QM/MM studies of enzymes

Combined quantum-mechanics/molecular-mechanics (QM/MM) methods are making rapid progress both methodologically and with respect to their range of application. Mechanistic studies on enzymes, including contributions towards the understanding of enzyme catalysis, continue to be a major target. They are joined by calculations of pK(a) values, redox properties, ground- and excited-state spectroscopic parameters, and excited-state dynamics. Methodological advances include improved QM/MM schemes, in particular new approaches for an effective treatment of the QM-MM electrostatic interactions, and the incorporation of new efficient and accurate QM methods in QM/MM schemes.     

QM/MM free energy simulations: recent progress and challenges

Due to the higher computational cost relative to pure molecular mechanical (MM) simulations, hybrid quantum mechanical/molecular mechanical (QM/MM) free energy simulations particularly require a careful consideration of balancing computational cost and accuracy. Here, we review several recent developments in free energy methods most relevant to QM/MM simulations and discuss several topics motivated by these developments using simple but informative examples that involve processes in water. For chemical reactions, we highlight the value of invoking enhanced sampling technique (e.g. replica-exchange) in umbrella sampling calculations and the value of including collective environmental variables (e.g. hydration level) in metadynamics simulations; we also illustrate the sensitivity of string calculations, especially free energy along the path, to various parameters in the computation. Alchemical free energy simulations with a specific thermodynamic cycle are used to probe the effect of including the first solvation shell into the QM region when computing solvation free energies. For cases where high-level QM/MM potential functions are needed, we analyse two different approaches: the QM/MM–MFEP method of Yang and co-workers and perturbative correction to low-level QM/MM free energy results. For the examples analysed here, both approaches seem productive although care needs to be exercised when analysing the perturbative corrections.     

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.     

Refined models of New Delhi metallo-beta-lactamase-1 with inhibitors: an QM/MM modeling study

New Delhi metallo-beta-lactamase 1 (NDM-1) has been identified as a potential target for the treatment of multi-drug resistance bacterial infections. We used molecular docking, normal MD, SIE, QM/MM MD simulations, QM/MM GBSA binding free energy, and QM/MM GBSA alanine-scanning mutagenesis techniques to investigate interactions of the NDM-1 with 11 inhibitors (Tigecycline, BAL30072, D-captopril, Penicillin G, Ampicillin, Carbenicillin, Cephalexin, Cefaclor, Nitrocefin, Meropenem, and Imipenem). From our normal MD and QM/MM simulations, the correlation coefficients between the predicted binding free energies and experimental values are .88 and .93, respectively. Then simulations, which combined QM/MM/GBSA and alanine-scanning mutagenesis techniques, were performed and our results show that two residues (Lys211 and His250) have the strongest impact on the binding affinities of the 11 NDM-1/inhibitors. Therefore, our approach theoretically suggests that the two residues (Lys211 and His250) are responsible for the selectivity of NDM-1 associated inhibitors.     

Substrate polarization in enzyme catalysis: QM/MM analysis of the effect of oxaloacetate polarization on acetyl-CoA enolization in citrate synthase

Citrate synthase is an archetypal carbon-carbon bond forming enzyme. It promotes the conversion of oxaloacetate (OAA) to citrate by catalyzing the deprotonation (enolization) of acetyl-CoA, followed by nucleophilic attack of the enolate form of this substrate on OAA to form a citryl-CoA intermediate and subsequent hydrolysis. OAA is strongly bound to the active site and its alpha-carbonyl group is polarized. This polarization has been demonstrated spectroscopically, [(Kurz et al., Biochemistry 1985;24:452-457; Kurz and Drysdale, Biochemistry 1987;26:2623-2627)] and has been suggested to be an important catalytic strategy. Substrate polarization is believed to be important in many enzymes. The first step, formation of the acetyl-CoA enolate intermediate, is thought to be rate-limiting in the mesophilic (pig/chicken) enzyme. We have examined the effects of substrate polarization on this key step using quantum mechanical/molecular mechanical (QM/MM) methods. Free energy profiles have been calculated by AM1/CHARMM27 umbrella sampling molecular dynamics (MD) simulations, together with potential energy profiles. To study the influence of OAA polarization, profiles were calculated with different polarization of the OAA alpha-carbonyl group. The results indicate that OAA polarization influences catalysis only marginally but has a larger effect on intermediate stabilization. Different levels of treatment of OAA are compared (MM or QM), and its polarization in the protein and in water analyzed at the B3LYP/6-31+G(d)/CHARMM27 level. Analysis of stabilization by individual residues shows that the enzyme mainly stabilizes the enolate intermediate (not the transition state) through electrostatic (including hydrogen bond) interactions: these contribute much more than polarization of OAA.     

QM/MM model study on properties and structure of some antibiotics in gas phase: Comparison of energy and NMR chemical shift

The combination of Quantum Mechanics (QM) and Molecular Mechanics (MM) methods has become an alternative tool for many applications for which pure QM and MM are not suitable. The QM/MM method has been used for different types of problems, for example: structural biology, surface phenomena, and liquid phase. In this paper, we have used these methods for antibiotics and then we compared results. The calculations were done by the full ab initio method (HF/3-21G) and the (HF/STO-3G) and QM/MM (ONIOM) method with HF (3-21G)/AM1/UFF and HF (STO-3G)/AM1/UFF. We found the geometry obtained by the QM/MM method to be very accurate, and we can use this rapid method in place of time consuming ab initio methods for large molecules. Comparison of energy values in the QM/MM and QM methods is given. In the present work, we compare chemical shifts and conclude that the QM/MM method is a perturbed full QM method. The work has been done on penicillin, streptomycin, benzyl penicillin, neomycin, kanamycin, gentamicin, and amoxicillin.     

QM/MM model study on properties and structure of some antibiotics in gas phase: Comparison of energy and NMR chemical shift

The combination of Quantum Mechanics (QM) and Molecular Mechanics (MM) methods has become an alternative tool for many applications for which pure QM and MM are not suitable. The QM/MM method has been used for different types of problems, for example: structural biology, surface phenomena, and liquid phase. In this paper, we have used these methods for antibiotics and then we compare results. The calculations were done by the full ab initio method (HF/3-21G) and the (HF/STO-3G) and QM/MM (ONIOM) method with HF (3-21G)/AM1/UFF and HF (STO-3G)/AM1/UFF. We found the geometry that has obtained by the QM/MM method to be very accurate, and we can use this rapid method in place of time consuming ab initio methods for large molecules. Comparison of energy values in the QM/MM and QM methods is given. In the present work, we compare chemical shifts and conclude that the QM/MM method is a perturbed full QM method. The work has been done on penicillin, streptomycin, benzyl penicillin, neomycin, kanamycin, gentamicin, and amoxicillin.     

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.     

Correlation between biological activity and binding energy in systems of integrin with cyclic RGD-containing binders: a QM/MM molecular dynamics study

We here report a combined quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) study on the binding interactions between the α(V)β(3) integrin and eight cyclic arginine-glycine-aspartate (RGD) containing peptides. The initial conformation of each peptide within the binding site of the integrin was determined by docking the ligand to the reactive site of the integrin crystal structure with the aid of docking software FRED. The subsequent QM/MM MD simulations of the complex structures show that these eight cyclic RGD-peptides have a generally similar interaction mode with the binding site of the integrin to the cyclo(RGDf-N[M]V) analog found in the crystal structure. Still, there are subtle differences in the interactions of peptide ligands with the integrin, which contribute to the different inhibition activities. The averaged QM/MM protein-ligand interaction energy (IE) is remarkably correlated to the biological activity of the ligand. The IE, as well as a three-variable model which is somewhat interpretable, thus can be used to predict the bioactivity of a new ligand quantitatively, at least within a family of analogs. The present study establishes a helpful protocol for advancing lead compounds to potent inhibitors.     

Optimization of cutting schemes for the evaluation of molecular electrostatic potentials in proteins via Moving-Domain QM/MM

This work presents new developments of the moving-domain QM/MM (MoD-QM/MM) method for modeling protein electrostatic potentials. The underlying goal of the method is to map the electronic density of a specific protein configuration into a point-charge distribution. Important modifications of the general strategy of the MoD-QM/MM method involve new partitioning and fitting schemes and the incorporation of dynamic effects via a single-step free energy perturbation approach (FEP). Selection of moderately sized QM domains partitioned between and C (from C=O), with incorporation of delocalization of electrons over neighboring domains, results in a marked improvement of the calculated molecular electrostatic potential (MEP). More importantly, we show that the evaluation of the electrostatic potential can be carried out on a dynamic framework by evaluating the free energy difference between a non-polarized MEP and a polarized MEP. A simplified form of the potassium ion channel protein Gramicidin-A from Bacillus brevis is used as the model system for the calculation of MEP. Figure Schematic representation of the Moving Domain QM/MM method     

Recent developments of the quantum chemical cluster approach for modeling enzyme reactions

The quantum chemical cluster approach for modeling enzyme reactions is reviewed. Recent applications have used cluster models much larger than before which have given new modeling insights. One important and rather surprising feature is the fast convergence with cluster size of the energetics of the reactions. Even for reactions with significant charge separation it has in some cases been possible to obtain full convergence in the sense that dielectric cavity effects from outside the cluster do not contribute to any significant extent. Direct comparisons between quantum mechanics (QM)-only and QM/molecular mechanics (MM) calculations for quite large clusters in a case where the results differ significantly have shown that care has to be taken when using the QM/MM approach where there is strong charge polarization. Insights from the methods used, generally hybrid density functional methods, have also led to possibilities to give reasonable error limits for the results. Examples are finally given from the most extensive study using the cluster model, the one of oxygen formation at the oxygen-evolving complex in photosystem II.

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.     

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.     

Chromophore Structure of Cyanobacterial Phytochrome Cph1 in the Pr State: Reconciling Structural and Spectroscopic Data by QM/MM Calculations

A quantum mechanics (QM)/molecular mechanics (MM) hybrid method was applied to the Pr state of the cyanobacterial phytochrome Cph1 to calculate the Raman spectra of the bound PCB cofactor. Two QM/MM models were derived from the atomic coordinates of the crystal structure. The models differed in the protonation site of His²⁶⁰ in the chromophore-binding pocket such that either the δ-nitrogen (M-HSD) or the ɛ-nitrogen (M-HSE) carried a hydrogen. The optimized structures of the two models display small differences specifically in the orientation of His²⁶⁰ with respect to the PCB cofactor and the hydrogen bond network at the cofactor-binding site. For both models, the calculated Raman spectra of the cofactor reveal a good overall agreement with the experimental resonance Raman (RR) spectra obtained from Cph1 in the crystalline state and in solution, including Cph1 adducts with isotopically labeled PCB. However, a distinctly better reproduction of important details in the experimental spectra is provided by the M-HSD model, which therefore may represent an improved structure of the cofactor site. Thus, QM/MM calculations of chromoproteins may allow for refining crystal structure models in the chromophore-binding pocket guided by the comparison with experimental RR spectra. Analysis of the calculated and experimental spectra also allowed us to identify and assign the modes that sensitively respond to chromophore-protein interactions. The most pronounced effect was noted for the stretching mode of the methine bridge A-B adjacent to the covalent attachment site of PCB. Due a distinct narrowing of the A-B methine bridge bond angle, this mode undergoes a large frequency upshift as compared with the spectrum obtained by QM calculations for the chromophore in vacuo. This protein-induced distortion of the PCB geometry is the main origin of a previous erroneous interpretation of the RR spectra based on QM calculations of the isolated cofactor.Abbreviations: Agp1, phytochrome from Agrobacterium tumefaciens; α-CPC, α-subunit of C-phycocyanin; BV, biliverdin IXα; B3LYP, three-parameter exchange functional according to Becke, Lee, Yang, and Parr; DFT, density functional theory; DrBphP, phytochrome from Deinococcus radiodurans; GAF, domain found in cGMP-specific phosphodiesterases; MM, molecular mechanics; MD, molecular dynamics; N-H ip, N-H in-plane bending; PCB, phycocyanobilin; PED, potential energy distribution; phyA, plant phytochrome; Pr, Pfr, red- and far-red absorbing parent states of phytochrome; PΦB, phytochromobilin; QM, quantum mechanics; RMSD, root mean-square deviation; RR, resonance Raman     

Protein effects in non-heme iron enzyme catalysis: insights from multiscale models

Many non-heme iron enzymes have similar sets of ligands but still catalyze widely different reactions. A key question is, therefore, the role of the protein in controlling reactivity and selectivity. Examples from multiscale simulations, primarily QM/MM, of both mono- and binuclear non-heme iron enzymes are used to analyze the stability of these models and what they reveal about the protein effects. Consistent results from QM/MM modeling are the importance of the hydrogen bond network to control reactivity and electrostatic stabilization of electron transfer from second-sphere residues. The long-range electrostatic effects on reaction barriers are small for many systems. In the systems where large electrostatic effects have been reported, these lead to higher barriers. There is thus no evidence of any significant long-range electrostatic effects contributing to the catalytic efficiency of non-heme iron enzymes. However, the correct evaluation of electrostatic contributions is challenging, and the correlation between calculated residue contributions and the effects of mutation experiments is not very strong. The largest benefits of QM/MM models are thus the improved active-site geometries, rather than the calculation of accurate energies. Reported differences in mechanistic predictions between QM and QM/MM models can be explained by differences in hydrogen bonding patterns in and around the active site. Correctly constructed cluster models can give results with similar accuracy as those from multiscale models, but the latter reduces the risk of drawing the wrong mechanistic conclusions based on incorrect geometries and are preferable for all types of modeling, even when using very large QM parts.     

Exploring the RING-Catalyzed Ubiquitin Transfer Mechanism by MD and QM/MM Calculations

Ubiquitylation is a universal mechanism for controlling cellular functions. A large family of ubiquitin E3 ligases (E3) mediates Ubiquitin (Ub) modification. To facilitate Ub transfer, RING E3 ligases bind both the substrate and ubiquitin E2 conjugating enzyme (E2) linked to Ub via a thioester bond to form a catalytic complex. The mechanism of Ub transfer catalyzed by RING E3 remains elusive. By employing a combined computational approach including molecular modeling, molecular dynamics (MD) simulations, and quantum mechanics/molecular mechanics (QM/MM) calculations, we characterized this catalytic mechanism in detail. The three-dimensional model of dimeric RING E3 ligase RNF4 RING, E2 ligase UbcH5A, Ub and the substrate SUMO2 shows close contact between the substrate and Ub transfer catalytic center. Deprotonation of the substrate lysine by D117 on UbcH5A occurs with almost no energy barrier as calculated by MD and QM/MM calculations. Then, the side chain of the activated lysine gets close to the thioester bond via a conformation change. The Ub transfer pathway begins with a nucleophilic addition that forms an oxyanion intermediate of a 4.23 kcal/mol energy barrier followed by nucleophilic elimination, resulting in a Ub modified substrate by a 5.65 kcal/mol energy barrier. These results provide insight into the mechanism of RING-catalyzed Ub transfer guiding the discovery of Ub system inhibitors.     

The reaction mechanism of paraoxon hydrolysis by phosphotriesterase from combined QM/MM simulations

Molecular dynamics simulations employing combined quantum mechanical and molecular mechanical (QM/MM) potentials have been carried out to investigate the reaction mechanism of the hydrolysis of paraoxon by phosphotriesterase (PTE). We used a dual-level QM/MM approach that synthesizes accurate results from high-level electronic structure calculations with computational efficiency of semiempirical QM/MM potentials for free energy simulations. In particular, the intrinsic (gas-phase) energies of the active site in the QM region are determined by using density functional theory (B3LYP) and second-order M?ller-Plesset perturbation theory (MP2) and the molecular dynamics free energy simulations are performed by using the mixed AM1:CHARMM potential. The simulation results suggest a revised mechanism for the phosphotriester hydrolysis mechanism by PTE. The reaction free energy profile is mirrored by structural motions of the binuclear metal center in the active site. The two zinc ions occupy a compact conformation with an average zinc-zinc distance of 3.5 +/- 0.1 A in the Michaelis complex, whereas it is elongated to 5.3 +/- 0.3 A at the transition state and product state. The substrate is loosely bound to the more exposed zinc ion (Znbeta2+) at an average distance of 3.8 A +/- 0.3 A. The P=O bond of the substrate paraoxon is activated by adopting a tight coordination to the Znbeta2+, releasing the coordinate to the bridging hydroxide ion and increasing its nucleophilicity. It was also found that a water molecule enters into the binding pocket of the loosely bound binuclear center, originally occupied by the nucleophilic hydroxide ion. We suggest that the proton of this water molecule is taken up by His254 at low pH or released to the solvent at high pH, resulting in a hydroxide ion that pulls the Znbeta2+ ion closer to form the compact configuration and restores the resting state of the enzyme.     

Multiscale methods for macromolecular simulations

In this article we review the key modeling tools available for simulating biomolecular systems. We consider recent developments and representative applications of mixed quantum mechanics/molecular mechanics (QM/MM), elastic network models (ENMs), coarse-grained molecular dynamics, and grid-based tools for calculating interactions between essentially rigid protein assemblies. We consider how the different length scales can be coupled, both in a sequential fashion (e.g. a coarse-grained or grid model using parameterization from MD simulations), and via concurrent approaches, where the calculations are performed together and together control the progression of the simulation. We suggest how the concurrent coupling approach familiar in the context of QM/MM calculations can be generalized, and describe how this has been done in the CHARMM macromolecular simulation package.