Theory of long-distance electron transfer in nanoscale biological structures

Macromolecular biological systems accomplishing the 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 disorder 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.     

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.     

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.     

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.     

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.     

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.     

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.     

A Nonadiabatic Theory for Ultrafast Catalytic Electron Transfer: A Model for the Photosynthetic Reaction Center

A non-adiabatic theory of Electron Transfer (ET), which improves the standard theory near the inversion point and becomes equivalent to it far from the inversion point, is presented. The complex amplitudes of the electronic wavefunctions at different sites are used as Kramers variables for describing the quantum tunneling of the electron in the deformable potential generated by its environment (nonadiabaticity) which is modeled as a harmonic classical thermal bath. After exact elimination of the bath, the effective electron dynamics is described by a discrete nonlinear Schrödinger equation with norm preserving dissipative terms and a Langevin random force, with a frequency cut-off, due to the thermalized phonons. This theory reveals the existence of a specially interesting marginal case when the linear and nonlinear coefficients of a two electronic states system are appropriately tuned for forming a Coherent Electron-Phonon Oscillator (CEPO). An electron injected on one of the electronic states of a CEPO generates large amplitude charge oscillations (even at zero temperature) associated with coherent phonon oscillations and electronic level oscillations. This fluctuating electronic level may resonate with a third site which captures the electron so that Ultrafast Electron Transfer (UFET) becomes possible. Numerical results are shown where two weakly interacting sites, a donor and a catalyst, form a CEPO that triggers an UFET to an acceptor. Without a catalytic site, a very large energy barrier prevents any direct ET. This UFET is shown to have many qualitative features similar to those observed in the primary charge separation in photosynthetic reaction centers. We suggest that more generally, CEPO could be a paradigm for understanding many selective chemical reactions involving electron transfer in biosystems.     

Theoretical studies of proton-coupled electron transfer reactions

A theoretical formulation for proton-coupled electron transfer (PCET) is described. This theory allows the calculation of rates and kinetic isotope effects and provides insight into the underlying fundamental principles of PCET reactions. Applications of this theory to PCET reactions in iron bi-imidazoline complexes, oxoruthenium polypyridyl complexes, osmium-benzoquinone systems, amidinium-carboxylate salt bridges, DNA-acrylamide complexes, and ruthenium polypyridyl-tyrosine systems are summarized. The mechanistic insight gained from theoretical calculations on these model systems is relevant to PCET in more complex biological processes such as photosynthesis and respiration.     

Phenomenon of Quantum Entanglement in a System Composed of Two Minimal Protocells

The quantum mechanical self-assembly of two separate photoactive supramolecular systems with different photosynthetic centers was investigated by means of density functional theory methods. Quantum entangled energy transitions from one subsystem to the other and the assembly of logically controlled artificial minimal protocells were modeled. The systems studied were based on different photoactive sensitizer molecules covalently bonded to a non-canonical oxo-guanine::cytosine supramolecule with the precursor of a fatty acid (pFA) molecule attached via Van der Waals forces, all surrounded by water molecules. The electron correlation interactions responsible for the weak hydrogen and Van der Waals chemical bonds increased due to the addition of polar water solvent molecules. The distances between the separated sensitizer, nucleotide, pFA, and water molecules are comparable to Van der Waals and hydrogen bonding radii. As a result, the overall system becomes compressed, resulting in photo-excited electron tunneling from the sensitizer (bis(4-diphenylamine-2-phenyl)-squarine or 1,4-bis(N,N-dimethylamino)naphthalene) to the pFA molecules. Absorption spectra as well as electron transfer trajectories associated with the different excited states were calculated using time dependent density functional theory methods. The results allow separation of the quantum entangled photosynthetic transitions within the same minimal protocell and with the neighboring minimal protocell. The transferred electron is used to cleave a “waste” organic molecule resulting in the formation of the desired product. A two variable, quantum entangled AND logic gate was proposed, consisting of two input photoactive sensitizer molecules and one output (pFA molecule). It is proposed that a similar process might be applied for the destruction of tumor cancer cells or to yield building blocks in artificial cells.     

EPR characterization of genetically modified reaction centers of Rhodobacter capsulatus

Electron paramagnetic resonance (EPR) has been used to investigate the cation and triplet states of Rhodobacter capsulatus reaction centers (RCs) containing amino acid substitutions affecting the primary donor, monomeric bacteriochlorophylls (Bchls), and the photoactive bacteriopheophytin (Bphe). The broadened line width of the cation radical in HisM200----Leu and HisM200----Phe reaction centers, whose primary donor consists of a Bchl-Bphe heterodimer, indicates a highly asymmetric distribution of the unpaired electron over the heterodimer. A T0 polarized triplet state with reduced yield is observed in heterodimer-containing RCs. The zero field splitting parameters indicate that this triplet essentially resides on the Bchl half of the heterodimer. The cation and triplet states of reaction centers containing HisM200----Gln, HisL173----Gln, GluL104----Gln, or GluL104----Leu substitutions are similar to those observed in wild type. Oligonucleotide-mediated mutagenesis has been used to change the histidine residues that are positioned near the central Mg2+ ions of the reaction center monomeric bacteriochlorophylls. Reaction centers containing serine substitutions at M180 and L153 or a threonine substitution at L153 have unaltered pigment compositions and are photochemically active. The cation and triplet states of HisL153----Leu reaction centers are similar to those observed in wild type. Triplet energy transfer to carotenoid is not observed at 100 K in HisM180----Arg chromatophores. These results have important implications for the structural requirements of tetrapyrrole binding and for our understanding of the mechanisms of primary electron transfer in the reaction center.     

Electron transfer from the water oxidizing complex at cryogenic temperatures: the S1 to S2 step

We report the detection of a "split" electron paramagnetic resonance (EPR) signal during illumination of dark-adapted (S(1) state) oxygen-evolving photosystem II (PSII) membranes at <20 K. The characteristics of this signal indicate that it arises from an interaction between an organic radical and the Mn cluster of PSII. The broad radical signal decays in the dark following illumination either by back-reaction with Qa*- or by forward electron transfer from the Mn cluster. The forward electron transfer (either from illumination at 11 K followed by incubation in the dark at 77 K or by illumination at 77 K) results in the formation of a multiline signal similar to, but distinct from, other well-characterized multiline forms found in the S0 and S2 states. The relative yield of the "S1 split signal", which we provisionally assign to S1X*, where X could be YZ* or Car*+, and that of the 77 K multiline signal indicate a relationship between the two states. An approximate quantitation of the yield of these signals indicates that up to 40-50% of PSII centers can form the S1 split signal. Ethanol addition removes the ability to observe the S1 split signal, but the multiline signal is still formed at 77 K. The multiline forms with <700 nm light and is not affected by near-infrared (IR) light, showing that we are detecting electron transfer in centers not responsive to IR illumination. The results provide important new information about the mechanism of electron abstraction from the water oxidizing complex (WOC).     

Ultrafast transient absorption studies on Photosystem I reaction centers from Chlamydomonas reinhardtii. 1. A new interpretation of the energy trapping and early electron transfer steps in Photosystem I

The energy transfer and charge separation kinetics in core Photosystem I (PSI) particles of Chlamydomonas reinhardtii has been studied using ultrafast transient absorption in the femtosecond-to-nanosecond time range. Although the energy transfer processes in the antenna are found to be generally in good agreement with previous interpretations, we present evidence that the interpretation of the energy trapping and electron transfer processes in terms of both kinetics and mechanisms has to be revised substantially as compared to current interpretations in the literature. We resolved for the first time i), the transient difference spectrum for the excited reaction center state, and ii), the formation and decay of the primary radical pair and its intermediate spectrum directly from measurements on open PSI reaction centers. It is shown that the dominant energy trapping lifetime due to charge separation is only 6-9 ps, i.e., by a factor of 3 shorter than assumed so far. The spectrum of the first radical pair shows the expected strong bleaching band at 680 nm which decays again in the next electron transfer step. We show furthermore that the early electron transfer processes up to approximately 100 ps are more complex than assumed so far. Several possibilities are discussed for the intermediate redox states and their sequence which involve oxidation of P700 in the first electron transfer step, as assumed so far, or only in the second electron transfer step, which would represent a fundamental change from the presently assumed mechanism. To explain the data we favor the inclusion of an additional redox state in the electron transfer scheme. Thus we distinguish three different redox intermediates on the timescale up to 100 ps. At this level no final conclusion as to the exact mechanism and the nature of the intermediates can be drawn, however. From comparison of our data with fluorescence kinetics in the literature we also propose a reversible first charge separation step which has been excluded so far for open PSI reaction centers. For the first time an ultrafast 150-fs equilibration process, occurring among exciton states in the reaction center proper, upon direct excitation of the reaction center at 700 nm, has been resolved. Taken together the data call for a fundamental revision of the present understanding of the energy trapping and early electron transfer kinetics in the PSI reaction center. Due to the fact that it shows the fastest trapping time observed so far of any intact PSI particle, the PSI core of C. reinhardtii seems to be best suited to further characterize the electron transfer steps and mechanisms in the reaction center of PSI.     

Enhanced Electron Transfer by Unsaturated Fatty Acids and Superoxide Dismutase

We have previously shown that unsaturated fatty acids (UFA) facilitate electron transfer between iron centers such as ferrous iron and ferricytochrome C. Extending this concept to a more physiologic model of fatty acids associated with proteins, we find that electron transfer is also enhanced in this model. While investigating whether free superoxide was involved in this electron transfer, we discovered that superoxide dismutase (SOD) enchanced the electron transfer. While the mechanism of electron transfer is unknown, the above findings are consistent with UFA and SOD participating in membrane redox systems.