Mechanism of proteolysis in matrix metalloproteinase‐2 revealed by QM/MM modeling

The mechanism of enzymatic peptide hydrolysis in matrix metalloproteinase‐2 (MMP‐2) was studied at atomic resolution through quantum mechanics/molecular mechanics (QM/MM) simulations. An all‐atom three‐dimensional molecular model was constructed on the basis of a crystal structure from the Protein Data Bank (ID: 1QIB), and the oligopeptide Ace‐Gln‐Gly～Ile‐Ala‐Gly‐Nme was considered as the substrate. Two QM/MM software packages and several computational protocols were employed to calculate QM/MM energy profiles for a four‐step mechanism involving an initial nucleophilic attack followed by hydrogen bond rearrangement, proton transfer, and C? N bond cleavage. These QM/MM calculations consistently yield rather low overall barriers for the chemical steps, in the range of 5–10 kcal/mol, for diverse QM treatments (PBE0, B3LYP, and BB1K density functionals as well as local coupled cluster treatments) and two MM force fields (CHARMM and AMBER). It, thus, seems likely that product release is the rate‐limiting step in MMP‐2 catalysis. This is supported by an exploration of various release channels through QM/MM reaction path calculations and steered molecular dynamics simulations. © 2015 Wiley Periodicals, Inc.     

Convergence in the QM‐only and QM/MM modeling of enzymatic reactions: A case study for acetylene hydratase

We report systematic quantum mechanics‐only (QM‐only) and QM/molecular mechanics (MM) calculations on an enzyme‐catalyzed reaction to assess the convergence behavior of QM‐only and QM/MM energies with respect to the size of the chosen QM region. The QM and MM parts are described by density functional theory (typically B3LYP/def2‐SVP) and the CHARMM force field, respectively. Extending our previous work on acetylene hydratase with QM regions up to 157 atoms (Liao and Thiel, J. Chem. Theory Comput. 2012, 8, 3793), we performed QM/MM geometry optimizations with a QM region M4 composed of 408 atoms, as well as further QM/MM single‐point calculations with even larger QM regions up to 657 atoms. A charge deletion analysis was conducted for the previously used QM/MM model ( M3a , with a QM region of 157 atoms) to identify all MM residues with strong electrostatic contributions to the reaction energetics (typically more than 2 kcal/mol), which were then included in M4 . QM/MM calculations with this large QM region M4 lead to the same overall mechanism as the previous QM/MM calculations with M3a , but there are some variations in the relative energies of the stationary points, with a mean absolute deviation (MAD) of 2.7 kcal/mol. The energies of the two relevant transition states are close to each other at all levels applied (typically within 2 kcal/mol), with the first (second) one being rate‐limiting in the QM/MM calculations with M3a ( M4 ). QM‐only gas‐phase calculations give a very similar energy profile for QM region M4 (MAD of 1.7 kcal/mol), contrary to the situation for M3a where we had previously found significant discrepancies between the QM‐only and QM/MM results (MAD of 7.9 kcal/mol). Extension of the QM region beyond M4 up to M7 (657 atoms) leads to only rather small variations in the relative energies from single‐point QM‐only and QM/MM calculations (MAD typically about 1–2 kcal/mol). In the case of acetylene hydratase, a model with 408 QM atoms thus seems sufficient to achieve convergence in the computed relative energies to within 1–2 kcal/mol.Copyright © 2013 Wiley Periodicals, Inc.     

Solvents effects on the mechanism of cellulose hydrolysis: A QM/MM study

This article reports a combined quantum mechanics/molecular mechanics (QM/MM) investigation on the acid hydrolysis of cellulose in water using two different models, cellobiose and a 40‐unit cellulose chain. The explicitly treated solvent molecules strongly influence the conformations, intramolecular hydrogen bonds, and exoanomeric effects in these models. As these features are largely responsible for the barrier to cellulose hydrolysis, the present QM/MM results for the pathways and reaction intermediates in water are expected to be more realistic than those from a former density functional theory (DFT) study with implicit solvent (CPCM). However, in a qualitative sense, there is reasonable agreement between the DFT/CPCM and QM/MM predictions for the reaction mechanism. Differences arise mainly from specific solute–solvent hydrogen bonds that are only captured by QM/MM and not by DFT/CPCM. © 2015 Wiley Periodicals, Inc.     

How Photoisomerization Drives Peptide Folding and Unfolding: Insights from QM/MM and MM Dynamics Simulations

Photoswitchable azobenzene cross‐linkers can control the folding and unfolding of peptides by photoisomerization and can thus regulate peptide affinities and enzyme activities. Using quantum mechanics/molecular mechanics (QM/MM) methods and classical MM force fields, we report the first molecular dynamics simulations of the photoinduced folding and unfolding processes in the azobenzene cross‐linked FK‐11 peptide. We find that the interactions between the peptide and the azobenzene cross‐linker are crucial for controlling the evolution of the secondary structure of the peptide and responsible for accelerating the folding and unfolding events. They also modify the photoisomerization mechanism of the azobenzene cross‐linker compared with the situation in vacuo or in solution.     

Probing the range of applicability of structure‐ and energy‐adjusted QM/MM link bonds

The hydrogen‐capping method is one of the most popular and widely used coupling‐schemes for quantum mechanics/molecular mechanics (QM/MM)‐molecular dynamics simulations of macromolecular systems. This is mostly due to the fact that it is fairly convenient to implement and parametrize, thus providing an excellent compromise between accuracy and computational effort. In this work, a viable and straight‐forward approach to optimize the placing of the link atom on a suitable distance ratio between the frontier atoms is discussed. To further increase the accuracy, instead of global parameters for all amino acids, different parameter sets for each type of amino acid are derived. The dependency of the link bond parameters on the chemical environment and the used QM‐method is probed to assess the range of applicability of the parametrization. Suitable sets of parameters for RI‐MP2, B3LYP, (RI)‐B3LYP‐D3, and RI‐BLYP‐D3 at triple‐zeta level for all relevant proteinogenic amino acids are presented. Furthermore, the scope and range of the perturbation, stemming from the introduction of link bonds is evaluated through application of the presented QM/MM scheme in calculations of the active site of 15S‐lipoxygenase. © 2015 Wiley Periodicals, Inc.     

The implementation of a fast and accurate QM/MM potential method in Amber

Version 9 of the Amber simulation programs includes a new semi-empirical hybrid QM/MM functionality. This includes support for implicit solvent (generalized Born) and for periodic explicit solvent simulations using a newly developed QM/MM implementation of the particle mesh Ewald (PME) method. The code provides sufficiently accurate gradients to run constant energy QM/MM MD simulations for many nanoseconds. The link atom approach used for treating the QM/MM boundary shows improved performance, and the user interface has been rewritten to bring the format into line with classical MD simulations. Support is provided for the PM3, PDDG/PM3, PM3CARB1, AM1, MNDO, and PDDG/MNDO semi-empirical Hamiltonians as well as the self-consistent charge density functional tight binding (SCC-DFTB) method. Performance has been improved to the point where using QM/MM, for a QM system of 71 atoms within an explicitly solvated protein using periodic boundaries and PME requires less than twice the cpu time of the corresponding classical simulation.     

QM/MM distortion energies in di‐ and oligosaccharides complexed with proteins*

To investigate whether linkages between monosaccharide residues are unusually distorted by their interactions with proteins, ? and ψ values for fragments of cellulose and starch were taken from the Protein Data Bank. These experimental conformations were then plotted on energy surfaces that were calculated with a hybrid of HF/6‐31G* and MM3(96) energies. Energy values corresponding to each crystallographic conformation were then pooled. Nearly 70% of the 210 structures had energies of 1 kcal mol^?1 or less. A cumulative frequency analysis showed that most points fell on a curve that had an exponential decrease in the number of observed structures as the energy increased. This is analogous to a Boltzmann distribution but at higher temperature. This analysis showed that more than 90% of the linkages were not unusually distorted, and the distribution was similar to that found for small‐molecule crystals of carbohydrates. However, above 2 kcal mol^?1, the observed points deviated from the curve. Most of these high‐energy observations were from linkages being broken by enzymatic attack, but others were not, and some scissile linkages were not unusually distorted. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 416–425, 2001 *     

The MM2QM tool for combining docking,molecular dynamics,molecular mechanics,and quantum mechanics†

The use of the MM2QM tool in a combined docking + molecular dynamics (MD) + molecular mechanics (MM) + quantum mechanical (QM) binding affinity prediction study is presented, and the tool itself is discussed. The system of interest is Mycobacterium tuberculosis (MTB) pantothenate synthetase in complexes with three highly similar sulfonamide inhibitors, for which crystal structures are available. Starting from the structure of MTB pantothenate synthetase in the “open” conformation and following the combined docking + MD + MM + QM procedure, we were able to capture the closing of the enzyme binding pocket and to reproduce the position of the ligands with an average root mean square deviation of 1.6 Å. Protein–ligand interaction energies were reproduced with an average error lower than 10%. The discussion on the MD part and a protein flexibility importance is carried out. The presented approach may be useful especially for finding analog inhibitors or improving drug candidates. © 2012 Wiley Periodicals, Inc.     

Binding affinities by alchemical perturbation using QM/MM with a large QM system and polarizable MM model

The most general way to improve the accuracy of binding‐affinity calculations for protein–ligand systems is to use quantum‐mechanical (QM) methods together with rigorous alchemical‐perturbation (AP) methods. We explore this approach by calculating the relative binding free energy of two synthetic disaccharides binding to galectin‐3 at a reasonably high QM level (dispersion‐corrected density functional theory with a triple‐zeta basis set) and with a sufficiently large QM system to include all short‐range interactions with the ligand (744–748 atoms). The rest of the protein is treated as a collection of atomic multipoles (up to quadrupoles) and polarizabilities. Several methods for evaluating the binding free energy from the 3600 QM calculations are investigated in terms of stability and accuracy. In particular, methods using QM calculations only at the endpoints of the transformation are compared with the recently proposed non‐Boltzmann Bennett acceptance ratio (NBB) method that uses QM calculations at several stages of the transformation. Unfortunately, none of the rigorous approaches give sufficient statistical precision. However, a novel approximate method, involving the direct use of QM energies in the Bennett acceptance ratio method, gives similar results as NBB but with better precision, ～3 kJ/mol. The statistical error can be further reduced by performing a greater number of QM calculations. © 2015 Wiley Periodicals, Inc.     

Electronic absorption spectra of pyridine and nicotine in aqueous solution with a combined molecular dynamics and polarizable QM/MM approach

The electronic absorption spectra of pyridine and nicotine in aqueous solution have been computed using a multistep approach. The computational protocol consists in studying the solute solvation with accurate molecular dynamics simulations, characterizing the hydrogen bond interactions, and calculating electronic transitions for a series of configurations extracted from the molecular dynamics trajectories with a polarizable QM/MM scheme based on the fluctuating charge model. Molecular dynamics simulations and electronic transition calculations have been performed on both pyridine and nicotine. Furthermore, the contributions of solute vibrational effect on electronic absorption spectra have been taken into account in the so called vertical gradient approximation. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Implementation of the IMOMM methodology for performing combined QM/MM molecular dynamics simulations and frequency calculations

A technique for implementing the integrated molecular orbital and molecular mechanics (IMOMM) methodology developed by Maseras and Morokuma that is used to perform combined quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations, frequency calculations and simulations of macromolecules including explicit solvent is presented. Although the IMOMM methodology is generalized to any coordinate system, the implementation first described by Maseras and Morokuma requires that the QM and MM gradients be transformed into internal coordinates before they are added together. This coordinate transformation can be cumbersome for macromolecular systems and can become ill-defined during the course of a molecular dynamics simulation. We describe an implementation of the IMOMM method in which the QM and MM gradients are combined in the cartesian coordinate system, thereby avoiding potential problems associated with using the internal coordinate system. The implementation can be used to perform combined QM/MM molecular dynamics simulations and frequency calculations within the IMOMM framework. Finally, we have examined the applicability of thermochemical data derived from IMOMM framework. Finally, we have examined the applicability of thermochemical data derived from IMOMM frequency calculations. Received: 11 May 1998 / Accepted: 14 August 1998 / Published online: 16 November 1998     

Hybrid QM/MM molecular dynamics simulations for an ionic SN2 reaction in the supercritical water: OH- + CH3Cl --> CH3OH + Cl-

A hybrid real space quantum mechanical/molecular mechanical (RS-QM/MM) method has been applied to an ionic S(N)2 reaction (OH- + CH3Cl --> CH3OH + Cl-) in water solution to investigate dynamic solvation effects of the supercritical water (SCW) on the reaction. It has been demonstrated that the approaching process of OH- to methyl group is prevented by water molecules in the ambient water (AW), while the reaction takes place easily in the gas phase. Almost the same solvation effect on the dynamics of OH- is observed in the SCW, though the bulk density of water is substantially reduced compared with that of the AW. It has been shown that the solvation of the SCW around the OH anion is locally identical to that of the AW due to the strong ion-dipole interactions between OH- and water molecules. At the transition state, the QM/MM simulations have revealed that the excess electron is quite flexible, and the charge volume, as well as the fractional charges on atoms, vary seriously depending on the instantaneous solvent configurations. However, it has been found that the solvation energy in the SCW can be qualitatively related to the HOMO volume of the system by Born's equation.     

The CHARMM–TURBOMOLE interface for efficient and accurate QM/MM molecular dynamics,free energies,and excited state properties

The quantum mechanical (QM)/molecular mechanical (MM) interface between Chemistry at HARvard Molecular Mechanics (CHARMM) and TURBOMOLE is described. CHARMM provides an extensive set of simulation algorithms, like molecular dynamics (MD) and free energy perturbation, and support for mature nonpolarizable and Drude polarizable force fields. TURBOMOLE provides fast QM calculations using density functional theory or wave function methods and excited state properties. CHARMM–TURBOMOLE is well‐suited for extended QM/MM MD simulations using first principles methods with large (triple‐ζ) basis sets. We demonstrate these capabilities with a QM/MM simulation of Mg²⁺(aq), where the MM outer sphere water molecules are represented using the SWM4‐NDP Drude polarizable force field and the ion and inner coordination sphere are represented using QM PBE, PBE0, and MP2 methods. The relative solvation free energies of Mg²⁺ and Zn²⁺ were calculated using thermodynamic integration. We also demonstrate the features for excited state properties. We calculate the time‐averaged solution absorption spectrum of indole, the emission spectrum of the indole excited state, and the electronic circular dichroism spectrum of an oxacepham. © 2014 Wiley Periodicals, Inc.     

Quantum molecular mechanics—a noniterative procedure for the fast Ab Initio calculation of closed shell systems

In this article, we advance the foundations of a strategy to develop a molecular mechanics method based not on classical mechanics and force fields but entirely on quantum mechanics and localized electron‐pair orbitals, which we call quantum molecular mechanics (QMM). Accordingly, we introduce a new manner of calculating Hartree–Fock ab initio wavefunctions of closed shell systems based on variationally preoptimized nonorthogonal electron pair orbitals constructed by linear combinations of basis functions centered on the atoms. QMM is noniterative and requires only one extremely fast inversion of a single sparse matrix to arrive to the one‐particle density matrix, to the electron density, and consequently, to the ab initio electrostatic potential around the molecular system, or cluster of molecules. Although QMM neglects the smaller polarization effects due to intermolecular interactions, it fully takes into consideration polarization effects due to the much stronger intramolecular geometry distortions. For the case of methane, we show that QMM was able to reproduce satisfactorily the energetics and polarization effects of all distortions of the molecule along the nine normal modes of vibration, well beyond the harmonic region. We present the first practical applications of the QMM method by examining, in detail, the cases of clusters of helium atoms, hydrogen molecules, methane molecules, as well as one molecule of HeH⁺ surrounded by several methane molecules. We finally advance and discuss the potentialities of an exact formula to compute the QMM total energy, in which only two center integrals are involved, provided that the fully optimized electron‐pair orbitals are known. © 2012 Wiley Periodicals, Inc.     

Comparison of radii sets,entropy, QM methods,and sampling on MM‐PBSA,MM‐GBSA,and QM/MM‐GBSA ligand binding energies of F. tularensis enoyl‐ACP reductase (FabI)

To validate a method for predicting the binding affinities of FabI inhibitors, three implicit solvent methods, MM‐PBSA, MM‐GBSA, and QM/MM‐GBSA were carefully compared using 16 benzimidazole inhibitors in complex with Francisella tularensis FabI. The data suggests that the prediction results are sensitive to radii sets, GB methods, QM Hamiltonians, sampling protocols, and simulation length, if only one simulation trajectory is used for each ligand. In this case, QM/MM‐GBSA using 6 ns MD simulation trajectories together with GB^neck2, PM3, and the mbondi2 radii set, generate the closest agreement with experimental values (r² = 0.88). However, if the three implicit solvent methods are averaged from six 1 ns MD simulations for each ligand (called “multiple independent sampling”), the prediction results are relatively insensitive to all the tested parameters. Moreover, MM/GBSA together with GB^HCT and mbondi, using 600 frames extracted evenly from six 0.25 ns MD simulations, can also provide accurate prediction to experimental values (r² = 0.84). Therefore, the multiple independent sampling method can be more efficient than a single, long simulation method. Since future scaffold expansions may significantly change the benzimidazole's physiochemical properties (charges, etc.) and possibly binding modes, which may affect the sensitivities of various parameters, the relatively insensitive “multiple independent sampling method” may avoid the need of an entirely new validation study. Moreover, due to large fluctuating entropy values, (QM/)MM‐P(G)BSA were limited to inhibitors’ relative affinity prediction, but not the absolute affinity. The developed protocol will support an ongoing benzimidazole lead optimization program. © 2015 Wiley Periodicals, Inc.     

Combined QM/MM and path integral simulations of kinetic isotope effects in the proton transfer reaction between nitroethane and acetate ion in water

An integrated Feynman path integral-free energy perturbation and umbrella sampling (PI-FEP/UM) method has been used to investigate the kinetic isotope effects (KIEs) in the proton transfer reaction between nitroethane and acetate ion in water. In the present study, both nuclear and electronic quantum effects are explicitly treated for the reacting system. The nuclear quantum effects are represented by bisection sampling centroid path integral simulations, while the potential energy surface is described by a combined quantum mechanical and molecular mechanical (QM/MM) potential. The accuracy essential for computing KIEs is achieved by a FEP technique that transforms the mass of a light isotope into a heavy one, which is equivalent to the perturbation of the coordinates for the path integral quasiparticle in the bisection sampling scheme. The PI-FEP/UM method is applied to the proton abstraction of nitroethane by acetate ion in water through molecular dynamics simulations. The rule of the geometric mean and the Swain-Schaad exponents for various isotopic substitutions at the primary and secondary sites have been examined. The computed total deuterium KIEs are in accord with experiments. It is found that the mixed isotopic Swain-Schaad exponents are very close to the semiclassical limits, suggesting that tunneling effects do not significantly affect this property for the reaction between nitroethane and acetate ion in aqueous solution.     

Quantum study of the active sites of the γ alumina surface (II): QM/MM (LSCF) approach to water, hydrogen disulfide and carbon monoxide adsorption

The mixed quantum mechanics/molecular mechanics (QM/MM) local self consistent field (LSCF) method is applied to study the adsorption of water, hydrogen sulfide, and carbon monoxide molecules on γ alumina surfaces. The effect of the long-range contributions included in the LSCF adsorption/dissociation energies are compared to cluster results. For the carbon monoxide, the long-range contributions do not change the adsorption energies in comparison with the cluster approach. In opposition, the long-range contributions lower the adsorption and dissociation energies of water and hydrogen disulfide. Cautions to be taken on the application of the LSCF method to γ alumina are also discussed.     

On the effect of a variation of the force field, spatial boundary condition and size of the QM region in QM/MM MD simulations

During the past years, the use of combined quantum-classical, QM/MM, methods for the study of complex biomolecular processes, such as enzymatic reactions and photocycles, has increased considerably. The quality of the results obtained from QM/MM calculations is largely dependent on five aspects to be considered when setting up a molecular model: the QM Hamiltonian, the MM Hamiltonian or force field, the boundary and coupling between the QM and MM regions, the size of the QM region and the boundary condition for the MM region. In this study, we systematically investigate the influence of a variation of the molecular mechanics force field and the size of the QM region in QM/MM MD simulations on properties of the photoactive part of the blue light photoreceptor protein AppA. For comparison, we additionally performed classical MD simulations and studied the effect of a variation of the type of spatial boundary condition. The classical boundary conditions and the force field used in a QM/MM MD simulation are shown to have non-neglegible effects upon the structural and energetic properties of the protein which makes it advisable to minimize computational artifacts in QM/MM MD simulations by application of periodic boundary conditions and a thermodynamically calibrated force field. A comparison of the structural and energetic properties of MD simulations starting from two alternative, different X-ray structures for the blue light utilizing flavin protein in its dark state indicates a slight preference of the two force fields used for the so-called Anderson structure over the Jung structure.