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.     

Structures in solutions from joint experimental-computational analysis: applications to cyclic molecules and studies of noncovalent interactions

The potential of an approach combining nuclear magnetic resonance (NMR) spectroscopy, molecular dynamics (MD) simulations, and quantum mechanical (QM) calculations for full structural characterizations in solution is assessed using cyclic organic compounds, namely, benzazocinone derivatives 1-3 with fused five- and eight-membered aliphatic rings, camphoric anhydride 4, and bullvalene 5. Various MD simulations were considered, using force field and semiempirical QM treatments, implicit and explicit solvation, and high-temperature MD calculations for selecting plausible molecular geometries for subsequent QM geometry optimizations using mainly B3LYP, M062X, and MP2 methods. The QM-predicted values of NMR parameters were compared to their experimental values for verification of the final structures derived from the MD/QM analysis. From these comparisons, initial estimates of quality thresholds (calculated as rms deviations) were 0.7-0.9 Hz for (3)J(HH) couplings, 0.07-0.11 ? for interproton distances, 0.05-0.08 ppm for (1)H chemical shifts, and 1.0-2.1 ppm for (13)C chemical shifts. The obtained results suggest that the accuracy of the MD analysis in predicting geometries and relative conformational energies is not critical and that the final geometry refinements of the structures selected from the MD simulations using QM methods are sufficient for correcting for the expected inaccuracy of the MD analysis. A unique example of C(sp(3))-H···N(sp(3)) intramolecular noncovalent interaction is also identified using the NMR/MD/QM and the natural bond orbital analyses. As the NMR/MD/QM approach relies on the final QM geometry optimization, comparisons of geometric characteristics predicted by different QM methods and those from X-ray and neutron diffraction measurements were undertaken using rigid and flexible cyclic systems. The joint analysis shows that intermolecular noncovalent interactions present in the solid state alter molecular geometries significantly compared to the geometries of isolated molecules from QM 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     

CPMD/GULP QM/MM interface for modeling periodic solids: Implementation and its application in the study of Y‐zeolite supported Rhn clusters

We report here the development of hybrid quantum mechanics/molecular mechanics (QM/MM) interface between the plane‐wave density functional theory based CPMD code and the empirical force‐field based GULP code for modeling periodic solids and surfaces. The hybrid QM/MM interface is based on the electrostatic coupling between QM and MM regions. The interface is designed for carrying out full relaxation of all the QM and MM atoms during geometry optimizations and molecular dynamics simulations, including the boundary atoms. Both Born–Oppenheimer and Car–Parrinello molecular dynamics schemes are enabled for the QM part during the QM/MM calculations. This interface has the advantage of parallelization of both the programs such that the QM and MM force evaluations can be carried out in parallel to model large systems. The interface program is first validated for total energy conservation and parallel scaling performance is benchmarked. Oxygen vacancy in α‐cristobalite is then studied in detail and the results are compared with a fully QM calculation and experimental data. Subsequently, we use our implementation to investigate the structure of rhodium cluster (Rh_n; n = 2 to 6) formed from Rh(C₂H₄)₂ complex adsorbed within a cavity of Y‐zeolite in a reducible atmosphere of H₂ gas. © 2016 Wiley Periodicals, Inc.     

An extensible interface for QM/MM molecular dynamics simulations with AMBER

We present an extensible interface between the AMBER molecular dynamics (MD) software package and electronic structure software packages for quantum mechanical (QM) and mixed QM and classical molecular mechanical (MM) MD simulations within both mechanical and electronic embedding schemes. With this interface, ab initio wave function theory and density functional theory methods, as available in the supported electronic structure software packages, become available for QM/MM MD simulations with AMBER. The interface has been written in a modular fashion that allows straight forward extensions to support additional QM software packages and can easily be ported to other MD software. Data exchange between the MD and QM software is implemented by means of files and system calls or the message passing interface standard. Based on extensive tests, default settings for the supported QM packages are provided such that energy is conserved for typical QM/MM MD simulations in the microcanonical ensemble. Results for the free energy of binding of calcium ions to aspartate in aqueous solution comparing semiempirical and density functional Hamiltonians are shown to demonstrate features of this interface. © 2013 Wiley Periodicals, Inc.     

A molecular mechanics model for imatinib and imatinib:kinase binding

Imatinib is an important anticancer drug, which binds specifically to the Abl kinase and blocks its signalling activity. To model imatinib:protein interactions, we have developed a molecular mechanics force field for imatinib and four close analogues, which is consistent with the CHARMM force field for proteins and nucleic acids. Atomic charges and Lennard‐Jones parameters were derived from a supermolecule ab initio approach. We considered the ab initio energies and geometries of a probe water molecule interacting with imatinib fragments at 32 different positions. We considered both a neutral and a protonated imatinib. The final RMS deviation between the ab initio and force field energies, averaged over both forms, was 0.2 kcal/mol. The model also reproduces the ab initio geometry and flexibility of imatinib. To apply the force field to imatinib:Abl simulations, it is also necessary to determine the most likely imatinib protonation state when it binds to Abl. This was done using molecular dynamics free energy simulations, where imatinib is reversibly protonated during a series of MD simulations, both in solution and in complex with Abl. The simulations indicate that imatinib binds to Abl in its protonated, positively‐charged form. To help test the force field and the protonation prediction, we did MD free energy simulations that compare the Abl binding affinities of two imatinib analogs, obtaining good agreement with experiment. Finally, two new imatinib variants were considered, one of which is predicted to have improved Abl binding. This variant could be of interest as a potential drug. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Mixed ab initio QM/MM modeling using frozen orbitals and tests with alanine dipeptide and tetrapeptide

Methodology is discussed for mixed ab initio quantum mechanics/molecular mechanics modeling of systems where the quantum mechanics (QM) and molecular mechanics (MM) regions are within the same molecule. The ab initio QM calculations are at the restricted Hartree–Fock level using the pseudospectral method of the Jaguar program while the MM part is treated with the OPLS force fields implemented in the IMPACT program. The interface between the QM and MM regions, in particular, is elaborated upon, as it is dealt with by “breaking” bonds at the boundaries and using Boys-localized orbitals found from model molecules in place of the bonds. These orbitals are kept frozen during QM calculations. Results from tests of the method to find relative conformational energies and geometries of alanine dipeptides and alanine tetrapeptides are presented along with comparisons to pure QM and pure MM calculations. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1468–1494, 1999     

QM/MM calculation of solvent effects on absorption spectra of guanine

Electronic spectra of guanine in the gas phase and in water were studied by quantum mechanical/molecular mechanical (QM/MM) methods. Geometries for the excited‐state calculations were extracted from ground‐state molecular dynamics (MD) simulations using the self‐consistent‐charge density functional tight binding (SCC‐DFTB) method for the QM region and the TIP3P force field for the water environment. Theoretical absorption spectra were generated from excitation energies and oscillator strengths calculated for 50 to 500 MD snapshots of guanine in the gas phase (QM) and in solution (QM/MM). The excited‐state calculations used time‐dependent density functional theory (TDDFT) and the DFT‐based multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke, in combination with two basis sets. Our investigation covered keto‐N7H and keto‐N9H guanine, with particular focus on solvent effects in the low‐energy spectrum of the keto‐N9H tautomer. When compared with the vertical excitation energies of gas‐phase guanine at the optimized DFT (B3LYP/TZVP) geometry, the maxima in the computed solution spectra are shifted by several tenths of an eV. Three effects contribute: the use of SCC‐DFTB‐based rather than B3LYP‐based geometries in the MD snapshots (red shift of ca. 0.1 eV), explicit inclusion of nuclear motion through the MD snapshots (red shift of ca. 0.1 eV), and intrinsic solvent effects (differences in the absorption maxima in the computed gas‐phase and solution spectra, typically ca. 0.1–0.3 eV). A detailed analysis of the results indicates that the intrinsic solvent effects arise both from solvent‐induced structural changes and from electrostatic solute–solvent interactions, the latter being dominant. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

A valence bond model for aqueous Cu(II) and Zn(II) ions in the AMOEBA polarizable force field

A general molecular mechanics (MM) model for treating aqueous Cu²⁺ and Zn²⁺ ions was developed based on valence bond (VB) theory and incorporated into the atomic multipole optimized energetics for biomolecular applications (AMOEBA) polarizable force field. Parameters were obtained by fitting MM energies to that computed by ab initio methods for gas‐phase tetra‐ and hexa‐aqua metal complexes. Molecular dynamics (MD) simulations using the proposed AMOEBA‐VB model were performed for each transition metal ion in aqueous solution, and solvent coordination was evaluated. Results show that the AMOEBA‐VB model generates the correct square‐planar geometry for gas‐phase tetra‐aqua Cu²⁺ complex and improves the accuracy of MM model energetics for a number of ligation geometries when compared to quantum mechanical (QM) computations. On the other hand, both AMOEBA and AMOEBA‐VB generate results for Zn²⁺–water complexes in good agreement with QM calculations. Analyses of the MD trajectories revealed a six‐coordination first solvation shell for both Cu²⁺ and Zn²⁺ ions in aqueous solution, with ligation geometries falling in the range reported by previous studies. © 2012 Wiley Periodicals, Inc.     

Hybrid molecular dynamics-quantum mechanics simulations of solute spectral properties in the condensed phase: evaluation of simulation parameters

We have explored the impact of a number of basic simulation parameters on the results of a recently developed hybrid molecular dynamics-quantum mechanics (MD-QM) method (Mercer et al., J Phys Chem B 1999, 103, 7720). The method utilizes MD simulations to explore the ground-state configuration space of the system and QM evaluation of those structures to yield the time-dependent electronic transition energy, which is transformed into the optical line-broadening function using the second-order cumulant expansion. Both linear and nonlinear optical spectra can then be generated for comparison to experiment. The dependence of the resulting spectra on the length of the MD trajectory, the QM sampling rate, and the QM model chemistry have all been examined. In particular, for the system of oxazine-4 in methanol studied here, at least 20 ps of MD trajectory are needed for qualitative convergence of linear spectral properties, and >100 ps is needed for quantitative convergence. Surprisingly, little difference is found between the 3-21G and 6-31G(d) basis sets, and the CIS and TD-B3LYP methods yield remarkably similar spectra. The semiempirical INDO/s method yields the most accurate results, reproducing the experimental Stokes shift to within 5% and the FWHM to within 20%. Nonlinear 3-pulse photon echo peak shift (3PEPS) decays have also been simulated. Decays are generally poorly reproduced, though the initial peak shift which depends on the overall coupling of motions to the solute transition energy is within 15% of experiment for all model chemistries other than those using the STO-3G basis.     

Solvent effect on the absorption spectra of coumarin 120 in water: A combined quantum mechanical and molecular mechanical study

The solvent effect on the absorption spectra of coumarin 120 (C120) in water was studied utilizing the combined quantum mechanical∕molecular mechanical (QM∕MM) method. In molecular dynamics (MD) simulation, a new sampling scheme was introduced to provide enough samples for both solute and solvent molecules to obtain the average physical properties of the molecules in solution. We sampled the structure of the solute and solvent molecules separately. First, we executed a QM∕MM MD simulation, where we sampled the solute molecule in solution. Next, we chose random solute structures from this simulation and performed classical MD simulation for each chosen solute structure with its geometry fixed. This new scheme allowed us to sample the solute molecule quantum mechanically and sample many solvent structures classically. Excitation energy calculations using the selected samples were carried out by the generalized multiconfigurational perturbation theory. We succeeded in constructing the absorption spectra and realizing the red shift of the absorption spectra found in polar solvents. To understand the motion of C120 in water, we carried out principal component analysis and found that the motion of the methyl group made the largest contribution and the motion of the amino group the second largest. The solvent effect on the absorption spectrum was studied by decomposing it in two components: the effect from the distortion of the solute molecule and the field effect from the solvent molecules. The solvent effect from the solvent molecules shows large contribution to the solvent shift of the peak of the absorption spectrum, while the solvent effect from the solute molecule shows no contribution. The solvent effect from the solute molecule mainly contributes to the broadening of the absorption spectrum. In the solvent effect, the variation in C-C bond length has the largest contribution on the absorption spectrum from the solute molecule. For the solvent effect on the absorption spectrum from the solvent molecules, the solvent structure around the amino group of C120 plays the key role.     

Classical and quantum mechanical/molecular mechanical molecular dynamics simulations of alanine dipeptide in water: comparisons with IR and vibrational circular dichroism spectra

We have implemented the combined quantum mechanical (QM)/molecular mechanical (MM) molecular dynamics (MD) simulations of alanine dipeptide in water along with the polarizable and nonpolarizable classical MD simulations with different models of water. For the QM/MM MD simulation, the alanine dipeptide is treated with the AM1 or PM3 approximations and the fluctuating solute dipole moment is calculated by the Mulliken population analysis. For the classical MD simulations, the solute is treated with the polarizable or nonpolarizable AMBER and polarizable CHARMM force fields and water is treated with the TIP3P, TIP4P, or TIP5P model. It is found that the relative populations of right-handed alpha-helix and extended beta and P(II) conformations in the simulation trajectory strongly depend on the simulation method. For the QM/MM MD simulations, the PM3/MM shows that the P(II) conformation is dominant, whereas the AM1/MM predicts that the dominant conformation is alpha(R). Polarizable CHARMM force field gives almost exclusively P(II) conformation and other force fields predict that both alpha-helical and extended (beta and P(II)) conformations are populated with varying extents. Solvation environment around the dipeptide is investigated by examining the radial distribution functions and numbers and lifetimes of hydrogen bonds. Comparing the simulated IR and vibrational circular dichroism spectra with experimental results, we concluded that the dipeptide adopts the P(II) conformation and PM3/MM, AMBER03 with TIP4P water, and AMBER polarizable force fields are acceptable for structure determination of the dipeptide considered in this paper.     

On the effect of a variation of the force field, spatial boundary condition and size of the QM region in QM/MM MD simulations

During the past years, the use of combined quantum-classical, QM/MM, methods for the study of complex biomolecular processes, such as enzymatic reactions and photocycles, has increased considerably. The quality of the results obtained from QM/MM calculations is largely dependent on five aspects to be considered when setting up a molecular model: the QM Hamiltonian, the MM Hamiltonian or force field, the boundary and coupling between the QM and MM regions, the size of the QM region and the boundary condition for the MM region. In this study, we systematically investigate the influence of a variation of the molecular mechanics force field and the size of the QM region in QM/MM MD simulations on properties of the photoactive part of the blue light photoreceptor protein AppA. For comparison, we additionally performed classical MD simulations and studied the effect of a variation of the type of spatial boundary condition. The classical boundary conditions and the force field used in a QM/MM MD simulation are shown to have non-neglegible effects upon the structural and energetic properties of the protein which makes it advisable to minimize computational artifacts in QM/MM MD simulations by application of periodic boundary conditions and a thermodynamically calibrated force field. A comparison of the structural and energetic properties of MD simulations starting from two alternative, different X-ray structures for the blue light utilizing flavin protein in its dark state indicates a slight preference of the two force fields used for the so-called Anderson structure over the Jung structure.     

The MM2QM tool for combining docking,molecular dynamics,molecular mechanics,and quantum mechanics†

The use of the MM2QM tool in a combined docking + molecular dynamics (MD) + molecular mechanics (MM) + quantum mechanical (QM) binding affinity prediction study is presented, and the tool itself is discussed. The system of interest is Mycobacterium tuberculosis (MTB) pantothenate synthetase in complexes with three highly similar sulfonamide inhibitors, for which crystal structures are available. Starting from the structure of MTB pantothenate synthetase in the “open” conformation and following the combined docking + MD + MM + QM procedure, we were able to capture the closing of the enzyme binding pocket and to reproduce the position of the ligands with an average root mean square deviation of 1.6 Å. Protein–ligand interaction energies were reproduced with an average error lower than 10%. The discussion on the MD part and a protein flexibility importance is carried out. The presented approach may be useful especially for finding analog inhibitors or improving drug candidates. © 2012 Wiley Periodicals, Inc.     

Multiscale electrostatic embedding simulations for modeling structure and dynamics of molecules in solution: A tutorial review

The main concepts and important technical details of electrostatic embedding quantum mechanics/molecular mechanics (QM/MM) simulations are explained and illustrated with the intent of assisting newcomers in performing and gauging the accuracy of such simulations, focused on smaller molecules in solution. Beginners are advised on how to increase the reliability and accuracy of the simulations through benchmarking. Central considerations on methodologies for QM/MM Molecular Dynamics (MD) simulations are presented, alongside technical fundamentals regarding the construction and manipulation of simulation systems using the python-based Atomic Simulation Environment (ASE). A worked example of QM/MM Born–Oppenheimer MD is included, and a flowchart summarizing the most salient decisions and tasks within the methodology is presented.     

Increasing the time step with mass scaling in Born‐Oppenheimer ab initio QM/MM molecular dynamics simulations

Born‐Oppenheimer ab initio QM/MM molecular dynamics simulation with umbrella sampling is a state‐of‐the‐art approach to calculate free energy profiles of chemical reactions in complex systems. To further improve its computational efficiency, a mass‐scaling method with the increased time step in MD simulations has been explored and tested. It is found that by increasing the hydrogen mass to 10 amu, a time step of 3 fs can be employed in ab initio QM/MM MD simulations. In all our three test cases, including two solution reactions and one enzyme reaction, the resulted reaction free energy profiles with 3 fs time step and mass scaling are found to be in excellent agreement with the corresponding simulation results using 1 fs time step and the normal mass. These results indicate that for Born‐Oppenheimer ab initio QM/MM molecular dynamics simulations with umbrella sampling, the mass‐scaling method can significantly reduce its computational cost while has little effect on the calculated free energy profiles. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009