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 (...

The effects of structural fluctuations on charge transfer in double-stranded DNA and peptide nucleic acid (PNA) are investigated. A palindromic sequence with two guanine bases that play the roles of hole donor and acceptor, separated by a bridge of two adenine bases, was analyzed using combined molecular dynamics (MD) and quantum-chemical methods. Surprisingly, electronic structure calculations on individual MD snapshots show significant frontier orbital electronic population on the bridge in approximately 10% of the structures. Electron-density delocalization to the bridge is found to be gated by fluctuations of the covalent conjugated bond structure of the aromatic rings of the nucleic bases. It is concluded, therefore, that both thermal hopping and superexchange should contribute significantly to charge transfer even in short DNA/PNA fragments. PNA is found to be more flexible than DNA, and this flexibility is predicted to produce larger rates of charge transfer.

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...

A multiscale simulation of a complex between the lac repressor protein (LacI) and a 107-bp-long DNA segment is reported. The complex between the repressor and two operator DNA segments is described by all-atom molecular dynamics; the size of the simulated system comprises either 226,000 or 314,000 atoms. The DNA loop connecting the operators is modeled as a continuous elastic ribbon, described mathematically by the nonlinear Kirchhoff differential equations with boundary conditions obtained from the coordinates of the terminal base pairs of each operator. The forces stemming from the looped DNA are included in the molecular dynamics simulations; the loop structure and the forces are continuously recomputed because the protein motions during the simulations shift the operators and the presumed termini of the loop. The simulations reveal the structural dynamics of the LacI-DNA complex in unprecedented detail. The multiple domains of LacI exhibit remarkable structural stability during the simulation, moving much like rigid bodies. LacI is shown to absorb the strain from the looped DNA mainly through its mobile DNA-binding head groups. Even with large fluctuating forces applied, the head groups tilt strongly and keep their grip on the operator DNA, while the remainder of the protein retains its V-shaped structure. A simulated opening of the cleft of LacI by 500-pN forces revealed the interactions responsible for locking LacI in the V-conformation.protein-DNA interaction ͉ molecular dynamics ͉ elastic rod model ͉ DNA loop ͉ large-scale protein motion T he lac repressor (LacI) is a celebrated DNA-binding protein that regulates the function of the lac operon (1), a set of genes responsible for the lactose metabolism in Escherichia coli. In the absence of lactose, LacI inhibits the expression of the operon by binding to two of three specifically recognized DNA sites, called operators, and causing the DNA between the operators to fold into a loop (2-4). Depending on which operators are bound, the loop may have a length of either 384 or 75 bp (4, 5). The smaller loop contains the promoter of the lac operon, which includes binding sites for RNA polymerase and the activator protein CAP (1).Several x-ray structures of LacI, both alone and in complex with DNA, were reported (4, 6, 7). The repressor is a homotetramer folded into a dimer of dimers, two massive ''arms'' connected at the ends by means of a four-helix bundle (Fig. 1). Each arm consists of a core and a DNA-binding head group domain; the lactose binding sites divide the core domains into two subdomains. This architecture is essential for the function of LacI. The protein binds two operators with its two head groups and holds them close together, enforcing the interoperator loop, while leaving the lactose binding sites inside the core domains open for lactose molecules to enter, disrupt the repressor, and induce the expression of the lac operon. At the same time, the loose connections between the LacI domains imply a great degree of structural flexibility that LacI n...