ARTICLES

Sci. Rep. Kanazawa Univ.
Vol. 63, pp. 1–13, 2019

Theoretical studies on electronic structure and propertiesof type I copper center in copper proteins
Isman K URNIAWAN,1,2 * Kazutomo K AWAGUCHI,1 Kimikazu S UGIMORI,3
Takeshi S AKURAI,4 Hidemi NAGAO1
1 Division of Mathematical and Physical Sciences, Graduate School of Natural Science and Technology,

Kanazawa University, Kanazawa 920-1192, Japan
2 School of Computing, Telkom University, 40257, Indonesia
3 Division of Higher Education Research and Development, Institute of Liberal Arts and Science,

Kanazawa University, Kanazawa 920-1192, Japan
4 Division of Material Chemistry, Graduate School of Natural Science and Technology,

Kanazawa University, Kanazawa 920-1192, Japan(Received August 8, 2018 and accepted in revised form October 29, 2018)

Abstract We present a cluster model representing type I copper (T1Cu) center of copper
protein, which corrsponds to Multicopper Oxidases, Azurin, Stelacyanin and so on. The
electronic structure and physical properties such as molecular orbital, atomic partial charge,
partial spin densities, ionization energy (IP) of reduced T1Cu, electron affinity (EA) of oxidized T1Cu, the bond and the angle constants etc. are calculated by using two typical
Density Functional Theory (DFT) functionals, which are B3LYP and M06, with 6-31G(d)basis set. We find the dependency of several properties such as atomic partial charge, partial
spin densities, IP, and EA on the DFT functionals. We also find that the DFT functionals givea better contribution to bond constants, especially in case of the interaction between copper
and the axial ligand. We calculate the maximum absorption wavelength of T1Cu center andfind relatively a good agreement with experimental data.
Keywords.

1

Type I copper center, density functional theory, electronic structure.

Introduction

Copper proteins play an important role in various biological processes such as electron transfer,redox reaction, oxygen transportation, activation and so on. The proteins can contain one or more
copper ions in their active sites. Copper proteins containing one copper ion are known as type 1
copper (T1Cu) protein, such as Azurin, Plastocyanin, Stellacyanin and so on, and copper proteins
containing more than two copper ions are known as Multicopper Oxidases (MCOs). MCOs contain two copper centers, which are T1Cu center and tri-nuclear copper (TNC) center, in whichthose centers are located at different sites. T1Cu center consists of one copper ion coordinated to
two histidines and a cysteine in a trigonal planar structure, and an axial ligand such as methionine* Corresponding author

Email: isman@wriron1.s.kanazawa-u.ac.jp

2

Theoretical studies on electronic structure and properties of type I copper center in copper proteinsand so on [1–3]. T1Cu center catches one electron from other proteins with higher redox potential
and transfer the electron to the TNC site [4–6]. During the reaction, dioxygen molecules are reduced to two water molecules in TNC site by using the transferring four electrons from T1Cu [7].
Many physical properties such as electronic structure, reaction, etc. of T1Cu have been experimentally investigated by many groups [7–12]. The existence of T1Cu has been characterizedfrom intense absorption at around 600 nm and narrow hyperfine splittings in the electron paramagnetic resonance (EPR) spectroscopy [7, 9]. The kinetic aspect of the electron transfer reaction
has been investigated by Holwerda and co-workers [8]. They found the dependency of the rateof electron transfer on pH value. Solomon and co-workers have also investigated the room temperature circular dichroism and magnetic circular dichroism spectra of several T1Cu protein suchas Stellacyanin, Plastocyanin, and Azurin [9]. Regarding the absorption and circular dichroism
intensities, they have pointed out band absorptions as representative of transition energy.
Several physical properties of MCOs have also been investigated by many groups [7, 13–28].
Solomon and coworkers have reviewed some reported physical properties such as electron paramagnetic spectra (EPR) and redox potential of MCOs [13]. The mechanism of oxygen binding andredox reaction on TNC site have also been proposed by several research groups [13, 14, 20, 25].
Roberts and coworkers have investigated the intermolecular and intramolecular electron transfers of MCOs using laser flash photolysis [17]. The direct electron transfer between MCOs andelectrode has been investigated by Shleev and coworkers [18]. They found the possibility of thelong-range electron transfer between MCOs and electrodes. Augustine and coworkers have also
investigated the contribution of the structure of active site in supporting the efficiency of oxygen
reduction in TNC [26]. They found that asymmetrical structure of TNC lead to a rapid and efficient
reduction reaction.
On the other hand, from the viewpoint of theoretical studies, the electronics structure of T1Cu
center has many interests in relation to the electron transfer between molecules. Solomon andco-workers have experimentally and theoretically investigated the electronic structure of T1Cu
center in several copper proteins [4, 29]. By quantum mechanical calculations, they presented
the X-ray properties of T1Cu center from the viewpoint of the metal-ligand bonding interaction.
Corni and co-workers have investigated the contribution of electronic properties of Azurin’s active
site to electron transfer reaction by using Density Functional methods [30]. They found that inspite of the similarity of the hybridization of azurin in two oxidation states their energy spectrums
were found to be different. Other many groups have also investigated the electronic properties andelectron transfer mechanism of T1Cu center in copper proteins [31, 32].
In quantum mechanics, density functional methods have been developed to improve the ability
in calculating a certain properties of a particular system. Zhao and Truhlar have presented theM06 suite of density functionals [33, 34]. This functional is well known to perform better thanB3LYP because of the implementation of meta-GGA functional in exchange-correlation functionalof DFT. The M06 functional has been utilized to calculate molecular properties of both organicand inorganic molecules with the promising results [35–37].
In our previous study, we have investigated the electronic structure of the oxidized state ofAzurin and have found the dependency of electronic properties on the active site structure [38].
We have also investigated the electronic structure of T1Cu center of Azurin obtained from two
stable configuration [39]. The solvent effect on the electronic structure of Azurin’s active site
has also been investigated by using Polarizable Continuum Model (PCM) [40]. The aim of thisstudy is to investigate the dependency of electronic structure and properties of T1Cu center on
DFT functional. We investigate properties such as molecular orbital, atomic partial charge, partial
spin densities, ionization energy (IP) of reduced T1Cu, electron affinity (EA) of oxidized T1Cu,

Isman K URNIAWAN, Kazutomo K AWAGUCHI, Kimikazu S UGIMORI, Takeshi S AKURAI, Hidemi NAGAO

3

Figure 1: The schematic diagram of Type I copper model cluster.

the bond and the angle constants. Amongst copper proteins containing T1Cu center, we present
cluster models for T1Cu center to investigate the physical properties as azurin, stellacyanin, andMCOs as typical examples. Particularly, we discuss the contribution of DFT functional to theproperties in relation to the interaction between Cu and ligands.

2

Computational Methods

In this section, we introduce the procedures to calculate the electronic properties and force fieldparameters of the T1Cu center. We investigate the T1Cu cluster obtained from three copper proteins of Multicopper Oxidase (MCOs), Azurin and Stellacyanin. The cluster model of T1Cu is
prepared from the X-ray crystal structure and then the electronic properties of the cluster were
calculated. We also estimate force field parameters around T1Cu by using quantum mechanicalcalculations. The development of the force field parameters of a metal cluster in metalloprotein
is required to be able to perform molecular dynamics simulation. The stability of the dynamics
around the metal in the cluster corresponds to the quality of the force field parameters. All of thecalculations are performed by using Gaussian 09 package [41].

2.1

Cluster Model for the Type I Copper Center

The cluster model of T1Cu is extracted from X-ray crystal structure of three copper proteins. In
the case of oxidized state, T1Cu clusters of MCOs, Azurin and Stellacyanin proteins are preparedfrom the X-ray crystal structure with the PDB ID being 4NER [27], 4AZU [42], and 1X9R [43],respectively. In the case of reduced state, the clusters of MCOs, Azurin and Stellacyanin proteinsare prepared from the X-ray crystal structure with the PDB ID being 4E9T [24], 1E5Y [44], and1X9U [43], respectively. The structure of the T1Cu cluster consists of a copper ion, two histidines,a cysteine, a methionine, and glutamine peptides as shown in Fig. 1. The hydrogen atoms are added
into the cluster and are optimized by using B3LYP/6-31G(d) method [38].

4

2.2

Theoretical studies on electronic structure and properties of type I copper center in copper proteins

Electronic Properties

Several electronic properties of T1Cu such as molecular orbital, atomic partial charges and partial
spin densities are calculated and analyzed. In this study, the atomic partial charges are estimatedby using Merz-Singh-Kollman scheme [45]. We also calculate other properties such as ionization
potential (IP) of reduced T1Cu, electron affinity (EA) of oxidized T1Cu and maximum absorption wavelength. The maximum absorption wavelengths are calculated by using time-dependent
density functional theory (TD-DFT) method combined with conductor-like polarizable continuum
model (CPCM). The value of ε is taken as 10 [46, 47] and Topological United Atoms model wasused as atomic radii.

2.3

Force Field Parameters

To determine the force field parameters, we calculate the total energies of T1Cu with several valuesof bond and angle distance by using B3LYP and M06. The bond distance is varied in the range
of ±0.1 Å from equilibrium distance with increment 0.02 Å, while angle distance is varied in therange of ±5◦ from equilibrium angle with increment 1◦ [48]. The value of total energy is used toconstruct a potential energy surface (PES) along the bond distance and angle. The curvature of
PES is fitted by using harmonic potential function, which is represented as ( [38])V (r, Kr ) = Kr (r − rc )2 ,

(2.1)

2

(2.2)

V (θ , Kθ ) = Kθ (θ − θc ) ,where Kr and Kθ represent the bond and angle constants, respectively, while rc and θc represent
the equilibrium bond and angle, respectively.

3

Results and Discussions

In this section, we present several properties of T1Cu obtained from several copper proteins. Several properties of T1Cu such as atomic partial charge, partial spin densities, ionization potential,
electron affinity, maximum absorption wavelength, bond and angle constants are discussed in relation to the dependency of those properties on DFT functional.

3.1

Electronic Properties

Firstly, we present a singly occupied molecular orbital (SOMO) of T1Cu in MCOs protein calculated by using M06, as shown in Fig. 2a. The shape of SOMO is mainly arised from dx2 −y2 orbitalof the copper ion, p orbitals of the sulfur and σ orbital of two nitrogen atoms. We find antibonding
orbitals in the interaction between copper ion and cysteine’s sulfur, two histidine’s nitrogen. The
orbital of methionine’s sulfur is not observed in the SOMO orbital indicating weak interaction
between copper ion and methionine residue. The shape of SOMO orbital is found to be similar to
the SOMO orbital of T1Cu presented in Ref. [4, 39].
The surface of spin density presented in Fig. 2b was calculated by using M06. The shape of thesurface is similar to SOMO orbital shown in Fig. 2a, which is a good agreement with our previous
study [39]. To obtain a detail information about spin properties, we present atomic partial spinaround T1Cu as shown in Table 1. Regarding DFT functional dependency, the partial spin density
on the copper ion by M06 is smaller than that by B3LYP. These results are consistently found in
all T1Cu cluster indicating that M06 produces partial spin density that is more delocalized aroundIsman K URNIAWAN, Kazutomo K AWAGUCHI, Kimikazu S UGIMORI, Takeshi S AKURAI, Hidemi NAGAO

(a)

5

(b)

Figure 2: The profile of (a) SOMO orbital and (b) spin density of oxidized type I copper cluster.
Table 1: The atomic spin distribution of oxidized state of type I copper center in several proteins
calculated by using B3LYP (M06) methods.
Atom
Cu
S1
S2 /O
N1
N2

Atomic Spin Distribution
MCOs
AzurinStellacyanin
0.53 (0.49) 0.49 (0.46) 0.57 (0.54)
0.38 (0.41) 0.43 (0.47) 0.33 (0.35)
0.00 (0.00) 0.00 (0.00) 0.00 (0.00)
0.04 (0.04) 0.03 (0.03) 0.05 (0.05)
0.19 (0.16) 0.03 (0.03) 0.04 (0.05)

GLN

MET

O

S2
CYS

CYS

HIS

HIS

S1

S1

N2

Cu

N2

Cu

N

N
N1

N1
HIS

HIS

N

MCOs and Azurin

N

Stelacyanin

copper ion. The delocalization implies that transfer integral between d-orbital on the copper ion
and p-orbital on the sulfur ion in cysteine is larger when M06 is adopted.
Our finding can be related to t/U ratio in simple Hubbard model. This ratio can be used todetermine which is the more dominant factor between transfer integral (t) and on-site repulsion (U)in the electron transfer process in copper protein. The large value of t/U ratio indicates the transfer
integral is more dominant and vice versa. In our results, the decreasing of the partial spin densityof copper ion, that indicate the delocalization of unpaired electron, lead to an increase of t/U ratio.
This implies that the transfer integral is more dominant in our calculation. We find a result related
to the t/U ratio that is similar to our previous study [38]. Atomic partial spin of methionine’s sulfur
is found to be zero in all T1Cu cluster. This indicates that the probability of unpaired electron ofcopper to be distributed to methionine’s sulfur is zero. The large distance between both atoms isthe main reason of the zero distribution of unpaired electron around methionine’s sulfur.
The distribution of atomic partial charge around T1Cu calculated by using B3LYP and M06
is shown in Table 2. Here, we present the atomic partial charge of all atoms of T1Cu cluster inoxidized and reduced state. However, for the analysis purpose, we focus on the atomic partial
charge of the copper ion and the cysteine’s sulfur atom because the bond between both atoms is
crucial in electron transfer process. We find that M06 calculation produces the partial charge of thecopper ion that is less positive and the partial charge of cysteine’s sulfur atom that is less negative
than that of B3LYP calculation. The tendency is consistently found in all T1Cu clusters. This

6

Theoretical studies on electronic structure and properties of type I copper center in copper proteins

Table 2: The atomic partial charge of type I copper center in several proteins calculated by using
B3LYP (M06) methods.
Atom
Cu
S1
S2 /O
N1
N2
N3
N4
C1
C2
C3
C4
C5
C6
C7
C8 /N5C9

MCOs
Ox+0.55 (+0.54)-0.45 (-0.41)-0.22 (-0.23)-0.35 (-0.37)+0.19 (+0.16)-0.17 (-0.18)+0.10 (+0.10)+0.16 (+0.18)-0.09 (-0.08)+0.58 (+0.58)+0.19 (+0.20)+0.03 (+0.02)+0.19 (+0.21)+0.17 (+0.14)+0.08 (+0.08)+0.05 (+0.04)

Red+0.36 (+0.33)-0.71 (-0.68)-0.21 (-0.22)-0.20 (-0.21)-0.06 (-0.05)-0.36 (-0.36)+0.15 (+0.14)+0.19 (+0.21)-0.01 (-0.01)+0.19 (+0.20)+0.12 (+0.14)-0.17 (-0.16)+0.55 (+0.56)+0.12 (+0.09)+0.06 (+0.06)+0.01 (-0.01)

Atomic Partial Charge
AzurinOx
Red+0.63 (+0.59) +0.36 (+0.31)-0.49 (-0.45)-0.78 (-0.75)-0.40 (-0.38)-0.34 (-0.32)-0.26 (-0.28)-0.22 (-0.22)+0.24 (+0.20) +0.21 (+0.19)-0.29 (-0.26)-0.26 (-0.23)+0.19 (+0.16) +0.18 (+0.16)+0.12 (+0.16) +0.08 (+0.10)-0.07 (-0.04)-0.10 (-0.09)+0.37 (+0.36) +0.24 (+0.24)+0.09 (+0.11) +0.08 (+0.09)-0.01 (+0.02)-0.13 (-0.12)+0.40 (+0.37) +0.43 (+0.41)+0.18 (+0.14) +0.14 (+0.10)+0.11 (+0.09) +0.11 (+0.09)+0.27 (+0.26) +0.11 (+0.10)

MET

C9

Stellacyanin
Ox+0.54 (+0.50)-0.58 (-0.55)-0.61 (-0.61)-0.03 (-0.03)+0.23 (+0.22)-0.26 (-0.27)+0.18 (+0.17)+0.05 (+0.06)-0.04 (-0.04)+0.15 (+0.16)+0.10 (+0.11)-0.05 (-0.05)+0.44 (+0.45)+0.11 (+0.08)-0.14 (-0.15)+0.94 (+0.96)

Red+0.33 (+0.28)-0.79 (-0.75)-0.60 (-0.60)-0.07 (-0.07)+0.18 (+0.17)-0.31 (-0.30)+0.12 (+0.10)+0.04 (+0.06)-0.11 (-0.11)+0.17 (+0.18)+0.10 (+0.12)-0.11 (-0.11)+0.55 (+0.56)+0.01 (-0.02)-0.15 (-0.15)+0.89 (+0.91)

C8
HIS

S2
CYS

C7

C6
S1

C4

C3

C1
N2

C2

MCOs and Azurin
GLN

C9
N5
CYS

HIS

O

C7

C6
S1

Multicopper oxidase
AzurinStellacyanin

EA/eV

4.86 (5.18)
5.04 (5.32)
4.87 (5.16)

4.77 (5.02)
4.84 (5.12)
4.44 (4.71)

C4
N1
HIS

C3
C2

C1
N2

Stelacyanin

λ /nm
calc.
exp.a
661 (672)
684 (695)
577 (580)

C5

N3

Cu

Table 3: The calculation results of ionization potential (IP), electron affinity (EA) and maximum
absorption wavelength (λ ) of type I copper center in various copper proteins calculated by using
B3LYP (M06) methods.
IP/eV

N4

N1
HIS

Ox: Oxidized state, Red: Reduced state.

Protein

C5

N3

Cu

610
631
609

a Ref. [4]finding points out that the negative charge of cysteine’s sulfur by M06 is more distributed onto thecopper ion and thus affect to the atomic partial charge.
Table 3 shows several physical properties, such as ionization potential (IP), electron affinity(EA), and maximum absorption wavelength (λ ) of all T1Cu cluster. The IP and EA values calculated by M06 are found to be consistently larger than those calculated by B3LYP. This indicatesthe dependency of IP and EA values on DFT functional. We also find that EA value is directly
proportional to ligand bond distance shown in Fig. 3. The most significant relationship is found in
the bond between copper and cysteine ’s sulfur that is indicated by a large slope of the curve. Thisfinding implies the significant contribution of this bond in supporting electron transfer process.
Bearing on maximum absorption wavelength, we find that the wavelength calculated by M06
is larger than that calculated by B3LYP. Here, the maximum absorption wavelength represents
the transition energy between σ orbital of cysteine’s sulfur and dx2 −y2 orbital of copper ion [9].
Meanwhile, the amount of energy required by an electron to move to an orbital with higher energy
is defined as band-gap energy. The value of this energy is known to be inversely proportional to
the wavelength. As a consequence, the higher value of the wavelength indicates a small value ofband-gap energy. In other words, the band-gap energy between σ orbital of cysteine’s sulfur anddx2 −y2 orbital of Cu tends by M06 is lower than those by B3LYP.

N4

Isman K URNIAWAN, Kazutomo K AWAGUCHI, Kimikazu S UGIMORI, Takeshi S AKURAI, Hidemi NAGAO

5.3

Cu−N(His402)/M06
Cu−S(Cys459)/M06
Cu−N(His464)/M06
Cu−S(Met469)/M06
Cu−N(His402)/B3LYP
Cu−S(Cys459)/B3LYP
Cu−N(His464)/B3LYP
Cu−S(Met469)/B3LYP

5.2
5.1
EA (V)

7

5
4.9
4.8
4.7
4.6

1.8

2

2.2

2.4

2.6

2.8

3

3.2

Distance (Å)

Figure 3: The value of electron affinity as a function of bond distance in T1Cu of MCOs protein.
The equilibrium distance is represented by middle point with increment point 0.05 Å.

3.2

Force Field Parameter

The potential energy surfaces (PES) along the bond and angle distance used in fitting procedure
are presented in Fig. 4. From fitting analysis, we obtain the bond constant of T1Cu in MCOs,
azurin and stellacyanin that are presented in Tables 4, 5 and 6, respectively. We find a significant
contribution of DFT functional to the bond constant. The bond constants calculated by M06
are found to be larger than those calculated by B3LYP. We find that the bond constant and thedifferences between copper and axial methionine in the oxidized state are very significant, and thedifferences of the bond constants in MCOs, azurin, and stellacyanin are 28.38 kcal/mol·Å2 , 20.91
kcal/mol·Å2 , and 26.48 kcal/mol·Å2 , respectively.
Since the larger bond constant represents the stronger interaction of the bond, M06 represents
the interaction between copper and ligand in a stronger way. A significant contribution of M06 isrevealed in the case of long-range interaction between copper and axial ligand. Although the bonddistance between copper and axial ligand is significantly larger than the other bonds, the interaction
is still considered as a covalent bond. Hence, the calculation method that is used to investigate thisinteraction should be able to account long-range interaction as well. From the results, we find that
M06 performs better than B3LYP in accounting the long-range interaction. One of the reasonsis the implementation of meta-GGA functional, instead of pure GGA, in exchange functionalof M06. The inclusion of kinetic energy density in exchange functional seems to contribute in
improving DFT calculation. The other reason is related to the ratio between HF and (meta)-GGA
exchange functionals and also the optimization of parameter.
The angle constants of T1Cu in MCOs, azurin and stellacyanin are provided in Tables 7, 8
and 9, respectively. In the matter of angle constants, we do not find any systematic contributionof DFT functional. By comparing to B3LYP, M06 produces the angle constants that are larger
in several angles, but also smaller in another angles. This indicates that the calculation of angle
constant is more complicated than the calculation of bond constant. The calculation of one angle
constant cannot be purely independent from that of other angle because the change of one angle
can lead to the change of other angles.
We also compare the force field of Azurin between our result and Ref. [38] as shown in Tables 5 and 8. In the case of equilibrium bond distance and equilibrium angle distance, our result
produces the values that are quite similar to those of Ref. [38], especially to the results of the M06
calculation. Also, the bond constants obtained from our calculation are close to the reference.
However, our result of angle constant is found to be deviated from the reference. This is related

8

Theoretical studies on electronic structure and properties of type I copper center in copper proteins−3957.4250−3957.4180

Cu−N(His402)
Cu−N(His464)
Cu−S(Cys459)
Cu−S(Met469)−3957.4260

N(His402)−Cu−N(His464)
N(His402)−Cu−S(Cys459)
N(His402)−Cu−S(Met469)
N(His464)−Cu−S(Cys459)
N(His464)−Cu−S(Met469)
S(Cys459)−Cu−S(Met469)−3957.4190−3957.4200−3957.4270
Energy (a.u.)

Energy (a.u.)−3957.4210−3957.4280−3957.4290−3957.4300−3957.4220−3957.4230−3957.4240−3957.4250−3957.4310−3957.4260−3957.4320−3957.4330−3957.4270
1.8

2

2.2

2.4
2.6
Distance (Å)

2.8

3−3957.4280

3.2

70

80

90

(a)

100
110
Distance (Å)

120

130

(b)

Figure 4: The potential energy surface (PES) along with (a) bond and (b) angle of oxidized stateof T1Cu in MCOs protein calculated by using M06.
Table 4: The fitting parameter for bond distance the T1Cu of MCOs protein calculated by using
B3LYP (M06) methods.
Bond

ReducedrcrPDB

Cu-N(His402)
Cu-N(His464)
Cu-S(Cys459)
Cu-S(Met469)

2.072
1.974
2.302
3.061

1.99 (1.95)
1.96 (1.92)
2.18 (2.14)
3.23 (2.96)

Oxidized
Kr

rPDB

rc

Kr

104.28 (129.56)
121.49 (152.54)
126.97 (149.02)
11.88 (32.57)

2.01
2.03
2.30
3.23

2.00 (1.92)
1.96 (1.95)
2.25 (2.20)
3.53 (3.12)

89.57 (139.47)
107.79 (112.10)
92.3 (113.79)
6.24 (34.62)

The units of distance (r) and force constant (Kr ) are Å and kcal mol−1 Å−2 , respectively.

Table 5: The fitting parameter for bond distance the T1Cu of Azurin protein calculated by using
B3LYP (M06) methods.
Bond
Cu-N(His46)
Cu-N(His117)
Cu-S(Cys112)
Cu-S(Met121)

rPDB
2.00
2.11
2.27
3.18

Reduced Staterc
Kr
1.97 (1.94)
2.00 (1.95)
2.14 (2.10)
3.56 (3.28)

109.39 (136.66)
106.04 (127.09)
135.11 (154.38)
9.69 (25.80)

rPDB

rc

Oxidized State
Kr

rca

Kra

2.06
2.19
2.28
3.33

1.96 (1.93)
2.05 (1.99)
2.20 (2.16)
3.79 (3.39)

107.82 (131.11)
72.16 (99.98)
96.67 (123.98)
7.02 (27.93)

1.948
2.157
3.342

128.45130.948
29.15

a Ref. [38]The units of distance (r) and force constant (Kr ) are Å and kcal mol−1 Å−2 , respectively.

to the complexity of the calculation due to the strong dependency between one angle and otherangles.
The reliability of our calculation is discussed according to the comparison of the calculated
results with available experimental data. In the case of maximum absorption wavelength, we finda deviation of values between our calculation and experimental data. However, the tendency ofthe value is a good agreement with the experimental data. This indicates that our calculation isreliable in the case of the relative value of maximum absorption wavelength. The bond distances
obtained from our calculation are also quite similar to the distance obtained from the X-ray crystal
structure. This points out the reliability of our calculation in predicting the bond distance around
T1Cu cluster.

140

Isman K URNIAWAN, Kazutomo K AWAGUCHI, Kimikazu S UGIMORI, Takeshi S AKURAI, Hidemi NAGAO

9Table 6: The fitting parameter for bond distance of the T1Cu of Stellacyanin protein calculated byusing B3LYP (M06) methods.
Bond
Cu-N(His45)
Cu-N(His91)
Cu-S(Cys86)
Cu-O(Gln96)

Reduced State
rc
Kr

rPDB
1.89
2.06
2.23
2.22

1.99 (1.95)
2.05 (2.00)
2.18 (2.13)
2.41 (2.28)

Oxidized State
rc
Kr

rPDB

101.46 (124.55)
99.84 (123.56)
128.73 (158.12)
29.21 (43.68)

2.17
2.06
2.24
2.52

2.02 (1.98)
2.05 (1.99)
2.22 (2.17)
2.83 (2.51)

83.15 (107.09)
85.78 (110.74)
92.33 (117.53)
9.55 (36.03)

The units of distance (r) and force constant (Kr ) are Å and kcal mol−1 Å−2 , respectively.

Table 7: The fitting parameter for angle distance of the T1Cu of MCOs protein calculated by using
B3LYP (M06) methods.
θPDB

Reduced State
θc
Kθ

θPDB

Oxidized State
θcKθ

N(His402)-Cu-N(His464)
N(His402)-Cu-S(Cys459)
N(His402)-Cu-S(Met469)
N(His464)-Cu-S(Cys459)
N(His464)-Cu-S(Met469)
S(Cys459)-Cu-S(Met469)

103
129
79
124
107
100

102 (102)131 (131)
78 (79)120 (124)
107 (107)
100 (99)

93 (72)93 (59)419 (529)
36 (50)375 (355)
236 (284)

105
126
78
128
102
100

105 (105)130 (126)
76 (77)121 (106)102 (102)100 (99)

78 (60)69 (62)359 (74)
26 (109)370 (348)
174 (246)

Cu-N(His402)-Cε
Cu-N(His402)-Cγ
Cu-N(His464)-Cε
Cu-N(His464)-Cγ
Cu-S(Cys459)-Cβ
Cu-S(Met469)-Cε
Cu-S(Met469)-Cγ

125
124
125
125
100
104
140

123 (125)
126 (124)
125 (127)
126 (124)
105 (100)
102 (103)
141 (140)

94 (86)98 (93)205 (280)
204 (278)
43 (92)181 (188)
240 (314)

127
125
127
125
100
103
141

125 (128)
127 (124)
127 (129)125 (123)
103 (98)
101 (102)143 (141)

89 (93)90 (94)210 (240)
202 (227)
40 (84)153 (127)
190 (324)

Angle

The units of angle (θ ) and force constant (Kθ ) are (◦ ) and kcal mol−1 rad−2 , respectively.

4

Conclusion

We have presented a cluster model representing type I copper (T1Cu) center of several copper
proteins, i.e. multicopper oxidases (MCOs), azurin and stellacyanin. Several physical properties
such as atomic partial charge, atomic partial spin, ionization potential of reduced T1Cu, electron
affinity of oxidized T1Cu, bond and the angle constants, etc. have been discussed in relation to
DFT functionals dependency by utilizing two typical DFT functionals, i.e. B3LYP and M06. We
have found the dependency of atomic partial charge and partial spin of T1Cu cluster on the DFT
functionals, which correspond to electron delocalization between Cu and cysteine’s sulfur and thus
lead the increasing of t/U ratio in simple Hubbard model. The ionization potential (IP) of reduced
T1Cu and the electron affinity (EA) of oxidized T1Cu have been approximately calculated withthe present cluster model and the dependency on DFT functional have been revealed. We havealso calculated the absorption wavelength of T1Cu and compared the results with experimental
data. A significant contribution of M06 in the case of bond constant has been unveiled, especiallyin long-range interaction between copper ion and axial ligand. We have found that the interaction
between copper ion and ligand is improved when M06 is adopted .

10Theoretical studies on electronic structure and properties of type I copper center in copper proteins

Table 8: The fitting parameter for angle distance of the T1Cu of Azurin protein calculated by using
B3LYP (M06) methods.
θPDB

Reduced State
θc
Kθ

θPDB

N(His46)-Cu-N(His117)
N(His46)-Cu-S(Cys112)
N(His46)-Cu-S(Met121)
N(His117)-Cu-S(Cys112)
N(His117)-Cu-S(Met121)
S(Cys112)-Cu-S(Met121)

104
132
75
124
84
110

105 (100)
139 (145)
73 (73)116 (110)
88 (88)110 (109)

64 (93)54 (103)558 (589)
44 (101)406 (367)
208 (287)

103
133
73
123
88
112

103 (105)
139 (137)
70 (71)115 (113)
91 (91)113 (112)

Cu-N(His46)-Cε
Cu-N(His46)-Cγ
Cu-N(His117)-Cε
Cu-N(His117)-Cγ
Cu-S(Cys112)-Cβ
Cu-S(Met121)-Cε
Cu-S(Met121)-Cγ

124
132
124
129
109
99
138

121 (123)135 (133)
121 (122)133 (131)107 (103)
97 (97)142 (142)

103 (104)103 (104)217 (334)
188 (227)
88 (157)425 (430)
245 (236)

126
130
128
127
108
98
137

125 (128)131 (128)
124 (126)
131 (129)
106 (102)
95 (95)142 (141)

Angle

Oxidized State
θc
Kθ

θca

Kθa

68 (70)43 (58)478 (457)
34 (44)387 (413)
155 (218)

120
88
111

12
112
96

105 (128)104 (132)215 (322)
205 (304)
75 (128)342 (349)
134 (161)

108
-

35
-

a Ref. [38]The units of angle (θ ) and force constant (Kθ ) are (◦ ) and kcal mol−1 rad−2 , respectively.

Table 9: The fitting parameter for angle distance of the T1Cu of Stellacyanin protein calculated byusing B3LYP (M06) methods.
θPDB

Reduced State
θc
Kθ

θPDB

Oxidized State
θcKθ

N(His45)-Cu-N(His91)
N(His45)-Cu-S(Cys86)
N(His45)-Cu-S(Met96)
N(His91)-Cu-S(Cys86)
N(His91)-Cu-O(Gln96)
S(Cys86)-Cu-O(Gln96)

100
128
94
126
95
105

97 (98)131 (135)91 (92)116 (116)
98 (98)105 (104)212 (213)
84 (88)367 (400)
39 (34)513 (529)
295 (394)

98
132
87
125
90
111

95 (97)134 (137)
83 (85)118 (102)92 (92)112 (111)130 (136)
63 (72)290 (319)
26 (148)522 (518)
184 (313)

Cu-N(His45)-Cε
Cu-N(His45)-Cγ
Cu-N(His91)-Cε
Cu-N(His91)-Cγ
Cu-S(Cys86)-Cβ
Cu-O(Glu96)-Cδ

121
129
127
123
108
117

121 (122)
130 (128)
123 (125)
127 (126)
109 (105)
115 (115)

95 (102)95 (102)297 (383)
294 (376)
77 (178)365 (364)

128
122
126
123
108
106

125 (128)126 (122)
122 (124)
127 (125)
110 (106)104 (103)

52 (61)54 (65)257 (404)
248 (384)
73 (126)260 (256)

Angle

The units of angle (θ ) and force constant (Kθ ) are (◦ ) and kcal mol−1 rad−2 , respectively.

References[1] P. M. Colman, H. C. Freeman, J. M. Guss, M. Murata, V. A. Norris, J. a. M. Ramshaw, and M. P. Venkatappa,“X-ray crystal structure analysis of plastocyanin at 2.7 Å resolution,” Nature, vol. 272, pp. 319–324, Mar. 1978.
[2] E. T. Adman and L. H. Jensen, “Structural Features of Azurin at 2.7 Å Resolution,” Israel Journal of Chemistry,
vol. 21, pp. 8–12, Jan. 1981.
[3] K. Paraskevopoulos, M. Sundararajan, R. Surendran, M. A. Hough, R. R. Eady, I. H. Hillier, and S. S. Hasnain,“Active site structures and the redox properties of blue copper proteins: atomic resolution structure of azurin
II and electronic structure calculations of azurin, plastocyanin and stellacyanin,” Dalton Trans., pp. 3067–3076,
June 2006.

Isman K URNIAWAN, Kazutomo K AWAGUCHI, Kimikazu S UGIMORI, Takeshi S AKURAI, Hidemi NAGAO

11[4] E. I. Solomon, M. J. Baldwin, and M. D. Lowery, “Electronic structures of active sites in copper proteins: contributions to reactivity,” Chem. Rev., vol. 92, pp. 521–542, June 1992.
[5] M. M. Harding, M. W. Nowicki, and M. D. Walkinshaw, “Metals in protein structures: a review of their principalfeatures,” Crystallography Reviews, vol. 16, pp. 247–302, Oct. 2010.
[6] D. E. Heppner, C. H. Kjaergaard, and E. I. Solomon, “Mechanism of the Reduction of the Native Intermediate in
the Multicopper Oxidases: Insights into Rapid Intramolecular Electron Transfer in Turnover,” J. Am. Chem. Soc.,
vol. 136, pp. 17788–17801, Dec. 2014.
[7] T. Sakurai and K. Kataoka, “Structure and function of type I copper in multicopper oxidases,” Cellular andMolecular Life Sciences, vol. 64, p. 2642, July 2007.
[8] R. A. Holwerda, S. Wherland, and a. H. B. Gray, “Electron Transfer Reactions of Copper Proteins,” Annual
Review of Biophysics and Bioengineering, vol. 5, no. 1, pp. 363–396, 1976.
[9] E. I. Solomon, J. W. Hare, D. M. Dooley, J. H. Dawson, P. J. Stephens, and H. B. Gray, “Spectroscopic studies ofstellacyanin, plastocyanin, and azurin. Electronic structure of the blue copper sites,” J. Am. Chem. Soc., vol. 102,
pp. 168–178, Jan. 1980.
[10] D. R. McMillin and M. C. Morris, “Further perspectives on the charge transfer transitions of blue copper proteins
and the ligand moieties in stellacyanin,” Proceedings of the National Academy of Sciences of the United States ofAmerica, vol. 78, pp. 6567–6570, Nov. 1981.
[11] E. Bouwman, W. L. Driessen, and J. Reedijk, “Model systems for type I copper proteins: structures of copper
coordination compounds with thioether and azole-containing ligands,” Coordination Chemistry Reviews, vol. 104,
pp. 143–172, July 1990.
[12] D. Qiu, S. Dong, J. Ybe, M. Hecht, and T. G. Spiro, “Variations in the Type I Copper Protein Coordination Group:
Resonance Raman Spectrum of 34s-, 65cu-, and 15n-Labeled Plastocyanin,” Journal of the American Chemical
Society, vol. 117, pp. 6443–6446, June 1995.
[13] E. I. Solomon, U. M. Sundaram, and T. E. Machonkin, “Multicopper Oxidases and Oxygenases,” Chem. Rev.,
vol. 96, pp. 2563–2606, Nov. 1996.
[14] E. I. Solomon, P. Chen, M. Metz, S.-K. Lee, and A. E. Palmer, “Oxygen Binding, Activation, and Reduction to
Water by Copper Proteins,” Angew. Chem. Int. Ed. Engl., vol. 40, pp. 4570–4590, Dec. 2001.
[15] N. Hakulinen, L.-L. Kiiskinen, K. Kruus, M. Saloheimo, A. Paananen, A. Koivula, and J. Rouvinen, “Crystal
structure of a laccase from Melanocarpus albomyces with an intact trinuclear copper site,” Nature Structural &Molecular Biology, vol. 9, pp. 601–605, Aug. 2002.
[16] K. Piontek, M. Antorini, and T. Choinowski, “Crystal Structure of a Laccase from the FungusTrametes versicolor
at 1.90-Å Containing a Full Complement of Coppers,” Journal of Biological Chemistry, vol. 277, pp. 37663–
37669, Oct. 2002.
[17] S. A. Roberts, A. Weichsel, G. Grass, K. Thakali, J. T. Hazzard, G. Tollin, C. Rensing, and W. R. Montfort,“Crystal structure and electron transfer kinetics of CueO, a multicopper oxidase required for copper homeostasis
in Escherichia coli,” PNAS, vol. 99, pp. 2766–2771, Mar. 2002.
[18] S. Shleev, J. Tkac, A. Christenson, T. Ruzgas, A. I. Yaropolov, J. W. Whittaker, and L. Gorton, “Direct electrontransfer between copper-containing proteins and electrodes,” Biosensors and Bioelectronics, vol. 20, pp. 2517–
2554, June 2005.
[19] M. Ferraroni, N. M. Myasoedova, V. Schmatchenko, A. A. Leontievsky, L. A. Golovleva, A. Scozzafava, and
F. Briganti, “Crystal structure of a blue laccase from Lentinus tigrinus: evidences for intermediates in the molecular oxygen reductive splitting by multicopper oxidases,” BMC Structural Biology, vol. 7, p. 60, 2007.
[20] T. Sakurai and K. Kataoka, “Basic and applied features of multicopper oxidases, CueO, bilirubin oxidase, andlaccase,” Chem Record, vol. 7, pp. 220–229, Jan. 2007.
[21] J. Yoon and E. I. Solomon, “Electronic structures of exchange coupled trigonal trimeric Cu(II) complexes: Spinfrustration, antisymmetric exchange, pseudo-A terms, and their relation to O2 activation in the multicopper oxidases,” Coordination Chemistry Reviews, vol. 251, pp. 379–400, Feb. 2007.
[22] L. Quintanar, C. Stoj, A. B. Taylor, P. J. Hart, D. J. Kosman, and E. I. Solomon, “Shall We Dance? How A
Multicopper Oxidase Chooses Its Electron Transfer Partner,” Accounts of Chemical Research, vol. 40, pp. 445–
452, June 2007.
[23] J. Yoon, B. D. Liboiron, R. Sarangi, K. O. Hodgson, B. Hedman, and E. I. Solomon, “The two oxidized formsof the trinuclear Cu cluster in the multicopper oxidases and mechanism for the decay of the native intermediate,”
Proceedings of the National Academy of Sciences, vol. 104, pp. 13609–13614, Aug. 2007.

12

Theoretical studies on electronic structure and properties of type I copper center in copper proteins[24] K. Kataoka, H. Komori, Y. Ueki, Y. Konno, Y. Kamitaka, S. Kurose, S. Tsujimura, Y. Higuchi, K. Kano, D. Seo,and T. Sakurai, “Structure and Function of the Engineered Multicopper Oxidase CueO from Escherichia coli
—Deletion of the Methionine-Rich Helical Region Covering the Substrate-Binding Site,” Journal of Molecular
Biology, vol. 373, pp. 141–152, Oct. 2007.
[25] K. Y. Djoko, L. X. Chong, A. G. Wedd, and Z. Xiao, “Reaction Mechanisms of the Multicopper Oxidase CueO
from Escherichia coli Support Its Functional Role as a Cuprous Oxidase,” Journal of the American Chemical
Society, vol. 132, pp. 2005–2015, Feb. 2010.
[26] A. J. Augustine, C. Kjaergaard, M. Qayyum, L. Ziegler, D. J. Kosman, K. O. Hodgson, B. Hedman, and E. I.
Solomon, “Systematic Perturbation of the Trinuclear Copper Cluster in the Multicopper Oxidases: The Role ofActive Site Asymmetry in Its Reduction of O2 to H2o,” Journal of the American Chemical Society, vol. 132,
pp. 6057–6067, May 2010.
[27] H. Komori, R. Sugiyama, K. Kataoka, K. Miyazaki, Y. Higuchi, and T. Sakurai, “New insights into the catalytic
active-site structure of multicopper oxidases,” Acta Crystallogr. D Biol. Crystallogr., vol. 70, pp. 772–779, Mar.
2014.
[28] I. Pardo and S. Camarero, “Laccase engineering by rational and evolutionary design,” Cellular and MolecularLife Sciences, vol. 72, no. 5, pp. 897–910, 2015.
[29] E. I. Solomon, R. K. Szilagyi, S. DeBeer George, and L. Basumallick, “Electronic Structures of Metal Sites inProteins and Models: Contributions to Function in Blue Copper Proteins,” Chem. Rev., vol. 104, pp. 419–458,
Feb. 2004.
[30] S. Corni, F. De Rienzo, R. Di Felice, and E. Molinari, “Role of the electronic properties of azurin active site in
the electron-transfer process,” International Journal of Quantum Chemistry, vol. 102, pp. 328–342, Jan. 2005.
[31] M. Pavelka and J. V. Burda, “Computational study of redox active centres of blue copper proteins: a computational
DFT study,” Molecular Physics, vol. 106, pp. 2733–2748, Dec. 2008.
[32] D. Robinson and N. A. Besley, “Modelling the spectroscopy and dynamics of plastocyanin,” Phys Chem Chem
Phys, vol. 12, pp. 9667–9676, Sept. 2010.
[33] Y. Zhao and D. G. Truhlar, “The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic
testing of four M06-class functionals and 12 other functionals,” Theor Chem Account, vol. 120, pp. 215–241, July
2007.
[34] Y. Zhao and D. G. Truhlar, “Computational characterization and modeling of buckyball tweezers: density functional study of concave-convex π · · · π interactions,” Phys. Chem. Chem. Phys., vol. 10, pp. 2813–2818, May
2008.
[35] U. Warde, L. Rhyman, P. Ramasami, and N. Sekar, “DFT Studies of the Photophysical Properties of Fluorescentand Semiconductor Polycyclic Benzimidazole Derivatives,” J Fluoresc, vol. 25, pp. 685–694, Mar. 2015.
[36] Y. Minenkov, Ȧ. Singstad, G. Occhipinti, and V. R. Jensen, “The accuracy of DFT-optimized geometries offunctional transition metal compounds: a validation study of catalysts for olefin metathesis and other reactions in
the homogeneous phase,” Dalton Trans., vol. 41, Apr. 2012.
[37] D. Coskun, S. V. Jerome, and R. A. Friesner, “Evaluation of the Performance of the B3lyp, PBE0, and M06
DFT Functionals, and DBLOC-Corrected Versions, in the Calculation of Redox Potentials and Spin Splittings forTransition Metal Containing Systems,” J. Chem. Theory Comput., vol. 12, pp. 1121–1128, Mar. 2016.
[38] T. Shuku, K. Sugimori, A. Sugiyama, H. Nagao, T. Sakurai, and K. Nishikawa, “Molecular orbital analysis ofactive site of oxidized azurin: Dependency of electronic properties on molecular structure,” Polyhedron, vol. 24,
pp. 2665–2670, Nov. 2005.
[39] A. Sugiyama, K. Sugimori, T. Shuku, T. Nakamura, H. Saito, H. Nagao, H. Kawabe, and K. Nishikawa, “Electronic structure of the active site with two configurations of azurin,” Int. J. Quantum Chem., vol. 105, pp. 588–595,
Jan. 2005.
[40] K. Sugimori, T. Shuku, A. Sugiyama, H. Nagao, T. Sakurai, and K. Nishikawa, “Solvent effects on electronic
structure of active site of azurin by polarizable continuum model,” Polyhedron, vol. 24, pp. 2671–2675, Nov.
2005.
[41] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone,
B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino,
G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima,Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd,
E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant,Isman K URNIAWAN, Kazutomo K AWAGUCHI, Kimikazu S UGIMORI, Takeshi S AKURAI, Hidemi NAGAO

13

S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo,
J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L.
Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels,
O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, and D. J. Fox, “Gaussian 09, Revision E.01,” 2009.
[42] H. Nar, A. Messerschmidt, R. Huber, M. van de Kamp, and G. W. Canters, “Crystal structure analysis of oxidized
Pseudomonas aeruginosa azurin at pH 5·5 and pH 9·0: A pH-induced conformational transition involves a peptide
bond flip,” Journal of Molecular Biology, vol. 221, pp. 765–772, Oct. 1991.
[43] M. Koch, M. Velarde, M. D. Harrison, S. Echt, M. Fischer, A. Messerschmidt, and C. Dennison, “Crystal structures of oxidized and reduced stellacyanin from horseradish roots,” Journal of the American Chemical Society,vol. 127, pp. 158–166, Jan. 2005.
[44] H. Nar, Rontgenkristallographische Strukturaufklarung Von Azurin Aus Pseudomonas Aeruginosa. PhD thesis,
1992.
[45] U. C. Singh and P. A. Kollman, “An approach to computing electrostatic charges for molecules,” J. Comput.
Chem., vol. 5, pp. 129–145, Apr. 1984.
[46] B. Mennucci, “Polarizable continuum model,” WIREs Comput Mol Sci, vol. 2, pp. 386–404, May 2012.
[47] T. V. Harris and R. K. Szilagyi, “Protein environmental effects on iron-sulfur clusters: A set of rules for constructing computational models for inner and outer coordination spheres,” J. Comput. Chem., vol. 37, pp. 1681–1696,
July 2016.
[48] C. Liu, B. Zhang, Y. Zhu, and M. Tang, “Evaluations of AMBER force field parameters by MINA approach forcopper-based nucleases,” Struct Chem, pp. 1–16, May 2016.