Ergodicity-Breaking in Thermal Biological Electron Transfer? Cytochrome C Revisited

Electrochemistry in sensing of molecular interactions of proteins and their behavior in an electric field

Electrochemical methods can be used not only for the sensitive analysis of proteins but also for deeper research into their structure, transport functions (transfer of electrons and protons), and sensing their interactions with soft and solid surfaces. Last but not least, electrochemical tools are useful for investigating the effect of an electric field on protein structure, the direct application of electrochemical methods for controlling protein function, or the micromanipulation of supramolecular protein structures. There are many experimental arrangements (modalities), from the classic configuration that works with an electrochemical cell to miniaturized electrochemical sensors and microchip platforms. The support of computational chemistry methods which appropriately complement the interpretation framework of experimental results is also important. This text describes recent directions in electrochemical methods for the determination of proteins and briefly summarizes available methodologies for the selective labeling of proteins using redox-active probes. Attention is also paid to the theoretical aspects of electron transport and the effect of an external electric field on the structure of selected proteins. Instead of providing a comprehensive overview, we aim to highlight areas of interest that have not been summarized recently, but, at the same time, represent current trends in the field.

Comment on "Applicability of perturbed matrix method for charge transfer studies at bio/metallic interfaces: a case of azurin" by O. Kontkanen, D. Biriukov and Z. Futera, Phys. Chem. Chem. Phys., 2023, , 12479

Polarizability is a fundamental property of all molecular systems describing the deformation of the molecular electronic density in response to an applied electric field. The question of whether polarizability of the active site needs to be included in theories of enzymatic activity remains open. Hybrid quantum mechanical/molecular mechanical calculations are hampered by difficulties faced by many quantum-chemistry algorithms to provide sufficiently accurate estimates of the anisotropic second-rank tensor of molecular polarizability. In this Comment, we provide general theoretical arguments for the values of polarizability of the quantum region or a molecule which have to be reproduced by electronic structure calculations.

Structural Determinants of Redox Conduction Favor Robustness over Tunability in Microbial Cytochrome Nanowires

Structural determinants of a 103-fold variation in electrical conductivity for helical homopolymers of tetra-, hexa-, and octa-heme cytochromes (named Omc- E, S, and Z, respectively) from Geobacter sulfurreducens are investigated with the Pathways model for electron tunneling, classical molecular dynamics, and hybrid quantum/classical molecular mechanics. Thermally averaged electronic couplings for through-space heme-to-heme electron transfer in the "nanowires" computed with density functional theory are ≤0.015 eV. Pathways analyses also indicate that couplings match within a factor of 5 for all "nanowires", but some alternative tunneling routes are found involving covalent protein backbone bonds (Omc- S and Z) or propionic acid-ligating His H-bonds on adjacent hemes (OmcZ). Reorganization energies computed from electrostatic vertical energy gaps or a version of the Marcus continuum expression parameterized on the total (donor + acceptor) solvent-accessible surface area typically agree within 20% and fall within the range 0.48-0.98 eV. Reaction free energies in all three "nanowires" are ≤|0.28| eV, even though Coulombic interactions primarily tune the site redox energies by 0.7-1.2 eV. Given the conserved energetic parameters, redox conductivity differs by < 103-fold among the cytochrome "nanowires". Redox currents do not exceed 3.0 × 10-3 pA at a physiologically relevant 0.1 V bias, with the slowest electron transfers being on a (μs) timescale much faster than typical (ms) enzymatic turnovers. Thus, the "nanowires" are proposed to be functionally robust to variations in structure that provide a habitat-customized protein interface. The 30 pA to 30 nA variation in conductivity previously reported from atomic force microscopy experiments is not intrinsic to the structures and/or does not result from the physiologically relevant redox conduction mechanism.

Applicability of perturbed matrix method for charge transfer studies at bio/metallic interfaces: a case of azurin

As the field of nanoelectronics based on biomolecules such as peptides and proteins rapidly grows, there is a need for robust computational methods able to reliably predict charge transfer properties at bio/metallic interfaces. Traditionally, hybrid quantum-mechanical/molecular-mechanical techniques are employed for systems where the electron hopping transfer mechanism is applicable to determine physical parameters controlling the thermodynamics and kinetics of charge transfer processes. However, these approaches are limited by a relatively high computational cost when extensive sampling of a configurational space is required, like in the case of soft biomatter. For these applications, semi-empirical approaches such as the perturbed matrix method (PMM) have been developed and successfully used to study charge-transfer processes in biomolecules. Here, we explore the performance of PMM on prototypical redox-active protein azurin in various environments, from solution to vacuum interfaces with gold surfaces and protein junction. We systematically benchmarked the robustness and convergence of the method with respect to the quantum-centre size, size of the Hamiltonian, number of samples, and level of theory. We show that PMM can adequately capture all the trends associated with the structural and electronic changes related to azurin oxidation at bio/metallic interfaces.

Ionogel-Electrode for the Study of Protein Tunnel Junctions under Physiologically Relevant Conditions

The study of charge transport through proteins is essential for understanding complicated electrochemical processes in biological activities while the reasons for the coexistence of tunneling and hopping phenomena in protein junctions still remain unclear. In this work, a flexible and conductive ionogel electrode is synthesized and is used as a top contact to form highly reproducible protein junctions. The junctions of proteins, including human serum albumin, cytochrome C and hemoglobin, show temperature-independent electron tunneling characteristics when the junctions are in solid states while with a different mechanism of temperature-dependent electron hopping when junctions are hydrated under physiologically relevant conditions. It is demonstrated that the solvent reorganization energy plays an important role in the electron-hopping process and experimentally shown that it requires ≈100 meV for electron hopping through one heme group inside a hydrated protein molecule connected between two electrodes.

Assessing the Functional and Structural Stability of the Met80Ala Mutant of Cytochrome c in Dimethylsulfoxide

The Met80Ala variant of yeast cytochrome c is known to possess electrocatalytic properties that are absent in the wild type form and that make it a promising candidate for biocatalysis and biosensing. The versatility of an enzyme is enhanced by the stability in mixed aqueous/organic solvents that would allow poorly water-soluble substrates to be targeted. In this work, we have evaluated the effect of dimethylsulfoxide (DMSO) on the functionality of the Met80Ala cytochrome c mutant, by investigating the thermodynamics and kinetics of electron transfer in mixed water/DMSO solutions up to 50% DMSO v/v. In parallel, we have monitored spectroscopically the retention of the main structural features in the same medium, focusing on both the overall protein structure and the heme center. We found that the organic solvent exerts only minor effects on the redox and structural properties of the mutant mostly as a result of the modification of the dielectric constant of the solvent. This would warrant proper functionality of this variant also under these potentially hostile experimental conditions, that differ from the physiological milieu of cytochrome c.

A 300-fold conductivity increase in microbial cytochrome nanowires due to temperature-induced restructuring of hydrogen bonding networks

Although proteins are considered as nonconductors that transfer electrons only up to 1 to 2 nanometers via tunneling, Geobacter sulfurreducens transports respiratory electrons over micrometers, to insoluble acceptors or syntrophic partner cells, via nanowires composed of polymerized cytochrome OmcS. However, the mechanism enabling this long-range conduction is unclear. Here, we demonstrate that individual nanowires exhibit theoretically predicted hopping conductance, at rate (>10¹⁰ s^-1) comparable to synthetic molecular wires, with negligible carrier loss over micrometers. Unexpectedly, nanowires show a 300-fold increase in their intrinsic conductance upon cooling, which vanishes upon deuteration. Computations show that cooling causes a massive rearrangement of hydrogen bonding networks in nanowires. Cooling makes hemes more planar, as revealed by Raman spectroscopy and simulations, and lowers their reduction potential. We find that the protein surrounding the hemes acts as a temperature-sensitive switch that controls charge transport by sensing environmental perturbations. Rational engineering of heme environments could enable systematic tuning of extracellular respiration.

Reorganization Free Energy of Copper Proteins in Solution, in Vacuum, and on Metal Surfaces

Metalloproteins, known to efficiently transfer electronic charge in biological systems, recently found their utilization in nanobiotechnological devices where the protein is placed into direct contact with metal surfaces. The feasibility of oxidation/reduction of the protein redox sites is affected by the reorganization free energies, one of the key parameters determining the transfer rates. While their values have been measured and computed for proteins in their native environments, i.e., in aqueous solution, the reorganization free energies of dry proteins or proteins adsorbed to metal surfaces remain unknown. Here, we investigate the redox properties of blue copper protein azurin, a prototypical redox-active metalloprotein previously probed by various experimental techniques both in solution and on metal/vacuum interfaces. We used a hybrid QM/MM computational technique based on DFT to explore protein dynamics, flexibility, and corresponding reorganization free energies in aqueous solution, vacuum, and on vacuum gold interfaces. Somewhat surprisingly, the reorganization free energy only slightly decreases when azurin is dried because the loss of the hydration shell leads to larger flexibility of the protein near its redox site. At the vacuum gold surfaces, the energetics of the structure relaxation depends on the adsorption geometry, however, significant reduction of the reorganization free energy was not observed. These findings have important consequences for the charge transport mechanism in vacuum devices, showing that the free energy barriers for protein oxidation remain significant even under ultra-high vacuum conditions.

AutoSolvate: A toolkit for automating quantum chemistry design and discovery of solvated molecules

The availability of large, high-quality datasets is crucial for artificial intelligence design and discovery in chemistry. Despite the essential roles of solvents in chemistry, the rapid computational dataset generation of solution-phase molecular properties at the quantum mechanical level of theory was previously hampered by the complicated simulation procedure. Software toolkits that can automate the procedure to set up high-throughput explicit-solvent quantum chemistry (QC) calculations for arbitrary solutes and solvents in an open-source framework are still lacking. We developed AutoSolvate, an open-source toolkit, to streamline the workflow for QC calculation of explicitly solvated molecules. It automates the solvated-structure generation, force field fitting, configuration sampling, and the final extraction of microsolvated cluster structures that QC packages can readily use to predict molecular properties of interest. AutoSolvate is available through both a command line interface and a graphical user interface, making it accessible to the broader scientific community. To improve the quality of the initial structures generated by AutoSolvate, we investigated the dependence of solute-solvent closeness on solute/solvent identities and trained a machine learning model to predict the closeness and guide initial structure generation. Finally, we tested the capability of AutoSolvate for rapid dataset curation by calculating the outer-sphere reorganization energy of a large dataset of 166 redox couples, which demonstrated the promise of the AutoSolvate package for chemical discovery efforts.

Bridging the Experiment-Calculation Divide: Machine Learning Corrections to Redox Potential Calculations in Implicit and Explicit Solvent Models

Prediction of redox potentials is essential for catalysis and energy storage. Although density functional theory (DFT) calculations have enabled rapid redox potential predictions for numerous compounds, prominent errors persist compared to experimental measurements. In this work, we develop machine learning (ML) models to reduce the errors of redox potential calculations in both implicit and explicit solvent models. Training and testing of the ML correction models are based on the diverse ROP313 data set with experimental redox potentials measured for organic and organometallic compounds in a variety of solvents. For the implicit solvent approach, our ML models can reduce both the systematic bias and the number of outliers. ML corrected redox potentials also demonstrate less sensitivity to DFT functional choice. For the explicit solvent approach, we significantly reduce the computational costs by embedding the microsolvated cluster in implicit bulk solvent, obtaining converged redox potential results with a smaller solvation shell. This combined implicit-explicit solvent model, together with GPU-accelerated quantum chemistry methods, enabled rapid generation of a large data set of explicit-solvent-calculated redox potentials for 165 organic compounds, allowing detailed investigation of the error sources in explicit solvent redox potential calculations.

Contributions to cytochrome c inner- and outer-sphere reorganization energy

Cytochromes c are small water-soluble proteins that catalyze electron transfer in metabolism and energy conversion processes. Hydrogenobacter thermophilus cytochrome c₅₅₂ presents a curious case in displaying fluxionality of its heme axial methionine ligand; this behavior is altered by single point mutation of the Q64 residue to N64 or V64, which fixes the ligand in a single configuration. The reorganization energy (λ) of these cytochrome c₅₅₂ variants is experimentally determined using a combination of rotating disc electrochemistry, chronoamperometry and cyclic voltammetry. The differences between the λ determined from these complementary techniques helps to deconvolute the contribution of the active site and its immediate environment to the overall λ (λ_Total). The experimentally determined λ values in conjunction with DFT calculations indicate that the differences in λ among the protein variants are mainly due to the differences in contributions from the protein environment and not just inner-sphere λ. DFT calculations indicate that the position of residue 64, responsible for the orientation of the axial methionine, determines the geometric relaxation of the redox active molecular orbital (RAMO). The orientation of the RAMO with respect to the heme is key to determining electron transfer coupling (H_AB) which results in higher ET rates in the wild-type protein relative to the Q64V mutant despite a 150 mV higher λ_Total in the former.

Efficient delocalization of the redox-active molecular orbital (RAMO) in HtWT results in an increase in H_AB value which in turn accelerates the electron transfer (ET) rate in spite of the higher reorganization energy (λ) than the HtQ64V mutant.

Electron Transfer-Induced Active Site Structural Relaxation in 64-Photolyase of Drosophila melanogaster

While catalytic electron flow and photoreactivation of CPD-photolyases are increasingly understood, the microscopic details of the 64-photolyase repair mechanism are perpetually debated. Here, we investigate in long-time (μs) molecular dynamics simulations combined with extensive quantum mechanical/molecular mechanical (QM/MM) simulations the primary electron transfer (ET) reactions in 64-photolyase of Drosophila melanogaster (D. melanogaster). The characterization of the relative energetics of locally excited and charge separated states in the (6-4) photoproduct enzyme repair complex reveals a charge-separated state involving the adenine moiety of the FADH^- cofactor that facilitates reduction of the photoproduct. Microscopic details of the collective reaction coordinate of ET reactions are identified that involve the reorganization of the hydrogen bond network and structural relaxation of the active site. The simulations reveal complex active site relaxation dynamics involving distinguished amino acids (Lys246, His365, and His369), conformational reorganization of the hydroxyl group of the (6-4) photoproduct, and a strengthening of hydrogen bonds with immobilized water molecules. In particular, rotation of the Lys246 side chain is found to impose a double-well character along the reaction coordinate of the ET reaction. Our findings suggest that the primary ET reactions in the (6-4) photoproduct enzyme repair complex of D. melanogaster are governed by a complex multi-minima active site relaxation dynamics and potentially precede the equilibration of the protein. ET pathways mediated by the adenine moiety and the 5' side of the photoproduct are proposed to be relevant for triggering the catalytic (6-4) photoproduct reactivation.

Ergodicity Breaking in Thermal Biological Electron Transfer? Cytochrome C Revisited II

It was recently suggested that cytochrome c operates in an ergodicity-breaking regime characterized by unusually large energy gap thermal fluctuations and associated reorganization free energies for heme oxidation of up to 3.0 eV. The large fluctuations were reported to lower activation free energy for oxidation of the heme cofactor by almost a factor of 2 compared to the case where ergodicity is maintained. Our group has recently investigated this claim computationally at several levels of theory and found no evidence for such large energy gap fluctuations. Here we address the points of our earlier work that have raised criticism and we also extend our previous investigation by considering a simple linear polarizability model for cytochrome c oxidation. We find very consistent results among all our computational approaches, ranging from classical molecular dynamics, to the linear polarizability model to QM(PMM)/MM to full QM(DFT)/MM electrostatic emdedding. None of them support the notion of very large energy gap fluctuations or ergodicity breaking. The deviation between our simulations and the ones reported in [ J. Phys. Chem. B 2017, 121, 4958] is traced back to rather large electric fields at the Fe site of the heme c cofactor in that study, not seen in our simulations, neither with the AMBER nor with the CHARMM force field. While ergodicity breaking effects may well occur in other biological ET, our numerical evidence suggests that this is not the case for cytochrome c.