Density functional theory calculations of redox properties of iron–sulphur protein analogues

Two local minima for structures of [4Fe-4S] clusters obtained with density functional theory methods

[4Fe-4S] clusters are essential cofactors in many proteins involved in biological redox-active processes. Density functional theory (DFT) methods are widely used to study these clusters. Previous investigations have indicated that there exist two local minima for these clusters in proteins. We perform a detailed study of these minima in five proteins and two oxidation states, using combined quantum mechanical and molecular mechanical (QM/MM) methods. We show that one local minimum (L state) has longer Fe-Fe distances than the other (S state), and that the L state is more stable for all cases studied. We also show that some DFT methods may only obtain the L state, while others may obtain both states. Our work provides new insights into the structural diversity and stability of [4Fe-4S] clusters in proteins, and highlights the importance of reliable DFT methods and geometry optimization. We recommend r2SCAN for optimizing [4Fe-4S] clusters in proteins, which gives the most accurate structures for the five proteins studied.

Hybrid Functional and Plane Waves based Ab Initio Molecular Dynamics Study of the Aqueous Fe2+ /Fe3+ Redox Reaction

Kohn-Sham density functional theory and plane wave basis set based ab initio molecular dynamics (AIMD) simulation is a powerful tool for studying complex reactions in solutions, such as electron transfer (ET) reactions involving Fe²⁺ /Fe³⁺ ions in water. In most cases, such simulations are performed using density functionals at the level of Generalized Gradient Approximation (GGA). The challenge in modelling ET reactions is the poor quality of GGA functionals in predicting properties of such open-shell systems due to the inevitable self-interaction error (SIE). While hybrid functionals can minimize SIE, standard plane-wave based AIMD at that level of theory is typically 150 times slower than GGA for systems containing ∼100 atoms. Among several approaches reported to speed-up AIMD simulations with hybrid functionals, the noise-stabilized MD (NSMD) procedure, together with the use of localized orbitals to compute the required exchange integrals, is an attractive option. In this work, we demonstrate the application of the NSMD approach for studying the Fe²⁺ /Fe³⁺ redox reaction in water. It is shown here that long AIMD trajectories at the level of hybrid density functionals can be obtained using this approach. Redox properties of the aqueous Fe²⁺ /Fe³⁺ system computed from these simulations are compared with the available experimental data for validation.

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.

Experimental and DFT Investigations Reveal the Influence of the Outer Coordination Sphere on the Vibrational Spectra of Nickel-Substituted Rubredoxin, a Model Hydrogenase Enzyme

Nickel-substituted rubredoxin (NiRd) is a functional enzyme mimic of hydrogenase, highly active for electrocatalytic and solution-phase hydrogen generation. Spectroscopic methods can provide valuable insight into the catalytic mechanism, provided the appropriate technique is used. In this study, we have employed multiwavelength resonance Raman spectroscopy coupled with DFT calculations on an extended active-site model of NiRd to probe the electronic and geometric structures of the resting state of this system. Excellent agreement between experiment and theory is observed, allowing normal mode assignments to be made on the basis of frequency and intensity analyses. Both metal-ligand and ligand-centered vibrational modes are enhanced in the resonance Raman spectra. The latter provide information about the hydrogen bonding network and structural distortions due to perturbations in the secondary coordination sphere. To reproduce the resonance enhancement patterns seen for high-frequency vibrational modes, the secondary coordination sphere must be included in the computational model. The structure and reduction potential of the Ni^IIIRd state have also been investigated both experimentally and computationally. This work begins to establish a foundation for computational resonance Raman spectroscopy to serve in a predictive fashion for investigating catalytic intermediates of NiRd.

Protein dynamics and the all-ferrous [Fe4 S4 ] cluster in the nitrogenase iron protein

In nitrogen fixation by Azotobacter vinelandii nitrogenase, the iron protein (FeP) binds to and subsequently transfers electrons to the molybdenum–FeP, which contains the nitrogen fixation site, along with hydrolysis of two ATPs. However, the nature of the reduced state cluster is not completely clear. While reduced FeP is generally thought to contain an [Fe₄S₄]¹⁺ cluster, evidence also exists for an all‐ferrous [Fe₄S₄]⁰ cluster. Since the former indicates a single electron is transferred per two ATPs hydrolyzed while the latter indicates two electrons could be transferred per two ATPs hydrolyzed, an all‐ferrous [Fe₄S₄]⁰ cluster in FeP is potenially two times more efficient. However, the 1+/0 reduction potential has been measured in the protein at both 460 and 790 mV, causing the biological significance to be questioned. Here, “density functional theory plus Poisson Boltzmann” calculations show that cluster movement relative to the protein surface observed in the crystal structures could account for both measured values. In addition, elastic network mode analysis indicates that such movement occurs in low frequency vibrations of the protein, implying protein dynamics might lead to variations in reduction potential. Furthermore, the different reductants used in the conflicting measurements of the reduction potential could be differentially affecting the protein dynamics. Moreover, even if the all‐ferrous cluster is not the biologically relevant cluster, mutagenesis to stabilize the conformation with the more exposed cluster may be useful for bioengineering more efficient enzymes.

Assessment of Quantum Mechanical Methods for Copper and Iron Complexes by Photoelectron Spectroscopy

Broken-symmetry density functional theory (BS-DFT) calculations are assessed for redox energetics [Cu(SCH₃)₂]^1–/0, [Cu(NCS)₂]^1–/0, [FeCl₄]^1–/0, and [Fe(SCH₃)₄]^1–/0 against vertical detachment energies (VDE) from valence photoelectron spectroscopy (PES), as a prelude to studies of metalloprotein analogs. The M06 and B3LYP hybrid functionals give VDE that agree with the PES VDE for the Fe complexes, but both underestimate it by ∼400 meV for the Cu complexes; other hybrid functionals give VDEs that are an increasing function of the amount of Hartree–Fock (HF) exchange and so cannot show good agreement for both Cu and Fe complexes. Range-separated (RS) functionals appear to give a better distribution of HF exchange since the negative HOMO energy is approximately equal to the VDEs but also give VDEs dependent on the amount of HF exchange, sometimes leading to ground states with incorrect electron configurations; the LRC-ωPBEh functional reduced to 10% HF exchange at short-range give somewhat better values for both, although still ∼150 meV too low for the Cu complexes and ∼50 meV too high for the Fe complexes. Overall, the results indicate that while HF exchange compensates for self-interaction error in DFT calculations of both Cu and Fe complexes, too much may lead to more sensitivity to nondynamical correlation in the spin-polarized Fe complexes.

Identifying sequence determinants of reduction potentials of metalloproteins

The reduction potential of an electron transfer protein is one of its most important functional characteristics. Although the type of redox site and the protein fold are the major determinants of the reduction potential of a redox-active protein, its amino acid sequence may tune the reduction potential as well. Thus, homologous proteins can often be divided into different classes, with each class characterized by a biological function and a reduction potential. Site-specific mutagenesis of the sequence determinants of the differences in the reduction potential between classes should change the reduction potential of a protein in one class to that of the other class. Here, a procedure is presented that combines energetic and bioinformatic analysis of homologous proteins to identify sequence determinants that are also good candidates for site-specific mutations, using the [4Fe-4S] ferredoxins and the [4Fe-4S] high-potential iron-sulfur proteins as examples. This procedure is designed to guide site-specific mutations or more computationally expensive studies, such as molecular dynamics simulations. To make the procedure more accessible to the general scientific community, it is being implemented into CHARMMing, a Web-based portal, with a library of density functional theory results for the redox site that are used in the setting up of Poisson-Boltzmann continuum electrostatics calculations for the protein energetics.

Identifying residues that cause pH-dependent reduction potentials

The pH dependence of the reduction potential E° for a metalloprotein indicates that the protonation state of at least one residue near the redox site changes and may be important for its activity. The responsible residue is usually identified by site-specific mutagenesis, which may be time-consuming. Here, the titration of E° for Chromatium vinosum high-potential iron-sulfur protein is predicted to be in good agreement with experiment using density functional theory and Poisson-Boltzmann calculations if only the sole histidine undergoes changes in protonation. The implementation of this approach into CHARMMing, a user-friendly web-based portal, allows users to identify residues in other proteins causing similar pH dependence.

Calculating standard reduction potentials of [4Fe-4S] proteins

The oxidation-reduction potentials of electron transfer proteins determine the driving forces for their electron transfer reactions. Although the type of redox site determines the intrinsic energy required to add or remove an electron, the electrostatic interaction energy between the redox site and its surrounding environment can greatly shift the redox potentials. Here, a method for calculating the reduction potential versus the standard hydrogen electrode, E°, of a metalloprotein using a combination of density functional theory and continuum electrostatics is presented. This work focuses on the methodology for the continuum electrostatics calculations, including various factors that may affect the accuracy. The calculations are demonstrated using crystal structures of six homologous HiPIPs, which give E° that are in excellent agreement with experimental results.

Characterizing the effects of the protein environment on the reduction potentials of metalloproteins

The reduction potentials of electron transfer proteins are critically determined by the degree of burial of the redox site within the protein and the degree of permanent polarization of the polypeptide around the redox site. Although continuum electrostatics calculations of protein structures can predict the net effect of these factors, quantifying each individual contribution is a difficult task. Here, the burial of the redox site is characterized by a dielectric radius R(p) (a Born-type radius for the protein), the polarization of the polypeptide is characterized by an electret potential ϕ(p) (the average electrostatic potential at the metal atoms), and an electret-dielectric spheres (EDS) model of the entire protein is then defined in terms of R(p) and ϕ(p). The EDS model shows that for a protein with a redox site of charge Q, the dielectric response free energy is a function of Q(2), while the electret energy is a function of Q. In addition, R(p) and ϕ(p) are shown to be characteristics of the fold of a protein and are predictive of the most likely redox couple for redox sites that undergo different redox couples.

Understanding rubredoxin redox sites by density functional theory studies of analogues

Determining the redox energetics of redox site analogues of metalloproteins is essential in unraveling the various contributions to electron transfer properties of these proteins. Since studies of the [4Fe-4S] analogues show that the energies are dependent on the ligand dihedral angles, broken symmetry density functional theory (BS-DFT) with the B3LYP functional and double-ζ basis sets calculations of optimized geometries and electron detachment energies of [1Fe] rubredoxin analogues are compared to crystal structures and gas-phase photoelectron spectroscopy data, respectively, for [Fe(SCH(3))(4)](0/1-/2-), [Fe(S(2)-o-xyl)(2)](0/1-/2-), and Na(+)[Fe(S(2)-o-xyl)(2)](1-/2-) in different conformations. In particular, the study of Na(+)[Fe(S(2)-o-xyl)(2)](1-/2-) is the only direct comparison of calculated and experimental gas phase detachment energies for the 1-/2- couple found in the rubredoxins. These results show that variations in the inner sphere energetics by up to ∼0.4 eV can be caused by differences in the ligand dihedral angles in either or both redox states. Moreover, these results indicate that the protein stabilizes the conformation that favors reduction. In addition, the free energies and reorganization energies of oxidation and reduction as well as electrostatic potential charges are calculated, which can be used as estimates in continuum electrostatic calculations of electron transfer properties of [1Fe] proteins.