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.     

A versatile AMBER-Gaussian QM/MM interface through PUPIL

The PUPIL package (Program for User Package Interfacing and Linking) originally was developed to interface different programs for multiscale calculations in materials sciences (Torras et al., J Comput Aided Mater Des 2006, 13, 201; Torras et al., Comput Phys Commun 2007, 177, 265). Here we present an extension of PUPIL to computational chemistry by interfacing two widely used computational chemistry programs: AMBER (molecular dynamics) and Gaussian (quantum chemistry). The benefit is to allow the application of the advanced MD techniques available in AMBER to a hybrid QM/MM system in which the forces and energy on the QM part can be computed by any of the methods available in Gaussian. To illustrate, we present two example applications: A MD calculation of alanine dipeptide in explicit water, and a use of the steered MD capabilities in AMBER to calculate the free energy of reaction for the dissociation of Angeli's salt.     

The adaptive buffered force QM/MM method in the CP2K and AMBER software packages

The implementation and validation of the adaptive buffered force (AdBF) quantum‐mechanics/molecular‐mechanics (QM/MM) method in two popular packages, CP2K and AMBER are presented. The implementations build on the existing QM/MM functionality in each code, extending it to allow for redefinition of the QM and MM regions during the simulation and reducing QM‐MM interface errors by discarding forces near the boundary according to the buffered force‐mixing approach. New adaptive thermostats, needed by force‐mixing methods, are also implemented. Different variants of the method are benchmarked by simulating the structure of bulk water, water autoprotolysis in the presence of zinc and dimethyl‐phosphate hydrolysis using various semiempirical Hamiltonians and density functional theory as the QM model. It is shown that with suitable parameters, based on force convergence tests, the AdBF QM/MM scheme can provide an accurate approximation of the structure in the dynamical QM region matching the corresponding fully QM simulations, as well as reproducing the correct energetics in all cases. Adaptive unbuffered force‐mixing and adaptive conventional QM/MM methods also provide reasonable results for some systems, but are more likely to suffer from instabilities and inaccuracies. © 2015 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

QM/MM method for metal–organic interfaces

We present a QM/MM method for modeling metal/organic interfaces, which incorporates contributions from long‐range electron correlation, characteristic to metals and non‐bonded interactions in organic systems. This method can be used to study structurally irregular systems. We apply the method to model finite size domains of self‐assembled monolayers on the gold (111) surface and discuss the influence of boundary effects on the electrostatic and electronic properties of these systems. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

New QM/MM implementation of the DFTB3 method in the gromacs package

The approximate density‐functional tight‐binding theory method DFTB3 has been implemented in the quantum mechanics/molecular mechanics (QM/MM) framework of the Gromacs molecular simulation package. We show that the efficient smooth particle–mesh Ewald implementation of Gromacs extends to the calculation of QM/MM electrostatic interactions. Further, we make use of the various free‐energy functionalities provided by Gromacs and the PLUMED plugin. We exploit the versatility and performance of the current framework in three typical applications of QM/MM methods to solve biophysical problems: (i) ultrafast proton transfer in malonaldehyde, (ii) conformation of the alanine dipeptide, and (iii) electron‐induced repair of a DNA lesion. Also discussed is the further development of the framework, regarding mostly the options for parallelization. © 2015 Wiley Periodicals, Inc.     

Interfacing Q-Chem and CHARMM to perform QM/MM reaction path calculations

A hybrid quantum mechanical/molecular mechanical (QM/MM) potential energy function with Hartree-Fock, density functional theory (DFT), and post-HF (RIMP2, MP2, CCSD) capability has been implemented in the CHARMM and Q-Chem software packages. In addition, we have modified CHARMM and Q-Chem to take advantage of the newly introduced replica path and the nudged elastic band methods, which are powerful techniques for studying reaction pathways in a highly parallel (i.e., parallel/parallel) fashion, with each pathway point being distributed to a different node of a large cluster. To test our implementation, a series of systems were studied and comparisons were made to both full QM calculations and previous QM/MM studies and experiments. For instance, the differences between HF, DFT, MP2, and CCSD QM/MM calculations of H2O...H2O, H2O...Na+, and H2O...Cl- complexes have been explored. Furthermore, the recently implemented polarizable Drude water model was used to make comparisons to the popular TIP3P and TIP4P water models for doing QM/MM calculations. We have also computed the energetic profile of the chorismate mutase catalyzed Claisen rearrangement at various QM/MM levels of theory and have compared the results with previous studies. Our best estimate for the activation energy is 8.20 kcal/mol and for the reaction energy is -23.1 kcal/mol, both calculated at the MP2/6-31+G(d)//MP2/6-31+G(d)/C22 level of theory.     

Prediction of pKas of Late Transition-Metal Hydrides via a QM/QM Approach

Three implicit solvation models, the conductor-like polarizable continuum model (C-PCM), the conductor-like screening model (COSMO), and universal implicit solvent model (SMD), combined with a hybrid two layer QM/QM approach (ONIOM), were utilized to calculate the pK_a values, using a direct thermodynamic scheme, of a set of Group 10 transition metal (TM) hydrides in acetonitrile. To obtain the optimal combination of quantum methods for ONIOM calculations with implicit solvation models, the influence of factors, such as the choice of density functional and basis set, the atomic radii used to build a cavity in the solvent, and the size of the model system in an ONIOM scheme, was examined. Additionally, the impact of Grimme's empirical dispersion correction and exact exchange was also investigated. The results were calibrated by experimental data. This investigation provides insight about effective models for the prediction of thermodynamic properties of TM-containing complexes with bulky ligands. © 2019 Wiley Periodicals, Inc.     

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.     

QM/QM docking method based on the variational finite localized molecular orbital approximation

We present a derivation of the semiempirical variational finite localized molecular orbital (VFL) approximation, which was introduced by Anikin et al. (J Chem Phys 2004, 121, 1266). On the basis of VFL approximation, we developed the novel semiempirical (quantum mechanical) QM/QM method in which a part of the system, including the ligand and protein active site, are treated self-consistently, while the protein bulk is considered as carrying a frozen electronic density matrix. The developed method is applied toward the QM docking study for the p56 LCK SH2 domain. The virtual search has predicted 10 most potent inhibitors by searching through the database of 200,000 empirically docked poses of 20,000 drug-like molecules. Energy score calculation of each complex roughly consisting of 1700 atoms took 14.54 s of single-CPU time at the NDDO AM1 level. The entire computation performed on a 32-CPU cluster would be accomplished in 1 day. Flexible ligand QM docking studies, performed on a subset of 10,000 poses, required 153.03 s of single-CPU time per complex. The entire calculation performed on the 32-CPU cluster would be finished in half-day.     

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.     

Quantifying Electronic Effects in QM and QM/MM Biomolecular Modeling with the Fukui Function

Multi-scale quantum-mechanical/molecular-mechanical(QM/MM) and large-scale QM simulation provide valuable insight into enzyme mechanism and structure-property relationships. Analysis of the electron density afforded through these methods can enhance our understanding of how the enzyme environment modulates reactivity at the enzyme active site. From this perspective, tools from conceptual density functional theory to interrogate electron densities can provide added insight into enzyme function. We recently introduced the highly parallelizable Fukui shift analysis(FSA) method, which identifies how frontier states of an active site are altered by the presence of an additional QM residue to identify when QM treatment of a residue is essential as a result of quantum-mechanically affecting the behavior of the active site. We now demonstrate and analyze distance and residue dependence of Fukui function shifts in pairs of residues representing different non-covalent interactions. We also show how the interpretation of the Fukui function as a measure of relative nucleophilicity provides insight into enzymes that carry out S_N2 methyl transfer. The FSA method represents a promising approach for the systematic, unbiased determination of quantum mechanical effects in enzymes and for other complex systems that necessitate multi-scale modeling.     

Electronic absorption spectra of pyridine and nicotine in aqueous solution with a combined molecular dynamics and polarizable QM/MM approach

The electronic absorption spectra of pyridine and nicotine in aqueous solution have been computed using a multistep approach. The computational protocol consists in studying the solute solvation with accurate molecular dynamics simulations, characterizing the hydrogen bond interactions, and calculating electronic transitions for a series of configurations extracted from the molecular dynamics trajectories with a polarizable QM/MM scheme based on the fluctuating charge model. Molecular dynamics simulations and electronic transition calculations have been performed on both pyridine and nicotine. Furthermore, the contributions of solute vibrational effect on electronic absorption spectra have been taken into account in the so called vertical gradient approximation. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

LICHEM: A QM/MM program for simulations with multipolar and polarizable force fields

We introduce an initial implementation of the LICHEM software package. LICHEM can interface with Gaussian, PSI4, NWChem, TINKER, and TINKER–HP to enable QM/MM calculations using multipolar/polarizable force fields. LICHEM extracts forces and energies from unmodified QM and MM software packages to perform geometry optimizations, single‐point energy calculations, or Monte Carlo simulations. When the QM and MM regions are connected by covalent bonds, the pseudo‐bond approach is employed to smoothly transition between the QM region and the polarizable force field. A series of water clusters and small peptides have been employed to test our initial implementation. The results obtained from these test systems show the capabilities of the new software and highlight the importance of including explicit polarization. © 2016 Wiley Periodicals, Inc.