Theory of intermolecular electron transfer in nanoscale biological structures

Macromolecular biological systems performing directed electron transfer are nano-sized structures. The distance between carrier molecules (cofactors), which represent practically isolated electron localization centers, reaches tens of angstroms. The electron transfer theory based on the concept of delocalized electron states, which is conventionally used in biophysics, is unable to adequately interpret the results of concrete observations in many cases. On the basis of the theory of electronic transitions in the case of localized states, developed in the physics of disordered matter, a mechanism of long-distance electron transfer in biological systems is suggested. The molecular relaxation of the microenvironment of electron localization centers that accompanies the electron transfer process is also considered.     

Problems of the theory of electron transfer in biological systems

Based on comparative analysis, it is shown that the electron transfer theory traditionally used in biophysics is often unable to explain the electron transfer regularities observed in biological molecular systems. The data for seven electron transfer reactions (direct and reverse) that occur in bacterial photosynthetic reaction centers (mainly, purple bacteria Rhodobacter sphaeroides) have been analyzed. Conceivable reasons for the discrepancy between the theoretical and experimental data are discussed and some approaches to overcoming this contradiction are offered.     

Biological electron transfer: progress and future directions.

The rich diversity among bacterial cytochromes has played a key role in the development of our understanding of biological electron transfer. Although studies to date have allowed the elucidation of the contributions of driving force, electrostatics interactions and surface topology to electron transfer kinetics in collision-dependent reactions, much remains to be learned. Little is known about intramolecular and intracomplex electron transfer. Several factors controlling intramolecular and intracomplex electron transfer can be defined. These include driving force, the distance between redox centers, the relative orientation of prosthetic groups, the nature of the intervening media and the molecular dynamics within the electron transfer complex. However, at the present time, we have only a limited understanding of the contribution of these factors to electron transfer kinetics in biologically relevant systems. Nevertheless, a wide range of techniques are now available which should soon provide the information necessary to describe in molecular terms the mechanism of intramolecular and intracomplex electron transfer. Principal among these new approaches are site-directed mutagenesis and NMR spectroscopy.     

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.     

Recent progress in biological charge transfer: Theory and simulation

In this contribution, we discuss three recent developments in atomistic biological charge transfer theory. First, in the context of Marcus' classical theory of charge transfer, key quantities of the theory such as driving forces and reorganization enthalpies are now accessible by thermodynamic integration schemes within standard molecular dynamics simulations at high accuracy. Second, direct simulations of charge transfer enable the computation of fast charge transfer reaction rates without having to resort to Marcus' theory. Finally, exploring the electronic structure beyond that of hitherto presumed centers of localization helps to identify new stepping stones of charge transfer reactions. This article is part of a Special Issue entitled: 17th European Bioenergetics Conference (EBEC 2012).     

The development of molecular fluorescent switches

Molecular systems in which fluorescence switches between 'on' and 'off' states when driven by chemical stimuli can be designed according to a few principles. The photochemical mechanisms examined are photoinduced electron transfer, internal charge transfer and excimer formation, with emphasis on the first category. These designs open the way to sharp signalling of small chemical species that perform critical biological functions.     

Sequential and coherent long-range electron transfer close to resonance with intermediate bridge groups, and new perspectives for in situ scanning tunnelling microscopy of adsorbed metalloproteins

 Three-level electron transfer follows superexchange patterns when the intermediate electronic level is off-resonance with the donor and acceptor levels. Close to resonance, new patterns emerge where the intermediate level is temporarily populated in vibrationally coherent or incoherent modes. We discuss energy and distance relations associated with such electron transfer modes. These appear to accord with fast electron transfer in several chemical and biological systems. We also discuss some recent observations on in situ scanning tunnelling microscopy of metalloproteins and large transition metal complexes which enable, in principle, a distinction between superexchange, coherent, and sequential three-level electron transfer. Received: 9 November 1997 / Accepted 16 March 1998     

Thermodynamics of electron transfer in oxygenic photosynthetic reaction centers: a pulsed photoacoustic study of electron transfer in photosystem I reveals a similarity to bacterial reaction centers in both volume change and entropy

The thermodynamic properties of electron transfer in biological systems are far less known in comparison with that of their kinetics. In this paper the enthalpy and entropy of electron transfer in the purified photosystem I trimer complexes from Synechocystis sp. PCC 6803 have been studied, using pulsed time-resolved photoacoustics on the 1 micros time scale. The volume contraction of reaction centers of photosystem I, which results directly from the light-induced charge separation forming P(700+F(A)/F(B-) from the excited-state P700*, is determined to be -26 +/- 2 A3. The enthalpy of the above electron-transfer reaction is found to be -0.39 +/- 0.1 eV. Photoacoustic estimation of the quantum yield of photochemistry in the purified photosystem I trimer complex showed it to be close to unity. Taking the free energy of the above reaction as the difference of their redox potentials in situ allows us to calculate an apparent entropy change (TDeltaS) of +0.35 +/- 0.1 eV. These values of DeltaV and TDeltaS are similar to those of bacterial reaction centers. The unexpected sign of entropy of electron transfer is tentatively assigned, as in the bacterial case, to the escape of counterions from the surface of the particles. The apparent entropy change of electron transfer in biological system is significant and cannot be neglected.     

A mechanism stabilizing a long-lived charge-separated state of photosynthetic reaction centers frozen under intense illumination

It is experimentally shown that slow chilling of photosynthetic reaction centers from purple bacteria Rhodobacter sphaeroides to <230 K under intense illumination leads to appearance of long-lived chargeseparated states (P⁺Q _A ^? ). This longevity implies that the recombination is blocked or the charge-separated state is stabilized. The longevity effect is caused by structural relaxation of reaction centers to a new equilibrium state that diminishes the free energy difference of recombination. The possible mechanism of such relaxation involves orientation of the polar water molecules in the semiquinone local electrostatic field. Detailed analysis of the longevity effect has been carried out, and its outcome supports the idea that many electron transfer reactions in biological systems are non-equilibrium.     

Electron transfer between globular proteins. Evaluation of a matrix element

The dependence of the matrix element of the probability of interprotein electron transfer on the mutual orientation of the donor and acceptor centers and the distance between them was calculated. The calculations were made under the assumption that electron transfer proceeds mainly by a collective excitation of polaron nature, like a solvated electron state. The results obtained are consistent with experimental data and indicate the nonexponential behavior of this dependence in the case when the distance transfer is less than 20 A.     

Biological electron transfer

Many oxidoreductases are constructed from (a) local sites of strongly coupled substrate-redox cofactor partners participating in exchange of electron pairs, (b) electron pair/single electron transducing redox centers, and (c) nonadiabatic, long-distance, single-electron tunneling between weakly coupled redox centers. The latter is the subject of an expanding experimental program that seeks to manipulate, test, and apply the parameters of theory. New results from the photosynthetic reaction center protein confirm that the electronic-tunneling medium appears relatively homogeneous, with any variances evident having no impact on function, and that control of intraprotein rates and directional specificity rests on a combination of distance, free energy, and reorganization energy. Interprotein electron transfer between cytochromec and the reaction center and in lactate dehydrogenase, a typical oxidoreductase from yeast, are examined. Rates of interprotein electron transfer appear to follow intraprotein guidelines with the added essential provision of binding forces to bring the cofactors of the reacting proteins into proximity.     

Light-induced charge separation in ruthenium based triads - New variations on an old theme

Success with artificial photosynthesis requires control of the photoinduced electron transfer reactions leading to charge-separated states. In this review, some new ideas to optimize such charge-separated states in ruthenium(II) polypyridyl based three-component systems with respect to: (1) long lifetimes and (2) ability to store sufficient energy for catalytic water splitting, are presented. To form long-lived charge-separated states, a manganese complex as electron donor and potential catalyst for water oxidation has been used. The recombination reaction is unusually slow because it occurs deep down in the Marcus normal region as a consequence of the large bond reorganization following the manganese oxidation. For the creation of high energy charge-separated states, a strategy using bichromophoric systems is presented. By consecutive excitations of the two chromophores, the formation of charge-separated states that lie higher in energy than either of the two excited states could in theory be achieved, the first results of which will be discussed in this review.     

The role of tunneling in enzyme catalysis of C-H activation

Recent data from studies of enzyme catalyzed hydrogen transfer reactions implicate a new theoretical context in which to understand C-H activation. This is much closer to the Marcus theory of electron transfer, in that environmental factors influence the probability of effective wave function overlap from donor to acceptor atoms. The larger size of hydrogen and the availability of three isotopes (H, D and T) introduce a dimension to the kinetic analysis that is not available for electron transfer. This concerns the role of gating between donor and acceptor atoms, in particular whether the system in question is able to tune distance between reactants to achieve maximal tunneling efficiency. Analysis of enzyme systems is providing increasing evidence of a role for active site residues in optimizing the inter-nuclear distance for nuclear tunneling. The ease with which this optimization can be perturbed, through site-specific mutagenesis or an alteration in reaction conditions, is also readily apparent from an analysis of the changes in the temperature dependence of hydrogen isotope effects.     

The role of tunneling in enzyme catalysis of C-H activation

Recent data from studies of enzyme catalyzed hydrogen transfer reactions implicate a new theoretical context in which to understand C-H activation. This is much closer to the Marcus theory of electron transfer, in that environmental factors influence the probability of effective wave function overlap from donor to acceptor atoms. The larger size of hydrogen and the availability of three isotopes (H, D and T) introduce a dimension to the kinetic analysis that is not available for electron transfer. This concerns the role of gating between donor and acceptor atoms, in particular whether the system in question is able to tune distance between reactants to achieve maximal tunneling efficiency. Analysis of enzyme systems is providing increasing evidence of a role for active site residues in optimizing the inter-nuclear distance for nuclear tunneling. The ease with which this optimization can be perturbed, through site-specific mutagenesis or an alteration in reaction conditions, is also readily apparent from an analysis of the changes in the temperature dependence of hydrogen isotope effects.     

Coupled motions direct electrons along human microsomal P450 Chains

Protein domain motion is often implicated in biological electron transfer, but the general significance of motion is not clear. Motion has been implicated in the transfer of electrons from human cytochrome P450 reductase (CPR) to all microsomal cytochrome P450s (CYPs). Our hypothesis is that tight coupling of motion with enzyme chemistry can signal "ready and waiting" states for electron transfer from CPR to downstream CYPs and support vectorial electron transfer across complex redox chains. We developed a novel approach to study the time-dependence of dynamical change during catalysis that reports on the changing conformational states of CPR. FRET was linked to stopped-flow studies of electron transfer in CPR that contains donor-acceptor fluorophores on the enzyme surface. Open and closed states of CPR were correlated with key steps in the catalytic cycle which demonstrated how redox chemistry and NADPH binding drive successive opening and closing of the enzyme. Specifically, we provide evidence that reduction of the flavin moieties in CPR induces CPR opening, whereas ligand binding induces CPR closing. A dynamic reaction cycle was created in which CPR optimizes internal electron transfer between flavin cofactors by adopting closed states and signals "ready and waiting" conformations to partner CYP enzymes by adopting more open states. This complex, temporal control of enzyme motion is used to catalyze directional electron transfer from NADPH→FAD→FMN→heme, thereby facilitating all microsomal P450-catalysed reactions. Motions critical to the broader biological functions of CPR are tightly coupled to enzyme chemistry in the human NADPH-CPR-CYP redox chain. That redox chemistry alone is sufficient to drive functionally necessary, large-scale conformational change is remarkable. Rather than relying on stochastic conformational sampling, our study highlights a need for tight coupling of motion to enzyme chemistry to give vectorial electron transfer along complex redox chains.     

Electron transfer between globular proteins. Dependence of the rate of transfer on distance

Based on the assumption that electron transfer between globular proteins occurs by a collective excitation of polaron type, the dependence of the rate of this process on the distance between the donor and acceptor centers with regard to their detailed electron structure was calculated. The electron structure of the heme was calculated by the quantum-chemical MNDO-PM3 method. The results were compared with experimental data on interprotein and intraglobular electron transfer. It is shown that, in the framework of this model, the electron transfer is not exponential and does not require a particular transfer pathway since the whole protein macromolecule is involved in the formation of the electron excited state.     

Quantitation of the rapid electron donors to P700, the functional plastoquinone pool, and the ratio of the photosystems in spinach chloroplasts

Recent studies of chloroplast architecture have emphasized the segregation of photosystem I and photosystem II in different regions of the lamellar membrane. The apparent localization of photosystem II reaction centers in regions of membrane appression and of photosystem I reaction centers in regions exposed to the chloroplast stroma has focused attention on the intervening electron carriers, carriers which must be present to catalyze electron transfer between such spatially separated reaction sites. Information regarding the stoichiometries of these intermediate carriers is essential to an understanding of the processes that work together to establish the mechanism and to determine the rate of the overall process. We have reinvestigated the numbers of photosystem I and photosystem II reaction centers, the numbers of intervening cytochrome b6/f complexes, and the numbers of molecules of the relatively mobile electron carriers plastoquinone and plastocyanin that are actively involved in electron transfer. Our investigations were based on a new experimental technique made possible by the use of a modified indophenol dye, methyl purple, the reduction of which provides a particularly sensitive and accurate measure of electron transfer. Using this dye, which accepts electrons exclusively from photosystem I, it was possible to drain electrons from each of the carriers. Thus, by manipulation of the redox condition of the various carriers and through the use of specific inhibitors we could measure the electron storage capacity of each carrier in turn. We conclude that the ratio of photosystem I reaction centers to cytochrome b6/f complexes to photosystem II reaction centers is very nearly 1:1:1. The pool of rapid donors of electrons to P700 includes not only the 2 reducing equivalents stored in the cytochrome b6/f complex but also those stored in slightly more than 2 molecules of plastocyanin per P700. More slowly available are the electrons from about 6 plastoquinol molecules per P700.     

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.     

Catalysis and electron transfer in protein crystals: the binary and ternary complexes of methylamine dehydrogenase with electron acceptors

Polarized absorption microspectrophotometry has been used to detect catalysis and intermolecular electron transfer in single crystals of two multiprotein complexes: (1) the binary complex between Paracoccus denitrificans methylamine dehydrogenase, which contains tryptophan-tryptophylquinone (TTQ) as a cofactor, and its redox partner, the blue copper protein amicyanin; (2) the ternary complex between the same two proteins and cytochrome c-551i. Continuous wave electron paramagnetic resonance has been used to compare the state of copper in polycrystalline powders of the two systems. While catalysis and intermolecular electron transfer from reduced TTQ to copper are too fast to be accessible to our measurements, heme reduction occurs over a period of several minutes. The observed rate constant is about four orders of magnitude lower than in solution. The analysis of the temperature dependence of this apparent constant provides values for the parameters H(AB), related to electronic coupling between the two centers, and lambda, the reorganizational energy, that are compatible with electron transfer being the rate-determining step. From these parameters and the known distance between copper and heme, it is possible to calculate the parameter beta, which depends on the nature of the intervening medium, obtaining a value typical of electron transfer across a protein matrix. These findings suggest that the ternary complex in solution might achieve a higher efficiency than the rigid crystal structure thanks to an as yet unidentified role of protein dynamics.