Quantum mechanically derived AMBER-compatible heme parameters for various states of the cytochrome P450 catalytic cycle

Molecular mechanics (MM) methods are computationally affordable tools for screening chemical libraries of novel compounds for sites of P450 metabolism. One challenge for MM methods has been the absence of a consistent and transferable set of parameters for the heme within the P450 active site. Experimental data indicate that mammalian P450 enzymes vary greatly in the size, architecture, and plasticity of their active sites. Thus, obtaining X-ray-based geometries for the development of accurate MM parameters for the major classes of hepatic P450 remains a daunting task. Our previous work with preliminary gas-phase quantum mechanics (QM)-derived atomic partial charges greatly improved the accuracy of docking studies of raloxifene to CYP3A4. We have therefore developed and tested a consistent set of transferable MM parameters based on gas-phase QM calculations of two model systems of the heme-a truncated (T-HM) and a full (F-HM) for four states of the P450 catalytic cycle. Our results indicate that the use of the atomic partial charges from the F-HM further improves the accuracy of docked predictions for raloxifene to CYP3A4. Different patterns for substrate docking are also observed depending on the choice of heme model and state. Newly parameterized heme models are tested in implicit and explicitly solvated MD simulations in the absence and presence of enzyme structures, for CYP3A4, and appear to be stable on the nanosecond simulation timescale. The new force field for the various heme states may aid the community for simulations of P450 enzymes and other heme-containing enzymes.     

Comparison of charge models for fixed-charge force fields: small-molecule hydration free energies in explicit solvent

In molecular simulations with fixed-charge force fields, the choice of partial atomic charges influences numerous computed physical properties, including binding free energies. Many molecular mechanics force fields specify how nonbonded parameters should be determined, but various choices are often available for how these charges are to be determined for arbitrary small molecules. Here, we compute hydration free energies for a set of 44 small, neutral molecules in two different explicit water models (TIP3P and TIP4P-Ew) to examine the influence of charge model on agreement with experiment. Using the AMBER GAFF force field for nonbonded parameters, we test several different methods for obtaining partial atomic charges, including two fast methods exploiting semiempirical quantum calculations and methods deriving charges from the electrostatic potentials computed with several different levels of ab initio quantum calculations with and without a continuum reaction field treatment of solvent. We find that the best charge sets give a root-mean-square error from experiment of roughly 1 kcal/mol. Surprisingly, agreement with experimental hydration free energies does not increase substantially with increasing level of quantum theory, even when the quantum calculations are performed with a reaction field treatment to better model the aqueous phase. We also find that the semiempirical AM1-BCC method for computing charges works almost as well as any of the more computationally expensive ab initio methods and that the root-mean-square error reported here is similar to that for implicit solvent models reported in the literature. Further, we find that the discrepancy with experimental hydration free energies grows substantially with the polarity of the compound, as does its variation across theory levels.     

Accurate metal-site structures in proteins obtained by combining experimental data and quantum chemistry

The use of molecular mechanics calculations to supplement experimental data in standard X-ray crystallography and NMR refinements is discussed and it is shown that structures can be locally improved by the use of quantum chemical calculations. Such calculations can also be used to interpret the structures, e.g. to decide the protonation state of metal-bound ligands. They have shown that metal sites in crystal structures are frequently photoreduced or disordered, which makes the interpretation of the structures hard. Similar methods can be used for EXAFS refinements to obtain a full atomic structure, rather than a set of metal-ligand distances.     

Accurate Backbone 13C and 15N Chemical Shift Tensors in Galectin-3 Determined by MAS NMR and QM/MM: Details of Structure and Environment Matter

Chemical shift tensors obtained from solid-state NMR spectroscopy are very sensitive reporters of structure and dynamics in proteins. While accurate ¹³C and ¹⁵N chemical shift tensors are accessible by magic angle spinning (MAS) NMR, their quantum mechanical calculations remain challenging, particularly for ¹⁵N atoms. Here we compare experimentally determined backbone ¹³C^α and ¹⁵N^H chemical shift tensors by MAS NMR with hybrid quantum mechanics/molecular mechanics/molecular dynamics (MD-QM/MM) calculations for the carbohydrate-binding domain of galectin-3. Excellent agreement between experimental and computed ¹⁵N^H chemical shift anisotropy values was obtained using the Amber ff15ipq force field when solvent dynamics was taken into account in the calculation. Our results establish important benchmark conditions for improving the accuracy of chemical shift calculations in proteins and may aid in the validation of protein structure models derived by MAS NMR.     

Force field parameters for the simulation of modified histone tails

We describe the development of force field parameters for methylated lysines and arginines, and acetylated lysine for the CHARMM all‐atom force field. We also describe a CHARMM united‐atom force field for modified sidechains suitable for use with fragment‐based docking methods. The development of these parameters is based on results of ab initio quantum mechanics calculations of model compounds with subsequent refinement and validation by molecular mechanics and molecular dynamics simulations. The united‐atom parameters are tested by fragment docking to target proteins using the MCSS procedure. The all‐atom force field is validated by molecular dynamics simulations of multiple experimental structures. In both sets of calculations, the computational predictions using the force field were compared to the corresponding experimental structures. We show that the parameters yield an accurate reproduction of experimental structures. Together with the existing CHARMM force field, these parameters will enable the general modeling of post‐translational modifications of histone tails. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

QM:QM electronic embedding using Mulliken atomic charges: energies and analytic gradients in an ONIOM framework

An accurate first-principles treatment of chemical reactions for large systems remains a significant challenge facing electronic structure theory. Hybrid models, such as quantum mechanics:molecular mechanics (QM:MM) and quantum mechanics:quantum mechanics (QM:QM) schemes, provide a promising avenue for such studies. For many chemistries, including important reactions in materials science, molecular mechanics or semiempirical methods may not be appropriate, or parameters may not be available (e.g., surface chemistry of compound semiconductors such as indium phosphide or catalytic chemistry of transition metal oxides). In such cases, QM:QM schemes are of particular interest. In this work, a QM:QM electronic embedding model within the ONIOM (our own N-layer integrated molecular orbital molecular mechanics) extrapolation framework is presented. To define the embedding potential, we choose the real-system low-level Mulliken atomic charges. This results in a set of well-defined and unique embedding charges. However, the parametric dependence of the charges on molecular geometry complicates the energy gradient that is necessary for the efficient exploration of potential energy surfaces. We derive an efficient form for the forces where a single set of self-consistent field response equations is solved. Initial tests of the method and key algorithmic issues are discussed.     

On heteroaromaticity of nucleobases. Bond lengths as multidimensional phenomena

Three hundred and nine carbon-carbon, carbon-nitrogen, and carbon-oxygen pi-bond lengths in high precision crystal structures of 31 purine and pyrimidine nucleobases were related to the Pauling pi-bond order, its analogues corrected to crystal packing effects, the numbers of non-hydrogen atoms around the bond, and the sum of atomic numbers of the bond atoms. Principal Component Analysis (PCA) and Hierarchical Cluster Analysis (HCA) demonstrated that the bond lengths in the nucleobases are three-dimensional phenomenon, characterized by nine distinct classes of bonds. Bond lengths predicted by Linear Regression models, Pauling Harmonic Potential Curves, Multiple Linear Regression, Principal Component, and Partial Least Squares Regression were compared to those calculated by molecular mechanics, semiempirical, and ab initio methods using PCA-HCA procedure on the calculated bond lengths, statistical parameters, and structural aromaticity indices. Incorporation of crystal packing effects into bond orders makes multivariate models to be competitive to semiempirical results, while further improvement of quantum chemical calculations can be achieved by geometry optimization of molecular clusters.     

Development of glycyl radical parameters for the OPLS-AA/L force field

On the basis of quantum chemical calculations C(alpha)-glycyl radical parameters have been developed for the OPLS-AA/L force field. The molecular mechanics hypersurface was fitted to the calculated quantum chemical surface by minimizing their molecular mechanics parameter dependent sum-of-squares deviations. To do this, a computer program in which the molecular mechanics energy derivatives with respect to the parameters were calculated analytically was developed, implementing the general method of Lifson and Warshel (J Chem Phys 1968, 49, 5116) for force field parameter optimization. This program, in principle, can determine the optimal parameter set in one calculation if enough representative value points on the quantum chemical potential energy surface are available and there is no linear dependency between the parameters. Some of the parameters in quantum calculations, including several new torsion types around a bond as well as angle parameters at a new central atom type, are not completely separable. Consequently, some restrictions and/or presumptions were necessary during parameter optimization. The relative OPLS-AA energies reproduced those calculated quantum chemically almost perfectly.     

Development of the force field parameters for phosphoimidazole and phosphohistidine

Phosphorylation of histidine-containing proteins is a key step in the mechanism of many phosphate transfer enzymes (kinases, phosphatases) and is the first stage in a wide variety of signal transduction cascades in bacteria, yeast, higher plants, and mammals. Studies of structural and dynamical aspects of such enzymes in the phosphorylated intermediate states are important for understanding the intimate molecular mechanisms of their functioning. Such information may be obtained via molecular dynamics and/or docking simulations, but in this case appropriate force field parameters for phosphohistidine should be explicitly defined. In the present article we describe development of the GROMOS96 force field parameters for phosphoimidazole molecule--a realistic model of the phosphohistidine side chain. The parameterization is based on the results of ab initio quantum chemical calculations with subsequent refinement and testing using molecular mechanics and molecular dynamics simulations. The set of force constants and equilibrium geometry is employed to derive force field for the phosphohistidine moiety. Resulting parameters and topology are incorporated into the molecular modeling package GROMACS and used in molecular dynamics simulations of a phosphohistidine-containing protein in explicit solvent.     

Conformational simulations of aqueous solvated alpha-conotoxin GI and its single disulfide analogues using a polarizable force field model

The solution conformation of alpha-conotoxin GI and its two single disulfide analogues are simulated using a polarizable force field in combination with the molecular fragmentation quantum chemical calculation. The polarizability is explicitly described by allowing the partial charges and fragment dipole moments to be variables, with values coming from the linear-scaling energy-based molecular fragmentation calculations at the B3LYP/6-31G(d) level. In comparison with the full quantum chemical calculations, the fragmentation approaches can yield precise ground-state energies, dipole moments, and static polarizabilities for peptides. The B3LYP/6-31G(d) charges and fragment-centered dipole moments are introduced in calculations of electrostatic terms in both AmberFF03 and OPLS force fields. Our test calculations on the gas-phase glucagon (PDB code: 1gcn) and solvated alpha-conotoxin GI (PDB code: 1not) demonstrate that the present polarization model is capable of describing the structural properties (such as the relative conformational energies, intramolecular hydrogen bonds, and disulfide bonds) with accuracy comparable to some other polarizable force fields (ABEEM/MM and OPLS-PFF) and the quantum mechanics/molecular mechanics (QM/MM) hybrid model. The employment of fragment-centered dipole moments in calculations of dipole-dipole interactions can save computational time in comparison with those polarization models using atom-centered dipole moments without much loss of accuracy. The molecular dynamics simulations using the polarizable force field demonstrate that two single disulfide GI analogues are more flexible and less structured than the native alpha-conotoxin GI, in agreement with NMR experiments. The polarization effect is important in simulations of the folding/unfolding process of solvated proteins.     

Density functional theory and empirical derived force fields for the delocalized polaron form of polyaniline. Application to properties determination of an isolated oligomer using molecular dynamics simulations

Normal mode analyses obtained from quantum chemical calculations at the DFT level of theory have been performed for the repetitive unit of the delocalized bipolaron form of polyaniline (PANI). Empirical molecular mechanics force field parameters were consecutively refined using the SPASIBA software and applied to the molecular dynamics properties of an isolated dodeca oligomer model of the leucoemeraldine form of PANI. It is shown that effects of protonation of the emeraldine base spread over the four rings constituting the repeating unit. Molecular dynamics simulations reveal alternative bendings of the whole chain with a time period of 18-20 ps for the model of PANI under study.     

Molecular structures and dynamics of the stepwise activation mechanism of a matrix metalloproteinase zymogen: challenging the cysteine switch dogma

Activation of matrix metalloproteinase zymogen (pro-MMP) is a vital homeostatic process, yet its molecular basis remains unresolved. Using stopped-flow X-ray spectroscopy of the active site zinc ion, we determined the temporal sequence of pro-MMP-9 activation catalyzed by tissue kallikrein protease in milliseconds to several minutes. The identity of three intermediates seen by X-ray spectroscopy was corroborated by molecular dynamics simulations and quantum mechanics/molecular mechanics calculations. The cysteine-zinc interaction that maintains enzyme latency is disrupted via active-site proton transfers that mediate transient metal-protein coordination events and eventual binding of water. Unexpectedly, these events ensue as a direct result of complexation of pro-MMP-9 and kallikrein and occur before proteolysis and eventual dissociation of the pro-peptide from the catalytic site. Here we demonstrate the synergism among long-range protein conformational transitions, local structural rearrangements, and fine atomic events in the process of zymogen activation.     

Reaction path potential for complex systems derived from combined ab initio quantum mechanical and molecular mechanical calculations

Combined ab initio quantum mechanical and molecular mechanical calculations have been widely used for modeling chemical reactions in complex systems such as enzymes, with most applications being based on the determination of a minimum energy path connecting the reactant through the transition state to the product in the enzyme environment. However, statistical mechanics sampling and reaction dynamics calculations with a combined ab initio quantum mechanical (QM) and molecular mechanical (MM) potential are still not feasible because of the computational costs associated mainly with the ab initio quantum mechanical calculations for the QM subsystem. To address this issue, a reaction path potential energy surface is developed here for statistical mechanics and dynamics simulation of chemical reactions in enzymes and other complex systems. The reaction path potential follows the ideas from the reaction path Hamiltonian of Miller, Handy and Adams for gas phase chemical reactions but is designed specifically for large systems that are described with combined ab initio quantum mechanical and molecular mechanical methods. The reaction path potential is an analytical energy expression of the combined quantum mechanical and molecular mechanical potential energy along the minimum energy path. An expansion around the minimum energy path is made in both the nuclear and the electronic degrees of freedom for the QM subsystem internal energy, while the energy of the subsystem described with MM remains unchanged from that in the combined quantum mechanical and molecular mechanical expression and the electrostatic interaction between the QM and MM subsystems is described as the interaction of the MM charges with the QM charges. The QM charges are polarizable in response to the changes in both the MM and the QM degrees of freedom through a new response kernel developed in the present work. The input data for constructing the reaction path potential are energies, vibrational frequencies, and electron density response properties of the QM subsystem along the minimum energy path, all of which can be obtained from the combined quantum mechanical and molecular mechanical calculations. Once constructed, it costs much less for its evaluation. Thus, the reaction path potential provides a potential energy surface for rigorous statistical mechanics and reaction dynamics calculations of complex systems. As an example, the method is applied to the statistical mechanical calculations for the potential of mean force of the chemical reaction in triosephosphate isomerase.     

Molecule‐specific determination of atomic polarizabilities with the polarizable atomic multipole model

Recently, many polarizable force fields have been devised to describe induction effects between molecules. In popular polarizable models based on induced dipole moments, atomic polarizabilities are the essential parameters and should be derived carefully. Here, we present a parameterization scheme for atomic polarizabilities using a minimization target function containing both molecular and atomic information. The main idea is to adopt reference data only from quantum chemical calculations, to perform atomic polarizability parameterizations even when relevant experimental data are scarce as in the case of electronically excited molecules. Specifically, our scheme assigns the atomic polarizabilities of any given molecule in such a way that its molecular polarizability tensor is well reproduced. We show that our scheme successfully works for various molecules in mimicking dipole responses not only in ground states but also in valence excited states. The electrostatic potential around a molecule with an externally perturbing nearby charge also exhibits a near‐quantitative agreement with the reference data from quantum chemical calculations. The limitation of the model with isotropic atoms is also discussed to examine the scope of its applicability. © 2012 Wiley Periodicals, Inc.     

MOLCAS 7: The Next Generation

Some of the new unique features of the MOLCAS quantum chemistry package version 7 are presented in this report. In particular, the Cholesky decomposition method applied to some quantum chemical methods is described. This approach is used both in the context of a straight forward approximation of the two‐electron integrals and in the generation of so‐called auxiliary basis sets. The article describes how the method is implemented for most known wave functions models: self‐consistent field, density functional theory, 2nd order perturbation theory, complete‐active space self‐consistent field multiconfigurational reference 2nd order perturbation theory, and coupled‐cluster methods. The report further elaborates on the implementation of a restricted‐active space self‐consistent field reference function in conjunction with 2nd order perturbation theory. The average atomic natural orbital basis for relativistic calculations, covering the whole periodic table, are described and associated unique properties are demonstrated. Furthermore, the use of the arbitrary order Douglas‐Kroll‐Hess transformation for one‐component relativistic calculations and its implementation are discussed. This section especially focuses on the implementation of the so‐called picture‐change‐free atomic orbital property integrals. Moreover, the ElectroStatic Potential Fitted scheme, a version of a quantum mechanics/molecular mechanics hybrid method implemented in MOLCAS, is described and discussed. Finally, the report discusses the use of the MOLCAS package for advanced studies of photo chemical phenomena and the usefulness of the algorithms for constrained geometry optimization in MOLCAS in association with such studies. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Atomistic modeling of enantioselection in chromatography

A review of atomistic molecular modeling studies related to chromatographic separations of enantiomers is presented. Only those types of calculations where direct interactions between a selector and a selectand are involved are described in this review; omitted are regression models. An emphasis is placed on comparing methods used for sampling potential energy surfaces implementing different methodologies like quantum and molecular mechanics for energy calculations, and molecular dynamics and Monte Carlo sampling strategies for simulations. Type I-V chiral stationary phases and additives for capillary electrophoresis and ion-pair chromatography are covered in this review.     

Theoretical modeling and interpretation of X-ray absorption spectra of liquid water

We report extensive calculations to examine the capability of theory to explain the XAS spectra of liquid water. Several aspects that enter the theoretical model are addressed, such as the quantum mechanical methods, the statistics and the XAS model. As input into our quantum mechanical calculations we will use structural information on liquid water obtained from first principles and from classical molecular dynamics simulations. As XAS models, we will examine the full core hole and the half core hole approximations to transition state theory. The quantum mechanics is performed on the basis of density functional theory. We conclude from this study that recent experimental results are fully consistent with, and can be completely explained by, present day theory, in particular, the pre-edge peak is reproduced. We also find that the average bond coordination in liquid water is 3.1 and that the assertion in a recent paper that the hydrogen bond number is much less than that cannot be substantiated. Our calculations emphasize that further advances in our understanding of water can only be made by more sophisticated spectroscopy with significantly increased resolution.     

Simulations of X-ray absorption spectra: the effect of the solvent

We perform quantum mechanics/molecular mechanics molecular dynamics simulations on the [Pt(2)(P(2)O(5)H(2))(4)](4-) (abbreviated PtPOP) complex; in water, dimethylformamide and ethanol. These are used to calculate the ground state X-ray absorption spectrum of the complex. The structural parameters from X-ray spectra are usually extracted using a fit of the experimental data. In such simulations the solvent is neglected meaning that any effect of the local environment will be compensated for by structural changes of the solute, leading to possible discrepancies in the extracted structural parameters. Our simulations show a significant solvent effect on the spectra, which has important implications for the structural analysis of molecules in solution.