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.     

Binding free energy calculation with QM/MM hybrid methods for Abl-Kinase inhibitor

We report a Quantum mechanics/Molecular Mechanics–Poisson-Boltzmann/ Surface Area (QM/MM-PB/SA) method to calculate the binding free energy of c-Abl human tyrosine kinase by combining the QM and MM principles where the ligand is treated quantum mechanically and the rest of the receptor by classical molecular mechanics. To study the role of entropy and the flexibility of the protein ligand complex in a solvated environment, molecular dynamics calculations are performed using a hybrid QM/MM approach. This work shows that the results of the QM/MM approach are strongly correlated with the binding affinity. The QM/MM interaction energy in our reported study confirms the importance of electronic and polarization contributions, which are often neglected in classical MM-PB/SA calculations. Moreover, a comparison of semi-empirical methods like DFTB-SCC, PM3, MNDO, MNDO-PDDG, and PDDG-PM3 is also performed. The results of the study show that the implementation of a DFTB-SCC semi-empirical Hamiltonian that is derived from DFT gives better results than other methods. We have performed such studies using the AMBER molecular dynamic package for the first time. The calculated binding free energy is also in agreement with the experimentally determined binding affinity for c-Abl tyrosine kinase complex with Imatinib.     

A comparative study of trypsin specificity based on QM/MM molecular dynamics simulation and QM/MM GBSA calculation

Hydrogen bonding and polar interactions play a key role in identification of protein-inhibitor binding specificity. Quantum mechanics/molecular mechanics molecular dynamics (QM/MM MD) simulations combined with DFT and semi-empirical Hamiltonian (AM1d, RM1, PM3, and PM6) methods were performed to study the hydrogen bonding and polar interactions of two inhibitors BEN and BEN1 with trypsin. The results show that the accuracy of treating the hydrogen bonding and polar interactions using QM/MM MD simulation of PM6 can reach the one obtained by the DFT QM/MM MD simulation. Quantum mechanics/molecular mechanics generalized Born surface area (QM/MM-GBSA) method was applied to calculate binding affinities of inhibitors to trypsin and the results suggest that the accuracy of binding affinity prediction can be significantly affected by the accurate treatment of the hydrogen bonding and polar interactions. In addition, the calculated results also reveal the binding specificity of trypsin: (1) the amidinium groups of two inhibitors generate favorable salt bridge interaction with Asp189 and form hydrogen bonding interactions with Ser190 and Gly214, (2) the phenyl of inhibitors can produce favorable van der Waals interactions with the residues His58, Cys191, Gln192, Trp211, Gly212, and Cys215. This systematic and comparative study can provide guidance for the choice of QM/MM MD methods and the designs of new potent inhibitors targeting trypsin.     

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.     

Hydrogen donor-acceptor fluctuations from kinetic isotope effects: a phenomenological model

Kinetic isotope effects (KIEs) and their temperature dependence can probe the structural and dynamic nature of enzyme-catalyzed proton or hydride transfers. The molecular interpretation of their temperature dependence requires expensive and specialized quantum mechanics/molecular mechanics (QM/MM) calculations to provide a quantitative molecular understanding. Currently available phenomenological models use a nonadiabatic assumption that is not appropriate for most hydride and proton-transfer reactions, while others require more parameters than the experimental data justify. Here we propose a phenomenological interpretation of KIEs based on a simple method to quantitatively link the size and temperature dependence of KIEs to a conformational distribution of the catalyzed reaction. This model assumes adiabatic hydrogen tunneling, and by fitting experimental KIE data, the model yields a population distribution for fluctuations of the distance between donor and acceptor atoms. Fits to data from a variety of proton and hydride transfers catalyzed by enzymes and their mutants, as well as nonenzymatic reactions, reveal that steeply temperature-dependent KIEs indicate the presence of at least two distinct conformational populations, each with different kinetic behaviors. We present the results of these calculations for several published cases and discuss how the predictions of the calculations might be experimentally tested. This analysis does not replace molecular QM/MM investigations, but it provides a fast and accessible way to quantitatively interpret KIEs in the context of a Marcus-like model.     

The MoD-QM/MM methodology for structural refinement of photosystem II and other biological macromolecules

Photosynthesis Research - Quantum mechanics/molecular mechanics (QM/MM) hybrid methods are currently the most powerful computational tools for studies of structure/function relations and structural...     

Theoretical approaches for dynamical ordering of biomolecular systems

Background

Living systems are characterized by the dynamic assembly and disassembly of biomolecules. The dynamical ordering mechanism of these biomolecules has been investigated both experimentally and theoretically. The main theoretical approaches include quantum mechanical (QM) calculation, all-atom (AA) modeling, and coarse-grained (CG) modeling. The selected approach depends on the size of the target system (which differs among electrons, atoms, molecules, and molecular assemblies). These hierarchal approaches can be combined with molecular dynamics (MD) simulation and/or integral equation theories for liquids, which cover all size hierarchies.

How does the protein environment optimize the thermodynamics of thiol sulfenylation? Insights from model systems to QM/MM calculations on human 2-Cys peroxiredoxin

Protein thiol/sulfenic acid oxidation potentials provide a tool to select specific oxidation agents, but are experimentally difficult to obtain. Here, insights into the thiol sulfenylation thermodynamics are obtained from model calculations on small systems and from a quantum mechanics/molecular mechanics (QM/MM) analysis on human 2-Cys peroxiredoxin thioredoxin peroxidase B (Tpx-B). To study thiol sulfenylation in Tpx-B, our recently developed computational method to determine reduction potentials relatively compared to a reference system and based on reaction energies reduction potential from electronic energies is updated. Tpx-B forms a sulfenic acid (R-SO^?) on one of its active site cysteines during reactive oxygen scavenging. The observed effect of the conserved active site residues is consistent with the observed hydrogen bond interactions in the QM/MM optimized Tpx-B structures and with free energy calculations on small model systems. The ligand effect could be linked to the complexation energies of ligand L with CH₃S^? and CH₃SO^?. Compared to QM only calculations on Tpx-B’s active site, the QM/MM calculations give an improved understanding of sulfenylation thermodynamics by showing that other residues from the protein environment other than the active site residues can play an important role.     

Comparison of a QM/MM force field and molecular mechanics force fields in simulations of alanine and glycine "dipeptides" (Ace-Ala-Nme and Ace-Gly-Nme) in water in relation to the problem of modeling the unfolded peptide backbone in solution

We compare the conformational distributions of Ace-Ala-Nme and Ace-Gly-Nme sampled in long simulations with several molecular mechanics (MM) force fields and with a fast combined quantum mechanics/molecular mechanics (QM/MM) force field, in which the solute's intramolecular energy and forces are calculated with the self-consistent charge density functional tight binding method (SCCDFTB), and the solvent is represented by either one of the well-known SPC and TIP3P models. All MM force fields give two main states for Ace-Ala-Nme, beta and alpha separated by free energy barriers, but the ratio in which these are sampled varies by a factor of 30, from a high in favor of beta of 6 to a low of 1/5. The frequency of transitions between states is particularly low with the amber and charmm force fields, for which the distributions are noticeably narrower, and the energy barriers between states higher. The lower of the two barriers lies between alpha and beta at values of psi near 0 for all MM simulations except for charmm22. The results of the QM/MM simulations vary less with the choice of MM force field; the ratio beta/alpha varies between 1.5 and 2.2, the easy pass lies at psi near 0, and transitions between states are more frequent than for amber and charmm, but less frequent than for cedar. For Ace-Gly-Nme, all force fields locate a diffuse stable region around phi = pi and psi = pi, whereas the amber force field gives two additional densely sampled states near phi = +/-100 degrees and psi = 0, which are also found with the QM/MM force field. For both solutes, the distribution from the QM/MM simulation shows greater similarity with the distribution in high-resolution protein structures than is the case for any of the MM simulations.     

Density functional theory calculations on entire proteins for free energies of binding: Application to a model polar binding site

In drug optimization calculations, the molecular mechanics Poisson‐Boltzmann surface area (MM‐PBSA) method can be used to compute free energies of binding of ligands to proteins. The method involves the evaluation of the energy of configurations in an implicit solvent model. One source of errors is the force field used, which can potentially lead to large errors due to the restrictions in accuracy imposed by its empirical nature. To assess the effect of the force field on the calculation of binding energies, in this article we use large‐scale density functional theory (DFT) calculations as an alternative method to evaluate the energies of the configurations in a “QM‐PBSA” approach. Our DFT calculations are performed with a near‐complete basis set and a minimal parameter implicit solvent model, within the self‐consistent calculation, using the ONETEP program on protein–ligand complexes containing more than 2600 atoms. We apply this approach to the T4‐lysozyme double mutant L99A/M102Q protein, which is a well‐studied model of a polar binding site, using a set of eight small aromatic ligands. We observe that there is very good correlation between the MM and QM binding energies in vacuum but less so in the solvent. The relative binding free energies from DFT are more accurate than the ones from the MM calculations, and give markedly better agreement with experiment for six of the eight ligands. Furthermore, in contrast to MM‐PBSA, QM‐PBSA is able to correctly predict a nonbinder. Proteins 2014; 82:3335–3346. © 2014 Wiley Periodicals, Inc.     

The non-additive contribution of hydroxyl substituents to Akt kinase–apigenin affinity

The natural product apigenin is a flavonoid derivative substituted by three hydroxyl functional groups at positions 4′, 5 and 7 [OH(4′), OH(5) and OH(7)] of the basic flavonoid skeleton, which has shown strong inhibition on the development, proliferation and invasion of tumour cells by binding specifically to Akt kinase to inactivate the Akt signalling pathway. In this study, a typical non-additivity of the three hydroxyl substituents’ contributions to Akt–apigenin binding affinity is demonstrated by combination of four empirical scoring functions, molecular dynamics simulations, molecular mechanics-Poisson–Boltzmann/surface area (MM/PBSA) analyses and hybrid quantum mechanics/molecular mechanics (QM/MM) calculations. It is found that (i) the empirical scoring functions are incapable of properly reflecting the non-additivity feature, which, however, can be well described by the more rigorous MM/PBSA and QM/MM methods, (ii) the hydroxyl group contributions to ligand binding affinity are deviated significantly from linear additive model due to the strong conjugate effect and σ-effect among them, that is, the co-contribution of the three hydroxyl groups is far less than the sum of their individual contributions and (iii) as might be expected, a strong interactive effect is observed for the two adjacent substituents OH(5) and OH(7) as compared with that of distant OH(5) and OH(4′) as well as OH(7) and OH(4′). In addition, the structural basis, energetic property and molecular mechanism of the non-additivity feature are also explored in detail using the natural population analysis and quantum mechanical 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.     

QM/MM investigation of structure and spectroscopic properties of a vanadium-containing peroxidase

We present a comprehensive analysis of the most likely ground state configuration of the resting state of vanadium dependent chloroperoxidase (VCPO) based on quantum mechanics/molecular mechanics (QM/MM) evaluations of ground state properties, UV-vis spectra and NMR chemical shifts. Within the QM/MM framework, density functional theory (DFT) calculations are used to characterize the resting state of VCPO via time-dependent density functional theory (TD-DFT) calculations of electronic excitation energies and NMR chemical shifts. Comparison with available experimental data allows us to determine the most likely protonation state of VCPO, a state which results in a doubly protonated axial oxygen, a site largely stabilized by hydrogen bonds. We found that the bulk of the protein that is beyond the immediate layer surrounding the cofactor, has an important electrostatic effect on the absorption maximum. Through examination of frontier orbitals, we analyze the nature of two bound water molecules and the extent to which relevant residues in the active site influence the spectroscopy calculations.     

An Alternative Mechanism for the Methylation of Phosphoethanolamine Catalyzed by Plasmodium falciparum Phosphoethanolamine Methyltransferase

The phosphobase methylation pathway catalyzed by the phosphoethanolamine methyltransferase in Plasmodium falciparum (PfPMT), the malaria parasite, offers an attractive target for anti-parasitic drug development. PfPMT methylates phosphoethanolamine (pEA) to phosphocholine for use in membrane biogenesis. Quantum mechanics and molecular mechanics (QM/MM) calculations tested the proposed reaction mechanism for methylation of pEA involving the previously identified Tyr-19–His-132 dyad, which indicated an energetically unfavorable mechanism. Instead, the QM/MM calculations suggested an alternative mechanism involving Asp-128. The reaction coordinate involves the stepwise transfer of a proton to Asp-128 via a bridging water molecule followed by a typical S_n2-type methyl transfer from S-adenosylmethionine to pEA. Functional analysis of the D128A, D128E, D128Q, and D128N PfPMT mutants shows a loss of activity with pEA but not with the final substrate of the methylation pathway. X-ray crystal structures of the PfPMT-D128A mutant in complex with S-adenosylhomocysteine and either pEA or phosphocholine reveal how mutation of Asp-128 disrupts a hydrogen bond network in the active site. The combined QM/MM, biochemical, and structural studies identify a key role for Asp-128 in the initial step of the phosphobase methylation pathway in Plasmodium and provide molecular insight on the evolution of multiple activities in the active site of the PMT.     

Lys169 of Human Glucokinase Is a Determinant for Glucose Phosphorylation: Implication for the Atomic Mechanism of Glucokinase Catalysis

Glucokinase (GK), a glucose sensor, maintains plasma glucose homeostasis via phosphorylation of glucose and is a potential therapeutic target for treating maturity-onset diabetes of the young (MODY) and persistent hyperinsulinemic hypoglycemia of infancy (PHHI). To characterize the catalytic mechanism of glucose phosphorylation by GK, we combined molecular modeling, molecular dynamics (MD) simulations, quantum mechanics/molecular mechanics (QM/MM) calculations, experimental mutagenesis and enzymatic kinetic analysis on both wild-type and mutated GK. Our three-dimensional (3D) model of the GK-Mg²⁺-ATP-glucose (GMAG) complex, is in agreement with a large number of mutagenesis data, and elucidates atomic information of the catalytic site in GK for glucose phosphorylation. A 10-ns MD simulation of the GMAG complex revealed that Lys169 plays a dominant role in glucose phosphorylation. This prediction was verified by experimental mutagenesis of GK (K169A) and enzymatic kinetic analyses of glucose phosphorylation. QM/MM calculations were further used to study the role of Lys169 in the catalytic mechanism of the glucose phosphorylation and we found that Lys169 enhances the binding of GK with both ATP and glucose by serving as a bridge between ATP and glucose. More importantly, Lys169 directly participates in the glucose phosphorylation as a general acid catalyst. Our findings provide mechanistic details of glucose phorphorylation catalyzed by GK, and are important for understanding the pathogenic mechanism of MODY.     

Theoretical investigation on the diatomic ligand migration process and ligand binding properties in non‐O2‐binding H‐NOX domain

The Nostoc sp (Ns) H‐NOX (heme‐nitric oxide or OXygen‐binding) domain shares 35% sequence identity with soluble guanylate cyclase (sGC) and exhibits similar ligand binding property with the sGC. Previously, our molecular dynamic (MD) simulation work identified that there exists a Y‐shaped tunnel system hosted in the Ns H‐NOX interior, which servers for ligand migration. The tunnels were then confirmed by Winter et al. [PNAS 2011;108(43):E 881–889] recently using x‐ray crystallography with xenon pressured conditions. In this work, to further investigate how the protein matrix of Ns H‐NOX modulates the ligand migration process and how the distal residue composition affects the ligand binding prosperities, the free energy profiles for nitric oxide (NO), carbon monooxide (CO), and O₂ migration are explored using the steered MDs simulation and the ligand binding energies are calculated using QM/MM schemes. The potential of mean force profiles suggest that the longer branch of the tunnel would be the most favorable route for NO migration and a second NO trapping site other than the distal heme pocket along this route in the Ns H‐NOX was identified. On the contrary, CO and O₂ would prefer to diffuse via the shorter branch of the tunnel. The QM/MM (quantum mechanics/molecular mechanics) calculations suggest that the hydrophobic distal pocket of Ns H‐NOX would provide an approximately vacuum environment and the ligand discrimination would be determined by the intrinsic binding properties of the diatomic gas ligand to the heme group. Proteins 2013; 81:1363–1376. © 2013 Wiley Periodicals, Inc.     

The Role of Gln61 in HRas GTP hydrolysis: a quantum mechanics/molecular mechanics study

Activation of the water molecule involved in GTP hydrolysis within the HRas·RasGAP system is analyzed using a tailored approach based on hybrid quantum mechanics/molecular mechanics (QM/MM) simulation. A new path emerges: transfer of a proton from the attacking water molecule to a second water molecule, then a different proton is transferred from this second water molecule to the GTP. Gln(61) will stabilize the transient OH(-) and H(3)O(+) molecules thus generated. This newly proposed mechanism was generated by using, for the first time to our knowledge, the entire HRas-RasGAP protein complex in a QM/MM simulation context. It also offers a rational explanation for previous experimental results regarding the decrease of GTPase rate found in the HRas Q61A mutant and the increase exhibited by the HRas Q61E mutant.     

COBRAMM 2.0 — A software interface for tailoring molecular electronic structure calculations and running nanoscale (QM/MM) simulations

We present a new version of the simulation software COBRAMM, a program package interfacing widely known commercial and academic software for molecular modeling. It allows a problem-driven tailoring of computational chemistry simulations with effortless ground and excited-state electronic structure computations. Calculations can be executed within a pure QM or combined quantum mechanical/molecular mechanical (QM/MM) framework, bridging from the atomistic to the nanoscale. The user can perform all necessary steps to simulate ground state and photoreactions in vacuum, complex biopolymer, or solvent environments. Starting from ground-state optimization, reaction path computations, initial conditions sampling, spectroscopy simulation, and photodynamics with deactivation events, COBRAMM is designed to assist in characterization and analysis of complex molecular materials and their properties. Interpretation of recorded spectra range from steady-state to time-resolved measurements. Various tools help the user to set up the system of interest and analyze the results.