On the length dependence of bridge-mediated electron transfer reactions

Peptides as Bio-Inspired Electronic Materials: An Electrochemical and First-Principles Perspective

Molecular electronics is at the forefront of interdisciplinary research, offering a significant extension of the capabilities of conventional silicon-based technology as well as providing a possible stand-alone alternative. Bio-inspired molecular electronics is a particularly intriguing paradigm, as charge transfer in proteins/peptides, for example, plays a critical role in the energy storage and conversion processes for all living organisms. However, the structure and conformation of even the simplest protein is extremely complex, and therefore, synthetic model peptides comprising well-defined geometry and predetermined functionality are ideal platforms to mimic nature for the elucidation of fundamental biological processes while also enhancing the design and development of single-peptide electronic components. In this Account, we first present intramolecular electron transfer within two synthetic peptides, one with a well-defined helical conformation and the other with a random geometry, using electrochemical techniques and computational simulations. This study reveals two definitive electron transfer pathways (mechanisms), the natures of which are dependent on secondary structure. Following on from this, electron transfer within a series of well-defined helical peptides, constrained by either Huisgen cycloaddition, ring-closing metathesis, or a lactam bridge, was determined. The electrochemical results indicate that each constrained peptide, in contrast to a linear counterpart, exhibits a remarkable shift of the formal potential to the positive (>460 mV) and a significant reduction of the electron transfer rate constant (up to 15-fold), which represent two distinct electronic "on/off" states. High-level calculations demonstrate that the additional backbone rigidity provided by the side-bridge constraints leads to an increased reorganization energy barrier, which impedes the vibrational fluctuations necessary for efficient intramolecular electron transfer through the peptide backbone. Further calculations reveal a clear mechanistic transition from hopping to superexchange (tunneling) stemming from side-bridge gating. We then extended our research to fine-tuning of the electronic properties of peptides through both structural and chemical manipulation, to reveal an interplay between electron-rich side chains and backbone rigidity on electron transfer. Further to this, we explored the possibility that the side-bridge constraints present in our synthetic peptides provide an additional electronic transport pathway, which led to the discovery of two distinct forms of quantum interferometer. The effects of destructive quantum interference appear essentially through both the backbone and an alternative tunneling pathway provided by the side bridge in the constrained β-strand peptide, as evidenced by a correlation between electrochemical measurements and conductance simulations for both linear and constrained β-strand peptides. In contrast, an interplay between quantum interference effects and vibrational fluctuations is revealed in the linear and constrained 3₁₀-helical peptides. Collectively, these exciting findings augment our fundamental knowledge of charge transfer dynamics and kinetics in peptides and also open up new avenues to design and develop functional bio-inspired electronic devices, such as on/off switches and quantum interferometers, for practical applications in molecular electronics.

Thermoelectric efficiency of single-molecule junctions with long molecular linkers

We report results of theoretical studies of thermoelectric efficiency of single-molecule junctions with long molecular linkers. The linker is simulated by a chain of identical sites described using a tight-binding model. It is shown that thermoelectric figure of merit ZT strongly depends on the bridge length, being controlled by the lineshape of electron transmission function within the tunnel energy range corresponding to HOMO/LUMO transport channel. Using the adopted model we demonstrate that ZT may significantly increase as the linker lengthens, and that gateway states on the bridge (if any) may noticeably affect the length-dependent ZT. Temperature dependences of ZT for various bridge lengths are analyzed. It is shown that broad minima emerge in ZT versus temperature curves whose positions are controlled by the bridge lengths.

A controllable mechanistic transition of charge transfer in helical peptides: from hopping to superexchange

A controllable mechanistic transition of charge transfer in helical peptides is demonstrated as a direct result of side-bridge gating.

Theory of Triplet Excitation Transfer in the Donor-Oxygen-Acceptor System: Application to Cytochrome b6f

Theoretical consideration is presented of the triplet excitation dynamics in donor-acceptor systems in conditions where the transfer is mediated by an oxygen molecule. It is demonstrated that oxygen may be involved in both real and virtual intramolecular triplet-singlet conversions in the course of the process under consideration. Expressions describing a superexchange donor-acceptor coupling owing to a participation of the bridging twofold degenerate oxygen's virtual singlet state are derived and the transfer kinetics including the sequential (hopping) and coherent (distant) routes are analyzed. Applicability of this theoretical description to the pigment-protein complex cytochrome b6f, by considering the triplet excitation transfer from the chlorophyll a molecule to distant β-carotene, is discussed.

Length-independent transport rates in biomolecules by quantum mechanical unfurling

Experiments on hole transfer in DNA between donor and acceptor moieties revealed transfer rates which are independent of the molecular bridge length (within experimental error). However, the physical origin of this intriguing observation is still unclear. The hopping model implies that the hole propagates in multiple steps along the bridge from one localized state to another, and therefore the longer the bridge, the slower the transfer. This can explain weak length-dependence but not a length-independent transfer rate. We show that the rigid molecular structure of a poly-A bridge supports single step transitions from a localized hole state to delocalized states, spread over the entire bridge. Since propagation to the bridge end is a single step process (termed quantum unfurling) the transfer rate becomes independent of the bridge length. This explanation is consistent with experimental results, and emphasizes the importance of structural order in charge transfer through bio-molecular systems.

A three-step kinetic model for electrochemical charge transfer in the hopping regime

Single-step nonadiabatic electron tunneling models are widely used to analyze electrochemical rates through self-assembled monolayer films (SAMs). For some systems, such as nucleic acids, long-range charge transfer can occur in a "hopping" regime that involves multiple charge transfer events and intermediate states. This report describes a three-step kinetic scheme to model charge transfer in this regime. Some of the features of the three-step model are probed experimentally by changing the chemical composition of the SAM. This work uses the three-step model and a temperature dependence of the charge transfer rate to extract the charge injection barrier for a SAM composed of a 10-mer peptide nucleic acid that operates in the hopping regime.

Diffusion Approach to Long Distance Charge Migration in DNA: Time-Dependent and Steady-State Analytical Solutions for the Product Yields

In this study we report analytical solutions for both time-dependent and steady-state problems of unbiased charge transfer through a regular DNA sequence via a hopping mechanism. The phenomenon is treated as a diffusion of charge in a one-dimensional array of equally spaced and energetically equivalent temporary trapping sites. The solutions take into account the rates of charge hopping (k), side reactions (k(r)), and charge transfer to a terminal charge acceptor (k(t)). A detailed analysis of the time-dependent problem is performed for the diffusion-controlled regime, i.e., under the assumption that k(t) >> k, which is also equivalent to the fast relaxation limit of charge trapping. The analysis shows that the kinetics of charge hopping through DNA is always multiexponential, but under certain circumstances it can be asymptotically approximated by a single-exponential term. In that case, the efficiency of charge transfer can be characterized by a single rate constant k(CT) = 1.23kN(-2) + k(r), where N is the DNA length expressed in terms of the number of equidistant trapping sites and k(r) is the rate of competing chemical processes. The absolute yield of charge transfer under steady-state conditions in general is obtained as Y(infinity) = omega [alpha sinh(alphaN) + omega cosh(alphaN)](-1), where alpha = (2k(r)/k)(1/2) and omega = 2k(t)/k. For the diffusion-controlled regime and small N, in particular, it turns into the known "algebraic" dependence Y(infinity) = [1 + (k(r)/k)N(2)](-1). At large N the solution is asymptotically exponential with the parameter alpha mimicking the tunneling parameter beta in agreement with earlier predictions. Similar equations and distance dependencies have also been obtained for the damage ratios at the intermediate and terminal trapping sites in DNA. The nonlinear least-squares fit of one of these equations to experimental yields of guanine oxidation available from the literature returns kinetic parameters that are in reasonable agreement with those obtained by Bixon et al. [Proc. Natl. Acad. Sci. U.S.A.1999, 96, 11713-11716] by numerical simulations, suggesting that these two approaches are physically equivalent.

Charge transmission through a molecular wire: The role of terminal sites for the current-voltage behavior

The current-voltage and the conductance-voltage characteristics are analyzed for a particular type of molecular wire embedded between two electrodes. The wire is characterized by internal molecular units where the lowest occupied molecular orbital (LUMO) levels are positioned much above the Fermi energy of the electrodes, as well as above the LUMO levels of the terminal wire units. The latter act as specific intermediate donor and acceptor sites which in turn control the current formation via the superexchange and sequential electron transfer mechanisms. According to the chosen wire structure, intramolecular multiphonon processes may block the superexchange component of the interelectrode current, resulting in a negative differential resistance of the molecular wire. A pronounced current rectification appears if (i) the superexchange component dominates the electron transfer between the terminal sites and if (ii) the multiphonon suppression of distant superexchange charge hopping events between those sites is nonsymmetric.

Analysis of Bridge-Mediated Pathways for Long-Range Charge Transfer Systems

With the density matrix decomposition scheme of the path integral method, an accurate quantitative analysis on bridge-mediated pathways in long-range charge transfer processes is presented. Unlike a donor-bridge-acceptor triad, a long-range charge transfer process with a number of bridges has additional pathways in which charges always migrate through bridges but not necessarily by incoherent nearest-neighbor hopping. By employing the density matrix decomposition and sorting the incoherent nearest-neighbor and the coherent next-nearest-neighbor hopping pathways, respective contributions to the charge transfer are evaluated quantitatively. Numerical results of two series of configurations with varying degrees of coherence within the system have found that, depending on the configuration, the contribution of the coherent pathways other than superexchange pathways is significant. In the presence of the coherence, long-range charge transfer dynamics may be dominated by the through-bridge mechanism that consists of the coherent through-bridge pathways as well as the incoherent nearest-neighbor hopping pathways.

Peptide electron transfer: more questions than answers

Nature has specifically designed proteins, as opposed to DNA, for electron transfer. There is no doubt about the electron transfer within proteins compared with the uncertain and continuing debate about charge transfer through DNA. However, the exact mechanism of electron transfer within peptide systems has been a source of controversy. Two different mechanisms for electron transfer between a donor and an acceptor, electron hopping and bridge-assisted superexchange, have been proposed, and are supported by experimental evidence and theoretical calculations. Several factors were found to affect the kinetics of this process, including peptide chain length, secondary structure and hydrogen bonding. Electrochemical measurements of surface-supported peptides have contributed significantly to the debate. Here we summarize the current approaches to the study of electron transfer in peptides with a focus on surface measurements and comment on these results in light of the current and often controversial debate on electron transfer mechanisms in peptides.

Evidence Against the Hopping Mechanism as an Important Electron Transfer Pathway for Conformationally Constrained Oligopeptides

The rate constant of intramolecular electron transfer through oligopeptides based on the alpha-aminoisobutyric acid residue was determined as a function of the peptide length and found to depend weakly on the donor-acceptor separation. By measuring the electron-transfer activation energy and estimating the energy gap between donor and bridge, we were able to discard the electron hopping mechanism.

Understanding Electron Transfer across Negatively-Charged Aib Oligopeptides

The physicochemical effects modulating the conformational behavior and the rate of intramolecular dissociative electron transfer in phthalimide-Aibn-peroxide peptides (n = 0-3) have been studied by an integrated density functional/continuum solvent model. We found that three different orientations of the phthalimide ring are possible, labeled Phihel, PhiC7, and PhipII. In the condensed phase, they are very close in energy when the system is neutral and short. When the peptide chain length increases and the system is negatively charged, Phihel becomes instead the most stable conformer. Our calculations confirm that the 3(10)-helix is the most stable secondary structure for the peptide bridge. However, upon charge injection in the phthalimide end of the phthalimide-Aib3-peroxide, the peptide bridge can adopt an alpha-helix conformation as well. The study of the dependence of the frontier orbitals on the length and on the conformation of the peptide bridge (in agreement with experimental indications) suggests that for n = 3 the process could be influenced by a 3(10) --> alpha-helix conformational transition of the peptide chain.

Bridge mediated two-electron transfer reactions: On the influence of intersite Coulomb interactions

Donor-acceptor two-electron transfer (TET) mediated by a linear molecular bridge is described theoretically. The particular case is considered where the TET takes place in the presence of a strong electronic intersite coupling within the bridge and against the background of fast vibrational relaxation processes. For such a situation the coarse-grained description of bridge-assisted electron transfer in molecular systems can be utilized [Petrov et al., J. Phys. Chem. B 106, 3092 (2002)]. In the present case it leads to kinetic equations and rate expression for TET reactions. Our recent treatment of completely nonadiabtic TET reactions [Petrov et al., J. Chem. Phys. 120, 4441 (2004)] including a reduction to single-exponential kinetics (with overall transfer rate K(TET)) is generalized here to the case of strong intrabridge coupling and the presence of intersite Coulomb interactions. The dependence of K(TET) on the bridge length which is determined by a separate stepwise and concerted contribution is discussed in detail. It is found that the intersite Coulomb interaction favors the TET if the donor and the acceptor are uncharged in their completely reduced states (with two excess electrons present).

Bridge mediated two-electron transfer reactions: Analysis of stepwise and concerted pathways

A theory of nonadiabatic donor (D)-acceptor (A) two-electron transfer (TET) mediated by a single regular bridge (B) is developed. The presence of different intermediate two-electron states connecting the reactant state D-(-)BA with the product state DBA-(-) results in complex multiexponential kinetics. The conditions are discussed at which a reduction to two-exponential as well as single-exponential kinetics becomes possible. For the latter case the rate KTET is calculated, which describes the bridge-mediated reaction as an effective two-electron D-A transfer. In the limit of small populations of the intermediate TET states D-B-A, DB-(-)A, D-BA-, and DB-A-, KTET is obtained as a sum of the rates KTET(step) and KTET(sup). The first rate describes stepwise TET originated by transitions of a single electron. It starts at D-(-)BA and reaches DBA-(-) via the intermediate state D-BA-. These transitions cover contributions from sequential as well as superexchange reactions all including reduced bridge states. In contrast, a specific two-electron superexchange mechanism from D-(-)BA to DBA-(-) defines KTET(sup). An analytic dependence of KTET(step) and KTET(sup) on the number of bridging units is presented and different regimes of D-A TET are studied.

Two-electron transfer reactions in proteins: bridge-mediated and proton-assisted processes

Nonadiabatic two-electron transfer (TET) reactions through donor-bridge-acceptor (DBA) systems is investigated within the approximation of fast vibrational relaxation. For TET reactions in which the population of bridging states remains small (less than 10(-2)) it is demonstrated that a multiexponential transition process reduces to three-state kinetics. The transfer starts at the state with two excess electrons at the D center (D(2-)BA), goes through the intermediate (transient) state with one electron at the D center and one at the A center (D-BA-), and ends up with the two electrons at the A center (DBA2-). Furthermore, if the population of the intermediate state becomes also small the two-exponential kinetics can be transformed with high accuracy to single-exponential D-A TET kinetics. The related overall transfer rate contains contributions from stepwise and from concerted TET. The latter process is determined by a specific two-electron superexchange coupling incorporating the bridging states (D-B-A and DB-A-) as well as the intermediate state (D-BA-). As an example, the reduction of micothione reductase by nicotinamide adenine dinucleotide phosphate is analyzed. Existing experimental data can be explained if one assumes that the proton-assisted reduction of the enzyme is realized by the concerted TET mechanism.