Ab initio quantum mechanical/molecular mechanical molecular dynamics simulation of enzyme catalysis: the case of histone lysine methyltransferase SET7/9

To elucidate enzyme catalysis through computer simulation, a prerequisite is to reliably compute free energy barriers for both enzyme and solution reactions. By employing on-the-fly Born-Oppenheimer molecular dynamics simulations with the ab initio quantum mechanical/molecular mechanical approach and the umbrella sampling method, we have determined free energy profiles for the methyl-transfer reaction catalyzed by the histone lysine methyltransferase SET7/9 and its corresponding uncatalyzed reaction in aqueous solution, respectively. Our calculated activation free energy barrier for the enzyme catalyzed reaction is 22.5 kcal/mol, which agrees very well with the experimental value of 20.9 kcal/mol. The difference in potential of mean force between a corresponding prereaction state and the transition state for the solution reaction is computed to be 30.9 kcal/mol. Thus, our simulations indicate that the enzyme SET7/9 plays an essential catalytic role in significantly lowering the barrier for the methyl-transfer reaction step. For the reaction in solution, it is found that the hydrogen bond network near the reaction center undergoes a significant change, and there is a strong shift in electrostatic field from the prereaction state to the transition state, whereas for the enzyme reaction, such an effect is much smaller and the enzyme SET7/9 is found to provide a preorganized electrostatic environment to facilitate the methyl-transfer reaction. Meanwhile, we find that the transition state in the enzyme reaction is a little more dissociative than that in solution.     

Ab initio and post-ab initio quantum chemical study of the heme spin states in electron transfer reactions

Quantum-chemical calculations of neutral and charged ironporphyrin (FeP, FeP⁺¹ and FeP⁻) systems were performed using B3LYP and MP2 methods. It was shown that all ground states of FeP (S = 1), FeP⁺¹ (S = 3/2) and FeP⁻ (S = 1/2) systems have C_2v symmetry. During the first step of electron transfer process an electron goes to β-LUMO − 1 Fe d_yz-orbital of FeP⁺¹. The second electron goes to β-LUMO of FeP which is attributed to π-system of porphyrin ring. The 3s- and 3p-orbitals do not play a significant role in the electron transfer process. The ability of FeP⁻¹ system to form π-dative chemical bond is low. The formation of π–π-complexes is preferable.     

Ab initio molecular dynamics simulation of ionic liquids

Ab initio Car-Parinnello molecular dynamics is used to simulate the structure and the dynamics of 1-butyl-3-methylimidazolium iodide ([bmim]I) ionic liquid at 300 K. Site-site pair correlation functions reveal that the anion has a strong interaction with any three C-H's of the imidazolium ring. The ring bends over and wraps around the anion such that the two nitrogen atoms take a distance to the anion. Electron donating butyl group contributes the electronic polarization in addition to geometrical (out-of-plane) polarization of the ring due to the liquid environment. This facilitates bending of the ring along the axis passing through nitrogen atoms. The average bending angle depends largely on the alkyl chain length and slightly on the anion type. Redistribution of electron density over the ring caused by the electron donating alkyl group provides additional independent evidence to the instability of lattice structure, hence the low melting point of the ionic liquid. Simulated viscosity and diffusion coefficients of [bmim]I are in quite agreement with the experiments.     

Ab initio investigation of benzene clusters: molecular tailoring approach

An exhaustive study on the clusters of benzene (Bz)(n), n = 2-8, at MP2/6-31++G(??) level of theory is reported. The relative strengths of CH-π and π-π interactions in these aggregates are examined, which eventually govern the pattern of cluster formation. A linear scaling method, viz., molecular tailoring approach (MTA), is efficiently employed for studying the energetics and growth patterns of benzene clusters consisting up to eight benzene (Bz) units. Accuracy of MTA-based calculations is appraised by performing the corresponding standard calculations wherever possible, i.e., up to tetramers. For benzene tetramers, the error introduced in energy is of the order of 0.1 mH (～0.06 kcal/mol). Although for higher clusters the error may build up, further corrections based on many-body interaction energy analysis substantially reduce the error in the MTA-estimate. This is demonstrated for a prototypical case of benzene hexamer. A systematic way of building up a cluster of n monomers (n-mer) which employs molecular electrostatic potential of an (n-1)-mer is illustrated. The trends obtained using MTA method are essentially identical to those of the standard methods in terms of structure and energy. In summary, this study clearly brings out the possibility of effecting such large calculations, which are not possible conventionally, by the use of MTA without a significant loss of accuracy.     

Improved pseudobonds for combined ab initio quantum mechanical/molecular mechanical methods

The pseudobond approach offers a smooth connection at the quantum mechanical/molecular mechanical interface which passes through covalent bonds. It replaces the boundary atom of the environment part with a seven-valence-electron atom to form a pseudobond with the boundary atom of the active part [Y. Zhang, T. S. Lee, and W. Yang, J. Chem. Phys. 110, 46 (1999)]. In its original formulation, the seven-valence-electron boundary atom has the basis set of fluorine and a parametrized effective core potential. Up to now, only the Cps(sp3)-C(sp3) pseudobond has been successfully developed; thus in the case of proteins, it can only be used to cut the protein side chains. Here we employ a different formulation to construct this seven-valence-electron boundary atom, which has its own basis set as well as the effective core potential. We have not only further improved Cps(sp3)-C(sp3) pseudobond, but also developed Cps(sp3)-C(sp2,carbonyl) and Cps(sp3)-N(sp3) pseudobonds for the cutting of protein backbones and nucleic acid bases. The basis set and effective core potential for the seven-valence-electron boundary atom are independent of the molecular mechanical force field. Although the parametrization is performed with density functional calculations using hybrid B3LYP exchange-correlation functional, it is found that the same set of parameters is also applicable to Hartree-Fock and MP2 methods, as well as DFT calculations with other exchange-correlation functionals. Tests on a series of molecules yield very good structural, electronic, and energetic results in comparison with the corresponding full ab initio quantum mechanical calculations.     

Ab initio molecular dynamics simulation of the energy-relaxation process of the protonated water dimer

Relaxation processes of the energy-rich protonated water dimer H+(H2O)2 were investigated by the ab initio molecular dynamics (AIMD) method. At first, the energy-rich H+(H2O)2 was reproduced by simulating a collision reaction between the protonated water monomer H3O+ and H2O. Next it was collided with N2 in order to observe the effects of intramolecular vibration redistribution and intermolecular energy transfer. Forty-eight AIMD simulations of the collision of H+(H2O)2 with N2 were performed by changing the initial orientation and the time interval between two collisions. It was revealed that the amount of energy transferred from H+(H2O)2 to N2 decreased the longer the time interval. The relationship between the intermolecular energy transfer and the vibrational states was examined with the use of an energy-transfer spectrogram (ETS), which is an analysis technique combining energy density analysis and short-time Fourier transform. The ETS demonstrates a characteristic vibrational mode for the energy transfer, which corresponds to the stretching of the hydrogen bond between H+(H2O)2 and N2 in an active complex.     

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.     

The solvation structure of Pb(II) in dilute aqueous solution: an ab initio quantum mechanical/molecular mechanical molecular dynamics approach

Structural properties of the hydrated Pb(II) ion have been investigated by ab initio quantum mechanical/molecular mechanical molecular dynamics simulations at Hartree-Fock quantum mechanical level. The first shell coordination number was found to be nine, and several other structural parameters such as angular distribution functions, radial distribution functions, and tilt- and theta-angle distributions allow the full characterization of the hydration structure of the Pb(II) ion.     

Ab initio molecular orbital studies of nonidentity allyl transfer reactions

Ab initio molecular orbital (MO) calculations are carried out on the nonidentity allyl transfer processes, X^? + CH₂CHCH₂Y ? CH₂CHCH₂ X + Y^?, with X^? = H, F, and Cl and Y = H, NH₂, OH, F, PH₂, SH, and Cl. The Marcus equation applies well to the allyl transfer reactions. The transition state (TS) position along the reaction coordinate and the TS structure are strongly influenced by the thermodynamic driving force, whereas the TS looseness is originated from the intrinsic barrier. The intrinsic barrier, ΔE, looseness, %L?, and absolute asymmetry, %AS?, are well correlated with the percentage bond elongation, %CY? = [(d ? d)/d] × 100 and/or %CX?. The %CY? and the bond orders indicate that a stronger nucleophile and/or a stronger nucleofuge (or a better leaving group) leads to an earlier TS on the reaction coordinate with a lesser degree of bond making as well as bond breaking. These are consistent with the Bell-Evans-Polanyi principle and the Leffler-Hammond postulate. © 1995 by John Wiley & Sons, Inc.     

Ab initio study of optimal control of ammonia molecular vibrational wavepackets: Towards molecular quantum computing

Optimal control theory is applied to a molecular vibrational system in light of its possible application to quantum computing (QC). We present the numerical results of an ammonia molecular vibrational model system with two modes: a bending mode and an asymmetric stretching mode. We demonstrate logic gates fundamental to QC algorithms, namely Hadamard and controlled-NOT gates. Our results show that averages of population transfers at each gate are above 93% high fidelity. A mode that has a double-well structured potential is found to have many transfer pathways, which facilitates obtaining optimal laser pulses.     

YinYang atom: a simple combined ab initio quantum mechanical molecular mechanical model

A simple interface is proposed for combined quantum mechanical (QM) molecular mechanical (MM) calculations for the systems where the QM and MM regions are connected through covalent bonds. Within this model, the atom that connects the two regions, called YinYang atom here, serves as an ordinary MM atom to other MM atoms and as a hydrogen-like atom to other QM atoms. Only one new empirical parameter is introduced to adjust the length of the connecting bond and is calibrated with the molecule propanol. This model is tested with the computation of equilibrium geometries and protonation energies for dozens of molecules. Special attention is paid on the influence of MM point charges on optimized geometry and protonation energy, and it is found that it is important to maintain local charge-neutrality in the MM region in order for the accurate calculation of the protonation and deprotonation energies. Overall the simple YinYang atom model yields comparable results to some other QM/MM models.     

Ab initio molecular dynamics simulation of a room temperature ionic liquid

Ab initio molecular dynamics simulations have been performed for the first time on the room-temperature organic ionic liquid dimethyl imidazolium chloride [DMIM][Cl] using density functional theory. The aim is to compare the local liquid structure with both that obtained from two different classical force fields and from neutron scattering experiments. The local structure around the cation shows significant differences compared to both the classical calculations and the neutron results. In particular, and unlike in the gas-phase ion pair, chloride ions tend to be located near a ring C-H proton in a position suggesting hydrogen bonding. The results are used to suggest ways in which the classical potentials may be improved.     

Ab initio molecular dynamics simulation of pressure-induced phase transition in MgS

Pressure-induced phase transition in MgS is studied using a constant pressure ab initio molecular dynamics method, and a solid evidence of existence of its high-pressure phase is provided. As predicted by total energy calculations, MgS undergoes a structural phase transformation from the rocksalt structure to a CsCl-type structure under hydrostatic pressure. The transformation mechanism is characterized, and two intermediate phases having P4/nmm and P2₁/m symmetries for the rocksalt-to-CsCl-type phase transformation of MgS are proposed, which is different from the previously proposed mechanisms. We also study this phase transition using the total energy calculations. Our predicted transition parameters and bulk properties are in good agreement with the earlier first principle simulations.     

四氰基乙烯-四甲基乙烯体系光诱导电子转移双势阱的从头算研 究

以两态模型为基础,用从头算方法,在DZP[所有原子带极化函数的Dunning(9s,5p)/(3s,2p)]基组水平上对四氰基乙烯与四甲基乙烯间的电子转移进行理论计算。通过孤立给体和受体的几何构型优化,计算了给体的电离能和受体的电子亲和能。计算表明,在光诱导电荷分离之后的返回电子转移处于高放热的Marcus反转区。通过碰撞配合物的结构优化和电荷分离处理,在线性反应坐标近似下得到四甲基乙烯-四氰基乙烯配合物电荷分离反应的双势阱,进而获得反应热,键重组能,以及跃迁能。     

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.     

Ab initio electron propagator theory of molecular wires. I. Formalism

Ab initio electron propagator methodology may be applied to the calculation of electrical current through a molecular wire. A new theoretical approach is developed for the calculation of the retarded and advanced Green functions in terms of the electron propagator matrix for the bridge molecule. The calculation of the current requires integration in a complex half plane for a trace that involves terminal and Green's-function matrices. Because the Green's-function matrices have complex poles represented by matrices, a special scheme is developed to express these "matrix poles" in terms of ordinary poles. An expression for the current is derived for a terminal matrix of arbitrary rank. For a single terminal orbital, the analytical expression for the current is given in terms of pole strengths, poles, and terminal matrix elements of the electron propagator. It is shown that Dyson orbitals with high pole strengths and overlaps with terminal orbitals are most responsible for the conduction of electrical current.     

Ab initio MO study for electron transfer matrix element in hydrogen-bonded system

The electronic coupling matrix element of electron transfer between donor and acceptor connected with hydrogen bonds has been studied in a model system. The calculated matrix element depends largely on the relative rotational conformation of the electron-donor and electron-acceptor sites and a simple orbital analysis has been presented. Along the approximate proton transfer coordinate, the energy potential is a double well and the matrix element has a single maximum at the center of the double well.     

An ab initio quantum mechanical charge field molecular dynamics simulation of a dilute aqueous HCl solution

An ab initio quantum mechanical charge field (QMCF) molecular dynamics simulation has been performed to study the structural and dynamical properties of a dilute aqueous HCl solution. The solute molecule HCl and its surrounding water molecules were treated at Hartree‐Fock level in conjunction with Dunning double‐ζ plus polarization function basis sets. The simulation predicts an average H? Cl bond distance of 1.28 Å, which is in good agreement with the experimental value. The H_HCl···O_w and Cl_HCl···H_w distances of 1.84 and 3.51 Å were found for the first hydration shell. At the hydrogen site of HCl, a single water molecule is the most preferred coordination, whereas an average coordination number of 12 water molecules of the full first shell was observed for the chloride site. The hydrogen bonding at the hydrogen site of HCl is weakened by proton transfer reactions and an associated lability of ligand binding. Two proton transfer processes were observed in the QMCF MD simulation, demonstrating acid dissociation of HCl. A weak structure‐making/breaking effect of HCl in water is recognized from the mean residence times of 2.1 and 0.8 ps for ligands in the neighborhood of Cl and H sites of HCl, respectively. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010