Effective Fragment Potential Research Articles

Intermolecular interactions in solution: elucidating the influence of the solvent.

A new approach for the analysis of intermolecular interactions in a solution is proposed. The changes in the interaction energy components due to the solvent effects are estimated on the basis of the interaction energy calculated in the presence of the electric field induced in a polarizable medium, or in the field of the effective fragment potentials. Obtained results indicate a significant increase in stabilization resulting from electrostatic interactions as a result of the cooperative interactions between interacting subsystems and solvent molecules.

Modeling of serine protease prototype reactions with the flexible effective fragment potential quantum mechanical/molecular mechanical method

A complete cycle of chemical transformations for the serine protease prototype reaction is modeled following calculations with the flexible effective fragment quantum mechanical/molecular mechanical (QM/MM) method. The initial molecular model is based on the crystal structure of the trypsin–bovine pancreatic trypsin inhibitor complex including all atoms of the enzyme within approximately 15–18 A of the oxygen center Oγ of the catalytic serine residue. Several selections of the QM/MM partitioning are considered. Fractions of the side chains of the residues from the catalytic triad (serine, histidine and aspartic acid) and a central part of a model substrate around the C–N bond to be cleaved are included into the QM subsystem. The remaining part, or the MM subsystem, is represented by flexible chains of small effective fragments, whose potentials explicitly contribute to the Hamiltonian of the QM part, but the corresponding fragment–fragment interactions are described by the MM force fields. The QM/MM boundaries are extended over the Cα–Cβ bonds of the peptides assigned to the QM subsystem in the enzyme, C–C and C–N bonds in model substrates. Multiple geometry optimizations have been performed by using the RHF/6-31G method in the QM part and OPLSAA or AMBER sets of MM parameters, resulting in a series of stationary points on the complex potential-energy surfaces. All structures generally accepted for the serine protease catalytic cycle have been located. Energies at the stationary points found have been recomputed at the MP2/6-31+G* level for the QM part in the protein environment. Structural changes along the reaction path are analyzed with special attention to hydrogen-bonding networks. In the case of a model substrate selected as a short peptide CH3(NHCO-CH2)2 – HN–CO–(CH2–NHCO)CH3 the computed energy profile for the acylation step shows too high activation energy barriers. The energetics of this rate-limiting step is considerably improved, if more realistic model for the substrate is considered, following the motifs of the ThrI11–GlyI12–ProI13-–CysI14–LysI15–AlaI16–ArgI17–IleI18–IleI19 sequence of the bovine pancreatic trypsin inhibitor.

Structures of the Peptide–Water Complexes Studied by the Hybrid Quantum Mechanical—Molecular Mechanical (QM/MM) Technique

Applications of a new approach to the hybrid quantum mechanical and molecular mechanical (QM/MM) theory based on the effective fragment potential technique to calculations of the structures of the peptide—water complexes are described. Our approach assumes that the MM subsystem is viewed as a flexible composition of effective fragments, while fragment–fragment interactions are replaced by MM force fields. In this work, the QM subsystem is composed of water molecules and the MM part refers to peptides. Different isomers of the hydrogen-bonded complex of the dipeptide N-acetyl-L-alanine N′-methylamide (AAMA) with four water molecules are considered, and the results of QM/MM calculations are compared to experimental data and to the results of the density functional theory (DFT) treatment. The properties of water chains inside polypeptide tubes, modeling proton wires inside ionic channels, are described.

Predicting shielding constants in solution using gauge invariant atomic orbital theory and the effective fragment potential method.

A method to approximate ab initio shielding constants is presented, in which the ab initio density matrix is replaced in the gauge invariant atomic orbital formalism with the density matrix resulting from an effective fragment potential calculation. The resulting first-order density matrix is then iterated to self-consistency. The method is compared with fully ab initio gauge invariant atomic orbital restricted Hartree-Fock calculations on hydrogen chloride, water, and ammonia solutes with up to nine solvent water molecules using the 6-31G, 6-31G(d,p), and 6-31+G(d,p) basis sets. Using the 6-31G(d,p) basis sets, the average of the average absolute deviations for the three environments tested is 0.34 ppm. This is sufficiently accurate to allow for the identification of specific (1)H nuclei in a solvated molecule when the chemical shift between nuclei is not less than 1 ppm. The success of the method at this level of approximation is due to a cancellation of errors between the paramagnetic and diamagnetic terms of the shielding constant: the diamagnetic term is underestimated by roughly the same amount that the paramagnetic term is overestimated.

The Application of the Effective Fragment Potential Method to Molecular Anion Solvation: A Study of Ten Oxyanion−Water Clusters, A-(H2O)1-4

The performance of the effective fragment potential (EFP) method, a quantum mechanical-molecular mechanical (QM-MM) method, to reproduce fully quantum mechanical results has been investigated. The enthalpies of hydration for 10 oxyanions (ClO4-, HSO4-, NO3-, H2PO4-, HCO3-, HCO2-, SO42-, HPO42-, CO32-, and PO43-) by one to four water molecules were studied. For monohydrate systems exhibiting small to moderate amounts of charge transfer (ClO4-, HSO4-, NO3-, H2PO4-, HCO3-, and HCO2-), the EFP method reproduces Hartree−Fock (HF) differential enthalpies of hydration remarkably well (mean difference = −0.1 and standard deviation = 0.9 kcal/mol). The EFP and HF calculations also successfully reproduce the available experimental data (EFP: mean difference = 2.0 and standard deviation = 0.8 kcal/mol; HF: mean difference = 1.8 and standard deviation = 1.0 kcal/mol). MP2 calculations show only a slight improvement in agreement with experiment over the HF calculations, indicating a small electron correlation effect...

QM/MM modeling of the glutathione–hydroxymethyl radical reaction in water

The reactions of hydroxymethyl radical ˙CH2OH with glutathione tripeptide GSH and with methylthiol CH3SH in water are modeled by using the effective fragment potential (EFP) based quantum mechanical–molecular mechanical (QM/MM) methods. In the case of glutathione, the reactive part of the cysteine residue of the tripeptide and the hydroxymethyl moiety are included to the quantum part. The remaining part of GSH assigned to the MM subsystem is represented by flexible chains of small effective fragments. The energy profiles for the condensed phase reactions have been constructed by using the transition state structure of the gas-phase reference reaction of hydroxymethyl radical ˙CH2OH with methylthiol CH3SH. Optimization of geometry parameters of the systems, including coordinates of environmental particles, leads to the structures at the top of the barrier, as well as for reagent interaction complexes and product interaction complexes. The energy difference between the top of the barrier and the reagent interaction complex is considered as a measure of activation energy, which allows us to treat all systems at the uniform level. According to simulation results, the activation barrier for the aqueous reaction of hydroxymethyl radical with methylthiol should be slightly higher, and for the aqueous reaction of hydroxymethyl radical with glutathione in the lowest energy conformation should be slightly lower than that of the reference gas-phase reaction. A conclusion about higher activation barrier for aqueous reaction ˙CH2OH+CH3SH in comparison to the gas-phase process, obtained here within the supermolecular approach, is consistent with the literature results of solvation models. It is shown that conformations of peptide chain of glutathione may modify the gas-phase reaction energy profile of the reacting species to a larger extent than the influence of water molecules. The role of the peptide chain seems to be to provide either beneficial or unfavorable arrangement of the reagents in the interaction complex.

Nitrite ion formation: Nonempirical simulation in terms of cluster model

AbstractNeutral and negatively charged nitrogen dioxide molecule either individual or involved in a complex cluster with up to 50 water molecules is nonempirically simulated in the second order of the Møller–Plesset perturbation theory with the unrestricted Hartree–Fock function with the use of atomic basis functions of the 6‐31++G** set and effective fragment potentials for a part of water molecules. The structures corresponding to the local minima of the potential energy surfaces of neutral and anionic clusters are considered, and their dissociation energies are estimated. The geometric parameters of the cavities formed around nitrogen dioxide and its anion in the H‐bond network of water clusters are compared. The vertical electron detachment energies of the anions and the electron affinities of the parent neutral complex clusters depending on the number of water molecules involved are used for estimating the corresponding energetic characteristics of infinitely diluted aqueous nitrogen dioxide systems. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Anion−Water Clusters A-(H2O)1-6, A = OH, F, SH, Cl, and Br. An Effective Fragment Potential Test Case

The ability of the effective fragment potential (EFP) method, a quantum mechanical/molecular mechanical (QM/MM) approach, to describe the hydration of five simple anions (OH-, F-, SH-, Cl-, and Br-) by one to six water molecules was investigated. The results were compared with experimental data and ab initio calculations: Hartree−Fock (HF) and second-order Moller−Plesset (MP2). With the exception of the addition of the first water molecule, the EFP method was able to reproduce both the experimental and HF differential enthalpies of hydration. None of the three levels of theory reliably reproduced the experimental total enthalpies of hydration, and the EFP and HF results were found to be in poor agreement. The charge-transfer/exchange-repulsion component of the model appears to be inadequate in describing systems exhibiting large amounts of charge transfer (e.g., the OH- and F- systems). Two model chemistries based upon the EFP method were also examined. While the use of HF and MP2 single-point energy cal...

Flexible effective fragment QM/MM method: Validation through the challenging tests

A new version of the QM/MM method, which is based on the effective fragment potential (EFP) methodology [Gordon, M. et al., J Phys Chem A 2001, 105, 293] but allows flexible fragments, is verified through calculations of model molecular systems suggested by different authors as challenging tests for QM/MM approaches. For each example, the results of QM/MM calculations for a partitioned system are compared to the results of an all-electron ab initio quantum chemical study of the entire system. In each case we were able to achieve approximately similar or better accuracy of the QM/MM results compared to those described in original publications. In all calculations we kept the same set of parameters of our QM/MM scheme. A new test example is considered when calculating the potential of internal rotation in the histidine dipeptide around the C(alpha)bond;C(beta) side chain bond.

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 Nδ1−H bond is stretched by a relatively modest amount (to about 1.060 A) 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 Hɛ1 (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 Hδ1 from His57 to Asp102 is predicted to be 5.5 kcal/mol.

Density functional theory based effective fragment potential method

The effective fragment potential (EFP) method, is a discrete method for the treatment of solvent effects, originally formulated using Hartree–Fock (HF) theory. Here, a density functional theory (DFT) based implementation of the EFP method is presented for water as a solvent. In developing the DFT based EFP method for water, all molecular properties (multipole moments, polarizability tensors, screening parameters, and fitting parameters for the exchange repulsion potential) are recalculated and optimized, using the B3LYP functional. Initial tests for water dimer, small water clusters, and the glycine–water system show good agreement with ab initio and DFT calculations. Several computed properties exhibit marked improvement relative to the Hartree–Fock based method, presumably because the DFT based method includes some dynamic electron correlation through the corresponding functional.

Continuum solvation of large molecules described by QM/MM: a semi-iterative implementation of the PCM/EFP interface

The direct inversion of the iterative subspace (DIIS) solution to the iterative integral equation formalism polarized continuum model (IEF–PCM, 2001 Theor. Chem. Acc. 105:1186) is applied to the effective fragment potential IEF–PCM interface (2002 J Chem Phys 116:5023). Compared to a direct matrix-inversion solution, the DIIS–PCM is up to an order of magnitude more efficient both in computing time and memory requirements for large systems. Multipole treatments of long-range electrostatic interactions further reduce the computing time by up to 50%. All the CPU intensive computations are parallelized. The data presented in this paper demonstrate that use of the iterative IEF–PCM is an efficient way to model bulk solvation of large biomolecules described by QM/MM.

Formation of Alkali Metal/Alkaline Earth Cation Water Clusters, M(H2O)1-6, M = Li+, Na+, K+, Mg2+, and Ca2+: An Effective Fragment Potential (EFP) Case Study

To assess the ability of the effective fragment potential (EFP) method to describe the hydration of simple cations, calculations have been carried out on alkali metal (Li+, Na+, and K+)/alkaline earth (Mg2+ and Ca2+) cation water clusters containing up to six water molecules. The restricted Hartree−Fock (RHF) and second-order Moller−Plesset (MP2) perturbation methods have also been employed in the study. It is shown that the EFP method is capable of accurately reproducing RHF differential standard enthalpies of hydration for the alkali metal and calcium cation water systems. The EFP method also reproduces experimental differential and total standard enthalpies of hydration for the alkali metal cation water complexes. Good agreement is also found among the EFP and ab initio levels of theory for the enthalpies of the calcium cation water clusters. Possible reasons for discrepancies between the EFP results and those obtained at the ab initio levels for the structures of the Na+(H2O)1-6 and Mg2+(H2O)1-6 clust...

Modeling of Biomolecular Systems with the Quantum Mechanical and Molecular Mechanical Method Based on the Effective Fragment Potential Technique: Proposal of Flexible Fragments

Development and applications of a new approach to hybrid quantum mechanical and molecular mechanical (QM/MM) theory based on the effective fragment potential (EFP) technique for modeling properties and reactivity of large molecular systems of biochemical significance are described. It is shown that a restriction of frozen internal coordinates of effective fragments in the original formulation of the theory (Gordon, M. S.; Freitag, M. A.; Bandyopadhyay, P.; Jensen, J. H.; Kairys, V.; Stevens, W. J. J. Phys. Chem. A 2001, 105, 293) can be removed by introducing a set of small EFs and replacing the EFP−EFP interactions by the customary MM force fields. The concept of effective fragments is also utilized to solve the QM/MM boundary problem across covalent bonds. The buffer fragment, which is common for both subsystems, is introduced and treated specially when energy and energy gradients are computed. An analysis of conformations of dipeptide−water complexes, as well as of dipepties with His and Lys residues, confirms the reliability of the theory. By using the Hartree−Fock and MP2 quantum chemistry methods with the OPLS-AA molecular mechanical force fields, we calculated the energy difference between the enzyme−substrate complex and the first tetrahedral intermediate for the model active site of the serine protease catalytic system. In another example, the multiconfigurational complete active space self-consistent field (CASSCF) method was used to model the homolytic dissociation of the peptide helix over the central C−N bonds. Finally, the potentials of internal rotation of the water dimer considered as a part of the water wire inside a polyglycine analogue of the ion channel gramicidin A were computed. In all cases, an importance of the peptide environment from MM subsystems on the computed properties of the quantum parts is demonstrated.

Computational studies of aliphatic amine basicity.

Computational studies have been used to examine the structural and energetic effects of adding small numbers of water molecules to ammonia, methylamine, dimethylamine, and trimethylamine, and their respective ammoniums ions using the effective fragment potential method. Distinct structural effects with only a few fragment water molecules are revealed. The complexity of structures increases with the number of water fragments with the water fragments forming complex networks. Structural and energetic effects are used to probe the so-called anomalous basicity effect of ammonia and the methylamines on going from the gas phase to aqueous solution.

Partial Hessian vibrational analysis: the localization of the molecular vibrational energy and entropy

The partial Hessian vibrational analysis (PHVA), in which only a subblock of the Hesssian matrix is diagonalized to yield vibrational frequencies for partially optimized systems, is extended to the calculation of vibrational enthalpy and entropy changes for chemical reactions. The utility of this method is demonstrated for various deprotonation reactions by reproducing full HVA values to within 0.1–0.4 kcal/mol, depending on the number atoms included in the PHVA. When combined with the hybrid effective fragment potential method [Gordon MS, et al. (2001) J Phys Chem A 105:293–307], the PHVA method can provide (harmonic) free-energy changes for localized chemical reactions in very large systems.

An integrated effective fragment—polarizable continuum approach to solvation: Theory and application to glycine

A new discrete/continuum solvation model has been developed by combining the effective fragment potential (EFP) for the discrete part and the polarizable continuum model (PCM) for the continuum part. The usefulness of this model is demonstrated by applying it to the calculation of the relative energies of the neutral and zwitterionic forms of glycine. These calculations were performed by treating glycine with ab initio wave functions. Water clusters were treated with both ab initio and EFP methods for comparison purposes, and the effect of the continuum was accounted for by the PCM model. The energy barrier connecting the zwitterionic and neutral three-water clusters was also examined. The computationally efficient EFP/PCM model gives results that are in close agreement with the much more expensive full ab initio/PCM calculation. The use of methods that account for electron correlation is necessary to obtain accurate relative energies for the isomers of glycine.

The Prediction of Protein pKa's Using QM/MM: The pKa of Lysine 55 in Turkey Ovomucoid Third Domain

A computational methodology for pKa predictions of small molecules based on an ab initio quantum mechanics (QM) description of the acid and a linearized Poisson−Boltzmann equation (LPBE) description of bulk solvation using the polarized continuum method is presented. This QM/LPBE method is capable of reproducing the pKa's of several functional groups found in amino acid residues with a root-mean-square deviation from experiment of 0.6 pH units. The practical applicability of the QM/LPBE method is extended to proteins by using a QM description of the ionizable residue and an effective fragment potential (MM) description of the rest of the protein. This QM/MM/LPBE method is used to predict a pKa of the Lys55 residue in turkey ovomucoid third domain of 11.0, which is in good agreement with the experimental value of 11.1.

On the Origin of Potential Barrier for the Reaction OH- + CO2 → HCO3- in Water: Studies by Using Continuum and Cluster Solvation Methods

The energy profiles for the reaction OH- + CO2 → HCO3- are analyzed following the results of calculations carried out using both a continuum solvation model and a cluster approach. The minimum energy path, computed with the quantum chemistry LMP2 and B3LYP approximations, corresponds to the activation-less process in the gas phase but shows a barrier on the way from the reactants to the product in the dielectric continuum medium. In the cluster approach, the reacting species were completely surrounded by 30 water molecules, each considered as an effective fragment potential (EFP) acting on the quantum system. Positions of all particles were optimized along the reaction coordinate in this quantum mechanical−molecular mechanical (QM/MM) approximation. The energy profile obtained with the QM/MM(EFP) approach is in remarkable agreement with the results of the continuum model, showing the barrier in the same region. An analysis of the arrangements of the water molecules around the reacting species, as well as ...

Energy profiles for the rate-limiting stage of the serine protease prototype reaction

The energy profiles of reaction, modeling the rate-limiting stage of serine protease catalyzed transformations, have been computed by quantum chemistry methods. The model includes fragments of the residues of the catalytic triad (serine, histidine, and aspartic acid), two water molecules as an oxyanion hole, represented by effective fragment potentials, and a formamide molecule as a substrate. Geometry optimizations have been performed along the reaction coordinate, chosen as the distance between oxygen of serine and carbon of substrate, by using the Hartree–Fock method. The density functional theory B3LYP/6-31+G(d,p) calculations have been employed to recalculate energies along the reaction path in the gas phase and in the dielectric environment. The computed barrier heights are fairly consistent with the data cited in the literature. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem 88: 34–40, 2002