Spin-dependent binding of dioxygen to heme and charge-transfer mechanism of spin-orbit coupling enhancement
Spin-orbit coupling (SOC) between the starting triplet ³A''(2) state from the entrance channel of the heme-O2 binding reaction and the final singlet ¹A'(1) open-shell state, which are dominated by the Fe^3+-O2-radical-pair structures, is studied. Simulated potential energy surface cro...
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Інститут молекулярної біології і генетики НАН України
2008
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| Zitieren: | Spin-dependent binding of dioxygen to heme and charge-transfer mechanism of spin-orbit coupling enhancement / B.F. Minaev, V.A. Minaeva // Ukrainica Bioorganica Acta. — 2008. — Т. 6, № 2. — С. 56-64. — Бібліогр.: 25 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860261050172047360 |
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| author | Minaev, B.F. Minaeva, V.A. |
| author_facet | Minaev, B.F. Minaeva, V.A. |
| citation_txt | Spin-dependent binding of dioxygen to heme and charge-transfer mechanism of spin-orbit coupling enhancement / B.F. Minaev, V.A. Minaeva // Ukrainica Bioorganica Acta. — 2008. — Т. 6, № 2. — С. 56-64. — Бібліогр.: 25 назв. — англ. |
| collection | DSpace DC |
| description | Spin-orbit coupling (SOC) between the starting triplet ³A''(2) state from the entrance channel of the heme-O2 binding reaction and the final singlet ¹A'(1) open-shell state, which are dominated by the Fe^3+-O2-radical-pair structures, is studied. Simulated potential energy surface cross sections along the reaction coordinate for these and other multiplets, calculated by density functional theory (DFT) agree with the recent DFT studies known from the literature. The heme-model includes Fe(II)-porphyrin complex with imidazol, or ammonia molecule, at the fith coordination position, which simulates the hystidine as an aminoacide residue of myoglobin. The SOC is induced mainly at the oxygen moiety by an orbital angular momentum change in the π8-shell during the triplet-singlet transition. This SOC model explains pretty well the efficient spin inversion during the heme-O2 binding.
Вивчено спін-орбітальну взаємодію (СОВ) між початковим триплетним ³А''(2) станом у вхідному каналі реакції зв’язування гем-О2 і кінцевим синглетним ¹А'(1) станом з відкритою оболонкою, які визначені домінувальним вкладом структури радикальної пари Fe^3+-O2-. Перетини модельних поверхонь потенціальної енергії вздовж координати реакції для цих мультиплетів, розраховані за теорією функціоналу густини (ТФГ), узгоджуються з недавніми розрахунками ТФГ, відомими з літератури. Модель гема включає Fe(II)-порфін, координований з імідазолом або амоніаком у п’ятій координаційній позиції йона заліза, які моделюють гістидин як амінокислотний залишок міоглобіну. СОВ індукується головним чином на кисні за рахунок зміни орбітального кутового моменту πg-оболонки при триплет-синглетному переході. Ця модель СОВ добре пояснює ефективну інверсію спіну в ході зв’язування гем-О2.
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Introduction. Hemoglobin and myoglobin are
important globular proteins that reversibly bind
the O2 molecule. Myoglobin is found in muscle
сells where it stores dioxygen and provides it to
the working muscles supplying oxidation energy
[1]. Hemoglobin is the O2 carrier in the red blood
cells; it is essentially a tetramer of four myoglo�
bin molecules. Both proteins contain ferrous iron
of a heme group, which is usually simulated by
Fe(II) porphyrin, where iron ion is tetra�coordi�
natied to nitrogen atoms of the tetra�pyrrole
rings [1�4]. The proximal histidine residue from
the protein side chain is also bound to the Fe(II)
ion leaving one empty position in the octahedral
coordination sphere around the ferrous iron.
Hemoglobin and myoglobin bind several small
gaseous molecules besides dioxygen, e.g. CO and
NO [1�3].
The binding of these diatomic ligands to
heme has been studied in biochemistry for over
hundred years [2]. It is well�established that the
structure of surrounding protein affects the li�
gand binding ability of the heme group; carbon
monoxide binds to free heme in solution much
stronger (2•104 times) than dioxygen, but in
myoglobin this factor is reduced to 25 times [4].
Thus, myoglobin seems to favour the O2 binding
before CO by 17 kJ/mol [1, 2, 4]. Such discrimi�
nation is of vital importance: without it we
would suffocate from CO that is produced in our
body during metabolism. The reason of the dis�
crimination was connected with different geo�
metric parameters of O2 and CO binding to the
hem iron: the Fe�C�O bond is linear, whereas
Fe�O�O bond is bent [4]. Hemoglobin and myo�
globin have a second, so�called distal, histidine
ligand (His�64) positioned above the Fe(II) ion,
but too far to coordinate directly to the iron. His�
64 is in the right position to affect the Fe�CO
group and to produce a tension. This idea was
supported by early crystal structures, showing
Fe�C�O angle of 120�130o [4], thus the idea pene�
trates into the textbooks [4, 5]. Some newer x�
ray measurements, IR spectra and DFT calcula�
56
Spin�dependent binding of dioxygen to heme and charge�
transfer mechanism of spin�orbit coupling enhancement
B.F. Minaev*, V.A. Minaeva
Bohdan Khmelnitskyi National University
81 Bvd. Shevchenko, Cherkasy, 18031, Ukraine
Summary. Spin�orbit coupling (SOC) between the starting triplet 3A''(2) state from the entrance channel of
the heme�O2 binding reaction and the final singlet 1A'(1) open�shell state, which are dominated by the Fe3+�O2
�
radical�pair structures, is studied. Simulated potential energy surface cross sections along the reaction coordi�
nate for these and other multiplets, calculated by density functional theory (DFT) agree with the recent DFT
studies known from the literature. The heme�model includes Fe(II)�porphyrin complex with imidazol, or ammo�
nia molecule, at the fith coordination position, which simulates the hystidine as an aminoacide residue of myo�
globin. The SOC is induced mainly at the oxygen moiety by an orbital angular momentum change in the πg�shell
during the triplet�singlet transition. This SOC model explains pretty well the efficient spin inversion during the
heme�O2 binding.
Keywords: hemoglobin, myoglobin, cytochrome oxidase, spin�orbit coupling, triplet�singlet spin inversion,
radical�pair structures, charge�transfer states, binding of diatomic ligands to heme.
www.bioorganica.org.ua
Ukrainica Bioorganica Acta 2 (2008) 56—64
* Corresponding author.
Tel./fax: +380472�458720
E�mail address: bfmin@rambler.ru
© B.F. Minaev, V.O. Minaeva, 2008
tions indicate that the Fe�C�O angle is nearly
linear in heme models; thus the idea of a strong�
ly bent Fe�C�O unit as the reason of the discri�
mination is nowadays agreed to be incorrect [1,
3]. Recent DFT calculations show that the FeO2
group is much more polar than the FeCO group
in hem models [1, 3, 6]. The electronic structure
of FeP complex with dioxygen is close to that of
a superoxide anion bound to a ferric ion and this
charge�transfer complex is in the singlet spin
state [1�4]. Thus electrostatic interaction bet�
ween distal histidine and Fe(III)�O�O� group is
stronger than that for the Fe�CO group; there�
fore the protein discriminates between O2 and
CO by hydrogen bonding and electrostatic inter�
action in myoglobin [1�3].
Another important factor of such discrimina�
tion is determined by electron spin [2, 3, 6]. Spin
is a general intrinsic quantum property of elect�
ron. Spin is an angular momentum with a length
of the momentum vector ,
where spin quantum number for one electron is
equal to S=1/2 and two projection [[[[[[[[
described by α and β wave functions exist (the
doublet state) [6]. The role of electron spin in
chemistry is well�recognized in terms of spin�
valence concept: a covalent chemical bond is
formed when atomic orbitals of two electrons
with opposite spins (αβ�βα) overlap each over.
This spin wave function is antisymmetric in
respect to permutation of two electrons. The
total spin of such pair is zero (S=0) and the state
is singlet (the only one state; no spin, no intrinsic
magnetic moment, the molecule is diamagnetic).
When spins are parallel (αα, ββ and αβ+βα) the
total spin has a quantum number S=1 in the
equation for the length of the total spin angular
momentum
(1).
and there are three spin states with different
projections on z�axis (triplet state). For
a simple covalent σ�bond (like in H2 molecule)
the triplet sate is unstable and molecule can
exist only in the singlet state with two opposite
spins. That is why almost all stable organic mol�
ecules contain an even number of electrons,
which can be divided into α and β pairs. They are
said to have paired spins or to be in the singlet
ground state and are diamagnetic.
Such diamagnetic substances normally do
not change zero spin during chemical reactions
[6�10]. An absence of the total electronic spin in
stable molecules leads to illusion that spin is not
important in organic chemistry and bioche�
mistry. In fact, the total electronic spin is the
main regulating factor in many metabolic
processes catalyzed by metal�organic enzymes,
such as cytochromes, horseradish peroxidase,
copper�aminoxidase [6�24]. Spin inversion is
especially important for many dioxygen reac�
tions, binding to hem, combustion and respira�
tion [10]. The importance of spin inversion is also
reflected in the Perutz model of the hemoglobin
cooperativety [2�4].
Dioxygen molecule is a famous exception to
the general rule: unlike many chemically stable
organic compounds the O2 molecule has the
triplet ground state, Eq. (1). According to Hund’s
rule, two unpaired electrons in two degenerate
πg,x� and πg,y�orbitals have a lower repulsive
energy in the triplet state compared to the sin�
glet state. Because of this oxygen is paramag�
netic (it has intrinsic magnetic moment due to
spins of two unpaired electrons) and its addition
to organic compounds is spin forbidden: starting
reactants have the total spin S=1 (from the O2),
whereas the oxidation products are diamagnetic
(S=0) [10]. This is the reason why organic matter
may exist in the oxygen�rich atmosphere.
Because of the spin prohibition, combustion of
organic fuels requires activation in the form of
high�temperature ignition stage [10], i.e., gene�
ration of primary radicals. Reaction of R• radical
(one unpaired electron, S=1/2, doublet state)
with O2 molecule is spin�allowed, since the star�
ting reactants (O2+R•) and product (RO2
•) both
have the doublet states, which provide the radi�
cal chain character of the combustion reactions
[10]:
(2).
Here the quantum cell [ ] denotes molecular
orbital (MO) with α spin. The radical RO2
• can
decompose into radical RO• and biradical •O•
thus providing branching chain reaction. In ra�
dical chain combustion the energy is released in
the form of heat and light without any specific
control (until the fuel exhaustion). Clearly, such
mechanism of oxidation by molecular oxygen
can not be realized in living cells. Cells meet their
Spin�dependent binding of dioxygen to heme and charge�transfer mechanism of spin�orbit coupling enhancement
57www.bioorganica.org.ua
2S
�
= �� )23()1( =+SS
Ms = ±(1/2)
2S
�
= �� 2)1( =+SS
Ms = ± ,0
� �� �� � � � � �� �� �
�
�
( 2 + R·) RO2·
energy needs in the course of metabolic proces�
ses using the strictly controlled energy of oxida�
tion of organic compounds in their reactions
with dioxygen, overcoming spin prohibition
without high�temperature ignition step of radi�
cal chain [18]. An aerobic life evolved due to spe�
cific kinetic prohibitions to reactions of para�
magnetic oxygen with diamagnetic organic sub�
stances. The main reason for sluggish O2 reacti�
vity at the ambient conditions is the spin prohi�
bition, namely, the starting reagents have two
unpaired spins (from O2 molecule), while in dia�
magnetic oxidation products (CO2, H2O, N2) all
spins are always paired. Overcoming of this pro�
hibition by generating radicals to interact with
dioxygen (like in combustion) is inadmissible to
living matter. Since the cells can not resist large
temperature gradients, they have to transform
the energy released through oxidation to some
kind of chemical energy prior to dissipation in
the form of heat. This occurs by combining oxi�
dation with the ATP synthesis. All versatile
energy�supplying metabolic processes and reac�
tions occur under subtle enzymatic regulation,
which is strictly spin�dependent [18].
The O2 molecule in the triplet ground state
has the following electronic configuration (1σg)2
(1σu)2 (2σg)2 (2σu)2 (3σg)2 (1πu)4 (1πg)2. The two
outer electrons in two degenerate 1πg�MO’s pro�
vide the lowest triplet state of the type [ ][ ],
where the quantum cells [ ][ ] denote the dege�
nerate πg�orbitals. These two unpaired electrons
in antibonding πg�MOs are responsible for spe�
cific character of the dioxygen interaction with
radicals (combustion) and chemically stable dia�
magnetic compounds (slow oxidation). Two anti�
bonding πg�vacancies makes it possible to trans�
form dioxygen into O2
� and O2
2� anions, the for�
mation of the latter being strongly dependent on
the presence of electron donors (enzymes) and
magnetic perturbations that affect the spin pro�
hibitions.
In this paper we want to understand the
spin�dependent mechanism of the O2 binding
step once dioxygen has moved from the solvent
through the protein α�helices and reached the
myoglobin distal cavity near the ferrous�heme
cofactor active site. This binding step which has
been extensively studied after flash�photolysis
[2�4] shows interesting kinetic features, like non
homogeneous decay, recombination barriers
etc., and indicates complicated spin�dependence
(especially in comparison with NO and CO bind�
ing to myoglobin). Explanation of such spin�de�
pendence is the main purpose of this work.
Spin�dependence of dioxygen reactions.
Spins can undergo «depairing» when exposed to
light; here an electron goes from doubly occu�
pied orbital [ ] to a vacant MO [ ] with the si�
multaneous spin flip [12, 13]:
(3).
According to the Pauli principle, both spins
can be parallel (total spin S=1) in the excited
state. This triplet state has three possible orien�
tations of the total spin vector, thus the singlet
→ triplet excitation includes three possible tran�
sitions to three spin sublevels. All of them are
spin�forbidden. This is a very strict prohibition,
since it can be removed only by influence of
magnetic interactions that are much weaker
than electric Coulomb interactions. The latter
determine energetics of chemical bonding, elec�
tronic «depairing» excitation and the pathways
of chemical reactions. The spin affects the ener�
gy through exchange interaction. A weak SOC
slightly mixes the singlet and triplet states of
molecules, which gives a non�zero rate for the
T→S transitions that are observed in the form of
phosphorescence and are well known as impor�
tant quenching processes in photochemistry [12,
13]. The nonradiative T�S transitions also play
an important role in the dark reactions, in par�
ticular, in catalysis [10]. Weak SOC acts as a
«key» needed to open a «heavy door», that is, the
system chooses a pathway of chemical reaction
with low activation barrier in the triplet state
instead of overcoming a high activation barrier
in the singlet state. Remind that the exchange
integral appears with different signs in the
energies of the S and T states, namely, two ra�
dicals form a chemical bond in the S state and
repel each other in the T�state [10]. The diffe�
rent S and T state behavior is important not only
for radical reactions, but also for many chemical
transformations which include spin «depairing»
during bond scission or proceed through biradi�
cal intermediate. This often occurs in catalysis
by transition metal compounds [8], especially in
hemoproteins [1�7].
Cytochrome oxidase catalyses the four�elec�
B.F. Minaev, V.A. Minaeva
58 Ukrainica Bioorganica Acta 2 (2008)
� �� �� � � �� �� � ��
�h
tron reduction of oxygen molecule to water [5].
No intermediates were detected in the reaction
O2+4e�+4H+=2H2O. However, many experimen�
tal measurements [5] have proved the formation
of O2
2�. The reaction centre of cytochrome oxi�
dase includes one heme ferrous ion and one cop�
per ion. The oxygen molecule binds to the heme
Fe2+ cation and to Cu+ ion that donate one elec�
tron each to form an O2
2� anion. This provides a
way to overcome the major obstacle to oxygen
activation, that is, spin inversion (T�S transi�
tion). Since the O2
2� dianion has a filled electron
shell, the ground state of this species is totally
symmetrical and characterized by the term M7.
Transfer of two electrons causes the ground�
state term, M8 of the O2 molecule, to transform
smoothly to the term M9 of the dianion. The
spin�orbit coupling between the states M10 and
M11 is symmetry�allowed [10]; therefore, the
reduction O2→O2
2� is also symmetry allowed
with inclusion of SOC. Transition of the active
site of cytochrome oxidase to the singlet state
removes spin prohibition for subsequent fast
chemical reactions up to formation of stable dia�
magnetic products [10].
It is often assumed that one can overcome the
spin prohibition to oxidation of organic sub�
strates with atmospheric oxygen by successive
addition of single electron and proton in the
successive reduction of O2
�. Further reactions of
diamagnetic hydrogen peroxide, produced in
such reduction, are spin allowed. It is assumed
[5] that removal of spin prohibition in such reac�
tions proceeds as in the case of radical�chain oxi�
dation, where the spin prohibition can be
removed upon formation of primary radicals. It
is important to stress a fundamental difference
between the enzymatic reactions involving ra�
dicals and the radical reactions in chain oxida�
tion processes. In the latter case radicals go to
the bulk of the gasous plasma flame (or in the
solution bulk) and do not longer retain the «spin
memory» about precursors. All participants of
biochemical oxidation reactions, i.e., dioxygen
and electron transfer agents, are confined wi�
thin the same active site of enzyme. If an elec�
tron is transferred to the oxygen molecule from
a diamagnetic enzyme M, i.e. , it
produces a triplet radical ion�pair (triplet pre�
cursor), all spins remain correlated, the «spin
memory» is retained and the spin prohibition to
subsequent reactions of the radical ion�pair thus
generated is not removed and can not lead to a
singlet product. For example, reaction O2 with
glucose oxidase [17, 24] involves flavine adenine
dinucleotide (FAD) and includes two stages;
namely, glucose oxidation to glucosolactone with
reduction of FAD to FADH2 and the reverse
cycle FADH2→FAD, with reduction of O2 to
H2O2. From the standpoint of dioxygen activa�
tion it is interesting to consider only the second
stage. After formation of a triplet radical pair,
bbb , the T→S transition
has to occur in order to provide the final pro�
ducts FAD + H2O2.
(4),
(5).
The last phase of the catalytic cycle accompa�
nied by the formation of hydrogen peroxide can
occur only in the singlet state. It involves abst�
raction of hydrogen atom from FADH2
+ and a
proton from the nearest histidine residue with
subsequent proton transfer to histidine across
the system of H�bonds in the protein chain [10].
The T→S transition has been explained [10] by a
relatively large SOC between the S and T states
of the radical pairs (5), which have different
orbital structures inside the superoxide ion. As
one can see in scheme (5), the T→S transition
includes an electron jump from one πg,x molecu�
lar orbital of the dioxygen to another πg,y orbital.
Such transformation is equivalent to orbital
rotation, or to a torque, which creates transient
magnetic field; finally this magnetic field indu�
ces a spin flip [24]. This simple consideration is
supported by direct quantum�mechanical calcu�
lations of the SOC integrals [10, 15, 17]. In the
following we want to show that a similar me�
chanism of SOC enhancement by charge trans�
fer can be applied for spin�dependent reaction
of dioxygen binding to heme.
Materials and methods. The O2 binding with
myoglobin model was studied recently by DFT
methods [2, 3, 8, 9]. Fully relaxed potential ener�
gy curves (PEC) were calculated for the seven
Spin�dependent binding of dioxygen to heme and charge�transfer mechanism of spin�orbit coupling enhancement
59www.bioorganica.org.ua
�
g
1
�
g
3
�
g
1
�
g
3
�
g
1
�� ��� MOMO 22
���� ��� 2222 FADFAD
� � � �� �
Triplet
FAD
transferech
22
arg
...
........ ���� ��
�
� � � �� �
Triplet
FAD
SOC
����
����
22 ...
.......... � � � �� �
Singlet
FAD ����
22 ...
..........
lowest electronic states in Ref. [3], while the PEC
for spin states S=0,1,2,3 at fixed geometry as a
functions of the Fe�O2 distances were presented
in Ref. [2]. In this work we have recalculated
some points R(Fe�O)=1.8, 2, 2.5 C with full geo�
metry optimization of other parameters for all
possible multiplets and accounting for different
symmetries (A' and A'') for the singlet and tri�
plet states. The model of oxyheme is shown in
Fig. 1, which includes protoporphyrin IX coordi�
nated with imidazol as a proximal histidine
residue. Its calculation gives the same singlet
ground state as for the simplified Fe(II)�Por�
phin�Imidazole�O2�model, which poses Cs sym�
metry [3]. More simple Fe(II)�Porphine�NH3�O2
model (Fig. 2) has also been used in this work for
DFT calculations in the vicinity of the equilibri�
um. The B3LYP/6�31G* method [11] has been
imployed and the results quite close to those
presented in Ref. [3] have been obtained for the
Fe(II)�Porphin�Imidazole�O2�model. For the mo�
del, shown in Fig. 2, all vibrational frequencies
and their intensity in the infrared and Raman
spectra have been calculated. Many normal
modes are similar to those, calculated in Refs. [6,
25]. An additional Fe�O2 stretching vibrational
frequency is calculated at 539 cm�1, which agrees
qualitatively well with the resonance Raman
band, observed at 567 cm�1 for oxy�hemoglobin
by Soret excitation [20]. This indicates reliability
of the chosen model and of the DFT method
used in this work.
Results and discussion. At the infinite sepa�
ration the deoxyheme has a quintet ground state
with the triplet state being very close in energy.
This is in agreement with experimental data,
showing that the isolated deoxyheme is a high�
spin quintet [1�9]. The optimized structure of
this Fe(II)P complex with imidazol at the fifth
coordination position agrees with the x�ray
analysis of the crystal structure of deoxymyo�
globin: Fe�N distances (2.08 C) in FeP are larger
than in the low�spin states (2.0 C) and the iron
ion is above the porphyrin ring plane by 0.28 C in
agreement with the x�ray data (0.36 C) [2, 3].
This illustrates the known fact, that the high�
spin iron ion is too large to fit into the porphyrin
ring cavity. When this deoxyheme interacts
with the triplet ground state dioxygen, there are
six unpaired electrons. Their interaction can
provides the septet (7A'', S=5) state, when both
subsystems have parallel spins. If they are ani�
parallel, the triplet state 3A'' occurs. At long Fe�
O distances (R>2.5 C) these states are degene�
rate (together with the intermediate quintet 5A''
state). The A'' symmetry is determined by the
oxygen degenerate πg orbitals, which have a' and
a'' symmetry in respect to the plane, which con�
tains O2 and imidazol molecules being coplanar
during the reaction. In general all spin states
which occur at each random collision of heme
and O2 should lead to oxigen binding, but with
different rate (even for different spin sublevels
of one multiplet). More detailed information
about O2 binding has been obtained in flash�
photolysis studies of O2 dissociation from heme,
when the fate of dioxygen depends on the com�
petition between intrinsic recombination rate
constant and protein relaxation, as well as the O2
escape from the protein [2, 7]. The great differ�
ent recombination dynamics of O2, CO and NO
molecules with heme have been attributed to
spin states of each ligand and to their possible
combinations with the iron spin [7]. The obser�
ved recombination kinetics can be influenced by
B.F. Minaev, V.A. Minaeva
60 Ukrainica Bioorganica Acta 2 (2008)
Fig. 1. Ferrous ion in protoporphyrin IX coordinated
with O2 and with imidazol as a proximal histidine
residue. This model of heme�cofactor has the singlet
open�shell ground state which is close to more sym�
metric Fe(II)�porphine�imidazole�O2 model.
Fig. 2. Fe(II)�porphine�NH3�O2 model also used in
this work for DFT calculations.
protein dynamics, if the intrinsic recombination
rate constant is slower than these dynamics. By
studies of viscosity and temperature depen�
dence, the general averaged time scale for the
recombination rate constant can be estimated [2,
7]. It is interesting to compare O2, CO and NO
molecules in this respect.
The CO recombination with heme is a single
exponential process characterized by a slow rate
constant k.106 s�1 at ambient temperature and a
low solvent viscosity (below viscosity of globin).
This intrinsic (geminate) recombination rate is
slower than both protein relaxation and CO
escape, thus the recombination yield is very
small (0.04) [7]. The rebinding of NO stable radi�
cal (S=Ѕ) is characterized by two�exponential
kinetics with the rapid (k1.108 s�1) and slow (k2
.5 106 s�1) rate constants under ambient condi�
tions [2]. Since the ground state heme has the
quintet spin state (S=2), there are two starting
states: (S=21/2) and (S=11/2) depending on
mutual spin orientation of two species, while the
recombination product has the doublet state
(S=1/2). Both type of geminate recombination
require spin change; the slow process includes
two step spin flip (S=21/2)→(S=11/2)→(S=1/2),
since spin�orbit coupling can mix states and
induces spin transition with selection rule ÎS=
1, and the rapid recombination occurs in one
step (S=11/2)→(S=1/2). The CO molecule is dia�
magnetic; all spins are paired, the total spin is
zero. The heme�CO adduct is also diamagnetic (S
=0). Since the ground state heme has the quintet
spin state (S=2), the geminate recombination
reaction is doubly spin forbidden. First it should
be quintet — triplet transition, which needs to
overcome an additional activation barrier (besi�
des the spin flip, induced by SOC) and then a
final triplet�singlet transition. This is the reason
why the CO recombination with heme is so slow,
in spite of the high binding energy [2].
Now we shall consider the dioxygen binding
in more details. The ground state of the oxy�
heme product is an open�shell singlet in agree�
ment with EPR experiment and Messbauer
spectra [2]. Thus the reaction of O2 binding to
heme is spin forbidden. At least the T�S transi�
tion has to occur [4].
Such spin flip can be induced by spin�orbit
coupling (SOC) between the T and S states. One
has to calculate the matrix element of the SOC
operator [10�12]
(6),
where ζА is a SOC constant for atom А (ζО=
153 сm�1), — are the orbital and spin angu�
lar momentum operators for the i�th electron,
respectively. This is effective single�electron
SOC approximation, which proved to be useful
in many spectroscopic and chemical applications
including spin�forbidden enzyme reactions [10�
18].
Since the deoxyheme has a quintet ground
state (four spins are unpaired, S=2), the adduct
with the triplet dioxygen (two unpaired spins)
would be expected to have either six (4+2=6)
unpaired spins or two (4�2=2) unpaired spins
depending on relative orientation of magnetic
moments of the heme and O2; the intermediate
quintet spin state is also possible for the ground
state spesies coupling. The triplet state of deoxy�
heme being very close in energy produces the
adducts with the triplet O2 which could be either
quintet (S=2), triplet (S=1), or singlet (S=0) de�
pending on ferromagnetic or antiferromagnetic
coupling of two species. Thus only triplet deoxy�
heme could provide the ground singlet state
product in the process of the antiferromagnetic
coupling with the triplet O2 in a spin�allowed
oxyheme formation without spin flip. Spin tran�
sition from the ground quintet to the close lying
triplet deoxyheme can be induced by SOC in the
3d shell of iron ion. In this case the primary elec�
tronic reorganization takes place in ferrous ion
at the equilibrium between the quintet and
triplet states already before dioxygen approach�
es the deoxyheme [3, 6]. All other recombination
processes include spin flip induced during heme
— O2 interaction; they seams to be more impor�
tant for dioxygen binding [1�7]. It could start
with the 3A''(2) state, which is repulsive at short�
er distance (R<2.5 C) together with the septet
7A''(1) state [3] (both are the ground state of the
entrance channel heme + O2 and go in parallel
with some other multiplets until the short dis�
tances limit (2.5�3 C). The energy gap is about
0.1 eV at these limits in agreement with Ref. [2,
3]. The optimized singlet ground state 1A'(1) is
lower in energy than other multiplets at least by
Spin�dependent binding of dioxygen to heme and charge�transfer mechanism of spin�orbit coupling enhancement
61www.bioorganica.org.ua
HSO= � ��� �����
i i
yiyixixiii
i
iAi sBsBsBsl ( ,,,,,
����
�
iAi sl ��
,,
� zizi sB ),, ,
0.4 eV; this oxyheme product is an open�shell
singlet of a complicated orbital and spin struc�
ture [3]. It has a short Fe�O distance (1.81 C) [3]
(reproduced in our DFT calculations, 1.84 C) in
contrast to the high�spin states (2�2.7 C). Our
result is close to the Fe3+�O2
� radical�pair struc�
ture in agreement with other DFT calculations
and Weiss model [1�3, 8, 9]. The spin densities
are equal to 0.94, �0.31, �0.72 for Fe�O�O chain,
the bond angle is of 118o. The O�O bond distance
(1.36 C) and vibration frequency (1110 cm�1) cor�
respond better to superoxide ion [20]. (The
closed�shell singlet has been obtained in a num�
ber of calculations [1, 19], however this result
has been revised latter [8, 9].)
Account of our data and the results of Refs.
[2, 3] allow us to consider the following scenario.
At the intermediate distances 2.5�3 C the star�
ting 3A''(2) state from the entrance channel
transfers to the triplet Fe3+�O2
� radical�pair. In
this region there are few crossing points bet�
ween S and T states, including the 3A''(2)�1A'(1)
states crossing, where spin change could occur
[2, 3]. A simplified electronic structure of the
3A''(2) and 1A'(1) states near the crossing of the
potential energy surfaces (PES) is presented in
scheme (7). The two outer electrons of the
ground triplet state dioxygen in two degenerate
πg�MO’s provide a scheme [ ][ ]; electron trans�
fer from Fe2+ to O2 in order to produce the radi�
cal pair Fe3+�O2
� (7) can be accomplished by the
occupation of either πg,x� or πg,y�orbitals. The
both radical pairs could be in T and S states; all
four states are almost degenerate at the inter�
mediate distances. Now we are interesting only
in those spin states which are presented in
scheme (7), since they correspond to the desired
T→S transition and to the final product of the O2
binding by heme. The scheme (7) is equivalent to
the scheme (5) and the same explanation for the
high SOC matrix element [10, 24] can be applied.
(7).
The starting triplet radical pair corresponds to
a charge�transfer (CT) state described by 3A''(2)
wave function ,
that is, transfer of an electron to the πg,x�orbital
of O2 molecule, whereas the singlet radical pair
corresponds to a CT state described by 1A'(1)
wave function ,
namely, transfer of an electron to another de�
generate orbital of oxygen, πg,y (ℜ means proper
antisymmetrization of the wave function. The
SOC arises between these CT states is the maxi�
mum possible for a system comprised of the
light oxygen atoms [10]. The matrix element of
the SOC operator (6) is equal to:
(8).
This SOC matrix element (8) is very close to a
value of about 80 cm�1, postulated in estimation
of Landau�Zener rate constant for T�S transi�
tions in spin�dependent O2 and NO binding to
heme [2, 21, 22]. With such a proposal for the
generally unknown SOC integral [2] a quite rea�
sonable estimation for the spin�dependent rate
constants of the CO, O2 and NO recombination in
heme proteins are obtained [2, 21, 22]. For CO
binding to heme a quintet�triplet�singlet step�
wise transition is necessary which explains mil�
lion times slower recombination rate in this case
in comparison with the O2 and NO recombina�
tion in heme proteins [2�4]. The gradient diffe�
rence at the location of crossing points which
enters the denominator of the Landau�Zener
expression of the rate constant for spin transi�
tion is quite small (0.1�0.2 eV/C) for O2 and NO
binding to heme [2, 3], thus the topology of the
binding curves supports a rapid recombination
of both ligands to hemo� and myoglobin.
The rapid NO rebinding to heme (k1.108 s�1)
includes one�step quartet�doublet transition;
since NO radical has one outer electron at
degenerate πx and πy orbitals, a quite similar the�
ory of SOC in quasidegenerate charge transfer
states, like that, presented in Eqs. (4)�(5), (7)�(8),
can be applied. The only deference is that the
SOC integral (8) now includes πx and πy orbitals
of NO molecule and thus is slightly smaller
(about 60 icm�1). The rate constant of spin transi�
tion in Landau�Zener model is determined by
the square of the SOC integral. This explains
that the rapid NO rebinding rate constant is
about 3 times slower than the rapid rate con�
stant of the O2 recombination in heme proteins
[2, 4].
B.F. Minaev, V.A. Minaeva
62 Ukrainica Bioorganica Acta 2 (2008)
� � � �� �
)2(",
.........
..........
3
2
3
ATriplet
Fe
SOC
����
����
� � � �� �
)1(',
.........
..........
1
2
3
ASinglet
Fe ����
|))()(()3(| ,,,
3 ������� ygxgxgT d
x
���
|))()(()3(| ,,,
1 ������� ygygxgT d
y
���
1313
2
1)1(')2(" <>=>=<< HAHA CT
Z
SOCT
Z
SO yx
1
,, 5.76
2
=>= icmiB Oygzxg
All previous analysis of SOC effects in hemo�
proteins were based on assumption that the SOC
integral in dioxygen binding to heme is deter�
mined by the iron ion and no attempt of direct
calculation has been done [2, 21, 24]. As follows
from our simple analysis, the SOC integral (8) is
determined entirely by SOC in oxygen molecule
and is connected with the degeneracy of two πg,x
and πg,y�orbitals in the open�shell of dioxygen.
This enhancement of SOC effect by inclusion of
charge�transfer to O2 and involvement of super�
oxide�ion structure seams to be quite general in
biochemistry [10]; it is applied also to those
enzymes which have no transition atoms, like
glucose oxidase, Eq. (4)�(5) [16, 17]. It is impor�
tant to stress that the rapid T�S transition in O2
binding to heme is not only forbidden by spin,
but also by orbital symmetry (it includes the
A''— A' symmetry change). Such double prohi�
bition is necessary in order to make the spin
change in chemical reaction to be effectively
allowed [10, 23].
Conclusions. We have recalculated some
potential energy surfaces (PES) cross sections
for different multiplets along the heme�O2 bin�
ding reaction coordinate in agreement with
Refs. [1�3]. The Fe(II)porphine molecule (heme
without side chains, shown in Fig. 1) coordinated
with imidazol or ammonia molecules (Fig. 2, both
are models of the proximal histidine) are used as
in other similar studies [1�3, 8, 9, 19, 22]. The
more realistic protoporphyrin IX model pro�
vides similar result for the ground state of the
heme active site. Results of previous works [1�3,
8, 9, 19, 22] indicate that the main reason for the
facilitated binding of O2 to heme is a broad cros�
sing region of the relevant spin states, which
provides significant spin transition probabilities.
They have shown that porphyrin is an ideal
Fe(II) ligand for the spin�flip problem, because
it tunes the spin states to be close in energy, gi�
ving parallel binding PES’s, small activation
energies and large transition probabilities in
terms of the Landau�Zener approach [2, 3]. But
none of these studies [1�3, 8, 9, 19, 22] have con�
sidered the reason for relatively large spin�orbit
coupling, which induces the necessary spin flip
in the heme�O2 binding reaction; a general
assumption that the SOC integral at Fe(II) ion of
about 80 cm�1, postulated in Ref. [21], have been
used instead. We have shown that such SOC
integral (8) is determined entirely by SOC in
oxygen moiety and is connected with the dege�
neracy of two πg,x� and πg,y�orbitals in the open�
shell of dioxygen. This is connected with charge
transfer (CT) and with the Fe3+�O2
� radical�pair
structure of the ground state 1A'(1) and the close
lying 3A''(2) state near the crossing of the poten�
tial energy surfaces (PES) is presented in
scheme (7). This scheme indicates that the
triplet and singlet states, 3A''(2) and 1A'(1), differ
by a single electron jump inside O2 from the πg,x
MO to the πg,y orbital. Such transformation is
equivalent to the electronic orbital rotation, i.e. a
torque, which creates transient magnetic field
during the T�S transition and this magnetic field
is responsible for the spin flip. In this model the
magnetic perturbation occurs entirely in the
oxygen moiety and the iron ion is silent.
Acknowledgment. This work is supported by
the State Foundation of Fundamental Investiga�
tions (DFFD), the project F25.5/008.
Надійшла в редакцію 20.05.2008 р.
Spin�dependent binding of dioxygen to heme and charge�transfer mechanism of spin�orbit coupling enhancement
63www.bioorganica.org.ua
Спін�залежне зв’язування кисню з гемом і механізм підсилення спін�орбітальної взаємодії
за рахунок переносу заряду
Б.П. Мінаєв, В.О. Мінаєва
Черкаський національний університет імені Богдана Хмельницького
б�р Шевченка, 81, Черкаси, 18031, Україна
Резюме. Вивчено спін�орбітальну взаємодію (СОВ) між початковим триплетним 3А''(2) станом у вхідному ка�
налі реакції зв’язування гем�О2 і кінцевим синглетним 1А'(1) станом з відкритою оболонкою, які визначені доміну�
вальним вкладом структури радикальної пари Fe3+�O2
�. Перетини модельних поверхонь потенціальної енергії
вздовж координати реакції для цих мультиплетів, розраховані за теорією функціоналу густини (ТФГ), узгоджу�
ються з недавніми розрахунками ТФГ, відомими з літератури. Модель гема включає Fe(II)�порфін, координований
з імідазолом або амоніаком у п’ятій координаційній позиції йона заліза, які моделюють гістидин як амінокислот�
ний залишок міоглобіну. СОВ індукується головним чином на кисні за рахунок зміни орбітального кутового момен�
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B.F. Minaev, V.A. Minaeva
64 Ukrainica Bioorganica Acta 2 (2008)
References
ту πg�оболонки при триплет�синглетному переході. Ця модель СОВ добре пояснює ефективну інверсію спіну в ході
зв’язування гем�О2.
Ключові слова: гемоглобін, міоглобін, цитохром оксидаза, спін�орбітальна взаємодія, триплет�синглетна спіно�
ва інверсія, структури радикальної пари, стани з переносом заряду, зв’язок двоатомних лігандів із гемом.
|
| id | nasplib_isofts_kiev_ua-123456789-7352 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1814-9758 |
| language | English |
| last_indexed | 2025-12-07T18:55:42Z |
| publishDate | 2008 |
| publisher | Інститут молекулярної біології і генетики НАН України |
| record_format | dspace |
| spelling | Minaev, B.F. Minaeva, V.A. 2010-03-29T11:13:41Z 2010-03-29T11:13:41Z 2008 Spin-dependent binding of dioxygen to heme and charge-transfer mechanism of spin-orbit coupling enhancement / B.F. Minaev, V.A. Minaeva // Ukrainica Bioorganica Acta. — 2008. — Т. 6, № 2. — С. 56-64. — Бібліогр.: 25 назв. — англ. 1814-9758 https://nasplib.isofts.kiev.ua/handle/123456789/7352 Spin-orbit coupling (SOC) between the starting triplet ³A''(2) state from the entrance channel of the heme-O2 binding reaction and the final singlet ¹A'(1) open-shell state, which are dominated by the Fe^3+-O2-radical-pair structures, is studied. Simulated potential energy surface cross sections along the reaction coordinate for these and other multiplets, calculated by density functional theory (DFT) agree with the recent DFT studies known from the literature. The heme-model includes Fe(II)-porphyrin complex with imidazol, or ammonia molecule, at the fith coordination position, which simulates the hystidine as an aminoacide residue of myoglobin. The SOC is induced mainly at the oxygen moiety by an orbital angular momentum change in the π8-shell during the triplet-singlet transition. This SOC model explains pretty well the efficient spin inversion during the heme-O2 binding. Вивчено спін-орбітальну взаємодію (СОВ) між початковим триплетним ³А''(2) станом у вхідному каналі реакції зв’язування гем-О2 і кінцевим синглетним ¹А'(1) станом з відкритою оболонкою, які визначені домінувальним вкладом структури радикальної пари Fe^3+-O2-. Перетини модельних поверхонь потенціальної енергії вздовж координати реакції для цих мультиплетів, розраховані за теорією функціоналу густини (ТФГ), узгоджуються з недавніми розрахунками ТФГ, відомими з літератури. Модель гема включає Fe(II)-порфін, координований з імідазолом або амоніаком у п’ятій координаційній позиції йона заліза, які моделюють гістидин як амінокислотний залишок міоглобіну. СОВ індукується головним чином на кисні за рахунок зміни орбітального кутового моменту πg-оболонки при триплет-синглетному переході. Ця модель СОВ добре пояснює ефективну інверсію спіну в ході зв’язування гем-О2. en Інститут молекулярної біології і генетики НАН України Spin-dependent binding of dioxygen to heme and charge-transfer mechanism of spin-orbit coupling enhancement Спін-залежне зв’язування кисню з гемом і механізм підсилення спін-орбітальної взаємодії за рахунок переносу заряду Article published earlier |
| spellingShingle | Spin-dependent binding of dioxygen to heme and charge-transfer mechanism of spin-orbit coupling enhancement Minaev, B.F. Minaeva, V.A. |
| title | Spin-dependent binding of dioxygen to heme and charge-transfer mechanism of spin-orbit coupling enhancement |
| title_alt | Спін-залежне зв’язування кисню з гемом і механізм підсилення спін-орбітальної взаємодії за рахунок переносу заряду |
| title_full | Spin-dependent binding of dioxygen to heme and charge-transfer mechanism of spin-orbit coupling enhancement |
| title_fullStr | Spin-dependent binding of dioxygen to heme and charge-transfer mechanism of spin-orbit coupling enhancement |
| title_full_unstemmed | Spin-dependent binding of dioxygen to heme and charge-transfer mechanism of spin-orbit coupling enhancement |
| title_short | Spin-dependent binding of dioxygen to heme and charge-transfer mechanism of spin-orbit coupling enhancement |
| title_sort | spin-dependent binding of dioxygen to heme and charge-transfer mechanism of spin-orbit coupling enhancement |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/7352 |
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