Harder,better, faster,stronger: Large-scale QM and QM/MM for predictive modeling in enzymes and proteins

Computational prediction of enzyme mechanism and protein function requires accurate physics-based models and suitable sampling. We discuss recent advances in large-scale quantum mechanical (QM) modeling of biochemical systems that have reduced the cost of high-accuracy models. Tradeoffs between sampling and accuracy have motivated modeling with molecular mechanics (MM) in a multiscale QM/MM or iterative approach. Limitations to both conventional density-functional theory and classical MM force fields remain for describing noncovalent interactions in comparison to experiment or wavefunction theory. Because predictions of enzyme action (i.e. electrostatics), free energy barriers, and mechanisms are sensitive to the protocol and embedding method in QM/MM, convergence tests and systematic methods for quantifying QM-level interactions are a needed, active area of development.     

The utility of residual dipolar couplings in detecting motion in carbohydrates: application to sucrose

The solution structure and dynamics of sucrose are examined using a combination of NMR residual dipolar coupling and molecular mechanics force fields. It is found that the alignment tensors of the individual rings are different, and that fitting 35 measured residual dipolar couplings to structures with specific phi, psi values indicates the presence of three major conformations: phi, psi=(120 degrees ,270 degrees), (45 degrees, 300 degrees) and (90 degrees ,180 degrees). Furthermore, fitting two structures simultaneously to the 35 residual dipolar couplings results in a substantial improvement in the fits. The existence of multiple conformations having similar stabilities is a strong indication of motion, due to the interconversion among these states. Results from four molecular mechanics force fields are in general agreement with the experimental results. However, there are major disagreements between force fields. Because fits of residual dipolar couplings to structures are dependent on the force field used to calculate the structures, multiple force fields were used to interpret NMR data. It is demonstrated that the pucker of the fructofuranosyl ring affects the calculated potential energy surface, and the fit to the residual dipolar couplings data. Previously published 13C nuclear relaxation results suggesting that sucrose is rigid are not inconsistent with the present results when motional timescales are considered.     

Determinants of reactivity and selectivity in soluble epoxide hydrolase from quantum mechanics/molecular mechanics modeling

Soluble epoxide hydrolase (sEH) is an enzyme involved in drug metabolism that catalyzes the hydrolysis of epoxides to form their corresponding diols. sEH has a broad substrate range and shows high regio- and enantioselectivity for nucleophilic ring opening by Asp333. Epoxide hydrolases therefore have potential synthetic applications. We have used combined quantum mechanics/molecular mechanics (QM/MM) umbrella sampling molecular dynamics (MD) simulations (at the AM1/CHARMM22 level) and high-level ab initio (SCS-MP2) QM/MM calculations to analyze the reactions, and determinants of selectivity, for two substrates: trans-stilbene oxide (t-SO) and trans-diphenylpropene oxide (t-DPPO). The calculated free energy barriers from the QM/MM (AM1/CHARMM22) umbrella sampling MD simulations show a lower barrier for phenyl attack in t-DPPO, compared with that for benzylic attack, in agreement with experiment. Activation barriers in agreement with experimental rate constants are obtained only with the highest level of QM theory (SCS-MP2) used. Our results show that the selectivity of the ring-opening reaction is influenced by several factors, including proximity to the nucleophile, electronic stabilization of the transition state, and hydrogen bonding to two active site tyrosine residues. The protonation state of His523 during nucleophilic attack has also been investigated, and our results show that the protonated form is most consistent with experimental findings. The work presented here illustrates how determinants of selectivity can be identified from QM/MM simulations. These insights may also provide useful information for the design of novel catalysts for use in the synthesis of enantiopure compounds.     

Catalytic mechanism and energy barriers for butyrylcholinesterase-catalyzed hydrolysis of cocaine

The geometries of the transition states, intermediates, and prereactive enzyme-substrate complex and the corresponding energy barriers have been determined by performing hybrid quantum mechanical/molecular mechanical (QM/MM) calculations on butyrylcholinesterase (BChE)-catalyzed hydrolysis of (-)- and (+)-cocaine. The energy barriers were evaluated by performing QM/MM calculations with the QM method at the MP2/6-31+G* level and the MM method using the AMBER force field. These calculations allow us to account for the protein environmental effects on the transition states and energy barriers of these enzymatic reactions, showing remarkable effects of the protein environment on intermolecular hydrogen bonding (with an oxyanion hole), which is crucial for the transition state stabilization and, therefore, on the energy barriers. The calculated energy barriers are consistent with available experimental kinetic data. The highest barrier calculated for BChE-catalyzed hydrolysis of (-)- and (+)-cocaine is associated with the third reaction step, but the energy barrier calculated for the first step is close to the highest and is so sensitive to the protein environment that the first reaction step can be rate determining for (-)-cocaine hydrolysis catalyzed by a BChE mutant. The computational results provide valuable insights into future design of BChE mutants with a higher catalytic activity for (-)-cocaine.     

Studies on the conformational behaviour of GlcNAc-Man3-GlcNAc2 oligosaccharides using molecular dynamics simulations

Three-dimensional structures of the natural substrate unit for the enzyme N-acetylglucosamine-transferase II, GlcNAc-Man3-GlcNAc2, were investigated by molecular modelling methods. Molecular dynamics (MD) and molecular mechanics calculations on two hexasaccharides, namely GlcNAc-Man3-GlcNAc2-Asn and GlcNAc-Man3-GlcNAc2-OMe were performed by the Biosym/MSI software using the CVFF and CFF95 force fields in vacuum. The MD simulations were calculated for 3 ns at different simulation temperatures and for two values of dielectric constant, = 1 and = 4. From each 3 ns trajectory, 3050 structures have been optimized. The local minima obtained have been clustered into families exhibiting similar values of glycosidic torsional angles phi, psi, and omega. The influence of the simulation conditions and force fields used on the conformational behaviour and structure of the title oligosaccharides is discussed.     

Recent developments in QM/MM methods towards open-boundary multi-scale simulations

Combined quantum mechanics/molecular mechanics (QM/MM) methods have been widely used in multi-scale modelling and simulations of physical, chemical and biological processes in complex environments. In this review, we provide an overview of the recently developed QM/MM algorithms, with emphasis on our works, towards the ultimate goal of establishing an open boundary between the QM and MM subsystems. The open boundary is characterised by on-the-fly exchanges of partial charges and atoms between the QM and MM subsystems, allowing us to focus on the small QM subsystem of primary interest in dynamics simulations. An open-boundary scheme has the promise to the utilisations of small QM subsystems, high-levels of QM theory and long simulation times, which can potentially lead to new insights.     

Differential stability of beta-sheets and alpha-helices in beta-lactamase: a high temperature molecular dynamics study of unfolding intermediates.

beta-Lactamase, which catalyzes beta-lactam antibiotics, is prototypical of large alpha/beta proteins with a scaffolding formed by strong noncovalent interactions. Experimentally, the enzyme is well characterized, and intermediates that are slightly less compact and having nearly the same content of secondary structure have been identified in the folding pathway. In the present study, high temperature molecular dynamics simulations have been carried out on the native enzyme in solution. Analysis of these results in terms of root mean square fluctuations in cartesian and [phi, psi] space, backbone dihedral angles and secondary structural hydrogen bonds forms the basis for an investigation of the topology of partially unfolded states of beta-lactamase. A differential stability has been observed for alpha-helices and beta-sheets upon thermal denaturation to putative unfolding intermediates. These observations contribute to an understanding of the folding/unfolding processes of beta-lactamases in particular, and other alpha/beta proteins in general.     

Power calculations for matched case-control studies

Power calculations are derived for matched case-control studies in terms of the probability po of exposure among the control patients, the correlation coefficient phi for exposure between matched case and control patients, and the odds ratio psi for exposure in case and control patients. For given Type I and Type II error probabilities alpha and beta, the odds ratio that can be detected with a given sample size is derived as well as the sample size needed to detect a specified value of the odds ratio. Graphs are presented for paired designs that show the relationship between sample size and power for alpha = .05, beta = .2, and different values of po, phi, and psi. The sample size needed for designs involving M matched control patients can be derived from these graphs by means of a simple equation. These results quantify the loss of power associated with increasing correlation between the exposure status of matched case and control patients. Sample size requirements are also greatly increased for values of po near 0 or 1. The relationship between sample size, psi, phi, and po is discussed and illustrated by examples.     

Polypeptide motions are dominated by peptide group oscillations resulting from dihedral angle correlations between nearest neighbors

To identify basic local backbone motions in unfolded chains, simulations are performed for a variety of peptide systems using three popular force fields and for implicit and explicit solvent models. A dominant "crankshaft-like" motion is found that involves only a localized oscillation of the plane of the peptide group. This motion results in a strong anticorrelated motion of the phi angle of the ith residue (phi(i)) and the psi angle of the residue i - 1 (psi(i-1)) on the 0.1 ps time scale. Only a slight correlation is found between the motions of the two backbone dihedral angles of the same residue. Aside from the special cases of glycine and proline, no correlations are found between backbone dihedral angles that are separated by more than one torsion angle. These short time, correlated motions are found both in equilibrium fluctuations and during the transit process between Ramachandran basins, e.g., from the beta to the alpha region. A residue's complete transit from one Ramachandran basin to another, however, occurs in a manner independent of its neighbors' conformational transitions. These properties appear to be intrinsic because they are robust across different force fields, solvent models, nonbonded interaction routines, and most amino acids.     

Comparison of multiple Amber force fields and development of improved protein backbone parameters

The ff94 force field that is commonly associated with the Amber simulation package is one of the most widely used parameter sets for biomolecular simulation. After a decade of extensive use and testing, limitations in this force field, such as over-stabilization of alpha-helices, were reported by us and other researchers. This led to a number of attempts to improve these parameters, resulting in a variety of "Amber" force fields and significant difficulty in determining which should be used for a particular application. We show that several of these continue to suffer from inadequate balance between different secondary structure elements. In addition, the approach used in most of these studies neglected to account for the existence in Amber of two sets of backbone phi/psi dihedral terms. This led to parameter sets that provide unreasonable conformational preferences for glycine. We report here an effort to improve the phi/psi dihedral terms in the ff99 energy function. Dihedral term parameters are based on fitting the energies of multiple conformations of glycine and alanine tetrapeptides from high level ab initio quantum mechanical calculations. The new parameters for backbone dihedrals replace those in the existing ff99 force field. This parameter set, which we denote ff99SB, achieves a better balance of secondary structure elements as judged by improved distribution of backbone dihedrals for glycine and alanine with respect to PDB survey data. It also accomplishes improved agreement with published experimental data for conformational preferences of short alanine peptides and better accord with experimental NMR relaxation data of test protein systems.     

Nuclear Overhauser effect and cross-relaxation rate determinations of dihedral and transannular interproton distances in the decapeptide tyrocidine A.

The following interproton distances are reported for the decapeptide tyrocidine A in solution: (a) r(phi) distances between NH(i) and H alpha (i), (b) r(psi) distances between NH (i + 1) and H alpha (i), (c) r(phi psi) distances between NH(i + 1) and NH(i), (d) NH in equilibrium NH transannular distances, (e) H alpha in equilibrium H alpha transannular distances, (f) r x 1 distances between H alpha and H beta protons, (g) NH(i) in equilibrium H beta (i) distances, (h) NH (i + 1) in equilibrium H beta (i) distances, (i) carboxamide-backbone protons and carboxamide-side chain proton distances, (j) side chain proton-side chain proton distances. The procedures for distance calculations were: NOE ratios and calibration distances, sigma ratios and calibration distances, and correlation times and sigma parameters. The cross-relaxation parameters were obtained from the product, say, of NOE 1 leads to 2 and the monoselective relaxation rate of proton 2; the NOEs were measured by NOE difference spectroscopy. The data are consistent with a type I beta-turn/ type II' beta-turn/ approximately antiparallel beta-pleated sheet conformation of tyrocidine A in solution and the NOEs, cross-relaxation parameters, and interproton distances serve as distinguishing criteria for beta-turn and beta-pleated sheet conformations. It should be borne in mind that measurement of only r phi and r psi distances for a decapeptide only defines the ( phi, psi)-space in terms of 4(10) possible conformations; the distances b-j served to reduce the degeneracy in possible (phi, psi)-space to one tyrocidine A conformation. The latter conformation is consistent with that derived from scalar coupling constants, hydrogen bonding studies, and proton-chromophore distance measurement, and closely resembles the conformation of gramicidin S.     

Refinement of the AMBER force field for nucleic acids: improving the description of alpha/gamma conformers

We present here the parmbsc0 force field, a refinement of the AMBER parm99 force field, where emphasis has been made on the correct representation of the alpha/gamma concerted rotation in nucleic acids (NAs). The modified force field corrects overpopulations of the alpha/gamma = (g+,t) backbone that were seen in long (more than 10 ns) simulations with previous AMBER parameter sets (parm94-99). The force field has been derived by fitting to high-level quantum mechanical data and verified by comparison with very high-level quantum mechanical calculations and by a very extensive comparison between simulations and experimental data. The set of validation simulations includes two of the longest trajectories published to date for the DNA duplex (200 ns each) and the largest variety of NA structures studied to date (15 different NA families and 97 individual structures). The total simulation time used to validate the force field includes near 1 mus of state-of-the-art molecular dynamics simulations in aqueous solution.     

DRF90: a polarizable force field

The direct reaction field (DRF) approach has proven to be a useful tool to investigate the influence of solvents on the quantum/classical behaviour of solute molecules. In this paper, we report the latest extension of this DRF approach, which consists of the gradient of the completely classical energy expressions of this otherwise QM/MM method. They can be used in (completely classical) molecular dynamics (MD) simulations and geometry optimizations, that can be followed by a number of single point QM/MM calculations on configurations obtained in these simulations/optimizations. We report all energy and gradient expressions, and results for a number of interesting (model) systems. They include geometry optimization of the benzene dimer as well as MD simulations of some solvents. The most stable configuration for the benzene dimer is shown to be the parallel-displaced form, which is slightly more stable (0.3 kcal/mol) than the T-shaped dimer.     

Protonation states of intermediates in the reaction mechanism of [NiFe] hydrogenase studied by computational methods

The [NiFe] hydrogenases catalyse the reversible conversion of H₂ to protons and electrons. The active site consists of a Fe ion with one carbon monoxide, two cyanide, and two cysteine (Cys) ligands. The latter two bridge to a Ni ion, which has two additional terminal Cys ligands. It has been suggested that one of the Cys residues is protonated during the reaction mechanism. We have used combined quantum mechanical and molecular mechanics (QM/MM) geometry optimisations, large QM calculations with 817 atoms, and QM/MM free energy simulations, using the TPSS and B3LYP methods with basis sets extrapolated to the quadruple zeta level to determine which of the four Cys residues is more favourable to protonate for four putative states in the reaction mechanism, Ni-SI_a, Ni-R, Ni-C, and Ni-L. The calculations show that for all states, the terminal Cys-546 residue is most easily protonated by 14–51 kJ/mol, owing to a more favourable hydrogen-bond pattern around this residue in the protein.     

Comparison of force fields to study the zinc-finger containing protein NPL4, a target for disulfiram in cancer therapy

Molecular dynamics (MD) simulations are a powerful approach to studying the structure and dynamics of proteins related to health and disease. Advances in the MD field allow modeling proteins with high accuracy. However, modeling metal ions and their interactions with proteins is still challenging. NPL4 is a zinc-binding protein and works as a cofactor for p97 to regulate protein homeostasis. NPL4 is of biomedical importance and has been proposed as the target of disulfiram, a drug recently repurposed for cancer treatment. Experimental studies proposed that the disulfiram metabolites, bis-(diethyldithiocarbamate)‑copper and cupric ions, induce NPL4 misfolding and aggregation. However, the molecular details of their interactions with NPL4 and consequent structural effects are still elusive. Here, biomolecular simulations can help to shed light on the related structural details. To apply MD simulations to NPL4 and its interaction with copper the first important step is identifying a suitable force field to describe the protein in its zinc-bound states. We examined different sets of non-bonded parameters because we want to study the misfolding mechanism and cannot rule out that the zinc may detach from the protein during the process and copper replaces it. We investigated the force-field ability to model the coordination geometry of the metal ions by comparing the results from MD simulations with optimized geometries from quantum mechanics (QM) calculations using model systems of NPL4. Furthermore, we investigated the performance of a force field including bonded parameters to treat copper ions in NPL4 that we obtained based on QM calculations.     

Application of a SCC-DFTB QM/MM approach to the investigation of the catalytic mechanism of fatty acid amide hydrolase

Self-consistent charge density functional tight binding (SCC-DFTB) is a promising method for hybrid quantum mechanics/molecular mechanics (QM/MM) simulations of enzyme-catalyzed reactions. The acylation reaction of fatty acid amide hydrolase (FAAH), a promising drug target, was investigated by applying a SCC-DFTB/CHARMM27 scheme. Calculated potential energy barriers resulted in reasonable agreement with experiments for oleamide (OA) and oleoylmethyl ester (OME) substrates, outperforming previous calculations performed at the PM3/CHARMM22 level. Furthermore, the experimental preference of FAAH in hydrolyzing OA faster than OME was adequately reproduced by calculations. All these findings indicate that the SCC-DFTB/CHARMM27 approach can be successfully applied to mechanistic investigations of FAAH-catalyzed reactions.     

Use of multistate Bennett acceptance ratio method for free-energy calculations from enhanced sampling and free-energy perturbation

Multistate Bennett acceptance ratio (MBAR) works as a method to analyze molecular dynamics (MD) simulation data after the simulations have been finished. It is widely used to estimate free-energy changes between different states and averaged properties at the states of interest. MBAR allows us to treat a wide range of states from those at different temperature/pressure to those with different model parameters. Due to the broad applicability, the MBAR equations are rather difficult to apply for free-energy calculations using different types of MD simulations including enhanced conformational sampling methods and free-energy perturbation. In this review, we first summarize the basic theory of the MBAR equations and categorize the representative usages into the following four: (i) perturbation, (ii) scaling, (iii) accumulation, and (iv) full potential energy. For each, we explain how to prepare input data using MD simulation trajectories for solving the MBAR equations. MBAR is also useful to estimate reliable free-energy differences using MD trajectories based on a semi-empirical quantum mechanics/molecular mechanics (QM/MM) model and ab initio QM/MM energy calculations on the MD snapshots. We also explain how to use the MBAR software in the GENESIS package, which we call mbar_analysis, for the four representative cases. The proposed estimations of free-energy changes and thermodynamic averages are effective and useful for various biomolecular systems.