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Density-functional calculations of the Cu, Zn superoxide dismutase redox
potential: The influence of active site distortion
Ricardo J.F. Branco, Pedro Alexandrino Fernandes, Maria Joao Ramos*
Requimte, Departamento de Quımica, Faculdade de Ciencias, Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal
Received 13 October 2004; accepted 2 December 2004
Available online 14 July 2005
Abstract
We have calculated the redox potential for a Cu, Zn superoxide dismutase active-site model. The active site of the enzyme contains a redox
active cooper ion coordinated to four histidine residues. The geometry of the active site cooper complex has a characteristic distortion, whose
biological significance has been discussed. The computational model contains 47 atoms representing the side chains of the histidine ligands
of the copper ion. Thermodynamic parameters were calculated using density-functional methods at the B3LYP level of theory. The energies
of the reduced and oxidized forms, allowed us to calculate the reduction potentials for the models. The difference between the reduction
potential of a freely optimized model in water (K0.58 V) and a model mimicking the distorted active site geometry (0.84 V) corresponds to
C1.42 V. It is expected that the more polar environment (water) stabilizes the oxidized state over the reduced state. However, the distortion
around the cooper ion also has a fundamental role in modulating the redox potential, which can be seen by comparing the calculated redox
potentials of two active site models, with unconstrained and distorted geometries, both inserted in a proteic environment (0.38 and 0.84 V,
respectively). The influence of the active site distortion on the high reduction potential characteristic of this kind of copper proteins, is clearly
highlighted by the results, confirming the role of the protein backbone on tuning the reduction potential that is essential for the catalytic
efficiency of the enzyme. Furthermore, these preliminary results show a deep contrast with the ones that have been obtained for the Blue
Copper Proteins, where it was not found any uncommon structural-function correlation between the geometry of the copper ion and its
reduction potential.
q 2005 Elsevier B.V. All rights reserved.
Keywords: Cu; Zn SOD; Redox potential; Active-site distortion
1. Introduction
Copper, Zinc superoxide dismutase (Cu, Zn SOD) is a
homodimeric enzyme, containing one copper and one zinc
ion per subunit, whose physiological role is the dismutation
of the superoxide radical to molecular oxygen and
hydrogen peroxide [1–3]. This class of enzymes has been
shown to be involved in anticancer and antiaging
mechanisms and recent results reveal that mutations in
the enzyme are associated with amyotrophic lateral
sclerosis [4]. Fig. 1 shows a schematic representation of
the resting oxidized enzyme, and its typical active site. The
commonly accepted catalytic mechanism, suggested by
0166-1280/$ - see front matter q 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.theochem.2004.12.046
* Corresponding author.
E-mail address: mjramos@fc.up.pt (M.J. Ramos).
Tainer et al. [5], involves the reduction of cupric Cu(II) to
cuprous ion Cu(I) by a first superoxide radical and the
reoxidation of Cu(I) to Cu(II) by a second one.
It is well known that copper complexes assume a
different geometry in a protein active site than they have
in solution or even in vacuum where the predominant
geometry is square planar [6]. In SOD’s active site the four
histidines surrounding copper are in a distorted square
planar geometry. The functional role and nature of this
distorted geometry has been extensively investigated in
copper proteins [6,7], while it remains unclear which is their
role in SOD enzymes. The results presented here show that
some unusual properties of SOD enzymes, like the fine-
tuning of the copper reduction potential, can be ascribed to
the distortion in the active site.
To evaluate the influence of the protein backbone strain
on the geometry of the active site we have to compute the
intrinsic strain energy with respect to the quadrangular
planar geometry, which is the most stable geometry for
Journal of Molecular Structure: THEOCHEM 729 (2005) 141–146
www.elsevier.com/locate/theochem
Fig. 1. Active-site model of Cu, Zn superoxide dismutase used for the calculations. Histidines 44, 46, 61 and 118 were modelled by imidazoles, in which the
blue atoms represent nitrogen, light grey represent carbon, and red represent oxygen. The central ions represent Cu(II) and Zn(II). Figure generated with
ViewerPro 5.0 by Accelrys Inc (For interpretation of the reference to colour in this legend, the reader is referred to the web version of this article.)
R.J.F. Branco et al. / Journal of Molecular Structure: THEOCHEM 729 (2005) 141–146142
tetra-coordinated Cu(II) complexes. Thereby we can
measure the induced strain by the energy difference between
the freely optimized model and the constrained one. It is not
clear whether the origin of these structural features is
primarily electronic or steric in nature [8].
2. Methodology
For each structure, the geometry of both the oxidized and
reduced forms of the complexes were optimized with the
hybrid and unrestricted density functional method UB3LYP
[9,10] using the GAUSSIAN 03 suite of programs [11]. The
quasi-relativistic Compac Effective Potentials of Stevens,
Krauss, Basch and Jasien [12–14] were used for all atoms as
implemented in GAUSSIAN 03, using the triple-z basis set
CEP-121 [12–14], with a contraction scheme for the valence
electrons (4211/411) for Cu, (121) for the light elements C,
N, O and (311) for the hydrogen atoms. For the copper atom
only the electrons from the first two levels were included in
the core potential (a total of ten electrons), being the
remaining 3s, 3p and 3d electrons treated explicitly.
To calculate redox potentials in charged systems, it is
important to evaluate solvent effects in the energetics.
Therefore, all energies were calculated under the influence of
a dielectric continuum. We have used a Polarized Continuum
Model, IEFPCM, as implemented in GAUSSIAN 03 [11], with a
dielectric constant of 4. This value has been shown to give
good agreement with experimental data in the active site of
proteins, and accounts for a dielectric constant of 3 for the
protein and 80 for the buried water molecules [15]. It is
usually assumed that geometry optimizations can be carried
out in vacuum, and transferred to the continuum to calculate
final energies, without introducing significant error [16].
Therefore, the reduction potentials in the continuum were
calculated as a difference of the single-point energy
calculation of both oxidation states, performed with the
respective vacuum optimized geometry, plus a correction for
the standard hydrogen electrode (SHE). The methodology
used here was described previously [17].
A model of the dimeric bovine erythrocyte Cu, Zn SOD
active site was constructed from the X-ray crystal structure
of the enzyme. Coordinates were taken from The Protein
Data Bank [18] under the accession code 2SOD. All
hydrogen atoms were added to the ligands using the
INISGHT II software package from Accelrys [19]. The
histidine residues (H61, H44, H46 and H118) were
modelled by neutral imidazole rings, with their b carbon
atoms replaced by hydrogen atoms. There are a number of
models of a similar type in the literature [20] arguing that
the imidazole ring contains most of the important chemical
effects, like p-electron polarizability and s-donor capability
[21]. Another assumption of the modelling is that zinc ion
has been replaced by a proton. This approximation was
supported by experimental results, which show that the apo-
protein has almost the same specific activity as the
holoprotein at physiological pH [22].
3. Models
3.1. The Cu(His)x models
We first analyse the results obtained for the [CuHis]C2/C,
[Cu(His)2]C2/C and [Cu(His)3]C2/C models. The emphasis
here in this section is the comparison of the equilibrium
bond length and angles of each one of optimized geometries
in both oxidation states. The copper atomic charge, spin and
redox potential are discussed in the next section of this
work. The bond length of the model [CuHis]C2/C is 1.95 A
in the oxidized state and 1.88 A for the reduced one. In the
model [Cu(His)2]C2/C the bond length is the same in
Cu(His)4
0,38 0,84
Cu(His)
ConstrainedFree
Cu(His)3Cu(His)2Cu-2,00
0,00
2,00
4,00
6,00
8,00
10,00
12,00
14,00
16,00
18,00
Model
E˚
(V)
ε=1ε=4ε=80
R.J.F. Branco et al. / Journal of Molecular Structure: THEOCHEM 729 (2005) 141–146 143
both states and equal to 1.88 A, and the angle between
two ligands approximately 1808, which means that the
model has a linear geometry as expected. Finally the
[Cu(His)3]C2/C model has an almost trigonal planar
geometry in which the angles between the ligands in the
plane are 106, 106 and 1488 for the oxidized state and 118,
119 and 1238 for the reduced one. This smooth deviation
from a perfect trigonal planar geometry is related with the
asymmetry in the planarity of the imidazole rings with
respect to the plane defined by the three ligands. These
dihedral angles change from 13, 71 and 73 to 37, 35 and 388
from the oxidized to the reduced state, respectively.
Fig. 2. Calculated redox potentials with increasing number of ligands
around copper. The largest cluster was built as a real model for the active
site of the Cu, Zn SOD enzyme. The free model was optimized without any
structural constraints. Some angles and dihedrals were constrained during
the optimization of the model that mimick the active site distortion. The
solvent effect was included through the polarizable continuum method
(IEFPCM).
3.2. Model for the free and constrained Cu(His)4
The free optimized [Cu(His)4]C2/C model converged to
a quadrangular planar geometry in the oxidized state and to
a tetrahedral geometry in the reduced state. The bond length
changes from 2.01 to 2.07 A for all ligands, upon reduction.
These results are in agreement with the increase in length
observed in the previous models. All the angles in the
reduced form are about 1098, characteristic of a perfect
tetrahedron, which means that Cu(I) has a preference for this
geometry, as it is well known, when tetra-coordinated
[23,24]. Even more interesting is the tendency for the
[Cu(His)4]C model, in a constrained framework, (with a
minimum number of angles and dihedral frozen in order to
mimic the crystal structure), to become trigonal planar upon
losing one of the ligands, thus reproducing the first step of
the commonly accepted catalytic mechanism [5].
4. Results and discussion
The redox potential can be calculated from the following
expression [17]:
E0 Z IPred CDE CDSHE (1)
The IPred term in (1) is the gas-phase ionization potential,
which was obtained by the difference between the energy of
the reduced and oxidized forms. This formulation assumes
that the geometry does not change upon reduction, therefore
corrections to the IPred to account relaxation of the structure
were not included [25]. Therefore, the geometry of the
oxidized complex was the one considered for these
calculations. The DEsolv term is the electrostatic solvation
energy of the oxidized minus the reduced model. Finally,
DSHE is the standard hydrogen electrode potential correc-
tion of K4.43 eV [26]. The experimental redox potentials
for Cu, Zn SOD have been measured and range from 0.32 to
0.40 V [27–31].
The addition of ligands to the first-sphere coordination of
copper ion causes a decrease in the calculated reduction
potential. Potential curves in Fig. 2 clearly depict this trend,
where each imidazole ring contributes to strengthen
the charge donation to the copper ion and consequently to
the reduction of their appetite for electrons, which means an
effective decrease of the reduction potential.
As, expected, the reduction potential slightly increases in
the constrained distorted model relatively to the free one
because the distortion imposed by the protein backbone
destabilizes more the oxidized form than the reduced one. It
is relevant to note that the geometry of the active site
complex is closer to tetrahedral than to quadrangular planar,
confirming the geometric source as responsible for the
increase in the redox potential. According to the Franck–
Condon restrictions this is one of the requirements to
achieve an efficient electron transfer with low reorgani-
zation energy, which makes the chemical reaction faster.
The distortion of the Cu(II) geometry increases the
reduction potential from C0.38 to C0.84 V in a proteic
environment. These results provide an argument in favour to
the induced-rack hypothesis, which states that the protein
framework forces the Cu(II) ion to bind in a geometry more
similar to the one preferred by the Cu(I) [32,33], avoiding
large rearrangements of the ligands during redox catalysis.
In fact, it is well known that the topography of the active site
must be critical to the enzyme’s function [5] and the results
show us how it can be useful for a fine-tuning of the redox
potential of the enzyme.
Moreover, the reduction potential curves in Fig. 2 for all
dielectric constants are nearly parallel and the lowest
values are in water (3Z78.39), which is the most polar
solvent in biological systems. This is expected as the
solvent with the greater 3 should stabilize the more charged
state (C2). We can conclude that the tuning of the
reduction potential is not exclusively dependent on solvent
polarization, since the three curves have a similar profile.
Finally, it should be noted that the calculated results in
protein environment (3Z4) are the ones that better
reproduce the experimental value of C0.40 V vs. NHE at
Table 1
Selected bond lengths in the Cu, Zn SOD active site model
Gas phase CuHis Cu(His)2 Cu(His)3 Cu(His)4 free Cu(His)4 const. Expta
Bond length (A) Ox Red Ox Red Ox Red Ox Red Ox Red Ox Red
Cu–NHis(1) 1.95 1.88 1.88 1.88 1.92 2.00 2.01 2.06 2.03 1.96 2.06 2.07
Cu–NHis(2) – – 1.88 1.88 1.92 1.99 2.01 2.07 2.01 2.16 2.02 1.98
Cu–NHis(3) – – – – 1.93 1.98 2.01 2.07 2.08 4.61 2.21 3.20
Cu–NHis(4) – – – – – – 2.01 2.07 2.06 1.96 2.07 2.00
a Experimental data taken from the crystallographic structure with PDB accession code 2SOD chain G [34] for the oxidized form and 1CBJ chain A [35] for
the reduced one.
R.J.F. Branco et al. / Journal of Molecular Structure: THEOCHEM 729 (2005) 141–146144
pH 7 for the bovine enzyme [29]. This is also in
accordance with a non solvent exposed active site.
The up-shift of the reduction potential, relative to water,
can be accounted for by assuming that induced-rack
coordination stabilizes the Cu(I) relative to the Cu(II)
geometry in the protein active site. Moreover, the lower
dielectric constant also favours the reduced state, raising the
reduction potential.
Looking at the Cu–NHis bond lengths in Table 1 we can
see that the slightly bond elongation is directly correlated to
the number of ligands in the copper coordination sphere. As
expected, the steric hindrance rises with the increasing
number of ligands, which induce lengthening in the Cu–NHis
bonds. In almost all reduced forms the optimal Cu(I)–NHis
distance is higher than in the oxidized state, since the lowest
unoccupied molecular orbital of the oxidized state
(LUMOox), which receives the electron upon reduction,
has an antibonding character. Consequently, Cu–NHis bonds
are longer, resulting in a weaker coordination sphere.
There is a point that should be interesting to discuss in
detail, and that is the natural trend the [Cu(His)4 constrained]C2
shows to acquire a trigonal geometry upon reduction, losing
one of its ligands, like it has been suggested in the protein
mechanism proposed by Tainer et al. [5]. On the other hand,
it is well known that Cu(II) ion assume a tetragonal planar
structure in almost all inorganic tetra-coordinated cupric
complexes, except in the Blue Copper Proteins [6], where it
is trigonal pyramidal. The tetragonal planar geometry was
also observed here in the optimized [Cu(His)4 free]C2 model.
However, Cu(I) is more stable in a tetrahedral or even in
ox
Cu(His)4 constrainedCu(His)4 freeCu(His)3Cu(His)2Cu(His)
red
0,50
0,60
0,70
0,80
0,90
1,00
1,10
1,20
Model
Cu
ch
arg
e (a
u)
ε=1ε=4ε=80
Fig. 3. Charge of the copper ion on Cu(His)n complexes as a function of the
number of ligands around copper. The points were linked with a dashed line
for visual simplicity.
a trigonal planar geometry, lowering the coordination
number from four to three, depending on which kind of
ligands are involved. In the Cu, Zn SOD active site there is
only one kind of ligand–histidine bonded to the copper.
Thus, we expect to obtain a tetrahedral geometry in the
reduced form, except when the active site pocket does not
have enough space or the protein rigidity does not allow for
geometry reorganization. In that case, a trigonal structure is
adopted by Cu(I) ion, which means a backward shift in the
metal ion position to the plane of the remaining ligands and
the breakage of the imidazole bridge between Cu and Zn.
This rearrangement does not cost too much energy, since it
does not cause dramatical changes in the ligand’s positions,
which are prerequisites for any thermodynamically and
kinetically favourable mechanism.
It should be noted the agreement between the calculated
bond lengths, especially in the constrained model, and the
experimental results. The constrained model shows a natural
trend to become three coordinated upon reduction, as it has
been experimentally reported [5,36–38].
Fig. 3 shows the variation of Mulliken’s charges of
copper in different models, which should give us some new
insights into the effect of distortion in the electronic
structure of the active site.
The calculated Mulliken charges are lower than the
formal charges typically assigned to the copper ion. This is
not surprising if we remember that the nitrogen imidazole
atoms are considered to be covalently bonded to the copper
ion and the bond strength depends on its s donotion
capacity. The charge donation involves the half filled
Cu(His) Cu(His)2 Cu(His)3 Cu(His)4 free Cu(His)4 constrained
0,00
0,10
0,20
0,30
0,40
0,50
0,60
0,70
0,80
Model
Cu
sp
in d
ensi
ty (
au)
ε=1ε=4ε=80
Fig. 4. The variation of the copper’s spin density as a function of the
number of ligands around copper. The points were linked with a dashed line
for a visual simplicity.
Fig. 5. Representation of the SOMO of the (a) free and (b) constrained optimized geometries (in oxidized form) for the largest model of Cu, Zn SOD enzyme.
Figure generated with MOLEKEL software [39].
R.J.F. Branco et al. / Journal of Molecular Structure: THEOCHEM 729 (2005) 141–146 145
copper’s 3d orbital and 2p ligand orbitals. Therefore, the
charge on the central metal ion is determined, in a certain
way, by the bonding or antibonding character of the only
single occupied valence orbital and by the extension of the
overlap between the copper and the ligand’s orbitals.
In Fig. 4 we can observe that the spin population on
copper is 0.66, 0.61 and 0.64 for the model with three
ligands and with four in both free and constrained
geometries, respectively. This means that each ligand
donates a total charge of 0.1 a.u. the 3d copper orbital.
This result is in perfect agreement with the one calculated
for Cu(NH3)42C [23].
As can be seen in Fig. 5 the single occupied molecular
orbital (SOMO) becomes a pure antibonding orbital in a
square plane geometry, with the lobes directed towards each
of the four equivalent ligands. On the other hand, despite the
fact that the distorted geometry is not as stable it partially
contributes to the decrease of the antibonding character,
creating a much more efficient charge transfer to the copper
and consequently a charge reduction on the metal ion.
5. Concluding remarks
The obtained results suggest that the protein folding is
crucial for the fine-tuning of the reduction potential in the
Cu, Zn SOD enzyme. The distortion of the copper geometry
caused by the protein folding is determinant for tuning the
reduction potential by increasing the potential in relation to
unconstrained complexes. This increased redox potential is
essential for the catalytic cycle, where copper has to be first
reduced by oxygen and subsequently re-oxidized by a
reaction intermediate. The value of the redox potential has
to be between the reduction potentials of the half-reactions
O2K/O2 (K0,16 V) and O2
K/H2O2 (C0,89 V). Curiously,
this effect is significantly different from the one that has
been reported for the Blue Copper Proteins [40] launching
again the discussion about the strain hypothesis and the
structural role in this class of copper enzymes.
Acknowledgements
We thank the Fundacao para a Ciencia e a Tecnologia
(FCT) and the National Foundation for Cancer Research
(NFCR) for financial support. RB further thanks the FCT for
a PhD grant.
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