J. Phys. Chem. 1995, 99, 1338-1348
1338
Electronic Structure of the Cu, Zn Superoxide Dismutase Active Site and Its Interactions with the Substrate Paolo Carloni,**tPeter E. Blichl, and Michele Parrinello IBM Research Division, Zurich Research Laboratory, 8803 Riischlikon, Switzerland Received: July 13, 1994; In Final Form: October 11, 1994@
First-principles density functional theory calculations have been carried out for various models of oxidized and reduced Cu, Zn superoxide dismutase (SOD) active sites and the adduct with its substrate, the superoxide anion. The electronic structure of the first stages of the enzymatic reaction is described. The electrontransfer process between the SOD copper(I1) ion and superoxide is discussed. A model potential energy functional derived from these calculations allows the interaction to be discussed for any configuration of the SOD Cu ion, the superoxide, and Arg141-the most important residue in terms of electrostatic effects. The model indicates that superoxide is bound to Cu and that Argl41 easily separates from the superoxide bonded to the active site.
peroxide by taking two protons and one electron from the reduced copper:
I. Introduction
Copper, zinc superoxide dismutase (SOD) is a dimeric enzyme (molecular weight 32 000) containing a copper and a cu2+ 0,. c u + 0, (1) zinc ion in each subunit.' In each of the two active sites present in the enzyme, a copper ion is coordinated by four histidine Cu' 0,. 2H' Cu2+ H,O, (2) residues in a distorted square-planar geometry. One of them, a histidinato, acts as a bridge between the copper and the zinc Within this scheme, it has been suggested that the bond ion. An aspartate and two other histidine residues complete between copper and His6 l-the bridging histidine-breaks down the coordination of the zinc ion. in the first step;54the imidazolate group of His61, being highly The copper ion, which is essential to the enzyme activity,, is basic, would then take a proton from the s ~ l v e n t .In~ the ~~~ located at the bottom of a shallow cavity in the protein. The second step the proton bonded to the His61 is transferred to a surface of this cavity bears numerous charged residues that are second superoxide molecule forming HOz-, while the imidabelieved to play an important role in the catalytic mechanism zolate bridge between copper and zinc is regenerated. by steering the substrate to the copper site. The zinc ion, on On the basis of quantum-mechanical calculations, Osman and the other hand, is completely buried in the protein. Bash48 and Rosi et a1.35,36proposed another model: They The physiological function of SOD is the dismutation of the suggested the formation of a stable copper- superoxide intersuperoxide radical anions. Superoxide is produced during the mediate that is able to oxidize a second superoxide molecule; oxygen metabolic cycle and is very reactive toward the cell^.^^^ in this case no breaking of the copper-His61 bond needs to be It is dismutated to molecular oxygen and hydrogen p e r o ~ i d e , ~ ~ ~ - ' ~ invoked: the latter being scavenged by other enzylnes, such as The rates for the catalytic process are very high ((2-3) x lo9 CU2+ 02,- (CUO,)+ (3) s-' M-' at 298 K)5,14and diff~sion-controlled.~~~~ The crystal structure of theooxidized form of erythocyte (CUO,)+ 02,- (CUO,) 0, (4) bovine isoenzyme is known at 2 A resolution.' Re~ently,'~ work on the crystal structure of the oxidized human isoenzyme has shown its similarity to the bovine isoenzyme; in particular, the (CuO,) 2H+ Cu2+ H,O, (5) geometries of the active site region are very similar. Since the discovery of its enzymatic activity in 1969 by We present here a theoretical description, using ab initio McCord and Fridovich,, several research groups have extendensity functional theory calculations and model energy funcsively investigated SOD as well as its mutants and its adducts tional calculations, of the interaction between the copper(I1) ion with inhibitors, both e~perimentallyl-~~ and t h e ~ r e t i c a l l y . ~ ~ - ~in ~ SOD active side and the substrate of SOD, the superoxide Two mechanisms have been proposed. In the most widely anion. These calculations have allowed us to understand some accepted mechanism,2,5.7.8,14.53-56 the enzyme copper ion is of the important factors that govern the electron-transfer (ET) repeatedly reduced and oxidized in a two-step process. In the process, from the copper(I1) ion to the superoxide. first step superoxide donates its electron to the copper ion. In 11. Computational Procedure the second step a second superoxide is reduced to hydrogen
+ + +
-
+ +
-
+
Permanent address: Department of Chemistry, University of Florence, Via Gino Capponi 7, 50121 Firenze, Italy Abstract published in Advance ACS Abstracts, December 15, 1994. @
0022-365419512099- 1338$09.00/0
-
-
+
+
+
+
A. Modeling. All the models were constructed starting from the crystal structure of bovine oxidized SOD, whose coordinates are available as a PDB file (entry 2SOD in the Brookhaven 0 1995 American Chemical Society
The Cu,Zn Superoxide Dismutase Active Site Data Banks8). At present it is not possible to perform simulations on the entire SOD with ab initio methods. Therefore we limit our considerations to one of the two independent active sites and active site channels, namely the one present in the “orange” subunit.’ The model of the active site contains the essential copper site, its four ligands, and one ammonium representing Argl41, which is the most relevant residue of SOD in terms of biological activity. There have been a number of approximations of a similar type in the literature. The reasons behind our modeling are the following. I. Modeling of the Active Site. Some simplified models have already been studied in the literature for the description of t h i ~ ~ * -or ~ Ostructurally similar active sites, such as the zinchistidine complexes in carbonic anhydrase and carboxypeptidase A: the histidine residues were replaced by ammonia in the simplest models4*-so~s9-63and by imidazoyl in the more sophisticated model^.^'-^^ Other simple models have also been described in the literature.& Whereas using ammonia molecules appears to be too substantial a simplification, we would argue that replacing the histidine groups with the imidazole molecules contains most of the important chemical effects, such as the n-electron polarizability and a-donor capability.62 Use of the methylated species will not alter the picture significantly but will considerably increase the computational effort. Therefore we have replaced the four histidine residues coordinating the copper ion by four imidazole rings. Another simplifying assumption of our model has been to describe the cationic effect of the zinc and its ligands, i.e., the complex [Zn(His)3Asp]+,by protonating the nitrogen atom Nd 1, which in the real protein binds to the zinc ion. Experimental data show that the zinc-free enzyme has almost the same specific activity as the holoprotein at physiological pH.12*67Also on the basis of experimental evidence, it was sugge~ted~.~ that the role of the zinc-His61 moiety is secondary in the catalytic process, its most likely role being that of electrostatically favoring the copper-superoxide interaction. This view was subsequently supported by partial electrostatic charge calculations for the active site of SOD,39which showed that its dipole moment is roughly oriented in the copper-zinc direction. 2. Modeling of the Active Site Channel. Several residues that form the active site channel, such as Argl41, Thr56, Thr135, Lys136, Glu130, and Glu13 1?* may be relevant to the enzymatic behavior of SOD16-20.22-24 for both their e l e c t r o s t a t i ~and ~~~ s t r u c t ~ r a Iroles. ~~.~~ However, it has been realized that none of these residues plays a crucial role in the catalysis, because simple copper histidine complexes are good superoxide scavenger^?^ and mutation of the above amino acids does not spoil the activity of the enzyme.17J9 Therefore, the investigation of the electronic structure of copper imidazole complexes is expected to provide detailed insight into the chemistry of copper in SOD as well. We decided, however, to include the guanidinum group for Argl41 in our model. This was done for two reasons: (1) It allows a comparison with previous quantum chemistry model calculations for the SOD active site, in which Argl41 was included to estimate the H-bond interaction between its guanidinum group and the distal oxygen of the superoxide and (2) the inclusion the most important electrostatic effect in the modeling (Argl41 is the charged residue closer to copper in the active site channel, the Nvl (Argl41) being only 5 A away from copper). In analogy to previous calculation^,^^,^^ we have modeled the guanidinum group as an ammonium cation.
J. Phys. Chem., Vol. 99, No. 4, 1995 1339 0
Figure 1. Schematic view of complex I11 between superoxide and SOD active site.
3. Hydration of the Channel. In the crystal structure of oxidized SOD two water molecules have been identified 2.8 and 3.2 A from the copper ion?0 Angular overlap calculations have shown that not even the water molecule closer to the copper contributes to its ligand field.30 Therefore, we have decided not to include these water molecules in our modeling. However, we have included a water molecule in our complexes, as far as possible from the active site, so as not to affect the electronic levels of the model (see section 111, Results and Analysis). The inclusion of this additional water molecule in our models is not meant to describe one of the water molecules mentioned above. In all the models but one (model V below), the presence of such a water is inconsequential. In V, however, the protonation of the imidazole is an essential feature; therefore in the set of calculations pertaining to V this additional water molecule is added in the form of H+ OH-, where the proton is attached to the nitrogen atom Nc2, which is bonded to the copper ion in oxidized SOD. This allows direct comparisons between energies of systems that contain an equal number of atoms, and thus we can profit from error cancellations, which in turn renders our estimate more precise. The oxygen atom of the water molecule or of the OH- group is 5.2 A from copper. B. Atomic Structures. The structural parameters for the molecules H20, 0 2 - , N&+, and OH- were taken from the projector augmented wave (PAW) optimized structure and are in good agreement with experiment. The hydrogen atoms of the imidazole were added assuming standard bond lengths and bond angles. I. Oxidized SOD Active Site (Total Charge +3). The imidazole rings were positioned as in the crystal structure. The ammonium group nitrogen was positioned at the location of the Ne2 of the guanidinum of Argl41 in the crystal structure.’ The resulting nitrogen-copper distance was 5.0 A. 11. Reduced SOD Active Site (Total Charge +2). After oxidation of the first superoxide molecule and before an eventual protonation process, the active site probably has a structure close to that of the oxidizied SOD. Therefore, we have studied this complex, which is virtually the same as I, the only difference being the total charge. 111. Complex Superoxide-OxidizedSOD Active Site (Total Charge +2). The mode of binding the superoxide to the active site of SOD is shown in Figure 1. As the exact position of the superoxide anion is not known, we have attempted to locate it
+
Carloni et al.
1340 J. Pliys. Cltem., Vol. 99, No. 4, 1995
Arg141
/-
A ,
c
8
His 61
0‘
‘
1
Figure 2. Schematic view of model V for reduced SOD active site.
using a few guiding principles: (1) The distal oxygen atom forms a hydrogen bond with the ammonium cation. (2) We reproduce Osman and Bash’s structure4*as closely as possible. (3) No overlap of van der Waals radii is allowed. (4) The angle 0-0-Cu has been postulated to be %120° and the copperoxygen distance to be ~2 A? Fortunately, these four criteria do not leave much arbitrariness. Furthermore, the results of the calculations are rather insensitive to the finer details of the superoxide position. Indeed, test calculations were made by placing the substrate in slightly different positions and revealed no significant change in the results. The resulting distance between the ammonium nitrogen and the distal oxygen is 3.5 A. The coordinates of this complex can be obtained from the authors. For this complex we have also performed a calculation in which the 0 2 - was allowed to adjust its position. After the optimization, the distance between Cu and the center of mass of 0 2 - turned out to be 2.75 A. IV. Complex Superoxide-Oxidized SOD Active Site (Total Charge +2). Molecular dynamics (MD) simulations on have shown that the guanidinum group of Argl41 undergoes large movements even on the picosecond time scale. Therefore, we may expect that the hydrogen bond and electrostatic interactions between the substrate and the arginine residue are stronger than those in 111. To test the influence of the bond distance between the superoxide and the arginine residue, we also constructed a structure that is identical to model 111, but the position of the NH4+ tation in the present model is closer to the distal oxygen (2.5 A) and is oriented differently. This leads to a much stronger hydrogen bond (apical oxygenhydrogen distance: NH4+ 1.5 A). V. Copper(I)Triimidazole Complex (Total Clmrge 4-2). This complex is a model of the reduced SOD active site, following the most widely accepted mechanism (reactions 1-2). We have tilted the imidazole representing His61 away from the copper ion (Figure 2) such that the distance from copper to the formerly bonded nitrogen atom is 3.4 A. This nitrogen atom has been protonated, and the water molecule has been deprotonated. The other three imidazole rings have been left in the same position as in oxidized SOD. The coordinates of this complex are available from the authors. C. Calculations. I . Local Densiv Approximation. The present work is based on the local density approximation (LDA) of the density functional the0ry.7”~~ This is a first-principles method and, in many cases, has been found to be superior to the Hartree-Fock (HF) approximation and similar in accuracy to the MP2 level.73 We use the LDA parameterization by
Perdew and ZungerJ4 which is based on Monte Carlo simulations of the free electron gas investigated by Ceperley and Alder.75 Some of our calculations were done using spinpolarized techniques. 2. Car- Parrinello Projector Augmented Wave Method. In this work, we exploit the ability of the Car-Paninello method76 to determine efficiently the electronic structure of large systems without symmetrty. Most existing implementations of the Car-Parrinello method are based on the pseudopotential approach, which allows the use of a simple plane-wave basis set. For first-row and transition-metal atoms, however, the pseudopotential approach becomes computationally very demanding. To avoid the restrictions of the conventional pseudopotential methods, we employ the PAW method developed by one of us.77 It borrows the concept of augmented wave functions from existing methods such as the linear augmented plane wave method7*but introduces a more general concept of augmentation, which is particularly convenient in combination with the Car-Pamnello method. The PAW method is comparbale in accuracy to the linear augmented plane wave method, which is believed to be the most accurate electronic structure method for LDA calculations. On the other hand, the time-limiting operations of the PAW method are very similar to those of the pseudopotential method, and hence it is substantially more favorable than conventional augmented wave methods. 3. Supercells. As our basis set is plane-wave based, it is convenient to use supercells also for isolated molecules. This implies that every molecule is repeated periodically, so that a kind of molecular crystal is formed. For charged systems, a homogeneous neutralizing background is added. The energy due to the interaction of periodic images and between the molecule and the background has been subtracted using a simple correction formula: we replace the compensating background by a constant, spherical charge density with the same density and charge as the positive background. Furthermore, we assume that the excess density is localized in a region that is small compared to the distance of the periodic images. In correcting for the periodic images under these approximations, we must add an energy of AE = 0.9N”-/rcin Hartree atomic units, where N is the excess number of electrons and (4n/3)rc3is equal to the volume of the supercell. Similarly all one-particle states are shifted by A6 = dAE/dN = -l.8N/rc. This correction has been made in all our total energies and one-particle energies. However, in our figures we did not apply the correction to the energy levels. 4. Projected Densiq of States. The analysis of the electronic structure in such a complex system is nontrivial. Here we make use of the projected density of states (PDOS):
which is an economical way to represent energy levels in complex systems. WR/nrthe angular momentum weight of the n-th state at the atomic site R, is obtained from a decomposition of the wave function into angular momenta. In practice, we found it convenient to smooth the PDOS with a Gaussian function. The width of this Gaussian has been chosen to be 0.27 eV (26 W/mol). 5. Machines. All calculations were performed by using the the PAW program77 running on IBM/RS 6000 530, 540, and 550 workstations. 6. Test Calculations. We first optimized the structure of the individual fragments for H20, NH4+, OH-, 0 2 - , and 0 2 . They constitute the various models of the SOD active site and
J. Phys. Chem., Vol. 99, No. 4, 1995 1341
The Cu, Zn Superoxide Dismutase Active Site TABLE 1: Comparison between Bond Distances (A) and Angles (deg) in Imidazole Molecule in the Optimized Structure and in the Crystal Structureg1” PAW
crystal structure
40
deviation
Bond Distances
1.374 1.384 1.329 1.384 1.378 1.036 1.103 1.102
1.358 1.381 1.333 1.389 1.378 1.053 1.087 1.086 1.087
1.101
0.016 0.003 -0.004 -0.005
0.000 -0.0 17
0.016 0.016 0.014
N( 1)-C(5)-H(5)
122.3 111.2 107.5 105.4 105.4 110.7 105.2 126.4 122.7 126.0 127.8 121.5 132.5
C(5)-N( 1)-C(2) N( 1)-C(2)-N(3) C(2)-N( 3)-C(4) N(3)-C(4)-C(5) N(3)-C(4)-C(5) C(4)-C(5)-N( 1) C(2)-N( 1)-H(N1) N( l)-C(2)-H(2) N(3)-C(2)-H(2) C(5)-C(4)-H(4) N( 3)-C(2)-H (4) C(4)-C(5)-H(5)
30
-
25
-
45
Bond Angles
123.0 111.8 107.2 105.3 105.3 109.8 106.0 127.0 123.7 124.5 128.0 122.2 131.0
-0.7
40
-0.6
35
0.3
0.1 0.1 0.9 -0.8 -0.6 -1.0 1.5 -0.2 -0.7 1.5
cn a
10 -
20
15
5 -
0 50
1
I
I
A
45
bond dist
0-0
1.36 (1.35)”
10
-30
-25
-20
-15 Energy (eV)
-10
-5
deviation
1.35”
-O.Ol(O.OO)(l
Figure 3. Total (solid line) and imidazole (dashed line) PDOS in (a) I, (b) 111, and (c) V. The Fermi levels of the complexes are indicated as dashed lines. At top left, the copper d-level splittings are also shown.
1.216
O.Ol(O.0l~
The PDOS of the various fragments to the total PDOS are indicated.
0.96’ 104.5‘
0.03 0.4
0.96”
0.03
7. Calculations of the Active Site Models. The same computational setup as in the test calculations was used, but the active site model required a larger supercell (15 A x 16 A x 12 A), which we then kept the same for all the models. This supercell ensures that the minimum distance between repeated images was 6 A, as in the test calculations. For I and 111 we also carried out spin-polarized calculations.
Oxygen Molecule
1.22 (1.22)”
(c)
exp
Superoxide Molecule
0-0
’
I
TABLE 2: Equilibrium Bond Distances (A) and Angles (de@ in the Superoxide Anion, Oxygen Molecule, Water Molecule, and Ammonium Cation Derived from PAW and Experiment (Calculations Non-Spin-Polarized unless Indicated Otherwise)
bond dist
i I
“As the molecule forms hydrogen bonds in the crystal, small discrepancies in the structural parameters of nitrogen and hydrogen atoms involved in hydrogen bonds are to be expected. (The values taken for the crystal structure are corrected for rigid-body librations; see also ref 91 for the atomic nomenclature.)
PAW
I
I
i
Water Molecule bond dist bond angle
0-H H-0-H
bond dist
0-H
0.99 104.9 Hydroxide Anion
0.99
Ammonium Ion Molecule bond dist
NH
1.01
1.03‘
0.02
a Value obtained for the spin-polarized calculation. See ref 92. See ref 93. See ref 94. See ref 95.
its adduct with the substrate. Our optimization procedure relaxed all the positions independently. We used large orthorhombic supercells whose size was determined by the system investigated. The minimum value of the distance between repeated images of the same molecule was 6 A. The edges of the resulting simulation box varied from 8 to 12 A. The calculations for the isolated oxygen moiety were done in a cubic cell with a side length of 8 A. The Kohn-Sham orbitals were expanded at the r point (k = 0) of the Brillouin zone in augmented plane waves. A cutoff of 30 Ry (39 x lo3 kJ/mol) was used. Spin-polarized calculations were carried out for the paramagnetic molecules 02+, 02-, and 02 in the singlet and the triplet spin state. Tables 1 and 2 show that this setup is in excellent agreement with experiment: the deviation from the experimental values are within 3.0% for bond lengths and 1.2% for bond angles.
m.
Results and Analysis
I. Oxidized SOD Active Site. In Figure 3a we show the results for this complex. Most of the total PDOS come from the imidazoles. Contributions from other species are easily identified, because they are related to the levels of the isolated species simply by a rigid energy shift for each fragment. As expected from pure geometrical considerations, the four imidazole nitrogen atoms bound to copper act as a-donors and produce a square-planar distort.ed ligand field:79the copper d,, d,,, and dyzlevels form a large, narrow, and nonbonding peak. Above and below this peak lie a bonding and an antibonding state derived from the d2-3 orbital and the ligands, which act as a-donors. Two small shoulders of the main peak are due to the d t orbital, hybridized with a fully symmetric combination of the ligand states. The bonding-antibonding splitting of the d2-3 derived states is 5.3 eV (51 1 kJ/mol). The d2-3 derived
Carloni et al.
1342 J. Pltys. Clwrn., Vol. 99, No. 4, 199.5
ce, Figure 5. Representation of complex 111 and the electronic density 0.01 au contour of its HOMO obtained with the non-spin-polarized calculation. For clarity, we have omitted the representationof the water molecule present in the complex. Figure obtained with MOVIE program by J. She1ley.
. . . ... ... .. ...
.. .:
-6
-
25
20
15
10
5
0
5
10
15
20
25
poos
Figure 4. Spin-dependent PDOS for complexes I and 111. (a) PDOS for I. Solid line: total PDOS; dashed line: Cu-d PDOS; dotted line: imidazole PDOS. (b) PDOS for 111 in the singlet configuration. Solid line: total PDOS; dashed line: Cu-d PDOS; dotted line: dioxygen PDOS. (c) PDOS for 111 in the triplet configuration. Notation as in (b).
antibonding level lies marginally above the highest occupied molecular orbitals (HOMOs) of the imidazole ligands. To estimate spin polarization effects on the semioccupied d,r?-,.2,we performed spin-polarized calculations. The overall features of the PDOS remain unaffected, but the HOMOs of d,+? character is spin-split by 0.7 1 eV (69 kJ/mol; Figure 4a). As a result the HOMO-LUMO (lowest unoccupied molecular orbital) gap is determined solely by the spin splitting, consistent with the observed paramagnetic behavior of the oxidized active site. A situation similar to that in the SOD active site occurs in hemocyanine model compounds, which have recently been studied with the Xa-scattered wave technique.80.8* These compounds, in which the metal ion is coordinated to four ligands (ammonia and peroxide anion) in a planar geometry, exhibit strong hybridization between the d.+,.? orbital and the ligands acting as o-donors. Moreover these model compounds exhibit little interaction between the ligands and the other d orbitals. 11. Reduced SOD Active Site. The first step of the reaction in the commonly accepted mechanism (reactions 1 and 2) is the ET to the SOD active site. We have therefore investigated the electronic structure of the reduced SOD active site. The most relevant result is that the ET cannot be understood in a
rigid band model, as would result from extended Huckel calculations.82 Instead, the Coulomb repulsion on the copper orbital shifts the d,;+ level significantly upwards, creating a new peak in a former gap of the electronic level distribution. The nonbonding peak is shifted up even further than the hybridized states. This is due to the somewhat larger spatial extent of the bonding and antibonding states compared to that of the nonbonding states, resulting from their hybridization with the ligands. The shift of the HOMO is as large as 2.85 eV (275 kJ/mol). 111. Complex Superoxide-OxidizedActive Site. Let us now turn to the discussion of the effect of bringing a superoxide molecule into close proximity with the copper ion. As in the previous case we first discuss the main features of the electronic structure for the non-spin-polarized calculation (Figure 3). Below - 15 eV (- 1447 kJ/mol) in our energy scale, the density of states is similar to a superposition of the density of states of the isolated fragments, which, owing to the electric field from the superoxide, are somewhat shifted from one another. At the Fermi level (Le., the energy midway between the HOMO and LUMO) a new peak containing three states is formed, in what was formerly a gap of about 2 eV (193 kJ/ mol). The character of the states identifies them as the antibonding d,r2-,.2 level of the copper and the two n* orbitals of the superoxide. Figure 5 is a visual representation of the molecular orbital. The almost perfect alignment of these levels is due to the large Coulomb repulsion on copper (already seen in 11) and superoxide: as shown in Figure 6, the charge transfer which occurs from the superoxide to the SOD copper shifts the HOMO of the SOD active site up and, accordingly, the superoxide HOMO levels down. The charge transfer comes to a halt when the two levels are aligned. This alignment does not depend on the fine details of the atomic structure as we have verified by calculations for somewhat different dioxygen positions. In the discussion of the spin polarization effects we must consider two possibilities because the unpaired spin in the superoxide anion and in the copper complex can give rise to either a singlet or a triplet state (Figure 4b,c). The singlet state is less stable by 0.12 eV (12 kJ/mol, Table 3). In both the
J. Phys. Chem., Vol. 99, No. 4, 1995 1343
The Cu, Zn Superoxide Dismutase Active Site
TABLE 3: Energies (kJ/mol) Obtained for Structures I-V, Oxygen, and Superoxide Molecules (Numbers in Parentheses Do Not Contain the Correction for the Positive Background) non-spin-polarized
I, oxidized active site 11, reduced active site 111, complex 02--0x. active site IV,complex 02--0x. active site V, copper(1) triimidazole complex 02-
0 2 02+
-615 -617 -701 -701 -616 -84 -84 -82
spin-polarized
847 (-617 125) 208 (-617 776) 512 (-702 080) 626 (-702 194) 935 (-617 503) 345 (-84 597) 155 921 (-83 173)
-615 868 (-617 146) -617 208 (-617 776)c -701 556 (-702 124)," -701 544 (-701 112) -84 366 (-84 618) -84 249a
Triplet state. Singlet state. Closed-shell system-non-spin-polarized calculation.
(02SOD)-
02-SOD'
Figure 6. Schematic representation of the position of the HOMO levels of SOD and dioxygen. (This representation has been obtained from the model energy functional developed in this paper.) Left: initial state, infinite separation of SOD and 0 2 - . Middle: dioxygen bonded to SOD active site (the electron is partially transferred and the HOMO levels are completely aligned). Right: final state with infinite separation between SOD and 0 2 .
singlet and the triplet configuration, there are large changes in the PDOS of copper and superoxide, because the details of the PDOS depend on the hybridization between copper and superoxide HOMO levels, and the relative position of these levels is altered by spin polarization. The spin splitting on isolated superoxide is 0.84 eV (81 kJ/mol) and that on the antibonding Cu d+2 level is 0.71 eV (69 kJ/mol). We conclude that the major role in the substrate-active site interaction is played by the metal ion, which strongly interacts electrostatically with the antibonding levels of the superoxide. The imidazole ligands are relevant to the catalytic reaction because their a-like interaction splits the d+yz levels into a lowlying level of bonding character and an antibonding state that becomes the HOMO, which is partially occupied in the oxidized form and is able to accept one electron from the superoxide. The most important feature of this interaction is represented by the large Coulomb repulsion between the levels on the copper site as well as between the levels on the superoxide, which makes the positions of the levels strongly dependent on the charge state. The binding energy against dissociation into a neutral oxygen molecule and the reduced SOD active site is 1.03 eV (99 kJ/ mol). Non-spin-polarized calculations overestimate this binding energy by 0.44 eV (42 kJ/mol). Our finding of a positive binding energy is in agreement with the predictions of HF
calculation^.^^^^^ However, Argl41 is a highly mobile and the optimization of its position is expected to lower the energy of the reduced SOD active site as well as that of the substrate SOD active site adduct substantially. The effect of the position of Argl41 on the bonded situation has been studied in the next complex. IV. Complex Superoxide-Oxidized Active Site. In this model we investigated the role of a possible hydrogen bond on the binding of superoxide to the active site. Osman and Bash suggested that Argl41 provides a hydrogen bond link that changes the chemistry of the superoxide ion.48.49We therefore
undertook a new calculation, in which the ammonium ion forms a much stronger H bond in moving from 2.5 to 1.5 A to the superoxide. We find that the electronic structure at the Fermi level, in particular the isolated peak originating from the antibonding copper level and the two n* orbitals on the superoxide, changes only slightly. Other levels are shifted in energy by the longrange Coulomb interaction with the ammonium, whose position has been modified. We attribute these changes to the Coulomb attraction to the nearby cation. The binding energy between the substrate and the active site is increased by 1.12 eV (114 kJ/mol), as derived from nonspin-polarized calculations. The increase of the binding energy is primarily due to the Coulomb interaction between superoxide aqnd the positively charged ammonium ion. V. Copper(I) Triimidazolate Complex. This structure corresponds to the second step in the most widely accepted scenario for the enzymatic reaction. The coordination of copper in the reduced SOD active site is reduced from four to three, and the free ligand picks up a proton from the environment, modeled here as a single water molecule. The total and copper PDOS in this case are shown in Figure 3c; we see that the system remains diamagnetic as do the four coordinated copper complex in reduced SOD. The change in the ligand field induces profound changes in the copper d-related energy levels. The HOMO maintains its d.2-y' character but the spread between bonding and antibonding d states is strongly reduced. As the large splitting of the Cu-d levels is responsible for making the Cu2+ stable, the smaller splitting favors the reduced SOD active site. Thus there is a subtle interplay between the ligand positions, the electron affhity of the enzyme and the ligand bond strength. A. Model Potential Energy Function for the Interaction between the SOD Active Site and the Superoxide. In the density functional theory as originally proposed by Hohenberg and K ~ h nit, is~ shown ~ that the energy of a system is a unique functional of the density which is minimum for the groundstate density. As the density functional is unknown, the practical use of this approach requires some approximations. Here we make an attempt to model the density functional for the system at hand by making a few drastic simplifications. We assume that for the purpose of describing the first step in the enzymatic processes it is not necessary to use the full electronic density but rather the occupation number of a restricted subset of states. We will verify later that this a reasonable assumption. We will determine the parameters by comparing ground state energies of states that differ in the total spin and in the number of electrons. We thus avoid the use of the Kohn-Sham-excited states, which are beyond the validity of the density functional theory. In the density functional theory, the true functional provides the energy of the system for arbitrary values of the density. Likewise, our model is assumed to yield the energy of the
1344 J. Pkys. Ckem., Vol. 99, No. 4, 1995 TABLE 4: Final Model Parameters (kJ/mol) Obtained by
the ab Initio Calculations (Parameters in Parentheses Extracted from Experiment) Eo = -84 155 EO
= -674 (-603)
Jo = 47 (47) Uo = 1120 (980)
Ed = -614 722 6d = -1934.5 J d = 42 u d = 559
system even if the occupation numbers are not those of the ground state. The validity of this assumption for values of the occupation number not included in the model construction will have to be tested with higher level calculations. The model functional serves several purposes. First, it allows us to summarize our findings in a particularly lucid way. Second, it allows us to determine the parameters that are important for the ET. Third, it allows us to extend our results to situations that have not yet been calculated explicitly. Finally, it allows the relevant electronic transitions to be included in classical MD simulations of the entire enzyme, which in turn allows an accurate description of solvent effects. The calculations described above indicate that the relevant one-electron levels involved in the ET are the two highest occupied levels of the superoxide molecule (four if spin states are counted) and the antibonding level on the SOD active site, given by the combination of Cu dx~-~2 and the four nearest imidazole dangling bonds. Furthermore, these levels depend strongly on occupation and to a lesser extent on the spin state. On the other hand, the covalent bond contribution between the copper and the superoxide levels is comparatively small. On the basis of these observations we construct a model that captures these effects in the simplest possible way. We set up a total energy functional that depends only on the relative positions of the copper ion, Argl41 and the dioxygen molecule, and on their spin occupations. The total energy is the sum of the energies of the isolated entities (Cu, Arg141, 0 2 ) and their electrostatic interaction. The model neglects hybridization effects between these entities, but emphasizes the electrostatic interaction between charges on one site and between different ions. Spin effects, though less important, are included for the sake of consistency. 1. Zsolated Species. In our model, the energy of an isolated species (denoted by X) depends on the occupation (nxt, nxr) of the relevant orbitals via
Here EXis the total energy of the reference state of X, E X is the energy of the HOMO in the reference state, U Xis the Coulomb repulsion of an electron in the HOMO, and JX is the spinsplitting parameter or the exchange coupling. The occupations nxt and 12x4 are always measured relative to the reference state. X is “0” if it denotes the oxygen moiety, “ d ’ if it denotes the copper site in SOD, and “N” if it denotes Argl41. The reference state for the oxygen moiety is the non-spinpolarized neutral molecule, whereas that of the copper site is the triple positively charged copper site in SOD. (The choice of the reference state is arbitrary as it merely defines the zero for the occupations.) The parameters for the isolated species are determined from the density functional calculations by fitting to the total energies and the one-electron energies of the isolated species in various charge states, namely, complexes I and 11, superoxide and oxygen. The ammonium, which is not directly involved in the ET, has a constant energy. The procedure is described in detail in the Appendix, and the results are given in Table 4.
Carloni et al. The most relevant result is that the Coulomb repulsion parameters are of the order of 5-12 eV (500-1200 !d/mol), which is larger than all other energies in the system. This is one justification to neglect the relatively weak covalent contributions of the total energy. Expression 7 resembles similar expressions in the Hubbard model in solid-state physicsg4 or the Pariser-Pan-Pople Hamiltonian in quantum chemistry.85 It can be regarded as a Taylor series of the ground-state energy up to second order in the deviation of the spin occupations from some reference state. The parameters implicitly take into account intramolecular structural relaxations of dioxygen. 2 . Coupling. Assuming a simple point charge model, the coupling energy term reads
Here r~ is the position of species X, and fix is its total charge of the reference state (in electron charges). We have condensed nxt nX1 inJo a single nFmber nx. The value of the constant C is 14.40 A eV (1389 A kJ/mol). To be able to study excited-states surfaces, we add an infinitesimally small hopping term between the Cu-d and the dioxygen JC* orbital. A total energy surface is selected by choosing the occupations of the resulting one-electron niveaux and minimizing the energy. In addition we introduce an infinitely strong hard-core potential that prevents the structure from collapsing. The radii of the hard-core spheres are the van der Waals radii. 3 . One-Electron Energies. The model provides the levels of the highest occupied orbitals for each spin direction. They are obtained as the derivative of the total energy:
+
(9) with respect to the occupations
These energy levels are the JC*orbital if X is the oxygen moiety and the d,Z-,z level on the copper site in SOD if X denotes that site. 4. Elimination of the Dependence on the Occupations. We can simplify this total energy expression for the electronic ground state by minimizing it with respect to the electronic occupations while keeping the number of electrons constant, ndt + 1241 + not nor = 2, and by setting the total spin equal to 1. This eliminates the explicit dependence on the occupations and yields a purely interatomic potential that depends only on the atomic positions. (The same procedure can be performed for.the singlet state, but then the total spin must vanish.) The resulting total energy reads
+
The Cu, Zn Superoxide Dismutase Active Site
J. Pliys. Chem., Vol. 99, No. 4, 1995 1345
where ZjN,d = c/lm - Tdl, Zj~,o= c/lm - rol and U 0 . d = c/lro - rdl. This expression is valid for occupations 0 -= not no1 < 1. The number of electrons on the dioxygen molecule is
+
As the d,+,2 state can accept only two electrons, the total energy of the system is that of the reduced SOD active site and the free oxygen molecule, which is given by
if eq 12 predicts a negative occupation. This total energy, given by eqs 11 and 13, depends only on the atomic positions, but it does so in a rather complex fashion, because it implicitly incorporates all the information on the charge redistribution between 0 2 and SOD active site. 5. Validation of the Model. We can test the validity of the model energy function by recalculating the binding energies of the adduct to the enzyme for the atomic positions as in models I11 and IV. This is a stringent test, because no information on the coupling has been used in fitting the parameters. The model predicts a binding energy of the superoxide of 1.08 eV (104 kJ/mol). which is in excellent agreement with the 1.03 eV (99 kJ/mol) obtained by full calculations. Considering that the model has to match energies that are of the order of 10 eV (lo00 kJ/mol), we find this agreement remarkable. The energy difference between IV and I11 is 0.77 eV (74 kJ/mol) in the model and 1.12 eV (1 14 kJ/mol) in the full calculation. The deviation of 0.41 eV (40 kJ/mol) is in part attributed to the hydrogen bond, whose contribution is not included in the model because we neglected hybridization effects. ,
IV. Discussion We will split our discussion into two parts. First, we invoke the calculation of Osman and Bash4*and show that our results based on a vacuum cluster calculation are in agreement with theirs. Later, based on our model, we attempt to guess the effect of the solvent and we show that, under reasonable hypotheses, our result may be compatible with a different scenario. The validation of this scenario requires more elaborate calculations that will be carried out in the future. We will refer mainly to the model functional developed in the preceding section, which presents and extends the findings of our first-principles calculations. For the sake of simplicity the discussion refers to the triplet configuration. Analogous conclusions can be drawn for the singlet configuration. I. Vacuum Calculations. Let us begin with the situation in which enzyme and substrate are completely separated. The electron is localized on the superoxide. (Note that this state is not the. ground state described by eq 11.) The ET from superoxide to the SOD copper(I1) is energetically favored by 13.43 eV (1296 kJ/mol), as obtained from the model energy functional, or 12.68 eV (1223 kJ/mol) in the full calculation.*6 However, owing to the large separation and the resulting small electron transition matrix elements,*' the ET cannot yet occur. This was already pointed out by Osman and Bash4*and is to be expected by the redox potentials of SOD and 0 2 - .
Figure 7. Potential energy surfaces as obtained from the model energy functional. Contour spacings are 0.26 eV (25 kJ/mol). Arrows indica!e the direction of decreasing energy. Tick marks are separated by 1 A. (a) Energy surface of superoxide. The electron configuration is the excited state encountered before the ET. (b) Ground-state energy surface of dioxygen. (c) Energy surface of Argl41 for a fixed Cu-0 distance.
The superoxide is electrostatically attracted by the copper(11) site and by the guanidinium group of Arg141 (Figure 7a).
It is expected to assume a position somewhere between the two ions. Initially, the copper and Argl41 are separated by %8 A." As Argl4l is a highly mobile group46, it is attracted to the superoxide, forming a Cu-02-Argl4 1 complex. If the superoxide is in the vicinity of the copper ion, a transition between electronic states is expected. The electronic states are (1) two degenerate states with energy E[SOD+02-], where the electron to be transferred occupies one or the other of the n* orbitals, and (2) the ground state with energy E[SODh-+02h-'], .with the electron delocalized over the copper d2+,s and the n* orbital. The molecular orbital energy levels in the ground state are completely aligned. The fraction d of the transferred electron increases with increasing Cu-0 distances; if Argl41 is not present, 6 is unity for distances larger than 6 A. Approach of the superoxide to the copper site lowers the E[SOD+02-] and E[SODh-+02h-*] energy surfaces, owing to the electrostatic attraction between the ions. However, the model energy functional indicates that the former energy surface decreases more rapidly than the latter. For the sake of simplicity, we ignore the presence of Argl41 and discuss its effect later. The model indicates that the intersection of the two energy surfaces occurs at a Cu-02 distance of 2.25 A. In this configuration, the distance between the copper and one oxygen of 0 2 - would be less than the bond length. Instead, at the Cu-02 distance of 2.75 A, obtained in the calculation in which the 0 2 - position is optimized (see Section 11, Computational Procedure), the model predicts that the energy gap between the two states is as large as 0.86 eV (83 kJ/mol). The gap is modified by the electrostatic potential from Argl41. The modification can be estimated using our model. For a rearrangement of Argl41 as in 111, the energy gap is reduced to 0.41 eV (40 kJ/moL). For any configuration of Argl41, it appears that, within our model, the gap is always at least some tens of electronvolts, a value much larger than kRT. Moreover, the presence of Argl41 increases the binding energy of superoxide in the ground state configuration: this energy is increased from 0.64 eV (62 kJ/mol) without Argl41 to 1.08 eV (104 kJ/mol) with Argl41 located as in 111, owing to the additional electrostatic binding of dioxygen to Argl41. The potential energy surface of the dioxygen moiety for the ground state is shown in Figure 7b. We conclude, therefore, that our calculations appear to be in agreement with previous results of Osman and Bash,"* namely, that ET in vacuum cannot take place.
Carloni et al.
1346 J. Phys. Chem., Vol. 99, No. 4, 1995 Using our model functional, let us now estimate whether Argl41 can dissociate from the Cu-02 complex. Indeed, the model developed allows the energetics of the Arg-02-Cu complex to be estimated as a function of the motion of the Argl41 and 0 2 . Because a fraction of an electron has been transferred, the attraction of the Argl41 to the copper site is reduced and this allows the arginine group to separate from the Cu-02 pair. The resulting total energy surface is shown in Figure 7c. With dioxygen located 2.76 A from the copper ion, the model predicts that Argl41 separates after overcoming a barrier that ranges between 0 and 0.2 eV (20 kJ/mol), depending on the choice of parameters. This barrier, which we consider an upper bound for the possible values, can easily be overcome thermally. We conclude therefore that Argl41 can easily separate from the superoxide bonded to the copper ion. 11. Solvent Effects. This part is obviously more speculative. The fluctuations of the environment can be as large as the order of magnitude of a chemical bond.88 These can easily lead to the crossing of the 0.41 eV energy gap necessary for the electronic transition SOD 0 2 SOD6- 0 2 d - 1 to occur. The picture would then be that of the most accepted mechanism (eq 1). Instead, we propose here a different and novel scenario. Namely, we suggest that the water molecule present in the cavity close to the copper ion may play a role. The binding of the superoxide to the enzyme competes with that of a water molecule to the enzyme. If the ligand-exchange reaction is considered, the effective binding energy between the reaction center and the substrate is reduced. We can estimate the binding energy of a water molecule to copper by considering the dipole interaction of water with the 2+ charge on the copper site, and we find binding energies of the order of 1 eV for a copper-water oxygen distance of about 3 A. This suggests that a substitution reaction can indeed displace dioxygen from its binding site. Our estimates would be consistent with a scenario in which the superoxide displaces a water molecule from the binding site before the electron transfer, and in tum is itself displaced after the electronic transition has brought the system into the electronic ground state. Therefore the model energy functional suggests the following mechanism for the first enzymatic reaction step of SOD: Initially the superoxide is attracted to the Cu(I1) ion strongly enough to displace a water molecule bound to it. Once a Cu-02 complex is formed, an electronic transition will bring the system from an excited state with the electron localized on the superoxide into the electronic ground state, in which the electron is delocalized about equally between dioxygen and the Cu-d orbital. Argl41, which has a very mobile, positively charged functional group, is electrostatically attracted to the superoxide and increases the efficiency of electronic transition by modulating the total energy surfaces of the excited and the ground state. After the electronic ground state has been reached, Argl41 can easily dissociate from the Cu-02 complex. However, once the electronic ground state has been reached, the binding energy of the Cu-02 complex is sufficiently small so that a water molecule from the solvent, which competes with superoxide for the position next to the copper ion, can displace dioxygen again from its binding site, which then completes the electron transfer to the copper ion.
+
-
+
V. Conclusions
The first-principles calculations carried out in this work show that a partial electron transfer process between SOD and its substrate occurs through the copper dX2-p and the n* orbitals of the superoxide. The electronic structure of the enzyme substrate complex is mainly influenced by Coulomb repulsion
and, to a lesser extent, by spin polarization effects of the paramagnetic copper(I1) ion and of superoxide n* orbitals. The covalent hybridization between the Cu-d and the superoxide n* orbitals is, in comparison, negligible. The position of the antibonding d,2-,2 orbital on copper depends sensitively on the position of the ligands. A breaking of a Cu-ligand bond, as proposed in the second reaction step of the most widely accepted mechanism, produces a change in the electronic structure of copper that could have an important effect on both the ionization potential and the electron affinity of the enzyme. A simple model energy functional describing the most important features of the enzyme-substrate interaction, including the electron transfer, has been derived from our calculations. This model has allowed us to extend the implications of our calculations to situations that have not been calculated with firstprinciples techniques. Our combined first-principles and model calculations essentially agree with the previous mechanism proposed by Osman and Bash,48 in that a stable SOD-02 complex is formed. However, our estimates also indicate that a different scenario might take place in a solvent, in which the SOD-02 complex is broken up by a substitution reaction with a water molecule. This hypothesis is speculative at the present stage. Use of combined classical MD and model approaches will provide a more realistic picture of the SOD-02- intreaction at the copper site in the presence of the solvent. We plan to explore this possibility by performing a classical MD simulation for which the quantum mechanical processes that occur in the enzymatic reaction center are described by our simplified model. This will allow us to treat the ET process in the presence of solvent effects and to verify whether the conclusions reached here and by Osman and Bash, which are based on in vacuo calculations, are still valid in the presence of solvent effects.
Acknowledgment. We gratefully acknowledge helpful discussions with L. Banci and M. Sprik. P.C. acknowledges the financial support by Fondazione IBM Italia. Appendix: Derivation of the Model Parameters We will discuss here a derivation of the model total energy functional and describe the procedure to extract the parameters. To derive this functional, we follow in spirit the density functional theory. However, instead of building an energy functional that depends on the spin density at every point of space, we consider here the total number of electrons for each spin, on either the isolated SOD active site or the isolated dioxygen. We construct a total energy functional E[nt, nil so that its value is equal to the minimum energy for all states (wave functions and atomic positions) of a species ( 0 2 or Cu) with the given set of electron numbers nt and ni. Now we expand this functional for some reference state into a Taylor series up to the second order in nt and n ~ . When we use a Taylor expansion of the total energy, we must understand whether it is differentiable in the region of interest. It is easy to see that this is not the case for the exact density functional: The gradient of E exhibits steps in the first derivative at integer occupations of magnitude E[n 11 - 2E[n]+ E[n - 11. This is a consequence of the electron numbers being discrete. For fractional occupations we must consider an ensemble of states with the next higher and the next lower integer occupation. Within the LDA, however, all states of the ensemble feel the same effective potential, which in tum depends on the fractional occupation. As a result, the total energy
+
The Cu, Zn Superoxide Dismutase Active Site obtained from the LDA is continuous as long as the same oneparticle state, or a degenerate set of one-particle states, is occupied. A step in the first derivative occurs only if a state that is separated by a gap in the one-particle spectrum from the already occupied states starts to be occupied. This implies that the model of dioxygen can be used to parameterize the LDA total energy for the occupations - 1 < not < 1 and - 1 < noi < 1. The reference state is chosen as the neutral, non-spinpolarized oxygen molecule. Similarly, the model for the SOD active site is valid for the occupations 0 < ndt < 1 and 0 < nd( < 1, where the occupations are the number of electrons in the d+p orbital. These regions cover the range of states that are of interest to us. The number of terms in the Taylor expansion are reduced by exploiting the invariance of the total energy with respect to spin reversal. The four remaining parameters in our model are the total energy of E of the reference state, the energy of the HOMO of the reference state E , the Coulomb repulsion U , and the spin splitting parameter J. We now turn to the parametrization we have adopted to obtain the values in Table 4. The parameters are obtained from our first-principles calculations of the isolated species, dioxygen and Cu(I1) embedded into its ligands, for various electron and spin occupations. The bare energy EO, its HOMO level E O , and its Coulomb repulsion UO are fist obtained from non-spin-polarized calculations on the oxygen molecule, the superoxide and the dioxygen cation. We find EO = -84 155 kJ/mol, €0 = -7.38 eV (-712 kJ/mol), and UO= 10.82 eV (1044 kJ/mol). The spin-splitting parameter on the oxygen molecule JOcan be obtianed from the energy difference between triplet oxygen and the non-spinpolarized oxygen, yielding J d = 0.49 eV (47 kJ/mol). All oxygen calculations are done such that both x* orbitals of each spin direction are occupied equally. This avoids the problem of the LDA splitting the orientational symmetry of the molecule in an incorrect way, which we attribute to the effect of the nonvanishing self-interaction in the LDA in combination with a partially occupied doublet of electronic states. With this set of parameters, a fraction of the electron goes into a diffuse scattering state, and a mixture of superoxide on one side and a neutral or partially charged oxygen molecule and a fraction of a free electron on the other side is obtained. A manifestation of this result is an overestimation of electron affinity by 0.77 eV (75 kJ/mol). Hence, we replaced the LDA energy of the supercell calculation of superoxide by the sum of the energy of the oxygen molecule and its electron affinity A = 0.46 eV (44 kJ/mol). The latter is obtianed from the LDA energies of the HF densities.89 The new parameters are EO = -6.99 eV (-674 kJ/mol) and UO = 11.61 eV (1120 kJ/mol). The energy of the neutral molecule and the spin-splitting parameter are unchanged. We can check that the new model is consistent with the overestimation of the electron affinity. If the molecular orbital energy is equal to the vacuum level, additional electrons go into a free electron state of energy zero. Hence the energy for the state with not = 0 and noi = 1 is equal to that with occupation noi = ( E O UO - Jo)/(Uo - Jo). This value is lower in energy than the superoxide energy used in the parameterization by ( E O UO - J o ) ~ / ( ~ U-O2Jo) = 0.64 eV (61 kJ/mol). Considering supercell size effects, the agreement with the actual calculated overestimate is very satisfactory. The good agreement with the experimental electron affinity in previous work89can be attributed to the use of the HF density. We now compare the model parameters with experimental data. The spin-splitting parameter is related to the energy
+
+
J. Phys. Chem., VoE. 99, No. 4, 1995 1347 difference between the triplet and singlet state of the oxygen molecule.g0 The experimental spin-splitting parameter is 0.49 eV (47 kJ/mol). The bare orbital energy and the Coulomb repulsion can be obtained from the experimental electron affinity A[02] = 0.46 eV (44 kJ/mol) and the ionization potential Z[O2] = 12.06 eV (1163 kJ/mol) of the oxygen molecule. The bare energy level is given by EO = (fiO7.1 A[02])/2 = -6.25 eV (-603 kJ/mol). The Coulomb repulsion can be obtained as UO = Z[O2] - A[02] - 3Jo = 10.16 eV (980 kJ/mol), using the experimental spin-splitting parameter. These numbers should be compared to the parameters quoted in Table 3. We obtain the parameters of the SOD active site in a way similar to the procedure described for dioxygen. As our calculatigns are done with the ammonium present at a distance of 5.25 A from the Cu site, the electrostatic coupling between the Cu atom and the ammonium must be included when we extract the parameters. The bare energy Ed, the bare HOMO level Ed, and the Coulomb repulsion parameter u d are again obtained from non-spin-polarized calculations: The Coulomb repulsion u d = 5.79 eV (559 kJ/mol) is the difference between the energy levels of the oxidized and that of the reduced SOD active site corrected for the interaction of the periodic images. The bare energy Ed = -614 722 kJ/mol and the bare HOMO level Ed = -20.05 eV (-1934.5 kJ/mol) are chosen such that the total energy of the oxidized and the reduced SOD active site are reproduced. The spin splitting on copper ion (0.44 eV) (42 kJ/mol) is derived from the total energy difference between the spin-polarized and the non-spin-polarized oxidized SOD. The value obtained from the spin splitting of the copper level in I would have been J d = 0.72 eV (69 kJ/mol).
+
References and Notes (1) Tainer, J. A,; Getzoff, E. D.; Beem, K. M.; Richardson, J. S.; Richardson, D. C. J . Mol. Biol. 1982, 160, 181. (2) McCord, J. M.; Fridovich, I. J . Biol. Chem. 1969, 244, 6049. (3) Fridovich, I. Adv. Enlym. 1974, 41, 35. (4) Fridovich, I. Adv. Enzym. Relat. Areas Mol. Biol. 1986, 58, 61. (5) Fee, J. A,; Bull, C. J . Biol. Chem. 1986, 261, 13000. (6) Fee, J. A.; Di Corleto, P. E. Biochemistry 1973, 12, 4893. (7) Tainer, J. A.; Getzoff, E. D.; Richardson, J. S.; Richardson, D. C. Nature (London) 1983, 306, 284. (8) Fee, J. A. In Metal Ions in Biological Systems; Sigel, H., Ed.; M. Dekker: New York, 1981; Vol. 13, p 259. (9) Fee, J. A. In Metal Ion Activation of Dioxygen; Spiro, T. G., Ed.; Wiley: New York, 1980; p 209. (10) Fee, J. A. In Oxygen and Oxy-Radicals in Chemistry and Biology; Rodgers, M. A. J., Powers, E. L., Eds.; Academic Press: New York, 1981; p 204. (11) Valentine, J. S.; Pantoliano, M. W. In Metal Ions in Biological Systems; Sigel, H., Ed.; M. Dekker: New York, 1981; Vol. 3, p 291. (12) Valentine, J. S.; Pantoliano, M. W.; McDonnel, P. J.; Burger, A. R. Proc. Natl. Acad. Sci. U S A . 1979, 76, 4245. (13) Banci, L.; Bertini, I.; Luchinat, C.; Piccioli, M. Coord. Chem. Rev. 1990, 100, 67. (14) Fielden, E. M.; Roberts, P. B.; Bray, R. C.; Lowe, D. J.; Mautner, G. N.; Rotilio, G.; Calabrese, L. Biochem. J . 1974, 139, 49. (15) Parge, H. E.; Hallewell, R. A.; Tainer, J. A. Proc. Natl. Acad. Sci. U S A . 1992, 89, 6109. (16) Beyer, W. F.; Fridovich, I.; Mullenbach, G. T.; Hallewell, R. A. J . Biol. Chem. 1987, 262, 11182. (17) Banci, L.; Bertini, I.; Luchinat, C.; Hallewell, R. A. J . Am. Chem. SOC.1988, 110, 3629. (18) Banci, L.; Bertini, I.; Luchinat, C.; Hallewell, R. A. Ann. N. Y. Acad. Sci. 1988, 542, 37. (19) Getzoff, E. D.; Cabelli, D. E.; Fisher, C. L.; Parge, H. E.; Viezzoli, M. S.; Banci, L.; Hallewell, R. A. Nature (London) 1992, 358, 347. (20) Banci, L.; Bertini, I.; Cabelli, D. E.; Hallewell, R. A,; Luchinat, C.; Viezzoli, M. S. Inorg. Chem. 1990, 29, 2398. (21) Banci, L.; Bertini, I.; Bauer, D.; Hallewell, R. A,; Viezzoli, M. S. Biochemistry 1993, 32, 4384 and references therein. (22) Bertini, I.; Banci, L.; Turano, P. Eur. Biophys. J . 1991, 19, 141. (23) Bertini, I.; Banci, L.; Luchinat, C.; Bielski, B. H. J.; Cabelli, D. E.; Mullenbach, G. T.; Hallewell, R. A. J . Am. Chem. SOC. 1989, I 1 1, 7 14. (24) Banci, L.; Bertini, I.; Cabelli, D. E.; Hallewell, R. A,; Luchinat, C.; Viezzoli, M. S. Free Radicals Res. Commun. 1991, 12-13, 239.
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