Article pubs.acs.org/JPCA
Understanding Rubredoxin Redox Sites by Density Functional Theory Studies of Analogues Yan Luo,† Shuqiang Niu,† and Toshiko Ichiye*,†,‡ †
Department of Chemistry, Georgetown University, Washington D.C. 20057, United States Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, United States
‡
S Supporting Information *
ABSTRACT: Determining the redox energetics of redox site analogues of metalloproteins is essential in unraveling the various contributions to electron transfer properties of these proteins. Since studies of the [4Fe−4S] analogues show that the energies are dependent on the ligand dihedral angles, broken symmetry density functional theory (BS-DFT) with the B3LYP functional and double-ζ basis sets calculations of optimized geometries and electron detachment energies of [1Fe] rubredoxin analogues are compared to crystal structures and gas-phase photoelectron spectroscopy data, respectively, for [Fe(SCH3)4]0/1−/2−, [Fe(S2-o-xyl)2]0/1−/2−, and Na+[Fe(S2-oxyl)2]1−/2− in different conformations. In particular, the study of Na+[Fe(S2-o-xyl)2]1−/2− is the only direct comparison of calculated and experimental gas phase detachment energies for the 1−/2− couple found in the rubredoxins. These results show that variations in the inner sphere energetics by up to ∼0.4 eV can be caused by differences in the ligand dihedral angles in either or both redox states. Moreover, these results indicate that the protein stabilizes the conformation that favors reduction. In addition, the free energies and reorganization energies of oxidation and reduction as well as electrostatic potential charges are calculated, which can be used as estimates in continuum electrostatic calculations of electron transfer properties of [1Fe] proteins.
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analogues in solution because the structure of the first solvation shell makes large contributions to E°. Thus, the recent electrospray photoelectron spectroscopy (PES) measurements of the vertical and adiabatic detachment energies (VDE and ADE, respectively) (Figure 1b) for iron−sulfur analogues are a breakthrough for probing the energetics directly in the gas phase, without any environmental contribution.7 The iron−sulfur electron transfer proteins, which are found in various biological processes such as photosynthesis, respiration, and nitrogen fixation,8 are ideal for examining the inner versus outer sphere contributions to reduction potentials because analogues have been synthesized that are good mimics of the protein sites.9 The simplest redox site, [Fe(SCys)4]1−/2−, contains the [1Fe] core and is mainly found in small electron transfer proteins including rubredoxin, desulforedoxin, desulfoferrodoxin, rubrerythrin, and nigerythrin, all of which have a similar rubredoxin fold or domain.10 The [1Fe] proteins have reduction potentials that differ by as much as ∼300 mV11,12 so understanding the molecular basis of these differences is important in determining how proteins can affect the reduction potential of their redox sites. Several analogues of the redox site have been synthesized, their electrochemical reduction
INTRODUCTION Proteins serve a vital role in the transport and utilization of cellular energy by performing electron transfer reactions.1,2 The rate is given by Marcus theory3 so that the reaction barrier at a given temperature is determined by the reaction free energy, ΔG°, and the reorganization energy, λ (Figure 1a). ΔG° is composed of the free energies of the oxidation of the donor and the reduction of the acceptor; thus, the standard reduction potential, E°, of an electron transfer protein is one of its most important functional characteristics.4 The reduction free energy, ΔredG°, is equal to the negative of the oxidation free energy and can be divided into contributions from the inner sphere due to oxidation/reduction of the redox site and the outer sphere due to electrostatic interaction of redox site with the environment, which consists of the surrounding protein and solvent.4−6 λ is similarly composed of the energy to reorganize the donor to its oxidized geometry and the acceptor to its reduced geometry, and each can also be divided into contributions from the inner sphere involving the structural change of the redox site and the outer sphere involving the structural change of the environment. Redox site analogues allow the inner sphere energetics to be studied without perturbations from the complex protein environment, which then allow further studies in which the protein effects are added.4,5 However, separating the contributions of the redox site from the solvent is difficult in E° of © 2012 American Chemical Society
Received: June 12, 2012 Revised: August 6, 2012 Published: August 10, 2012 8918
dx.doi.org/10.1021/jp3057509 | J. Phys. Chem. A 2012, 116, 8918−8924
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BP86 functional gives poorer energies.6 Moreover, our recent studies of [4Fe−4S] proteins have shown that the reduction potentials combining ΔredGin from BS-DFT calculations of gasphase analogues with ΔredGout from Poisson−Boltzmann (PB) continuum electrostatic calculations of protein crystal structures using partial charges for the redox site from the BS-DFT calculations are in good agreement with experiment.32 However, these studies also show the conformational dependence of the detachment energies.33 Computational studies of [1Fe] sites have played a particularly important role. Our earlier BS-DFT studies25 of the geometry, electronic structure, and reduction energetics of [Fe(SCH3)4]0/1−/2− and [Fe(SCH3)3]0/1− focused on calibrating density functionals and basis sets against experiment. These studies showed that spin-unrestricted B3LYP gives the best results among several hybrid functionals tested in comparison with experiment and with energies at coupled-cluster (CCSD and CCSD(T)) theory levels. In addition, the double-ζ basis sets 6-31G**34 and DZVP235 both give good geometry compared to experiment, and adding diffuse functions to the sulfurs in 6-31G** gives the best redox energies. Recently, Hillier and co-workers have used comparisons of similar calculations with similar experimental redox properties to deduce semiempirical parameters for several rubredoxin analogues.36 Also, the inner-sphere reorganization energy of [Fe(SCH3)4]1−/2− has previously been investigated by Ryde and co-workers also using spin-unrestricted B3LYP but with the double-ζ basis set of Schäfer et al.37 for the iron and 6-31G* basis set34 for the other atoms.22 Overall, calculations using the B3LYP functional and double-ζ basis sets appear to give a good description of the redox energetics of [1Fe] protein analogues. Here, BS-DFT calculations using spin-unrestricted B3LYP with double-ζ basis sets of several redox site analogues of [1Fe] investigate the 1−/2− redox couple of the [1Fe] rubredoxins. While previous studies were only of [Fe(SCH3)4]0/1−/2− in the protein conformation, here the structure and redox energetics of [Fe(SCH3)4]0/1−/2−, [Fe(S2-o-xyl)2]0/1−/2−, and Na+[Fe(S2-oxyl)2]1−/2− in different conformations are calculated. First, the optimized geometries, VDE, and ADE are compared to crystal structures and PES data, respectively; vertical attachment energies (VAE) are also calculated for completeness. Since the PES detachment energies for Na+[Fe(S2-o-xyl)2]1−/2− are the only gas phase measurements for the 1−/2− couple, thermodynamic cycles are used to extend the experimental data to the 1−/2− couple.25 These results show that variations in the inner sphere energetics by up to ∼0.4 eV can be caused by differences in the ligand dihedral angles in either or both redox states. Also, free energies of oxidation and reduction, reorganization energies, and electrostatic potential charges were calculated.
Figure 1. Schematic reaction coordinate diagram for an electron transfer reaction: (a) electron transfer between molecule D−A and DA−, (b) electron detachment of A− to A and electron attachment of A to A−.
potentials have been measured in solution,13 and their PES oxidation potentials have been measured in the gas phase.7,14 However, the biologically relevant 1−/2− redox couple is not directly accessible in the PES experiments since [Fe(SR)4]2− analogues are not stable in the gas phase, while Na+[Fe(SR)4]2− analogues, which are stable in the gas phase, have the added contribution of the cationic sodium.14 Computational chemistry has been important in understanding the redox energies as well as electronic structures of Fe−S redox sites.6 Broken-symmetry density functional theory (BS-DFT) approach15 is useful for treating the strong spinpolarized interactions in iron−sulfur sites observed in Mössbauer, electron paramagnetic resonance (EPR), and PES experiments.8,9,16,17 Noodleman, Case, and co-workers have obtained good electronic structures and Heisenberg spin coupling contributions to magnetic properties for iron−sulfur clusters constrained to experimental geometries using BS-DFT with local density approximation functionals and spin projection methods.18,19 More recently, they have investigated the redox energetics of the [4Fe−4S] analogues and proteins using the local density functionals with the BP86 exchange and correlation functionals.20 However, B3LYP21 is the most widely used hybrid functional for transition metal systems, especially first-row transition metals, because hybrid generalized gradient approximation (GGA) methods usually give better structural and energetic properties.22−24 Our systematic investigations using B3LYP for [1Fe],25,26 [2Fe−2S],27−29 and [4Fe−4S]30,31 analogues are in good agreement with PES detachment energies, while comparisons with the literature show that
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METHODS Spin-unrestricted DFT calculations with Beck’s original three parameter fit38 using the Lee−Yang−Parr correlation functional (B3LYP)21 were performed for [Fe(SCH3)4]0/1−/2−, [Fe(S2-oxyl)2]0/1−/2−, and Na+[Fe(S2-o-xyl)2]1−/2− analogues of the rubredoxin (Rd) redox site using the Gaussian03 package39 except as noted. The molecular orbital visualizations were performed using the extensible computational chemistry environment (Ecce) software.40 The geometries were optimized and energies calculated using DZVP235 and 6-31G**34 basis sets with an integration grid of 75 radial shells and 302 angular points per shell (75,302). Since Na+ does not have a 8919
dx.doi.org/10.1021/jp3057509 | J. Phys. Chem. A 2012, 116, 8918−8924
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Scheme 1. Thermodynamic Cycle between [Fe(S2-o-xyl)2]2− and [Fe(S2-o-xyl)2]1−
DZVP2 basis set in Gaussian03, the all-electron DGauss DZVP basis set35 was used for Na+. The frequencies for the vibrational energies and free energies were always calculated at the level of the geometry optimization. Electrostatic potential fitting (ESP) charges were obtained using the CHELPG scheme.41 In addition, single-point energies of the B3LYP/6-31G** optimized geometries were calculated with sp-type diffuse functions42,43 added to the sulfur atoms of 6-31G** using NWChem44 with an integration grid of 70,590 on the C and O, 123,770 on the S, and 130,974 on the Fe; these are referred to as 6-31(++)SG**//6-31G** basis set calculations. Calculations of the energetics of the reduction reaction A + e− → A− have been described thoroughly6 and so are only summarized here. The VDE and VAE (Figure 1b), assuming that most of the coordinates are in their ground vibrational state, are calculated as −
D2d structure similar to that in rubredoxin48 (Figure 2) using B3LYP with the 6-31G** and DZVP2 basis sets. The S4 and
−
A A A A VDE ≈ [Eelec (A−) − Eelec (A−)] + [Evib,0 (A) − Evib,0 (A−)] −
−
A A A A VAE ≈ [Eelec (A) − Eelec (A)] + [Evib,0 (A−) − Evib,0 (A)]
(1)
where Eelec is the calculated electronic energy for the molecule in the superscript at the optimized geometry of the molecule in parentheses, and Evib,0 is the calculated vibrational energy at 0 K or ZPE. The ADE (Figure 1b) is calculated as −
−
A A A A ADE ≈ [Eelec (A) − Eelec (A−)] + [Evib,0 (A) − Evib,0 (A−)]
(2)
Finally, ΔredG (Figure 1a) are calculated as −
−
A A A − A Δred G = [Eelec (A−) − Eelec (A)] + [Evib, T (A ) − E vib, T (A)] −
A − A − T[Stotal, T (A ) − Stotal, T (A)]
(3)
where Evib,T is the vibrational energy and Stotal,T is the total entropy, both at temperature T = 298.15 K. Finally, λred = VDE − ADE is the reorganization energy from A to A− on the potential energy surface of A, and λoxd = ADE + VAE is the reorganization energy from A− to A on the potential energy surface of A−, assuming the reorganization energies along the free energy curves are the same as those along the potential energy curves. Experimental ADEs for analogues with redox couples inaccessible by experiment are estimated using thermodynamic cycles from experimental ADE of other species and calculated binding energies. For instance, the estimated experimental ADE for [Fe(SCH3)4]2− is from the experimental ADE of [Fe(SCH3)3]− and the calculated binding energies of −SCH3− to [Fe(SCH3)3]1− and of −SCH3− to [Fe(SCH3)3]0 as in previous work,25 with the new results here in the lowest gas phase conformation and including the ZPE. In addition, the estimated experimental ADE for [Fe(S2-o-xyl)2]2− is from the experimental ADE of Na+[Fe(S2-o-xyl)2]2− and the calculated binding energies of Na+ to [Fe(SCH3)4]2− and of Na+ to [Fe(SCH3)4]− (Scheme 1). All binding energies were obtained using 6-31(++)SG**//6-31G** basis sets with the ZPE obtained using 6-31G**.
Figure 2. Ball and stick rendering of [Fe(SCH3)4]1− in both analogueand protein-like conformations, [Fe(S2-o-xyl)2]1− and Na+[Fe(S2-oyl)2]1−.
D2d structures of [Fe(SCH3)4]1− will be referred to as the crystal and protein conformation, respectively. Selected internal coordinates of the core (Table 1) and the conformation (Table 2) are given here, and more complete geometries are given in ref 49. Here, “S” refers to S1 and S2, and “S′” refers to S3 and S4 (Figure 2). For the [Fe(SCH3)4]1− and [Fe(S2-o-xyl)2]1− analogues, the calculated Fe−S bond lengths, the S−Fe−S
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RESULTS AND DISCUSSION Geometries. Full geometry optimizations were performed for [Fe(SCH3)4]2−/1−/0, [Fe(S2-o-xyl)2]2−/1−/0, and Na+[Fe(S2o-xyl)2]2−/1− beginning from crystal structures (S4) of analogues45−47 as well as [Fe(SCH3)4]2−/1−/0 in an approximate 8920
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Table 1. DFT Optimized and Experimental Geometries of the Core: Fe−S Bond Lengths (rFe−S, in Å) and S−Fe−S Bond Angles (θS−Fe−S and θS−Fe−S′, in deg) θS−Fe−Sa
rFe−S analogue [Fe(SCH3)4]2− [Fe(SCH3)4]1−b [Fe(SCH3)4]0 [Fe(SCH3)4]2−c [Fe(SCH3)4]1−c [Fe(SCH3)4]0c [Fe(S2-o-xyl)2]2−d [Fe(S2-o-xyl)2]1−d [Fe(S2-o-xyl)2]0 Na+-[Fe(S2-o-xyl)2]2−e Na+-[Fe(S2-o-xyl)2]1−
DZVP2
6-31G**
2.418 2.303 2.217 2.412 2.308 2.213 2.431 2.385 2.311 2.286 2.213 2.213 2.511 2.326 2.370 2.254
2.428 2.315 2.228 2.424 2.319 2.228 2.445 2.388 2.324 2.296 2.313 2.230 2.533 2.341 2.384 2.264
exptl 2.263
2.368 2.342 2.275 2.259
2.376 2.336
DZVP2
6-31G**
109.7 110.2 130.8 109.9 110.6 128.5 107.7 120.2 106.9 118.0 97.5 113.0 112.3 116.0 111.8 112.0
113.7 110.5 133.0 112.2 110.6 128.4 107.0 120.0 107.0 117.8 82.5 114.9 114.2 119.4 111.0 113.0
θS−Fe−S′a exptl 114.2
106.6 122.3 109.2 112.2
107.0 103.5
DZVP2
6-31G**
109.3 109.0 100.0 109.3 108.9 100.9 107.0 107.0 107.8 107.8 111.3 111.3 107.2 107.2 108.3 108.3
107.4 108.9 99.0 108.6 108.9 100.9 107.3 107.3 108.0 108.0 113.9 113.9 105.9 105.9 108.2 108.2
exptl 107.0
106.8 106.8 108.9 108.9
111.5 111.5
a θS−Fe−S is an average of two S−Fe−S angles about the principal axis: θS1−Fe−S2 (top) and θS3−Fe−S4 (bottom); θS−Fe−S′ is an average of four S−Fe−S angles perpendicular to the principal axis: θS1−Fe−S3, θS1−Fe−S4, θS2−Fe−S3, and θS2−Fe−S4. bExptl from ref 45; variations in rFe−S are 0.001 Å and in θS−Fe−S are
