Theoretical study of the 1,3-hydrogen shift of triazene in water

The 1,3-hydrogen shift of triazene in aqueous solution was studied with a combination of QM/MM methods. First, the different species involved were characterized and the activation free-energies calculated with ASEP/MD, a method that makes use of the mean field approximation. Then the reaction dynamics was simulated with a QM/MM/MD method. A very strong influence of the solvent was observed, both specific, with the participation of a water molecule, and from the rest of the solvent. The effect of solvation on the geometry and electron distribution of triazene is important: N-N bond lengths tend to be more similar and the molecule acquires a planar structure. For the transition state structure, a substantial degree of ionic nature was found. Dynamic solvent effects were also analyzed.     

QuanPol: A full spectrum and seamless QM/MM program

The quantum chemistry polarizable force field program (QuanPol) is implemented to perform combined quantum mechanical and molecular mechanical (QM/MM) calculations with induced dipole polarizable force fields and induced surface charge continuum solvation models. The QM methods include Hartree–Fock method, density functional theory method (DFT), generalized valence bond theory method, multiconfiguration self‐consistent field method, Møller–Plesset perturbation theory method, and time‐dependent DFT method. The induced dipoles of the MM atoms and the induced surface charges of the continuum solvation model are self‐consistently and variationally determined together with the QM wavefunction. The MM force field methods can be user specified, or a standard force field such as MMFF94, Chemistry at Harvard Molecular Mechanics (CHARMM), Assisted Model Building with Energy Refinement (AMBER), and Optimized Potentials for Liquid Simulations‐All Atom (OPLS‐AA). Analytic gradients for all of these methods are implemented so geometry optimization and molecular dynamics (MD) simulation can be performed. MD free energy perturbation and umbrella sampling methods are also implemented. © 2013 Wiley Periodicals, Inc.     

A QM/MM study of the binding of RAPTA ligands to cathepsin B

We have carried out quantum mechanical (QM) and QM/MM (combined QM and molecular mechanics) calculations, as well as molecular dynamics (MD) simulations to study the binding of a series of six RAPTA (Ru(II)-arene-1,3,5-triaza-7-phosphatricyclo-[3.3.1.1] decane) complexes with different arene substituents to cathepsin B. The recently developed QM/MM-PBSA approach (QM/MM combined with Poisson–Boltzmann solvent-accessible surface area solvation) has been used to estimate binding affinities. The QM calculations reproduce the antitumour activities of the complexes with a correlation coefficient (r ²) of 0.35–0.86 after a conformational search. The QM/MM-PBSA method gave a better correlation (r ² = 0.59) when the protein was fixed to the crystal structure, but more reasonable ligand structures and absolute binding energies were obtained if the protein was allowed to relax, indicating that the ligands are strained when the protein is kept fixed. In addition, the best correlation (r ² = 0.80) was obtained when only the QM energies were used, which suggests that the MM and continuum solvation energies are not accurate enough to predict the binding of a charged metal complex to a charged protein. Taking into account the protein flexibility by means of MD simulations slightly improves the correlation (r ² = 0.91), but the absolute energies are still too large and the results are sensitive to the details in the calculations, illustrating that it is hard to obtain stable predictions when full flexible protein is included in the calculations.     

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     

A new method to locate saddle points for reactions in solution by using the free-energy gradient method and the mean field approximation

A new method for calculating saddle points of reactions in solution is presented. The main characteristics of the method are: (1) the solute-solvent system is described by the averaged solvent electrostatic potential/molecular dynamics method (ASEP/MD). This is a quantum mechanics/molecular mechanics method (QM/MM) that makes use of the mean field approximation (MFA) and that permits one to simultaneously optimize the electronic structure and geometry of the solute molecule and the solvent structure around it. (2) The transition state is located by the joint use of the free-energy gradient method and the mean field approximation. An application to the study of the Menshutkin reaction between NH(3) and CH(3)Cl in aqueous solution is discussed. The accuracy and usefulness of the proposed method is checked through comparison with other methods.     

Conformational dependence of charges in protein simulations

We have studied the conformational dependence of molecular mechanics atomic charges for proteins by calculating the charges fitted to the quantum mechanical (QM) electrostatic potential (ESP) for all atoms in complexes between avidin and seven biotin analogues for 20 snapshots from molecular dynamics simulations. We have studied how various other charge sets reproduce those charges. The QM charges, even if averaged over all snapshots or all residues, in general have a larger magnitude than standard Amber charges, indicating that the restraint toward zero in the restrained ESP method is too strong. This has a significant influence on the electrostatic conformational energies and the interaction energy between the biotin ligand and the protein, giving a difference between the QM and Amber charges of 43 and 8 kJ/mol for the negatively charged and neutral biotin analogues, respectively (3-4%). However, this energy difference is strongly reduced if the solvation energy (calculated by the Poisson-Boltzmann or Generalized Born methods) is added, viz., to 7 kJ/mol for charged and 3 kJ/mol for uncharged ligand. In fact, charges need to be recalculated with a QM method only for residues within 7 or 4 A of the ligand, if the error should be less than 4 kJ/mol. Unfortunately, the QM charges do not give significantly better MM/PBSA estimates of ligand-binding affinities than standard Amber charges.     

基于分子动力学模拟和连续介质模型的自由能计算方法*

近些年,基于分子动力学模拟和连续介质模型的自由能计算方法受到了越来越多的关注,其中MM/PBSA就是最具代表性的方法.在MM/PBSA中,体系的焓变采用分子力学(MM)的方法计算得到;溶剂效应中极性部分对自由能的贡献通过解Poisson-Boltzmann(PB)方程的方法计算得到;溶液效应中非极性部分对自由能的贡献则通过分子表面积(SA)计算得到.本文结合我们科研组的工作,就近几年MM/PBSA方法的最新进展做了较为详细的阐述,同时对MM/PBSA的发展前景进行了展望.     

Communication: Quantum polarized fluctuating charge model: a practical method to include ligand polarizability in biomolecular simulations

We present a simple and practical method to include ligand electronic polarization in molecular dynamics (MD) simulation of biomolecular systems. The method involves periodically spawning quantum mechanical (QM) electrostatic potential (ESP) calculations on an extra set of computer processors using molecular coordinate snapshots from a running parallel MD simulation. The QM ESPs are evaluated for the small-molecule ligand in the presence of the electric field induced by the protein, solvent, and ion charges within the MD snapshot. Partial charges on ligand atom centers are fit through the multi-conformer restrained electrostatic potential (RESP) fit method on several successive ESPs. The RESP method was selected since it produces charges consistent with the AMBER/GAFF force-field used in the simulations. The updated charges are introduced back into the running simulation when the next snapshot is saved. The result is a simulation whose ligand partial charges continuously respond in real-time to the short-term mean electrostatic field of the evolving environment without incurring additional wall-clock time. We show that (1) by incorporating the cost of polarization back into the potential energy of the MD simulation, the algorithm conserves energy when run in the microcanonical ensemble and (2) the mean solvation free energies for 15 neutral amino acid side chains calculated with the quantum polarized fluctuating charge method and thermodynamic integration agree better with experiment relative to the Amber fixed charge force-field.     

Probing the transition from hydrophilic to hydrophobic solvation with atomic scale resolution

Picosecond and femtosecond X-ray absorption spectroscopy is used to probe the changes of the solvent shell structure upon electron abstraction of aqueous iodide using an ultrashort laser pulse. The transient L(1,3) edge EXAFS at 50 ps time delay points to the formation of an expanded water cavity around the iodine atom, in good agreement with classical and quantum mechanical/molecular mechanics (QM/MM) molecular dynamics (MD) simulations. These also show that while the hydrogen atoms pointed toward iodide, they predominantly point toward the bulk solvent in the case of iodine, suggesting a hydrophobic behavior. This is further confirmed by quantum chemical (QC) calculations of I(-)/I(0)(H(2)O)(n=1-4) clusters. The L(1) edge sub-picosecond spectra point to the existence of a transient species that is not present at 50 ps. The QC calculations and the QM/MM MD simulations identify this transient species as an I(0)(OH(2)) complex inside the cavity. The simulations show that upon electron abstraction most of the water molecules move away from iodine, while one comes closer to form the complex that lives for 3-4 ps. This time is governed by the reorganization of the main solvation shell, basically the time it takes for the water molecules to reform an H-bond network. Only then is the interaction with the solvation shell strong enough to pull the water molecule of the complex toward the bulk solvent. Overall, much of the behavior at early times is determined by the reorientational dynamics of water molecules and the formation of a complete network of hydrogen bonded molecules in the first solvation shell.     

Theoretical study of the relative stability of rotational conformers of alpha and beta-D-glucopyranose in gas phase and aqueous solution

The alpha-beta anomer energy difference and the stability of 10 rotamers of counterclockwise D-glucopyranose were studied in vacuo and in aqueous solution at the B3LYP/6-31+G(d,p) level. To obtain the solute charge distribution and the solvent structure around it, we used the averaged solvent electrostatic potential from molecular dynamics method, ASEP/MD, which alternates molecular dynamics and quantum mechanics calculations in an iterative procedure. The main characteristics of the anomeric equilibrium, both in vacuo and in solution, are well reproduced. The relative stability of the different anomers is related to the availability of the free pairs of electrons in the anomeric oxygen to interact with the water molecules. The influence of solvation in the conformer equilibrium is also analyzed.     

Redox entropy of plastocyanin: developing a microscopic view of mesoscopic polar solvation

We report applications of analytical formalisms and molecular dynamics (MD) simulations to the calculation of redox entropy of plastocyanin metalloprotein in aqueous solution. The goal of our analysis is to establish critical components of the theory required to describe polar solvation at the mesoscopic scale. The analytical techniques include a microscopic formalism based on structure factors of the solvent dipolar orientations and density and continuum dielectric theories. The microscopic theory employs the atomistic structure of the protein with force-field atomic charges and solvent structure factors obtained from separate MD simulations of the homogeneous solvent. The MD simulations provide linear response solvation free energies and reorganization energies of electron transfer in the temperature range of 280-310 K. We found that continuum models universally underestimate solvation entropies, and a more favorable agreement is reported between the microscopic calculations and MD simulations. The analysis of simulations also suggests that difficulties of extending standard formalisms to protein solvation are related to the inhomogeneous structure of the solvation shell at the protein-water interface combining islands of highly structured water around ionized residues along with partial dewetting of hydrophobic patches. Quantitative theories of electrostatic protein hydration need to incorporate realistic density profile of water at the protein-water interface.     

Ab initio quantum mechanical charge field (QMCF) molecular dynamics: a QM/MM – MD procedure for accurate simulations of ions and complexes

A new formalism for quantum mechanical / molecular mechanical (QM/MM) dynamics of chemical species in solution has been developed, which does not require the construction of any other potential functions except those for solvent–solvent interactions, maintains all the advantages of large simulation boxes and ensures the accuracy of ab initio quantum mechanics for all forces acting in the chemically most relevant region. Interactions between solute and more distant solvent molecules are incorporated by a dynamically adjusted force field corresponding to the actual molecular configuration of the simulated system and charges derived from the electron distribution in the solvate. The new formalism has been tested with some examples of hydrated ions, for which accurate conventional ab initio QM/MM simulations have been previously performed, and the comparison shows equivalence and in some aspects superiority of the new method. As this simulation procedure does not require any tedious construction of two-and three-body interaction potentials inherent to conventional QM/MM approaches, it opens the straightforward access to ab initio molecular dynamics simulations of any kind of solutes, such as metal complexes and other composite species in solution.     

Fragmentation-based QM/MM simulations: length dependence of chain dynamics and hydrogen bonding of polyethylene oxide and polyethylene in aqueous solutions

Molecular fragmentation quantum mechanics (QM) calculations have been combined with molecular mechanics (MM) to construct the fragmentation QM/MM method for simulations of dilute solutions of macromolecules. We adopt the electrostatics embedding QM/MM model, where the low-cost generalized energy-based fragmentation calculations are employed for the QM part. Conformation energy calculations, geometry optimizations, and Born-Oppenheimer molecular dynamics simulations of poly(ethylene oxide), PEO(n) (n = 6-20), and polyethylene, PE(n) ( n = 9-30), in aqueous solution have been performed within the framework of both fragmentation and conventional QM/MM methods. The intermolecular hydrogen bonding and chain configurations obtained from the fragmentation QM/MM simulations are consistent with the conventional QM/MM method. The length dependence of chain conformations and dynamics of PEO and PE oligomers in aqueous solutions is also investigated through the fragmentation QM/MM molecular dynamics simulations.     

Computer simulations of the solvation dynamics of Coumarin 153 in dimethylsulfoxide

We report molecular dynamics (MD) simulations of the solvation dynamics of Coumarin 153 in liquid dimethylsulfoxide using two distinct sets of partial charges for the coumarin probe. The excited state dipole moment of the coumarin and the dynamic Stokes shift in solution depend significantly on the type of charge distributions used. Nevertheless, the overall characteristics of the solvation responses obtained from both sets of charges are very similar and show good agreement with time-dependent Stokes shift experiments. Microscopic details of the solvent reorganization around the probe are discussed in light of the charge transfer upon photoexcitation.