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

Nickel-Dithiolene Cofactors as Electron Donors and Acceptors in Protein Hosts

Metal dithiolene compounds are attracting considerable attention in the field of molecular electronics, particularly as constituents of materials with high charge-carrier mobilities. Recent experiments on cable bacteria that perform centimeter-scale charge transport suggest that Ni-bis(dithiolene) cofactors are important components of the bacterial conductive network. Further, current-voltage experiments of cable-bacteria-conductive sheaths have measured high conductivity values as compared to other electron-transfer bacteria. An important question is how the Ni-bis(dithiolene) structures participating as electron donors/acceptors contribute to the high conductivity. Currently, the protein and cofactor structures of these bacterial networks are largely unknown. Given this limitation, in this work, we explore the more general question of how Ni-bis(dithiolene) molecules would perform as electron donor and acceptor centers in protein-mediated charge transfer. Our aim is to deduce order-of-magnitude higher bounds for charge-transfer rates in such systems as a function of donor-acceptor distance, protein-bridge (amino acid) sequence, cofactor size, and redox state. These bounds are useful for predicting charge-transfer mechanisms and estimating rates in the absence of detailed structural information on protein wires that may use Ni-bis(dithiolene) redox cofactors. Our analysis is also relevant to the design of artificial Ni-bis(dithiolene) protein wires.

Cytochrome "nanowires" are physically limited to sub-picoamp currents that suffice for cellular respiration

Mineral-respiring microorganisms from hydrothermal vents to terrestrial soils express filaments that electrically connect intracellular respiration to extracellular geochemistry. Filaments dubbed "cytochrome nanowires" (CNs) have been resolved by CryoEM, but whether they are the two-decades-long sought-after physiological "nanowires" remains unproven. To assess their functional competence, we analyzed biological redox conduction in all CNs by computing driving forces in the presence of redox anti-cooperativities, reorganization energies with electronic polarizability, and Marcus rates for diffusive and protein-limited flux models. The chain of heme cofactors in any CN must be densely packed to realize weak (≤0.01 eV) electronic coupling for electron transfer, as evidenced by a single Soret band produced from coincidental absorptions on multiple hemes. Dense packing, in turn, has three consequences: (1) limited driving forces (≤|0.3| eV) due to shared electrostatic microenvironments, (2) strong (≤0.12 eV) redox anti-cooperativities that would accentuate the free energy landscape if the linear heme arrangement did not dictate a contra-thermodynamic oxidation order, and (3) an entropic penalty that is offset by thioether 'tethers' of the hemes to the protein backbone. These linkages physically necessitate the rate-throttling T-stacked motif (10-fold slower than the other highly conserved slip-stacked motif). If the sequence of slip- and T-stacked hemes in the CNs had the fastest known nanosecond rates at every step, a micron-long filament would carry a diffusive 0.02 pA current at a physiological 0.1 V, or a protein-limited current of 0.2 pA. Actual CNs have sub-optimal (≤102-fold lower), but sufficient conductivities for cellular respiration, with at most thousands of filaments needed for total cellular metabolic flux. Reported conductivities once used to argue for metallic-like pili against the cytochrome hypothesis and now attributed to CNs remain inconsistent by 102-105-fold with the physical constraints on biological redox conduction through multiheme architectures.

Protein Medium Facilitates Electron Transfer in Photosynthetic Heliobacterial Reaction Center

This computational study addresses the question of how large membrane-bound proteins of electron transport chains facilitate fast vector-based charge transport. We study electron transfer reactions following ultrafast initial charge separation induced by absorption of light by P800 primary pair and leading to the electron localization at the A0 cofactor. Two subsequent, much slower reactions, electron transfer to the iron-sulfur cluster Fx and reduction of the menaquinone (MQ) cofactor, are studied by combining molecular dynamics simulations, electronic structure calculations, and theoretical modeling. The low value of the electronic coupling between A0 and Fx brings this reaction to the microsecond time scale even at the zero activation barrier. In contrast, A0-MQ electron transfer occurs on a subnanosecond time scale and might become the preferred route for charge transport. We elucidate mechanistic properties of the protein medium allowing fast, vectorial charge transfer. The electric field is high and inhomogeneous inside the protein and is coupled to high polarizabilities of cofactors to significantly lower the reaction barrier. The A0-MQ separation puts this reaction at the edge between the plateau characterizing the reaction dynamical control and exponential falloff due to electronic tunneling. A strong separation in relaxation times of the medium dynamics for the forward and backward reactions promotes vectorial charge transfer.

Delineating redox cooperativity in water-soluble and membrane multiheme cytochromes through protein design

Nature has evolved diverse electron transport proteins and multiprotein assemblies essential to the generation and transduction of biological energy. However, substantially modifying or adapting these proteins for user-defined applications or to gain fundamental mechanistic insight can be hindered by their inherent complexity. De novo protein design offers an attractive route to stripping away this confounding complexity, enabling us to probe the fundamental workings of these bioenergetic proteins and systems, while providing robust, modular platforms for constructing completely artificial electron-conducting circuitry. Here, we use a set of de novo designed mono-heme and di-heme soluble and membrane proteins to delineate the contributions of electrostatic micro-environments and dielectric properties of the surrounding protein medium on the inter-heme redox cooperativity that we have previously reported. Experimentally, we find that the two heme sites in both the water-soluble and membrane constructs have broadly equivalent redox potentials in isolation, in agreement with Poisson-Boltzmann Continuum Electrostatics calculations. BioDC, a Python program for the estimation of electron transfer energetics and kinetics within multiheme cytochromes, also predicts equivalent heme sites, and reports that burial within the low dielectric environment of the membrane strengthens heme-heme electrostatic coupling. We conclude that redox cooperativity in our diheme cytochromes is largely driven by heme electrostatic coupling and confirm that this effect is greatly strengthened by burial in the membrane. These results demonstrate that while our de novo proteins present minimalist, new-to-nature constructs, they enable the dissection and microscopic examination of processes fundamental to the function of vital, yet complex, bioenergetic assemblies.

Controlling heme redox properties in peptide amphiphile fibers with sequence and heme loading ratio

Controlling the reduction midpoint potential of heme B is a key factor in many bioelectrochemical reactions, including long-range electron transport. Currently, there are a number of globular model protein systems to study this biophysical parameter; however, there are none for large polymeric protein model systems (e.g., the OmcS protein from G. sulfurreducens). Peptide amphiphiles, short peptides with a lipid tail that polymerize into fibrous structures, fill this gap. Here, we show a peptide amphiphile model system where one can tune the electrochemical potential of heme B by changing the loading ratio and peptide sequence. Changing the loading ratio resulted in the most significant increase, with values as high as -22 mV down to -224 mV. Circular dichroism spectra of certain sequences show Cotton effects at lower loading ratios that disappear as more heme B is added, indicating an ordered environment that becomes disrupted if heme B is overpacked. These findings can contribute to the design of functional self-assembling biomaterials.

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.

Electron transfer in a crystalline cytochrome with four hemes

Diffusion of electrons over distances on the order of 100 μm has been observed in crystals of a small tetraheme cytochrome (STC) from Shewanella oneidensis [J. Huang et al. J. Am. Chem. Soc. 142, 10459-10467 (2020)]. Electron transfer between hemes in adjacent subunits of the crystal is slower and more strongly dependent on temperature than had been expected based on semiclassical electron-transfer theory. We here explore explanations for these findings by molecular-dynamics simulations of crystalline and monomeric STC. New procedures are developed for including time-dependent quantum mechanical energy differences in the gap between the energies of the reactant and product states and for evaluating fluctuations of the electronic-interaction matrix element that couples the two hemes. Rate constants for electron transfer are calculated from the time- and temperature-dependent energy gaps, coupling factors, and Franck-Condon-weighted densities of states using an expression with no freely adjustable parameters. Back reactions are considered, as are the effects of various protonation states of the carboxyl groups on the heme side chains. Interactions with water are found to dominate the fluctuations of the energy gap between the reactant and product states. The calculated rate constant for electron transfer from heme IV to heme Ib in a neighboring subunit at 300 K agrees well with the measured value. However, the calculated activation energy of the reaction in the crystal is considerably smaller than observed. We suggest two possible explanations for this discrepancy. The calculated rate constant for transfer from heme I to II within the same subunit of the crystal is about one-third that for monomeric STC in solution.

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.

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.

Electron Tunneling in Biology: When Does it Matter?

Electrons can tunnel between cofactor molecules positioned along biological electron transport chains up to a distance of ≃ 20 Å on the millisecond time scale of enzymatic turnover. This tunneling range determines the design of biological energy chains facilitating the cross-membrane transport of electrons. Tunneling distance and cofactors' redox potentials become the main physical parameters affecting the rate of electron transport. In addition, universal charge-transport properties are assigned to all proteins, making protein identity, flexibility, and dynamics insignificant. This paradigm is challenged by dynamical models of electron transfer, showing that the electron hopping rate is constant within the crossover distance R* ≃ 12 Å, followed with an exponential falloff at longer distances. If this hypothesis is fully confirmed, natural and man-made energy chains for electron transport should be best designed by placing redox cofactors near the crossover distance R*. Protein flexibility and dynamics affect the magnitude of the maximum hopping rate within the crossover distance. Changes in protein flexibility between forward and backward transitions contribute to vectorial charge transport. For biological energy chains, charge transport through proteins is not defined by universal parameters, and protein identity matters.

Effect of Water Deuteration on Protein Electron Transfer

Traditional theories of long-range protein electron transfer describe the reaction rate in terms of the tunneling distance and the reaction free energy. They do not recognize two physical effects: (i) local wetting of the active site by hydration water and (ii) protein identity affecting the rate through dynamics and flexibility. We find, by molecular dynamics simulations, a significant, ∼25 times, slowing down of the rate of protein electron transfer upon deuteration. H/D substitution changes the rate constant pre-exponential factor in the regime of electron transfer controlled by medium dynamics. Switching from light to heavy water increases the effective medium relaxation time. The effect is caused by both a global change in the flexibility of the protein backbone and locally stronger hydrogen bonds to charged residues.

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.