Molecular Basis for Directional Electron Transfer*

Biological macromolecules involved in electron transfer reactions display chains of closely packed redox cofactors when long distances must be bridged. This is a consequence of the need to maintain a rate of transfer compatible with metabolic activity in the framework of the exponential decay of electron tunneling with distance. In this work intermolecular electron transfer was studied in kinetic experiments performed with the small tetraheme cytochrome from Shewanella oneidensis MR-1 and from Shewanella frigidimarina NCIMB400 using non-physiological redox partners. This choice allowed the effect of specific recognition and docking to be eliminated from the measured rates. The results were analyzed with a kinetic model that uses the extensive thermodynamic characterization of these proteins reported in the literature to discriminate the kinetic contribution of each heme to the overall rate of electron transfer. This analysis shows that, in this redox chain that spans 23 Å, the kinetic properties of the individual hemes establish a functional specificity for each redox center. This functional specificity combined with the thermodynamic properties of these soluble proteins ensures directional electron flow within the cytochrome even outside of the context of a functioning respiratory chain.

Biological macromolecules involved in electron transfer reactions display chains of closely packed redox cofactors when long distances must be bridged. This is a consequence of the need to maintain a rate of transfer compatible with metabolic activity in the framework of the exponential decay of electron tunneling with distance. In this work intermolecular electron transfer was studied in kinetic experiments performed with the small tetraheme cytochrome from Shewanella oneidensis MR-1 and from Shewanella frigidimarina NCIMB400 using non-physiological redox partners. This choice allowed the effect of specific recognition and docking to be eliminated from the measured rates. The results were analyzed with a kinetic model that uses the extensive thermodynamic characterization of these proteins reported in the literature to discriminate the kinetic contribution of each heme to the overall rate of electron transfer. This analysis shows that, in this redox chain that spans 23 Å , the kinetic properties of the individual hemes establish a functional specificity for each redox center. This functional specificity combined with the thermodynamic properties of these soluble proteins ensures directional electron flow within the cytochrome even outside of the context of a functioning respiratory chain.
Shewanella are facultative anaerobic ␥-proteobacteria capable of reducing a multitude of organic and inorganic substrates, including soluble and insoluble metallic compounds containing iron, manganese, uranium, or chromium (1). Shewanella arouse widespread interest in the science and in the engineering communities due to their role in geological phenomena such as global weathering and formation of minerals, their possible application in bioremediation of contaminated environments polluted with heavy metals, and their biotechnological applications for energy production in microbial fuel cells (1)(2)(3).
The anaerobic respiratory flexibility found in these bacteria is associated with the presence of numerous multiheme cytochromes (4). One of the most abundant is the small tetraheme cytochrome (STC) 2 that has a 12-kDa molecular mass and contains four c-type hemes (5). Although the physiological role of STC in Shewanella oneidensis MR-1 (SoSTC) is still unknown, in S. frigidimarina NCIMB400 (SfSTC) it was shown to participate in iron respiration (6). The three-dimensional structure of SoSTC was determined for the reduced and oxidized states by x-ray crystallography (7), and recently the solution structure was solved for the reduced state of SfSTC (8). These studies showed that, despite the diversity found in the amino acid sequence of these cytochromes (64% identical), the architecture of their heme core is highly conserved with the hemes organized in a chain spanning 23 Å for the most distant heme irons (7,8). The determination of the structure of SoSTC led to the proposal that this protein may work as a nonspecific electron harvester (7). This proposal was refined by considering that hemes I-III would feed electrons to heme IV on the basis of the thermodynamic characterization of SoSTC at high pH (9). With the full thermodynamic characterization in the physiological pH range, specific roles for the hemes were proposed, with heme I serving as the electron entry gate and heme IV as the electron exit (10). A similar situation was found for SfSTC, but the roles of the hemes I and IV are exchanged (11). Nevertheless, functional aspects of the redox activity of these proteins remain unexplored: do the intrinsic redox properties of the hemes lead to functional specificity as proposed on the basis of the thermodynamic characterization, or will this specificity arise only upon interaction with physiological partners? To answer this question, kinetic studies of reduction and oxidation of SoSTC and SfSTC were performed using a non-physiological electron donor and acceptor to avoid physiological bias that may result from specific recognition and docking of partners.

EXPERIMENTAL PROCEDURES
Protein Sample-Tetraheme cytochromes were purified from the soluble fraction of Shewanella as previously described for SoSTC (10) and SfSTC (6). Stock solutions of SoSTC and SfSTC were degassed with cycles of vacuum and argon to remove dissolved oxygen. All sample manipulations were made inside an anaerobic chamber (M-Braun 150) containing Ͻ1 ppm oxygen. Dilutions to the desired concentration of protein were made in 100 mM Tris maleate buffer at different pH values. The actual concentration of the protein was determined after each experiment by UV-visible spectroscopy using ⑀ 552 nm ϭ 120 000 M Ϫ1 cm Ϫ1 for the reduced state. The pH of the samples was checked after each experiment.
The reducing kinetic experiments were performed with sodium dithionite, and the oxidizing experiments were performed with ferric-NTA. Sodium dithionite was recrystallized to give Ͼ95% pure material according to the method described in the literature (12), adapted to be performed inside the anaerobic chamber. The stock solution of ferric-NTA was prepared as described in the literature at pH 7.0 (13).
Solid sodium dithionite was added to degassed 5 mM Tris maleate buffer at pH 8.5 to give approximately the final desired concentration. The ionic strength of this buffer was set to 100 mM by addition of KCl. Stock solution of ferric-NTA was added to degassed 5 mM Tris maleate buffer with KCl to obtain a 100 mM ionic strength at pH 7.0, giving the final desired approximate concentration. The actual concentration of sodium dithionite and ferric-NTA was determined using ⑀ 314 nm ϭ 8000 M Ϫ1 cm Ϫ1 (14) and ⑀ 260 nm ϭ 6000 M Ϫ1 cm Ϫ1 (15), respectively.
Kinetic Experiments-Kinetic data were obtained using a stopped-flow instrument (SHU-61VX2 from TgK Scientific) placed inside the anaerobic chamber. Data were collected at 552 nm, and the temperature was maintained at 298 Ϯ 1 K using an external circulating bath.
For the reduction kinetic experiments the reference value for the optical density of the protein in the fully oxidized state was obtained by mixing the protein with potassium ferricyanide, and the reference value for the optical density in the fully reduced state was obtained from the final absorbance taken at effectively infinite time after each experiment. For the oxidation kinetic experiments the reference value for the optical density of the protein in the fully reduced state was obtained by mixing the protein with sodium dithionite, and the reference value for the optical density in the fully oxidized state was obtained from the final absorbance taken at effectively infinite time after each experiment.
Ferric-NTA speciates differently according to the solution pH. For this reason experiments were performed only at pH 7 where Ͼ90% of ferric-NTA is found in the form of FeOH-NTA (13). To perform rapid mixing kinetics with partially oxidized protein, oxygen was bubbled before the experiment to give the desired degree of oxidation.
The nature of the reducing agent was determined according to the method of Lambeth and Palmer (16), which showed that the reducing species for both STCs is the bisulfite radical (SO 2 . ). In these kinetic experiments the electron acceptor and donor chosen perform one-electron transfer steps, which is a requirement for the application of the kinetic model described below (17). Kinetic Analysis-Kinetic data obtained for the reduction of the two cytochromes at different pH values were normalized to have oxidized fraction versus time. The kinetic data obtained for the oxidation of both proteins were normalized to have reduced fraction versus time. The timescale was corrected to account for the dead time of the apparatus. At least two data sets for each experimental condition were averaged, to reduce electrical noise.
For each protein the experimental data of the reduction experiments were fitted simultaneously at all pH values to a kinetic model that allows the discrimination of the contribution of each redox center in the overall electron transfer process in multicenter redox proteins (17). For the case of the oxidation experiments for each protein, the data obtained for the fully reduced and partially oxidized conditions were fitted simultaneously to the kinetic model. The application of the kinetic model requires fast intramolecular electron transfer and slow intermolecular electron exchange, because only in these conditions is there thermodynamic re-equilibration within the protein between each of the sequential electron transfer steps.
NMR data show that these conditions are met by both STCs studied in this work at the typical concentration used for stopped-flow experiments (10,11). For STC, the complete diagram of redox microstates involves 16 protonated and 16 deprotonated microstates (Fig. 1). These are in fast equilibrium due to fast proton exchange, as deduced from NMR data (10,11). Upon reaction with the electron donor/acceptor these 32 microstates can be interconverted through 64 possible electron transfer microsteps. Fast equilibrium within microstates belonging to the same stage of oxidation (fast intramolecular electron exchange) leads to the collapse of this system to four sequential one-electron transfer steps, as presented in Fig. 1.
k I to k IV are the macroscopic rate constants of each sequential step and are set by the weighted average of the microscopic rate constants of all microsteps that participate in that macroscopic step. The weight is given by the relative fractional occupation of the microstates in each stage, which is known from the detailed thermodynamic characterization.
Each of these microscopic rate constants k i j is parsed into an intrinsic contribution of the heme that is being reduced (k i 0 ) and a contribution of the driving force of the particular step using an exponential term derived from Marcus theory (18) (Equation 2). The driving force arises from the difference between the reduction potential of the electron donor (e D ) and the reduction potential of the heme being reduced in that microstep (e i j ) in the reduction process. In the oxidation process the driving force arises from the difference between the reduction potential of the heme and the reduction potential of the electron acceptor (e A ). The reduction potential of the heme that is being reduced/ oxidized in each particular microstep is given by the thermodynamic properties of the proteins, which are known from the literature and include the redox-Bohr effect (10,11). Therefore, each individual heme is characterized by a reference rate constant, k i 0 , on the assumption that the reorganization energy () and structural factors are essentially constant upon reduction or oxidation of the protein. This is a reasonable assumption considering that the structures of SoSTC show very small redox linked modifications (7).
The reducing/oxidizing agent must be a single-electron donor/ acceptor to have one-electron transfer reactions. Simplification of the kinetic analysis is achieved by using excess of reducing/oxidizing agent, because irreversible electron transfer and pseudo-first order conditions are met giving rise to differential equations that have an analytical solution. The fit of the kinetic data were performed using the Nelder-Mead algorithm implemented in MATLAB (19).

RESULTS
The kinetic traces obtained by reduction of SoSTC and SfSTC with sodium dithionite show pH dependence for both STCs (Fig. 2). The kinetic traces obtained by oxidation of both proteins by ferric-NTA are presented in Fig. 3. Being limited to work at a single pH required that experiments were performed using samples with the cytochrome preequilibrated at two different levels of reduction. This way intermolecular equilibrium is established before the experiment starts, therefore, providing a starting point that depends on the thermodynamic properties of the hemes. This allows the contribution of the various hemes to be parsed in the absence of pH-dependent experiments. The fit of the experimental data to the kinetic model gives the reference rate constants for the hemes presented in Tables 1 and 2.
The reduction of both proteins is faster at low pH, which is in agreement with the increase in the driving force known from the detailed thermodynamic characterization of both STCs, which showed that the reduction potentials are less negative at lower pH (10,11). However, the effect of protonation on the redox properties of the hemes at low pH is insufficient to fully account for the reduction rates, with this effect more pronounced for SfSTC. This suggests that in the low end of the physiological pH range other factors that are not accounted by the model begin to have a significant contribution. For instance if the solution pH affects the electron transfer rates in ways not related with the change in driving force, such as changes that modify the access of the reducing agent without affecting significantly the reduction potentials of the hemes, this cannot be fit by the model. Nonetheless, the model captures well the trend of the kinetic traces for the reduction of both proteins in the  physiological pH range by fitting the four reference rate constants of the individual hemes.
In the case of oxidation, speciation of ferric-NTA posed a particular challenge. When several species of the redox partner co-exist, the kinetic trace is shaped by the summed contribution of the various partners. The good fit observed for both proteins using four reference rate constants for the hemes shows that the residual minor forms of ferric-NTA present at pH 7 had a negligible effect on the experimental data.
The reference rate constants are related with the microscopic rate constants of the individual redox transitions by an exponential term derived from Marcus theory (18), which accounts for the driving force associated with the electron transfer in each of these microsteps. Using the reference rate constants, the driving force for each transition, and the population fraction of each microscopic state, the contribution of each heme to each of the sequential macroscopic reduction and oxidation steps can be determined (Tables 3 and 4), showing that in both proteins one of the hemes clearly dominates the electron uptake and delivery processes.
In SoSTC heme I is the only heme that participates in the reduction of this protein, and the thermodynamic properties (10) show that it is the heme that presents the lowest reduction potential. Because there is fast intramolecular electron exchange inside the protein, the electrons that enter SoSTC through heme I are seamlessly distributed among the other hemes due to the favorable driving force.
The oxidation of SoSTC is also dominated by heme I, which is the first heme to be oxidized. This heme has the more negative potential and therefore the strongest driving force for oxidation by ferric-NTA. However, because heme I is more negative than the other hemes, this provides a small uphill step for draining the other electrons through this heme, which together with the significant exposure of heme IV provides the opportunity for its minor participation.
In SfSTC heme IV dominates the electron uptake and delivery process, with a small contribution from heme I. The minor contribution of this heme in the uptake of electrons arises from the combined effect of significant exposure (see below) and larger driving force than for heme IV. In this protein the reduction process occurs in a similar way to SoSTC, but in this case the electrons enter mainly through heme IV, also the heme with the lowest reduction potential (11). Just as with the reduction process, oxidation of SfSTC by ferric-NTA mirrors what was found for SoSTC with hemes I and IV exchanged.
The reduction and oxidation of these proteins via a specific heme is a consequence of the fact that intramolecular electron transfer is much faster than electron uptake from the donor. This allows each electron to re-equilibrate among the four hemes before the next one is received or donated. As a consequence, the redox state of each individual heme can be known at each point (Fig. 4).
Because the kinetic model accounts separately for the contribution of the driving force to the rates of electron transfer in the exponential term derived from Marcus theory, the intrinsic rate constants of the hemes depend on structural factors. For both STCs heme I and heme IV present the largest global accessibility to the reducing and oxidizing agents, whereas hemes II and III are less exposed ( Table 5). The present data indicate that accessibility plays a dominant role in setting the reference rate constants. In this context it is unlikely that physiological partners of STC will interact with these proteins via hemes II or III, because they will be of larger size than SO 2 . and ferric-NTA, and the rates of non-adiabatic electron transfer reactions decay exponentially with distance (20). The results of this work are in agreement with recently reported molecular dynamic simulations of electron transfer between STC and a solid iron surface, which showed faster electron transfer for hemes I and IV (21). One final aspect of the results that merits a comment is the observation that the reference rate constants obtained for SfSTC are slower than those for SoSTC. However, this difference does not correlate with the overall exposure. Even considering that different methods of structural characterization have

Heme IV
Step 1

TABLE 4
Fraction of electrons that leave SoSTC and SfSTC in each one-electron transfer step with ferric-NTA, calculated using the thermodynamic parameters (10, 11) and the reference rate constants presented in Table 2 SoSTC SfSTC been applied to these two proteins, another factor can come into play. SfSTC has more negatively charged residues and fewer positively charged residues than SoSTC. These are distributed throughout the protein and modify the overall electrostatics as can be appreciated by the lower isoelectric point of SfSTC versus that of SoSTC, pI 4.6 and 5.5, respectively. These differences contribute unfavorably toward the interaction of SfSTC with negatively charged electron donors or acceptors such as SO 2 . and ferric-NTA.
It is not clear why these two homologous proteins have a different functional specificity of the hemes. However, it should be mentioned that the genomic context of STC is different for the two organisms, which suggest different physiological roles. In S. oneidensis it is coded upstream of a b-type cytochrome, whereas in S. frigidimarina it is found downstream of an assimilatory nitrate reductase (5). Furthermore, although knock-out experiments of STC gene did not lead to a defective phenotype in iron reduction in S. oneidensis, in S. frigidimarina it was shown that STC participates in iron respiration (6).

DISCUSSION
Kinetic and thermodynamic information are essential to understand the molecular details of the electron transfer mechanisms in redox proteins. In the case of interactions with physiological partners, the rate-determining step may not be a true electron transfer process and dominated by recognition and binding events (22). In this context, the use of non-physiological small inorganic redox partners provides a window into the physicochemical factors that determine the reactivity of the various centers in redox proteins with multiple centers of the same nature.
The results obtained for SoSTC and SfSTC show a clear trend, where the heme with the lowest potential is the entry and exit gate for electrons, which are distributed by fast intramolecular electron exchange among the other hemes according to the thermodynamic properties. In both cytochromes the temporal evolution of the reduction curves for the individual hemes shows that heme III is the first heme to be reduced and the last to be oxidized, the heme that has the least negative reduction potential. However, it has been shown for other multicenter redox proteins that having a reduced center in the middle of a redox chain does not delay significantly electron transfer along the chain of cofactors (23). Reduction of heme III is coupled with protonation, and for SoSTC, this effect was shown to be a consequence of fractional contributions of several acid-base centers in the protein that cause a stronger effect in heme III, changing the electrostatic environment in the whole of the protein (10,11). Uptake of protons coupled to reduction may provide a way to maintain the electrostatic stability of such a small protein upon full reduction with four negative charges.
In both STCs, the heme that is responsible for the electron uptake is the last to become reduced. This way the electron donor always finds the accepting heme available to receive electrons until the protein is fully reduced, because the electrons are drained away from this heme, according to the redox properties. This is important in the context of the asymmetry of the intermolecular electron transfer reaction landscape previously identified for interacting redox partners (24). When meeting a partner, of the multiple possible docking conformations, only a small fraction is efficient for "forward" electron transfer. However, the correct conformation is very efficient for "back reaction" (24). Having the heme with the least driving force as the entry gate ensures that the received electrons will spontaneously move along the chain of hemes, therefore decreasing the  likelihood of back reactions. The fast intramolecular electron exchange ensures that this occurs before the arrival of the next redox partner, which is known from NMR data to be a slow process (10). In the case of oxidation the reverse situation is observed. The first heme to be oxidized is that with the strongest driving force, making the first oxidation step more favorable than any of the other steps. Therefore, the STCs appear to be designed to be easily charged (with electrons) but not so easily discharged.
Interestingly, this type of behavior was never reported previously in other multiheme cytochromes. In cytochromes c 3 from sulfate-reducing bacteria, which also contain four hemes and for which reduction kinetics were measured, there is no obvious specificity in electron uptake by a particular heme and several display significant contributions in receiving the electrons (25). Most likely, the three-dimensional structure is responsible for this different kinetic behavior. In STC the hemes are arranged in a chain spanning 23 Å (iron-iron distance) that forces an organized pathway for electron transfer, whereas in cytochrome c 3 the hemes are arranged in a globular manner, with all the hemes in close contact with each other (26). Furthermore, the STCs unlike the cytochrome c 3 do not display clearly distinct positive and negatively charged surface regions.
The present data analyzed in the context of the structure of both STCs and their detailed thermodynamic characterization, showed that in STC the heme chain allows an efficient electron uptake by a specific heme and electron flow through the chain of hemes in a unidirectional way, therefore preventing backflow. A respiratory chain is the appropriate place for implementation of such control measures of electron flow, because backflow of the electrons would lead to metabolic arrest. The periplasmic space of metal-respiring organisms such as Shewanella, which is crowded with multiple cytochromes, requires exquisite control of the electron flow to ensure that extracellular respiration occurs without spurious dissipation of the reducing power. Furthermore, oxidation is more efficient through the same heme as reduction, therefore enhancing the effect by making a nonspecific ternary complex less favorable.
The results reported here show how the interplay between the thermodynamic and the kinetic properties of the redox centers in STC lead to functional specificity and directional electron transfer. This occurs despite the absence of specific interactions with physiological partners, and outside of the context of a functioning respiratory chain. Being rooted in the fundamental thermodynamic and kinetic properties of the individual redox centers, these findings are likely to be of widespread relevance for multicenter redox proteins. They show how individual proteins, even if they are soluble, can contribute to set the directionality of the electron flow, by specific recognition and binding of redox partners close to the appropriate redox centers.
Despite these advances on the characterization of the exquisite control of the redox activity of multiheme cytochromes, the detailed characterization of the periplasmic redox network of metal-respiring organisms such as S. oneidensis MR-1 remains a work in progress. The results reported in this work show that the STC cytochromes are more than a simple conduit of electrons between their donor and acceptor, because specific properties of the centers are established even outside of the physiological context. Future work will focus on determining the degree to which the interaction with physiological partners modulates the detailed mechanisms of inter-protein electron transfer.