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.     

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.     

The generalized hybrid orbital method for combined quantum mechanical/molecular mechanical calculations: formulation and tests of the analytical derivatives

 Hybrid quantum mechanical (QM) and molecular mechanical (MM) potentials are becoming increasingly important for studying condensed-phase systems but one of the outstanding problems in the field has been how to treat covalent bonds between atoms of the QM and MM regions. Recently, we presented a generalized hybrid orbital (GHO) method that was designed to tackle this problem for hybrid potentials using semiempirical QM methods [Gao et al. (1998) J Phys Chem A 102: 4714–4721]. We tested the method on some small molecules and showed that it performed well when compared to the purely QM or MM potentials. In this article, we describe the formalism for the determination of the GHO energy derivatives and then present the results of more tests aimed at validating the model. These tests, involving the calculation of the proton affinities of some model compounds and a molecular dynamics simulation of a protein, indicate that the GHO method will prove useful for the application of hybrid potentials to solution-phase macromolecular systems. Received: 4 October 1999 / Accepted: 18 December 1999 / Published online: 5 June 2000     

A charge-scaling method to treat solvent in QM/MM simulations

 We present a method to treat the solvent efficiently in hybrid quantum mechanical/molecular mechanical simulations of chemical reactions in enzymes. The method is an adaptation of an approach developed for molecular-mechanical free-energy simulations. The charges of each of the exposed ionizable groups are scaled, and the system is simulated in the presence of a limited number of explicit solvent molecules to obtain a reasonable set of structures. Continuum electrostatics methods are then used to correct the energies. Variations in the procedure are discussed with an emphasis on modifications from the original protocol. We illustrate the method by applying it to the study of a hydrolysis reaction in a highly charged system comprising a complex between the base excision repair enzyme uracil-DNA glycosylase and double-stranded DNA. The resulting adiabatic reaction profile is in good agreement with experiment, in contrast to that obtained without scaling the charges. Received: 5 October 2001 / Accepted: 6 September 2002 / Published online: 28 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: M. Karplus e-mail: marci@tammy.harvard.edu     

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.     

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.     

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     

Transition states from empirical force fields

 This is an overview of the use of empirical force fields in the study of reaction mechanisms. Empirical-valence-bond-type methods (including reactive force field and multiconfigurational molecular mechanics) produce full reaction surfaces by mixing, in the simplest case, known force fields describing reactants and products. The SEAM method instead locates approximate transition structures by energy minimization along the intersection of the component force fields. The transition-state force-field approach (including Q2MM) designs a new force field mimicking the transition structure as an energy minimum. The scope and applicability of the various methods are compared. Received: 17 April 2002 / Accepted: 26 July 2002 / Published online: 4 November 2002 Correspondence to: P.-O. Norrby e-mail: pon@kemi.dtu.dk     

Quantum mechanics and mixed quantum mechanics/molecular mechanics simulations of model nerve agents with acetylcholinesterase

 The accurate modeling of biological processes presents major computational difficulties owing to the inherent complexity of the macromolecular systems of interest. Simulations of biochemical reactivity tend to require highly computationally intensive quantum mechanical methods, but localized chemical effects tend to depend significantly on properties of the extended biological environment – a regime far more readily examined with lower-level classical empirical models. Mixed quantum/classical techniques are gaining in popularity as a means of bridging these competing requirements. Here we present results comparing two quantum mechanics/molecular mechanics implementations (the SIMOMM technique of Gordon et al. as implemented in GAMESS, and the ONIOM technique of Morokuma et al. found in Gaussian 98) as performed on the enzyme acetylcholinesterase and model nerve agents. This work represents part of the initial phase of a DoD HPCMP Challenge project in which we are attempting to reliably characterize the biochemical processes responsible for nerve agent activity and inhibition, thereby allowing predictions on compounds unrelated to those already studied. Received: 10 October 2001 / Accepted: 13 November 2002 / Published online: 1 April 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: M. M. Hurley e-mail: hurley@arl.army.mil     

A thermodynamic and kinetic study of the formation of C<Subscript>20</Subscript> compounds encapsulating H,He and Ne atoms

 Binding energies of helium, neon and atomic hydrogen encapsulated inside a C₂₀ cage were calculated using an ab initio method at the B3LYP/6-31+G⋆ level of theory. The standard equilibrium constants for the reactions of noble-gas atoms going into the C₂₀ molecular cage have also been studied. The transition states for the reactions of C₂₀ with hydrogen and helium were further obtained with an ab initio method at the B3LYP/6-31+G⋆ level and the rate constants were estimated by using conventional transition-state theory. It was found that the hydrogen and helium atoms are extremely difficult to put into the C₂₀ cage. Once inside the cage, a helium atom can hardly get out, while a hydrogen atom can easily escape from the cage. The results are expected to enrich fullerene science and be helpful for fullerene applications such as storage. Received: 2 November 2002 / Accepted: 19 December 2002 / Published online: 30 April 2003 Correspondence to: R. Q. Zhang, e-mail: aprqz@cityu.edu.hk Acknowledgements. The work described in this paper was jointly supported by a grant from the City University of Hong Kong (project no. 7001222) and a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (project no. 9040633/CityU, 1011/01P].     

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.     

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     

Molecular recognition by β-cyclodextrin derivatives: molecular dynamics, free-energy perturbation and molecular mechanics/ Poisson–Boltzmann surface area goals and problems

 The complexation of p-tert-butylphenyl p-tert-butylbenzoate and N-(p-tert-butylphenyl)-p-tert-butylbenzamide with a β-cyclodextrin derivative formed by two cyclodextrin units linked by a disulfide bridge on one of the C6 atoms has been studied by computational methods. The better amide solubility and the better internal interactions of the ester complex explain the experimentally observed better association constant for the ester. The free-energy perturbation methodology and molecular mechanics/Poisson–Boltzmann surface area analysis have been used to explain the problem and to compare the results. Received: 14 April 2002 / Accepted: 11 August 2002 / Published online: 4 November 2002 Acknowledgements. The Kollman group at the University of California San Francisco is gratefully acknowledged for support and encouragement throughout all this study. The authors thank UAB for inland and outland fellowships to I.B.. Financial support was obtained from grant no. PPQ2000-0369 from the “Ministerio de Ciencia y Tecnologia” (Spain). Intensive computations were performed either with the computers of the Kollman group or with those of CESCA-C⁴ (Catalonia, Spain). Correspondence to: C. Jaime e-mail: carlos.jaime@uab.es     

Two-electron distribution functions and intracules

 Two-electron distribution functions and intracules are functions of electronic coordinates and occupy an important, and frequently overlooked, middle ground between the beguiling simplicity of electron densities and the bewildering complexity of wavefunctions. We survey the functions that have been considered by earlier workers and introduce two new ones, the Wigner intracule and the action intracule, that have not previously been discussed. To illustrate their usefulness, we consider the intracules of jellium, a few small atoms and the dissociating hydrogen molecule. Received: 26 July 2002 / Accepted: 20 October 2002 / Published online: 30 January 2003 Correspondence to: P.M.W. Gill e-mail: peter.gill@nott.ac.uk     

Correlating basis sets for the H atom and the alkali-metal atoms from Li to Rb

 Contracted Gaussian-type function sets are developed for correlating p, d, and f functions for a valence electron of the hydrogen atom and alkali-metal atoms from Li to Rb. A segmented contraction scheme is used for its compactness and efficiency. Contraction coefficients and exponents are determined by minimizing the deviation from the K orbitals of the atoms. The present basis sets yield an accuracy comparable to the correlation-consistent basis set for the hydrogen atom and also give a similar high accuracy for the alkali-metal atoms. In the calculations of spectroscopic constants of alkali hydrides, the decontraction of the p function plays an important role, especially for LiH. The contributions of d and f functions are nontrivial for KH and RbH. Received: 6 September 2002 / Accepted: 13 November 2002 / Published online: 19 March 2003 Acknowledgements. This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education of Japan. Correspondence to: T. Noro e-mail: tashi@sci.hokudai.ac.jp     

A DFT study of pyramidalized alkenes: 7-oxasesquinorbornenes and 7,7′-dioxasesquinorbornenes

  DFT calculations of 7′–oxasesquinorbornenes and 7,7′-dioxasesquinorbornenes using the B3LYP/6–31G* method are reported. All the investigated structures (syn- and anti- derivatives) showed significant non-planarity of the central double bond, with the exception of those anti-derivatives possessing symmetrical structures. The influence of the replacement of the methylene groups at position 7- of the norbornene fragment with oxygen and the introduction of second and third (peripheral) double bonds and benzene rings on the molecular and electronic structures of these molecules have also been investigated. Received: 11 November 2002 / Accepted: 6 June 2002 / Published online: 29 April 2003     

Enzyme mechanisms with hybrid quantum and molecular mechanical potentials. I. Theoretical considerations

The application of hybrid quantum mechanical and molecular mechanical (QM/MM) potentials to the study of chemical reactions in enzymes is outlined. The discussion is general and addresses the difficulties encountered in an enzyme QM/MM study. First, general criteria for determining whether a particular enzyme is an appropriate candidate for a QM/MM approach are outlined. Methods for obtaining starting structures are detailed. The importance of choosing appropriate levels of ab initio or semiempirical theory is emphasized. Approaches for interfacing the QM and MM regions are briefly discussed, with greater detail given to describing our CHARMM-GAMESS interface. Techniques for partitioning the system into QM and MM regions are explored. Link atom placement, as distant from reacting atoms as possible within the confines of computational efficiency, is examined in some detail. Methods for determining reaction paths are also discussed. © 1996 John Wiley & Sons, Inc.     

Molecular structure and Bader's theory

 It is shown that a supposed catastrophe of Bader's theory of atoms in molecules, suggested by Cassam-chena? and Jayatilaka [Theor Chem Acc (2001) 105: 213] is merely a consequence of the approximate character of the adiabatic Born–Oppenheimer theory of molecular structure, and that nonadiabatic approaches could be in accordance with Bader's ideas. Received: 4 April 2001 / Accepted: 5 September 2001 / Published online: 3 June 2002     

The dynamo library for molecular simulations using hybrid quantum mechanical and molecular mechanical potentials

The Dynamo module library has been developed for the simulation of molecular systems using hybrid quantum mechanical (QM) and molecular mechanical (MM) potentials. Dynamo is not a program package but is a library of Fortran 90 modules that can be employed by those interested in writing their own programs for performing molecular simulations. The library supports a range of different types of molecular calculation including geometry optimizations, reaction‐path determinations and molecular dynamics and Monte Carlo simulations. This article outlines the general structure and capabilities of the library and describes in detail Dynamo's semiempirical QM/MM hybrid potential. Results are presented to indicate three particular aspects of this implementation—the handling of long‐range nonbonding interactions, the nature of the boundary between the quantum mechanical and molecular mechanical atoms and how to perform path‐integral hybrid‐potential molecular dynamics simulations. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1088–1100, 2000