Secondary Structure Conformations and Long Range Electronic Interactions in Oligopeptides

Adenine Fine-Tunes DNA Photolyase's Repair Mechanism

The comparative study of DNA repair by mesophilic and extremophilic photolyases helps us understand the evolution of these enzymes and their role in preserving life on our changing planet. The mechanism of repair of cyclobutane pyrimidine dimer lesions in DNA by electron transfer from the flavin adenine dinucleotide cofactor is the subject of intense interest. The role of adenine in mediating this process remains unresolved. Using microsecond molecular dynamics simulations, we find that adenine mediates the electron transfer in both mesophile and extremophile DNA photolyases through a similar mechanism. In fact, in all photolyases studied, the molecular conformations with the largest electronic couplings between the enzyme cofactor and DNA show the presence of adenine in 10-20% of the strongest-coupling tunneling pathways between the atoms of the electron donor and acceptor. Our theoretical analysis finds that adenine serves the critical role of fine-tuning rather than maximizing the donor-acceptor coupling within the range appropriate for the repair function.

Cofactor Dynamics Couples the Protein Surface to the Heme in Cytochrome c, Facilitating Electron Transfer

Electron transport through biomolecules and in biological transport networks is of great importance to bioenergetics and biocatalysis. More generally, it is of crucial importance to understand how the pathways that connect buried metallocofactors to other cofactors, and to protein surfaces, affect the biological chemistry of metalloproteins. In terms of electron transfer (ET), the strongest coupling pathways usually comprise covalent and hydrogen bonded networks, with a limited number of through-space contacts. Herein, we set out to determine the relative roles of hydrogen bonds involved in ET via an established heme-to-surface tunneling pathway in cytochrome (cyt) c (i.e., heme-W59-D60-E61-N62). A series of cyt c variants were produced where a ruthenium tris(diimine) photooxidant was placed at position 62 via covalent modification of the N62C residue. Surprisingly, variants where the H-bonding residues W59 and D60 were replaced (i.e., W59F and D60A) showed no change in ET rate from the ferrous heme to Ru(III). In contrast, changing the composition of an alternative tunneling pathway (i.e., heme-M64-N63-C62) with the M64L substitution shows a factor of 2 decrease in the rate of heme-to-Ru ET. This pathway involves a through-space tunneling step between the heme and M64 residue, and such steps are usually disfavored. To rationalize why the heme-M64-N63-C62 is preferred, molecular dynamics (MD) simulations and Pathways analysis were employed. These simulations show that the change in heme-Ru ET rates is attributed to different conformations with compressed donor-acceptor distances, by ∼2 Å in pathway distance, in the M64-containing protein as compared to the M64L protein. The change in distance is correlated with changes in the electronic coupling that are in accord with the experimentally observed heme-Ru ET rates. Remarkably, the M64L variation at the core of the protein translates to changes in cofactor dynamics at the protein surface. The surface changes identified by MD simulations include dynamic anion-π and dipole-dipole interactions. These interactions influence the strength of tunneling pathways and ET rates by facilitating decreases in through-space tunneling distances in key coupling pathways.

Why Are DNA and Protein Electron Transfer So Different?

The corpus of electron transfer (ET) theory provides considerable power to describe the kinetics and dynamics of electron flow at the nanoscale. How is it, then, that nucleic acid (NA) ET continues to surprise, while protein-mediated ET is relatively free of mechanistic bombshells? I suggest that this difference originates in the distinct electronic energy landscapes for the two classes of reactions. In proteins, the donor/acceptor-to-bridge energy gap is typically several-fold larger than in NAs. NA ET can access tunneling, hopping, and resonant transport among the bases, and fluctuations can enable switching among mechanisms; protein ET is restricted to tunneling among redox active cofactors and, under strongly oxidizing conditions, a few privileged amino acid side chains. This review aims to provide conceptual unity to DNA and protein ET reaction mechanisms. The establishment of a unified mechanistic framework enabled the successful design of NA experiments that switch electronic coherence effects on and off for ET processes on a length scale of multiple nanometers and promises to provide inroads to directing and detecting charge flow in soft-wet matter.

Charge-Transfer Knowledge Graph among Amino Acids Derived from High-Throughput Electronic Structure Calculations for Protein Database

The charge-transfer coupling is an important component in tight-binding methods. Because of the highly complex chemical structure of biomolecules, the anisotropic feature of charge-transfer couplings in realistic proteins cannot be ignored. In this work, we have performed the first large-scale quantitative assessment of charge-transfer preference by calculating the charge-transfer couplings in all 20 × 20 possible amino acid side-chain combinations, which are extracted from available high-quality structures of thousands of protein complexes. The charge-transfer database quantitatively shows distinct features of charge-transfer couplings among millions of amino acid side-chain combinations. The overall distribution of charge-transfer couplings reveals that only one average or representative structure cannot be regarded as the typical charge-transfer preference in realistic proteins. This work provides us an alternative route to comprehensively understand the charge-transfer couplings for the overall distribution of realistic proteins in the foreseen big data scenario.

Bidirectional Electron-Transfer in Polypeptides with Various Secondary Structures

The protein-mediated bidirectional electron transfer (ET) is the foundation of protein molecular wire, and plays an important role in the rapid detection of oxo-guanine-adenine DNA mismatches by MutY glycosylase. However, the influences of structural transitions on bidirectional ET are still not clear. In this work, the modified through-bond coupling (MTBC) model was further refined to correlate the structural transition and ET rate more quantitatively. With this model, various polyglycine structures (3₁₀-helix, α-helix, β-sheets, linear, polyproline helical I and II) were studied to explore the influences of structural transitions on bidirectional ET. It was found that the HOMO-LUMO gaps (ΔE) in CN (from the carboxyl to amino terminus) direction are much lower than that in opposite direction, except for polypro I. However, with the equal tunneling energy, the differences between bidirectional ET rates are slight for all structures. In structural transitions, we found that the ET rates are not only affected by the Ramachandran angles, but also correlated to the alignment of C = O vectors, the alignment of peptide planes and the rearrangement of other structure factors. The detailed information can be used to rationalize the inhomogeneous ET across different protein structures and design more efficient protein molecular wires.

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.

Electron transfer, decoherence, and protein dynamics: insights from atomistic simulations

Electron transfer in biological systems drives the processes of life. From cellular respiration to photosynthesis and enzymatic catalysis, electron transfers (ET) are chemical processes on which essential biological functions rely. Over the last 40 years, scientists have sought understanding of how these essential processes function in biology. One important breakthrough was the discovery that Marcus theory (MT) of electron transfer is applicable to biological systems. Chemists have experimentally collected both the reorganization energies (λ) and the driving forces (ΔG°), two parameters of Marcus theory, for a large variety of ET processes in proteins. At the same time, theoretical chemists have developed computational approaches that rely on molecular dynamics and quantum chemistry calculations to access numerical estimates of λ and ΔG°. Yet another crucial piece in determining the rate of an electron transfer is the electronic coupling between the initial and final electronic wave functions. This is an important prefactor in the nonadiabatic rate expression, since it reflects the probability that an electron tunnels from the electron donor to the acceptor through the intervening medium. The fact that a protein matrix supports electron tunneling much more efficiently than vacuum is now well documented, both experimentally and theoretically. Meanwhile, many chemists have provided examples of the rich physical chemistry that can be induced by protein dynamics. This Account describes our studies of the dynamical effects on electron tunneling. We present our analysis of two examples of natural biological systems through MD simulations and tunneling pathway analyses. Through these examples, we show that protein dynamics sustain efficient tunneling. Second, we introduce two time scales: τcoh and τFC. The former characterizes how fast the electronic coupling varies with nuclear vibrations (which cause dephasing). The latter reflects the time taken by the system to leave the crossing region. In the framework of open quantum systems, τFC is a short time approximation of the characteristic decoherence time of the electronic subsystem in interaction with its nuclear environment. The comparison of the respective values of τcoh and τFC allows us to probe the occurrence of non-Condon effects. We use ab initio MD simulations to analyze how decoherence appears in several biological cofactors. We conclude that we cannot account for its order of magnitude by considering only the atoms or bonds directly concerned with the transfer. Decoherence results from contributions from all atoms of the system appearing with a time delay that increases with the distance from the primarily concerned atoms or bonds. The delay and magnitude of the contributions depend on the chemical nature of the system. Finally, we present recent developments based on constrained DFT for efficient and accurate evaluations of the electronic coupling in ab initio MD simulations. These are promising methods to study the subtle fluctuations of the electronic coupling and the mechanisms of electronic decoherence in biological systems.

Charge transfer in dynamical biosystems, or the treachery of (static) images

The 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.

Distance-independent charge recombination kinetics in cytochrome c-cytochrome c peroxidase complexes: compensating changes in the electronic coupling and reorganization energies

Charge recombination rate constants vary no more than 3-fold for interprotein ET in the Zn-substituted wild type (WT) cytochrome c peroxidase (CcP):cytochrome c (Cc) complex and in complexes with four mutants of the Cc protein (i.e., F82S, F82W, F82Y, and F82I), despite large differences in the ET distance. Theoretical analysis indicates that charge recombination for all complexes involves a combination of tunneling and hopping via Trp191. For three of the five structures (WT and F82S(W)), the protein favors hopping more than that in the other two structures that have longer heme → ZnP distances (F82Y(I)). Experimentally observed biexponential ET kinetics is explained by the complex locking in alternative coupling pathways, where the acceptor hole state is either primarily localized on ZnP (slow phase) or on Trp191 (fast phase). The large conformational differences between the CcP:Cc interface for the F82Y(I) mutants compared to that the WT and F82S(W) complexes are predicted to change the reorganization energies for the CcP:Cc ET reactions because of changes in solvent exposure and interprotein ET distances. Since the recombination reaction is likely to occur in the inverted Marcus regime, an increased reorganization energy compensates the decreased role for hopping recombination (and the longer transfer distance) in the F82Y(I) mutants. Taken together, coupling pathway and reorganization energy effects for the five protein complexes explain the observed insensitivity of recombination kinetics to donor-acceptor distance and docking pose and also reveals how hopping through aromatic residues can accelerate long-range ET.

Hole transfer in LNA and 5-Me-2'-deoxyzebularine-modified DNA

We report the measurement of hole-transfer rate constants (k(ht)) in locked nucleic acid (LNA) and 5-Me-2'-deoxyzebularine (B)-modified DNA. LNA modification, which makes DNA more rigid, caused a decrease of more than 2 orders of magnitude in k(ht), whereas B modification, which increases DNA flexibility, increased k(ht) by more than 20-fold. The present results clearly showed that hole-transfer efficiency in DNA can be increased by increasing DNA flexibility.

Exploring biological electron transfer pathway dynamics with the Pathways plugin for VMD

We describe the new Pathways plugin for the molecular visualization program visual molecular dynamics. The plugin identifies and visualizes tunneling pathways and pathway families in biomolecules, and calculates relative electronic couplings. The plugin includes unique features to estimate the importance of individual atoms for mediating the coupling, to analyze the coupling sensitivity to thermal motion, and to visualize pathway fluctuations. The Pathways plugin is open source software distributed under the terms of the GNU's Not Unix (GNU) public license.

B-DNA to zip-DNA: simulating a DNA transition to a novel structure with enhanced charge-transport characteristics

The forced extension of a DNA segment is studied in a series of steered molecular dynamics simulations, employing a broad range of pulling forces. Throughout the entire force range, the formation of a zipper-like (zip-) DNA structure is observed. In that structure, first predicted by Lohikoski et al., the bases of the DNA strands interdigitate with each other and form a single-base aromatic stack. Similar motifs, albeit only a few base pairs in extent, have been observed in experimental crystal structures. Analysis of the dynamics of structural changes in pulled DNA shows that S-form DNA, thought to be adopted by DNA under applied force, serves as an intermediate between B-DNA and zip-DNA. Therefore, the phase transition plateau observed in force-extension curves of DNA is suggested to reflect the B-DNA to zip-DNA structural transition. Electronic structure analysis of purine bases in zip-DNA indicates a several-fold to order of magnitude increase in the π-π electronic coupling among nearest-neighbor nucleobases, compared to B-DNA. We further observe that zip-DNA does not require base pair complementarity between DNA strands, and we predict that the increased electronic coupling in zip-DNA will result in a much higher rate of charge transfer through an all-purine zip-DNA compared to B-DNA of equal length.

QM/MM methods: looking inside heme proteins biochemistry

Mixed quantum mechanics/molecular mechanics methods offer a valuable computational tool for understanding biochemical events. When combined with conformational sampling techniques, they allow for an exhaustive exploration of the enzymatic mechanism. Heme proteins are ubiquitous and essential for every organism. In this review we summarize our efforts towards the understanding of heme biochemistry. We present: 1) results on ligand migration on globins coupled to the ligand binding event, 2) results on the localization of the spin density in compound I of cytochromes and peroxidases, 3) novel methodologies for mapping the electron transfer pathways and 4) novel data on Tryptophan 2,3-dioxygenase. For this enzyme our results strongly indicate that the distal oxygen will end up on the C3 indole carbon, whereas the proximal oxygen will end up in the C2 position. Interestingly, the process involves the formation of an epoxide and a heme ferryl intermediate. The overall energy profile indicates an energy barrier of approximately 18 kcal/mol and an exothermic driving force of almost 80 kcal/mol.

Fluctuations in biological and bioinspired electron-transfer reactions

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 donor-acceptor (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.

Steering electrons on moving pathways

Electron 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 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, <H(DA)(2)>, and the Franck-Condon weighted density of states, rho(FC), to describe the rate, (2pi/variant Planck's over 2pi)<H(DA)(2)>rho(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 pathways 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 pure real relationships among donor orbital amplitudes), influence the electronic dynamics? In this Account, we describe our recent studies that address puzzling questions of how conformational distributions, excited-state polarization, and electronic and nuclear dynamical effects influence ET in macromolecules. Indeed, conformational and dynamical effects arise in all transport regimes, including the tunneling, resonant transport, and hopping regimes. Importantly, these effects can induce switching among ET mechanisms.

Langevin dynamics of conformational transformations induced by the charge-curvature interaction

The role of thermal fluctuations in the conformational dynamics of a single closed filament is studied. It is shown that, due to the interaction between charges and bending degrees of freedom, initially circular chains may undergo transformation to polygonal shape.

Electron transfers in proteins: investigations with a modified through-bond coupling model

By integrating the merits of previous models, a modified through-bond coupling (MTBC) model is proposed in this work and shows obvious improvement compared with previous models. With the MTBC model, the dominant electron coupling pathways in the polypeptide chains were identified, where the N-H bonds were found to be essential to the electron couplings. The local structures of peptides and proteins were finely characterized by the electron couplings and decay factors since they are structure sensitive. The neighboring carbonyl O-O distances are qualitatively correlated with the decay factors, and the deviations from the transconfigurations will weaken the coupling interactions. When the two amino acids being studied are not close in sequence, the couplings through hydrogen bonds are probably the main pathway because the electron transfers in this way save many steps, albeit the decay factor is less than that of per bond, consistent with the classical electron-tunneling model developed by Beratan [Science 252, 1285 (1991)]. It was found that the MTBC model can be effectively extended to study the electron transfers in complex biological systems with the combination of the fragment approach, which takes into account the contributions of key hydrogen bonds.

Conformational transformations induced by the charge-curvature interaction at finite temperature

The role of thermal fluctuations in the conformational dynamics of a single closed filament is studied. It is shown that, due to the interaction between charges and bending degrees of freedom, initially circular aggregates may undergo transformation to a polygonal shape. The transition occurs in the cases of hardening and softening charge-bending interaction. In the former case the charge and curvature are smoothly distributed along the chain, while in the latter spontaneous kink formation is initiated. The transition to a noncircular conformation is analogous to a phase transition of the second kind.

PNA versus DNA: effects of structural fluctuations on electronic structure and hole-transport mechanisms

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.

Average electron tunneling route of the electron transfer in protein media

We present a new theoretical method to determine and visualize the average tunneling route of the electron transfer (ET) in protein media. In this, we properly took into account the fluctuation of the tunneling currents and the quantum-interference effect. The route was correlated with the electronic factor <TDA(2)> in the case of ET by the elastic tunneling mechanism. We expanded <TDA(2)> by the interatomic tunneling currents <Jab(2)>'s. Incorporating the quantum-interference effect into the mean-square interatomic tunneling currents, denoted as <Jab(2)>, we could express <TDA(2)> as a sum of variant Planck's over 2pi(2)<Jab(2)>. Drawing the distribution of <Jab(2)> on the protein structure, we obtain the <Jab(2)> map which visually represents which parts of bonds and spaces most significantly contribute to <TDA(2)>. We applied this method to the ET from the bacteriopheophytin anion to the primary quinone in the bacterial photosynthetic reaction center of Rhodobacter sphaeroides. We obtained <Jab(2)>'s by a combined method of molecular dynamics simulations and quantum chemical calculations. In calculating <Jab(2)>, we found that much destructive interference works among the interatomic tunneling currents even after taking the average. We drew the <Jab(2)> map by a pipe model where atoms a and b are connected by a pipe with width proportional to the magnitude of <Jab(2)>. We found that two groups of <Jab(2)>'s, which are mutually coupled with high correlation in each group, have broad pipes and form the average tunneling routes, called Trp route and Met route. Each of the two average tunneling routes is composed of a few major pathways in the Pathways model which are fused at considerable part to each other. We also analyzed the average tunneling route for the ET by the inelastic tunneling mechanism.

Conformationally averaged score functions for electronic propagation in proteins

We explore the influence of conformational dynamics on protein-mediated electron donor-acceptor interactions. We introduce a thermally averaged score function to characterize electronic propagation from redox cofactors into the protein and solvent. The score function is explored for myoglobin at the extended-Hückel level, and the results are compared with those of simpler models. The conformationally averaged quantum results are consistent with the empirical analysis of the Pathways model. Notably, subtle effects of quantum interference among multiple coupling pathways that arise in static structures are largely averaged out when protein thermal motion is included. Propagation through bulk water near the single-protein interface decays rapidly with distance.

Incorporating electron-transfer functionality into synthetic metalloproteins from the bottom-up

The alpha-helical coiled-coil motif serves as a robust scaffold for incorporating electron-transfer (ET) functionality into synthetic metalloproteins. These structures consist of a supercoiling of two or more aplha helices that are formed by the self-assembly of individual polypeptide chains whose sequences contain a repeating pattern of hydrophobic and hydrophilic residues. Early work from our group attached abiotic Ru-based redox sites to the most surface-exposed positions of two stranded coiled-coils and used electron-pulse radiolysis to study both intra- and intermolecular ET reactions in these systems. Later work used smaller metallopeptides to investigate the effects of conformational gating within electrostatic peptide-protein complexes. We have recently designed the C16C19-GGY peptide, which contains Cys residues located at both the "a" and "d" positions of its third heptad repeat in order to construct a nativelike metal-binding domain within its hydrophobic core. It was shown that the binding of both Cd(II) and Cu(I) ions induces the peptide to undergo a conformational change from a disordered random coil to a metal-bridged coiled-coil. However, whereas the Cd(II)-protein exists as a two-stranded coiled-coil, the Cu(I) derivative exists as a four-stranded coiled-coil. Upon the incorporation of other metal ions, metal-bridged peptide dimers, tetramers, and hexamers are formed. The Cu(I)-protein is of particular interest because it exhibits a long-lived (microsecond) room-temperature luminescence at 600 nm. The luminophore in this protein is thought to be a multinuclear CuI4Cys4(N/O)4 cage complex, which can be quenched by exogenous electron acceptors in solution, as shown by emission-lifetime and transient-absorption experiments. It is anticipated that further investigation into these systems will contribute to the expanding effort of bioinorganic chemists to prepare new kinds of functionally active synthetic metalloproteins.

Conformational transformations induced by the charge-curvature interaction: Mean-field approach

A simple phenomenological model for describing the conformational dynamics of biological macromolecules via the nonlinearity-induced instabilities is proposed. It is shown that the interaction between charges and bending degrees of freedom of closed molecular aggregates may act as drivers giving impetus to conformational dynamics of biopolymers. It is demonstrated that initially circular aggregates may undergo transformation to polygonal shapes and possible application to aggregates of bacteriochlorophyl a molecules is considered.

Photoinduced electron transfer in alpha-helical polypeptides: dependence on conformation and electron donor-acceptor distance

Long distance electron transfer in proteins is a multiple-pathway process whose kinetics is modulated by the dynamics of flexible peptide chains. Such complexity can be observed even in relatively simple systems, eg. donor bridge acceptor, where the bridge is a polypeptide alpha-helix. We have investigated a series of 24-residue helical polypeptides that exist as monomers in water alcohol media. The principal chromophore and electron acceptor, a pyrene moiety, is connected to the N-terminus via a flexible linker. The electron donor, a tryptophan residue, was placed various distances away from the pyrene-labeled terminus. Time-resolved emission spectroscopy, associated with the fluorescent pendant, pyrene, was employed to study the photoinduced electron-transfer kinetics for the polypeptide analogs. Mechanisms involving only through-bond pathways could not account for the pattern of measured fast charge-separation rates. When the electron donor was placed far enough from the acceptor (i.e. at least six residues apart), a decrease in the electron-transfer rates with the donor acceptor distance was observed. The emission decays for polypeptides with the electron donor exhibited complex behavior and could not be fit using a single-exponential function. For the treatment of the time-resolved data, a multi-exponential model was developed that is based on the assumption of a Gaussian distribution of the classical electronic coupling beta values among the conformers responsible for the observed electron-transfer processes. This approach proved to be informative because, in addition to the mean values of the electron-transfer rate constants, the widths of the distributions of these rates illustrate the size of the conformational space explored by the flexible chains that provide pathways for electron transfer.

Protein dynamics and electron transfer: electronic decoherence and non-Condon effects

We compute the autocorrelation function of the donor-acceptor tunneling matrix element <T(DA)(t)T(DA)(0)> for six Ru-azurin derivatives. Comparison of this decay time to the decay time of the time-dependent Franck-Condon factor {computed by Rossky and coworkers [Lockwood, D. M., Cheng, Y.-K. & Rossky, P. J. (2001) Chem. Phys. Lett. 345, 159-165]} reveals the extent to which non-Condon effects influence the electron-transfer rate. <T(DA)(t)T(DA)(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.

Interference, Fluctuation, and Alternation of Electron Tunneling in Protein Media. 1. Two Tunneling Routes in Photosynthetic Reaction Center Alternate Due to Thermal Fluctuation of Protein Conformation

Electron tunneling routes for the electron transfer from the bacteriopheophytin anion to the primary quinone in the bacterial photosynthetic reaction center of Rhodobactor sphaeroides are investigated by a combined method of molecular dynamics simulations for the protein conformation fluctuation and quantum chemical calculations for the electronic states of the donor, acceptor, and protein medium. The analysis of the tunneling route is made by mapping interatomic electron tunneling currents for each protein conformation. We found that there are two dominant routes mainly passing through Trp(M252) (Trp route) or mainly passing through Met(M218) (Met route). Actual electron tunneling pathways alternate between the two routes, depending on the protein conformation which varies with time. When either the Trp route or the Met route dominates, the electron tunneling matrix element /T(DA)/ becomes large. When both the Trp route and the Met route dominate, /T(DA)/ becomes very small due to the destructive interference of the electron tunneling currents between the two routes. We found that a linear relationship exists between the value of /T(DA)/ and the inverse of the degree of destructive interference Q for a wide range of values (ca. 3-10(3) for Q). A similar relationship was also found previously for electron transfer in ruthenium-modified azurins, suggesting that this relationship holds true in general. From these results, we are led to the conclusion that /T(DA)/ cannot exceed a maximum value at Q = 1, even if much variation of /T(DA)/ happens due to the fluctuation of protein conformation. We also conclude that the property of the electron transfer alternates between constructive and destructive interference, due to the fluctuation of protein conformation. It is impossible to keep a system in either constructive or destructive interference because thermal fluctuation of protein conformation takes place.

Ab Initio Based Calculations of Electron-Transfer Rates in Metalloproteins

A long-standing challenge in electron-transfer theory is to compute accurate rates of long-distance reactions in proteins. We describe an ab initio Hartree-Fock approach to compute electronic-coupling interactions and electron-transfer rates in proteins that allows the favorable comparison with experiment. The method includes the following key features; each is essential for reliable rate computations: (1) summing contributions over multiple tunneling pathways, (2) averaging couplings over thermally accessible protein conformations, (3) describing donor and acceptor electronic structure explicitly, including solvation effects, and averaging coupling over multiple energy-level crossings of the nearly degenerate donor-acceptor ligand-field states, and (4) eliminating basis set artifacts associated with diffuse basis functions. The strong dependence of coupling on donor-acceptor distance and on pathway interferences causes large variations of the computed electron-coupling values with protein geometry, and the strongest coupled conformers dominate the electron-transfer rate. As such, averaging over thermally accessible conformers of the protein and of the redox cofactors is essential. This approach was tested on six ruthenium-modified azurin derivatives using the high temperature nonadiabatic rate expression and compared with simpler pathways, average barrier, and semiempirical INDO models. Results of ab initio Hartree-Fock calculations with a split-valence basis set are in good agreement with the experimental rates. Predicted rates in the longer-distance derivatives are underestimated by 3-8-fold. This analysis indicates that the key ingredients needed for quantitatively reliable protein electron-transfer rate calculations are accessible.

Distance dependence of electron transfer across peptides with different secondary structures: the role of Peptide energetics and electronic coupling

The charge-transfer transition energies and the electronic-coupling matrix element, |H(DA)|, for electron transfer from aminopyridine (ap) to the 4-carbonyl-2,2'-bipyridine (cbpy) in cbpy-(gly)(n)-ap (gly = glycine, n = 0-6) molecules were calculated using the Zerner's INDO/S, together with the Cave and Newton methods. The oligopeptide linkages used were those of the idealized protein secondary structures, the alpha-helix, 3(10)-helix, beta-strand, and polyproline I- and II-helices. The charge-transfer transition energies are influenced by the magnitude and direction of the dipole generated by the peptide secondary structure. The electronic coupling |H(DA)| between (cbpy) and (ap) is also dependent on the nature of the secondary structure of the peptide. A plot of 2.ln|H(DA)| versus the charge-transfer distance (assumed to be the dipole moment change between the ground state and the charge-transfer states) showed that the polyproline II structure is a more efficient bridge for long-distance electron-transfer reactions (beta = 0.7 A(-1)) than the other secondary structures (beta approximately 1.3 A(-1)). Similar calculations on charged dipeptide derivatives, [CH(3)CONHCH(2)CONHCH(3)](+/)(-), showed that peptide-peptide interaction is more dependent on conformation in the cationic than in the anionic dipeptides. The alpha-helix and polyproline II-helix both have large peptide-peptide interactions (|H(DA)| > 800 cm(-1)) which arise from the angular dependence of their pi-orbitals. Such an interaction is much weaker than in the beta-strand peptides. These combined results were found to be consistent with electron-transfer rates experimentally observed across short peptide bridges in polyproline II (n = 1-3). These results can also account for directional electron transfer observed in an alpha-helical structure (different ET rates versus the direction of the molecular dipole).