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.     

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.     

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.     

DRF90: a polarizable force field

The direct reaction field (DRF) approach has proven to be a useful tool to investigate the influence of solvents on the quantum/classical behaviour of solute molecules. In this paper, we report the latest extension of this DRF approach, which consists of the gradient of the completely classical energy expressions of this otherwise QM/MM method. They can be used in (completely classical) molecular dynamics (MD) simulations and geometry optimizations, that can be followed by a number of single point QM/MM calculations on configurations obtained in these simulations/optimizations. We report all energy and gradient expressions, and results for a number of interesting (model) systems. They include geometry optimization of the benzene dimer as well as MD simulations of some solvents. The most stable configuration for the benzene dimer is shown to be the parallel-displaced form, which is slightly more stable (0.3 kcal/mol) than the T-shaped dimer.     

Photochemical Reaction Dynamics of the Primary Event of Vision Studied by Means of a Hybrid Molecular Simulation

The photoisomerization reaction dynamics of a retinal chromophore in the visual receptor rhodopsin was investigated by means of hybrid quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations. The photoisomerization reaction of retinal constitutes the primary step of vision and is known as one of the fastest reactions in nature. To elucidate the molecular mechanism of the high efficiency of the reaction, we carried out hybrid ab initio QM/MM MD simulations of the complete reaction process from the vertically excited state to the photoproduct via electronic transition in the entire chromophore-protein complex. An ensemble of reaction trajectories reveal that the excited-state dynamics is dynamically homogeneous and synchronous even in the presence of thermal fluctuation of the protein, giving rise to the very fast formation of the photoproduct. The synchronous nature of the reaction dynamics in rhodopsin is found to originate from weak perturbation of the protein surroundings and from dynamic regulation of volume-conserving motions of the chromophore. The simulations also provide a detailed view of time-dependent modulations of hydrogen-out-of-plane vibrations during the reaction process, and identify molecular motions underlying the experimentally observed dynamic spectral modulations.     

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.     

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.     

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.     

Calculation of binding energy using BLYP/MM for the HIV-1 integrase complexed with the S-1360 and two analogues

Integrase (IN) is one of the three human immunodeficiency virus type 1 (HIV-1) enzymes essential for effective viral replication. S-1360 is a potent and selective inhibitor of HIV-1 IN. In this work, we have carried out molecular dynamics (MD) simulations using a hybrid Quantum Mechanics/Molecular Mechanics (QM/MM) approach, to determine the protein-ligand interaction energy for S-1360 and two analogues. Analysis of the MD trajectories reveals that the strongest protein-inhibitor interactions, observed in the three studied complexes, are established with Lys-159 residue and Mg(2+) cation. Calculations of binding energy using BLYP/MM level of theory reveal that there is a direct relationship between this theoretical computed property and the experimental determined anti-HIV activity.     

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.     

Elucidation of the protonation states of the catalytic residues in mtKasA: implications for inhibitor design

KasA (β-ketoacyl ACP synthase I) is involved in the biosynthetic pathway of mycolic acids, an essential component of the cell wall in Mycobacterium tuberculosis. It was shown that KasA is essential for the survival of the pathogen and thus could serve as a new drug target for the treatment of tuberculosis. The active site of KasA was previously characterized by X-ray crystallography. However, questions regarding the protonation state of specific amino acids, the orientation of the histidine groups within the active site, and additional conformers being accessible at ambient temperatures remain open and have to be addressed prior to the design of new inhibitors. We investigate the active site of KasA in this work by means of structural motifs and relative energies. Molecular dynamics (MD) simulations, free energy perturbation computations, and calculations employing the hybrid quantum mechanics/molecular mechanics (QM/MM) method made it possible to determine the protonation status and reveal important details about the catalytic mechanism of KasA. Additionally, we can rationalize the molecular basis for the acyl-transfer activity in the H311A mutant. Our data strongly suggest that inhibitors should be able to inhibit different protonation states because the enzyme can switch easily between a zwitterionic and neutral state.     

Emerging Methods and Applications to Decrypt Allostery in Proteins and Nucleic Acids

Many large protein-nucleic acid complexes exhibit allosteric regulation. In these systems, the propagation of the allosteric signaling is strongly coupled to conformational dynamics and catalytic function, challenging state-of-the-art analytical methods. Here, we review established and innovative approaches used to elucidate allosteric mechanisms in these complexes. Specifically, we report network models derived from graph theory and centrality analyses in combination with molecular dynamics (MD) simulations, introducing novel schemes that implement the synergistic use of graph theory with enhanced simulations methods and ab-initio MD. Accelerated MD simulations are used to construct “enhanced network models”, describing the allosteric response over long timescales and capturing the relation between allostery and conformational changes. “Ab-initio network models” combine graph theory with ab-initio MD and quantum mechanics/molecular mechanics (QM/MM) simulations to describe the allosteric regulation of catalysis by following the step-by-step dynamics of biochemical reactions. This approach characterizes how the allosteric regulation changes from reactants to products and how it affects the transition state, revealing a tense-to-relaxed allosteric regulation along the chemical step. Allosteric models and applications are showcased for three paradigmatic examples of allostery in protein-nucleic acid complexes: (i) the nucleosome core particle, (ii) the CRISPR-Cas9 genome editing system and (iii) the spliceosome. These methods and applications create innovative protocols to determine allosteric mechanisms in protein-nucleic acid complexes that show tremendous promise for medicine and bioengineering.     

The investigation of the secondary structure propensities and free-energy landscapes of peptide ligands by replica exchange molecular dynamics simulations

The conformational states of two peptide sequences that bind to staphylococcal enterotoxin B are sampled by replica exchange molecular dynamic (REMD) simulations in explicit water. REMD simulations were treated with 52 replicas in the range of 280–501 K for both peptides. The conformational ensembles of both peptides are dominated by random coil, bend and turn structures with a small amount of helical structures for each temperature. In addition, while an insignificant presence of β-bridge structures were observed for both peptides, the β-sheet structure was observed only for peptide 3. The results obtained from simulations at 300 K are consistent with the experimental results obtained from circular dichroism spectroscopy. From the analysis of REMD results, we also calculated hydrophobic and hydrophilic solvent accessible surface areas for both peptides, and it was observed that the hydrophobic segments of the peptides tend to form bend or turn structures. Moreover, the free-energy landscapes of both peptides were obtained by principal component analysis to understand how the secondary structural properties change according to their complex space. From the free-energy analysis, we have found several minima for both peptides at decreased temperature. For these obvious minima of both peptides, it was observed that the random coil, bend and turn structures are still dominant and the helix, β-bridge or β-sheet structures can appear or disappear with respect to minima. On the other hand, when we compare the results of REMD with conventional MD simulations for these peptides, the configurations of peptide 3 might be trapped in energy minima during the conventional MD simulations. Hence, it can be said that the REMD simulations have provided a sufficiently high sampling efficiency.     

Numerical studies of the membrane fluorescent dyes dynamics in ground and excited states

Fluorescence methods are widely used in studies of biological and model membranes. The dynamics of membrane fluorescent markers in their ground and excited electronic states and correlations with their molecular surrounding within the fully hydrated phospholipid bilayer are still not well understood. In the present work, Quantum Mechanical (QM) calculations and Molecular Dynamics (MD) simulations are used to characterize location and interactions of two membrane polarity probes (Prodan; 6-propionyl-2-dimethylaminonaphthalene and its derivative Laurdan; 2-dimethylamino-6-lauroylnaphthalene) with the dioleoylphosphatidylcholine (DOPC) lipid bilayer model. MD simulations with fluorophores in ground and excited states are found to be a useful tool to analyze the fluorescent dye dynamics and their immediate vicinity. The results of QM calculations and MD simulations are in excellent agreement with available experimental data. The calculation shows that the two amphiphilic dyes initially placed in bulk water diffuse within 10 ns towards their final location in the lipid bilayer. Analysis of solvent relaxation process in the aqueous phase occurs on the picoseconds timescale whereas it takes nanoseconds at the lipid/water interface. Four different relaxation time constants, corresponding to different relaxation processes, where observed when the dyes were embedded into the membrane.     

Achieving ergodic sampling using replica-exchange free-energy calculations

Seamless combination of multiple-walker strategies with importance-sampling free-energy methods relying upon perturbation theory and the application of time-dependent biases on collective variables is explored as an alternate avenue to achieve ergodic sampling in molecular simulations. Free-energy perturbation is associated with a parallel-tempering scheme, wherein both temperatures and the Hamiltonians representative of the various strata of a stratification scheme are swapped sequentially. In addition, adaptive biasing force simulations are performed at different temperatures in a replica-exchange context, updating continuously across the different replicas the gradient of the free energy along the relevant collective variable. Performance of the proposed methodology is evaluated in two distinct applications, namely the computation of the entropy of hydration of ethanol, following either an alchemical or a geometrical route, and the entropy that underlies the reversible folding of a short peptide.     

Molecular modeling of green fluorescent protein: structural effects of chromophore deprotonation

Molecular dynamics (MD) simulations were carried out to study the conformational rearrangement induced by deprotonation of the fluorescent chromophore in GFP, as well as the associated changes in the hydrogen-bonding network. For both the structures with either a neutral or an anionic chromophore, it was found that the beta-barrel was stable and rigid, and the conformation of the chromophore was consistent with the available x-ray structure. The conformational change in Thr203 due to deprotonation was also found to be consistent with the three-state isomerization model. Although GFP is highly fluorescent, denatured-GFP is nonfluorescent, indicating that the environment of the protein plays an important role in its fluorescence behavior. Our MD simulations, which explore the effect of the protein shell on the conformation of the chromophore, find the flexibility of the central chromophore to be significantly restricted due to the rigid nature of the protein shell. The hydrogen-bonding between the chromophore and neighboring residues was also shown to contribute to the chromophore rigidity. In addition to the MD studies, quantum mechanics/molecular mechanics (QM/MM) ONIOM calculations were carried out to investigate the effect of the beta-barrel on the internal rotation in the chromophore. Along with providing quantitative values for torsional rotation barriers about the bridging bond in the chromophore, the ONIOM calculations also validate our MD force field parameters.     

Theoretical Insights into Catalytic Mechanism of Protein Arginine Methyltransferase 1

Protein arginine methyltransferase 1 (PRMT1), the major arginine asymmetric dimethylation enzyme in mammals, is emerging as a potential drug target for cancer and cardiovascular disease. Understanding the catalytic mechanism of PRMT1 will facilitate inhibitor design. However, detailed mechanisms of the methyl transfer process and substrate deprotonation of PRMT1 remain unclear. In this study, we present a theoretical study on PRMT1 catalyzed arginine dimethylation by employing molecular dynamics (MD) simulation and quantum mechanics/molecular mechanics (QM/MM) calculation. Ternary complex models, composed of PRMT1, peptide substrate, and S-adenosyl-methionine (AdoMet) as cofactor, were constructed and verified by 30-ns MD simulation. The snapshots selected from the MD trajectory were applied for the QM/MM calculation. The typical S_N2-favored transition states of the first and second methyl transfers were identified from the potential energy profile. Deprotonation of substrate arginine occurs immediately after methyl transfer, and the carboxylate group of E144 acts as proton acceptor. Furthermore, natural bond orbital analysis and electrostatic potential calculation showed that E144 facilitates the charge redistribution during the reaction and reduces the energy barrier. In this study, we propose the detailed mechanism of PRMT1-catalyzed asymmetric dimethylation, which increases insight on the small-molecule effectors design, and enables further investigations into the physiological function of this family.     

Thermodynamics calculation of protein–ligand interactions by QM/MM polarizable charge parameters

The calculation of protein–ligand binding free energy (ΔG) is of great importance for virtual screening and drug design. Molecular dynamics (MD) simulation has been an attractive tool to investigate this scientific problem. However, the reliability of such approach is affected by many factors including electrostatic interaction calculation. Here, we present a practical protocol using quantum mechanics/molecular mechanics (QM/MM) calculations to generate polarizable QM protein charge (QMPC). The calculated QMPC of some atoms in binding pockets was obviously different from that calculated by AMBER ff03, which might significantly affect the calculated ΔG. To evaluate the effect, the MD simulations and MM/GBSA calculation with QMPC for 10 protein–ligand complexes, and the simulation results were then compared to those with the AMBER ff03 force field and experimental results. The correlation coefficient between the calculated ΔΔG using MM/GBSA under QMPC and the experimental data is .92, while that with AMBER ff03 force field is .47 for the complexes formed by streptavidin or its mutants and biotin. Moreover, the calculated ΔΔG with QMPC for the complexes formed by ERβ and five ligands is positively related to experimental result with correlation coefficient of .61, while that with AMBER ff03 charge is negatively related to experimental data with correlation coefficient of .42. The detailed analysis shows that the electrostatic polarization introduced by QMPC affects the electrostatic contribution to the binding affinity and thus, leads to better correlation with experimental data. Therefore, this approach should be useful to virtual screening and drug design.