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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