NMR chemical shifts in the low–pH form of a-chymotrypsin. A QM/MM and ONIOM–NMR study

 The relationship between hydrogen bonding and NMR chemical shifts in the catalytic triad of low-pH α-chymotrypsin is investigated by combined use of the effective fragment potential [(2001) J Phys Chem A 105:293] and ONIOM–NMR [(2000) Chem Phys Lett 317:589] methods. Our study shows that while the His57 N^δ1−H bond is stretched by a relatively modest amount (to about 1.060 ?) this lengthening, combined with the polarization due to the molecular environment, is sufficient to explain the experimentally observed chemical shifts of 18.2 ppm. Furthermore, the unusual down-field shift of H^ɛ1 (9.2 ppm) observed experimentally is reproduced and shown to be induced by interactions with the C=O group of Ser214 as previously postulated. The free-energy cost of moving H^δ1 from His57 to Asp102 is predicted to be 5.5 kcal/mol. Received: 26 September 2001 / Accepted: 6 September 2002 / Published online: 21 January 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 222nd National Meeting of the American Chemical Society, 2001 Correspondence to: J. H. Jensen e-mail: jan-jensen@uiowa.edu Acknowledgements. This work was supported by a Research Innovation Award from the Research Corporation and a type G starter grant from the Petroleum Research Fund. The calculations were performed on IBM RS/6000 workstations obtained through a CRIF grant from the NSF (CHE-9974502) and on supercomputers at the National Center for Supercomputer Applications at Urbana-Champaign. The authors are indebted to Visvaldas Kairys for help with the CHARMM program, and to Daniel Quinn for many helpful discussions.     

Evaluation of an ab initio quantum mechanical/molecular mechanical hybrid-potential link-atom method

 Hybrid potentials have become a common tool in the study of many condensed-phase processes and are the subject of much active research. An important aspect of the formulation of a hybrid potential concerns how to handle covalent bonds between atoms that are described with different potentials and, most notably, those at the interface of the quantum mechanical (QM) and molecular mechanical (MM) regions. Several methods have been proposed to deal with this problem, ranging from the simple link-atom method to more sophisticated hybrid-orbital techniques. Although it has been heavily criticized, the link-atom method has probably been the most widely used in applications, especially with hybrid potentials that use semiempirical QM methods. Our aim in this paper has been to evaluate the link-atom method for ab initio QM/MM hybrid potentials and to compare the results it gives with those of previously published studies. Given its simplicity and robustness, we find that the link-atom method can produce results of comparable accuracy to other methods as long as the charge distribution on the MM atoms at the interface is treated appropriately. Received: 27 September 2002 / Accepted: 21 October 2002 / Published online: 8 January 2003 Correspondence to: M. J. Field e-mail: mjfield@ibs.fr Acknowledgements. The authors thank the Institut de Biologie Structurale – Jean-Pierre Ebel, the Commissariat à l'Energie Atomique and the Centre National de la Recherche Scientifique for support of this work.     

Semiempirical QM/MM potential with simple valence bond (SVB) for enzyme reactions. Application to the nucleophilic addition reaction in haloalkane dehalogenase

 We present a method for the correction of errors in combined QM/MM calculations using a semiempirical Hamiltonian for enzyme reactions. Since semiempirical models can provide a reasonable representation of the general shape of the potential energy surface for chemical reactions, we introduce a simple valence bond-like (SVB) term to correct the energies at critical points on the potential energy surface. The present SVB term is not a stand-alone potential energy function, but it is used purely for introducing small energy corrections to the semiempirical Hamiltonian to achieve the accuracy needed for modeling enzymatic reactions. We show that the present coupled QM-SVB/MM approach can be parameterized to reproduce experimental and ab initio results for model reactions, and have applied the PM3-SVB/MM potential to the nucleophilic addition reaction in haloalkane dehalogenase. In a preliminary energy minimization study, the PM3-SVB/MM results are reasonable, suggesting that it may be used in free energy simulations to assess enzymatic reaction mechanism. Received: 1 November 2001 / Accepted: 6 September 2002 / Published online: 19 February 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 222nd National Meeting of the American Chemical Society, 2001 Correspondence to: Lakshmi S. Devi-Kesavan e-mail: kesavan@chem.umn.edu Acknowledgments. The work is partially supported by the NIH and the NSF.     

Coupled semiempirical quantum mechanics and molecular mechanics (QM/MM) calculations on the aqueous solvation free energies of ionized molecules

The aqueous solvation free energies of ionized molecules were computed using a coupled quantum mechanical and molecular mechanical (QM/MM) model based on the AM1, MNDO, and PM3 semiempirical molecular orbital methods for the solute molecule and the TIP3P molecular mechanics model for liquid water. The present work is an extension of our model for neutral solutes where we assumed that the total free energy is the sum of components derived from the electrostatic/polarization terms in the Hamiltonian plus an empirical “nonpolar” term. The electrostatic/polarization contributions to the solvation free energies were computed using molecular dynamics (MD) simulation and thermodynamic integration techniques, while the nonpolar contributions were taken from the literature. The contribution to the electrostatic/polarization component of the free energy due to nonbonded interactions outside the cutoff radii used in the MD simulations was approximated by a Born solvation term. The experimental free energies were reproduced satisfactorily using variational parameters from the vdW terms as in the original model, in addition to a parameter from the one-electron integral terms. The new one-electron parameter was required to account for the short-range effects of overlapping atomic charge densities. The radial distribution functions obtained from the MD simulations showed the expected H-bonded structures between the ionized solute molecule and solvent molecules. We also obtained satisfactory results by neglecting both the empirical nonpolar term and the electronic polarization of the solute, i.e., by implementing a nonpolarization model. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1028–1038, 1999     

Investigation of the S<Subscript>0</Subscript>S<Subscript>1</Subscript> excitation in bacteriorhodopsin with the ONIOM(MO:MM) hybrid method

 We have investigated the S₀ and S₁ electronic states in bacteriorhodopsin using a variety of QM/MM levels. The decomposition of the calculated excitation energies into electronic and electrostatic components shows that the interaction of the chromophore with the protein electric field increases the excitation energy, while polarization effects are negligible. Therefore, the experimentally observed reduction in excitation energy from solution phase to protein environment (the Opsin shift) does not come from the electrostatic interaction with the protein environment, but from either the interaction ofthe chromophore with the solvent or counter ion, or structural effects. Our high-level ONIOM(TD– B3LYP:Amber) calculation predicts the excitation energy within 8 kcal/mol from experiment, the discrepancy probably being caused by the neglect of polarization of the protein environment. In addition, we have shown that the level of optimization is extremely critical for the calculation of accurate excitation energies in bacteriorhodopsin. Received: 13 October 2001 / Accepted: 6 September 2002 / Published online: 3 February 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 222nd National Meeting of the American Chemical Society, 2001 Correspondence to: K. Morokuma e-mail: morokuma@emory.edu     

Exploring the quantum mechanical/molecular mechanical replica path method: a pathway optimization of the chorismate to prephenate Claisen rearrangement catalyzed by chorismate mutase

 A replica path method has been developed and extended for use in complex systems involving hybrid quantum/classical (quantum mechanical/molecular mechanical) coupled potentials. This method involves the definition of a reaction path via replication of a set of macromolecular atoms. An “important” subset of these replicated atoms is restrained with a penalty function based on weighted root-mean-square rotation/translation best-fit distances between adjacent (i±1) and next adjacent (i±2) pathway steps. An independent subset of the replicated atoms may be treated quantum mechanically using the computational engine Gamess-UK. This treatment can be performed in a highly parallel manner in which many dozens of processors can be efficiently employed. Computed forces may be projected onto a reference pathway and integrated to yield a potential of mean force (PMF). This PMF, which does not suffer from large errors associated with calculated potential-energy differences, is extremely advantageous. As an example, the QM/MM replica path method is applied to the study of the Claisen rearrangement of chorismate to prephenate which is catalyzed by the Bacillus subtilis isolated, chorismate mutase. Results of the QM/MM pathway minimizations yielded an activation enthalpy ΔH ^†† of 14.9 kcal/mol and a reaction enthalpy of −19.5 kcal/mol at the B3LYP/6-31G(d) level of theory. The resultant pathway was compared and contrasted with one obtained using a forced transition approach based on a reaction coordinate constrained repeated walk procedure (ΔH ^†† =20.1 kcal/mol, ΔH _rxn = −20.1 kcal/mol, RHF/4-31G). The optimized replica path results compare favorably to the experimental activation enthalpy of 12.7±0.4 kcal/mol. Received: 16 December 2001 / Accepted: 6 September 2002 / Published online: 8 April 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 22nd National Meeting of the American Chemical Society, 2001. Correspondence to: H.L. Woodcock e-mail: hlwood@ccqc.uga.edu Acknowledgements. The authors thank Eric Billings, Xiongwu Wu, and Stephen Bogusz for helpful discussions and related work. The authors also show grateful appreciation to The National Institutes of Health and The National Science Foundation for support of the current research.     

A new QM/MM method oriented to the study of ionic liquids

The interest on room temperature ionic liquids has grown in the last decades because of their use as all‐purpose solvent and their low environmental impact. In the present work, a new theoretical procedure is developed to study pure ionic liquids within the framework of the quantum mechanics/molecular mechanics method. Each type of ion (cation or anion) is considered as an independent entity quantum mechanically described that follows a differentiated path in the liquid. The method permits, through an iterative procedure, the full coupling between the polarized charge distribution of the ions and the liquid structure around them. The procedure has been tested with 1‐ethyl‐3‐methylimidazolium tetrafluoroborate. It was found that, similar to non‐polar liquids and as a consequence of the low value of the reaction field, the cation and anion charge distributions are hardly polarized by the rest of molecules in the liquid. Their structure is characterized by an alternance between anion and cation shells as evidenced by the coincidence of the first maximum of the anion–anion and cation–cation radial distribution functions with the first minimum of the anion‐cation. Some degree of stacking between the cations is also found. © 2015 Wiley Periodicals, Inc.     

Comparison of solvent reaction field representations

 Alternative ways are examined for representing a reaction field to treat the important effects of long-range electrostatic interaction with a solvent in electronic structure calculations on the properties of a solute. Several extant boundary element methods for approximate representation of the solvent reaction field in terms of surface charge distributions are considered, and analogous new methods for approximate representation in terms of surface dipole distributions are introduced. Illustrative computational results are presented on representative small neutral and ionic solutes to evaluate the relative accuracy of various methods. Received: 2 July 2001 / Accepted: 10 September 2001 / Published online: 19 December 2001     

Recent advances in quantum mechanical/molecular mechanical calculations of enzyme catalysis: hydrogen tunnelling in liver alcohol dehydrogenase and inhibition of elastase by α-ketoheterocycles

 Hybrid quantum mechanical (QM)/molecular mechanical (MM) calculations are used to study two aspects of enzyme catalysis, Kinetic isotope effects associated with the hydride ion transfer step in the reduction of benzyl alcohol by liver alcohol dehydrogenase are studied by employing variational transition-state theory and optimised multidimensional tunnelling. With the smaller QM region, described at the Hartree–Fock ab initio level, together with a parameterised zinc atom charge, good agreement with experiment is obtained. A comparison is made with the proton transfer in methylamine dehydrogenase. The origin of the large range in pharmacological activity shown by a series of α-ketoheterocycle inhibitors of the serine protease, elastase, is investigated by both force field and QM/MM calculations. Both models point to two different inhibition mechanisms being operative. Initial QM/MM calculations suggest that these are binding, and reaction to form a tetrahedral intermediate, the latter process occurring for only the more potent set of inhibitors. Recieved 3 October 2001 / Accepted: 6 September 2002 / Published online: 31 January 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 222nd National Meeting of the American Chemical Society, 2001 Correspondence to: I. H. Hillier Acknowledgements. We thank EPSRC and BBSRC for support of the research and D.G. Truhlar for the use of the POLYRATE code.     

New QM/MM implementation of the DFTB3 method in the gromacs package

The approximate density‐functional tight‐binding theory method DFTB3 has been implemented in the quantum mechanics/molecular mechanics (QM/MM) framework of the Gromacs molecular simulation package. We show that the efficient smooth particle–mesh Ewald implementation of Gromacs extends to the calculation of QM/MM electrostatic interactions. Further, we make use of the various free‐energy functionalities provided by Gromacs and the PLUMED plugin. We exploit the versatility and performance of the current framework in three typical applications of QM/MM methods to solve biophysical problems: (i) ultrafast proton transfer in malonaldehyde, (ii) conformation of the alanine dipeptide, and (iii) electron‐induced repair of a DNA lesion. Also discussed is the further development of the framework, regarding mostly the options for parallelization. © 2015 Wiley Periodicals, Inc.     

Parameterization of semiempirical methods to treat nucleophilic attacks to biological phosphates: AM1/d parameters for phosphorus

 This paper reports a new AM1/d model for phosphorus that can be used to model nucleophilic attack of phosphates relevant for biological phosphate hydrolysis reactions. The parameters were derived from a quantum dataset calculated with hybrid density-functional theory [B3LYP/6-311++G(3df,2p)//B3LYP/6-31++G(d,p)] of phosphates and phosphoranes in various charge states, and on transitions states for nucleophilic attacks. A suite of non-linear optimization methods is outlined for semiempirical parameter development based on integrated evolutionary (genetic), Monte Carlo simulated annealing and direction set minimization algorithms. The performance of the new AM1/d model and the standard AM1 and MNDO/d models are compared with the density-functional results. The results demonstrate that the strategy of developing semiempirical parameters specific for biological reactions offers considerable promise for application to large-scale biological problems. Received: 15 January 2002 / Accepted: 6 September 2002 / Published online: 28 March 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 222nd National Meeting of the American Chemical Society, 2001 Correspondence to: D.M. York e-mail: york@chem.umn.edu Acknowledgements. D.M.Y. is grateful for financial support provided by the National Institutes of Health (grant 1R01-GM62248-01A1) and the Donors of The Petroleum Research Fund, administered by the American Chemical Society, and the Minnesota Supercomputing Institute through a 6-month research scholar award (X.L.). Computational resources were provided by the Minnesota Supercomputing Institute.     

GTKDynamo: A PyMOL plug‐in for QC/MM hybrid potential simulations

Hybrid quantum chemical/molecular mechanical (QCMM) potentials are very powerful tools for molecular simulation. They are especially useful for studying processes in condensed phase systems, such as chemical reactions that involve a relatively localized change in electronic structure and where the surrounding environment contributes to these changes but can be represented with more computationally efficient functional forms. Despite their utility, however, these potentials are not always straightforward to apply since the extent of significant electronic structure changes occurring in the condensed phase process may not be intuitively obvious. To facilitate their use, we have developed an open‐source graphical plug‐in, GTKDynamo that links the PyMOL visualization program and the pDynamo QC/MM simulation library. This article describes the implementation of GTKDynamo and its capabilities and illustrates its application to QC/MM simulations. © 2013 Wiley Periodicals, Inc.     

The adaptive buffered force QM/MM method in the CP2K and AMBER software packages

The implementation and validation of the adaptive buffered force (AdBF) quantum‐mechanics/molecular‐mechanics (QM/MM) method in two popular packages, CP2K and AMBER are presented. The implementations build on the existing QM/MM functionality in each code, extending it to allow for redefinition of the QM and MM regions during the simulation and reducing QM‐MM interface errors by discarding forces near the boundary according to the buffered force‐mixing approach. New adaptive thermostats, needed by force‐mixing methods, are also implemented. Different variants of the method are benchmarked by simulating the structure of bulk water, water autoprotolysis in the presence of zinc and dimethyl‐phosphate hydrolysis using various semiempirical Hamiltonians and density functional theory as the QM model. It is shown that with suitable parameters, based on force convergence tests, the AdBF QM/MM scheme can provide an accurate approximation of the structure in the dynamical QM region matching the corresponding fully QM simulations, as well as reproducing the correct energetics in all cases. Adaptive unbuffered force‐mixing and adaptive conventional QM/MM methods also provide reasonable results for some systems, but are more likely to suffer from instabilities and inaccuracies. © 2015 The Authors. Journal of Computational Chemistry Published by 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.     

The search for stationary points on a quantum mechanical/molecular mechanical potential-energy surface

 We propose a methodology to locate stationary points on a quantum mechanical/molecular mechanical potential-energy surface. This algorithm is based on a suitable approximation of an initial full Hessian matrix, either a modified Broyden–Fletcher–Goldfarg–Shanno or a Powell update formula for the location of, respectively, a minimum or a transition state, and the so-called rational function optimization. The latter avoids the Hessian matrix inversion required by a quasi-Newton–Raphson method. Some examples are presented and analyzed. Received: 16 July 2001 / Accepted: 9 October 2001 / Published online: 9 January 2002     

Effective modeling of intrinsic and environmental effects on the structure and electron plaramagnetic resonance parameters of nitroxides by an integrated quantum mechanical/molecular mechanics/polarizable continuum model approach

 Experimental and density functional theory geometries have been used to extend the AMBER force field to nitroxides. An optimum set of transferable atomic charges for the calculation of electrostatic interactions both in vacuo and in aqueous solution has been obtained by averaging the charges obtained by a restrained electrostatic potential fitting of representative compounds. Besides reliable structural data, our implementation allows the computation of accurate spectromagnetic properties by single-point B3LYP computations on geometries optimized at the AMBER level. Solvent shifts in aqueous solution can be reproduced quantitatively by a mixed model in which specific solvent effects are described by two water molecules strongly coordinated to the nitroxide oxygen, while bulk effects are described by the polarizable continuum model. Received: 17 September 1999 / Accepted: 3 February 2000 / Published online: 29 June 2000     

A proposed modification of CBS-4M model chemistry for application to molecules of increasing molecular size

 In order to calculate more accurately the enthalpies of formation, ΔH _f°(298 K), for large molecules using the CBS-4M method, a new formulation of the empirical higher-level correction to the energy is proposed: ΔE=a|S|² _{i i} I _{i i} +b(n _α+n _β)+cΔ<S ²>+Σn _i d _{i .} The new methodology (CBS-4MB) applied to a set of 114 molecules of different size significantly decreases the mean absolute deviation from 3.78 to 2.06 kcal/mol. Received: 7 February 2001 / Accepted: 5 April 2001 / Published online: 13 June 2001