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

The energetics and evolution of oxidoreductases in deep time

The core metabolic reactions of life drive electrons through a class of redox protein enzymes, the oxidoreductases. The energetics of electron flow is determined by the redox potentials of organic and inorganic cofactors as tuned by the protein environment. Understanding how protein structure affects oxidation-reduction energetics is crucial for studying metabolism, creating bioelectronic systems, and tracing the history of biological energy utilization on Earth. We constructed ProtReDox (https://protein-redox-potential.web.app), a manually curated database of experimentally determined redox potentials. With over 500 measurements, we can begin to identify how proteins modulate oxidation-reduction energetics across the tree of life. By mapping redox potentials onto networks of oxidoreductase fold evolution, we can infer the evolution of electron transfer energetics over deep time. ProtReDox is designed to include user-contributed submissions with the intention of making it a valuable resource for researchers in this field.

Virtual Model Compound Approach for Calculating Redox Potentials of [Fe2S2]-Cys4 Centers in Proteins - Structure Quality Matters

The midpoint potential of the [Fe2S2]-Cys4-cluster in proteins is known to vary between -200 and -450 mV. This variation is caused by the different electrostatic environment of the cluster in the respective proteins. Continuum electrostatics can quantify the impact of the protein environment on the redox potential. Thus, if the redox potential of a [Fe2S2]-Cys4-cluster model compound in aqueous solution would be known, then redox potentials in various protein complexes could be calculated. However, [Fe2S2]-Cys4-cluster models are not water-soluble, and thus, their redox potential can not be measured in aqueous solution. To overcome this problem, we introduce a method that we call Virtual Model Compound Approach (VMCA) to extrapolate the model redox potential from known redox potentials of proteins. We carefully selected high-resolution structures for our analysis and divide them into a fit set, for fitting the model redox potential, and an independent test set, to check the validity of the model redox potential. However, from our analysis, we realized that the some structures can not be used as downloaded from the PDB but had to be re-refined in order to calculate reliable redox potentials. Because of the re-refinement, we were able to significantly reduce the standard deviation of our derived model redox potential for the [Fe2S2]-Cys4-cluster from 31 mV to 10 mV. As the model redox potential, we obtained -184 mV. This model redox potential can be used to analyze the redox behavior of [Fe2S2]-Cys4-clusters in larger protein complexes.

Multireference Protonation Energetics of a Dimeric Model of Nitrogenase Iron-Sulfur Clusters

Characterizing the electronic structure of the iron-sulfur clusters in nitrogenase is necessary to understand their role in the nitrogen fixation process. One challenging task is to determine the protonation state of the intermediates in the nitrogen fixing cycle. Here, we use a dimeric iron-sulfur model to study relative energies of protonation at C, S, or Fe. Using a composite method based on coupled cluster and density matrix renormalization group energetics, we converge the relative energies of four protonated configurations with respect to basis set and correlation level. We find that accurate relative energies require large basis sets as well as a proper treatment of multireference and relativistic effects. We have also tested ten density functional approximations for these systems. Most of them give large errors in their relative energies. The best performing functional in this system is B3LYP, which gives mean absolute and maximum deviations of only 10 and 13 kJ/mol with respect to our correlated wave function estimates, respectively, comparable to the uncertainty in our correlated estimates. Our work provides benchmark results for the calibration of new approximate electronic structure methods and density functionals for these problems.

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.

Characterization of the Geometrical and Electronic Structures of the Active Site and Its Effects on the Surrounding Environment in Reduced High-Potential Iron-Sulfur Proteins Investigated by the Density Functional Theory Approach

The high-potential iron-sulfur protein (HiPIP) is an electron-transporting protein that functions in the photosynthetic electron-transfer system and possesses a cubane-type [4Fe-4S] cluster in the active center. Characterization of the geometrical and electronic structures of the [4Fe-4S] cluster leads to an understanding of the functions in HiPIP, which are expected to be influenced by the environment surrounding the [4Fe-4S] cluster. This work characterized the geometrical and electronic structures of the [4Fe-4S] cluster in the reduced HiPIP and evaluated their effects on the protein environment using the density functional theory (DFT) approach. DFT calculations showed that the structural asymmetry and spin delocalization between iron atoms allowed for the acquisition of a unique stable geometrical and electronic structure in the open-shell singlet. In addition, the formation of an Fe-Fe bond accompanying the spin delocalization was found to depend on the interatomic distance. A comparison of the calculated stable structures with and without consideration of the amino acids around the [4Fe-4S] cluster demonstrated that the surrounding amino acids stabilized the unique geometrical and electronic structure of the [4Fe-4S] cluster in HiPIP.

Quantum Mechanical Calculations of Redox Potentials of the Metal Clusters in Nitrogenase

We have calculated redox potentials of the two metal clusters in Mo-nitrogenase with quantum mechanical (QM) calculations. We employ an approach calibrated for iron-sulfur clusters with 1-4 Fe ions, involving QM-cluster calculations in continuum solvent and large QM systems (400-500 atoms), based on structures from combined QM and molecular mechanics (QM/MM) geometry optimisations. Calculations on the P-cluster show that we can reproduce the experimental redox potentials within 0.33 V. This is similar to the accuracy obtained for the smaller clusters, although two of the redox reactions involve also proton transfer. The calculated P¹⁺/P^N redox potential is nearly the same independently of whether P¹⁺ is protonated or deprotonated, explaining why redox titrations do not show any pH dependence. For the FeMo cluster, the calculations clearly show that the formal oxidation state of the cluster in the resting E₀ state is MoIIIFe3IIFe4III , in agreement with previous experimental studies and QM calculations. Moreover, the redox potentials of the first five E₀-E₄ states are nearly constant, as is expected if the electrons are delivered by the same site (the P-cluster). However, the redox potentials are insensitive to the formal oxidation states of the Fe ion (i.e., whether the added protons bind to sulfide or Fe ions). Finally, we show that the later (E₄-E₈) states of the reaction mechanism have redox potential that are more positive (i.e., more exothermic) than that of the E₀/E₁ couple.