J Biol Inorg Chem (2014) 19:1287–1293 DOI 10.1007/s00775-014-1185-7

ORIGINAL PAPER

The iron–sulfur core in Rieske proteins is not symmetric Md. Ehesan Ali • Nisanth N. Nair • Marius Retegan Frank Neese • Volker Staemmler • Dominik Marx

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Received: 11 April 2014 / Accepted: 30 July 2014 / Published online: 24 August 2014 Ó SBIC 2014

Abstract At variance with ferredoxins, Rieske-type proteins contain a chemically asymmetric iron–sulfur cluster. Nevertheless, X-ray crystallography apparently finds their [2Fe–2S] cores to be structurally symmetric or very close to symmetric (i.e. the four iron–sulfur bonds in the [2Fe– 2S] core are equidistant). Using a combination of advanced density-based approaches, including finite-temperature molecular dynamics to access thermal fluctuations and free-energy profiles, in conjunction with correlated wavefunction-based methods we clearly predict an asymmetric core structure. This reveals a fundamental and intrinsic difference within the iron–sulfur clusters hosted by Rieske proteins and ferredoxins and thus opens up a new dimension for the ongoing efforts in understanding the role of Rieske-type [2Fe–2S] cluster in electron transfer processes that occur in almost all biological systems. Keywords Iron-sulfur protein  Extended brokensymmetry  Constraint spin-density dynamics

Electronic supplementary material The online version of this article (doi:10.1007/s00775-014-1185-7) contains supplementary material, which is available to authorized users. Md. E. Ali (&)  V. Staemmler  D. Marx Lehrstuhl fu¨r Theoretische Chemie, Ruhr-Universita¨t Bochum, 44780 Bochum, Germany e-mail: [email protected] N. N. Nair Department of Chemistry, Indian Institute of Technology Kanpur, Kanpur 208016, India M. Retegan  F. Neese Max-Planck-Institut fu¨r Chemische Energiekonversion, Stiftstrasse 34–36, 45470 Mu¨lheim an der Ruhr, Germany

Introduction Iron–sulfur cluster containing proteins play a vital role in various biological electron transfer reactions such as aerobic respiration, photosynthesis, and biodegradation of various alkene and aromatic compounds [1–3]. [2Fe–2S] iron–sulfur clusters are mostly observed in ferredoxins and Rieske-type proteins. In ferredoxins, each of the two iron centers of the rhombic [2Fe–2S] core is bound to two cysteine residues and the [2Fe–2S] core is highly symmetric with four equal Fe–Sb bond lengths. Rieske-type proteins have a similar [2Fe–2S] structure, but the two cysteine residues at one of the Fe centers have been replaced with two histidine ligands [1]. Thus, the two iron atoms are in two different chemical environments as depicted in Fig. 1. One thus expects that the [2Fe–2S] cluster will reflect this chemical asymmetry by possessing two distinct sets of FeN–Sb and FeS–Sb bond lengths; see caption of Fig. 1 for definitions. However, the available large amount of X-ray crystallographic data reported in the literature, e.g. in the Protein Data Bank (PDB), paints a distictly different picture and thus is in conflict with chemical intuition. Nearly all of these studies, in particular those with an appropriately high ˚ and better [2, 4–6], report an essentially resolution of 1.5 A symmetric core structure for the Rieske type iron–sulfur ˚ between cofactor with tiny differences of less than 0.02 A the FeN–Sb and FeS–Sb bond lengths, which range between ˚ . It is unclear why a chemically asymmetric 2.20 and 2.26 A covalent bonding environment should yield such a symmetric [2Fe–2S] complex. At this point, the puzzle arises whether the structural asymmetry is indeed negligible despite the pronounced chemical asymmetry or whether the structural refinements have been based on symmetric modeling that prevents

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Fig. 1 Molecular model of the Rieske [2Fe–2S] complex. The histidine and cysteine residues ligated to the iron–sulfur core are modelled with imidazole and –SH groups, respectively. The localized up- and down-spin densities of the ground state are depicted in red and blue. FeN and FeS denote the Fe atoms bound to histidine and cysteine, respectively, and Sb1/Sb2 denote the bridging sulfur atoms. Color code: N: blue, C: cyan, S: yellow: Fe: magenta, H: grey

solving for an asymmetric core structure. It could also be that the Fe–Sb distances in the [2Fe–2S] core and thus the structural asymmetry get averaged out at finite temperatures as a result of thermal fluctuations. A last possibility to reconcile the X-ray crystallographic data with chemical expectations is that the protein environment could have a strong symmetrizing influence on the structure, thus forcing all Fe–S bonds to become equal [7]. In our previous studies on ferredoxin, however, we did not find any significant difference in the structure of the [2Fe–2S] core when comparing the molecular gas phase complex with the full protein environment [8–11] and it is difficult to see why this should be systematically different for [2Fe–2S] clusters in Rieske proteins. In such a situation, theory becomes indispensable. However, accurate and thus predictive computational studies of such [2Fe–2S] complexes are most challenging due to the antiferromagnetic (AFM) coupling between the Fe atoms. In the oxidized state (i.e. two Fe3þ ions with d 5 configuration and spin S = 5/2), the AFM coupling leads to an open-shell singlet ground state that has an intrinsic multiconfigurational character. This low-spin (LS) state can neither be reliably described by single-reference representations within wavefunction-based theory, nor by a standard Kohn–Sham determinant in density-based (DFT) approaches. A practical DFT description of the LS state can be obtained from the broken-symmetry (BS) approach introduced by Noodleman [12] with the aim to extract information on the magnetic coupling.

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Indeed, several DFT calculations for different molecular models of the Rieske [2Fe–2S] cluster in the gas phase are available, all of them using Noodleman’s original scheme. Geometry optimizations using semilocal (GGA) functionals [13, 14], such as BLYP, PW91 or PBE, consistently yield symmetric core structures—apparently in good agreement with the experiment. However, it is well established that such GGA approaches strongly suffer from the self-interaction error (SIE). This delocalizes the magnetic orbitals artificially, strongly shrinks the Fe–Sb bond lengths resulting in a smaller core and, finally, overestimates the magnitude of the AFM exchange coupling dramatically; see e.g. Refs. [10, 15, 16] for recent work on iron–sulfur clusters and references therein for comprehensive discussions. Thus the observed ‘good match’ between experiments and structures obtained with GGA functionals is probably due to the wrong reason. With standard hybrid functionals [7, 17–19], on the other hand, asymmetric core structures were obtained with rather large values for the asymmetry parameter, Dd ¼ dFeNSb  dFeSSb , varying between about 0.10 ˚ (here dFeNSb denotes the average of the two and 0.15 A FeN–Sb distances and similarly for dFeSSb ). An overview on the structures of Rieske-type [2Fe–2S] clusters calculated using a variety of density-based and wavefunction-based methods, including in particular the value of the asymmetry parameter Dd, is provided in the SI. Therein, Table S3 collects the results from the present study as well as from the literature. Thus, all results obtained by means of hybrid functionals (such as B3LYP, PBE0 or M06), all correcting for the SIE and leading to much more accurate magnetic interactions than the semilocal GGA functionals (such as BLYP, PBE or BP86), evidently contradict the conclusions from X-ray crystallography. This stunning disagreement is well documented in the literature—yet it remains unresolved.

Results and discussion To shed light onto the conflicting experimental and computational results we have optimized potential energy curves along the asymmetry parameter, Dd. This has been done using a conventional single-determinant brokensymmetry approach [BS with the PBE functional, BS(PBE)] and our recently developed constrained spindensity two-determinant method (CEBS) [16], see ‘‘Methods’’ for background and computational details. In these static calculations, full geometry optimizations were performed for the molecular complex depicted in Fig. 1, except for Dd, which was kept constant and varied in steps ˚ . In view of the pK a values [20] of 7.4 and 9.2, as of 0.02 A determined for the two histidine residues in the Rieske

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BS(PBE)

CEBS

MCAS-CI

˚) Dd (A  ˚) dFeSb (A

0.05

0.13

0.14

2.18

2.26

2.26

J (cm1 )

473

237

180

ΔE (kcal/mol)

Table 1 Properties of the potential energy curves plotted in Fig. 2a at the respective minima

0.8 BS CEBS MCAS-CI EBS

0.4

dFeSb is the average over all four Fe–Sb distances

(a)

ΔF (kcal/mol)

protein, the fully protonated oxidized form has been used since the high-resolution crystal structures [2, 4–6] have been obtained at pH 6 or less. Figure 2a shows the calculated potential curves together with the results of singlepoint calculations using our modified CAS-CI approach [21] (MCAS-CI, see ‘‘Methods’’ for details) [9, 10, 16] based on structures optimized at the CEBS level; the most relevant data are collected in Table 1. The negative value of the spin coupling constant J, as defined by the standard ^ ¼ 2J S^A S^B where S^A and S^B are the Heisenberg model, H effective local spin operators at the two iron atoms A and B, indicating an antiferromagnetic coupling. It is noted in passing that MCAS-CI is a rather accurate wavefunctionbased approach that correctly describes the multi-reference character of the antiferromagnetic ground state and includes electron correlation effects crucial for reliable results for the coupling constant [21]. The reported MCASCI data are the most accurate electronic structure results reported so far for an iron–sulfur cofactor of this size. In accordance with previous studies, the standard broken-symmetry approach with semilocal functionals, here BS(PBE), leads to a much more symmetric core, ˚ , compared to the asymmetric scenarios as Dd ¼ 0:05 A obtained from the two advanced methods, CEBS and ˚ , respectively. Calculations MCAS-CI, 0:13 and 0:14 A using larger models confirm the asymmetry. Thus, taking the LS state properly into account (by spin projection using two determinants in CEBS) together with localizing the magnetic orbitals at the Fe centers (by constraining spin densities in CEBS) clearly yields a distinctly asymmetric [2Fe–2S] core structure. Furthermore, geometry optimizations using post-Hartree–Fock methods such as MP2 (for the high-spin state only) and CASSCF(10,10) (for the LS state, with all 10 d-electrons in the active space) also provide a similarly large asymmetry, Dd  0.15 to ˚ . Thus, all advanced electronic structure methods 0.21 A support an asymmetric [2Fe–2S] core structure for the Rieske-type model complex in the gas phase. Similarly, the average Fe–Sb distance is considerably ˚ , than in both shorter in the BS(PBE) calculation, 2.18 A advanced approaches, CEBS and MCAS-CI, which yield ˚ . The latter value is in remarkable agreement with 2.26 A the result of the highest resolution X-ray crystal structure

0

-0.2

-0.1

0

0.1

-0.2

-0.1

0

0.1

0.8

0.4

(b) 0

Δ d (Å) Fig. 2 a Relative total energies of the Rieske model complex from Fig. 1 using the methods as indicated (see text) as a function of the asymmetry parameter, Dd. b Relative free energy profiles at 300 K obtained from CEBS (red) and EBS (green) ab initio molecular dynamics corresponding to strongly asymmetric and essentially symmetric [2Fe–2S] Rieske cores, respectively

˚ , Fe–S contained in the PDB (code 1JM1, resolution 1.1 A ˚ ) [22]. All this is in line with the known fact distance 2.26 A that the SIE in the simple GGA functionals leads to an overestimation of the overlap of the magnetic orbitals, which causes too strong Fe–S bonds and too short Fe–S distances in the [2Fe–2S] core as well as too large antiferromagnetic couplings. Complementing the structure, we have computed the AFM exchange coupling constant J along the potential energy profiles. Since the value of J depends mainly on the Fe–S–Fe angle and the average Fe–Sb distance in the [2Fe– 2S] core [11], both of which do not change much along the potential curves, J is nearly constant along Dd so that we report in Table 1 only the value at the minimum. The standard broken-symmetry method yields a much too large negative value for J, whereas the CEBS and in particular the MCAS-CI data compare much more convincingly to the only J value, 161 cm1 , reported in the literature [23]. This value has been measured for a dianionic model complex with bulky diskatylmethane-based ligands instead of histidines. For this model complex, our CEBS method yields optimized bond lengths and a fully symmetric [2Fe– ˚ , in excellent agreement with 2S] core structure, Dd  0 A the experimental X-ray structure [23].

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experimental 321

P(dFe-S ) (arbt. units)

FeN-Sb1 FeS -Sb1 FeS-Sb2 FeN-Sb2

332

350

362

265 284

433

385

asymmetric core

429 379

314 327 255 264

398

339 347

415

b

287 362

symmetric core 298 378 272

250

313

285

300

332

397

350

400

450

Raman shift (cm−1 )

1.8

2

2.2

2.4

2.6 1.8

2

2.2

2.4

2.6

Fe-S b distance (Å) Fig. 3 Probability distribution of the four iron–sulfur distances in the [2Fe–2S] Rieske core obtained at 300 K with CEBS dynamics (shaded area) and EBS for reference

Despite these clear predictions of the static electronic structure calculations, it is still conceivable that the asymmetry in the potential energy profile of the Riesketype [2Fe–2S] core can be averaged out by structural fluctuations induced by finite temperatures. This possibility has been checked explicitly by performing ab initio molecular dynamics (AIMD) simulations [24] at room temperature using the identical CEBS approach as employed for geometry optimizations [16]. The probability distribution functions, PðdFeSb Þ, for the four iron–sulfur bonds in the [2Fe–2S] core are plotted in Fig. 3. In case of EBS based on PBE, which does not correct for the SIE, the ˚ for all four bonds. In stark conmaxima appear at 2.17 A trast, a clear splitting of the distributions into long and short Fe–Sb bonds is observed when CEBS dynamics is used: the average of the most probable FeN–Sb and FeS–Sb ˚ , respectively; bond lengths turns out to be 2.22 and 2.31 A it is noted in passing that preliminary QM/MM–CEBS simulations which include the protein environment support this finding. In conclusion, the CEBS approach predicts an asymmetric core even after adding structural fluctuation effects as induced by thermal vibrations at 300 K. Last but not least, the free energy change along the asymmetry parameter Dd is calculated using CEBS dynamics and plotted in Fig. 2b; here, EBS simulations are used to provide the reference data. The mimimum of the free energy curve obtained from the finite-temperature EBS ˚ , while it is at 0:13 A ˚ simulations appears at Dd ¼ 0:0 A when CEBS is used. The interesting finding is that the thermal fluctuations indeed fully symmetrize the close-to-symmetric static EBS structure, whereas the asymmetry of the CEBS structure is still as pronounced as in the static case! Most importantly, the asymmetry of the Rieske-type [2Fe–2S] core as supported by all our calculations is in

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Fig. 4 Experimental resonance Raman spectrum of T4moC obtained at 488 nm (reproduced from Ref. [26]) and corresponding simulated RR spectra based on computational models with asymmetric and symmetric [2Fe–2S] core structures, see text

accord with spectroscopic data. The electronic structure of Rieske-type model compounds have been investigated by means of sulfur K-edge X-ray absorption spectroscopy [25]. A strong difference in the covalency of the FeN–Sb versus the FeS–Sb bonds has been observed, with the covalency of the FeN–Sb bonds being 18 % higher than of the FeS–Sb bonds. This directly implies that the FeS–Sb bonds must be quite a bit longer such that the overall core structure is expected to be clearly asymmetric, which is exactly what we have obtained theoretically using CEBS and MCAS-CI. The strongest support for the asymmetry of the [2Fe–2S] Rieske core is provided by a comparison of experimental resonance Raman (RR) spectra [26–28] with the results of the present calculations. We have chosen the Rieske core from T4moC for which a detailed experimental study of the RR spectra has been published [26]. A large model comprising 175 atoms was built starting from the X-ray structure (PDB code 1VM9) [5]; see ‘‘Methods’’ and SI for details. In agreement with the results for the smaller model shown in Fig. 1, geometry optimizations resulted in a ˚ , for nearly symmetric [2Fe–2S] core, Dd ¼ 0:01 A ˚ , for BS(PBE) and a more asymmetric core, Dd ¼ 0:07 A BS(PBE0). Based on 15 N isotope labeling [26] as well as on additional 34 S labeling in our simulations, the peaks in the red-shaded region in the RR spectrum depicted in Fig. 4, are assigned to FeN–N stretches and those in the blueshaded region primarily to terminal ligand vibrations; see SI for further analyses. The modes at 255 and 264 cm1 computed for the asymmetric core correspond to the 265 cm1 resonance in experiment, whereas there is bascially no intensity when the symmetric core is used. The peaks in the high-energy region, 370–450 cm1 (green shading), are assigned to relatively pure Fe–Sb

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vibrations with some contributions from the ligands. The intense peak at 429 cm1 in the simulated spectrum of the asymmetric core corresponds to the 410 cm1 peak in the experiment and is unambiguously assigned to the core breathing mode. In stark contrast to both experiment and the computed spectrum for the asymmetric core, the intensity of all peaks in this energy region is very low in the simulated spectrum of the symmetric core. In particular, the most prominent [2Fe–2S] core breathing mode at 410 cm1 is essentially absent for the symmetric core. Thus, Fig. 4 clearly shows that the RR spectrum simulated for the asymmetric Rieske core is in much better agreement with experiment than that for the symmetric one. This holds true in particular for the high-energy region of the pure [2Fe–2S] core vibrations. In conclusion, all evidence we have provided indicates that the core structure of the [2Fe–2S] cofactor in Rieske proteins is asymmetric even at finite temperatures, which should be quantified in future X-ray crystallography experiments using refined approaches.

Methods

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Ab Initio molecular dynamics simulations The CEBS technique allows one to perform ab initio molecular dynamics (AIMD) [24] simulations to probe thermal fluctuation effects on structure and to compute free energy profiles. All AIMD simulations and the static optimizations of structures using CEBS were carried out using our in-house version of the CPMD program package [30]. They were performed in vacuo on the Rieske model depicted in Fig. 1 in a ˚ . The Perdew–Burke– non-periodic cubic box of length 20.1 A Ernzerhof [31] (PBE) exchange-correlation functional was used within the two-determinant spin-constrained CEBS approach, using a plane wave pseudopotential approach [24] with a kinetic energy cutoff of 25 Ry for the valence orbitals. The atomic core electrons were taken into consideration via Vanderbilt’s ultra soft pseudopotentials [24]. Additional dprojectors for sulfur as well as scalar relativistic corrections and semi-core states for iron were accounted for in the pseudopotentials. In AIMD, the system was initially equilibrated at 300 K for 3 ps using Nose´–Hoover chain thermostatting [24] and a 10 ps long NVT trajectory was generated subsequently for the data analysis. The time step for the AIMD simulations was set to 0.6 fs.

Constrained spin-density approach: CEBS

Post-Hartree–Fock calculations

To cope systematically with the known intricacies of AFM couplings in iron–sulfur complexes we have developed the extended broken-symmetry scheme, EBS [9], which is a general spin-projected multi-determinant DFT approach to magnetic complexes. To cure the SIE, EBS has been combined subsequently with post-GGA electronic structure methods using a Hubbard–U correction, EBSþU [10], and a constrained spin-density DFT approach [29], CEBS [16]. Importantly, CEBS prevents spurious spin delocalization to the bridging sulfur atoms by constraining the spindensity at specific sites, here at Fe centers. It is important to note that although the two Kohn–Sham determinants underlying the present CEBS implementation [16] are obtained using the PBE functional which is of GGA type, the CEBS method as such is no longer a GGA approach due to applying the spin-density contraints. It allows for geometry optimizations that are consistent with the spin projection and has been shown to perform favorably for a molecular ferredoxin complex [16]. A third post-GGA approach, relying on a hybrid density functional, has been combined recently with EBS and demonstrated to provide impressive accuracy for iron–sulfur and even mixed valence complexes [15]. The reader is referred to this earlier work [15, 16] for theoretical background, benchmarking, and validation of the CEBS method [16] that is employed here.

Apart from performing geometry optimization using many different post-GGA density functionals as reported in the SI, we also optimized molecular geometries of the Rieske model systems using the wavefunction-based MP2 and CASSCF(10,10) post-Hartree–Fock methods; all ten singly occupied MOs with substantial amount of d-character were chosen as the active space for the CAS calculations. Moreover, we have computed the potential energy curve and the magnetic exchange interactions using our accurate modified CAS-CI approach [21], MCAS-CI(10,10). In this modification of a conventional CAS-CI calculation the energies of the charge transfer configurations, which are responsible for the antiferromagnetic coupling, are lowered by a certain amount R. This energy shift R, which is somewhat related in spirit to applying a Hubbard correction U within DFT [10], simulates the relaxation of the wavefunctions after charge transfer excitations and has been determined approximately from calculations on mononuclear complexes. In the present study a value of 13.6 eV was used for R, which is rather close to the 15.0 eV as determined for ferredoxin [21]. A change of 10 % in R has no influence on the MCAS-CI potential energy curve shown in Fig. 2a, but modifies J by about 20 cm1 . The basis set for our HF and MCAS-CI calculations had VTZP quality, while 6-311?G(d,p) was used for our CASSCF and MP2 calculations.

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Resonance Raman spectra The RR spectra were calculated using the independent mode displaced harmonic oscillator (IMDHO) model [32, 33] as implemented in the ORCA program [34]. Broken-symmetry geometry optimization of a 175 atom cluster model of T4moC [5], see SI for details, was performed using the GGA functional PBE and its hybrid version PBE0, which leads to the BS(PBE) and BS(PBE0) structures. Based upon these structures, which provide a symmetric and asymmetric [2Fe– 2S] core for BS(PBE) and BS(PBE0), respectively, the vibrational frequencies were calculated using the recently developed efficient implementation of the analytical differentiation of the SCF energy. Further details on the RR calculations are reported in the SI. Acknowledgments We thank Professor Hofmann (Bochum) for his help in assessing X-ray crystallographic data. Md. E. Ali is grateful to support by the Alexander von Humboldt-Foundation via his Humboldt Postdoctoral Fellowship and D.M. acknowledges partial financial support from DFG. The calculations have been carried out using resources from NIC (Ju¨lich), RV-NRW and SNIC-NSC(Linko¨ping).

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References 1. Iwata S, Saynovits M, Link T, Michel H (1996) Structure of a water soluble fragment of the ‘Rieske’ iron sulfur protein of the bovine heart mitochondrial cytochrome bc(1) complex determined by mad phasing at 1.5 angstrom resolution. Structure 4:567–579 2. Kolling DJ, Brunzelle JS, Lhee S, Crofts AR, Nair SK (2007) Atomic resolution structures of rieske iron–sulfur protein: role of hydrogen bonds in tuning the redox potential of iron–sulfur clusters. Structure 15:29–38 3. Leggate EJ, Bill E, Essigke T, Ullmann GM, Hirst J (2004) Formation and characterization of an all-ferrous rieske cluster and stabilization of the [2Fe–2S]0 core by protonation. Proc Natl Acad Sci 101:10913–10918 4. Karlsson A et al (2003) Crystal structure of naphthalene dioxygenase: side-on binding of dioxygen to iron. Science 299:1039–1042 5. Moe LA, Bingman CA, Wesenberg GE, Phillips GN Jr, Fox BG (2006) Structure of T4moC, the Rieske-type ferredoxin component of toluene 4-monooxygenase. Acta Cryst D Biol Cryst 62:476–482 6. Friemann R et al (2008) Structures of the multicomponent Rieske non-heme iron toluene 2,3-dioxygenase enzyme system. Acta Cryst D Biol Cryst 65:24–33 7. Kuznetsov AM, Zueva EM, Masliy AN, Krishtalik LI (2010) Redox potential of the rieske ironsulfur protein: Quantumchemical and electrostatic study. Biochim Biophys Acta Bioenerg 1797:347–359 8. Schreiner E, Nair NN, Pollet R, Staemmler V, Marx D (2007) Dynamical magnetostructural properties of anabaena ferredoxin. Proc Natl Acad Sci 104:20725–20730 9. Nair NN, Schreiner E, Pollet R, Staemmler V, Marx D (2008) Magnetostructural dynamics with the extended broken symmetry formalism: Antiferromagnetic [2Fe–2S] complexes. J Chem Theor Comput 4:1174–1188 10. Nair NN, Ribas-Arino J, Staemmler V, Marx D (2010) Magnetostructural dynamics from Hubbard-U corrected

123

20.

21.

22.

23. 24. 25.

26.

27. 28.

29.

30. 31. 32.

spinprojection:[2Fe–2S] complex in ferredoxin. J Chem Theor Comput 6:569–575 Fiethen SA et al (2010) Revealing the magnetostructural dynamics of [2Fe–2S] ferredoxins from reduced-dimensionality analysis of antiferromagnetic exchange coupling uctuations. J Phys Chem B 114:11612–11619 Noodleman L, Davidson ER (1986) Ligand spin polarization and antiferromagnetic coupling in transition metal dimers. Chem Phys 109:131–143 Ullmann M, Noodleman L, Case D (2002) Density functional calculation of pka values and redox potentials in the bovine Rieske iron–sulfur protein. J Bio Inorg Chem 7:632–639 Shoji M et al (2007) Theory of chemical bonds in metalloenzymes iv: Hybrid-dft study of rieske-type [2Fe–2S] clusters. Int J Quant Chem 107:609–627 Bovi D, Guidoni L (2012) Magnetic coupling constants and vibrational frequencies by extended broken symmetry approach with hybrid functionals. J Chem Phys 137:114107 Md E Ali, Nair NN, Staemmler V, Marx D (2012) Constrained spin-density dynamics of an iron–sulfur complex: ferredoxin cofactor. J Chem Phys 136:224101 Sigfridsson E, Olsson MHM, Ryde U (2001) Inner-sphere reorganization energy of iron–sulfur clusters studied with theoretical methods. Inorg Chem 40:2509–2519 Bassan A, Blomberg MRA, Borowski T, Siegbahn PEM (2004) Oxygen activation by rieske non-heme iron oxygenases, a theoretical insight. J Phys Chem B 108:13031–13041 Shimizu M, Katsuda N, Katsurada T, Mitani M, Yoshioka Y (2008) Mechanism on two-electron oxidation of ubiquinol at the qp site in cytochrome bc1 complex: B3lyp study with broken symmetry. J Phys Chem B 112:15116–15126 Hsueh K-L, Westler WM, Markley JL (2010) NMR investigations of the Rieske protein from thermus thermophilus support a coupled proton and electron transfer mechanism. J Am Chem Soc 132:7908–7918 Fink K, Staemmler V (2013) A modified CAS-CI approach for an efficient calculation of magnetic exchange coupling constants. Mol Phys 111:2594–2605 Bo¨nisch H, Schmidt CL, Scha¨fer G, Ladenstein R (2002) The structure of the soluble domain of an archaeal rieske ironsulfur protein at 1.10; resolution. J Mol Biol 319:791–805 Ballmann J et al (2008) A synthetic analogue of rieske-type [2Fe– 2S] clusters. Angew Chem Int Ed 47:9537–9541 Marx D, Hutter J (2009) Ab initio molecular dynamics: basic theory and advanced methods. Cambridge University Press, Cambridge Rose K et al (1999) Investigation of the electronic structure of 2fe2s model complexes and the rieske protein using ligand k-edge x-ray absorption spectroscopy. J Am Chem Soc 121:2353–2363 Rotsaert FAJ, Pikus JD, Fox BG, Markley JL, Sanders-Loehr J (2003) N-Isotope effects on the Raman spectra of Fe2S2 ferredoxin and Rieske ferredoxin: evidence for structural rigidity of metal sites. J Biol Inorg Chem 8:318–326 Kuila D et al (1992) Resonance Raman studies of Rieske-type proteins. Biochim Biophys Acta 1140:175–183 Iwasaki T et al (2006) Resonance Raman characterization of archaeal and bacterial Rieske protein variants with modified hydrogen bond network around the [2Fe–2S] center. Protein Sci 15:2019–2024 Rudra I, Wu Q, Voorhis TV (2006) Accurate magnetic exchange couplings in transition-metal complexes from constrained density-functional theory. J Chem Phys 124:024103 J. Hutter et al. CPMD, see http://www.cpmd.org. Perdew J, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865–3868 Petrenko T, Neese F (2007) Analysis and prediction of absorption band shapes, fluorescence band shapes, resonance raman

J Biol Inorg Chem (2014) 19:1287–1293 intensities, and excitation profiles using the time-dependent theory of electronic spectroscopy. J Chem Phys 127:164319 33. Petrenko T, Neese F (2012) Efficient and automatic calculation of optical band shapes and resonance raman spectra for larger

1293 molecules within the independent mode displaced harmonic oscillator model. J Chem Phys 137:234107 34. Neese F (2012) Wiley Interdiscip Rev Comput Mol Sci (WIRES) 2:73–78

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