Structure and Redox Properties of the Protein, Rubredoxin, and Its Ligand and Metal Mutants Studied by Electronic Structure Calculation

Benchmark Study of Redox Potential Calculations for Iron-Sulfur Clusters in Proteins

Redox potentials have been calculated for 12 different iron–sulfur sites of 6 different types with 1–4 iron ions. Structures were optimized with combined quantum mechanical and molecular mechanical (QM/MM) methods, and the redox potentials were calculated using the QM/MM energies, single-point QM methods in a continuum solvent or by QM/MM thermodynamic cycle perturbations. We show that the best results are obtained with a large QM system (∼300 atoms, but a smaller QM system, ∼150 atoms, can be used for the QM/MM geometry optimization) and a large value of the dielectric constant (80). For absolute redox potentials, the B3LYP density functional method gives better results than TPSS, and the results are improved with a larger basis set. However, for relative redox potentials, the opposite is true. The results are insensitive to the force field (charges of the surroundings) used for the QM/MM calculations or whether the protein and solvent outside the QM system are relaxed or kept fixed at the crystal structure. With the best approach for relative potentials, mean absolute and maximum deviations of 0.17 and 0.44 V, respectively, are obtained after removing a systematic error of −0.55 V. Such an approach can be used to identify the correct oxidation states involved in a certain redox reaction.

We have studied redox potentials of 12 iron−sulfur sites of 6 types with 1−4 iron ions. Structures were optimized with combined quantum mechanical and molecular mechanical (QM/MM) methods, and the redox potentials were calculated with QM/MM, QM calculations in a continuum solvent or by QM/MM thermodynamic cycle perturbations. The best results are obtained with the second approach using ∼300 atoms in the QM model and a large dielectric constant.

Theoretical Modeling of Redox Potentials of Biomolecules

The estimation of the redox potentials of biologically relevant systems by means of theoretical-computational approaches still represents a challenge. In fact, the size of these systems typically does not allow a full quantum-mechanical treatment needed to describe electron loss/gain in such a complex environment, where the redox process takes place. Therefore, a number of different theoretical strategies have been developed so far to make the calculation of the redox free energy feasible with current computational resources. In this review, we provide a survey of such theoretical-computational approaches used in this context, highlighting their physical principles and discussing their advantages and limitations. Several examples of these approaches applied to the estimation of the redox potentials of both proteins and nucleic acids are described and critically discussed. Finally, general considerations on the most promising strategies are reported.

Combined Electrostatically Embedded Multiconfiguration Molecular Mechanics and Molecular Mechanical Method: Application to Molecular Dynamics Simulation of a Chemical Reaction in Aqueous Solution with Hybrid Density Functional Theory

We here combine the electrostatically embedded multiconfiguration molecular mechanics (EE-MCMM) method for generating global potential energy surfaces in the presence of an electrostatic potential with molecular mechanics (MM). The resulting EE-MCMM/MM method is illustrated by applying it to carry out a molecular dynamics simulation for the symmetric bimolecular reaction Cl(-) + CH3Cl' → ClCH3 + Cl'(-) in aqueous solution with hybrid density functional theory as the quantum mechanical level. The potential of mean force is calculated, and the free energy barrier is found to be 25.3 kcal/mol, which is in good agreement with previous work. The advantage of the combined EE-MCMM and MM method is that the number of quantum mechanical calculations required for the active subsystem is very small compared to straight direct dynamics.

Importance of polarization effect in the study of metalloproteins: application of polarized protein specific charge scheme in predicting the reduction potential of azurin

Molecular dynamics (MD) simulation is commonly used in the study of protein dynamics, and in recent years, the extension of MD simulation to the study of metalloproteins is gaining much interest. Choice of force field is crucial in MD studies, and the inclusion of metal centers complicates the process of accurately describing the electrostatic environment that surrounds the redox centre. Herein, we would like to explore the importance of including electrostatic contribution from both protein and solvent in the study of metalloproteins. MD simulations with the implementation of thermodynamic integration will be conducted to model the reduction process of azurin from Pseudomonas aeruginosa. Three charge schemes will be used to derive the partial charges of azurin. These charge schemes differ in terms of the amount of immediate environment, respective to copper, considered during charge fitting, which ranges from the inclusion of copper and residues in the first coordination sphere during density functional theory charge fitting to the comprehensive inclusion of protein and solvent effect surrounding the metal centre using polarized protein-specific charge scheme. From the simulations conducted, the relative reduction potential of the mutated azurins respective to that of wild-type azurin (ΔEcal) were calculated and compared with experimental values. The ΔEcal approached experimental value with increasing consideration of environmental effect hence substantiating the importance of polarization effect in the study of metalloproteins. This study also attests the practicality of polarized protein-specific charge as a computational tool capable of incorporating both protein environment and solvent effect into MD simulations.

Performance comparison of computational methods for modeling alpha-helical structures

Geometry optimization results are reported for secondary structural elements of small proteins and polypeptides. Emphasis is placed on how well molecular mechanics as well as semiempirical, ab initio, and density functional methods describe α-helical and related structures in purely theoretical models (Gly10, Ile10) as well as in realistic models (an α-helical region of calmodulin, and the complete structure of a small protein). Many of the methods examined here were found to provide unsatisfactory descriptions of the hydrogen-bonding interactions within polypeptide-type structures, as the α-helical canonical secondary structure motif was not reproduced accurately. Ab initio and DFT methods provided reasonable results only when solvation models were included, although Hartree-Fock failed even with solvation in one of the test cases; among the semiempirical methods, one of the PM6 implementations performed very well.

Reduction potentials and acidity constants of Mn superoxide dismutase calculated by QM/MM free-energy methods

We used two theoretical methods to estimate reduction potentials and acidity constants in Mn superoxide dismutase (MnSOD), namely combined quantum mechanical and molecular mechanics (QM/MM) thermodynamic cycle perturbation (QTCP) and the QM/MM-PBSA approach. In the latter, QM/MM energies are combined with continuum solvation energies calculated by solving the Poisson-Boltzmann equation (PB) or by the generalised Born approach (GB) and non-polar solvation energies calculated from the solvent-exposed surface area. We show that using the QTCP method, we can obtain accurate and precise estimates of the proton-coupled reduction potential for MnSOD, 0.30±0.01 V, which compares favourably with experimental estimates of 0.26-0.40 V. However, the calculated potentials depend strongly on the DFT functional used: The B3LYP functional gives 0.6 V more positive potentials than the PBE functional. The QM/MM-PBSA approach leads to somewhat too high reduction potentials for the coupled reaction and the results depend on the solvation model used. For reactions involving a change in the net charge of the metal site, the corresponding results differ by up to 1.3 V or 24 pK(a) units, rendering the QM/MM-PBSA method useless to determine absolute potentials. However, it may still be useful to estimate relative shifts, although the QTCP method is expected to be more accurate.

QM/MM methods for biomolecular systems

Combined quantum-mechanics/molecular-mechanics (QM/MM) approaches have become the method of choice for modeling reactions in biomolecular systems. Quantum-mechanical (QM) methods are required for describing chemical reactions and other electronic processes, such as charge transfer or electronic excitation. However, QM methods are restricted to systems of up to a few hundred atoms. However, the size and conformational complexity of biopolymers calls for methods capable of treating up to several 100,000 atoms and allowing for simulations over time scales of tens of nanoseconds. This is achieved by highly efficient, force-field-based molecular mechanics (MM) methods. Thus to model large biomolecules the logical approach is to combine the two techniques and to use a QM method for the chemically active region (e.g., substrates and co-factors in an enzymatic reaction) and an MM treatment for the surroundings (e.g., protein and solvent). The resulting schemes are commonly referred to as combined or hybrid QM/MM methods. They enable the modeling of reactive biomolecular systems at a reasonable computational effort while providing the necessary accuracy.

Calculation of redox properties: understanding short- and long-range effects in rubredoxin

In this computational study we show that for rubredoxin, a small and comparatively simple iron-sulfur protein, it is possible to combine a full ab initio description of the electronic structure of the protein in explicit solvent with sampling of the relevant time scale of the protein dynamics by using a hybrid method based on a force field molecular dynamics/density functional theory scheme. Applying this scheme within the framework of Marcus theory we are able to reproduce the experimental redox potential difference of 60 mV between a mesophilic and thermophilic rubredoxin within an accuracy of 20 mV and explain it in terms of short-range contributions from a few residues close to the metal center. We also compute the reorganization free energy for oxidation of the protein obtaining 720 meV for the mesophilic and 590 meV for thermophilic variant. Decomposition of the reorganization energy by using the classical force field shows that this quantity is largely determined by the solvent, with both short-range (an oxidation induced change of coordination number) and long-range (dielectric) contributions. The 130 meV higher value for the mesophilic form is analyzed in terms of detailed differences in the solvent structure around the metal center and the dielectric response. These results underline the importance of a molecular description of the solvent and of a correct inclusion of the polarization effects.

The binding of nitric oxide at the Cu(i) site of copper nitrite reductase and of inorganic models: DFT calculations of the energetics and EPR parameters of side-on and end-on structures

Density functional theory calculations have been used to probe the end-on and side-on bonding motifs of nitric oxide at the Cu(i) centre in the enzyme copper nitrite reductase and in three inorganic model systems. We find that irrespective of a range of functionals used, the end-on structure is preferred by up to 40 kJ mol(-1), although this preference is smaller for the enzyme than for the inorganic model systems. We have calculated the g-tensor and atomic hyperfine coupling constants for these structures. When compared to available experimental data, for one model compound the calculated EPR parameters definitely favour an end-on structure, although this preference is somewhat less for the enzyme. Our prediction of NO end-on binding in the enzyme is at variance with structural data.

Atomic Resolution Crystal Structures, EXAFS, and Quantum Chemical Studies of Rusticyanin and Its Two Mutants Provide Insight into Its Unusual Properties,

Rusticyanin from the extremophile Thiobacillus ferrooxidans is a blue copper protein with unusually high redox potential and acid stability. We present the crystal structures of native rusticyanin and of its Cu site mutant His143Met at 1.27 and 1.10 A, respectively. The very high resolution of these structures allows a direct comparison with EXAFS data and with quantum chemical models of the oxidized and reduced forms of the proteins, based upon both isolated and embedded clusters and density functional theory (DFT) methods. We further predict the structure of the Cu(II) form of the His143Met mutant which has been experimentally inaccessible due to its very high redox potential. We also present metrical EXAFS data and quantum chemical calculations for the oxidized and reduced states of the Met148Gln mutant, this protein having the lowest redox potential of all currently characterized mutants of rusticyanin. These data offer new insights into the structural factors which affect the redox potential in this important class of proteins. Calculations successfully predict the structure and the order of redox potentials for the three proteins. The calculated redox potential of H143M ( approximately 400 mV greater than native rusticyanin) is consistent with the failure of readily available chemical oxidants to restore a Cu(II) species of this mutant. The structural and energetic effects of mutating the equatorial cysteine to serine, yet to be studied experimentally, are predicted to be considerable by our calculations.

Can the semiempirical PM3 scheme describe iron-containing bioinorganic molecules?

A set of iron parameters for use in the semiempirical PM3 method have been developed to allow the structure and redox properties of the active sites of iron-containing proteins to be accurately modeled, focussing on iron-sulfur, iron-heme, and iron-only hydrogenases. Data computed at the B3LYP/6-31G* level for a training set of 60 representative complexes have been employed. A gradient-based optimization algorithm has been used, and important modifications of the core repulsion function have been highlighted. The derived parameters lead in general to good predictions of the structure and energetics of molecules both within and outside the training set, and overcome the extensive deficiencies of a B3LYP/STO-3G model. Particularly encouraging is the success of the parameters in describing [4Fe-4S] cubanes. The derived parameter set provides a starting point should greater accuracy for a more restricted range of compounds be required.