The Reorganization Energy in Cytochrome c is ... - ACS Publications

LETTER pubs.acs.org/JPCL

The Reorganization Energy in Cytochrome c is Controlled by the Accessibility of the Heme to the Solvent Carlo Augusto Bortolotti,*,† Magdalena E. Siwko,‡,§ Elena Castellini,† Antonio Ranieri,† Marco Sola,† and Stefano Corni*,§ †

Department of Chemistry, University of Modena and Reggio Emilia, via Campi 183, 41125, Modena, Italy Department of Physics, University of Modena and Reggio Emilia, via Campi 213/A, 41125, Modena, Italy § Center S3, Institute of Nanoscience - CNR, Modena, Italy ‡

bS Supporting Information ABSTRACT: Elucidation of the molecular determinants of the reorganization energy λ is central to the understanding of fundamental biological processes based on energy transduction pathways. Here, we use a combined experimental/theoretical approach to electrochemically determine the reorganization energy for a number of cytochrome c variants and compute structure-related properties relevant to the kinetics of the electron transfer process through molecular dynamics simulations. We find that the exposure of the heme group to solvent controls the reorganization energy of the investigated proteins. Therefore, fine-tuning of the kinetics of the electron transfer process can be achieved through modulation of the accessibility of the iron to the surrounding water. Our findings lead the way for a new strategy for the design of protein-based bioelectronic materials, requiring fast and efficient electron transfer. SECTION: Biophysical Chemistry

E

lectron transfer (ET) reactions are key events in the energy transduction pathways in living organisms, where they play a central role in a variety of fundamental biological processes, such as photosynthesis and respiration.1,2 The rate of a nonadiabatic ET reaction can be expressed, according to the semiclassical Marcus theory,3 as kET ¼

2 2 2π HDA 0 pffiffiffiffiffiffiffiffiffiffiffiffiffiffieðΔG þ λÞ =4λRT p 4πλRT

ð1Þ

In the past years, much effort2,49 has been devoted to elucidating the role of the intervening protein medium in determining the electronic coupling matrix element between the electronic states of the reactants and the products, HDA. Nevertheless, the rate of the ET process also depends on two other parameters: the free energy of the ET reaction ΔG0 and the reorganization energy, λ, which corresponds to the energy needed for the reactants to move from the equilibrium reactant geometry to the equilibrium product geometry, without transferring electrons.10 Although different experimental approaches2,11 and theoretical frameworks1218 have been employed to measure and calculate values for different redox species, the molecular determinants of the reorganization energy are still unclear and subject to extensive debate. Elucidating the role of both protein and solvent in tuning the rate of ET reactions is fundamental not only for a deeper understanding of biological processes, but also for improving the design and production of bioelectronic devices, whose performances heavily rely on the rate with which electrons move in and out the immobilized r 2011 American Chemical Society

biomolecule.11,1922 The total reorganization energy for an ET reaction involving a metalloprotein includes contributions from the active-site, the surrounding protein matrix and the solvent. The first quantity is usually referred to as inner-sphere reorganization energy (λin), which is related mainly to the geometrical rearrangement of the active site that receives/donates the electron. The sum of the other two terms yields the outer-sphere reorganization energy (λout), which takes into account the changes in the polarization of the protein scaffold and the solvent upon reduction/oxidation.3 Throughout evolution, proteins have optimized mechanisms to reduce both inner- and outer-sphere contributions, respectively, by constraining the coordination geometry and the protein matrix surrounding the metal site, which is also made inaccessible to solvent.2,15 The relative weight of the inner- and outer-sphere terms in determining the reorganization energy is still an open question. In this work, we used a combined experimental and theoretical approach to evaluate the effects of solvent access into the heme crevice on the reorganization energy of cytochrome c (cytc). In particular, we electrochemically determined the ET rate constant and the reorganization energy for the heterogeneous ET reaction for wild-type (WT) cytc and compared them to those for single and multiple Lys-to-Ala mutants involving surface-exposed charged Received: June 1, 2011 Accepted: June 30, 2011 Published: June 30, 2011 1761

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Figure 1. Three-dimensional structure of cytochrome c. Molecular surface is represented in transparent gray and is superimposed to the cartoon representation. Lysine residues 72, 73, and 79 are colored in red. The heme group and the iron axial ligands (His18 and Met80) are displayed as sticks. The model was prepared using the VMD software.23

residues, namely, K72A, K79A, K72A/K79A, and K72A/K73A/ K79A variants (see Figure 1). We then used molecular dynamics (MD) simulations to evaluate the effects of mutations on the protein structure and to discuss the main contributions to the reorganization free energy. Moreover, through such MD simulations, we could take into consideration the dynamic character of proteinsolvent interactions, which are known to be central for a deep understanding of the structure/function relationships.10,24,25 This investigation, which focuses on the effect of single point mutations on the whole protein structure and properties, would also help addressing the question15 of whether reorganization energy is a local or collective effect, namely, whether λ is contributed mainly by a few residues or is the result of an overall rearrangements of the protein structure. We observe that reorganization energy is correlated with the solvent accessibility of the heme group, and that the access of water to the prosthetic group is modulated by mutations in a complex way, that cannot be predicted by local effects of mutations only. The three lysine residues subjected to mutation are involved in the interaction of cytc with biological partners2628 and serve as heme iron ligands at high pH in the so-called alkaline transition, which severely affects the ET process.29 Moreover, mutation of positively charged lysines with smaller, uncharged and hydrophobic alanines would affect the repulsive interactions on the surface along with the surface electrostatic potential, which is known to modulate the ET process through redox state-dependent changes in the interaction with the solvent.17,30 Therefore, these mutations are expected to induce changes in the overall packing of the protein matrix and in the accessibility of the heme group to solvent. The typical voltammetric response of freely diffusing WT yeast iso-1-cytochrome c contains the one-electron signal corresponding to the heme iron reduction/oxidation process (Figure 2). Similar responses were obtained for all the Lys to Ala variants under the same conditions (data not shown). The heterogeneous ET constant ks for WT and mutated cytc were determined with the Nicholson method.31 The ks values at 20 °C are listed in Table 1. Compared to WT, mutants invariably feature an increase in ks, which is more pronounced for the double and triple mutants. The changes in ks do not correlate with changes in overall protein charge. This is not surprising, since the kinetic constant for ET is a complex parameter, which is composed by a pre-exponential factor and an enthalpic activation term. In order to relate the

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Figure 2. Cyclic voltammogram for WT cytochrome c. Cyclic voltammogram for WT recombinant untrimethylated C102T Saccharomyces cerevisiae iso-1-cytochrome c on a 4-mercaptopyridine-modified gold electrode in 10 mM phosphate buffer and 5 mM sodium perchlorate, pH 6. Scan rate = 0.05 V s1, T = 298 K.

changes in the ET kinetics to molecular determinants, one has to focus separately on one of the terms composing the overall kinetic constant. By determining ks at different temperatures and using the Arrhenius equation, the activation enthalpies (ΔH#) for all the species can be determined. Assuming that the contribution of the activation entropy to the overall ΔG# is negligible,32,33 the reorganization energy λ can be calculated (Table 1). ΔH# further decreases for the double mutant K72A/K79A; the additional mutation in position 73 leading from double to triple variant has a small, if any, effect on the kinetics of the ET process. These results show that changes in the surface charges close to the heme group affect the reorganization energy of the protein to a larger extent than the redox potential. Since the dominant factor in the reorganization energy is thought to be the outer sphere term (λout), mainly contributed by the solvent,2,17 it is conceivable that mutations affect protein solvation and heme exposure to solvent to different extents. Since neither X-ray nor NMR structural data for the investigated mutants are available, MD simulations were carried out to investigate the effects of the substitutions on the protein structure. Although the overall folding of the protein was not perturbed by Lys to Ala substitutions, small but significant rearrangements of the Ω-loop spanning residues 71 to 85 could be detected during the MD run. To prove the reliability of our MD simulations, we calculated the outer-sphere reorganization energy lambda for WT, K79A, K72A, K72A/K79A, K72A/K73A/K79A and compared it to the experimental values. Previous works addressed the problem of calculating the reorganization energies of proteins from classical MD simulations.1214,34 In these works, the outersphere reorganization energy was evaluated by different approaches (linear response, energy gap fluctuations, thermodynamics integrations). We also used one of these methods (energy gap fluctuations) to calculate λout. For the inner-sphere reorganization energy, λin, a quantum mechanical approach is deemed necessary.14,35 Here, we compare mutants with a conserved heme iron axial ligation, therefore λin is not expected to change significantly. Therefore, this contribution is not considered further. Nevertheless, it is worth recalling that interesting structural effects in the heme have been revealed by high-level calculations (see ref 36 1762

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Table 1. Experimental and Calculated Parameters for WT Cytochrome c from Yeast and Its Lys to Ala Mutantsa E0,I (V)b,c,d

ks (cm s1)d,e

ΔH# (kJ/mol)f

λ (eV)f

SASA (Å2)g

Calc. λout (eV)g

WT

0.260

0.0083

11.96

0.48

57.4 (4.8)

0.733 (0.055)

K79A

0.264

0.0092

11.63

0.47

79.8 (6.6)

0.801 (0.041)

K72A

0.251

0.0091

11.75

0.47

88.1 (7.5)

0.713 (0.077)

K72A/K79A

0.263

0.0139

9.73

0.39

61.4 (2.5)

0.623 (0.022)

K72A/K73A/K79A

0.264

0.0137

10.46

0.42

73.5 (5.7)

0.720 (0.026)

species

a

Values were obtained in 10 mM phosphate buffer, 5 mM sodium perchlorate, pH 6 on a gold electrode modified with 4-mercapto-pyridine. b Average 0 error on E0 is (0.002 V. c From ref 29. d At 20 °C. e Estimated error is 4%. f Estimated error is 8%. g Estimated error is given in brackets.

Figure 3. Experimental versus theoretical reorganization energy. Plot of the electrochemically determined values of the reorganization energy λ versus outer-sphere reorganization energy values, λout, calculated from MD simulations. The solid line is the linear regression between the data points.

and refs within). We remark that our aim here is not a detailed computational investigation of λout, which would require more refined calculations, but a consistency check on the capability of the simulations to reproduce experimental trends. The calculated λout are larger than the experimental values (Table1), but the correlation of the two data sets is meaningful (Figure 3). For WT, the calculated λout agrees with a previous estimate obtained with a similar computational setup.12 The larger λout values compared to experimental λ are likely the consequence of the nonpolarizable force field used in the calculations, which was recently proposed to introduce some overestimation in the reorganization energies values.15 Moreover, the experimental system involves ET to an electrode, that can further decrease λout with respect to the ET in solution.16 It is also possible that neglecting the contribution of the electronic coupling matrix element HDA in the experimental determination of λ introduces a systematic underestimation of the reorganization energy.37 Therefore, these calculations indicate that the present MD simulations can reliably be exploited to evaluate meaningful physicochemical properties of interest for the species under investigations. Among these, we focused on the accessibility of the heme group to solvent. Moreover, this observation further strengthens the key role of λout on the overall reorganization energy. The calculated solvent accessible surface area (SASA) values resulting from the MD simulations are listed in Table 1. Single mutants K79A and K72A show increased SASA values compared

Figure 4. Experimental λ versus calculated SASA electrochemically determined values for total reorganization energy λ are plotted against SASA restricted to the heme region, calculated from MD simulations. The solid line is the linear regression between the four mutants.

to WT. The result for K79A is not surprising, as Lys79 is placed on the rim of the heme cleft, therefore mutation to Ala conceivably favors water access to the heme center. On the other hand, the behavior of K72A is puzzling, as Lys72 is located farther from the heme pocket. However, careful inspection of the MD trajectories reveals that in both cases the structural changes upon mutation are not limited to local events (e.g., breaking of a single H-bond), but they rather result from a slight but significant rearrangement of the entire Ω-loop regions of the protein. Both double and triple mutants show a marked decrease in the calculated SASA compared to single mutants. It is likely that double and triple mutations lift the steric hindrance of the aminoacidic side chain and the electrostatic repulsions, resulting in a tighter protein packing and a decrease in the SASA value for both species. Most notably, we found that the reorganization energies λ obtained electrochemically and the calculated SASA for this protein series are correlated (Figure 4). For the four investigated mutants, the total reorganization energy linearly increases with increasing exposure of the cofactor to solvent. The analysis of the average number of water molecules neighboring heme for the four mutants provides the same picture (see Figure 1 in the Supporting Information). This finding sustains the recent theory-based investigation on the key role played by solvent accessibility to the prosthetic group on the ET kinetics of heme proteins.15 The data point for WT cytc is out of the correlation. The experimental λ is almost as high as that of K72A and K79A species, while calculations indicate that its heme group is much less exposed to solvent. The 1763

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reason for this discrepancy is not obvious; nevertheless, one could hypothesize that the electrostatic interaction between the side chains of residues 72 and 79 affects the fashion with which the SASA influences the reorganization energy. Indeed, for all the mutants considered here, the long-range repulsion between 72 and 79 is turned off by substitution of one or both lysines. Visual inspection of the MD trajectories allowed identifying a few structural differences between the mutants that are related to solvent accessibility: the mutation K79A remove a bulky side chain (that of Lys) placed within the heme crevice, which results in improved solvent accessibility, the loop portion between residues Ser40 and Tyr48 appears to be less tight in the single mutants than in the double and the triple ones, leaving sometimes the possibility to the solvent to access heme on that side. The basic determinants of these difference (such as long-range electrostatic repulsion between positive amino acids or cooperative changes in the hydrogen bond network) could not be identified unambiguously. In conclusion, this work brings to light a relationship between a single structural property (the SASA of the heme group) and a complex, functional parameter (the reorganization energy for ET). This would also offer a tool fine-tuning the reorganization energy of a heme protein by designing point mutations that modulate the solvent accessibility of the prosthetic center. This approach, which is definitely less time-consuming and more straightforward than the enhancement of the ET rate by modifying the ET pathways, could be very useful for biomolecular electronics applications, in which the regulation of the ET kinetics is crucial to optimize the performance of the devices.

’ EXPERIMENTAL SECTION Experimental Methods. WT recombinant untrimethylated Saccharomyces cerevisiae iso-1-cytochrome c and its variants (K72A, K79A, K72A/K79A, and K72A/K73A/K79A) were expressed in Escherichia coli and purified following the procedure described elsewhere.29 Electrochemical experiments were carried out at different scan rates (0.025 V s1) using a cell for small volume samples (0.5 mL) under argon. A 1 mm-diameter polycrystalline gold wire was used as a working electrode, and a Pt ring (A = 1 cm2) and a saturated calomel electrode (SCE) were used as counter and reference electrodes, respectively. The electric contact between the SCE and the working solution was obtained with a Vycor set. The electrode surface was modified by dipping the polished electrode into a 1 mM solution of 4-mercaptopyridine for 2 min and then rinsing it with nanopure water. Sodium perchlorate (5 mM) was used as the base electrolyte. All the redox potentials reported here are referred to the standard hydrogen electrode (SHE). The Nicholson method was used to determine the ET rate constant ks, assuming the charge transfer coefficient R = 0.5 and the number of the electrons n = 1 for a monoelectronic process.31 The activation enthalpy ΔH# was obtained using the Arrhenius equation #

ks ¼ A0 eΔH =RT

ð2Þ

namely, from the slope of the ln ks versus 1/T. We then assumed that the contribution of the entropy of activation to the ΔG# of the ET is negligibly small, therefore ΔH# ≈ ΔG#.38,33 The reorganization energy λ for ET of the different cytochrome c species was then estimated using Marcus theory, i.e., ΔG# = λ/4.39 Computational Methods. As the starting point of the MD simulations, the structure of the yeast iso-1-cytochrome c (PDB id code:

1YCC, named cytc) was used, suitably mutated for K79A, K72A, K72A/K79A, and K72A/K73A/K79A. The OPLS-AA force field was used to describe the protein. The atom types and the charges of the porphirin, coordinating Met and His, and Cys were obtained from the Charmm force field40 and dihedral angles for the HemeDiOxy-residue.41 The systems were prepared as follows: After the energy minimization in vacuum, the structures were solvated with about 8900 SPC water molecules such that the distance between the protein and the wall was at least 0.12 nm. The final size of the box was 6.6  6.6  6.6 nm3. The simulations were performed at pH 7, which gives total charge on the protein equal to +5. This charge was neutralized with chloride ions distributed randomly in the box replacing five SPC waters. Energy minimization was performed again, and it was followed by a short MD simulation (300 ps) with position restraints on the protein part to relax the solvent. After that, the unrestrained MD simulation of 300 ps was performed. After equilibration, the production run simulations were performed for 100 ns. Further details on the simulations, and the descriptions of the calculation of λout and of SASA are given in the Supporting Information.

’ ASSOCIATED CONTENT

bS

Supporting Information. Description of the electrochemical setup, simulation details, analysis of number of water molecules neighboring heme, and further details on electrochemical results. This material is available free of charge via the Internet at the http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] (C.A.B); stefano. [email protected] (S.C.).

’ ACKNOWLEDGMENT M.E.S. and S.C. thank IIT under the Seed project MOPROSURF and MIUR under the FIRB project ITALNANONET. M. E.S. also acknowledges support from PRIN/COFIN contract 20087NX9Y7. ’ REFERENCES (1) Moser, C. C.; Keske, J. M.; Warncke, K.; Farid, R. S.; Dutton, P. L. Nature of Biological Electron Transfer. Nature 1992, 355, 796–802. (2) Gray, H. B.; Winkler, J. R. Electron Tunneling Through Proteins. Q. Rev. Biophys. 2003, 36, 341–372. (3) Marcus, R.; Sutin, N. Electron Transfer in Chemistry and Biology. Biochem. Biophys. Acta, Bioenerg. 1985, 811, 265–322. (4) Karpishin, T. B.; Grinstaff, M. W.; Komar-Panicucci, S.; McLendon, G.; Gray, H. B. Electron Transfer in Cytochrome c Depends upon the Structure of the Intervening Medium. Structure 1994, 2, 415–422. (5) Casimiro, D. R.; Wong, L.; Con, J. L.; Zewert, T. E.; Richards, J. H.; Chang, I. J. Y.; Winkler, J. R.; Gray, H. B. Electron Transfer in Ruthenium/Zinc Electron Transfer in Ruthenium/Zinc Porphyrin Derivatives of Recombinant Human Myoglobins. Analysis of Tunneling Pathways in Myoglobin and Cytochrome c. J. Am. Chem. Soc. 1993, 115, 1485–1489. (6) Jones, M. L.; Kurnikov, I. V.; Beratan, D. N. The Nature of Tunneling Pathway and Average Packing Density Models for ProteinMediated Electron Transfer. J. Phys. Chem. A 2002, 106, 2002–2006. (7) Page, C. C.; Moser, C. C.; Chen, X.; Dutton, P. L. Natural Engineering Principles of Electron Tunnelling in Biological Oxidation Reduction. Nature 1999, 402, 47–52. 1764

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The Journal of Physical Chemistry Letters (8) Alessandrini, A.; Corni, S.; Facci, P. Unravelling Single Metalloprotein Electron Transfer by Scanning Probe Techniques. Phys. Chem. Chem. Phys. 2006, 8, 4383–4397. (9) Beratan, D. N.; Betts, J. N.; Onuchic, J. N. Tunneling Pathway and Redox-State-Dependent Electronic Couplings at Nearly Fixed Distance in Electron Transfer Proteins. J. Phys. Chem. 1992, 96, 2852–2855. (10) Bendall, D. Protein Electron Transfer; BIOS Scientific Publisher Ltd: Oxford, U.K., 1996. (11) Murgida, D. H.; Hildebrandt, P. Electrostatic-Field Dependent Activation Energies Modulate Electron Transfer of Cytochrome c. J. Phys. Chem. B 2002, 106, 12814–12819. (12) Simonson, T. Gaussian Fluctuations and Linear Response in an Electron Transfer Protein. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 6544–6549. (13) Muegge, I.; Qi, P. X.; Wand, A. J.; Chu, Z. T.; Warshel, A. The Reorganization Energy of Cytochrome c Revisited. J. Phys. Chem. B 1997, 101, 825–836. (14) Blumberger, J.; Klein, M. L. Reorganization Free Energies for Long-Range Electron Transfer in a Porphyrin-Binding Four-Helix Bundle Protein. J. Am. Chem. Soc. 2006, 128, 13854–13867. (15) Tipmanee, V.; Oberhofer, H.; Park, M.; Kim, K.; Blumberger, J. Prediction of Reorganization Free Energies for Biological Electron Transfer: A Comparative Study of Ru-Modified Cytochromes and a 4-Helix Bundle Protein. J. Am. Chem. Soc. 2010, 132, 17032–17040. (16) Corni, S. The Reorganization Energy of Azurin in Bulk Solution and in the Electrochemical Scanning Tunneling Microscopy Setup. J. Phys. Chem. B 2005, 109, 3423–3430. (17) Cascella, M.; Magistrato, A.; Tavernelli, I.; Carloni, P.; Rothlisberger, U. Role of Protein Frame and Solvent for the Redox Properties of Azurin from Pseudomonas aeruginosa. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 19641–19646. (18) Skourtis, S. S.; Waldeck, D. H.; Beratan, D. N. Fluctuations in Biological and Bioinspired Electron-Transfer Reactions. Annu. Rev. Phys. Chem. 2010, 61, 461–485. (19) Davidson, V. L. Protein Control of True, Gated, and Coupled Electron Transfer Reactions. Acc. Chem. Res. 2007, 41, 730–738. (20) Alvarez-Paggi, D.; Martn, D. F.; DeBiase, P. M.; Hildebrandt, P.; Mart, M. A.; Murgida, D. H. Molecular Basis of Coupled Protein and Electron Transfer Dynamics of Cytochrome c in Biomimetic Complexes. J. Am. Chem. Soc. 2010, 132, 5769–5778. (21) Willner, I.; Katz, E. Integration of Layered Redox Proteins and Conductive Supports for Bioelectronic Applications. Angew. Chem., Int. Ed. 2000, 39, 1180–1218. (22) Cracknell, J. A.; Vincent, K. A.; Armstrong, F. A. Enzymes as Working or Inspirational Electrocatalysts for Fuel Cells and Electrolysis. Chem. Rev. 2008, 108, 2439–2461. (23) Humphrey, W.; Dalke, A.; Schulten, K. VMD  Visual Molecular Dynamics. J. Mol. Graphics 1996, 14, 33–38. (24) Stock, A. Relating Dynamics to Function. Nature 1999, 400, 221–222. (25) Sagle, L. B.; Zimmermann, J.; Matsuda, S.; Dawson, P. E.; Romesberg, F. E. Redox-Coupled Dynamics and Folding in Cytochrome c. J. Am. Chem. Soc. 2006, 128, 7909–7915. (26) Pepelina, T. Y.; Chertkova, R. V.; Dolgikh, D. A.; Kirpichnikov, M. P. The Role of Individual Lysine Residues of Horse Cytochrome c in the Formation of Reactive Complexes with Components of the Respiratory Chain. Russ. J. Bioorg. Chem. 2010, 36, 90–96. (27) Jankowska, K. I.; Pagba, C. V.; Piatnitski Chekler, E. L.; Deshayes, K.; Piotrowiak, P. Electrostatic Docking of a Supramolecular Host-Guest Assembly to Cytochrome c Probed by Bidirectional Photoinduced Electron Transfer. J. Am. Chem. Soc. 2010, 132, 16423–16431. (28) Lange, C.; Hunte, C. Crystal Structure of the Yeast Cytochrome bc1 Complex with its Bound Substrate Cytochrome c. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 2800–2805. (29) Battistuzzi, G.; Borsari, M.; Bortolotti, C. A.; Di Rocco, G.; Ranieri, A.; Sola, M. Effects of Mutational (Lys to Ala) Surface Charge Changes on the Redox Properties of Electrode-Immobilized Cytochrome c. J. Phys. Chem. B 2007, 111, 10281–10287. (30) Ly, H. K.; Marti, M. A.; Martin, D. F.; Alvarez-Paggi, D.; Meister, W.; Kranich, A.; Weidinger, I. M.; Hildebrandt, P.; Murgida,

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D. H. Thermal Fluctuations Determine the Electron-Transfer Rates of Cytochrome c in Electrostatic and Covalent Complexes. ChemPhysChem 2010, 11, 1225–1235. (31) Nicholson, R. S. Theory and Application of Cyclic Voltammetry for Measurement of Electrode Reaction Kinetics. Anal. Chem. 1965, 37, 1351–1355. (32) Weber, K. S.; Creager, S. E. Reorganization Energetics for Ferrocene Oxidation/Reduction in Self-Assembled Monolayers on Gold. J. Electroanal. Chem. 1998, 458, 17–22. (33) Weaver, J. M. Interpretation of Activation Parameters for Simple Electrode-Reactions. J. Phys. Chem. 1976, 80, 2645–2651. (34) Sterpone, F.; Ceccarelli, M.; Marchi, M. Linear Response and Electron Transfer in Complex Biomolecular Systems and a Reaction Center Protein. J. Phys. Chem. B 2003, 107, 11208–11215. (35) Sigfridsson, E.; Olsson, M. H. M.; Ryde, U. A Comparison of the Inner-Sphere Reorganization Energies of Cytochromes, Iron Sulfur Clusters, and Blue Copper Proteins. J. Phys. Chem. B 2001, 105, 5546–5552. (36) Walker, V. E. J.; Castillo, N.; Matta, C. F.; Boyd, R. J. The Effect of Multiplicity on the Size of Iron(II) and the Structure of Iron(II) Porphyrins. J. Phys. Chem. A 2010, 114, 10315–10319. (37) Eberson, L.; Shaik, S. S. Electron-Transfer Reactions of Radical Anions: Do They Follow Outer- or Inner-Sphere Mechanisms? J. Am. Chem. Soc. 1990, 112, 4484–4489. (38) Yee, E. L.; Weaver, M. J. Functional Dependence upon Ligand Composition of the Reaction Entropies for Some Transition-Metal Redox Couples Containing Mixed Ligands. Inorg. Chem. 1980, 19, 1077–1079. (39) Song, S.; Clark, R. A.; Bowden, E. F.; Tarlov, M. J. Characterization of Cytochrome c/Alkanthiolate Structures Prepared by SelfAssembly on Gold. J. Phys. Chem. 1993, 97, 6564–6572. (40) Autenrieth, F.; Tajkhorshid, E.; Baudry, J.; Luthey-Schulten, Z. Classical Force Field Parameters for the Heme Prosthetic Group of Cytochrome c. J. Comput. Chem. 2004, 25, 1613–1622. (41) Gogonea, V.; Shy, J. M.; Biswas, P. K. Electronic Structure, Ionization Potential, and Electron Affinity of the Enzyme Cofactor (6R)5,6,7,8-Tetrahydrobiopterin in the Gas Phase, Solution, and Protein Environments. J. Phys. Chem. B 2006, 110, 22861–22871.

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