8768
J. Phys. Chem. B 1999, 103, 8768-8772
Electronic Structure of a Rieske Iron-Sulfur Complex and the Calculation of Its Reduction Potential Sambhu N. Datta,* Vijay Nehra, and Abhishek Jha Department of Chemistry, Indian Institute of Technology, Bombay, Powai, Mumbai 400 076, India ReceiVed: June 1, 1999
The electronic structure of a Rieske iron-sulfur complex of spinach chloroplast has been investigated by the CNDO/2 method. The crystallographic coordinates were obtained from the Protein Data Bank at Brookhaven National Laboratory. The protein chain was truncated in such a way that the entity Fe2S2 along with its four ligands was separated from the rest of the chain. The separated species retains the essential structural features of the Rieske iron-sulfur complex. It consists of the basic Fe2S2 unit, two histidine residues, and two cysteine residues such that each Fe atom is tetrahedrally coordinated. The orbital angular momenta of the iron atoms are found to be fully quenched. The HOMOs and the first few LUMOs are basically π type orbitals of the Fe2S2 cluster with predominantly large contributions from the sulfur orbitals. The reduction potential calculated for the soluble Rieske iron-sulfur fragment in an aqueous solution at pH 7 is 0.370 V at 25 °C, which is in excellent agreement with the experimentally determined midpoint potential, 0.375 V. The calculated potential for the Rieske cluster in the condensed phase of thylakoid is 0.252 V, which agrees with the placement of the Rieske complex in the Z-scheme of photosynthesis in green plants.
1. Introduction The Rieske iron-sulfur complex is a residue protein subunit anchored in the thylakoid membrane of a chloroplast. It is a high-potential electron acceptor, and it donates an electron to cytochrome-f according to the Z-scheme of photosynthesis in green plants. The redox partners of the Fe2S2 complex are the donors, the plastoquinones, and the acceptor, cytochrome-f. By using the low-temperature EPR, Zhang et al.1 have determined the midpoint reduction potential of a soluble, 139-residue COOH-terminal polypeptide fragment of the Rieske iron-sulfur protein of the cytochrome b6f complex from spinach chloroplasts. The midpoint potential at pH 7 is 375 mV. The position of the Rieske complex in the Z-scheme indicates that it has a reduction potential in the range 0.2-0.3 V (around 0.25 V) in the condensed phase of the thylakoid membrane. The Rieske iron-sulfur complex is a part of the intact chloroplast cytchrome b6f complex. The latter has one copy of the four polypeptides, with cytochrome-f being the largest of the four. The other two are the heme-containing cytochrome b6 and the cofactor-free subunit IV. In the Rieske iron-sulfur complex, the two irons of the Fe2S2 cluster are attached to two cysteine and two histidine ligands (Figure 1). The Rieske complex is one of the species in the chain of electron carriers in photosynthesis. A knowledge of its electronic structure is a crucial requirement for a theoretical determination of the involved electron-transfer rates. Hence it is of considerable interest to both theoretical and experimental chemists. As part of our ongoing investigations on the redox processes occurring in the Z-scheme,2-8 we have calculated the redox potential of the Rieske iron-sulfur protein by using the CNDO/2 method. The crystallographic molecular structure selected for our quantum chemical investigation is described in section 2. The method of calculation is discussed in section 3. The computed results and the calculation of the reduction potential are given in section 4. The energies and the molecular orbitals
Figure 1. Fe2S2 cluster along with the two cysteine and two histidine residues coordinated to it. This structure was separated from the crystallographic structure of the Rieske protein.
computed in this work will be used to determine the rates of electron transfer from plastoquinone to the iron-sulfur protein and from the Rieske complex to the cytochrome f cation. 2. Molecular Geometry The crystallographic coordinates were downloaded from the Protein Data Bank at Brookhaven National Laboratory (file 1RFS of the Rieske soluble fragment from spinach; http://www3.ncbi.nlm.nih.gov/htbin-post/Entrez/ query?db)m&form)6&dopt)r&uid)9810 4089). Figure 2 shows the wire model of the protein, the position of the Fe2S2 moiety, and all the water molecules in the protein. None of the water molecules are in the immediate vicinity of the Fe2S2 cluster. Therefore, they have not been considered as part of the complex for the CNDO calculations.
10.1021/jp991758b CCC: $18.00 © 1999 American Chemical Society Published on Web 09/24/1999
Rieske Iron-Sulfur Complex
J. Phys. Chem. B, Vol. 103, No. 41, 1999 8769
Figure 3. Model Rieske iron-sulfur complex [Fe2S2-pr] that has been used for the calculations. Each cysteine sulfur atom is covalently bonded to a hydrogen atom that is shown in this figure but not in Figure 1.
Figure 2. Position of the Fe2S2 cluster in the Rieske iron-sulfur protein as obtained from the protein databank.
The Fe2S2 cluster has an approximately square-planar geometry, the two iron atoms being diagonally opposite each other. Furthermore, each Fe atom is coordinated to two ligands. Thus, each Fe atom is placed in an approximately tetrahedral environment. It had been postulated that the two Fe atoms of the cluster are coordinated by three cysteines and a single histidine residue located in a loop structure.9 However, it was shown by electron nuclear double resonance (ENDOR) and electron spin-echo envelope modulation (ESEEM) that 2Fe-2S centers are coordinated by at least one and probably two N-ligands.10 The structure downloaded from the protein databank unambiguously shows one Fe atom coordinated to two cysteine ligands and the other to two histidine ligands (Figure 1). The protein is too big for a reliably accurate quantum chemical calculation at present. Therefore, we had to choose a smaller specimen that preserves the fundamental features of the Fe-S complex, retaining the ligands directly coordinated to the iron atoms. Thus, we modified the protein chain in a suitable way. The four cysteine and histidine residues that are coordinated to the irons of Fe2S2 were modified to the respective amino acids (see Figure 3; also see Figure 1). Henceforth this complex will be referred to as the Rieske Fe-S complex, [Fe2S2-pr]. For the calculations we have used the widely accepted value of 8.5 as the dielectric constant of the condensed phase of the photosystems.5-7 3. Method of Calculation The CNDO/2 and INDO methods11 yield good values of thermochemical properties. The INDO method is known to yield very accurate free energy changes,3-7 but the CNDO method nevertheless yields reasonably good values.3-5,12 We relied on the CNDO calculation because of the reasons mentioned in our earlier work.8 Our CNDO program had been modified for the estimation of medium polarization effects12 in terms of the Born term and Onsager’s energy correction due to the feedback field. We used the G92W software13 to compute the Onsager radius. The recommended a0 value for the calculations given by G92W was 11.57 au for the complex under study from which the Fe2S2 cluster had been removed for computing the CNDO molecular
volume. The Fe2S2 cluster is strongly attached to the four ligands (amino acid residues) by coordinate bonds. The four ligands are stretched approximately along the vertices of a tetrahedron, and the largest distance of the atoms from the center of the Fe2S2 cluster is about 7.65 Å. The other atoms of the Rieske protein lie outside the bulbous region that encompasses the Fe2S2-ligand complex. This indicates that the effective volume would be much greater than that calculated by the MO method, and it involves the excluded volume, that is, the empty space within the bulbous region. This situation is drastically different from the plastoquinones QI and QII,3-7 which are trapped in rather flat cavities, or cytochrome f 8, in which the metal atom is attached to only two amino acid residues aligned along the vertical direction with respect to the porphyrin plane. Thus, we expect the effective molecular radius for the Rieske complex to be considerably greater. Because of this, the calculation of the redox potential for the Rieske complex in the condensed phase of thylakoid was based on two values of the molecular radius, the G92W value, 11.57 au, and a somewhat larger value, 19.67 au. The latter value (10.41 Å, or 19.67 au) was obtained by adding one hydrogen bond length, 1.8 Å, and the radius of the water molecule, 0.96 Å, to the maximum distance from the center. Indeed, we found that a radius of about 19.67 au can very nicely explain the observed potentials. Zhang et al.1 carried out a single-crystal X-ray diffraction study of the soluble Rieske fragment from spinach chloroplast. There is one molecule per asymmetric unit with about 30% solvent content, and the crystal belongs to the triclinic space group P1 with cell parameters a ) 29.1 Å, b ) 31.9 Å, c ) 35.8 Å, R ) 95.6°, β ) 107.1°, and γ ) 117.3°. Because of the very high solvent content, we decided to use the shortest lattice constant as the effective diameter of the fragment in water. Hence the calculation of the redox potential of the soluble fragment in the aqueous phase was based on the effective radius 14.55 Å, or 27.50 au. Another midpoint potential had been reported earlier, albeit for the Rieske cluster from a different source. Liebl et al.14 found that the midpoint potential is 165 mV at pH 7 for the Rieske cluster in equilibrium with the menaquinone pool of Bacillus PS 3, a gram-positive thermophilic eubacterium. To make a comparison with this result, we retained the downloaded structure with the requisite modifications, but considered the menaquinone pool as an aqueous phase and used the estimated radius 19.67 au for the cluster.
8770 J. Phys. Chem. B, Vol. 103, No. 41, 1999
Datta et al. the process
TABLE 1: Computed Molecular Characteristics of the Species under Investigationa
speciesb
1 H (g) f H+(aq) + e- (g) 2 2
dipole spin Hartree-Fock total Onsager moment (D)c multiplicity energy (au)c radius (Å)d
Fe2S2 Fe2S2+ histidine I histidine II cysteine I cysteine II [Fe2S2-pr] [Fe2S2-pr]+
-65.6804 -65.3303 -120.8513 -121.0066 -85.5992 -85.5440 -479.2069 -478.9883
9 10 1 1 1 1 9 10
4.19 4.23 3.86 3.86 6.12 6.12
1.2609 1.3609 6.5228 7.3634 5.9324 3.8926 7.2033 4.7024
a Molecular geometries are fixed and correspond to the Rieske ironsulfur protein crystallographic geometry that has been obtained from the Protein Data Bank as discussed in the text. b [Fe2S2-pr] and [Fe2S2pr]+ represent the Rieske iron-sulfur complex and its cation, respectively. These include as ligands the amino acids instead of the residues. c CNDO/2 results. d Calculated by using G92W, without the Fe2S2 cluster.
A note on the computation: As the species involved are considerably large and we have more or less retained the crystallographic geometry for them, a straightforward use of the CNDO program does not always give convergent results. To overcome this problem, the program was executed for the various fragments (Fe2S2 cluster, two histidines, and two cysteines) to obtain the density matrices in each case. These density matrices were used as initial data for the CNDO/2 calculation on the whole complex. With this tactic, the calculations on the complex [Fe2S2-pr] and its cation [Fe2S2-pr]+ became rapidly convergent. The spin multiplicity used for the uncharged complex was 9, and that for the monopositive cation was 10. The presence of the iron atoms hindered the calculation of thermal energies of the main species by G92W. However, it is known that the thermal energy difference between a neutral metal complex and its cation is quite small, on the order of 1 kcal mol -1, or about 0.05 eV. This is hardly significant when compared with the range of error of CNDO values for the concerned energy differences, which is of the order of (0.1 eV. We took the kinetic energy of the free (gaseous) electron into account. There should be no error in the evaluation of the oxidation (reduction) potential since the same value was taken for the oxidation (reduction) of the hydrogen molecule. The oxidation (reduction) potential of a species is always scaled with the oxidation (reduction) potential of hydrogen, which in the normal state is set at zero. The (PV-TS) terms would be negligibly small in the present case, and they were ignored in all the calculations. 4. Results and Discussion In our previous work8 we have shown that the change in free energy ∆G1/2H2fH+(aq) calculated by the CNDO/2 method for
(1)
is 5.133 eV at 298.15 K at pH 7. This value is in good agreement with the experimentally observed values and has been used throughout in our calculations. Computed molecular characteristics of the Fe2S2 cluster, the ligands, the Rieske iron-sulfur complex [Fe2S2-pr], and its cation [Fe2S2-pr]+, all at the crystallographic geometry of the Rieske protein, are given in Table 1. The cluster and the complex were found to be most stable in the high-spin forms. Thus, the neutral species with two FeII atoms was found to be stable with spin multiplcity 9, whereas the oxidized form with one iron in +2 oxidation state and one in +3 oxidation state had spin multiplicity 10. These multiplicities can be easily accounted for by crystal field theory. Although each iron atom is approximately tetrahedrally surrounded, the local point group symmetry is more like C2V. Therefore, in the weak crystal field, the d6d6 and d5d6 systems have respectively eight and nine unpaired electrons. Nevertheless, the simple crystal field picture breaks down as discussed in the following. The HOMOs and the LUMOs of each iron-sulfur complex have been identified as π type orbitals of the Fe2S2 cluster, most of them having large contributions from the orbitals of the sulfur atoms. Table 2 shows some of the orbital energies. The HOMOs are quasi-degenerate. The iron orbitals, being quite low in energy, give a negligibly small contribution to the HOMOs in each case. The molecular orbitals which can be identified as primarily orbitals of the iron atoms are listed along with the respective orbital energies and the nature of the orbitals in Table 3. Even the first few LUMOs have insignificantly small contributions from the iron orbitals. So, it can be concluded that the orbital angular momenta of the iron atoms have been fully quenched. Molecular orbital energy level diagrams for the Rieske complex and its cation are shown in Figure 4. These diagrams completely agree with the trends that one expects from a qualitative molecular orbital treatment. The spin angular momenta have not been quenched, since the first few HOMOs are quite close to each other in energy, and the URHF treatment tends to stabilize the higher spin states by varying the spatial components of the R and β spin-orbitals in an unequal manner even when the exchange integrals are completely neglected, as in the CNDO/2 method. Table 4 illustrates the calculation of the reduction potential of the monopositive cation of the Rieske iron-sulfur complex, [Fe2S2-pr]+. Here, as stated earlier, we have adopted the dielectric constant 8.5 for the membrane phase and 78.5 for the aqueous phase at 298.15 K. Each calculation was performed with the G92W radius (a0 ) 11.57 au) and then repeated by
TABLE 2: Orbital Energies of the HOMOs and LUMOs of the Two Complexes orbitals of spin R species
spin multiplicity
no.
[Fe2S2-pr]
9
118 119 120 121 122 123 118 119 120 121 122 123
[Fe2S2-pr]+
10
nature
HOMO LUMO
HOMO LUMO
orbitals of spin β energy (au)
no.
-0.2928 -0.2872 -0.2821 0.0141 0.0281 0.0853 -0.4848 -0.4768 -0.4562 -0.1219 -0.1092 -0.0537
110 111 112 113 114 115 109 110 111 112 113 114
nature
HOMO LUMO
HOMO LUMO
energy (au) -0.2980 -0.2929 -0.2843 0.0149 0.0288 0.0853 -0.4869 -0.4736 -0.4555 -0.1530 -0.1201 -0.1010
Rieske Iron-Sulfur Complex
J. Phys. Chem. B, Vol. 103, No. 41, 1999 8771
TABLE 3: Orbital Energies for Orbitals with Large Contributions from Iron Orbitals orbitals of spin R
orbitals of spin β
species
spin multiplicity
no.
nature
energy (au)
no.
nature
energy (au)
[Fe2S2-pr]
9
[Fe2S2-pr]+
10
82 83 84 85 86 87 88 89 90 91 92 93 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84
3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d
-0.5529 -0.5507 -0.5474 -0.5455 -0.5436 -0.5435 -0.5424 -0.5414 -0.5409 -0.5394 -0.5388 -0.5358 -0.7459 -0.7427 -0.7381 -0.7361 -0.7351 -0.7339 -0.7327 -0.7319 -0.7305 -0.7290 -0.7284 -0.7267 -0.7260 -0.7220 -0.7203
82 83 84 133 134 147 149 150 151 152 153 154 115 116 117 118 119 120 121 122 135 136 138 139 140 141 143
3d 3d 3d 4s, 4p 4p 3d 3d 3d 3d 3d 3d 3d 4p, 3d 4s, 4p 4s, 4p, 3d 4s, 4p, 3d 4s, 3d 3d 4s, 4p, 3d 4p 3d 3d 3d 3d 3d, 4p 3d 3d, 4p
-0.5459 -0.5449 -0.5422 0.1973 0.2013 0.2554 0.2639 0.2650 0.2664 0.2681 0.2700 0.2702 -0.0573 -0.0552 -0.0007 0.0098 0.0174 0.0235 0.0254 0.0309 0.0708 0.0773 0.0800 0.0840 0.0857 0.0869 0.0926
TABLE 4: Calculation of the Reduction Potential (E) of [Fe2S2-pr] Cation at 25 °Ca phaseb aqueous
∆ECNDO ∆Esolution (au) a0 (Å) (au) -0.2187
6.12 14.55 10.41 condensed -0.2187 6.12 10.41
0.0412 0.0178 0.0248 0.0369 0.0222
∆Etotalc (eV)
calc
E (V) expt
-4.8673 -0.266 -5.5030 0.370 0.375d -5.3137 0.181 0.165e -4.9847 -0.148 -5.3851 0.252 ≈0.25f
a The reaction studied is [Fe S -pr]+ (2S+1 ) 10) + e- ) [Fe S 2 2 2 2 pr] (2S+1 ) 9), where [Fe2S2-pr] is the Rieske iron-sulfur complex. b Dielectric constant is 78.5 for the aqueous phase and 8.5 for the condensed phase inside the thylakoid membrane. c The kinetic energy of the free electron, 0.03855 eV, has been subtracted to obtain the total ∆E. d Midpoint potential of the soluble Rieske fragment from spinach chloroplast, determined by Zhang et al.1 e Midpoint potential of the Rieske cluster in Bacillus PS 3 in equilibrium with the menaquinone pool at pH 7, determined by Liebl et al.14 f From the approximate relative position of the Rieske complex in the Z-scheme.
Figure 4. Molecular orbital energy level diagrams for [Fe2S2-pr] and its monopositive cation [Fe2S2-pr]+.
using the estimated radius (a0 ) 19.67 au) that accounts for the excluded volume in the condensed phase and the effective radius (a0 ) 27.50 au) for the soluble Rieske fragment. The use of the G92W radius leads to slightly negative reduction potentials, but the excluded volume effect and the effectively large volume of the soluble cluster rectify the results. The reduction potential finally calculated for [Fe2S2-pr]+ in an aqueous phase at pH 7 is 0.370 V. This is in excellent agreement with the experimentally determined midpoint potential for the reduction of the [Fe2S2-pr]+ cation, 0.375 V.1 The condensed phase value 0.252 V also agrees very well with the placement of cytochrome f in Z-scheme at around 0.25 V. When we used the condensed phase radius (a0 ) 19.67 au) but the dielectric constant of water, we calculated a redox
potential of 0.181 V at pH 7. This value is in very good agreement with the midpoint potential 0.165 V determined by Liebl et al.14 for the Bacillus PS 3 Rieske cluster in equilibrium with the menaquinone pool at pH 7. 5. Conclusions In this work we have presented a semiempirical calculation of the reduction potential of the Rieske iron-sulfur complex. Since the molecule is too large for our computing abilities, we truncated the protein chain but retained the fundamental structural features of the complex. The CNDO total energies show that the reduction potential of the soluble fragment in an aqueous medium is about 0.370 V. This result is in extremely good agreement with the experimentally determined midpoint value of 0.375 V at pH 7. The difference from the experimental free energy change is less than 0.001 au, which, despite the highly complex nature of the effects arising from different interactions, is exceedingly small. Similarly, the reduction
8772 J. Phys. Chem. B, Vol. 103, No. 41, 1999 potential calculated for the complex present in the condensed phase of thylakoid in equilibrium with the surrounding aqueous medium at physiological pH is about 0.252 V, which matches excellently with the placement of the Rieske protein in Z-scheme of green-plant photosynthesis. This success is in fact another demonstration that the Pariser-Parr-Pople development of semiempirical theories is ideally suitable for thermochemical calculations involving biological molecules. The results also point out that the CNDO estimate of ∆G1/2H2fH+(aq), which we prepared in an earlier work,8 has been entirely consistent. In addition, this work shows that the G92W radius may not always give the correct molecular radius, and depending upon the structure of the complex and the protein environment in its immediate vicinity, one has to take a larger value that can account for the molecular radius in a realistic way. The surprisingly high accuracy of the calculated reduction potentials owes its origin to the choice of the molecular radius. If the molecular radius changes by about 1 Å, the reduction potential can change by 0.03 V or more. The present choices have been spectacularly successful, which is somewhat fortuitious. The thermal energy differences between the metal complexes and their cations and all the other (PV-TS) terms have been neglected in this work. These effects can at most contribute a few hundred calories to the change in Gibbs free energy and thus change the calculated potentials by about (0.1 V. In summary, the calculated semiempirical electronic structure of the representative Fe-S complex is a good approximation to the valence electronic structure in the real specimen, the Rieske protein. It is also obvious that the iron-sulfur complex
Datta et al. lies within a spheroidal cavity made by the surrounding protein environment such that the effective molecular radius is somewhat greater than the radius calculated by the MO method. Our ultimate objective is to determine the rate of electron transfers from plastoquinone to the monopositive cation of the Fe2S2 complex and from the iron-sulfur complex to cytochrome f +. This work provides the basis for our future investigations. Acknowledgment. Financial support from CSIR is gratefully acknowledged. References and Notes (1) Zhang, H.; Carrell, C. J.; Huang, D.; Sled, V.; Onishi, T.; Smith, J. L.; Cramers, W. A. J. Biol. Chem. 1996, 271, 31360. (2) Datta, S. N.; Priyadarshy, S. Chem. Phys. Lett. 1990, 173, 360. (3) Mallik, B.; Datta, S. N. Int. J. Quantum Chem. 1994, 52, 629. (4) Datta, S. N.; Mallik, B. Int. J. Quantum Chem. 1995, 53, 37. (5) Datta, S. N.; Mallik, B. Int. J. Quantum Chem. 1997, 61, 865. (6) Datta, S. N.; Mallik, B. J. Phys. Chem. B 1997, 101, 4171. (7) Datta, S. N.; Mallik, B. J. Phys. Chem. B 1997, 101, 5191. (8) Datta, S. N.; Prabhakar, B. G. S.; Nehra, V. J. Phys. Chem. B 1999, 103, 2291. (9) Gatti, D. L.; Meinhardt, S. W.; Onishi, T.; Tzagoloff, A. J. Mol. Biol. 1989, 205, 421. (10) Telser, J.; Hoffman, B. M.; LoBrutto, R.; Onishi, T.; Tsai, AhLim; Simpkin, D.; Palmer, G. FEBS Lett. 1987, 214, 117. (11) Pople, J. A.; Beveridge, D. L. Approximate Molecular Orbital Theory; McGraw-Hill: New York, 1990. (12) Datta, S. N.; Deshpande, R. Ind. J. Pure Appl. Phys. 1997, 35, 483. (13) Gaussian 92 for Windows; Gaussian Inc.: Pittsburgh, 1992. (14) Liebl, U.; Pezennec, S.; Riedel, A.; Kellner, E.; Nitschke, W. J. Mol. Biol. 1992, 267, 14068.
