104-residue complexes, which include the residues involved in inhibitor binding. Computations were done in parallel using uncorrelated (HF) as well as correlated (DFT, LMP2, MP2) computations, and the comparisons extended to corresponding captopril complexes (Antony et al., J Comput Chem 2002, 23, 1281). The magnitudes of the SIBFA intermolecular interaction energies were found to correctly reproduce their QC counterparts and their trends for a total of twenty complexes.