QM/MM Methods for Biomolecular Systems

Two are better than one : Quantum mechanics/molecular mechanics (QM/MM) methods are the state‐of‐the‐art computational technique for treating reactive and other “electronic” processes in biomolecular systems. This Review presents the general methodological aspects of the QM/MM approach, its use within optimization and simulation techniques, and its areas of application, always with a biomolecular focus.

     

QM/MM vibrational mode tracking

Vibrational spectroscopy is a powerful tool to investigate the structure and dynamics of biomolecules. When small subsystems of large molecules such as active centers of enzymes are studied, quantum chemical calculations based on quantum mechanics/molecular mechanics (QM/MM) coupling schemes are a valuable means to interpret the spectra. The goal of this work is a methodological pilot study on how to selectively and thus efficiently extract certain vibrational information for extended molecular systems described by QM/MM methods. This is achieved by an extension of the mode tracking algorithm and a comparison with the partial Hessian diagonalization approach. After validating the methodology for the CO stretching vibration of 2-butanone and a delocalized CO stretch in acetylacetone, the stretching and bending modes of the CO ligand in CO myoglobin are tracked. Such systems represent an ideal application for mode tracking, because only a few strongly localized vibrations are sought for, while the large remainder of the molecule is of interest only as far as it affects these local vibrations. This influence is treated exactly by mode tracking.     

Developing adaptive QM/MM computer simulations for electrochemistry

We report the development of adaptive QM/MM computer simulations for electrochemistry, providing public access to all sources via the free and open source software development model. We present a modular workflow‐based MD simulation code as a platform for algorithms for partitioning space into different regions, which can be treated at different levels of theory on a per‐timestep basis. Currently implemented algorithms focus on targeting molecules and their solvation layers relevant to electrochemistry. Instead of using built‐in forcefields and quantum mechanical methods, the code features a universal interface, which allows for extension to a range of external forcefield programs and programs for quantum mechanical calculations, thus enabling the user to readily implement interfaces to those programs. The purpose of this article is to describe our codes and illustrate its usage. © 2016 Wiley Periodicals, Inc.     

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.     

QM/MM Studies on Cyclodextrin-Alcohol Interaction

The main objective of this study is to provide an insight into the interactions involved during adsorption of the alcohols on β-CD composite nanostructured membrane. Interactions between β-cyclodextrin (β-CD) and alcohols (methanol, ethanol and butanol) are studied using the QM/MM method. Magnitude of interaction energies show that the alcohols are adsorbed on the membrane. In addition, the thermochemical analysis suggests that the formation of these host-guest complexes is enthalpy driven.     

Prediction of the potency of inhibitors of adenosine deaminase by QM/MM calculations

QM/MM calculations show that the potency of a range of inhibitors of adenosine deaminase correlates with the relative stability of the reaction intermediate at the active site, rather than with the inhibitor binding energy.     

3D QSAR analyses of novel tyrosine kinase inhibitors based on pharmacophore alignment

In an effort to develop a quantitative ligand-binding model for the receptor tyrosine kinases, a pharmacophore search was first used to identify structural features that are common in two novel sets of 12 molecules of the 3-substituted indolin-2-ones and 19 compounds of the benzylidene malononitriles with low-to-high affinity for HER2, a kind of receptor tyrosine kinase. The common pharmacophore model based on these 31 compounds was used as a template to obtain the aligned molecular aggregate, which provided a good starting point for 3D-QSAR analysis of only the 19 benzylidene malononitriles. Two molecular field analysis (MFA) techniques, including CoMFA and CoMSIA, were used to derive the quantitative structure-activity relationships of the studied molecules. From the studied results, it was obvious that the 3D-QSAR models based on the pharmacophore alignment were superior to those based on the simple atom-by-atom fits. Considering the flexibility of the studied molecules and the difference between the active conformers and the energy-lowest conformers, the pharmacophore model can usually provide the common features for the flexible regions. Moreover, the best CoMSIA model based on the pharmacophore hypothesis gave good statistical measure from partial least-squares analysis (PLS) (q(2) = 0.71), which was slightly better than the CoMFA one. Our study demonstrated that pharmacophore modeling and CoMSIA research could be effectively combined. Results obtained from both methods helped with understanding the specific activity of some compounds and designing new specific HER2 inhibitors.     

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.     

Exploring SCC-DFTB paths for mapping QM/MM reaction mechanisms

A new first-order procedure for locating transition structures (TS) that employs hybrid quantum mechanical/molecular mechanical (QM/MM) potentials has been developed. This new technique (RPATh+RESD) combines the replica path method (RPATh) and standard reaction coordinate driving (RCD) techniques in an approach that both efficiently determines reaction barriers and successfully eliminates two key weaknesses of RCD calculations (i.e., hysteresis/discontinuities in the path and the sequential nature of the RCD procedure). In addition, we have extended CHARMM's QM/MM reaction pathway methods, the RPATh and nudged elastic band (NEB) methods, to incorporate SCC-DFTB wave functions. This newly added functionality has been applied to the chorismate mutase-catalyzed interconversion of chorismate to prephenate, which is a key step in the shikimate pathway of bacteria, fungi, and other higher plants. The RPATh+RESD barrier height (DeltaE=5.7 kcal/mol) is in good agreement with previous results from full-energy surface mapping studies (Zhang, X.; Zhang, X.; Bruice, T. C. Biochemistry 2005, 44, 10443-10448). Full reaction paths were independently mapped with RPATh and NEB methods and showed good agreement with the final transition state from the RPATh+RESD "gold standard" and previous high-level QM/MM transition states (Woodcock, H. L.; Hodoscek, M.; Gilbert, T. B.; Gill, P. M. W.; Schaefer, H. F.; Brooks, B. R. J. Comput. Chem. 2007, 28, 1485-1502). The SCC-DFTB TS geometry most closely approximates the MP2/6-31+G(d) QM/MM result. However, the barrier height is underestimated and possibly points to an area for improvement in SCC-DFTB parametrization. In addition, the steepest descents (SD) minimizer for the NEB method was modified to uncouple the in-path and off-path degrees of freedom during the minimization, which significantly improved performance. The convergence behavior of the RPATh and NEB was examined for SCC-DFTB wave functions, and it was determined that, in general, both methods converge at about the same rate, although the techniques used for convergence may be different. For instance, RPATh can effectively use the adopted basis Newton-Raphson (ABNR) minimizer, where NEB seems to require a combination of SD and ABNR.     

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     

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 QM/MM study of cisplatin-DNA oligonucleotides: from simple models to realistic systems

QM/MM calculations were employed to investigate the role of hydrogen bonding and pi stacking in several single- and double-stranded cisplatin-DNA structures. Computed geometrical parameters reproduce experimental structures of cisplatin and its complex with guanine-phosphate-guanine. Following QM/MM optimisation, single-point DFT calculations allowed estimation of intermolecular forces through atoms in molecules (AIM) analysis. Binding energies of platinated single-strand DNA qualitatively agree with myriad experimental and theoretical studies showing that complexes of guanine are stronger than those of adenine. The topology of all studied complexes confirms that platination strongly affects the stability of both single- and double-stranded DNAs: Pt-N-H...X (X = N or O) interactions are ubiquitous in these complexes and account for over 70 % of all H-bonding interactions. The pi stacking is greatly reduced by both mono- and bifunctional complexation: the former causes a loss of about 3-4 kcal mol(-1), whereas the latter leads to more drastic disruption. The effect of platination on Watson-Crick GC is similar to that found in previous studies: major redistribution of energy occurs, but the overall stability is barely affected. The BH&H/AMBER/AIM approach was also used to study platination of a double-stranded DNA octamer d(CCTG*G*TCC)d(GGACCAGG), for which an experimental structure is available. Comparison between theory and experiment is satisfactory, and also reproduces previous DFT-based studies of analogous structures. The effect of platination is similar to that seen in model systems, although the effect on GC pairing was more pronounced. These calculations also reveal weaker, secondary interactions of the form Pt...O and Pt...N, detected in several single- and double-stranded DNA.     

Electronic and geometric properties of ETS-10: QM/MM studies of cluster models

Hybrid DFT/MM methods have been used to investigate the electronic and geometric properties of the microporous titanosilicate ETS-10. A comparison of finite length and periodic models demonstrates that band gap energies for ETS-10 can be well represented with relatively small cluster models. Optimization of finite clusters leads to different local geometries for bulk and end sites, where the local bulk TiO6 geometry is in good agreement with recent experimental results. Geometry optimizations reveal that any asymmetry within the axial O-Ti-O chain is negligible. The band gap in the optimized model corresponds to a O(2p) --> Tibulk(3d) transition. The results suggest that the three Ti atom, single chain, symmetric, finite cluster is an effective model for the geometric and electronic properties of bulk and end TiO6 groups in ETS-10.