Pathways,pathway tubes,pathway docking,and propagators in electron transfer proteins

The simplest views of long-range electron transfer utilize flat one-dimensional barrier tunneling models, neglecting structural details of the protein medium. The pathway model of protein electron transfer reintroduces structure by distinguishing between covalent bonds, hydrogen bonds, and van der Waals contacts. These three kinds of interactions in a tunneling pathway each have distinctive decay factors associated with them. The distribution and arrangement of these bonded and nonbonded contacts in a folded protein varies tremendously between structures, adding a richness to the tunneling problem that is absent in simpler views. We review the pathway model and the predictions that it makes for protein electron transfer rates in small proteins, docked proteins, and the photosynthetic reactions center. We also review the formulation of the protein electron transfer problem as an effective two-level system. New multi-pathway approaches and improved electronic Hamiltonians are described briefly as well.     

Dynamics of electron transfer pathways in cytochrome C oxidase

Cytochrome c oxidase mediates the final step of electron transfer reactions in the respiratory chain, catalyzing the transfer between cytochrome c and the molecular oxygen and concomitantly pumping protons across the inner mitochondrial membrane. We investigate the electron transfer reactions in cytochrome c oxidase, particularly the control of the effective electronic coupling by the nuclear thermal motion. The effective coupling is calculated using the Green's function technique with an extended Huckel level electronic Hamiltonian, combined with all-atom molecular dynamics of the protein in a native (membrane and solvent) environment. The effective coupling between Cu(A) and heme a is found to be dominated by the pathway that starts from His(B204). The coupling between heme a and heme a(3) is dominated by a through-space jump between the two heme rings rather than by covalent pathways. In the both steps, the effective electronic coupling is robust to the thermal nuclear vibrations, thereby providing fast and efficient electron transfer.     

Electron tunneling pathways in proteins: influences on the transfer rate

A strategy for calculating the tunneling matrix element dependence on the medium intervening between donor and acceptor in specific proteins is described. The scheme is based on prior studies of small molecules and is general enough to allow inclusion of through bond and through space contributions to the electronic tunneling interaction. This strategy should allow the prediction of relative electron transfer rates in a number of proteins. It will therefore serve as a design tool and will be explicitly testable, in contrast with calculations on single molecules. As an example, the method is applied to ruthenated myoglobin and the tunneling matrix elements are estimated. Quantitative improvements of the model are described and effects due to motion of the bridging protein are discussed. The method should be of use for designing target proteins having tailored electron transfer rates for production with site directed mutagenesis. The relevance of the technique to understanding certain photosynthetic reaction center electron transfer rates is discussed.     

Electron transfer in quinoproteins

Soluble quinoprotein dehydrogenases oxidize a wide range of sugar, alcohol, amine, and aldehyde substrates. The physiological electron acceptors for these enzymes are not pyridine nucleotides but are other soluble redox proteins. This makes these enzymes and their electron acceptors excellent systems with which to study mechanisms of long-range interprotein electron transfer reactions. The tryptophan tryptophylquinone (TTQ)-dependent methylamine dehydrogenase (MADH) transfers electrons to a blue copper protein, amicyanin. It has been possible to alter the rate of electron transfer by using different redox forms of MADH, varying reaction conditions, and performing site-directed mutagenesis on these proteins. From kinetic and thermodynamic analyses of the reaction rates, it was possible to determine whether a change in rate is due a change in Delta G(0), electronic coupling, reorganization energy or kinetic mechanism. Examples of each of these cases are discussed in the context of the known crystal structures of the electron transfer protein complexes. The pyrroloquinoline quinone (PQQ)-dependent methanol dehydrogenase transfers electrons to a c-type cytochrome. Kinetic and thermodynamic analyses of this reaction indicated that this electron transfer reaction was conformationally coupled. Quinohemoproteins possess a quinone cofactor as well as one or more c-type hemes within the same protein. The structures of a PQQ-dependent quinohemoprotein alcohol dehydrogenase and a TTQ-dependent quinohemoprotein amine dehydrogenase are described with respect to their roles in intramolecular and intermolecular protein electron transfer reactions.     

Present status and future directions of research in electron-transfer mediated by DNA

 This commentary article presents an overview of recent experimental results on DNA-mediated electron transfer (ET) from the perspective of semiclassical ET theory. The question concerning whether or not DNA can act as a wire is addressed. Much of the article focuses on a discussion of the decay of electronic coupling (β) between electron donors and acceptors with increasing donor/acceptor separation in DNA and in protein systems. In particular, the dependence of the electronic coupling itself (H _AB) on the energy gap between the tunneling energy of the reactants and the virtual ionic states of the DNA bridge is highlighted. The article concludes by suggesting that future experimental and theoretical work in this field should focus on the tunneling gap energies of the systems studied and that special attention should be paid to systems that are likely to be in the "small tunneling gap" regime. It is these systems that are expected to exhibit enhanced electronic couplings and consequently enhanced rates of long-distance ET. Received, accepted: 5 January 1998     

Electron transfer in proteins: in search of preferential pathways

Electron migration between and within proteins is one of the most prevalent forms of biological energy conversion processes. Electron transfer reactions take place between active centers such as transition metal ions or organic cofactors over considerable distances at fast rates and with remarkable specificity. The electron transfer is attained through weak electronic interaction between the active sites, so that considerable research efforts are centered on resolving the factors that control the rates of long-distance electron transfer reactions in proteins. These factors include (in addition to the distance and nature of the microenvironment separating the reactants) thermodynamic driving force and the configurational changes required upon reaction. Several of these aspects are addressed in this review, which is based primarily on recent work performed by the authors on model systems of blue copper-containing proteins. These proteins serve almost exclusively in electron transfer reactions, and as it turns out, their metal coordination sites are endowed with properties uniquely optimized for their function.     

Electron flow through metalloproteins

Electron transfers in photosynthesis and respiration commonly occur between metal-containing cofactors that are separated by large molecular distances. Understanding the underlying physics and chemistry of these biological electron transfer processes is the goal of much of the work in our laboratories. Employing laser flash-quench triggering methods, we have shown that 20 Å, coupling-limited Fe(II) to Ru(III) and Cu(I) to Ru(III) electron tunneling in Ru-modified cytochromes and blue copper proteins can occur on the microsecond timescale both in solutions and crystals; and, further, that analysis of these rates suggests that distant donor-acceptor electronic couplings are mediated by a combination of sigma and hydrogen bonds in folded polypeptide structures. Redox equivalents can be transferred even longer distances by multistep tunneling, often called hopping, through intervening amino acid side chains. In recent work, we have found that 20 Å hole hopping through an intervening tryptophan is several hundred-fold faster than single-step electron tunneling in a Re-modified blue copper protein.     

Characterization of Electron Tunneling and Hole Hopping Reactions between Different Forms of MauG and Methylamine Dehydrogenase within a Natural Protein Complex

Respiration, photosynthesis, and metabolism require the transfer of electrons through and between proteins over relatively long distances. It is critical that this electron transfer (ET) occur with specificity to avoid cellular damage, and at a rate that is sufficient to support the biological activity. A multistep hole hopping mechanism could, in principle, enhance the efficiency of long-range ET through proteins as it does in organic semiconductors. To explore this possibility, two different ET reactions that occur over the same distance within the protein complex of the diheme enzyme MauG and different forms of methylamine dehydrogenase (MADH) were subjected to kinetic and thermodynamic analysis. An ET mechanism of single-step direct electron tunneling from diferrous MauG to the quinone form of MADH is consistent with the data. In contrast, the biosynthetic ET from preMADH, which contains incompletely synthesized tryptophan tryptophylquinone, to the bis-Fe(IV) form of MauG is best described by a two-step hole hopping mechanism. Experimentally determined ET distances matched the distances determined from the crystal structure that would be expected for single-step tunneling and multistep hopping. Experimentally determined relative values of electronic coupling (H(AB)) for the two reactions correlated well with the relative H(AB) values predicted from computational analysis of the structure. The rate of the hopping-mediated ET reaction is also 10-fold greater than that of the single-step tunneling reaction despite a smaller overall driving force for the hopping-mediated ET reaction. These data provide insight into how the intervening protein matrix and redox potentials of the electron donor and acceptor determine whether the ET reaction proceeds via single-step tunneling or multistep hopping.     

Distance metrics for heme protein electron tunneling

There is no doubt that distance is the principal parameter that sets the order of magnitude for electron-tunneling rates in proteins. However, there continue to be varying ways to measure electron-tunneling distances in proteins. This distance uncertainty blurs the issue of whether the intervening protein medium has been naturally selected to speed or slow any particular electron-tunneling reaction. For redox cofactors lacking metals, an edge of the cofactor can be defined that approximates the extent in space that includes most of the wavefunction associated with its tunneling electron. Beyond this edge, the wavefunction tails off much more dramatically in space. The conjugated porphyrin ring seems a reasonable edge for the metal-free pheophytins and bacteriopheophytins of photosynthesis. For a metal containing redox cofactor such as heme, an appropriate cofactor edge is more ambiguous. Electron-tunneling distance may be measured from the conjugated heme macrocycle edge or from the metal, which can be up to 4.8 A longer. In a typical protein medium, such a distance difference normally corresponds to a approximately 1000 fold decrease in tunneling rate. To address this ambiguity, we consider both natural heme protein electron transfer and light-activated electron transfer in ruthenated heme proteins. We find that the edge of the conjugated heme macrocycle provides a reliable and useful tunneling distance definition consistent with other biological electron-tunneling reactions. Furthermore, with this distance metric, heme axially- and edge-oriented electron transfers appear similar and equally well described by a simple square barrier tunneling model. This is in contrast to recent reports for metal-to-metal metrics that require exceptionally poor donor/acceptor couplings to explain heme axially-oriented electron transfers.     

Correlation of electron transfer rate in photosynthetic reaction centers with intraprotein dielectric properties

A number of the electrogenic reactions in photosystem I, photosystem II, and bacterial reaction centers (RC) were comparatively analyzed, and the variation of the dielectric permittivity (epsilon) in the vicinity of electron carriers along the membrane normal was calculated. The value of epsilon was minimal at the core of the complexes and gradually increased towards the periphery. We found that the rate of electron transfer (ET) correlated with the value of the dielectric permittivity: the fastest primary ET reactions occur in the low-polarity core of the complexes within the picosecond time range, whereas slower secondary reactions take place at the high-polarity periphery of the complexes within micro- to millisecond time range. The observed correlation was quantitatively interpreted in the framework of the Marcus theory. We calculated the reorganization energy of ET carriers using their van der Waals volumes and experimentally determined epsilon values. The electronic coupling was calculated by the empirical Moser-Dutton rule for the distance-dependent electron tunneling rate in nonadiabatic ET reactions. We concluded that the local dielectric permittivity inferred from the electrometric measurements could be quantitatively used to estimate the rate constant of ET reactions in membrane proteins with resolved atomic structure with the accuracy of less than one order of magnitude.     

A molecular mechanism of the energetic coupling of a sequence of electron transfer reactions to endergonic reactions.

A molecular mechanism of the energetic coupling of a sequence of electron transfer reactions to endergonic reactions is proposed and discussed from a physical point of view. The scheme represents a synthesis of concepts of electron transfer by tunneling and the conformational and chemiosmotic aspects of energy coupling processes. Its relation to existing experimental information and theoretical models is discussed, and further experimental tests are suggested.     

Correlation of electron transfer rate in photosynthetic reaction centers with intraprotein dielectric properties

A number of the electrogenic reactions in photosystem I, photosystem II, and bacterial reaction centers (RC) were comparatively analyzed, and the variation of the dielectric permittivity (ε) in the vicinity of electron carriers along the membrane normal was calculated. The value of ε was minimal at the core of the complexes and gradually increased towards the periphery. We found that the rate of electron transfer (ET) correlated with the value of the dielectric permittivity: the fastest primary ET reactions occur in the low-polarity core of the complexes within the picosecond time range, whereas slower secondary reactions take place at the high-polarity periphery of the complexes within micro- to millisecond time range. The observed correlation was quantitatively interpreted in the framework of the Marcus theory. We calculated the reorganization energy of ET carriers using their van der Waals volumes and experimentally determined ε values. The electronic coupling was calculated by the empirical Moser-Dutton rule for the distance-dependent electron tunneling rate in nonadiabatic ET reactions. We concluded that the local dielectric permittivity inferred from the electrometric measurements could be quantitatively used to estimate the rate constant of ET reactions in membrane proteins with resolved atomic structure with the accuracy of less than one order of magnitude.     

Photo-induced charge transfer. A critical test of the mechanism and range of biological electron transfer processes.

The vibronic coupling theory of electron tunneling between biomolecules requires that all such tunnelings involve vibronic coupling, finds temperature dependence to tunneling at finite temperatures, and predicts relatively short tunneling distances. This theory might be expected to apply to most electron transfers involved in the membrane-bound electron transfer reactions of photosynthesis and oxidative phosphorylation. This paper calculates the properties of a weak charge-transfer optical absorption band, whose predicted characteristics are a direct and simple consequence of the model that describes vibronically coupled tunneling. The new absorption band provides the basis for a critical experimental test of the constructs and parameters of the tunneling theory. If the tunneling theory is valid, the oscillator strength of such bands will be the most reliable measure of the tunneling matrix element and of the distance between the sites exchanging an electron.     

Mechanism for electron transfer within and between proteins

Examination of a growing range of electron transfer proteins is clarifying what design elements are and are not naturally selected. Intraprotein electron transfer between natural redox centers is generally engineered to be robust and resistant to mutational changes and thermal fluctuations, by using chains of redox centers connected by electron tunneling distances of 14 A or less. This assures that tunneling rates are faster than the typical millisecond bond-breaking at catalytic sites. Interprotein electron transfer addresses the potential problem of slow diffusion by designing attractive docking sites that permit a conformational search for short tunneling distances.     

Electrochemistry of heme-thiolate proteins

Heme-thiolate proteins (HTPs) play critical biological roles by catalyzing challenging chemical reactions. The ability of HTPs to selectively oxidize inert substrates under mild conditions has led to much research aimed at the development of useful in vitro oxidation technology. Very complex electron transfer machinery is required to support HTP chemistry, and electrochemical methods provide many of the needed components. The challenge is to find a system that has good electrode-enzyme electronic coupling that, in turn, would drive catalytic turnover at relatively high rates. Several systems reviewed herein have shown promise in experimental work on components that could be part of a molecular machine for the selective oxidation of organic substrates.     

Electron transfer in ferredoxin: are tunneling pathways evolutionarily conserved?

A theoretical study of electron transfer (ET) pathways in a recently crystallized Clostridium acidurici ferredoxin is reported. The electronic structure of the protein complex is treated at the semiempirical extended Hückel level, and the tunneling pathways are calculated with the rigorous quantum mechanical method of tunneling currents. The model predicts two pathways between the two [4Fe-4S] cubanes: a strong one running directly from Cys(14) to Cys(43) and a weaker one from Cys(14) via Ile(23) to Cys(18), whereas other amino acids do not play a significant role in the electron tunneling. The cysteine ligands conduct almost all of the current when Ile(23) is mutated to valine in silico, so that there is no appreciable change in the ET rate. The calculated value of the transfer matrix element is consistent with the experimentally determined rate of transfer. Results of the sequence analysis performed on this ferredoxin reveal that Ile(23) is a highly variable amino acid compared with the cubane-ligating cysteine amino acids, even though Ile(23) lies directly between the donor and acceptor complexes. We further argue that the homologous proteins with a [3Fe-4S] cofactor, which does not have one of the four cysteine ligands, use the same tunneling pathways as those in this ferredoxin, on the basis of the high homology as well as the absolute conservation of Cys(14) and Cys(43) which serve as the main tunneling conduit. Our results explain why mutation of amino acids around and between the donor and acceptor cubane clusters, including that of Ile(23), does not appreciably affect the rate of transfer and add support to the proposal that there exist evolutionarily conserved electron tunneling pathways in biological ET reactions.     

Mechanisms for regulating electron transfer in multi-centre redox proteins.

Protein-mediated electron transfer is a key process in nature. Many of the proteins involved in such electron transfers are complex and contain a number of redox-active cofactors. The very complexity of these multi-centre redox proteins has made it difficult to fully understand the various electron transfer events they catalyse. This is sometimes because the electron transfer steps themselves are gated or coupled to other processes such as proton transfer. However, with the molecular structures of many of these proteins now available it is possible to probe these electron transfer reactions at the molecular level. It is becoming apparent that many of these multi-centre redox proteins have rather subtle and elegant ways for regulating electron transfer. The purpose of this article is to illustrate how nature has used different approaches to control electron transfer in a number of different systems. Illustrative examples include: thermodynamic control of electron transfer in flavocytochromes b(2) and P450 BM3; a novel control mechanism involving calmodulin-binding-dependent electron transfer in neuronal nitric oxide synthase; the probable gating of electron transfer by ATP hydrolysis in nitrogenase; conformational gating of electron transfer in cytochrome cd(1); the regulation of electron transfer by protein dynamics in the cytochrome bc(1) complex; and finally the coupling of electron transfer to proton transfer in cytochrome c oxidase.     

Intramolecular electron transfer in [4Fe-4S] proteins: estimates of the reorganization energy and electronic coupling in Chromatium vinosum ferredoxin

The semi-classical electron transfer theory has been very successful in describing reactions occurring in biological systems, but the relevant parameters in the case of iron-sulfur proteins remain unknown. The recent discovery that 2[4Fe-4S] proteins homologous to Chromatium vinosum ferredoxin contain clusters with different reduction potentials now gives the opportunity to study the dependence of the intramolecular electron transfer rate between these clusters as a function of the driving force. This work shows how decreasing the reduction potential difference between the clusters by site-directed mutagenesis of C. vinosum ferredoxin modifies the rate of electron hopping between the two redox sites of the protein by measuring the line broadening of selected 1H NMR signals. Beside the shifts of the reduction potentials, no signs of large structural changes or of significant alterations of the intrinsic kinetic parameters among the different variants of C. vinosum ferredoxin have been found. A reorganization energy of less than 0.5 eV was deduced from the dependence of the electron transfer rates with the reduction potential difference. This small value is associated with a weak electronic coupling between the two closely spaced clusters. This set of parameters, determined for the first time in an iron-sulfur protein, may help to explain how efficient vectorial electron transfer occurs with a small driving force in the many enzymatic systems containing a 2[4Fe-4S] domain.     

Dramatic modulation of electron transfer in protein complexes by crosslinking.

The transfer of electrons between proteins is an essential step in biological energy production. Two protein redox partners are often artificially crosslinked to investigate the poorly understood mechanism by which they interact. To better understand the effect of crosslinking on electron transfer rates, we have constructed dimers of azurin by crosslinking the monomers. The measured electron exchange rates, combined with crystal structures of the dimers, demonstrate that the length of the linker can have a dramatic effect on the structure of the dimer and the electron transfer rate. The presence of ordered water molecules in the protein-protein interface may considerably influence the electronic coupling between redox centers.