Complexes of thiomandelate and captopril mercaptocarboxylate inhibitors to metallo-beta-lactamase by polarizable molecular mechanics. Validation on model binding sites by quantum chemistry

Using the polarizable molecular mechanics method SIBFA, we have performed a search for the most stable binding modes of D- and L-thiomandelate to a 104-residue model of the metallo-beta-lactamase from B. fragilis, an enzyme involved in the acquired resistance of bacteria to antibiotics. Energy balances taking into account solvation effects computed with a continuum reaction field procedure indicated the D-isomer to be more stably bound than the L-one, conform to the experimental result. The most stably bound complex has the S(-) ligand bridging monodentately the two Zn(II) cations and one carboxylate O(-) H-bonded to the Asn193 side chain. We have validated the SIBFA energy results by performing additional SIBFA as well as quantum chemical (QC) calculations on small (88 atoms) model complexes extracted from the 104-residue complexes, which include the residues involved in inhibitor binding. Computations were done in parallel using uncorrelated (HF) as well as correlated (DFT, LMP2, MP2) computations, and the comparisons extended to corresponding captopril complexes (Antony et al., J Comput Chem 2002, 23, 1281). The magnitudes of the SIBFA intermolecular interaction energies were found to correctly reproduce their QC counterparts and their trends for a total of twenty complexes.     

Importance of explicit smeared lone‐pairs in anisotropic polarizable molecular mechanics. Torture track angular tests for exchange‐repulsion and charge transfer contributions

A correct representation of the short‐range contributions such as exchange‐repulsion (E _rep) and charge‐transfer (E _ct) is essential for the soundness of separable, anisotropic polarizable molecular mechanics potentials. Within the context of the SIBFA procedure, this is aimed at by explicit representations of lone pairs in their expressions. It is necessary to account for their anisotropic behaviors upon performing not only in‐plane, but also out‐of‐plane, variations of a probe molecule or cation interacting with a target molecule or molecular fragment. Thus, E _rep and E _ct have to reproduce satisfactorily the corresponding anisotropies of their quantum chemical (QC) counterparts. A significant improvement of the out‐of‐plane dependencies was enabled when the sp² and sp localized lone‐pairs are, even though to a limited extent, delocalized on both sides of the plane, above and below the atom bearer but at the closely similar angles as the in‐plane lone pair. We report calibration and validation tests on a series of monoligated complexes of a probe Zn(II) cation with several biochemically relevant ligands. Validations are then performed on several polyligated Zn(II) complexes found in the recognition sites of Zn‐metalloproteins. Such calibrations and validations are extended to representative monoligated and polyligated complexes of Mg(II) and Ca(II). It is emphasized that the calibration of all three cations was for each ΔE contribution done on a small training set bearing on a limited number of representative N , O , and S monoligated complexes. Owing to the separable nature of ΔE , a secure transferability is enabled to a diversity of polyligated complexes. For these the relative errors with respect to the target ΔE (QC) values are generally < 3%. Overall, the article proposes a full set of benchmarks that could be useful for force field developers. © 2017 Wiley Periodicals, Inc.     

Quantum‐chemistry based calibration of the alkali metal cation series (Li+Cs+) for large‐scale polarizable molecular mechanics/dynamics simulations

The alkali metal cations in the series Li⁺? Cs⁺ act as major partners in a diversity of biological processes and in bioinorganic chemistry. In this article, we present the results of their calibration in the context of the SIBFA polarizable molecular mechanics/dynamics procedure. It relies on quantum‐chemistry (QC) energy‐decomposition analyses of their monoligated complexes with representative O? , N? , S? , and Se? ligands, performed with the aug‐cc‐pVTZ(‐f) basis set at the Hartree–Fock level. Close agreement with QC is obtained for each individual contribution, even though the calibration involves only a limited set of cation‐specific parameters. This agreement is preserved in tests on polyligated complexes with four and six O? ligands, water and formamide, indicating the transferability of the procedure. Preliminary extensions to density functional theory calculations are reported.     

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.     

Conformation-dependent intermolecular interaction energies of the triphosphate anion with divalent metal cations. Application to the ATP-binding site of a binuclear bacterial enzyme. A parallel quantum chemical and polarizable molecular mechanics investigation

We have explored the conformation-dependent interaction energy of the triphosphate moiety, a key constituent of ATP and GTP, with a closed-shell divalent cation, Zn2+, used as a probe. This was done using the SIBFA polarizable molecular mechanics procedure. We have resorted to a previously developed approach in which triphosphate is built out from its elementary constitutive fragments, and the intramolecular, interfragment, interaction energies are computed simultaneously with their intermolecular interactions with the divalent cation. This approach has enabled reproduction of the values of the intermolecular interaction energies from ab initio quantum-chemistry with relative errors <3%. It was extended to the complex of a nonhydrolyzable analog of ATP with the active site of a bacterial enzyme having two Mg2+ cations as cofactors. We obtained following energy-minimization a very close overlap of the ATP analog over its position from X-ray crystallography. For models of the ATP analog-enzyme complex encompassing up to 169 atoms, the values of the SIBFA interaction energies were found to match their DFT counterparts with relative errors of <2%.     

A quantum mechanics/molecular mechanics study of the protein-ligand interaction for inhibitors of HIV-1 integrase

Human immunodeficiency virus type-1 integrase (HIV-1 IN) is an essential enzyme for effective viral replication. Diketo acids such as L-731,988 and S-1360 are potent and selective inhibitors of HIV-1 IN. In this study, we used molecular dynamics simulations, within the hybrid quantum mechanics/molecular mechanics (QM/MM) approach, to determine the protein-ligand interaction energy between HIV-1 IN and L-731,988 and 10 of its derivatives and analogues. This hybrid methodology has the advantage that it includes quantum effects such as ligand polarisation upon binding, which can be very important when highly polarisable groups are embedded in anisotropic environments, as for example in metal-containing active sites. Furthermore, an energy decomposition analysis was performed to determine the contributions of individual residues to the enzyme-inhibitor interactions on averaged structures obtained from rather extensive conformational sampling. Analysis of the results reveals first that there is a correlation between protein-ligand interaction energy and experimental strand transfer into human chromosomes and secondly that the Asn-155, Lys-156 and Lys-159 residues and the Mg(2+) ion are crucial to anti-HIV IN activity. These results may explain the available experimental data.     

Calculation of wave‐functions with frozen orbitals in mixed quantum mechanics/molecular mechanics methods. II. Application of the local basis equation

The application of the local basis equation (Ferenczy and Adams, J. Chem. Phys. 2009 , 130, 134108) in mixed quantum mechanics/molecular mechanics (QM/MM) and quantum mechanics/quantum mechanics (QM/QM) methods is investigated. This equation is suitable to derive local basis nonorthogonal orbitals that minimize the energy of the system and it exhibits good convergence properties in a self‐consistent field solution. These features make the equation appropriate to be used in mixed QM/MM and QM/QM methods to optimize orbitals in the field of frozen localized orbitals connecting the subsystems. Calculations performed for several properties in divers systems show that the method is robust with various choices of the frozen orbitals and frontier atom properties. With appropriate basis set assignment, it gives results equivalent with those of a related approach [G. G. Ferenczy previous paper in this issue] using the Huzinaga equation. Thus, the local basis equation can be used in mixed QM/MM methods with small size quantum subsystems to calculate properties in good agreement with reference Hartree–Fock–Roothaan results. It is shown that bond charges are not necessary when the local basis equation is applied, although they are required for the self‐consistent field solution of the Huzinaga equation based method. Conversely, the deformation of the wave‐function near to the boundary is observed without bond charges and this has a significant effect on deprotonation energies but a less pronounced effect when the total charge of the system is conserved. The local basis equation can also be used to define a two layer quantum system with nonorthogonal localized orbitals surrounding the central delocalized quantum subsystem. © 2013 Wiley Periodicals, Inc.     

Intramolecular interaction energies in model alanine and glycine tetrapeptides. Evaluation of anisotropy, polarization, and correlation effects. A parallel ab initio HF/MP2, DFT, and polarizable molecular mechanics study

An extension of the SIBFA polarizable molecular mechanics procedure to flexible oligopeptides is reported. The procedure is evaluated by computing the relative conformational energies, deltaE(conf), of the alanine tetrapeptide in 10 representative conformations, which were originally derived by Beachy et al. (J Am Chem Soc 1997, 119, 5908) to benchmark molecular mechanics procedures with respect to ab initio computations. In the present study, a particular emphasis is on the separable nature of the components of the energy and the particular impact of the polarization energy component on deltaE(conf). We perform comparisons with respect to single-point HF, DFT, LMP2, and MP2 computations done at the SIBFA-derived energy minima. Such comparisons are made first for the 10 conformers derived from phi/psi torsional angle energy-minimization (the rigid rotor approach), and, in a second step, after allowing additional relaxation of the C(alpha) centered valence angles. In both series of energy-minimization, the SIBFA deltaE(conf) compared best with the LMP2 results using the 6-311G** basis set, the rms being 1.3 kcal/mol. In the absence of the polarization component, the rms is 3.5 kcal/mol. In both series of minimizations, the magnitudes of deltaE(conf), computed as differences with respect to the most stable conformer taken as energy zero, decrease along the series: HF > DFT > LMP2 > SIBFA > MP2, indicative of increasing stabilization of the most highly folded conformers.     

Chemical reaction dynamics of PeCB and TCDD decomposition: A tight‐binding quantum chemical molecular dynamics study with first‐principles parameterization

The decomposition reaction dynamics of 2,3,4,4′,5‐penta‐chlorinated biphenyl (2,3,4,4′,5‐PeCB), 3,3′,4,4′,5‐penta‐chlorinated biphenyl (3,3′,4,4′,5‐PeCB), and 2,3,7,8‐tetra‐chlorinated dibenzo‐p‐dioxin (2,3,7,8‐TCDD) was clarified for the first time at atomic and electronic levels, using our novel tight‐binding quantum chemical molecular dynamics method with first‐principles parameterization. The calculation speed of our new method is over 5000 times faster than that of the conventional first‐principles molecular dynamics method. We confirmed that the structure, energy, and electronic states of the above molecules calculated by our new method are quantitatively consistent with those by first‐principles calculations. After the confirmation of our methodology, we investigated the decomposition reaction dynamics of the above molecules and the calculated dynamic behaviors indicate that the oxidation of the 2,3,4,4′,5‐PeCB, 3,3′,4,4′,5‐PeCB, and 2,3,7,8‐TCDD proceeds through an epoxide intermediate, which is in good agreement with the previous experimental reports and consistent with our static density functional theory calculations. These results proved that our new tight‐binding quantum chemical molecular dynamics method with first‐principles parameterization is an effective tool to clarify the chemical reaction dynamics at reaction temperatures. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Convergence in the QM‐only and QM/MM modeling of enzymatic reactions: A case study for acetylene hydratase

We report systematic quantum mechanics‐only (QM‐only) and QM/molecular mechanics (MM) calculations on an enzyme‐catalyzed reaction to assess the convergence behavior of QM‐only and QM/MM energies with respect to the size of the chosen QM region. The QM and MM parts are described by density functional theory (typically B3LYP/def2‐SVP) and the CHARMM force field, respectively. Extending our previous work on acetylene hydratase with QM regions up to 157 atoms (Liao and Thiel, J. Chem. Theory Comput. 2012, 8, 3793), we performed QM/MM geometry optimizations with a QM region M4 composed of 408 atoms, as well as further QM/MM single‐point calculations with even larger QM regions up to 657 atoms. A charge deletion analysis was conducted for the previously used QM/MM model ( M3a , with a QM region of 157 atoms) to identify all MM residues with strong electrostatic contributions to the reaction energetics (typically more than 2 kcal/mol), which were then included in M4 . QM/MM calculations with this large QM region M4 lead to the same overall mechanism as the previous QM/MM calculations with M3a , but there are some variations in the relative energies of the stationary points, with a mean absolute deviation (MAD) of 2.7 kcal/mol. The energies of the two relevant transition states are close to each other at all levels applied (typically within 2 kcal/mol), with the first (second) one being rate‐limiting in the QM/MM calculations with M3a ( M4 ). QM‐only gas‐phase calculations give a very similar energy profile for QM region M4 (MAD of 1.7 kcal/mol), contrary to the situation for M3a where we had previously found significant discrepancies between the QM‐only and QM/MM results (MAD of 7.9 kcal/mol). Extension of the QM region beyond M4 up to M7 (657 atoms) leads to only rather small variations in the relative energies from single‐point QM‐only and QM/MM calculations (MAD typically about 1–2 kcal/mol). In the case of acetylene hydratase, a model with 408 QM atoms thus seems sufficient to achieve convergence in the computed relative energies to within 1–2 kcal/mol.Copyright © 2013 Wiley Periodicals, Inc.     

Comparison of radii sets,entropy, QM methods,and sampling on MM‐PBSA,MM‐GBSA,and QM/MM‐GBSA ligand binding energies of F. tularensis enoyl‐ACP reductase (FabI)

To validate a method for predicting the binding affinities of FabI inhibitors, three implicit solvent methods, MM‐PBSA, MM‐GBSA, and QM/MM‐GBSA were carefully compared using 16 benzimidazole inhibitors in complex with Francisella tularensis FabI. The data suggests that the prediction results are sensitive to radii sets, GB methods, QM Hamiltonians, sampling protocols, and simulation length, if only one simulation trajectory is used for each ligand. In this case, QM/MM‐GBSA using 6 ns MD simulation trajectories together with GB^neck2, PM3, and the mbondi2 radii set, generate the closest agreement with experimental values (r² = 0.88). However, if the three implicit solvent methods are averaged from six 1 ns MD simulations for each ligand (called “multiple independent sampling”), the prediction results are relatively insensitive to all the tested parameters. Moreover, MM/GBSA together with GB^HCT and mbondi, using 600 frames extracted evenly from six 0.25 ns MD simulations, can also provide accurate prediction to experimental values (r² = 0.84). Therefore, the multiple independent sampling method can be more efficient than a single, long simulation method. Since future scaffold expansions may significantly change the benzimidazole's physiochemical properties (charges, etc.) and possibly binding modes, which may affect the sensitivities of various parameters, the relatively insensitive “multiple independent sampling method” may avoid the need of an entirely new validation study. Moreover, due to large fluctuating entropy values, (QM/)MM‐P(G)BSA were limited to inhibitors’ relative affinity prediction, but not the absolute affinity. The developed protocol will support an ongoing benzimidazole lead optimization program. © 2015 Wiley Periodicals, Inc.     

Less is more when simulating unsulfated glycosaminoglycan 3D‐structure: Comparison of GLYCAM06/TIP3P,PM3‐CARB1/TIP3P,and SCC‐DFTB‐D/TIP3P predictions with experiment

The 3D‐structure of extracellular matrix glycosaminoglycans is central to function, but is currently poorly understood. Resolving this will provide insight into their heterogeneous biological roles and help to realize their significant therapeutic potential. Glycosaminoglycan chemical isoforms are too numerous to study experimentally and simulation provides a tractable alternative. However, best practice for accurate calculation of glycosaminoglycan 3D‐structure within biologically relevant nanosecond timescales is uncertain. Here, we evaluate the ability of three potentials to reproduce experimentally observed glycosaminoglycan monosaccharide puckering, disaccharide 3D‐conformation, and characteristic solvent interactions. Temporal dynamics of unsulfated chondroitin, chondroitin‐4‐sulfate, and hyaluronan β(1→3) disaccharides were simulated within TIP3P explicit solvent unrestrained for 20 ns using the GLYCAM06 force‐field and two semi‐empirical quantum mechanics methods, PM3‐CARB1 and SCC‐DFTB‐D (both within a hybrid QM/MM formalism). Comparison of calculated and experimental properties (vicinal couplings, nuclear Overhauser enhancements, and glycosidic linkage geometries) showed that the carbohydrate‐specific parameterization of PM3‐CARB1 imparted quantifiable benefits on monosaccharide puckering and that the SCC‐DFTB‐D method (including an empirical correction for dispersion) best modeled the effects of hexosamine 4‐sulfation. However, paradoxically, the most approximate approach (GLYCAM06/TIP3P) was the best at predicting monosaccharide puckering, 3D‐conformation, and solvent interactions. Our data contribute to the debate and emerging consensus on the relative performance of these levels of theory for biological molecules. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Intramolecular chelation of Zn2+ by α‐ and β‐mercaptocarboxamides. A parallel ab initio and polarizable molecular mechanics investigation. Assessment of the role of multipole transferability

α‐ and β‐mercaptocarboxamides constitute the Zn²⁺‐ligating entity of several highly potent metalloenzyme inhibitors. We have studied their interaction energies with Zn²⁺ using the polarizable molecular mechanics procedure SIBFA, and compared them to the corresponding ab initio supermolecule ones. Such validations are necessary to subsequently undertake simulations on complexes of Zn²⁺–metalloenzymes with inhibitors. If the distributed multipoles and polarizabilities are those derived for each ligand in its appropriate Zn²⁺‐binding conformation, a close reproduction of the ab initio binding energies is afforded. However, this representation is not tractable upon increasing the size of the ligands and/or to explore a continuum of binding conformations. This makes it necessary to construct the ligands by resorting to a library of constitutive fragments, namely in this case methanethiolate, formamide, and methane covalently connected together. A close reproduction of the ab initio interaction energies is enabled, but only if the ligand–ligand interactions are computed simultaneously with those occurring with Zn²⁺. This representation accounts for the nonadditivity occurring in the Zn²⁺–methanethiolate–formamide complex, and justifies the use of the distributed multipoles on the fragments for the construction of larger and flexible molecules. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1038–1047, 2001     

Extension of the CHARMM general force field to sulfonyl‐containing compounds and its utility in biomolecular simulations

Presented is an extension of the CHARMM General Force Field (CGenFF) to enable the modeling of sulfonyl‐containing compounds. Model compounds containing chemical moieties such as sulfone, sulfonamide, sulfonate, and sulfamate were used as the basis for the parameter optimization. Targeting high‐level quantum mechanical and experimental crystal data, the new parameters were optimized in a hierarchical fashion designed to maintain compatibility with the remainder of the CHARMM additive force field. The optimized parameters satisfactorily reproduced equilibrium geometries, vibrational frequencies, interactions with water, gas phase dipole moments, and dihedral potential energy scans. Validation involved both crystalline and liquid phase calculations showing the newly developed parameters to satisfactorily reproduce experimental unit cell geometries, crystal intramolecular geometries, and pure solvent densities. The force field was subsequently applied to study conformational preference of a sulfonamide based peptide system. Good agreement with experimental IR/NMR data further validated the newly developed CGenFF parameters as a tool to investigate the dynamic behavior of sulfonyl groups in a biological environment. CGenFF now covers sulfonyl group containing moieties allowing for modeling and simulation of sulfonyl‐containing compounds in the context of biomolecular systems including compounds of medicinal interest. © 2012 Wiley Periodicals, Inc.