Structure and dynamics of La(III) in aqueous solution – An ab initio QM/MM MD approach

Ab initio QM/MM MD simulations have allowed to clarify some of the ambiguities arising from various studies on the hydrated La(III) ion. Both nine- and ten-coordinated hydrates co-exist and interchange in a dissociative process on the nano- or even subnanosecond scale, and thus much faster than any other trivalent main group or transition metal ions. The weak ion–ligand bond (53 N/m) supplies a reasonable explanation for it. The simulation results for La(III) are also compared to those for the isoelectronic ions Cs(I) and Ba(II) obtained by the same ab initio MD procedure, leading to conclusions on the influence of central ion charge on structural and dynamic properties of hydrate complexes.     

Structure-breaking effects of solvated Rb(I) in dilute aqueous solution--an ab initio QM/MM MD approach

Structural properties of the hydrated Rb(I) ion have been investigated by ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations at the double-zeta HF quantum mechanical level. The first shell coordination number was found to be 7.1, and several other structural parameters such as angular distribution functions, radial distribution functions and tilt- and theta-angle distributions allowed the full characterization of the hydration structure of the Rb(I) ion in dilute aqueous solution. Velocity autocorrelation functions were used to calculate librational and vibrational motions, ion-ligand motions, as well as reorientation times. Different dynamical parameters such as water reorientation, mean ligand residence time, the number of ligand exchange processes, and rate constants were also analyzed. The mean ligand residence time for the first shell was determined as tau = 2.0 ps.     

Extension of QM/MM docking and its applications to metalloproteins

To overcome the limitation of conventional docking methods which assume fixed charge model from force field parameters, combined quantum mechanics/molecular mechanics (QM/MM) method has been applied to docking as a variable charge model and shown to exhibit improvement on the docking accuracy over fixed charge based methods. However, it has also been shown that there are a number of examples for which adoption of variable‐charge model fails to reproduce the native binding modes. In particular, for metalloproteins, previously implemented method of QM/MM docking failed most often. This class of proteins has highly polarized binding sites at which high‐coordinate‐numbered metal ions reside. We extend the QM/MM docking method so that protein atoms surrounding the binding site along with metal ions are included as quantum region, as opposed to only ligand atoms. This extension facilitates the required scaling of partial charges on metal ions leading to prediction of correct binding modes in metalloproteins. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

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     

Mixed ab initio QM/MM modeling using frozen orbitals and tests with alanine dipeptide and tetrapeptide

Methodology is discussed for mixed ab initio quantum mechanics/molecular mechanics modeling of systems where the quantum mechanics (QM) and molecular mechanics (MM) regions are within the same molecule. The ab initio QM calculations are at the restricted Hartree–Fock level using the pseudospectral method of the Jaguar program while the MM part is treated with the OPLS force fields implemented in the IMPACT program. The interface between the QM and MM regions, in particular, is elaborated upon, as it is dealt with by “breaking” bonds at the boundaries and using Boys-localized orbitals found from model molecules in place of the bonds. These orbitals are kept frozen during QM calculations. Results from tests of the method to find relative conformational energies and geometries of alanine dipeptides and alanine tetrapeptides are presented along with comparisons to pure QM and pure MM calculations. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1468–1494, 1999     

QM/MM vibrational mode tracking

Vibrational spectroscopy is a powerful tool to investigate the structure and dynamics of biomolecules. When small subsystems of large molecules such as active centers of enzymes are studied, quantum chemical calculations based on quantum mechanics/molecular mechanics (QM/MM) coupling schemes are a valuable means to interpret the spectra. The goal of this work is a methodological pilot study on how to selectively and thus efficiently extract certain vibrational information for extended molecular systems described by QM/MM methods. This is achieved by an extension of the mode tracking algorithm and a comparison with the partial Hessian diagonalization approach. After validating the methodology for the CO stretching vibration of 2-butanone and a delocalized CO stretch in acetylacetone, the stretching and bending modes of the CO ligand in CO myoglobin are tracked. Such systems represent an ideal application for mode tracking, because only a few strongly localized vibrations are sought for, while the large remainder of the molecule is of interest only as far as it affects these local vibrations. This influence is treated exactly by mode tracking.     

Quantifying Electronic Effects in QM and QM/MM Biomolecular Modeling with the Fukui Function

Multi-scale quantum-mechanical/molecular-mechanical(QM/MM) and large-scale QM simulation provide valuable insight into enzyme mechanism and structure-property relationships. Analysis of the electron density afforded through these methods can enhance our understanding of how the enzyme environment modulates reactivity at the enzyme active site. From this perspective, tools from conceptual density functional theory to interrogate electron densities can provide added insight into enzyme function. We recently introduced the highly parallelizable Fukui shift analysis(FSA) method, which identifies how frontier states of an active site are altered by the presence of an additional QM residue to identify when QM treatment of a residue is essential as a result of quantum-mechanically affecting the behavior of the active site. We now demonstrate and analyze distance and residue dependence of Fukui function shifts in pairs of residues representing different non-covalent interactions. We also show how the interpretation of the Fukui function as a measure of relative nucleophilicity provides insight into enzymes that carry out S_N2 methyl transfer. The FSA method represents a promising approach for the systematic, unbiased determination of quantum mechanical effects in enzymes and for other complex systems that necessitate multi-scale modeling.     

Importance of accurate charges in molecular docking: quantum mechanical/molecular mechanical (QM/MM) approach

The extent to which accuracy of electric charges plays a role in protein-ligand docking is investigated through development of a docking algorithm, which incorporates quantum mechanical/molecular mechanical (QM/MM) calculations. In this algorithm, fixed charges of ligands obtained from force field parameterization are replaced by QM/MM calculations in the protein environment, treating only the ligands as the quantum region. The algorithm is tested on a set of 40 cocrystallized structures taken from the Protein Data Bank (PDB) and provides strong evidence that use of nonfixed charges is important. An algorithm, dubbed "Survival of the Fittest" (SOF) algorithm, is implemented to incorporate QM/MM charge calculations without any prior knowledge of native structures of the complexes. Using an iterative protocol, this algorithm is able in many cases to converge to a nativelike structure in systems where redocking of the ligand using a standard fixed charge force field exhibits nontrivial errors. The results demonstrate that polarization effects can play a significant role in determining the structures of protein-ligand complexes, and provide a promising start towards the development of more accurate docking methods for lead optimization applications.     

A minimal implementation of the AMBER-GAUSSIAN interface for ab initio QM/MM-MD simulation

For applying to a number of theoretical methodologies based on an ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics method connecting AMBER9 with GAUSSIAN03, we have developed an AMBER-GAUSSIAN interface (AG-IF), which can be one of the simplest architectures. In the AG-IF, only a few subroutines addition is necessary to retrieve the QM/MM energy and forces, obtained by GAUSSIAN, for solving a set of Newtonian equations of motion in AMBER. It is, therefore, easy to be modified for individual applications since AG-IF utilizes most of those functions originally equipped not only in AMBER but also in GAUSSIAN. In the present minimal implementation, only AMBER is modified, whereas GAUSSIAN is left unchanged. Moreover, a different method of calculating electrostatic forces of MM atoms interacting with QM region is proposed. Using the AG-IF, we also demonstrate three examples of application: (i) the QM versus MM comparison in the radial distribution function, (ii) the free energy gradient method, and (iii) the charge from interaction energy and forces.     

Structure and dynamics of hydrated NH(4) (+): an ab initio QM/MM molecular dynamics simulation

A combined ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulation has been performed to investigate solvation structure and dynamics of NH(4) (+) in water. The most interesting region, the sphere includes an ammonium ion and its first hydration shell, was treated at the Hartree-Fock level using DZV basis set, while the rest of the system was described by classical pair potentials. On the basis of detailed QM/MM simulation results, the solvation structure of NH(4) (+) is rather flexible, in which many water molecules are cooperatively involved in the solvation shell of the ion. Of particular interest, the QM/MM results show fast translation and rotation of NH(4) (+) in water. This phenomenon has resulted from multiple coordination, which drives the NH(4) (+) to translate and rotate quite freely within its surrounding water molecules. In addition, a "structure-breaking" behavior of the NH(4) (+) is well reflected by the detailed analysis on the water exchange process and the mean residence times of water molecules surrounding the ion.     

Contributions of pauli repulsions to the energetics and physical properties computed in QM/MM methods

Conventional combined quantum mechanical/molecular mechanical (QM/MM) methods lack explicit treatment of Pauli repulsions between the quantum‐mechanical and molecular‐mechanical subsystems. Instead, classical Lennard‐Jones (LJ) potentials between QM and MM nuclei are used to model electronic Pauli repulsion and long‐range London dispersion, despite the fact that the latter two are inherently of quantum nature. Use of the simple LJ potential in QM/MM methods can reproduce minimal geometries and energies of many molecular clusters reasonably well, as compared to full QM calculations. However, we show here that the LJ potential cannot correctly describe subtle details of the electron density of the QM subsystem because of the neglect of Pauli repulsions between the QM and MM subsystems. The inaccurate electron density subsequently affects the calculation of electronic and magnetic properties of the QM subsystem. To explicitly consider Pauli interactions with QM/MM methods, we propose a method to use empirical effective potentials on the MM atoms. The test case of the binding energy and magnetic properties of a water dimer shows promising results for the general application of effective potentials to mimic Pauli repulsions in QM/MM calculations. © 2013 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.     

Methodological aspects of QM/MM calculations: A case study on matrix metalloproteinase‐2

We address methodological issues in quantum mechanics/molecular mechanics (QM/MM) calculations on a zinc‐dependent enzyme. We focus on the first stage of peptide bond cleavage by matrix metalloproteinase‐2 (MMP‐2), that is, the nucleophilic attack of the zinc‐coordinating water molecule on the carbonyl carbon atom of the scissile fragment of the substrate. This step is accompanied by significant charge redistribution around the zinc cation, bond cleavage, and bond formation. We vary the size and initial geometry of the model system as well as the computational protocol to demonstrate the influence of these choices on the results obtained. We present QM/MM potential energy profiles for a set of snapshots randomly selected from QM/MM‐based molecular dynamics simulations and analyze the differences in the computed profiles in structural terms. Since the substrate in MMP‐2 is located on the protein surface, we investigate the influence of the thickness of the water layer around the enzyme on the QM/MM energy profile. Thin water layers (0–2 Å) give unrealistic results because of structural reorganizations in the active‐site region at the protein surface. A 12 Å water layer appears to be sufficient to capture the effect of the solvent; the corresponding QM/MM energy profile is very close to that obtained from QM/MM/SMBP calculations using the solvent macromolecular boundary potential (SMBP). We apply the optimized computational protocol to explain the origin of the different catalytic activity of the Glu116Asp mutant: the energy barrier for the first step is higher, which is rationalized on structural grounds. © 2016 Wiley Periodicals, Inc.     

One- and three-parameter density functional theory and high level ab initio theory study of the CH+CH disproportionation reaction

Complete basis set (CBS) ab initio computational studies were performed with the target being to explore the CH+CH potential energy surface. Several closed and open shell intermediates were located on the potential energy surface. Computed enthalpies for the branching reactions, as well as heats of formation are in excellent agreement. Although CBS computed energies are of high quality, this computational study is not capable of predicting the branching product ratio due to fact that neither the MP2 nor the 6-311G(2d,2p) basis set are sufficient to locate the reactant complexes and the transition state structures for the hydrogen and carbon transfer reactions in the reaction complexes. To properly explore the CH+CH potential energy surface a much higher ab initio theory level is required.     

Interfacing Q-Chem and CHARMM to perform QM/MM reaction path calculations

A hybrid quantum mechanical/molecular mechanical (QM/MM) potential energy function with Hartree-Fock, density functional theory (DFT), and post-HF (RIMP2, MP2, CCSD) capability has been implemented in the CHARMM and Q-Chem software packages. In addition, we have modified CHARMM and Q-Chem to take advantage of the newly introduced replica path and the nudged elastic band methods, which are powerful techniques for studying reaction pathways in a highly parallel (i.e., parallel/parallel) fashion, with each pathway point being distributed to a different node of a large cluster. To test our implementation, a series of systems were studied and comparisons were made to both full QM calculations and previous QM/MM studies and experiments. For instance, the differences between HF, DFT, MP2, and CCSD QM/MM calculations of H2O...H2O, H2O...Na+, and H2O...Cl- complexes have been explored. Furthermore, the recently implemented polarizable Drude water model was used to make comparisons to the popular TIP3P and TIP4P water models for doing QM/MM calculations. We have also computed the energetic profile of the chorismate mutase catalyzed Claisen rearrangement at various QM/MM levels of theory and have compared the results with previous studies. Our best estimate for the activation energy is 8.20 kcal/mol and for the reaction energy is -23.1 kcal/mol, both calculated at the MP2/6-31+G(d)//MP2/6-31+G(d)/C22 level of theory.     

High level of ab initio and density functional theory computational study of structural and energetic properties of tetrafluorhydrazine rotamers

The HF, MP2, MP3, MP4, and QCISD ab initio methods were compared with local, hybrid, and gradient-corrected density functional theory (DFT) methods for computing structures and energies of N2F4 rotamers. In all DFT calculations 6-311 + G(2d) basis set was used. The generated structures energies of trans- and gauche-N₂F₄ rotamers, and their dissociation energies to nitrogen difluoride were compared with experimental data. Suitable hybrid and gradient-corrected DFT methods for determining structures and energies for these and similar molecular systems were discussed.     

Producing DFT/MM enzyme reaction trajectories from SCC‐DFTB/MM driving forces to probe the underlying electronics of a glycosyltransferase reaction

The SCC‐DFTB/MIO/CHARMM free energy surface for a glycosyltransferase, TcTS, is benchmarked against a DFT/MM reaction trajectory using the same CHARMM MM force field ported to the NWChem package. The popular B3LYP functional, against which the MIO parameter set was parameterized is used to optimize TS structures and run DFT reaction dynamics. A novel approach was used to generate reaction forces from a SCC‐DFTB/MIO/CHARMM reaction surface to drive B3LYP/6‐31G/MM and B3LYP/6‐31G(d)/MM reaction trajectories. Although TS structures compare favorably, differences stemming primarily from a minimal basis set approximation prevented a successful 6‐31G(d) FEARCF reaction dynamics trajectory. None the less, the dynamic evolution of the B3LYP/6‐31G/MM‐computed electron density provided an opportunity to perform NBO analysis along the reaction trajectory. Here, we illustrate that a successful ab initio reaction trajectory is computationally accessible when the underlying potential energy function of the semi‐empirical method used to produce driving forces is sufficiently close to the ab initio potential. © 2017 Wiley Periodicals, Inc.     

Transition state structure invariance to model system size and calculation levels: a QM/MM study of the carboxylation step catalyzed by Rubisco

The present study elucidates structural features related to the molecular mechanism in the carboxylation step of the reaction catalyzed by Rubisco. Starting from the initial X-ray Protein Data Bank structure of a Rubisco monomer, the reactive subsystem in vacuo is subjected to quantum chemical semiempirical and ab initio studies, while the effects of the protein environments are included by means of a hybrid quantum mechanical/molecular mechanical (QM/MM) approach. The QM/MM is used to characterize the transition structure for carboxylation inside the protein. The calculations were made with the AM1/CHARMM/GRACE scheme. Comparisons between the in vacuo and in situ transition structures show remarkable invariance with respect to geometric parameters, index and transition vector amplitudes. The transition state couples the carbon dioxide attack to the C2 center of the substrate in its dienol form with a simultaneous intramolecular hydrogen transfer from the C2 atom to the hydroxyl group linked to the C3 center. This study suggests that carboxylation may be simultaneously coupled to the activation of the C3 center in the enzyme. Received: 24 March 1998 / Accepted: 3 September 1998 / Published online: 10 December 1998     

QM/MM connection atoms for the multistate treatment of organic and biological molecules

We present an extension of our semiempirical floating occupation MO-CI approach for the determination of ground and excited state potential energy surfaces of interest in photochemistry. The QM/MM variant of the method, which allows for electrostatic and van der Waals interactions between the QM and MM subsystems, is supplemented with a treatment of covalent interactions based on Antes and Thiels connection atom approach. We concentrate on the correct treatment of electrostatic interactions concerning the connection atom, on the specific requirements for the representation of excited states, and on the transferability of the optimal parameters. We show the viability of the method with four examples of connection atoms: S in a thioether bridge, acylic C, aliphatic C, and N in a peptide. The results obtained with the QM/MM treatment compare well with all-QM results of the same level.