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

Combining crystallography with quantum mechanics

In standard crystallographic refinement of biomacromolecules, the crystallographic raw data are supplemented by empirical restraints that ensure that the structure makes chemical sense. These restraints are typically accurate for amino acids and nucleic acids, but less so for cofactors, substrates, inhibitors, ligands and metal sites. In quantum refinement, this potential is replaced by more accurate quantum mechanical (QM) calculations. Several implementations have been presented, differing in the level of QM and whether it is used for the entire structure or only for a site of particular interest. It has been shown that the method can improve and correct errors in crystal structures and that it can be used to determine protonation and tautomeric states of various ligands and to decide what is really seen in the structure by refining different interpretations and using standard crystallographic and QM quality measures to decide which fits the structure best.

Refinement of protein structures using a combination of quantum-mechanical calculations with neutron and X-ray crystallographic data

Neutron crystallography is a powerful method to determine the positions of H atoms in macromolecular structures. However, it is sometimes hard to judge what would constitute a chemically reasonable model, and the geometry of H atoms depends more on the surroundings (for example the formation of hydrogen bonds) than heavy atoms, so that the empirical geometry information for the H atoms used to supplement the experimental data is often less accurate. These problems may be reduced by using quantum-mechanical calculations. A method has therefore been developed to combine quantum-mechanical calculations with joint crystallographic refinement against X-ray and neutron data. A first validation of this method is provided by re-refining the structure of the galectin-3 carbohydrate-recognition domain in complex with lactose. The geometry is improved, in particular for water molecules, for which the method leads to better-resolved hydrogen-bonding interactions. The method has also been applied to the active copper site of lytic polysaccharide monooxygenase and shows that the protonation state of the amino-terminal histidine residue can be determined.

Quantum Crystallography: Current Developments and Future Perspectives

Crystallography and quantum mechanics have always been tightly connected because reliable quantum mechanical models are needed to determine crystal structures. Due to this natural synergy, nowadays accurate distributions of electrons in space can be obtained from diffraction and scattering experiments. In the original definition of quantum crystallography (QCr) given by Massa, Karle and Huang, direct extraction of wavefunctions or density matrices from measured intensities of reflections or, conversely, ad hoc quantum mechanical calculations to enhance the accuracy of the crystallographic refinement are implicated. Nevertheless, many other active and emerging research areas involving quantum mechanics and scattering experiments are not covered by the original definition although they enable to observe and explain quantum phenomena as accurately and successfully as the original strategies. Therefore, we give an overview over current research that is related to a broader notion of QCr, and discuss options how QCr can evolve to become a complete and independent domain of natural sciences. The goal of this paper is to initiate discussions around QCr, but not to find a final definition of the field.

Quantum Refinement Does Not Support Dinuclear Copper Sites in Crystal Structures of Particulate Methane Monooxygenase

Particulate methane monooxygenase (pMMO) is one of the few enzymes that can activate methane. The metal content of this enzyme has been highly controversial, with suggestions of a dinuclear Fe site or mono-, di-, or trinuclear Cu sites. Crystal structures have shown a mono- or dinuclear Cu site, but the resolution was low and the geometry of the dinuclear site unusual. We have employed quantum refinement (crystallographic refinement enhanced with quantum-mechanical calculations) to improve the structure of the active site. We compared a number of different mono- and dinuclear geometries, in some cases enhanced with more protein ligands or one or two water molecules, to determine which structure fits two sets of crystallographic raw data best. In all cases, the best results were obtained with mononuclear Cu sites, occasionally with an extra water molecule. Thus, we conclude that there is no crystallographic support for a dinuclear Cu site in pMMO.

QM/MM Study of the Conversion of Oxophlorin into Verdoheme by Heme Oxygenase

Heme oxygenase is an enzyme that degrades heme, thereby recycling iron in most organisms, including humans. Pervious density functional theory (DFT) calculations have suggested that iron(III) hydroxyheme, an intermediate generated in the first step of heme degradation by heme oxygenase, is converted to iron(III) superoxo oxophlorin in the presence of dioxygen. In this article, we have studied the detailed mechanism of conversion of iron(III) superoxo oxophlorin to verdoheme by using combined quantum mechanics and molecular mechanics (QM/MM) calculations. The calculations employed the B3LYP method and the def2-QZVP basis set, considering dispersion effects with the DFT-D3 approach, obtaining accurate energies with large QM regions of almost 1000 atoms. The reaction was found to be exothermic by -35 kcal/mol, with a rate-determining barrier of 19 kcal/mol in the doublet state. The protein environment and especially water in the enzyme pocket significantly affects the reaction by decreasing the reaction activation energies and changing the structures by providing strategic hydrogen bonds.

Quantum crystallography

Approximate wavefunctions can be improved by constraining them to reproduce observations derived from diffraction and scattering experiments. Conversely, charge density models, incorporating electron-density distributions, atomic positions and atomic motion, can be improved by supplementing diffraction experiments with quantum chemically calculated, tailor-made electron densities (form factors). In both cases quantum chemistry and diffraction/scattering experiments are combined into a single, integrated tool. The development of quantum crystallographic research is reviewed. Some results obtained by quantum crystallography illustrate the potential and limitations of this field.

Quantum chemical approaches to [NiFe] hydrogenase

The mechanism by which [NiFe] hydrogenase catalyses the oxidation of molecular hydrogen is a significant yet challenging topic in bioinorganic chemistry. With far-reaching applications in renewable energy and carbon mitigation, significant effort has been invested in the study of these complexes. In particular, computational approaches offer a unique perspective on how this enzyme functions at an electronic and atomistic level. In this article, we discuss state-of-the art quantum chemical methods and how they have helped deepen our comprehension of [NiFe] hydrogenase. We outline the key strategies that can be used to compute the (i) geometry, (ii) electronic structure, (iii) thermodynamics and (iv) kinetic properties associated with the enzymatic activity of [NiFe] hydrogenase and other bioinorganic complexes.

How Accurately Can Extended X-ray Absorption Spectra Be Predicted from First Principles? Implications for Modeling the Oxygen-Evolving Complex in Photosystem II

First principle calculations of extended X-ray absorption fine structure (EXAFS) data have seen widespread use in bioinorganic chemistry, perhaps most notably for modeling the Mn4Ca site in the oxygen evolving complex (OEC) of photosystem II (PSII). The logic implied by the calculations rests on the assumption that it is possible to a priori predict an accurate EXAFS spectrum provided that the underlying geometric structure is correct. The present study investigates the extent to which this is possible using state of the art EXAFS theory. The FEFF program is used to evaluate the ability of a multiple scattering-based approach to directly calculate the EXAFS spectrum of crystallographically defined model complexes. The results of these parameter free predictions are compared with the more traditional approach of fitting FEFF calculated spectra to experimental data. A series of seven crystallographically characterized Mn monomers and dimers is used as a test set. The largest deviations between the FEFF calculated EXAFS spectra and the experimental EXAFS spectra arise from the amplitudes. The amplitude errors result from a combination of errors in calculated S0(2) and Debye-Waller values as well as uncertainties in background subtraction. Additional errors may be attributed to structural parameters, particularly in cases where reliable high-resolution crystal structures are not available. Based on these investigations, the strengths and weaknesses of using first-principle EXAFS calculations as a predictive tool are discussed. We demonstrate that a range of DFT optimized structures of the OEC may all be considered consistent with experimental EXAFS data and that caution must be exercised when using EXAFS data to obtain topological arrangements of complex clusters.

The Importance of the MM Environment and the Selection of the QM Method in QM/MM Calculations: Applications to Enzymatic Reactions

In this chapter, we discuss the influence of an anisotropic protein environment on the reaction mechanisms of saccharopine reductase and uroporphyrinogen decarboxylase, respectively, via the use of a quantum mechanical and molecular mechanical (QM/MM) approach. In addition, we discuss the importance of selecting a suitable DFT functional to be used in a QM/MM study of a key intermediate in the mechanism of 8R-lipoxygenase, a nonheme iron enzyme. In the case of saccharopine reductase, while the enzyme utilizes a substrate-assisted catalytic pathway, it was found that only through treating the polarizing effect of the active site, via the use of an electronic embedding formalism, was agreement with experimental kinetic data obtained. Similarly, in the case of uroporphyrinogen decarboxylase, the effect of the protein environment on the catalytic mechanism was found to be such that the calculated rate-limiting barrier is in good agreement with related experimentally determined values for the first decarboxylation of the substrate. For 8R-lipoxygenase, it was found that the geometries and energies of the multicentered open-shell intermediate complexes formed during the mechanism are quite sensitive to the choice of the density functional theory method. Thus, while density functional theory has become the method of choice in QM/MM studies, care must be taken in the selection of a particular high-level method.

Analyses of cobalt-ligand and potassium-ligand bond lengths in metalloproteins: trends and patterns

Cobalt and potassium are biologically important metal elements that are present in a large array of proteins. Cobalt is mostly found in vivo associated with a corrin ring, which represents the core of the vitamin B12 molecule. Potassium is the most abundant metal in the cytosol, and it plays a crucial role in maintaining membrane potential as well as correct protein function. Here, we report a thorough analysis of the geometric properties of cobalt and potassium coordination spheres that was performed with high resolution on a representative set of structures from the Protein Data Bank and complemented by quantum mechanical calculations realized at the DFT level of theory (B3LYP/ SDD) on mononuclear model systems. The results allowed us to draw interesting conclusions on the structural characteristics of both Co and K centers, and to evaluate the importance of effects such as their association energies and intrinsic thermodynamic stabilities. Overall, the results obtained provide useful data for enhancing the atomic models normally applied in theoretical and computational studies of Co or K proteins performed at the quantum mechanical level, and for developing molecular mechanical parameters for treating Co or K coordination spheres in molecular mechanics or molecular dynamics studies.

Quantum mechanics/molecular mechanics study of oxygen binding in hemocyanin

We report a combined quantum mechanics/molecular mechanics (QM/MM) study on the mechanism of reversible dioxygen binding in the active site of hemocyanin (Hc). The QM region is treated by broken-symmetry density functional theory (DFT) with spin projection corrections. The X-ray structures of deoxygenated (deoxyHc) and oxygenated (oxyHc) hemocyanin are well reproduced by QM/MM geometry optimizations. The computed relative energies strongly depend on the chosen density functional. They are consistent with the available thermodynamic data for oxygen binding in hemocyanin and in synthetic model complexes when the BH&HLYP hybrid functional with 50% Hartree-Fock exchange is used. According to the QM(BH&HLYP)/MM results, the reaction proceeds stepwise with two sequential electron transfer (ET) processes in the triplet state followed by an intersystem crossing to the singlet product. The first ET step leads to a nonbridged superoxo CuB(II)-O2(•-) intermediate via a low-barrier transition state. The second ET step is even more facile and yields a side-on oxyHc complex with the characteristic Cu2O2 butterfly core, accompanied by triplet-singlet intersystem crossing. The computed barriers are very small so that the two ET processes are expected to very rapid and nearly simultaneous.

QM/MM investigations of organic chemistry oriented questions

About 35 years after its first suggestion, QM/MM became the standard theoretical approach to investigate enzymatic structures and processes. The success is due to the ability of QM/MM to provide an accurate atomistic picture of enzymes and related processes. This picture can even be turned into a movie if nuclei-dynamics is taken into account to describe enzymatic processes. In the field of organic chemistry, QM/MM methods are used to a much lesser extent although almost all relevant processes happen in condensed matter or are influenced by complicated interactions between substrate and catalyst. There is less importance for theoretical organic chemistry since the influence of nonpolar solvents is rather weak and the effect of polar solvents can often be accurately described by continuum approaches. Catalytic processes (homogeneous and heterogeneous) can often be reduced to truncated model systems, which are so small that pure quantum-mechanical approaches can be employed. However, since QM/MM becomes more and more efficient due to the success in software and hardware developments, it is more and more used in theoretical organic chemistry to study effects which result from the molecular nature of the environment. It is shown by many examples discussed in this review that the influence can be tremendous, even for nonpolar reactions. The importance of environmental effects in theoretical spectroscopy was already known. Due to its benefits, QM/MM can be expected to experience ongoing growth for the next decade.In the present chapter we give an overview of QM/MM developments and their importance in theoretical organic chemistry, and review applications which give impressions of the possibilities and the importance of the relevant effects. Since there is already a bunch of excellent reviews dealing with QM/MM, we will discuss fundamental ingredients and developments of QM/MM very briefly with a focus on very recent progress. For the applications we follow a similar strategy.

[Computational mutation analysis of enzymatic reaction]

Density functional theory (DFT) calculations are established as a useful research tool to investigate the structures and reactivity of biological systems; however, their high computational costs still restrict their applicability to systems of several tens up to a few hundred atoms. Recently, a combined quantum mechanical/molecular mechanical (QM/MM) approach has become an important method to study enzymatic reactions. In the past several years, we have investigated B12-dependent diol dehydratase using QM/MM calculations. The enzyme catalyzes chemically difficult reactions by utilizing the high reactivity of free radicals. In this paper, we explain our QM/MM calculations for the structure and reactivity of diol dehydratase and report key findings with respect to the catalytic roles of the active-site amino acid residues, computational mutational analysis of the active-site amino acid residues, assignment of the central metal ion, and function of the central metal ion. Our QM/MM calculations can correctly describe the structures and activation barriers of intermediate and transition states in the protein environment. Moreover, predicted relative activities of mutants are consistent with experimentally observed reactivity. These results will encourage the application of QM/MM research to the mechanistic study of enzymatic reactions, functional analysis of active-site residues, and rational design of enzymes with new catalytic functions.

Evaluating the enthalpic contribution to ligand binding using QM calculations: effect of methodology on geometries and interaction energies

As a result of research on ligand efficiency in the pharmaceutical industry, there is greater focus on optimizing the strength of polar interactions within receptors, so that the contribution of overall size and lipophilicity to binding can be decreased. A number of quantum mechanical (QM) methods involving simple probes are available to assess the H-bonding potential of different heterocycles or functional groups. However, in most receptors, multiple features are present, and these have distinct directionality, meaning very minimalist models may not be so ideal to describe the interactions. We describe how the use of gas phase QM models of kinase protein-ligand complex, which can more closely mimic the polar features of the active site region, can prove useful in assessing alterations to a core template, or different substituents. We investigate some practical issues surrounding the use of QM cluster models in structure based design (SBD). These include the choice of the method; semi-empirical, density functional theory or ab-initio, the choice of the basis set, whether to include implicit or explicit solvation, whether BSSE should be included, etc. We find a combination of the M06-2X method and the 6-31G* basis set is sufficiently rapid, and accurate, for the computation of structural and energetic parameters for this system.

PDB ligand conformational energies calculated quantum-mechanically

We present here a greatly updated version of an earlier study on the conformational energies of protein-ligand complexes in the Protein Data Bank (PDB) [Nicklaus et al. Bioorg. Med. Chem. 1995, 3, 411-428], with the goal of improving on all possible aspects such as number and selection of ligand instances, energy calculations performed, and additional analyses conducted. Starting from about 357,000 ligand instances deposited in the 2008 version of the Ligand Expo database of the experimental 3D coordinates of all small-molecule instances in the PDB, we created a "high-quality" subset of ligand instances by various filtering steps including application of crystallographic quality criteria and structural unambiguousness. Submission of 640 Gaussian 03 jobs yielded a set of about 415 successfully concluded runs. We used a stepwise optimization of internal degrees of freedom at the DFT level of theory with the B3LYP/6-31G(d) basis set and a single-point energy calculation at B3LYP/6-311++G(3df,2p) after each round of (partial) optimization to separate energy changes due to bond length stretches vs bond angle changes vs torsion changes. Even for the most "conservative" choice of all the possible conformational energies-the energy difference between the conformation in which all internal degrees of freedom except torsions have been optimized and the fully optimized conformer-significant energy values were found. The range of 0 to ~25 kcal/mol was populated quite evenly and independently of the crystallographic resolution. A smaller number of "outliers" of yet higher energies were seen only at resolutions above 1.3 Å. The energies showed some correlation with molecular size and flexibility but not with crystallographic quality metrics such as the Cruickshank diffraction-component precision index (DPI) and R(free)-R, or with the ligand instance-specific metrics such as occupancy-weighted B-factor (OWAB), real-space R factor (RSR), and real-space correlation coefficient (RSCC). We repeated these calculations with the solvent model IEFPCM, which yielded energy differences that were generally somewhat lower than the corresponding vacuum results but did not produce a qualitatively different picture. Torsional sampling around the crystal conformation at the molecular mechanics level using the MMFF94s force field typically led to an increase in energy.

Full quantum-mechanical structure of the human protein Metallothionein-2

Metallothioneins (MT) are small, metal-binding proteins with diverse functions related to metal ion homeostasis. This paper presents the full 384-388-atom structures of the two native Zn(II)- and the Cd(II)-containing domains of human MT2, optimized with density functional theory. The presented structures are accurate to ~0.03 Å for bond lengths and thus provide new physical insight into the detailed electronic structures of MTs, in particular with accurate accounts of bridging vs. terminal bonds not available from NMR or EXAFS. The MT protein enhances the asymmetry, as compared to the protein-free clusters, causing a hierarchy in binding that most likely allows MTs to transfer ions to multiple targets in vivo. The protein polarization is substantial and occurs primarily via the terminal sulfurs, a key mechanism in providing domain-specific electronic structures. The β-domain polarizes its smaller cluster less on average, due to its less polarizable, higher negative charge density, as reflected in longer MS bond lengths and smaller bond orders. This may explain why MT2β is more reactive and dynamic and why MTs have evolved two different-size, asymmetric domains with different metal binding affinities fit for different molecular targets of metal ion transfer.

Structure and dynamics of a dizinc metalloprotein: effect of charge transfer and polarization

Structures and dynamics of a recently designed dizinc metalloprotein (DFsc) (J. Mol. Biol. 2003, 334, 1101) are studied by molecular dynamics simulation using a dynamically adapted polarized force field derived from fragment quantum calculation for protein in solvent. To properly describe the effect of charge transfer and polarization in the present approach, quantum chemistry calculation of the zinc-binding group is periodically performed (on-the-fly) to update the atomic charges of the zinc-binding group during the MD simulation. Comparison of the present result with those obtained from simulations under standard AMBER force field reveals that charge transfer and polarization are critical to maintaining the correct asymmetric metal coordination in the DFsc. Detailed analysis of the result also shows that dynamic fluctuation of the zinc-binding group facilitates solvent interaction with the zinc ions. In particular, the dynamic fluctuation of the zinc-zinc distance is shown to be an important feature of the catalytic function of the di-ion zinc-binding group. Our study demonstrates that the dynamically adapted polarization approach is computationally practical and can be used to study other metalloprotein systems.

QM/MM X-ray refinement of zinc metalloenzymes

Zinc metalloenzymes play an important role in biology. However, due to the limitation of molecular force field energy restraints used in X-ray refinement at medium or low resolutions, the precise geometry of the zinc coordination environment can be difficult to distinguish from ambiguous electron density maps. Due to the difficulties involved in defining accurate force fields for metal ions, the QM/MM (quantum-mechanical/molecular-mechanical) method provides an attractive and more general alternative for the study and refinement of metalloprotein active sites. Herein we present three examples that indicate that QM/MM based refinement yields a superior description of the crystal structure based on R and R(free) values and on the inspection of the zinc coordination environment. It is concluded that QM/MM refinement is an useful general tool for the improvement of the metal coordination sphere in metalloenzyme active sites.

Conformational variability of benzamidinium-based inhibitors

Determining the structure of a small molecule bound to a biological receptor (e.g., a protein implicated in a disease state) is a necessary step in structure-based drug design. The preferred conformation of a small molecule can change when bound to a protein, and a detailed knowledge of the preferred conformation(s) of a bound ligand can help in optimizing the affinity of a molecule for its receptor. However, the quality of a protein/ligand complex determined using X-ray crystallography is dependent on the size of the protein, the crystal quality, and the realized resolution. The energy restraints used in traditional X-ray refinement procedures typically use "reduced" (i.e., neglect of electrostatics and dispersion interactions) Engh and Huber force field models that, while quite suitable for modeling proteins, often are less suitable for small molecule structures due to a lack of validated parameters. Through the use of ab initio QM/MM-based X-ray refinement procedures, this shortcoming can be overcome especially in the active site or binding site of a small-molecule inhibitor. Herein, we demonstrate that ab initio QM/MM refinement of an inhibitor/protein complex provides insights into the binding of small molecules beyond what is available using more traditional refinement protocols. In particular, QM/MM refinement studies of benzamidinium derivatives show variable conformational preferences depending on the refinement protocol used and the nature of the active-site region.

Interpretation of protein/ligand crystal structure using QM/MM calculations: case of HIV-1 protease/metallacarborane complex

Deltahedral metallacarborane compounds have recently been discovered as potent, specific, stable, and nontoxic inhibitors of HIV-1 protease (PR), the major target for AIDS therapy. The 2.15 A-resolution X-ray structure has exhibited a nonsymmetrical binding of the parental compound [Co(3+)-(C2B9H11)2](-) (GB-18) into PR dimer and a symmetrical arrangement in the crystal of two PR dimer complexes into a tetramer. In order to explore structural and energetic details of the inhibitor binding, quantum mechanics coupled with molecular mechanics approach was utilized. Realizing the close positioning of anionic inhibitors in the active site cavity, the possibility of an exchange of structural water molecules Wat50 and Wat128 by Na+ counterions was studied. The energy profiles for the rotation of the GB-18 molecules along their longitudinal axes in complex with PR were calculated. The results show that two Na+ counterions are present in the active site cavity and provide energetically favorable and unfavorable positions for carbon atoms within the carborane cages. Eighty-one rotamer combinations of four molecules of GB-18 bound to PR out of 4 x 10(5) are predicted to be highly populated. These results lay ground for further calculations of interaction energies between GB-18 and amino acids of PR active site and will make it possible to interpret computationally the binding of similar metallacarborane molecules to PR as well as to resistant PR variants. Moreover, this computational tool will allow the design of new, more potent metallacarborane-based HIV-1 protease inhibitors.

The influence of X-rays on the structural studies of peroxide-derived myoglobin intermediates

In recent years, the awareness of potential radiation damage of metal centers in protein crystals during crystallographic data collection has received increasing attention. The radiation damage can lead to radiation-induced changes and reduction of the metal sites. One of the research fields where these concerns have been comprehensively addressed is the study of the reaction intermediates of the heme peroxidase and oxygenase reaction cycles. For both the resting states and the high-valent intermediates, the X-rays used in the structure determination have given undesired side effects through radiation-induced changes to the trapped intermediates. However, X-rays have been used to generate and trap the peroxy/hydroperoxy state in crystals. In this review, the structural work and the influence of X-rays on these intermediates in myoglobin are summarized and viewed in light of analogous studies on similar intermediates in peroxidases and oxygenases.

Solution NMR structure of a designed metalloprotein and complementary molecular dynamics refinement

We report the solution NMR structure of a designed dimetal-binding protein, di-Zn(II) DFsc, along with a secondary refinement step employing molecular dynamics techniques. Calculation of the initial NMR structural ensemble by standard methods led to distortions in the metal-ligand geometries at the active site. Unrestrained molecular dynamics using a nonbonded force field for the metal shell, followed by quantum mechanical/molecular mechanical dynamics of DFsc, were used to relax local frustrations at the dimetal site that were apparent in the initial NMR structure and provide a more realistic description of the structure. The MD model is consistent with NMR restraints, and in good agreement with the structural and functional properties expected for DF proteins. This work demonstrates that NMR structures of metalloproteins can be further refined using classical and first-principles molecular dynamics methods in the presence of explicit solvent to provide otherwise unavailable insight into the geometry of the metal center.

A theoretical study of the principles regulating the specificity for Al(III) against Mg(II) in protein cavities

Several toxic effects arise from Al's presence in living systems, one of them being the alteration of the natural role of enzymes and non-enzyme proteins. Al(III) is capable of entering protein active sites that in normal conditions should be occupied by other metals. Even if Mg(II) is an ubiquitous metal in biological systems, the interference of aluminium in magnesium metabolism is not clear yet. In this work, a systematic study of the affinity of Al(III) for different protein binding sites is presented, with special attention on structural parameters, the role of the charge and the presence of different ligands in the protein cavity. The specificity of the binding site for Al(III) against Mg(II) has been studied, and also the thermodynamical propensity of a Mg(II)/Al(III) exchange. Quantum mechanical methods that proved to be reliable in previous works have been used, namely, the density functional theory (DFT) and polarizable continuum model (PCM).