Biological electron-transfer (ET) reactions are typically described in the framework of coherent two-state electron tunneling or multistep hopping. However, these ET reactions may involve multiple redox cofactors in van der Waals contact with each other and with vibronic broadenings on the same scale as the energy gaps among the species. In this regime, fluctuations of the molecular structures and of the medium can produce transient energy level matching among multiple electronic states. This transient degeneracy, or flickering electronic resonance among states, is found to support coherent (ballistic) charge transfer. Importantly, ET rates arising from a flickering resonance (FR) mechanism will decay exponentially with distance because the probability of energy matching multiple states is multiplicative. The distance dependence of FR transport thus mimics the exponential decay that is usually associated with electron tunneling, although FR transport involves real carrier population on the bridge and is not a tunneling phenomenon. Likely candidates for FR transport are macromolecules with ET groups in van der Waals contact: DNA, bacterial nanowires, multiheme proteins, strongly coupled porphyrin arrays, and proteins with closely packed redox-active residues. The theory developed here is used to analyze DNA charge-transfer kinetics, and we find that charge-transfer distances up to three to four bases may be accounted for with this mechanism. Thus, the observed rapid (exponential) distance dependence of DNA ET rates over distances of K K K K15 Å does not necessarily prove a tunneling mechanism.vibronic coupling | resonant tunneling pathways | superexchange | coherence | gated transport C hemical structure and, importantly, structural fluctuations determine the mechanism and kinetics of charge transfer. Redox energy fluctuations are of particular significance when transport barrier heights and the energy fluctuations are of similar magnitude. Indeed, the sensitivity of biological electrontransfer (ET) rates to conformational fluctuations and consequent (transient) delocalization is the topic of intense interest (1-3). Resonant enhancement of biological ET rates is consistent with a growing body of physical and structural data found in DNA ET through stacked nucleobases (4), extended delocalized structures of bacterial photosynthesis (including the special pair, bridging chlorophyll and pheophytin) (5), the polaronic states of oxidized porphyrin arrays up to seven porphyrin diameters in spatial extent (6), micrometer-scale bacterial nanowires (7, 8), multiheme oxidoreductases (9, 10), amino acid side chains in ribonucleotide reductase (11), engineered protein-based hopping-chains (12), and centimeter-scale charge-transport chains in filamentous bacteria (13). Here, we describe a transient or flickering resonance (FR) mechanism for ET. The FR mechanism arises when thermal fluctuations produce geometries that enable charge delocalization across the entire structure by bringing the donor (D), bridge (B), and acceptor (...

DNA and DNA-based polymers are of interest in molecular electronics because of their versatile and programmable structures. However, transport measurements have produced a range of seemingly contradictory results due to differences in the measured molecules and experimental set-ups, and transporting significant current through individual DNA-based molecules remains a considerable challenge. Here, we report reproducible charge transport in guanine-quadruplex (G4) DNA molecules adsorbed on a mica substrate. Currents ranging from tens of picoamperes to more than 100 pA were measured in the G4-DNA over distances ranging from tens of nanometres to more than 100 nm. Our experimental results, combined with theoretical modelling, suggest that transport occurs via a thermally activated long-range hopping between multi-tetrad segments of DNA. These results could re-ignite interest in DNA-based wires and devices, and in the use of such systems in the development of programmable circuits.

Central to theories of electron transfer (ET) is the idea that nuclear motion generates a transition state that enables electron flow to proceed, but nuclear motion also induces fluctuations in the donoracceptor (DA) electronic coupling that is the rate-limiting parameter for nonadiabatic ET. The interplay between the DA energy gap and DA coupling fluctuations is particularly noteworthy in biological ET, where flexible protein and mobile water bridges take center stage. Here, we discuss the critical timescales at play for ET reactions in fluctuating media, highlighting issues of the Condon approximation, average medium versus fluctuation-controlled electron tunneling, gated and solvent relaxation controlled electron transfer, and the influence of inelastic tunneling on electronic coupling pathway interferences. Taken together, one may use this framework to establish principles to describe how macromolecular structure and structural fluctuations influence ET reactions. This framework deepens our understanding of ET chemistry in fluctuating media. Moreover, it provides a unifying perspective for biophysical charge-transfer processes and helps to frame new questions associated with energy harvesting and transduction in fluctuating media.

ConspectusElectron transfer (ET) reactions provide a nexus among chemistry, biochemistry, and physics. These reactions underpin the "power plants" and "power grids" of bioenergetics, and they challenge us to understand how evolution manipulates structure to control ET kinetics. Ball-and-stick models for the machinery of electron transfer, however, fail to capture the rich electronic and nuclear dynamics of ET molecules: these static representations disguise, for example, the range of thermally accessible molecular conformations. The influence of structural fluctuations on electron-transfer kinetics is amplified by the exponential decay of electron tunneling probabilities with distance, as well as the delicate interference among coupling pathways. Fluctuations in the surrounding medium can also switch transport between coherent and incoherent ET mechanisms-and may gate ET so that its kinetics is limited by conformational interconversion times, rather than by the intrinsic ET time scale. Moreover, preparation of a charge-polarized donor state, or of a donor state with linear or angular momentum, can have profound dynamical and kinetic consequences. In this Account, we establish a vocabulary to describe how the conformational ensemble and the prepared donor state influence ET kinetics in macromolecules. This framework is helping to unravel the richness of functional biological ET pathways, which have evolved in within fluctuating macromolecular structures.The conceptual framework for describing nonadiabatic ET seems disarmingly simple: compute the ensemble averaged (mean-squared) donor-acceptor (DA) tunneling interaction, , and the Franck-Condon weighted density of states, ρ FC , to describe the rate: (2π/ħ) ρ FC . Modern descriptions of the thermally averaged electronic coupling and of the Franck-Condon factor establish a useful predictive framework in biology, chemistry, and nanoscience. Describing the influence of geometric and energetic fluctuations on ET allows us to address a rich array of mechanistic and kinetic puzzles. How strongly is a protein's fold imprinted on the ET kinetics, and might thermal fluctuations "wash out" signatures of structure? What is the influence of thermal fluctuations on ET kinetics beyond averaging of the tunneling barrier structure? Do electronic coupling mechanisms change as donor and acceptor reposition in a protein, and what are the consequences for the ET kinetics? Do fluctuations access minority species that dominate tunneling? Can energy exchanges between the electron and bridge vibrations generate vibronic signatures that label some of the D-to-A pathway traversed by the electron, thus eliminating unmarked pathways that would otherwise contribute to the DA coupling (as in other "which way" or double-slit experiments)? Might medium fluctuations drive tunneling-hopping mechanistic transitions? How does the donor-state preparation -in particular its polarization toward the acceptor and its momentum characteristics (which may introduce complex rather than pur...

We compute the autocorrelation function of the donor-acceptor tunneling matrix element ͗TDA(t)TDA ( (0)͘ is studied as a function of donor-acceptor distance, tunneling pathway structure, tunneling energy, and temperature to explore the structural and dynamical origins of non-Condon effects. For azurin, the correlation function is remarkably insensitive to tunneling pathway structure. The decay time is only slightly shorter than it is for solvent-mediated electron transfer in small organic molecules and originates, largely, from fluctuations of valence angles rather than bond lengths.correlation functions ͉ Franck-Condon breakdown ͉ dephasing ͉ coupling pathways ͉ redox reactions T he interplay among nuclear motion and electronic dynamics is the subject of increasing focus in the field of electron transfer (ET) processes (1-8). Recent research has focused on the effects of bridge nuclear motion on ET, with chemical, biological, and electronic device applications (see refs. 9-11 for reviews). Early theoretical analysis indicates that tunneling matrix element modulation by bridge dynamics can alter the free energy dependence of ET reaction rates by causing the Born-Oppenheimer (12) and FranckCondon approximations to fail (13-15). More recently, theoretical studies explored ET kinetics in systems with fluctuating donoracceptor matrix elements (16-24). Bridge motion can cause large and rapid donor-acceptor matrix element fluctuations, affecting the tunneling pathway structure and the interferences among pathways (25-37). The coupling matrix element fluctuations may have large contributions from solvent-polarization fluctuations (23), and these fluctuations facilitate electronically forbidden and gated . Finally, bridge-nuclear relaxation creates inelastic tunneling pathway channels (11,20,24,(47)(48)(49) that can change the mechanism of ET from superexchange to resonant tunneling to sequential hopping (11,(41)(42)(43)(44)(50)(51)(52)(53)(54)(55)(56)(57)(58)(59)(60)(61)(62) and can lead to breakdown of the Born-Oppenheimer approximation (63, 64).The goal of this work is to characterize tunneling matrix element fluctuations in azurin and, in particular, to examine their influence on the ET rate and on the validity of the Franck-Condon approximation. Franck-Condon breakdown can reduce the ET rate in the case of activationless ET reactions and enhance the rate for activated ET (18). ET in Ru-modified azurin is nearly activationless, and the protein is often approximated as being a rigid medium for tunneling because the tunneling pathways traverse a ␤ sheet. In this work, we compute the effects of tunneling matrix element fluctuations on the rate as a function of distance, temperature, protein structural fluctuations, and intervening pathway structure. Further, we identify the types of motion that cause the coupling to fluctuate.The general derivation of the nonadiabatic rate expression for fluctuating donor-acceptor matrix elements cannot assume the validity of the Franck-Condon separation. As explained below, the Franck...

ConspectusThe image is not the thing. Just as a pipe rendered in an oil painting cannot be smoked, quantum mechanical coupling pathways rendered on LCDs do not convey electrons. The aim of this Account is to examine some of our recent discoveries regarding biological electron transfer (ET) and transport mechanisms that emerge when one moves beyond treacherous static views to dynamical frameworks.Studies over the last two decades introduced both atomistic detail and macromolecule dynamics to the description of biological ET. The first model to move beyond the structureless square-barrier tunneling description is the Pathway model, which predicts how protein secondary motifs and folding-induced through-bond and through-space tunneling gaps influence kinetics. Explicit electronic structure theory is applied routinely now to elucidate ET mechanisms, to capture pathway interferences, and to treat redox cofactor electronic structure effects. Importantly, structural sampling of proteins provides an understanding of how dynamics may change the mechanisms of biological ET, as ET rates are exponentially sensitive to structure. Does protein motion average out tunneling pathways? Do conformational fluctuations gate biological ET? Are transient multistate resonances produced by energy gap fluctuations? These questions are becoming accessible as the static view of biological ET recedes and dynamical viewpoints take center stage.This Account introduces ET reactions at the core of bioenergetics, summarizes our team’s progress toward arriving at an atomistic-level description, examines how thermal fluctuations influence ET, presents metrics that characterize dynamical effects on ET, and discusses applications in very long (micrometer scale) bacterial nanowires. The persistence of structural effects on the ET rates in the face of thermal fluctuations is considered. Finally, the flickering resonance (FR) view of charge transfer is presented to examine how fluctuations control low-barrier transport among multiple groups in van der Waals contact. FR produces exponential distance dependence in the absence of tunneling; the exponential character emerges from the probability of matching multiple vibronically broadened electronic energies within a tolerance defined by the rms coupling among interacting groups. FR thus produces band like coherent transport on the nanometer length scale, enabled by conformational fluctuations. Taken as a whole, the emerging context for ET in dynamical biomolecules provides a robust framework to design and interpret the inner workings of bioenergetics from the molecular to the cellular scale and beyond, with applications in biomedicine, biocatalysis, and energy science.

Extracellular appendages of the dissimilatory metal-reducing bacterium Shewanella oneidensis MR-1 were recently shown to sustain currents of 1010 electrons per second over distances of 0.5 microns [El-Naggar et al., Proc. Natl. Acad. Sci. U. S. A., 2010, 107, 18127]. However, the identity of the charge localizing sites and their organization along the “nanowire” remain unknown. We use theory to predict redox cofactor separation distances that would permit charge flow at rates of 1010 electrons per second over 0.5 microns for voltage biases of ≤1V, using a steady-state analysis governed by a non-adiabatic electron transport mechanism. We find the observed currents necessitate a multi-step hopping transport mechanism, with charge localizing sites separated by less than 1 nm and reorganization energies that rival the lowest known in biology.

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