Dual-topology/dual-coordinate free-energy simulation using QM/MM force field

We have developed a dual-topology/dual-coordinate free-energy simulation method for use with a QM/MM force field. By combining two parallel processes into one alchemical process, we are able to compute the double free-energy difference (delta deltaF) within a single simulation, which eliminates half of the expensive quantum-mechanical simulation in general. The method has been tested in computing the solvation free-energy differences of several molecular pairs and shows close agreement with experimental results.     

Chaperoned alchemical free energy simulations: a general method for QM, MM, and QM/MM potentials

A general method for alchemical free energy simulations using QM, MM, and QM/MM potential is developed by introducing "chaperones" to restrain the structures, particularly near the end points. A calculation of the free energy difference between two triazole tautomers in aqueous solution is used to illustrate the method.     

Prediction and rationalization of protein pKa values using QM and QM/MM methods

We describe the development and application of a computational method for the prediction and rationalization of pKa values of ionizable residues in proteins, based on ab initio quantum mechanics (QM) and the effective fragment potential (EFPs) method (a hybrid QM/MM method). The theoretical developments include (1) a covalent boundary method based on frozen localized orbitals, (2) divide-and-conquer methods for the ab initio computation of protein EFPs consisting of multipoles up to octupoles and dipole polarizability tensors, (3) a method for computing vibrational free energies for a localized molecular region, and (4) solutions of the polarized continuum model of bulk solvation equations for protein-sized systems. The QM-based pKa prediction method is one of the most accurate methods currently available and can be used in cases where other pKa prediction methods fail. Preliminary analysis of the computed results indicate that many pKa values (1) are primarily determined by hydrogen bonds rather than long-range charge-charge interactions and (2) are relatively insensitive to large-scale dynamical fluctuations of the protein structure.     

51V NMR chemical shifts calculated from QM/MM models of vanadium chloroperoxidase

(51)V NMR chemical shifts calculated from QM/MM-optimized (QM=quantum mechanical; MM=molecular mechanical) models of vanadium-dependent chloroperoxidase (VCPO) are presented. An extensive number of protonation states for the vanadium cofactor (active site of the protein) and a number of probable positional isomers for each of the protonation states are considered. The size of the QM region is increased incrementally to observe the convergence behavior of the (51)V NMR chemical shifts. A total of 40 models are assessed by comparison to experimental solid-state (51)V NMR results recently reported in the literature. Isotropic chemical shifts are found to be a poor indicator of the protonation state; however, anisotropic chemical shifts and the nuclear quadrupole tensors appear to be sensitive to changes in the proton environment of the vanadium nuclei. This detailed investigation of the (51)V NMR chemical shifts computed from QM/MM models provides further evidence that the ground state is either a triply protonated (one axial water and one equatorial hydroxyl group) or a doubly protonated vanadate moiety in VCPO. Particular attention is given to the electrostatic and geometric effects of the protein environment. This is the first study to compute anisotropic NMR chemical shifts from QM/MM models of an active metalloprotein for direct comparison with solid-state MAS NMR data. This theoretical approach enhances the potential use of experimental solid-state NMR spectroscopy for the structural determination of metalloproteins.     

Nuclear-magnetic-resonance shielding constants calculated by pseudospectral methods

We have developed an algorithm based upon pseudospectral (PS) ab initio electronic structure methods for evaluating nuclear magnetic shielding constants using gauge-including atomic orbitals (GIAOs) in the spin-restricted and spin-unrestricted formalisms of Hartree-Fock (HF) theory and density-functional theory (DFT). The nuclear magnetic shielding constants for both 1H and 13C calculated using PS methodology for 21 small molecules have absolute mean errors of less than 0.3 ppm in comparison with analytic integral results. CPU timing comparisons between PS methods and conventional methods carried out for seven large molecules ranging from 510 to 1285 basis functions demonstrate that the PS methods are an order of magnitude more efficient than the conventional methods. PS-HF was between 9 and 26 times faster than conventional integral technology, and PS-DFT (Becke three-parameter Lee-Yang-Parr) was between 6 and 21 times faster.     

Binding affinities by alchemical perturbation using QM/MM with a large QM system and polarizable MM model

The most general way to improve the accuracy of binding‐affinity calculations for protein–ligand systems is to use quantum‐mechanical (QM) methods together with rigorous alchemical‐perturbation (AP) methods. We explore this approach by calculating the relative binding free energy of two synthetic disaccharides binding to galectin‐3 at a reasonably high QM level (dispersion‐corrected density functional theory with a triple‐zeta basis set) and with a sufficiently large QM system to include all short‐range interactions with the ligand (744–748 atoms). The rest of the protein is treated as a collection of atomic multipoles (up to quadrupoles) and polarizabilities. Several methods for evaluating the binding free energy from the 3600 QM calculations are investigated in terms of stability and accuracy. In particular, methods using QM calculations only at the endpoints of the transformation are compared with the recently proposed non‐Boltzmann Bennett acceptance ratio (NBB) method that uses QM calculations at several stages of the transformation. Unfortunately, none of the rigorous approaches give sufficient statistical precision. However, a novel approximate method, involving the direct use of QM energies in the Bennett acceptance ratio method, gives similar results as NBB but with better precision, ～3 kJ/mol. The statistical error can be further reduced by performing a greater number of QM calculations. © 2015 Wiley Periodicals, Inc.     

Computing the NMR spectrum of a bulk ionic liquid phase by QM/MM methods

The dependence of (1)H and (13)C NMR chemical shifts of 1-butyl-3-methylimidazolium ([bmim])-based room-temperature ionic liquids on the counteranion ([BF(4)], [MeSO(4)]) is investigated experimentally and computationally. The local structure of the ionic liquids is investigated by means of DFT calculations of the structure of ion pairs and molecular dynamics simulations. Clusters extracted from the simulation runs are used to calculate (1)H and (13)C chemical shifts by means of QM/MM methods with various partition schemes. Proton H2 of the imidazolium ring is the most sensitive to the counteranion; its chemical shift is strongly dependent on subtle details of the arrangement of the two closest anions. It is shown that a correct spacing of signals can be attained by including the two anions closest to C2 and H2 in the QM layer.     

Binding-affinity predictions of HSP90 in the D3R Grand Challenge 2015 with docking,MM/GBSA,QM/MM,and free-energy simulations

We have estimated the binding affinity of three sets of ligands of the heat-shock protein 90 in the D3R grand challenge blind test competition. We have employed four different methods, based on five different crystal structures: first, we docked the ligands to the proteins with induced-fit docking with the Glide software and calculated binding affinities with three energy functions. Second, the docked structures were minimised in a continuum solvent and binding affinities were calculated with the MM/GBSA method (molecular mechanics combined with generalised Born and solvent-accessible surface area solvation). Third, the docked structures were re-optimised by combined quantum mechanics and molecular mechanics (QM/MM) calculations. Then, interaction energies were calculated with quantum mechanical calculations employing 970–1160 atoms in a continuum solvent, combined with energy corrections for dispersion, zero-point energy and entropy, ligand distortion, ligand solvation, and an increase of the basis set to quadruple-zeta quality. Fourth, relative binding affinities were estimated by free-energy simulations, using the multi-state Bennett acceptance-ratio approach. Unfortunately, the results were varying and rather poor, with only one calculation giving a correlation to the experimental affinities larger than 0.7, and with no consistent difference in the quality of the predictions from the various methods. For one set of ligands, the results could be strongly improved (after experimental data were revealed) if it was recognised that one of the ligands displaced one or two water molecules. For the other two sets, the problem is probably that the ligands bind in different modes than in the crystal structures employed or that the conformation of the ligand-binding site or the whole protein changes.     

Revealing the molecular mechanisms of proteolysis of SARS-CoV-2 Mpro by QM/MM computational methods

SARS-CoV-2 M^pro is one of the enzymes essential for the replication process of the virus responsible for the COVID-19 pandemic. This work is focused on exploring its proteolysis reaction by means of QM/MM methods. The resulting free energy landscape of the process provides valuable information on the species appearing along the reaction path and suggests that the mechanism of action of this enzyme, taking place in four steps, slightly differs from that of other cysteine proteases. Our predictions, which are in agreement with some recently published experimental data, can be used to guide the design of COVID-19 antiviral compounds with clinical potential.

The molecular mechanism of the proteolysis reaction catalyzed by SARS-CoV-2 M^pro, one of the enzymes essential for the replication process of the virus responsible for the COVID-19 pandemic, is described using computational QM/MM methods.     

Insight into enzymatic C-F bond formation from QM and QM/MM calculations

The C-F bond-forming step in the fluorinase, the only native fluorination enzyme characterized to date, has been studied. The enzyme catalyzes the reaction between S-adenosyl-L-methionine (SAM) and fluoride ions to form 5'-fluoro-5'-deoxyadenosine (5'-FDA) and L-methionine. To obtain an insight into the mechanism of this unusual enzymatic reaction and to elucidate the role of the enzyme in catalysis, we have explored the conformational energetics of SAM and the intrinsic reactivity patterns of SAM and fluoride with DFT (BP86) and continuum solvent methods, before investigating the full enzymatic system with combined DFT/CHARMM calculations. We find that the enzymatic reaction follows an S(N)2 reaction mechanism, concurring with the intrinsic reactivity preferences in solution. The formation of sulfur ylides is thermodynamically strongly disfavored, and an alternative elimination-addition mechanism involving the concerted anti-Markovnikov addition of HF to an enol ether is energetically viable, but kinetically prohibitive. The S(N)2 activation energy is 92 (112) kJ mol(-)(1) in solution, but only 53 (63) kJ mol(-1) in the enzyme, and the reaction energy in the enzyme is -25 (-34) kJ mol(-1) (values in parentheses are B3LYP single-point energies). The fluorinase thus lowers the barrier for C-F bond formation by 39 (49) kJ mol(-)(1). A decomposition analysis shows that the major role of the enzyme is in the preparation and positioning of the substrates.     

MM and QM/MM Modeling of Threonyl-tRNA Synthetase: Model Testing and Simulations

Aminoacyl-tRNA synthetases are centrally important enzymes in protein synthesis. We have investigated threonyl-tRNA synthetase from E. coli, complexed with reactants, using molecular mechanics and combined quantum mechanical/molecular mechanical (QM/MM) techniques. These modeling methods have the potential to provide molecular level understanding of enzyme catalytic processes. Modeling of this enzyme presents a number of challenges. The procedure of system preparation and testing is described in detail. For example, the number of metal ions at the active site, and their positions, were investigated. Molecular dynamics simulations suggest that the system is most stable when it contains only one magnesium ion, and the zinc ion is removed. Two different QM/MM methods were tested in models based on the findings of MM molecular dynamics simulations. AM1/CHARMM calculations resulted in unrealistic structures for the phosphates in this system. This is apparently due to an error of AM1. PM3/CHARMM calculations proved to be more suitable for this enzyme system. These results will provide a useful basis for future modeling investigations of the enzyme mechanism and dynamics.