The reversible opening of water channels in cytochrome c modulates the heme iron reduction potential

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.

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.

Structural Dynamics of the Precatalytic State of Human Cytochrome c upon T28C, G34C, and A50C Mutations: A Molecular Dynamics Simulation Perspective

The native structure of cytochrome c (cytc) contains hexacoordinate heme iron with His18 and Met80 residues ligated at the axial sites. Mutations of cytc at Ω-loops have been investigated in modulating the peroxidase activity and, hence, related to the initiation of the apoptotic pathway. Our previous experimental data reported on the peroxidase activity of the cysteine-directed mutants at different parts of the Ω-loop of human cytc (hCytc), that is, T28C, G34C, and A50C. In this work, we performed 1 μs molecular dynamics (MD) simulations to elucidate the detailed structural and dynamic changes upon these mutations, particularly at the proximal Ω-loop. The structures of hCytc were modeled in the hexacoordinated form, which was referred to as the "precatalytic state". The results showed that the structural features of the G34C mutant were more distinctive than those of other mutants. G34C mutation caused local destabilization and flexibility at the proximal Ω-loop (residues 12-28) and an extended distance between this Ω-loop region and heme iron. Besides, analysis of the orientation of the Arg38 side chain of the G34C mutant revealed the Arg38 conformer facing away from the heme iron. The obtained MD results also suggested structural diversity of the precatalytic states for the three hCytc mutants, specifically the effect of G34C mutation on the flexibility of the proximal Ω-loops. Therefore, our MD simulations combined with previous experimental data provide detailed insights into the structural basis of hCytc that could contribute to its pro-apoptotic function.

Reorganization energy of electron transfer

The theory of electron transfer reactions establishes the conceptual foundation for redox solution chemistry, electrochemistry, and bioenergetics. Electron and proton transfer across the cellular membrane provide all energy of life gained through natural photosynthesis and mitochondrial respiration. Rates of biological charge transfer set kinetic bottlenecks for biological energy storage. The main system-specific parameter determining the activation barrier for a single electron-transfer hop is the reorganization energy of the medium. Both harvesting of light energy in natural and artificial photosynthesis and efficient electron transport in biological energy chains require reduction of the reorganization energy to allow fast transitions. This review article discusses mechanisms by which small values of the reorganization energy are achieved in protein electron transfer and how similar mechanisms can operate in other media, such as nonpolar and ionic liquids. One of the major mechanisms of reorganization energy reduction is through non-Gibbsian (nonergodic) sampling of the medium configurations on the reaction time. A number of alternative mechanisms, such as electrowetting of active sites of proteins, give rise to non-parabolic free energy surfaces of electron transfer. These mechanisms, and nonequilibrium population of donor-acceptor vibrations, lead to a universal phenomenology of separation between the Stokes shift and variance reorganization energies of electron transfer.

Theory of Protein Charge Transfer: Electron Transfer between Tryptophan Residue and Active Site of Azurin

One reaction step in the conductivity relay of azurin, electron transfer between the Cu-based active site and the tryptophan residue, is studied theoretically and by classical molecular dynamics simulations. Oxidation of tryptophan results in electrowetting of this residue. This structural change makes the free energy surfaces of electron transfer nonparabolic as described by the Q-model of electron transfer. We analyze the medium dynamical effect on protein electron transfer produced by coupled Stokes-shift dynamics and the dynamics of the donor-acceptor distance modulating electron tunneling. The equilibrium donor-acceptor distance falls in the plateau region of the rate constant, where it is determined by the protein-water dynamics, and the probability of electron tunneling does not affect the rate. The crossover distance found here puts most intraprotein electron-transfer reactions under the umbrella of dynamical control. The crossover between the medium-controlled and tunneling-controlled kinetics is combined with the effect of the protein-water medium on the activation barrier to formulate principles of tunability of protein-based charge-transfer chains. The main principle in optimizing the activation barrier is the departure from the Gaussian-Gibbsian statistics of fluctuations promoting activated transitions. This is achieved either by incomplete (nonergodic) sampling, breaking the link between the Stokes-shift and variance reorganization energies, or through wetting-induced structural changes of the enzyme's active site.

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.

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.

Molecular insights on the conformational dynamics of a P76C mutant of human cytochrome c and the enhancement on its peroxidase activity

In apoptotic pathway, the interaction of Cytochrome c (Cytc) with cardiolipin in vivo is a key process to induce peroxidase activity of Cytc and trigger the release of Cytc in the inner mitochondria into cytosol. The peroxidase active form of Cytc occurs due to local conformational changes that support the opening of the heme crevice and the loss of an axial ligand between Met80 and heme Fe. Structural adjustments at the Ω-loop segments of Cytc are required for such process. To study the role of the distal Ω-loop segments comprising residues 71-85 in human Cytc (hCytc), we investigated a cysteine mutation at Pro76, one of the highly conserved residues in this loop. The effect of P76C mutant was explored by the combination of experimental characterizations and molecular dynamics (MD) simulations. The peroxidase activity of the P76C mutant was found to be significantly increased by ∼13 folds relative to the wild type. Experimental data on global denaturation, alkaline transition, heme bleaching, and spin-labeling Electron Spin Resonance were in good agreement with the enhancement of peroxidase activity. The MD results of hCytc in the hexacoordinate form suggest the important changes in P76C mutant occurred due to the unfolding at the central Ω-loop (residues 40-57), and the weakening of H-bond between Tyr67 and Met80. Whereas the experimental data implied that the P76C mutant tend to be in equilibrium between the pentacoordinate and hexacoordinate forms, the MD and experimental information are complementary and were used to support the mechanisms of peroxidase active form of hCytc.

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.

Hydrogen bonding rearrangement by a mitochondrial disease mutation in cytochrome bc 1 perturbs heme b H redox potential and spin state

To perform their specific electron-transfer relay functions, hemes commonly adopt low spin states with fine-tuned redox potentials. Understanding molecular elements controlling these properties is crucial for the description of natural proteins and engineering redox-active systems. We describe unusual effects of mitochondrial disease-related mutation in cytochrome bc₁, based on which we identify a dual role of hydrogen bonding to the propionate group of heme b_H. We observe that stabilization of the hydrogen bond in mutant enhances the redox potential but destabilizes the low spin state of oxidized heme. This demonstrates a critical role of the hydrogen bonding, and heme-protein interactions in general, to secure a suitable redox potential and spin state, a notion that might be universal for other heme proteins.

Hemes are common elements of biological redox cofactor chains involved in rapid electron transfer. While the redox properties of hemes and the stability of the spin state are recognized as key determinants of their function, understanding the molecular basis of control of these properties is challenging. Here, benefiting from the effects of one mitochondrial disease–related point mutation in cytochrome b, we identify a dual role of hydrogen bonding (H-bond) to the propionate group of heme b_H of cytochrome bc₁, a common component of energy-conserving systems. We found that replacing conserved glycine with serine in the vicinity of heme b_H caused stabilization of this bond, which not only increased the redox potential of the heme but also induced structural and energetic changes in interactions between Fe ion and axial histidine ligands. The latter led to a reversible spin conversion of the oxidized Fe from 1/2 to 5/2, an effect that potentially reduces the electron transfer rate between the heme and its redox partners. We thus propose that H-bond to the propionate group and heme-protein packing contribute to the fine-tuning of the redox potential of heme and maintaining its proper spin state. A subtle balance is needed between these two contributions: While increasing the H-bond stability raises the heme potential, the extent of increase must be limited to maintain the low spin and diamagnetic form of heme. This principle might apply to other native heme proteins and can be exploited in engineering of artificial heme-containing protein maquettes.

Altered structure and dynamics of pathogenic cytochrome c variants correlate with increased apoptotic activity

Mutation of cytochrome c in humans causes mild autosomal dominant thrombocytopenia. The role of cytochrome c in platelet formation, and the molecular mechanism underlying the association of cytochrome c mutations with thrombocytopenia remains unknown, although a gain-of-function is most likely. Cytochrome c contributes to several cellular processes, with an exchange between conformational states proposed to regulate changes in function. Here, we use experimental and computational approaches to determine whether pathogenic variants share changes in structure and function, and to understand how these changes might occur. Three pathogenic variants (G41S, Y48H, A51V) cause an increase in apoptosome activation and peroxidase activity. Molecular dynamics simulations of these variants, and two non-naturally occurring variants (G41A, G41T), indicate that increased apoptosome activation correlates with the increased overall flexibility of cytochrome c, particularly movement of the Ω loops. Crystal structures of Y48H and G41T complement these studies which overall suggest that the binding of cytochrome c to apoptotic protease activating factor-1 (Apaf-1) may involve an 'induced fit' mechanism which is enhanced in the more conformationally mobile variants. In contrast, peroxidase activity did not significantly correlate with protein dynamics. Thus, the mechanism by which the variants increase peroxidase activity is not related to the conformational dynamics of the native hexacoordinate state of cytochrome c. Recent molecular dynamics data proposing conformational mobility of specific cytochrome c regions underpins changes in reduction potential and alkaline transition pK was not fully supported. These data highlight that conformational dynamics of cytochrome c drive some but not all of its properties and activities.

Cooperative protein-solvent tuning of proton transfer energetics: carbonic anhydrase as a case study

We investigate the coupling between the proton transfer (PT) energetics and the protein-solvent dynamics using the intra-molecular PT in wild type (wt) human carbonic anhydrase II and its ten-fold faster mutant Y7F/N67Q as a test case. We calculate the energy variation upon PT, and from that we also calculate the PT reaction free energy, making use of a hybrid quantum mechanics/molecular dynamics approach. In agreement with the experimental data, we obtain that the reaction free energy is basically the same in the two systems. Yet, we show that the instantaneous PT energy is on average lower in the mutant possibly contributing to the faster PT rate. Analysis of the contribution to the PT energetics of the solvent and of each protein residue, also not in the vicinity of the active site, provides evidence for electrostatic tuning of the PT energy arising from the combined effect of the solvent and the protein environment. These findings open up a way to the more general task of the rational design of mutants with either enhanced or reduced PT rate.

Artificial Photosynthesis: Is Computation Ready for the Challenge Ahead?

A tremendous effort is currently devoted to the generation of novel hybrid materials with enhanced electronic properties for the creation of artificial photosynthetic systems. This compelling and challenging problem is well-defined from an experimental point of view, as the design of such materials relies on combining organic materials or metals with biological systems like light harvesting and redox-active proteins. Such hybrid systems can be used, e.g., as bio-sensors, bio-fuel cells, biohybrid photoelectrochemical cells, and nanostructured photoelectronic devices. Despite these efforts, the main bottleneck is the formation of efficient interfaces between the biological and the organic/metal counterparts for efficient electron transfer (ET). It is within this aspect that computation can make the difference and improve the current understanding of the mechanisms underneath the interface formation and the charge transfer efficiency. Yet, the systems considered (i.e., light harvesting protein, self-assembly monolayer and surface assembly) are more and more complex, reaching (and often passing) the limit of current computation power. In this review, recent developments in computational methods for studying complex interfaces for artificial photosynthesis will be provided and selected cases discussed, to assess the inherent ability of computation to leave a mark in this field of research.

Tuning Proton Transfer Thermodynamics in SARS-Cov-2 Main Protease: Implications for Catalysis and Inhibitor Design

In this comutational work a hybrid quantum mechanics/molecular mechanics approach, the MD-PMM approach, is used to investigate the proton transfer reaction the activates the catalytic activity of SARS-CoV-2 main protease. The proton transfer thermodynamics is investigated for the apo ensyme (i.e., without any bound substrate or inhibitor) and in the presence of a inhibitor, N3, which was previously shown to covalently bind SARS-CoV-2 main protease.

Study on effects of co-solvents on the structure of DhaA by molecular dynamics simulation

With the increasing application of enzymes in various research fields, the choices of co-solvents in enzymatic preparations which directly related to the catalytic activity have been attracted attention. Thus, researching on the stabilization or destabilization behaviors of enzymes in different solvents is extremely essential. In this study, the structural changes of DhaA in two typical aprotic co-solvents (acetonitrile and tetrahydrofuran) were firstly investigated by molecular dynamics (MD) simulation. The simulation results revealed the strong van der Waals force between co-solvents and DhaA which could induce the structural change of enzyme. Interestingly, the differences of molecular size and the electrostatic force with enzyme of two co-solvents led to quite different influences on DhaA. As for acetonitrile, solvent molecules could penetrate into the catalytic site of DhaA which promoted by the electrostatic interaction. On the contrary, tetrahydrofuran molecules were mainly distributed around the catalytic site due to the relative weak electrostatic interaction and steric resistance effect. It can be concluded that different co-solvent can affect the key domains, substrate pathway and catalytic pocket of DhaA.Communicated by Ramaswamy H. Sarma.

Fully Atomistic Multiscale Approach for pKa Prediction

The ionization state of titratable amino acids strongly affects proteins structure and functioning in a large number of biological processes. It is therefore essential to be able to characterize the pK_a of ionizable groups inside proteins and to understand its microscopic determinants in order to gain insights into many functional properties of proteins. A big effort has been devoted to the development of theoretical approaches for the prediction of deprotonation free energies, yet the accurate theoretical/computational calculation of pK_a values is recognized as a current challenge. A methodology based on a hybrid quantum/classical approach is here proposed for the computation of deprotonation free energies. The method is applied to calculate the pK_a of formic acid, methylammonium, and methanethiol, providing results in good agreement with the corresponding experimental estimates. The pK_a is also calculated for aspartic acid and lysine as single residues in solution and for three aspartic/glutamic acids inside a well-characterized protein: hen egg white lysozyme. While for small molecules the method is able to deal with multiple protonation states of all titratable groups, this becomes computationally very expensive for proteins. The calculated pK_a values for the single amino acids (except for the zwitterionic aspartic acid) and inside the protein display a systematic shift with respect to the experimental values that suggests that the fine balance between hydrophobic and polar interactions might be not accurately reproduced by the usual classical force-fields, thus affecting the computation of deprotonation free energies. The calculated pK_a shifts inside the protein are in good agreement with the corresponding experimental ones (within 1 pK_a unit), well reproducing the pK_a changes due to the protein environment even in the case of large pK_a shifts.

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.

Alanine to serine substitutions drive thermal adaptation in a psychrophilic diatom cytochrome c6

In this study, we investigate the thermodynamic mechanisms by which electron transfer proteins adapt to environmental temperature by directly comparing the redox properties and folding stability of a psychrophilic cytochrome c and a mesophilic homolog. Our model system consists of two cytochrome c₆ proteins from diatoms: one adapted specifically to polar environments, the other adapted generally to surface ocean environments. Direct electrochemistry shows that the midpoint potential for the mesophilic homolog is slightly higher at all temperatures measured. Cytochrome c₆ from the psychrophilic diatom unfolds with a melting temperature 10.4 °C lower than the homologous mesophilic cytochrome c₆. Changes in free energy upon unfolding are identical, within error, for the psychrophilic and mesophilic protein; however, the chemical unfolding transition of the psychrophilic cytochrome c₆ is more cooperative than for the mesophilic cytochrome c₆. Substituting alanine residues found in the mesophile with serine found in corresponding positions of the psychrophile demonstrates that burial of the polar serine both decreases the thermal stability and decreases the midpoint potential. The mutagenesis data, combined with differences in the m-value of chemical denaturation, suggest that differences in solvent accessibility of the hydrophobic core underlie the adaptation of cytochrome c₆ to differing environmental temperature.

A Heme Propionate Staples the Structure of Cytochrome c for Methionine Ligation to the Heme Iron

Ligand-switch reactions at the heme iron are common in biological systems, but their mechanisms and the features of the polypeptide fold that support dual ligation are not well understood. In cytochrome c (cyt c), two low-stability loops (Ω-loop C and Ω-loop D) are connected by the heme propionate HP6. At alkaline pH, the native Met80 ligand from Ω-loop D switches to a Lys residue from the same loop. Deprotonation of an as yet unknown group triggers the alkaline transition. We have created the two cyt c variants T49V/K79G and T78V/K79G with altered connections of these two loops to HP6. Electronic absorption, NMR, and EPR studies demonstrate that at pH 7.4 ferric forms of these variants are Lys-ligated, whereas ferrous forms maintain the native Met80 ligation. Measurements of protein stability, cyclic voltammetry, pH-jump and gated electron-transfer kinetics have revealed that these Thr to Val substitutions greatly affect the alkaline transition in both ferric and ferrous proteins. The substitutions modify the stability of the Met-ligated species and reduction potentials of the heme iron. The kinetics of ligand-switch processes are also altered, and analyses of these effects implicate redox-dependent differences in metal-ligand interactions and the role of the protein dynamics, including cross-talk between the two Ω-loops. With the two destabilized variants, it is possible to map energy levels for the Met- and Lys-ligated species in both ferric and ferrous proteins and assess the role of the protein scaffold in redox-dependent preferences for these two ligands. The estimated shift in the heme iron reduction potential upon deprotonation of the "trigger" group is consistent with those associated with deprotonation of an HP, suggesting that HP6, on its own or as a part of a hydrogen-bonded cluster, is a likely "trigger" for the Met to Lys ligand switch.

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

It was recently suggested that certain redox proteins operate in an ergodicity-breaking regime to facilitate biological electron transfer (ET). A signature for this is a large variance reorganization free energy (several electronvolts) but a significantly smaller Stokes reorganization free energy due to incomplete protein relaxation on the time scale of the ET event. Here we investigate whether this picture holds for oxidation of cytochrome c in aqueous solution, at various levels of theory including classical molecular dynamics with two additive and one electronically polarizable force field, and QM/MM calculations with the QM region treated by full electrostatic DFT embedding and by the perturbed matrix method. Sampling the protein and energy gap dynamics over more than 250 ns, we find no evidence for ergodicity-breaking effects. In particular, the inclusion of electronic polarizability of the heme group at QM/MM levels did not induce nonergodic effects, contrary to previous reports by Matyushov et al. The well-known problem of overestimation of reorganization free energies with additive force fields is cured when the protein and solvent are treated as electronically polarizable. Ergodicity-breaking effects may occur in other redox proteins, and our results suggest that long simulations, ideally on the ET time scale, with electronically polarizable force fields are required to obtain strong numerical evidence for them.

Evidence of a Thermodynamic Ramp for Hole Hopping to Protect a Redox Enzyme from Oxidative Damage

Redox proteins and enzymes are at risk of irreversible oxidative damage from highly oxidizing intermediates generated in the active site in the case of unsuccessful functional reaction. Chains of tyrosine and/or tryptophan residues have been recently proposed to provide protection to the active site and the whole protein by delivering oxidizing equivalents (holes) out of the protein via a multistep hopping mechanism. In the present work we use a hybrid quantum/classical theoretical-computational methodology based on the perturbed matrix method and on molecular dynamics simulations to calculate the oxidation potential difference along a chain of tyrosine and tryptophan residues in a human redox enzyme of major importance, a superoxide dismutase, which acts as antioxidant defense. We show that the hole hopping is thermodynamically favored along such a chain and that the hopping propensity is strongly affected by the protein environment and in particular by the active site and its second coordination sphere.

Myoglobinopathy is an adult-onset autosomal dominant myopathy with characteristic sarcoplasmic inclusions

Myoglobin, encoded by MB, is a small cytoplasmic globular hemoprotein highly expressed in cardiac myocytes and oxidative skeletal myofibers. Myoglobin binds O_2, facilitates its intracellular transport and serves as a controller of nitric oxide and reactive oxygen species. Here, we identify a recurrent c.292C>T (p.His98Tyr) substitution in MB in fourteen members of six European families suffering from an autosomal dominant progressive myopathy with highly characteristic sarcoplasmic inclusions in skeletal and cardiac muscle. Myoglobinopathy manifests in adulthood with proximal and axial weakness that progresses to involve distal muscles and causes respiratory and cardiac failure. Biochemical characterization reveals that the mutant myoglobin has altered O₂ binding, exhibits a faster heme dissociation rate and has a lower reduction potential compared to wild-type myoglobin. Preliminary studies show that mutant myoglobin may result in elevated superoxide levels at the cellular level. These data define a recognizable muscle disease associated with MB mutation.

Myoglobin is a hemeprotein that reversibly binds oxygen and gives muscle its red color. Here, the authors report a genetic variant in the MB gene that associates with myoglobinopathy, an autosomal dominant progressive myopathy, and altered oxygen binding properties of the mutant protein.

Gating the electron transfer at a monocopper centre through the supramolecular coordination of water molecules within a protein chamber mimic

Functionality of enzymes is strongly related to water dynamic processes.

Functionality of enzymes is strongly related to water dynamic processes. The control of the redox potential for metallo-enzymes is intimately linked to the mediation of water molecules in the first and second coordination spheres. Here, we report a unique example of supramolecular control of the redox properties of a biomimetic monocopper complex by water molecules. It is shown that the copper complex based on a calix[6]arene covalently capped with a tetradentate [tris(2-methylpyridyl)amine] (tmpa) core, embedding the metal ion in a hydrophobic cavity, can exist in three different states. The first system displays a totally irreversible redox behaviour. It corresponds to the reduction of the 5-coordinate mono-aqua-Cu^II complex, which is the thermodynamic species in the +II state. The second system is detected at a high redox potential. It is ascribed to an “empty cavity” or “water-free” state, where the Cu^I ion sits in a 4-coordinate trigonal environment provided by the tmpa cap. This complex is the thermodynamic species in the +I state under “dry conditions”. Surprisingly, a third redox system appears as the water concentration is increased. Under water-saturation conditions, it displays a pseudo-reversible behaviour at a low scan rate at the mid-point from the water-free and aqua species. This third system is not observed with the Cu-tmpa complex deprived of a cavity. In the calix[6]cavity environment, it is ascribed to a species where a pair of water molecules is hosted by the calixarene cavity. A molecular mechanism for the Cu^II/Cu^I redox process with an interplay of (H₂O)_x (x = 0, 1, 2) hosting is proposed on the basis of computational studies. Such an unusual behaviour is ascribed to the unexpected stabilization of the Cu^I state by inclusion of the pair of water molecules. This phenomenon strongly evidences the drastic influence of the interaction between water molecules and a hydrophobic cavity on controlling the thermodynamics and kinetics of the Cu^II/Cu^I electron transfer process.

Wetting of the Protein Active Site Leads to Non-Marcusian Reaction Kinetics

Enzymes exist in continuously fluctuating water bath dramatically affecting their function. Water not only forms the solvation shell but also penetrates into the protein interior. Changing the wetting pattern of the protein's active site in response to altering redox state initiates a highly nonlinear structural change and non-Gaussian electrostatic fluctuations at the active site. The free-energy surfaces of electron transfer are highly nonparabolic (non-Marcusian), as shown by atomistic molecular dynamics simulations of hydrated ferredoxin protein and by an analytical model in agreement with simulations. The reorganization energy of electron transfer passes through a spike marking equal probabilities of the wet and dry states of the active site. The activation thermodynamics affected by wetting leads to a non-Arrhenius, passing through a maximum, plot for the reaction rate vs the inverse temperature.

Termination of Biological Function at Low Temperatures: Glass or Structural Transition?

Energy of life is produced by electron transfer in energy chains of respiration or photosynthesis. A small input of free energy available to biology puts significant restrictions on how much free energy can be lost in each electron-transfer reaction. We advocate the view that breaking ergodicity, leading to violation of the fluctuation-dissipation theorem (FDT), is how proteins achieve high reaction rates without sacrificing the reaction free energy. Here we show that a significant level of nonergodicity, represented by a large extent of the configurational temperature over the kinetic temperature, is maintained in the entire physiological range for the cytochrome c electron transfer protein. The protein returns to the state consistent with the FDT below the crossover temperature close to the temperature of the protein glass transition. This crossover leads to a sharp increase in the activation barrier of electron transfer and is displayed by a kink in the Arrhenius plot for the reaction rate constant.

Electron-transfer chain in respiratory complex I

Complex I is a part of the respiration energy chain converting the redox energy into the cross-membrane proton gradient. The electron-transfer chain of iron-sulfur cofactors within the water-soluble peripheral part of the complex is responsible for the delivery of electrons to the proton pumping subunit. The protein is porous to water penetration and the hydration level of the cofactors changes when the electron is transferred along the chain. High reaction barriers and trapping of the electrons at the iron-sulfur cofactors are prevented by the combination of intense electrostatic noise produced by the protein-water interface with the high density of quantum states in the iron-sulfur clusters caused by spin interactions between paramagnetic iron atoms. The combination of these factors substantially lowers the activation barrier for electron transfer compared to the prediction of the Marcus theory, bringing the rate to the experimentally established range. The unique role of iron-sulfur clusters as electron-transfer cofactors is in merging protein-water fluctuations with quantum-state multiplicity to allow low activation barriers and robust operation. Water plays a vital role in electron transport energetics by electrowetting the cofactors in the chain upon arrival of the electron. A general property of a protein is to violate the fluctuation-dissipation relation through nonergodic sampling of its landscape. High functional efficiency of redox enzymes is a direct consequence of nonergodicity.

Theory and Electrochemistry of Cytochrome c

Extensive simulations of cytochrome c in solution are performed to address the apparent contradiction between large reorganization energies of protein electron transfer typically reported by atomistic simulations and much smaller values produced by protein electrochemistry. The two sets of data are reconciled by deriving the activation barrier for electrochemical reaction in terms of an effective reorganization energy composed of half the Stokes shift (characterizing the medium polarization in response to electron transfer) and the variance reorganization energy (characterizing the breadth of electrostatic fluctuations). This effective reorganization energy is much smaller than each of the two components contributing to it and is fully consistent with electrochemical measurements. Calculations in the range of temperatures between 280 and 360 K combine long, classical molecular dynamics simulations with quantum calculations of the protein active site. The results agree with the Arrhenius plots for the reaction rates and with cyclic voltammetry of cytochrome c immobilized on self-assembled monolayers. Small effective reorganization energy, and the resulting small activation barrier, is a general phenomenology of protein electron transfer allowing fast electron transport within biological energy chains.

Extending the essential dynamics analysis to investigate molecular properties: application to the redox potential of proteins

Here, a methodology is proposed to investigate the collective fluctuation modes of an arbitrary set of observables, maximally contributing to the fluctuation of another functionally relevant observable. The methodology, based on the analysis of fully classical molecular dynamics (MD) simulations, exploits the essential dynamics (ED) method, originally developed to analyse the collective motions in proteins. We apply this methodology to identify the residues that are more relevant for determining the reduction potential (E(0)) of a redox-active protein. To this aim, the fluctuation modes of the single-residue electrostatic potentials mostly contributing to the fluctuations of the total electrostatic potential (the main determinant of E(0)) are investigated for wild-type azurin and two of its mutants with a higher E(0). By comparing the results here obtained with a previous study on the same systems [Zanetti-Polzi et al., Org. Biomol. Chem., 2015, 13, 11003] we show that the proposed methodology is able to identify the key sites that determine E(0). This information can be used for a general deeper understanding of the molecular mechanisms on the basis of the redox properties of the proteins under investigation, as well as for the rational design of mutants with a higher or lower E(0). From the results of the present analysis we propose a new azurin mutant that, according to our calculations, shows a further increase of E(0).

Polarizability of the active site of cytochrome c reduces the activation barrier for electron transfer

Enzymes in biology’s energy chains operate with low energy input distributed through multiple electron transfer steps between protein active sites. The general challenge of biological design is how to lower the activation barrier without sacrificing a large negative reaction free energy. We show that this goal is achieved through a large polarizability of the active site. It is polarized by allowing a large number of excited states, which are populated quantum mechanically by electrostatic fluctuations of the protein and hydration water shells. This perspective is achieved by extensive mixed quantum mechanical/molecular dynamics simulations of the half reaction of reduction of cytochrome c. The barrier for electron transfer is consistently lowered by increasing the number of excited states included in the Hamiltonian of the active site diagonalized along the classical trajectory. We suggest that molecular polarizability, in addition to much studied electrostatics of permanent charges, is a key parameter to consider in order to understand how enzymes work.

The dynamics of the β-propeller domain in Kelch protein KLHL40 changes upon nemaline myopathy-associated mutation

The nemaline myopathy-associated E528K mutation in the KLHL40 alters the communication between the Kelch propeller blades.

A dynamical approach to non-adiabatic electron transfers at the bio-inorganic interface

A methodology is proposed to investigate the role of the energy fluctuations, determined by the dynamical evolution of a system, and the role of non-adiabaticity in affecting the kinetic rate of electron transfer reactions at the bio-inorganic interface.

A few key residues determine the high redox potential shift in azurin mutants

The wide range of variability of the reduction potential (E(0)) of blue-copper proteins has been the subject of a large number of studies in the past several years. In particular, a series of azurin mutants have been recently rationally designed tuning E(0) over a very broad range (700 mV) without significantly altering the redox-active site [Marshall et al., Nature, 2009, 462, 113]. This clearly suggests that interactions outside the primary coordination sphere are relevant to determine E(0) in cupredoxins. However, the molecular determinants of the redox potential variability are still undisclosed. Here, by means of atomistic molecular dynamics simulations and hybrid quantum/classical calculations, the mechanisms that determine the E(0) shift of two azurin mutants with high potential shifts are unravelled. The reduction potentials of native azurin and of the mutants are calculated obtaining results in good agreement with the experiments. The analysis of the simulations reveals that only a small number of residues (including non-mutated ones) are relevant in determining the experimentally observed E(0) variation via site-specific, but diverse, mechanisms. These findings open the path to the rational design of new azurin mutants with different E(0).

Progress and challenges in simulating and understanding electron transfer in proteins

This Review presents an overview of the most common numerical simulation approaches for the investigation of electron transfer (ET) in proteins. We try to highlight the merits of the different approaches but also the current limitations and challenges. The article is organized into three sections. Section 2 deals with direct simulation algorithms of charge migration in proteins. Section 3 summarizes the methods for testing the applicability of the Marcus theory for ET in proteins and for evaluating key thermodynamic quantities entering the reaction rates (reorganization energies and driving force). Recent studies interrogating the validity of the theory due to the presence of non-ergodic effects or of non-linear responses are also described. Section 4 focuses on the tunneling aspects of electron transfer. How can the electronic coupling between charge transfer states be evaluated by quantum chemistry approaches and rationalized? What interesting physics regarding the impact of protein dynamics on tunneling can be addressed? We will illustrate the different sections with examples taken from the literature to show what types of system are currently manageable with current methodologies. We also take care to recall what has been learned on the biophysics of ET within proteins thanks to the advent of atomistic simulations.

Real-time dynamic adsorption processes of cytochrome c on an electrode observed through electrochemical high-speed atomic force microscopy

An understanding of dynamic processes of proteins on the electrode surface could enhance the efficiency of bioelectronics development and therefore it is crucial to gain information regarding both physical adsorption of proteins onto the electrode and its electrochemical property in real-time. We combined high-speed atomic force microscopy (HS-AFM) with electrochemical device for simultaneous observation of the surface topography and electron transfer of redox proteins on an electrode. Direct electron transfer of cytochrome c (cyt c) adsorbed on a self-assembled monolayers (SAMs) formed electrode is very attractive subject in bioelectrochemistry. This paper reports a real-time visualization of cyt c adsorption processes on an 11-mercaptoundecanoic acid-modified Au electrode together with simultaneous electrochemical measurements. Adsorbing cyt c molecules were observed on a subsecond time resolution simultaneously with increasing redox currents from cyt c using EC-HS-AFM. The root mean square roughness (R_RMS) from the AFM images and the number of the electrochemically active cyt c molecules adsorbed onto the electrode (Γ) simultaneously increased in positive cooperativity. Cyt c molecules were fully adsorbed on the electrode in the AFM images when the peak currents were steady. This use of electrochemical HS-AFM significantly facilitates understanding of dynamic behavior of biomolecules on the electrode interface and contributes to the further development of bioelectronics.

How the Reorganization Free Energy Affects the Reduction Potential of Structurally Homologous Cytochromes

Differences in the reduction potential E(0) among structurally similar metalloproteins cannot always be fully explained on the basis of their 3-D structures. We investigate the molecular determinants to E(0) using the mixed quantum mechanics/molecular mechanics approach named perturbed matrix method (PMM); after comparison with experimental values to assess the reliability of our calculations, we investigate the relationship between the change in free energy upon reduction ΔA(0) and the reorganization energy. We find that the reduction potential of cytochromes can be regarded as the result of the sum of two terms, one being mostly dependent on the energy fluctuations within a limited range around the mean transition energy and the second being mostly dependent linearly on the difference Δλ = λred - λox of the reorganization free energies for the ox → red (λred) and for the red → ox (λox) relaxations.