Coherence-assisted electron diffusion across the multi-heme protein-based bacterial nanowire

On the fundamentals of quantum rate theory and the long-range electron transport in respiratory chains

It has been shown that both the electron-transfer rate constant of an electrochemical reaction and the conductance quantum are correlated with the concept of quantum capacitance. This simple association between the two separate concepts has an entirely quantum rate basis that encompasses the electron-transfer rate theory as originally proposed by Rudolph A. Marcus whether statistical mechanics is appropriately taken into account. I have prepared a concise review of the quantum mechanical rate theory principles focused on its quantum electrodynamics character to demonstrate that it can reconcile the conflicting views established on attempting to use the super-exchange (supported on electron transfer) or 'metallic-like' (supported on conductance quantum) mechanisms separately to explain the highly efficient long-range electron transport observed in the respiratory processes of living cells. The unresolved issues related to long-range electron transport are clarified in light of the quantum rate theory with a discussion focused on Geobacter sulfurreducens films as a reference standard of the respiration chain. Theoretical analyses supported by experimental data suggest that the efficiency of respiration within a long-range electron transport path is intrinsically a quantum mechanical event that follows relativistic quantum electrodynamics principles as addressed by quantum rate theory.

To be or not to be a cytochrome: electrical characterizations are inconsistent with Geobacter cytochrome 'nanowires'

Geobacter sulfurreducens profoundly shapes Earth's biogeochemistry by discharging respiratory electrons to minerals and other microbes through filaments of a two-decades-long debated identity. Cryogenic electron microscopy has revealed filaments of redox-active cytochromes, but the same filaments have exhibited hallmarks of organic metal-like conductivity under cytochrome denaturing/inhibiting conditions. Prior structure-based calculations and kinetic analyses on multi-heme proteins are synthesized herein to propose that a minimum of ~7 cytochrome 'nanowires' can carry the respiratory flux of a Geobacter cell, which is known to express somewhat more (≥20) filaments to increase the likelihood of productive contacts. By contrast, prior electrical and spectroscopic structural characterizations are argued to be physiologically irrelevant or physically implausible for the known cytochrome filaments because of experimental artifacts and sample impurities. This perspective clarifies our mechanistic understanding of physiological metal-microbe interactions and advances synthetic biology efforts to optimize those interactions for bioremediation and energy or chemical production.

Long-Range Electron Transport Rates Depend on Wire Dimensions in Cytochrome Nanowires

The ability to redirect electron transport to new reactions in living systems opens possibilities to store energy, generate new products, or probe physiological processes. Recent work by Huang et al. showed that 3D crystals of small tetraheme cytochromes (STC) can transport electrons over nanoscopic to mesoscopic distances by an electron hopping mechanism, making them promising materials for nanowires. However, fluctuations at room temperature may distort the nanostructure, hindering efficient electron transport. Classical molecular dynamics simulations of these fluctuations at the nano- and mesoscopic scales allowed us to develop a graph network representation to estimate maximum electron flow that can be driven through STC wires. In longer nanowires, transient structural fluctuations at protein-protein interfaces tended to obstruct efficient electron transfer, but these blockages are ameliorated in thicker crystals where alternative electron transfer pathways become more efficient. The model implies that more flexible proteinprotein interfaces limit the required minimum diameter to carry currents commensurate with conventional electronics.

Protein charge transfer far from equilibrium: a theoretical perspective

Potential differences for protein-assisted electron transfer across lipid bilayers or in bio-nano setups can amount to several 100 mV; they lie far outside the range of linear response theory. We describe these situations by Pauli-master equations that are based on Marcus theory of charge transfer between self-trapped electrons and that obey Kirchhoff's current law. In addition, we take on-site blockade effects and a full non-linear response of the local potentials into account. We present analytical and numerical current-potential curves and electron populations for multi-site model systems and biological electron transfer chains. Based on these, we provide empirical rules for electron populations and chemical potentials along the chain. The Pauli-master mean-field results are validated by kinetic Monte Carlo simulations. We briefly discuss the biochemical and evolutionary aspects of our findings.

Heavy Water Reduces the Electronic Conductance of Protein Wires via Deuteron Interactions with Aromatic Residues

Proteins are versatile, self-assembling nanoelectronic components, but their hopping conductivity is expected to be influenced by solvent fluctuations. The role of the solvent was investigated by measuring the single molecule conductance of several proteins in both H2O and D2O. The conductance of a homologous series of protein wires decreases more rapidly with length in D2O, indicating a 6-fold decrease in carrier diffusion constant relative to the same protein in H2O. The effect was found to depend on the specific aromatic amino acid composition. A tryptophan zipper protein showed a decrease in conductance similar to that of the protein wires, whereas a phenylalanine zipper protein was insensitive to solvent changes. Tryptophan contains an indole amine, whereas the phenylalanine aromatic ring has no exchangeable protons, so the effect of heavy water on conductance is a consequence of specific D- or H-interactions with the aromatic residues.

Long-Range Conductivity in Proteins Mediated by Aromatic Residues

Single-molecule measurements show that many proteins, lacking any redox cofactors, nonetheless exhibit electrical conductance on the order of a nanosiemen over 10 nm distances, implying that electrons can transit an entire protein in less than a nanosecond when subject to a potential difference of less than 1 V. This is puzzling because, for fast transport (i.e., a free energy barrier of zero), the hopping rate is determined by the reorganization energy of approximately 0.8 eV, and this sets the time scale of a single hop to at least 1 μs. Furthermore, the Fermi energies of typical metal electrodes are far removed from the energies required for sequential oxidation and reduction of the aromatic residues of the protein, which should further reduce the hopping current. Here, we combine all-atom molecular dynamics (MD) simulations of non-redox-active proteins (consensus tetratricopeptide repeats) with an electron transfer theory to demonstrate a molecular mechanism that can account for the unexpectedly fast electron transport. According to our MD simulations, the reorganization energy produced by the energy shift on charging (the Stokes shift) is close to the conventional value of 0.8 eV. However, the non-ergodic sampling of molecular configurations by the protein results in reaction-reorganization energies, extracted directly from the distribution of the electrostatic energy fluctuations, that are only ∼0.2 eV, which is small enough to enable long-range conductivity, without invoking quantum coherent transport. Using the MD values of the reorganization energies, we calculate a current decay with distance that is in agreement with experiment.

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.

Microbial nanowires: type IV pili or cytochrome filaments?

A dynamic field of study has emerged involving long-range electron transport by extracellular filaments in anaerobic bacteria, with Geobacter sulfurreducens being used as a model system. The interest in this topic stems from the potential uses of such systems in bioremediation, energy generation, and new bio-based nanotechnology for electronic devices. These conductive extracellular filaments were originally thought, based upon low-resolution observations of dried samples, to be type IV pili (T4P). However, the recently published atomic structure for the T4P from G. sulfurreducens, obtained by cryo-electron microscopy (cryo-EM), is incompatible with the numerous models that have been put forward for electron conduction. As with all high-resolution structures of T4P, the G. sulfurreducens T4P structure shows a partial melting of the α-helix that substantially impacts the aromatic residue positions such that they are incompatible with conductivity. Furthermore, new work using high-resolution cryo-EM shows that conductive filaments thought to be T4P are actually polymerized cytochromes, with stacked heme groups forming a continuous conductive wire, or extracellular DNA. Recent atomic structures of three different cytochrome filaments from G. sulfurreducens suggest that such polymers evolved independently on multiple occasions. The expectation is that such polymerized cytochromes may be found emanating from other anaerobic organisms.

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.

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

Helical homopolymers of multiheme cytochromes catalyze biogeochemically significant electron transfers with a reported 10 3 -fold variation in conductivity. Herein, classical molecular dynamics and hybrid quantum/classical molecular mechanics are used to elucidate the structural determinants of the redox potentials and conductivities of the tetra-, hexa-, and octaheme outer-membrane cytochromes E, S, and Z, respectively, from Geobacter sulfurreducens . Second-sphere electrostatic interactions acting on minimally polarized heme centers are found to regulate redox potentials over a computed 0.5-V range. However, the energetics of redox conduction are largely robust to the structural diversity: Single-step electronic couplings (⟨H mn ⟩), reaction free energies , and reorganization energies (λ mn ) are always respectively <|0.026|, <|0.26|, and between 0.5 - 1.0 eV. With these conserved parameter ranges, redox conductivity differed by less than a factor of 10 among the 'nanowires' and is sufficient to meet the demands of cellular respiration if 10 2 - 10 3 'nanowires' are expressed. The 'nanowires' are proposed to be differentiated by the protein packaging to interface with a great variety of environments, and not by conductivity, because the rate-limiting electron transfers are elsewhere in the respiratory process. Conducting-probe atomic force microscopy measurements that find conductivities 10 3 -10 6 -fold more than cellular demands are suggested to report on functionality that is either not used or not accessible under physiological conditions. The experimentally measured difference in conductivity between Omc- S and Z is suggested to not be an intrinsic feature of the CryoEM-resolved structures.

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 Thermal Response of Redox Conduction for Anti-Arrhenius Kinetics in a Microbial Cytochrome Nanowire

A micrometers-long helical homopolymer of the outer-membrane cytochrome type S (OmcS) from Geobacter sulfurreducens is proposed to transport electrons to extracellular acceptors in an ancient respiratory strategy of biogeochemical and technological significance. OmcS surprisingly exhibits higher conductivity upon cooling (anti-Arrhenius kinetics), an effect previously attributed to H-bond restructuring and heme redox potential shifts. Herein, the temperature sensitivity of redox conductivity is more thoroughly examined with conventional and constant-redox and -pH molecular dynamics and quantum mechanics/molecular mechanics. A 30 K drop in temperature constituted a weak perturbation to electron transfer energetics, changing electronic couplings (⟨H_mn⟩), reaction free energies (ΔG_mn), reorganization energies (λ_mn), and activation energies (E_a) by at most |0.002|, |0.050|, |0.120|, and |0.045| eV, respectively. Changes in ΔG_mn reflected -0.07 ± 0.03 V shifts in redox potentials that were caused in roughly equal measure by altered electrostatic interactions with the solvent and protein. Changes in intraprotein H-bonding reproduced the earlier observations. Single-particle diffusion and multiparticle steady-state flux models, parametrized with Marcus theory rates, showed that biologically relevant incoherent hopping cannot qualitatively or quantitatively describe electrical conductivity measured by atomic force microscopy in filamentous OmcS. The discrepancy is attributed to differences between solution-phase simulations and solid-state measurements and the need to model intra- and intermolecular vibrations explicitly.

Long-range charge transport in homogeneous and alternating-rigidity chains

We study the interplay of intrinsic-electronic and environmental factors in long-range charge transport across molecular chains with up to N ∼ 80 monomers. We describe the molecular electronic structure of the chain with a tight-binding Hamiltonian. Thermal effects in the form of electron decoherence and inelastic scattering are incorporated with the Landauer–Büttiker probe method. In short chains of up to ten units, we observe the crossover between coherent (tunneling, ballistic) motion and thermally-assisted conduction, with thermal effects enhancing the current beyond the quantum coherent limit. We further show that unconventional (nonmonotonic with size) transport behavior emerges when monomer-to-monomer electronic coupling is made large. In long chains, we identify a different behavior, with thermal effects suppressing the conductance below the coherent-ballistic limit. With the goal to identify a minimal model for molecular chains displaying unconventional and effective long-range transport, we simulate a modular polymer with alternating regions of high and low rigidity. Simulations show that, surprisingly, while charge correlations are significantly affected by structuring environmental conditions, reflecting charge delocalization, the electrical resistance displays an averaging effect, and it is not sensitive to this patterning. We conclude by arguing that efficient long-range charge transport requires engineering both internal electronic parameters and environmental conditions.

Electronic Structure of de Novo Peptide ACC-Hex from First Principles

Proteins are promising components for bioelectronic devices due in part to their biocompatibility, flexibility, and chemical diversity, which enable tuning of material properties. Indeed, an increasingly broad range of conductive protein supramolecular materials have been reported. However, due to their structural and environmental complexity, the electronic structure, and hence conductivity, of protein assemblies is not well-understood. Here we perform an all-atom simulation of the physical and electronic structure of a recently synthesized self-assembled peptide antiparallel coiled-coil hexamer, ACC-Hex. Using classical molecular dynamics and first-principles density functional theory, we examine the interactions of each peptide, containing phenylalanine residues along a hydrophobic core, to form a hexamer structure. We find that while frontier electronic orbitals are composed of phenylalanine, the peptide backbone and remaining residues, including those influenced by solvent, also contribute to the electronic density. Additionally, by studying dimers extracted from the hexamer, we show that structural distortions due to atomic fluctuations significantly impact the electronic structure of the peptide bundle. These results indicate that it is necessary to consider the full atomistic picture when using the electronic structure of supramolecular protein complexes to predict electronic properties.

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.

Nanomaterials Facilitating Microbial Extracellular Electron Transfer at Interfaces

Electrochemically active bacteria can transport their metabolically generated electrons to anodes, or accept electrons from cathodes to synthesize high-value chemicals and fuels, via a process known as extracellular electron transfer (EET). Harnessing of this microbial EET process has led to the development of microbial bio-electrochemical systems (BESs), which can achieve the interconversion of electrical and chemical energy and enable electricity generation, hydrogen production, electrosynthesis, wastewater treatment, desalination, water and soil remediation, and sensing. Here, the focus is on the current understanding of the microbial EET process occurring at both the bacteria-electrode interface and the biotic interface, as well as some attempts to improve the EET by using various nanomaterials. The behavior of nanomaterials in different EET routes and their influence on the performance of BESs are described. The inherent mechanisms will guide rational design of EET-related materials and lead to a better understanding of EET mechanisms.

The porphyrin ring rather than the metal ion dictates long-range electron transport across proteins suggesting coherence-assisted mechanism

The fundamental biological process of electron transfer (ET) takes place across proteins with common ET pathways of several nanometers. Recent discoveries push this limit and show long-range extracellular ET over several micrometers. Here, we aim in deciphering how protein-bound intramolecular cofactors can facilitate such long-range ET. In contrast to natural systems, our protein-based platform enables us to modulate important factors associated with ET in a facile manner, such as the type of the cofactor and its quantity within the protein. We choose here the biologically relevant protoporphyrin molecule as the electron mediator. Unlike natural systems having only Fe-containing protoporphyrins, i.e., heme, as electron mediators, we use here porphyrins with different metal centers, or lacking a metal center. We show that the metal redox center has no role in ET and that ET is mediated solely by the conjugated backbone of the molecule. We further discuss several ET mechanisms, accounting to our observations with possible contribution of coherent processes. Our findings contribute to our understanding of the participation of heme molecules in long-range biological ET.

The blind men and the filament: Understanding structures and functions of microbial nanowires

Extracellular electron transfer via filamentous protein appendages called 'microbial nanowires' has long been studied in Geobacter and other bacteria because of their crucial role in globally-important environmental processes and their applications for bioenergy, biofuels, and bioelectronics. Thousands of papers thought these nanowires as pili without direct evidence. Here, we summarize recent discoveries that could help resolve two decades of confounding observations. Using cryo-electron microscopy with multimodal functional imaging and a suite of electrical, biochemical, and physiological studies, we find that rather than pili, nanowires are composed of cytochromes OmcS and OmcZ that transport electrons via seamless stacking of hemes over micrometers. We discuss the physiological need for two different nanowires and their potential applications for sensing, synthesis, and energy production.

Intrinsic electrical properties of cable bacteria reveal an Arrhenius temperature dependence

Filamentous cable bacteria exhibit long-range electron transport over centimetre-scale distances, which takes place in a parallel fibre structure with high electrical conductivity. Still, the underlying electron transport mechanism remains undisclosed. Here we determine the intrinsic electrical properties of the conductive fibres in cable bacteria from a material science perspective. Impedance spectroscopy provides an equivalent electrical circuit model, which demonstrates that dry cable bacteria filaments function as resistive biological wires. Temperature-dependent electrical characterization reveals that the conductivity can be described with an Arrhenius-type relation over a broad temperature range (− 195 °C to + 50 °C), demonstrating that charge transport is thermally activated with a low activation energy of 40–50 meV. Furthermore, when cable bacterium filaments are utilized as the channel in a field-effect transistor, they show n-type transport suggesting that electrons are the charge carriers. Electron mobility values are ~ 0.1 cm²/Vs at room temperature and display a similar Arrhenius temperature dependence as conductivity. Overall, our results demonstrate that the intrinsic electrical properties of the conductive fibres in cable bacteria are comparable to synthetic organic semiconductor materials, and so they offer promising perspectives for both fundamental studies of biological electron transport as well as applications in microbial electrochemical technologies and bioelectronics.