Download Redox Reactions of NO and O in Iron Enzymes Mattias Blomberg

Redox Reactions of NO and O2 in Iron Enzymes
A Density Functional Theory Study
Mattias Blomberg
Stockholm University
Department of Physics
2006
Thesis for the degree of doctor in philosophy in chemical physics
Department of Physics
Stockholm University
Sweden
c Mattias Blomberg 2006
°
ISBN 91–7155-208–1 pp i–viii, 1–71
Printed by Universitetsservice US-AB, Stockholm
Abstract
In the present thesis the density functional B3LYP has been used to
study reactions of NO and O2 in redox active enzymes.
Reduction of nitric oxide (NO) to nitrous oxide (N2 O) is an important part in the bacterial energy conservation (denitrification). The
reduction of NO in three different bimetallic active sites leads to the
formation of hyponitrous acid anhydride (N2 O2−
2 ). The stability of
this intermediate is crucial for the reaction rate. In the two diiron
systems, respiratory and scavenging types of NOR, it is possible to
cleave the N–O bond, forming N2 O, without any extra protons or
electrons. In a heme–copper oxidase, on the other hand, both a proton and an electron are needed to form N2 O. In addition to being an
intermediate in the denitrification, NO is a toxic agent. Myoglobin in
the oxy–form reacts with NO forming nitrate (NO−
3 ) at a high rate,
which should make this enzyme an efficient NO scavenger. Peroxynitrite (ONOO− ) is formed as a short–lived intermediate and isomerizes
to nitrate through a radical reaction.
In the mechanism for pumping protons in cytochrome oxidase,
thermodynamics, rather than structural changes, might guide protons
to the heme propionate for further translocation.
The dioxygenation of arachidonic acid in prostaglandin endoperoxide H synthase forms the bicyclic prostaglandin G2 , through a cascade of radical reactions. The mechanism proposed by Hamberg and
Samuelsson is energetically feasible.
i
List of Papers
I. L. M. Blomberg, M. R. A. Blomberg and P. E. M. Siegbahn, A
Theoretical Study on the Binding of O2 , NO and CO to Heme
Proteins, J. Inorg. Biochem. 99 2005 949–958.
II. P. E. M. Siegbahn, M. R. A. Blomberg and L. M. Blomberg, Theoretical Study of the Energetics of Proton Pumping and Oxygen
Reduction in Cytochrome Oxidase, J. Phys. Chem. B 107 2003
10946–10955.
III. L. M. Blomberg, M. R. A. Blomberg and P. E. M. Siegbahn, A
Theoretical Study on Nitric Oxide Reductase Activity in a ba3 -type
Heme-Copper Oxidase, Biochim. Biophys. Acta 1757 2006 31–46.
IV. L. M. Blomberg, M. R. A. Blomberg and P. E. M. Siegbahn, Reduction of Nitric Oxide in Bacterial Nitric Oxide Reductase - A
Theoretical Model Study, Submitted for publication.
V. L. M. Blomberg, M. R. A. Blomberg and P. E. M. Siegbahn, Theoretical Study of the Reduction of Nitric Oxide in an A-type Flavoprotein, In manuscript.
VI. L. M. Blomberg, M. R. A. Blomberg and P. E. M. Siegbahn, A Theoretical Study of Myoglobin Working as a Nitric Oxide Scavenger,
J. Biol. Inorg. Chem. 9 2004 923–935.
VII. L. M. Blomberg, M. R. A. Blomberg, P. E. M. Siegbahn, W. A.
van der Donk and A.-L. Tsai, A Quantum Chemical Study of the
Synthesis of Prostaglandin G2 by the Cyclooxygenase Active Site
in Prostaglandin Endoperoxide H Synthase 1, J. Phys. Chem. B
107 2003 3297–3308.
Reprints are made with permission from the publishers.
iii
Contribution to the papers
I have performed the quantum chemical investigations and prepared
the manuscripts of all except one of the papers included in the present
thesis. The exception is Paper II, where my contribution is limited to
performing the calculations on model a shown in Fig. 3 and the model
shown in Fig. 6. Furthermore, I have been active in the discussions
during the project. The manuscript was written by my co-authors.
iv
Preface
The bioenergetic apparatus, used by the cell to store the energy released in the oxidation of food coupled to the reduction of an electron
acceptor, has fascinated the scientific community for decades. This
process is often referred to as respiration, and the electron acceptor
can be either O2 in aerobic conditions or nitric oxides in an anaerobic
environment. Many of the mechanisms in these processes are still not
fully understood.
In the present thesis reactions of NO and O2 in redox active enzymes have been studied using the quantum chemical method density
functional theory. The development of the methods, as well as the
rapid increase in computational power, have made it possible to use
quantum chemistry as a tool to investigate reaction mechanisms also
in large systems such as enzymes. A quantum chemical investigation
aims to probe the free energy surface of a reaction mechanism elucidating a feasible reaction path. A major part of this thesis concerns
the reactions of nitric oxide, both as an intermediate in denitrification, as well as the scavenging of NO, which is as a toxic agent. The
most important results are summarized in the first part of the thesis,
whereas the seven full length scientific papers are attached at the end.
The first chapter in the thesis provides a brief overview of the
theoretical methods used in the investigations. Furthermore, basic
concepts important for quantum chemistry applied to biochemistry
are introduced.
The second chapter contains an introductory overview of two heme–
containing enzymes, myoglobin and cytochrome oxidase, whose structures are the basis for a major part of the present thesis. Furthermore,
the binding of the diatomics O2 , NO and CO to heme proteins, investigated in Paper I, is discussed. Most of the studied reaction mechanisms in the thesis are initiated by the binding of either NO or O2
to iron.
A mechanism for translocation of protons by cytochrome c oxidase, which was originally investigated in Paper II, is discussed in
Chapter 3. The possibility that the protons are thermodynamically
v
guided toward a translocation site, rather than going to the binuclear
center to be consumed in the reduction of O2 , is investigated.
The fourth chapter summarizes the investigations on the reduction
of nitric oxide to nitrous oxide and water in three different systems.
The first investigated enzyme catalyzing the reduction of nitric oxide
is a ba3 –type oxidase (Paper III). The natural substrate in this enzyme is O2 , and the mechanism for the reduction of NO is of interest
for the comparison to the reduction of dioxygen. Furthermore, cytochrome oxidases are structurally similar to respiratory nitric oxide
reductases, and the mechanisms for NO reduction may share common
features. In these reductive reactions electrons and protons enter the
system during the catalytic cycle. The energetics of the electron and
proton transfers were treated by parametrizing the calculated results
using experimental reduction potentials. Furthermore, the mechanism
for the reduction of nitric oxide in models of the bacterial respiratory nitric oxide reductase (NOR) are discussed (Paper IV). The
structure of NOR has not been determined, and the coordination of
the non-heme FeB , corresponding to CuB in cytochrome oxidase, is
uncertain. Therefore, the reduction of NO was investigated for two
models of the binuclear center differing in the coordination of FeB .
The third enzymatic system discussed in Chapter 4 is a non–heme
diiron site in an A–type flavoprotein. The A-type flavoproteins are
widespread among bacteria and archae, and have been proposed to
protect the cells against nitrosative stress, by reducing nitric oxide to
nitrous oxide and water (Paper V).
In the fifth chapter the mechanism of the dioxygen carrier myoglobin working as a nitric oxide dioxygenase is discussed. The oxy–
form of myoglobin have been shown to react with nitric oxide forming
nitrate as the product. The mechanism of this reaction was investigated in Paper VI.
The sixth chapter summarizes the mechanism for the dioxygenation of an unsaturated fatty acid to the signal molecule prostaglandin
G2 (Paper VII). This is the enzyme covalently inhibited by the active substance in the pain–killer aspirin.
vi
Contents
Preface
v
1 Quantum chemistry applied
1.1 Wave function methods . . . . . . . . . . .
1.2 Density functional theory . . . . . . . . . .
1.3 Benchmark tests for DFT and wave function
1.4 Basis set selection . . . . . . . . . . . . . .
1.5 Enzyme catalysis . . . . . . . . . . . . . . .
1.6 Transition state theory . . . . . . . . . . .
1.7 Selection of the active site model . . . . . .
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methods
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2 Introduction to heme proteins
2.1 Heme prosthetic group . . . . . . . . . . .
2.2 Myoglobin . . . . . . . . . . . . . . . . . .
2.3 Cytochrome oxidase . . . . . . . . . . . . .
2.4 Binding of O2 , NO and CO to ferrous heme
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3 Proton translocation in cytochrome oxidase
3.1 Thermodynamics of proton translocation . . . . . . . . .
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4 NO
4.1
4.2
4.3
4.4
4.5
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reduction
Energetics of proton and electron transfers .
NOR activity in a heme-copper oxidase . . .
Reduction of NO in model systems of NOR
Reduction of NO in a scavenging NOR . . .
Summary . . . . . . . . . . . . . . . . . . .
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5 Myoglobin working as a nitric oxide scavenger
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6 Synthesis of prostaglandin G2 in PGHS–1
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7 Concluding Remarks
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vii
References
65
Acknowledgments
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viii
1
Quantum chemistry
applied
The use of quantum mechanics to solve chemical problems is called
quantum chemistry. In principle all properties of a system can be obtained by solving the time–dependent Schrödinger equation, which
is the general equation in quantum mechanics. In the present thesis, ground state chemical reactions have been studied. In this case
it is sufficient to use the time–independent form of the Schrödinger
equation (ĤΨ = EΨ) as a starting point. However, the equations
obtained for a molecular system are far too complicated to be solved.
Hence approximations are necessary, and some of these will be briefly
introduced in the present chapter.
Furthermore, the accuracy of the density functional B3LYP, which
has been employed in the present thesis, is discussed. Basic concepts
as enzyme catalysis and transition state theory, are important for
understanding the activity of an enzyme and how to relate rates to
energy barriers, and are therefore introduced in the the present chapter. Employing a quantum chemical method to an enzymatic reaction
involves the problem of truncating the protein to a feasible size, and
modeling of enzyme active sites is therefore also discussed.
1.1
Wave function methods
The basic and most useful information that can be obtained by applying a quantum chemical method to a chemical system is the energy.
By following the changes in energy along a reaction path, equilibrium and rate constants can be calculated. The energy, among many
other properties, can be obtained by solving the time–independent
1
1 Quantum chemistry applied
Schrödinger equation. In quantum chemistry mainly two approaches
are used to calculate the properties of a system, and they are called
wave function methods and density functional theory (DFT), respectively. Wave function methods1 are trying to find approximate solutions to the Schrödinger equation by finding the wave function (Ψ),
and the corresponding energy eigenvalues (E). Density functional theory on the other hand calculates approximate energies as a functional
of the electron density. Initially, the wave function methods are discussed, followed by an introduction to the DFT approach in the next
section.
The Schrödinger equation cannot be solved exactly for many–
particle systems, i.e. beyond H+
2 , and therefore a number of approximations have to be introduced. The first approximation is based upon
the large difference in mass between nuclei and electrons, and assumes
that the electrons follow the movement of the nuclei instantaneously.
The electrons can thereby be approximated to move in a field of fixed
nuclei (Born–Oppenheimer approximation). The kinetic energy of the
nuclei can then be neglected, and the nuclei–nuclei repulsion will be
constant for a fixed geometry. Thus, the Schrödinger equation can
be separated into a nuclei and an electronic part. By calculating the
electronic energy for different nuclei arrangements a potential energy
surface is obtained, where the global minimum defines the equilibrium
structure of a molecule.
The Born–Oppenheimer approximation gives the form of the Hamilton operator. Furthermore, an approximation of the unknown wave
function is needed. The basic wave function method is called the
Hartree–Fock (HF) method. In HF the wave function is based on
a description of each electron as a one–electron wave function, called
molecular orbital or spin orbital. The molecular orbitals in a molecule
are usually constructed as a linear combination of the atomic orbitals
of the corresponding atoms (LCAO, Linear Combination of Atomic
Orbitals) called basis functions. Furthermore, the wave function has
to be consistent with basic quantum mechanics, and must change sign
if the coordinates of two electrons are interchanged, i.e. be antisymmetric. The anti–symmetry principle also fulfills the Pauli principle 2
and is achieved by constructing the wave function as a Slater Determinant. Each column in the Slater determinant contains a spin orbital
and the rows are labeled by the electron coordinates. The shape of
the orbitals in a single Slater determinant can then be optimized by
1 The present introduction to wave function methods is very brief and a more
thorough introduction and more references can be found in general textbooks, e.g.
refs. [1, 2].
2 The Pauli principle states that two electrons cannot have all quantum numbers equal.
2
1.1 Wave function methods
minimizing the energy according to the variational principle in quantum mechanics. A better fit to the HF wave function can be obtained
by increasing the number of basis functions in the basis set used to
describe the molecular orbitals, at the expense of an increase in computer time.
According to the properties of the the anti–symmetric wave function (Slater determinant), electrons with the same spin cannot occupy
the same point in space. Thus, electrons having the same spin avoid
each other. The decrease in energy due to the anti–symmetry of the
Slater determinant is called exchange energy, and this property is well
described by the HF method.
However, due to the single determinant used in Hartree–Fock one
electron experience the average field of the other electrons in the system. This is the major problem of the HF method, since in a real
system the motion of all electrons are correlated. Thus, in a real system the average distance between electrons is larger and consequently
the total repulsion is lower as compared to HF. The difference between
the exact energy3 of a system and the HF energy is usually used to define the correlation energy. The lack of correlation in the HF method
gives substantial errors in relative energies of molecules, which makes
it a poor method for exploring chemical reactions.
To improve the accuracy beyond the Hartree–Fock method more of
the correlation between electrons has to be included. Electron correlation can be included by adding more determinants when constructing
the wave function. By moving an electron from an occupied orbital in
the original determinant to an unoccupied orbital, a new determinant
can be created. The more determinants in the wave function, the more
the electrons can correlate their movements, decreasing the electron–
electron repulsion. Examples of electron correlation methods are the
the Møller–Plesset perturbation methods (e.g. MP2 and MP4), configuration interaction method (e.g. CISD) and coupled cluster methods
(e.g. CCSD(T)). All the methods mentioned above are built upon the
single determinant HF method. Thus, when a single determinant is
a bad initial approximation the problem will be ”inherited” to the
wave function including correlation. This occurs when a system is of
multiconfigurational character (near degeneracy). In these cases the
multiconfigurational self–consistent field (MCSCF) and the complete
active space (CASSCF) methods, are better starting points. These
methods add more determinants and optimize both their orbitals and
coefficients. However, these configurations still lack electron correla3 The exact non–relativistic ground state energy within the Born–Oppenheimer
approximation.
3
1 Quantum chemistry applied
tion. CASPT2 is a perturbation corrected CASSCF, which improves
the results.
Adding electron correlation corrections greatly improve the results
compared to Hartree–Fock. However, the high accuracy is achieved at
the expense of increased computer time as a result of both the scaling4 and the slow basis set convergence5 . To increase the efficiency
composite techniques have been developed, which use extrapolation
schemes to add effects from different methods. The G2 [3] and G3 [4]
methods are among the most accurate methods which can be employed today. However, also these methods are computationally very
demanding, and cannot be used to treat larger molecules6 .
In the present thesis a simplified form of the G2 extrapolation
scheme called G2–MP2 [6, 7] has been used to test the accuracy of the
B3LYP functional (Paper VII). The G2–MP2 method is a coupled
cluster calculation with an MP2 basis set correction (eq. 1.1).
EG2MP2 = ECCSD(T)/6–31G(p) + EMP2/6–311+G(2df,2p) − EMP2/6–31G(p)
(1.1)
This scheme provides an effective approach for an estimation of relative CCSD(T)/6–311+G(2df,2p) energies.
The wave function methods described above can reach very high
accuracy by adding more determinants and more basis functions, and
for small systems the target of chemical accuracy (1 kcal/mol) can
be achieved. However, these calculations are computationally very
demanding and thus only relatively small systems can be treated.
However, to study larger system, as in the present thesis, alternative
methods have to be used.
1.2
Density functional theory
The use of density functional theory (DFT)7 has increased rapidly
during the last decade. The advantage of DFT compared to the classical wave function methods is the high accuracy to computational
cost ratio.
The foundation which DFT is built upon is the Hohenberg–Kohn
theorem [9], which states that for a non–degenerate ground state the
4 Dependence of the computer time on the number of basis functions as N 6−7 ,
depending on the method, compared to N4 for HF.
5 How fast a property, as e.g. the energy, converges with the number and the
angular momentum of the functions in the basis set.
6 In the G3 test sets [5] calculations on systems up to C
10 have been performed.
7 For overviews of density functional theory, see refs. [2, 8].
4
1.2 Density functional theory
electronic energy is given by a unique functional of the electron density of the system, E[ρ], and the determination of the complicated
many–electron wave function is not needed. Furthermore, there is a
variational principle, similar to the one used in wave function theory, and thus the energy can be calculated using similar minimizing
procedures. The fundamental problem in DFT is that the functional
connecting the energy with a given electron density is not known.
As a starting point, the energy functional can be expressed as the
sum of the kinetic energy (T ), the electron–electron repulsion (Eee )
and the electron–nuclei attraction (Ene ).
E [ρ] = T [ρ] + Eee [ρ] + Ene [ρ]
(1.2)
The introduction of orbitals by Kohn and Sham [10] was an important contribution to density functional theory, and made it possible to
numerically determine the electronic ground state of a many–electron
system more accurately. The non–interacting one electron orbitals,
called Kohn–Sham orbitals (φi ), make it possible to express the electron density as the sum of the squared orbitals. Thus, the real system of interacting electrons is described through a system of non–
interacting particles. In this formulation large parts of eq. 1.2 can be
calculated exactly and the energy functional can be written as:
EDF T = Ts [ρ] + J [ρ] + Ene [ρ] + Exc [ρ]
(1.3)
The first three terms in eq. 1.3 are known. Ts [ρ] is the exact kinetic energy of the non–interacting particles, J[ρ] and Ene [ρ] are the classical
electron–electron and electron–nuclei Coulomb interactions, respectively. Exc [ρ] is the exchange–correlation energy containing the difference in kinetic energy between the real interacting system and the
system of non–interacting electrons, and the difference between the
quantum-mechanical electron–electron interactions and the classical
Coulomb interactions. The exchange–correlation term is related but
not exactly corresponding to the correlation and exchange energies
discussed for the wave function methods above. Minimizing the total energy of a determinant constructed by Kohn–Sham orbitals with
respect to their shape gives the Kohn–Sham eigenvalue equation:
ĥks φi (r) = ²i φi (r)
(1.4)
where ĥks is the one–electron operator given in eq. 1.5, with the analytical expression for Ts [ρ] and J[ρ].
1
ĥks = − ∇2 + Vne +
2
Z
5
∂Exc [ρ]
ρ(r0 )
dr0 +
0
|r − r |
∂ρ(r)
(1.5)
1 Quantum chemistry applied
ĥks depends explicitly on the electron density, i.e. the shape of the
Kohn–Sham orbitals, and eq. 1.4 can thus only be solved iteratively.
If the exact form of Exc was known the exact total energy including
correlation would be obtained. Thus, the accuracy of a DFT method
depends on how well the exchange–correlation functional can be approximated.
The contributions to the exchange–correlation functional are usually separated into exchange and correlation parts. Many exchange
and correlation functionals have been developed over the years. However, two major improvements have increased the accuracy of DFT
methods significantly. The first important step was to introduce corrections depending on the gradient of the electron density, which
was followed by Becke’s introduction of the use of Hartree–Fock exchange [11]. DFT methods including HF exchange are called hybrid
methods. The dominating hybrid functional is the B3LYP functional,
which has been used in the present thesis. In B3LYP the exchange–
correlation functional is a linear combination of local and gradient
corrected exchange and correlation and HF exchange, using a few
empirical parameters [11]. The B3LYP functional can be written:
B3LY P
Fxc
= (1−A)FxSlater +AFxHF +BFxBecke +CFcLY P +(1−C)FcV W N
(1.6)
where FxSlater is the Slater local (LSDA) exchange functional, FxHF is
the HF exchange functional, FxBecke is Becke’s gradient correction to
the LSDA exchange functional [12], FcLY P is the correlation functional
constructed by Lee, Yang and Parr [13] and FcV W N is the correlation
functional by Vosko, Wilk and Nusair [14]. The three coefficients A, B
and C were determined by Becke [15] by fitting them to thermochemical data, using the PW91 functional instead of the gradient part of
the LYP correlation functional [16].
1.3
Benchmark tests for DFT and wave function methods
The best way of testing the accuracy of a quantum chemical method
is to compare computed results with a set of accurate and well defined
experimental data. The accuracy of wave function and DFT methods
has been evaluated for different test sets of molecules, and the performance of some of the methods discussed in Sections 1.1 and 1.2 are
shown in Table 1.1. The B3LYP functional, which has been used in
the present thesis, performs quite well compared to the non–hybrid
DFT method BLYP and also compared to the wave function meth6
1.4 Basis set selection
Table 1.1: Mean absolute errors in different test sets for selected DFT
and wave function methods in kcal/mol. BLYP is a combination of E xSlater
and EcV W N together with gradient contributions from ExBecke and EcLY P .
B3LYP is the hybrid functional discussed in Section 1.2.
G2-1a
Wave function methods
HF
MP2
G2
G3
74.5
7.43
-
G2/97b
1.50
G3/99c
a Data for 55 molecules [17].
b Data for 297 molecules [18].
c Data for 376 molecules [5].
1.01c
1.07
DFT methods
BLYP B3LYP
4.95
2.20
5.77
7.60
3.31
4.27
ods HF and MP2. As already stated, the G2 [3] and G3 [4] methods
are very accurate but computationally very demanding. In addition
to the excellent performance to cost ratio of the B3LYP functional,
DFT methods benefit from a faster basis set convergence regarding
the energy, as compared to wave function methods.
The test sets discussed above do not include any transition metal data.
Since the present thesis treats systems containing iron and copper the
performance for transition metal systems is crucial. However, there are
not many transition metal systems for which accurate experimental
data are available. A few examples of metal–ligand bond strengths
are discussed below.
Investigations of the metal–ligand bond strengths in MR+ complexes, where M is a first row transition metal and R is H, CH2 ,
CH3 [19] or OH [20], respectively, give typical errors of 3.6–5.5 kcal/mol
for the B3LYP functional. Furthermore, studies of the successive bond
strengths of CO in Fe(CO)+
5 and Ni(CO)4 [19] together with the M–
CO bond energy in M(CO)6 where M is Cr, Mo and W, give an
average error of 2.6 kcal/mol for the B3LYP functional [21]. Thus,
even though transition metal systems are difficult to treat due to the
the near degeneracy of the 3d orbitals, the B3LYP functional succeeds
much better than expected.
1.4
Basis set selection
The accuracy of the results obtained in a quantum chemical investigation depends both on the method and the basis set used in the
calculations. In density functional theory the basis set is used to de7
1 Quantum chemistry applied
scribe the Kohn–Sham orbitals. Including more functions give a better
description, but also increases the computational cost. The final energies are not very sensitive to the size of the basis set used in the
geometry optimizations [22], i.e. determination of minima and transition states. Therefore, a small basis set of double–ζ quality (lacvp 8 )
has been used in the geometry optimizations. For accurate evaluation
of the energies a larger basis set was used, most commonly the triple–
ζ basis set lacv3p**+, including single polarization on all first and
second row atoms as well as a diffuse function on all non–hydrogens.
Most systems in the present thesis includes iron and/or copper ions.
A large number of electrons in these metal ions are never involved in
the chemical reaction studied, i.e. the core electrons. In the lacvp and
lacv3p basis sets, the core electrons are replaced by a non–relativistic
effective core potential (ECP) to save computer time. The effect of
adding a single polarization function on iron (f) on the bond strength
of the diatomic molecules O2 , NO and CO was investigated in Paper
I, giving an increase in the bond strength of 1–2 kcal/mol.
1.5
Enzyme catalysis
Enzymes are catalysts, i.e. they accelerate a reaction compared to the
rate in the absence of the catalyst, without being consumed. Hence,
the barrier of the reaction has to be reduced in the presence of the
enzyme, which is illustrated in Fig. 1.1. In the uncatalyzed reaction
(A), the barrier of the reaction, ∆G‡ , is the relative free energy of
the reactant and the transition state (TS). In the corresponding enzyme catalyzed reaction (B), the substrate first binds to the enzyme
and forms an enzyme–substrate (ES) complex, which then reacts and
forms the product bound to the enzyme. In this case the barrier for
the reaction is the relative free energy between the ES complex and
the transition state. Since the same products are formed in both cases,
∆G0 has to be the same for both reaction paths, see Fig. 1.1. ∆G0 and
∆G‡ determine the equilibrium constant and the rate of the reaction
step, respectively.
Often a reaction occurs in a series of steps, with intermediates of
various stability, before the product is formed. In a reaction containing
many steps the largest difference in energy between an intermediate
and a transition state, in the forward reaction, corresponds to the rate
limiting step. The overall rate for an enzymatic reaction containing
a sequence of steps can be described by a single first–order rate constant kcat . If one of several steps in an enzymatic reaction is clearly
8 Implemented
in JAGUAR [23].
8
1.5 Enzyme catalysis
TS
TS
S
E+S
ES
EP
P
E+P
A
B
Figure 1.1: Schematic free energy profile for an uncatalyzed (A) and an
enzyme catalyzed (B) reaction.
rate–limiting, then kcat is equivalent to the rate constant of this single step. The maximum rate of an enzyme, called turnover rate, is
obtained at saturating substrate concentration, and can often be experimentally determined. This is of large practical use, since the rate
limiting barrier obtained in a quantum chemical investigation, can
be compared to the experimental turnover rate in the enzyme using
transition state theory (Section 1.6). The turnover rate in enzymes
can differ substantially, but most of them have rates in the order of
1 s−1 to 10000 s−1 .
Enzymes are very efficient in catalyzing chemical reactions9 . The
catalyzing power can be explained by the enzyme bringing the substrates together, and arranging them in the best configuration for
making and/or breaking chemical bonds. The binding energy due to
intermolecular forces such as salt bridges, hydrogen bonds, van der
Waals forces and hydrophobic interactions counteract the entropy cost
of forming the enzyme–substrate (ES) complex. The enzyme should
not bind the substrate too hard, since the formation of a deep energy
minimum would decrease the efficiency of the enzyme. Most of the
stabilization by the enzyme is instead concentrated to the transition
state structure, which has been demonstrated by so called transition
state analogs being excellent inhibitors. These analogs are unreactive
species with geometric properties close to the transition state structure of the natural substrate. The binding energy of the substrate and
especially the transition state structure gives the specificity of an en9 An
overview on enzyme catalysis can be found in ref. [24].
9
1 Quantum chemistry applied
zyme by energetically discriminating between the natural substrates
and other competing reactants. Enzymes are therefore often very selective, both in choice of substrate and in the stereochemistry of the
reaction. Different enzymes can have very different specificity, some
are so specific that they have only one known substrate, while others
catalyze the same type of reaction for a multitude of substrates.
In redox enzymes on the other hand, the catalytic power is more
due to the ability of the redox center to accept or donate electrons
than stabilizing a transition state structure by intermolecular forces.
However, the stabilization of intermediates and transition states can
also be of importance. The redox active metal center usually consists of one or several transition metal ions such as Fe, Cu, Co or
Mn etc. The metal ion is either bound directly to the polypeptide
residues10 of the enzyme, or to a prosthetic group, which in turn is
tightly bound to the protein. By donating or accepting an electron,
redox enzymes often produce radical intermediates of the substrate
during the reaction. These activated species can then react through
an inter– or intra–molecular radical reaction, and reactions which are
very unfavorable in the absence of the enzyme can occur. In the end
of the reaction sequence the electron can be taken or given back by
the redox center, and a stable product can be released. Many reactions in the present thesis are parts of electron transfer chains. In
these enzymes the redox active metal center reduces the substrate
by donating electrons, which oxidizes the metal center. Before a new
substrate can react, the metal center has to be reduced back to the
original state by electrons coming from another source.
A chemical reaction catalyzed by an enzyme can consist of many
steps, as discussed above. Furthermore, there can be several different reaction paths leading to the same product. Quantum chemistry
can be used to explore these different paths, identifying intermediates (minima) and transition states (saddle points), and a potential
energy surface can be created. Some of the intermediates can be very
short–lived species, which are impossible or difficult to detect by experiments. Thus, quantum chemistry is a powerful tool for probing
the potential energy surface for the right reaction mechanism. The
potential energy surface defines the thermodynamics and kinetics of
the investigated reaction. The major criterion for discriminating between different mechanisms is the experimental turnover rate for the
particular enzyme.
10 An
amino acid unit in a polypeptide is called a residue.
10
1.6 Transition state theory
1.6
Transition state theory
The rate will be determined by the barrier height of the reaction
and the energy distribution of the molecules in the system, i.e. the
temperature. In transition state theory (TST), the transition state
structure is postulated to be in equilibrium with all reactant molecules
along the reaction coordinate, leading to the following expression for
the rate constant:
k=
kB T − ∆G‡
e RT
h
(1.7)
where kB is Boltzmann’s constant and h is Planck’s constant. An additional factor, κ ≤ 1, the transmission coefficient, is often added to
eq. 1.7. The transmission coefficient takes into account the possibility that some of the transition state complexes return to the reactants, and furthermore possible tunneling effects. Tunneling can have
an effect on barrier heights in reactions containing atoms with small
masses, and can be of importance in proton and hydrogen atom transfers. However, considering the rate constant’s exponential dependence
on the activation energy and the accuracy of the B3LYP functional of
3–5 kcal/mol, as discussed in Section 1.3, the effect of the transmission coefficient can be ignored (κ = 1). Due to the uncertainty of the
method, the rate obtained from the calculations can be wrong by 2–3
orders of magnitude, and the rate constant cannot be accurately predicted. However, the difference in barrier heights for different reaction
mechanisms are often more than 15 kcal/mol, which makes it possible
to discriminate between them. The geometry of the transition state
and reactants can be optimized using quantum chemical methods and
the barrier height is obtained as the relative electronic energy. The
free energy corrections are then added separately by calculating the
Hessians11 .
1.7
Selection of the active site model
Enzymes are very large molecules consisting of thousands of atoms.
To date the computational power limits a quantum chemical investigation with the method employed in the present thesis (B3LYP) to
a size of at most 100–200 atoms. Thus, the real system has to be reduced to a model containing only the parts important for the studied
enzyme activity. This works well as long as the activity of an enzyme
depends mainly on a concentrated part, and the protein matrix can
11 Second
derivatives of the energy with respect to the nuclear coordinates.
11
1 Quantum chemistry applied
be regarded as a passive protection for the reaction center. The small
part of the protein catalyzing a reaction is called the active site.
All residues important for the catalytic activity have to be included in the active site model. The residues are commonly reduced
to smaller molecules to save computational time. This approach is
well tested and has only minor effects on the results [25]. The rigidity
imposed on the active site by the protein matrix is usually modeled
by constraining one atom12 for each residue during the geometry optimization. The choice of the model is a very important part in a
computational study, and crucial for the resulting potential energy
surface. One way of testing the model used, which is often applied
in the present thesis, is to extend it and analyze the effect of e.g. a
certain residue or the restrictions imposed.
The parts of the enzyme excluded from the model are treated as a
homogenous dielectric medium with ² = 4, mimicking the bulk properties of the protein matrix. In the present thesis the self–consistent
reaction field method implemented in JAGUAR [26] has been used in
the solvent calculations. Generally, the effects on the relative energies
by the solvent are in the order of 3–4 kcal/mol. Larger relative energy changes due to the solvent effects are an indication of something
important missing in the model, e.g. a hydrogen bond, and such effects have to be investigated. The protein matrix can also be treated
by a QM/MM (quantum mechanics/molecular mechanics) approach.
The active site is then treated using for example B3LYP, whereas a
computationally less expensive molecular mechanics method is used
to treat the rest of the enzyme. A QM/MM method describes the
system better, but has a built in problem with treating the boundary between the two methods used. Furthermore, the large MM part
is hard to control, which makes it difficult to separate real catalytic
effects from artificial ones, as for example close lying local minima.
The same type of problem can occur also when a pure QM calculation
becomes very large, thus an increase in model size may not always be
an advantage.
12 For example the α–carbon, which connects the side chain of the residue with
the polypeptide chain.
12
2
Introduction to heme
proteins and the binding
of O2, NO and CO
Enzymes are very efficient catalysts, which is a prerequisite for making
many of the chemical reactions needed in biology occur at feasible
rates under physiological conditions. For many years very little was
known about the structures of these catalysts. However, in 1957 the
first three–dimensional picture of a protein molecule was obtained,
and the enzyme was myoglobin. Myoglobin is related to hemoglobin,
the oxygen–carrier in red blood cells responsible for the transportation
of dioxygen. Both myoglobin and hemoglobin bind O2 reversibly, and
are crucial for all vertebrates, which are dependent on a circulatory
system providing all cells with dioxygen. Myoglobin is present in the
muscle cells, working both as a storage of dioxygen and a facilitator
of the diffusion of O2 to the mitochondria.
In the mitochondria the energy available in food is converted into
the energy currency in biological systems, ATP, by reducing O2 to water. The enzyme catalyzing the reduction of O2 , cytochrome oxidase,
and the enzymes transporting O2 have some features in common, they
all depend on the presence of a non–polypeptide unit, a heme group.
The heme group is a very common type of prosthetic group, which is
present in many classes of enzymes, such as; catalases, peroxidases,
cytochromes, globins etc. In the present chapter the structures of the
heme group itself and the enzymes myoglobin and cytochrome oxidase
are introduced. A large part of the present thesis will be about reactions catalyzed by these types of structures. Furthermore, since the
initiation of many of the chemical reactions discussed in the present
13
2 Introduction to heme proteins
thesis is the binding of O2 or NO to ferrous heme, the results on the
properties and differences in binding between O2 , NO and CO, originally reported in Paper I, are summarized in the present chapter.
2.1
Heme prosthetic group
A heme consists of a tetrapyrrole ring, commonly called porphyrin,
with the substituents differing between different types of heme. The
iron coordinating to the porphyrin has two empty coordination sites,
which can be occupied by different residues such as histidine, tyrosine,
cysteine, methionine etc. In the present thesis enzymes incorporating
hemes of type a and b coordinating one or two axial histidine ligands
are discussed. A histidine coordinating to the heme iron is called a
proximal histidine. The iron protoporphyrin shown in Fig. 2.1 is of
type b, which has four methyl, two vinyl and two propionate side
chains. Heme a differs from heme b by the vinyl group on ring B
being exchanged for a so called farnesyl chain. However, in most of
the models used in the calculations, the heme group is truncated to a
porphyrin without substituents, and the same model is used for both
heme a and b. When studying the properties of different hemes experimentally, it can be an advantage to have a model system instead
of studying the whole protein. Therefore numerous porphyrins have
been synthesized, and since the dioxygen transport, i.e. the binding of dioxygen to heme, have been of great scientific interest for
a long time, many of these synthetic complexes are models of the
hemoglobin/myoglobin active site, see Fig. 2.2. The key features of
-
COO-
OOC
A
D
N
N
Fe
N
N
C
B
Fe-protoporphyrin (IX)
Figure 2.1: The protoporphyrin (IX) prosthetic group with iron coordinating to the four nitrogens. This type of porphyrin corresponds to heme b.
14
2.2 Myoglobin
the synthetic models of hemoglobin/myoglobin are an iron porphyrin
having an imidazole coordinating to the iron, whereas one position is
open for the binding of for example dioxygen.
The stability of the spin states of the heme iron depend on both
the number and the type of ligands coordinating to the two empty
positions. For a heme coordinated by one histidine with the sixth
position empty the preferable spin state for a ferrous heme (Fe(II))
is a quintet, using the B3LYP functional, which is in agreement with
experiments [27]. When also the sixth position is filled, the heme
prefers being a low–spin species, corresponding to a closed shell singlet
or a doublet in the ferrous (Fe(II)) and ferric (Fe(III)) states [27],
respectively. It should be noted that the B3LYP functional sometimes
fails to accurately compute the spin splittings [28].
2.2
Myoglobin
Myoglobin is a soluble monomeric enzyme, whereas hemoglobin is a
dimer of dimers, i.e. consists of two α and two β units. A simplified
active site of myoglobin (horse heart), which is very similar to the active site of hemoglobin, is shown in Fig. 2.2. The heme iron is bound
to the enzyme by the so called proximal histidine making the iron
five–coordinated with one position open for the binding of dioxygen.
On the same side as this binding site, a so called distal histidine is located at an optimal position for hydrogen bonding to O2 coordinated
to the heme iron. The distal histidine has been shown to be crucial for
discerning between the diatomics, O2 , NO and CO, by favoring the
O
CO
O
C C
C
O
C
C
N
C
C C
C
C C C
C C
CN
C
C
C
N
N
C Fe
C
C
Proximal His
N
C
C
N
C
C
N
CC
C
Distal His
C
N C
CC
C C C
C
C C
C
C
C
C
C
Figure 2.2: The dioxygen binding site in Horse heart myoglobin [29], showing the distal and the proximal histidine.
15
2 Introduction to heme proteins
binding of O2 by mainly electro–static interactions [30]. Without favoring O2 , low concentrations of CO produced by catabolic processes
would inhibit the enzyme, which could lead to suffocation. The heme
group is located in a crevice in the enzyme, and apart from the proximal and distal histidine the surroundings consist mainly of nonpolar
residues. Furthermore, the ionic propionate groups are located at the
surface of the enzyme in contact with the solution. Ferrous heme has
a high affinity for dioxygen. However, dioxygen is activated by binding to the porphyrin. Therefore, O2 has to be protected during the
transportation, which is done by the protein matrix surrounding the
heme in myoglobin/hemoglobin, preventing potential reactants from
approaching the bound dioxygen. Thus, a free porphyrin would not
be suitable for O2 transportation.
2.3
Cytochrome oxidase
In contrast to the simple function of hemoglobin/myoglobin discussed
above, the final destination for dioxygen transportation, cytochrome
oxidase, is a part of a very complex chain of enzymes. Cytochrome c
oxidase (CcO) is the terminal enzyme in the respiratory chain in eukaryotic and many aerobic prokaryotic organisms. In this enzyme O2
is reduced to water and this reaction is coupled to the translocation of
protons across a mitochondrial or bacterial membrane. The gradient
created is used by ATP synthase to drive the endergonic reaction of
ADP + Pi → ATP to store the energy released when NADH (food)
Intermembrane space (p-side)
4H
4H+
+
+
+
+
+
2H
+
+
IV
+
III
I
-
-
-
-
-
+
+
+
Fe Cu B
QH2
II
+
Cyt
-
F0
-
-
H+
Succinate
NAD
NADH + H
+
+
1
2
Fumarate
O2 2H
+
+
H 2O
F1
Cytoplasm (n-side)
ADP
+
Pi
ATP
Figure 2.3: The respiration chain: Electrons come to the Quinon (Q) from
Complexes I and II. QH2 works as a mobile carrier of protons and electrons.
The electrons are passed to Complex III, which sends them to the mobile
cytochrome c. Complex IV (cytochrome c oxidase) uses the electrons to
reduce O2 to H2 O, while pumping protons. In ATP synthase (F0 and F1 )
the protons reenter to the n–side and ATP is produced.
16
2.3 Cytochrome oxidase
propionate A
O
O
O C
propionate D O C
C
C
C
C
C
C
C
His376
C
CC
C
C
N
N C
C
C
N
C
C C
O
Cu
N
N
C C
N
His290
N
C
C
C
Fe
C N
C
C
C
C
C
His291
C
N
C
C
C
C
C
N
N
C
C C
C
His240
C
C
C
C
C
N
C
O C
C C
C
O
C C
farnesyl chain
C C
C C
Tyr244
Figure 2.4: Crystal structure of the binuclear center in cytochrome c oxidase from bovine heart [32], showing the proximal histidine and the three
histidines coordinating CuB . Note that the farnesyl chain is cut off in the
picture.
is oxidized and O2 is reduced to water, see Fig. 2.3 for an overview of
the respiration chain.
The reversed reaction, ATP → ADP + Pi , is coupled to endergonic
reactions in the cell to make them thermodynamically more favorable.
ADP is released and the cycle can be repeated. Cytochrome c oxidase
(CcO) is a membrane bound protein and contains four redox active
metal centers responsible for the electron transport in the enzyme.
In eukaryotes the respiratory chain is located in the inner membrane
of the mitochondria, whereas in prokaryotes it is located in the inner
membrane of the prokaryotic cell.
The electron, coming from the preceding member in the respiratory chain (complex III, Fig. 2.3) via an electron carrier, cytochrome
c in eukaryotes, enters at CuA , which is located close to the p–side
of the membrane. It is in the binuclear center (Fig. 2.4) the actual
chemistry of the O2 reduction takes place. For each molecule of O2
reduced, eight protons are taken up from the inside of the membrane
(n–side). Four of these protons are used in the reduction of dioxygen
forming two water molecules, while the remaining four protons are
translocated to the outside of the membrane [31]. The translocation
of protons has been investigated in Paper II, and is further discussed
in Chapter 3.
17
2 Introduction to heme proteins
In the binuclear center in cytochrome c oxidase, heme a3 is ligated
by a proximal histidine, whereas CuB has three histidine ligands, see
Fig. 2.4. Furthermore, one of the histidine ligands of CuB (His240) is
covalently linked to a tyrosine residue (Tyr244). During turnover of
cytochrome c oxidase O2 binds to the fully reduced binuclear center,
heme–a3 –Fe(II)–CuB (I), and the O–O bond is cleaved. The turnover
rate of cytochrome oxidase can be decreased by other molecules competing with O2 for the empty binding site. For example, NO is known
to inhibit cytochrome oxidase and the low concentrations of NO in
the cell have been proposed to control the rate of the respiration.
2.4
Binding of O2 , NO and CO to ferrous
heme
The binding properties of the diatomics O2 , NO and CO are especially important in myoglobin/hemoglobin and cytochrome oxidase,
since the binding of O2 has to be favored to avoid suffocation. Enzymes normally distinguish between substrates by their shape and
polarity. However, in this case all three substrates are very similar in
this respect. Furthermore, both NO and CO are known to have a very
high affinity for ferrous iron compared to dioxygen. Carbon monoxide
is for example used experimentally to trap enzymes in their ferrous
state, and NO is known to bind to almost all ferrous complexes [33].
Three models of different systems have been used in the study of
the binding of O2 , NO and CO to ferrous porphyrins, see Fig. 2.5.
The main reason for the study was to evaluate how well the B3LYP
functional describes the binding of dioxygen, nitric oxide and carbon
monoxide to ferrous heme. Mainly the distal side differs between the
models, with the distal histidine and CuB –center incorporated in the
models of myoglobin and cytochrome oxidase, respectively. Model A
was used to represent a synthetic porphyrin in solution. The bond distances and the angles for the different ligands in the three models are
indicated in Fig. 2.6. The structures of all the diatomics investigated
are very stable and do not depend much on the distal environment.
Binding O2 to a ferrous iron forms an open–shell singlet state, which
can be regarded as a superoxide antiferromagnetically coupled to a
ferric low spin heme. Molecular oxygen has a bond length of 1.25 Å
and the ground state is a triplet. The superoxide character of dioxygen coordinating to a ferrous porphyrin can be seen both in the O–O
bond length of ∼1.35 Å and the single unpaired electron on O2 , see
Fig. 2.6.
When NO binds to a ferrous heme the degree of oxidation of the
iron depends on the distal side of the heme. In the porphyrin model
18
2.4 Binding of O2 , NO and CO to ferrous heme
A
C
O
N
C
C
C
C
C
C
N
N
C
Fe
C
N
C
C
C
C
C
C
C
N
C
C
C
C
N
C
C
C
C
N
O
N
C C
C NC C
C
C
C
NC
N
C
C
C
C Cu
N
N C
B
C
N
N
C C
C C
C
C
C
N
C
C
N
C
Fe
C
C
N
C
N
C
C
C
C
C
C C
C
C
C
N
O
C
N
N
C
C
C
C
C
C
C
C
C
N
C
C
N
C
C
Fe
N
C
C
C
C
N
N
C
C
C
C
O
C
C
C
C
N
Figure 2.5: Models used in the study on the binding of O2 , NO and CO to
ferrous heme, here shown binding NO. A: porphyrin, B: myoglobin and C:
cytochrome oxidase.
the iron can be regarded as ferrous with one spin on NO forming a
doublet state, whereas in the models of myoglobin and cytochrome
oxidase the iron is partly oxidized to a state in between ferrous and
ferric. The oxidation of the heme iron coordinating NO, reduces the
latter to a more nitroxyl anion character, antiferromagnetically coupled to the low spin heme, see Fig. 2.6. Both O2 and NO have bent geometries, and this can be explained by a favorable interaction between
the dz2 –orbital on iron and the π ∗ –orbital on O2 and NO [34], respectively. The difference in energy between the dz2 – and π ∗ –orbitals
increases for the diatomics in the order O2 , NO and CO, explaining
why O2 has the most bent geometry. CO binding to the ferrous heme
does not oxidize the iron, and the geometry is almost straight in all
the models, see Fig. 2.6.
The geometries obtained for O2 , NO and CO in the present study
agree well with previous studies, both experimental [30, 35–37] and
theoretical [38–45].
The calculated bond strengths cannot be compared directly with
the experimental data, since the latter consists of equilibrium constants and dissociation rates. Relative equilibrium constants can be
used to evaluate the relative binding energies both between different
19
2 Introduction to heme proteins
b
O
a
O
116-118
a
Fe
Fe
N
N
N
a
b
sFe
sO-O
O
b O
N 138-140
b
Fe
a
N
N
A
B
C
1.89 1.88 1.90
1.35 1.36 1.37
1.12 1.10 1.11
-1.03 -1.02 -0.97
a
b
sFe
sN-O
176-180
C
a
N
A
B
1.82 1.81
1.20 1.21
-0.05 0.19
-0.92 -1.12
C
1.81
1.22
0.30
-1.21
a
b
A
1.80
1.17
B
1.78
1.17
C
1.78
1.17
Figure 2.6: Schematic picture of the geometry of the diatomics O 2 , NO
and CO coordinating to a ferrous porphyrin. The variation of the angle is
indicated in the drawings. Bond distances (in Å) and spin populations are
tabulated for the three models investigated: porphyrin (A), myoglobin (B)
and cytochrome oxidase (C).
ligands in the same system, and for the same type of ligand in different
systems. The dissociation rate (kof f ) corresponds to the barrier for a
diatomic molecule leaving its coordination to the heme. By assuming
that the binding rate (kon ) corresponds to a free energy barrier of 10
kcal/mol, which mainly corresponds to the loss in translational entropy, a rough estimate of the binding energies can be obtained. For
further discussion of the validity of this assumption see Paper I.
Table 2.1: Calculated and estimated experimental binding energies for O 2 ,
NO and CO [30, 36].
Calc. ∆G
O2
NO
CO
2.4
-2.5 -6.9
-8.1
-2.8 -6.2
-4.1
-1.3 -4.2
Estimated exp.
O2
NO
-2.3
-6.1 -12.8
-8.7
∆Gb
CO
-8.5
-9.7
Porph.a
Mb
Cyt.
oxidase
a In experiment mono–3–(1–imidazoyl)–propylamide
mono–methyl ester.
b Calculated from the dissociation barriers by assuming
that the barrier for binding the ligands to the heme iron
is 10 kcal/mol.
20
2.4 Binding of O2 , NO and CO to ferrous heme
Table 2.2: Relative binding energies comparing the molecules O 2 , NO and
CO. The experimental relative binding energies are calculated from equilibrium constants [30, 36].
Calc. ∆∆G
CO/O2
NO/O2
Exp. ∆∆G
NO/CO
CO/O2
NO/O2
Porph.a
-9.3
-4.9
+4.4
-5.8
Mb
+1.9
+5.3
+3.4
-1.9
-7.1
Cyt.
+0.1
+2.8
+2.9
oxidase
a In exp. mono–3–(1–imidazoyl)–propylamide monomethyl ester.
NO/CO
-5.2
-3.2
The calculated and estimated experimental free energies of binding for the three diatomics are listed in Table 2.1. It is clear that
with O2 in myoglobin as the only exception, the bond strengths are
underestimated in all cases where experimental data are available.
For NO the deviations are surprisingly large, exceeding the normal
uncertainty of approximately 3–5 kcal/mol. One part of the underestimation of the bond strengths could be due to the van der Waals
interactions, which are missing in DFT. The absolute bond strengths
and trends between the different ligands are similar for myoglobin and
cytochrome oxidase, which implies that the mechanism for stabilizing
O2 , NO and CO is similar in the two systems. The binding of O2 is
favored compared to CO and NO by the presence of CuB . This observation is of interest since it implies that the electrostatic effect of
the distal side is of importance also in cytochrome oxidase, favoring
the binding of O2 to avoid inhibition of the respiration.
In Table 2.2 the relative binding energies of the different diatomics
in the same systems are listed. The relative binding energies for CO
and O2 are reasonable. However, the comparatively larger error in the
calculated bond strengths for NO gives large errors also in the relative
bond strengths when compared to O2 and CO.
The agreement with experiments of the relative binding energies
for one diatomic in between different models are much better, with
one exception, see Table 2.3. Experimentally the effect on the binding
energy of O2 from the distal histidine corresponds to an increase in
the bond strength by 2.5 kcal/mol. However, in the calculations the
corresponding effect is 10.5 kcal/mol. The accuracy in the description
of a hydrogen bond by the B3LYP functional is expected to be much
better than this. A reason for the exaggerated effect of including the
histidine could be that in the deoxy form of myoglobin the histidine
21
2 Introduction to heme proteins
Table 2.3: Relative binding energies in porphyrin, myoglobin and cytochrome oxidase for each of the molecules O2 , NO and CO. The experimental values are obtained from equilibrium constants [30, 36].
Mb/Porph.
Mb/Cyt. oxidase
Calc.
Exp.
Calc.
Exp.
O2
-10.5
-2.5
-4.0
NO
-0.3
±1a
-1.5
-3.0
CO
+0.7
+1.5
-2.0
+0.1
a Relative binding energy of NO in WT Mb
and apolar distal histidine mutants.
is hydrogen bonding to another residue and when O2 binds this bond
has to be broken.
In conclusion, all bond strengths between ferrous heme and the
diatomics O2 , NO and CO, except for dioxygen in myoglobin, are underestimated by the B3LYP functional. However, the relative bond
strengths of the same molecule in different heme environments are
much better described. It should be noted that this type of weak
bonds are very complicated and difficult to describe compared to
stronger more covalent bonds, where the errors generally are significantly smaller.
22
3
Proton translocation in
cytochrome oxidase
The process of reducing dioxygen to water and storing the energy
released in form of ATP is still not fully understood. As discussed in
Chapter 2, an important part of the bioenergetic apparatus in the cell
is the respiratory chain, i.e. the complex chain of enzymes shown in
Fig. 2.4, which are pumping protons across the mitochondrial (bacterial) inner membrane, creating an electro–chemical gradient. The
protons are allowed to return to the inside of the membrane only by
passing the enzyme ATP synthase, where the exergonicity of the protons flowing back is driving the otherwise endergonic production of
ATP. Cytochrome c oxidase is the terminal enzyme of the respiratory chain, where the reduction of O2 occurs, which is coupled to the
translocation of protons across the membrane. The mechanism with
which the protons are pumped was investigated in Paper II.
To pump protons against an electro–chemical gradient costs energy, which in cytochrome oxidase is counterbalanced by the energy
released when O2 is reduced to water. During the reduction of one
equivalent of molecular oxygen four protons and four electrons are
needed. In addition four protons are pumped across the membrane.
The overall reaction is shown in eq. 3.1.
+
+
O2 + 8HIN
+ 4e− → 2H2 O + 4HOU
T
(3.1)
The protons are transported from the inside of the membrane
(H+
IN , n–side), via the experimentally identified D– and K–channels [46],
either to be consumed in the reduction process at the binuclear center (H+
bnc ), or to be translocated to the outside of the membrane
(H+
OU T , p–side). The binuclear center is located approximately 2/3
23
3 Proton translocation in cytochrome oxidase
4H+
cyt c
+
+
e-
+
p-side
+
+
+
+
+
+
CuA
e1/3
heme a3
O2
heme a
CuB
e-
200 mV
2H2O
2/3
-
-
-
-
-
8H
+
-
-
-
n-side
-
Figure 3.1: Schematic picture of cytochrome oxidase.
of the membrane thickness from the inside of the membrane. The
electrons, which are entering at CuA , go via heme a to the binuclear
center, see Fig. 3.1. The experimentally known working potential over
the membrane is 200 mV, which corresponds to 4.6 kcal/mol. In total
eight charges are moved across the membrane potential during one
turnover, four protons and four electrons to the binuclear center, and
the four protons translocated across the whole membrane. To move
these charges costs 36.9 kcal/mol, which corresponds to the energy
stored from the reduction of O2 . An overview of the catalytic cycle
for the O2 reduction with the experimentally observed intermediates
is shown in Fig. 3.2.
A fundamental problem to be solved in bioenergetics is the mechanism of proton translocation. How do cytochrome c oxidase pump
protons against the membrane potential, whereas the protons on the
24
3.1 Thermodynamics of proton translocation
A
TyrOH
Cu(I)
PM
O-O TyrO
Cu(II)
cleav.
F
TyrOH
TyrOH
+
Cu(II)
Hout
+
Cu(II)
Hout
OH
Fe(II)
+
Hout
OH
OH
+
H ,eO
Fe(IV)
O2
E
O
+
H ,e- OH
O
Fe(IV)
Fe(III)
O2
H+,e-
TyrOH
Cu(I)
R
+
Hout
TyrOH
Cu(I)
OH2
OH2
+
H ,eOH
Fe(III)
OH2
Fe(II)
2H2O
Figure 3.2: The catalytic cycle of cytochrome oxidase.
outside are prevented to flow back, even though this is thermodynamically favored. Furthermore, the protons being pumped must be
prevented from reaching the binuclear center, wasting the energy by
forming water before being translocated. Several mechanisms have
been proposed for the translocation of protons, based either on structural changes at the binuclear center [47–49] or by thermodynamic
control [50, 51]. In general some type of gating seems to be needed to
guide the protons in the right direction, preventing both the translocated protons and protons from the outside from going to the binuclear center. In the present chapter a possible mechanism for translocating protons is discussed.
3.1
Thermodynamics of proton translocation
During the reduction of O2 protons are both consumed at the binuclear center, as well as translocated to the outside of the membrane,
as discussed above. To address this problem by quantum chemistry,
the position where the protons can be regarded as being translocated
has to be defined. The propionates of heme a3 have been proposed
to play an important role in the proton translocation [52], and in the
investigation in Paper II it is assumed that the protons will pass via
the propionates of heme a3 . The surroundings of the two propionates
are quite different, propionate A is hydrogen bonding to a protonated
aspartate (Asp364), whereas propionate D forms a salt bridge with an
arginine (Arg438). To limit the required computer time two models
extended in different regions of the active site were used. The heme
a3 model (left side) includes Arg438 and Asp426, whereas the heme
a3 –CuB model (right side) includes the CuB center, see Fig. 3.3. The
energies were obtained by correcting the heme a3 –CuB model for the
effect by the presence of Arg438 and Asp426. Due to the salt bridge
25
3 Proton translocation in cytochrome oxidase
heme
3
heme
model
Farnesyl
hydroxyl
Asp364
3-CuB model
His240
Tyr244
His290
His291
Prop A
Farnesyl
hydroxyl
His376
Prop A
Prop D
Prop D
His376
Asp438
Figure 3.3: Models used to describe the binuclear center in cytochrome oxidase. The heme a3 -CuB model was corrected by the effect from the presence
of Arg438 and Asp364 using the heme a3 model.
between Arg438 and propionate D, the proton affinity of the latter
is constantly lower compared to propionate A. Therefore, the proton
being pumped is assumed to be located at propionate A.
To evaluate the energetics of dioxygen reduction coupled to proton pumping an energy profile has to be constructed. In order to do
this the energetics of all the proton and electron transfers, both to the
binuclear center and across the membrane, have to be obtained. The
proton affinities (pKa ) for both propionate A, and for the intermediates formed at the binuclear center, during the catalytic cycle were
calculated. By comparing the proton affinities at the binuclear center
with the proton affinity at the propionate for the same intermediate, the thermodynamically most favored position can be evaluated.
The difference in proton affinity will thermodynamically guide the
incoming proton to the most favored position. One example of the
procedure used in the study can be seen in the upper part of Fig.
3.4, where the calculated proton affinity for the oxo–group and propionate A in intermediate F are indicated before and after an electron
has been transferred from heme a. Before the electron transfer the
proton affinity is 4 kcal/mol higher for propionate A compared to
Fe(IV)=O, whereas after the electron transfer the oxo–group has a
40 kcal/mol higher proton affinity as compared to the propionate. In
that case the proton will clearly go to the oxo–group to be consumed
in the reduction of O2 and no protons will go to the propionate for
pumping.
However, the calculated electron affinities of heme a3 compared
to heme a, as well as calculations on the O–O bond cleavage mechanism [53, 54], indicate that an extra proton has to be present at the
26
3.1 Thermodynamics of proton translocation
Unprotonated
p-side
p-side
PA=295
OOC
+1
O Cu(II)
H TyrOH
Fe(IV) O
EA=62
PA=303
COO
e-
OOC
COO
+0
O Cu(II)
H TyrOH
Fe(III) O
PA=291
PA=343
n-side
n-side
Protonated
p-side
p-side
PA=285
OOC
Fe(IV) O
EA=113
PA=295
COO
H
O Cu(II)
H TyrOH
+2
e
-
OOC
COO
Fe(III) O
PA=268
+1
H
O Cu(II)
H TyrOH
PA=290
n-side
n-side
Figure 3.4: Calculated proton and electron affinities for intermediate F
with (lower) and without (upper) an extra proton at the binuclear center
(kcal/mol).
binuclear center before the electron enters. The latter can also be
viewed as the proton first has to be transferred from the inside of the
membrane to the binuclear center, and then the electron transfer occurs. This scenario is modeled as having a water molecule, instead of
a hydroxyl group, coordinating to CuB (II) in intermediate F. The resulting proton affinities are shown in the lower part of Fig. 3.4, which
shows that with an extra proton present at the binuclear center the
proton affinity is 17 and 5 kcal/mol higher for the propionate before
and after the electron is transferred, respectively. This is one of the
main results in the investigation in Paper II, which implies that
with the extra proton no gating is needed at this point, and the proton will be thermodynamically guided to the propionate for further
translocation. The next proton coming from the inside of the membrane is assumed to repel the proton sitting on propionate A, which
then moves toward the outside of the membrane.
The energetics of the electron transfers were evaluated by calculating the relative electron affinity for heme a and heme a3 . Furthermore,
a few experimental energies, such as the overall energy of the reaction
and the difference in reduction potential between cytochrome c and
heme a were used to obtain a reference value for the proton affinity
of the solution (pH=7) on the inside of the membrane. The reference
27
3 Proton translocation in cytochrome oxidase
value was then used to evaluate the thermodynamics of all proton
transfers during the catalytic cycle and an energy profile could be
constructed, with or without the potential over the membrane. For a
detailed description of all steps during one catalytic cycle see Paper
II. In Fig. 3.5 the resulting energy profile with a 200 mV potential
over the membrane is shown. The potential affects all charge transfers
across the membrane as discussed above. The pumping of one proton
across the membrane can be described as following: An electron is
transferred to the binuclear center, e.g. O → OR , which is indicated
by e− in Fig. 3.5. The reduction of the binuclear center is followed by
a proton taken from the inside of the membrane to the propionate,
e.g. OR → ET , which is shown as H+
in . In the next step a proton is
moved from the inside of the membrane to the binuclear center for
the O2 reduction, and the proton on the propionate is repelled to the
+
outside of the membrane, e.g. ET → E, this is indicated by H+
bnc , Hout .
Expelling the proton on the propionate to the outside of the membrane is an endergonic step. However, the overall exergonicity in the
catalytic cycle will drive the reaction forward. As can be seen in Fig.
3.5 none of the barriers caused by the proton and electron transfers
are prohibitively high, which means that the mechanism used for the
pumping of protons is thermodynamically feasible. However, it should
be noted that some form of gate is needed also in this type of translo-
O
10
E
9.1
5
H+bnc
H+out
ER
e-
H+in
R
eH+bnc
4.4
-5
H+in
H+out
PM
0
OT
4.2
H+bnc
H+out
OR
F
O2
-2.9
e-
ET
FT1
-4.5
PR
H+bnc
H+out
e-
H+in
FT2
FR
-6.1 H+in
-8.9
-10
OT
Figure 3.5: Energy profile for one catalytic cycle reducing O 2 to H2 O in
cytochrome oxidase with a membrane potential of 200 mV. H +
out corresponds
to a proton being translocated from propionate A to the outside of the membrane, H+
bnc corresponds to a proton moved from the inside of the membrane
to the binuclear center and H+
in corresponds to a proton moved from the inside of the membrane to propionate A.
28
3.1 Thermodynamics of proton translocation
cation mechanism. The protons on the outside of the membrane have
to be prevented from going to the propionate, and the protons on the
propionate must not go to the binuclear center.
The proton pumping has been studied further [53, 55] and the
models used have been improved by including more of the protein
in the propionate region and several water molecules. These studies
showed that the relative proton affinities of the propionate and at
the binuclear center do change with the increased size of the model.
However, the differences are quite small and the overall picture of
the process does not change. Thus, the main conclusions made in the
study in Paper II, i.e. that a gate may not be needed at the binuclear
center due to the relatively high proton affinity of propionate A, might
still be valid.
It should be noted that no barriers for the electron and proton
transfers or for the O–O bond cleavage are included in the energy
profile. The O–O bond is cleaved with an experimental barrier of 12.5
kcal/mol compared to compound A, which is formed when O2 binds
to compound R (Fe(II) CuB (I)). Thus, with the present energy profile
the total barrier for the O–O bond cleavage is too high, which has to
be further investigated.
29
4
NO reduction – a part of
the denitrification
Denitrification is one of the main parts of the global nitrogen cycle,
see Fig. 4.1. Nitrogen is introduced into the biosphere by biological
and chemical fixation of N2 (g) and removed by denitrification, which
is the only process returning a large amount of fixed nitrogen to the
atmosphere. Denitrification is a part of the bioenergetics in so called
denitrifying bacteria, where nitrate (NO−
3 ) is reduced to dinitrogen
(N2 ) in four steps.
Bacteria living in environments with constant or alternately low
concentration of dioxygen, can utilize nitrogen oxide species as termi-
N2
N2 fixation
N 2O
NO3-
NH3
organic
nitrogen
NO
nitrate
reductase
n it
r ifi -
c at
ion
assimilation
NO2-
Figure 4.1: Inorganic nitrogen cycle, highlighting the denitrification.
31
4 NO reduction
NO
N2
551
NIR
-
NO2
Periplasm (p-side)
-
N2O
-
NO2
H
NO3
+
+
+
+
+
+
+
+
551
+
++
+
H
-
QH2
-
-
-
++
-
+
+
QH2
-
-
-
-
cyt
-
N2O + H2O
551
+
+
+
+
+
+
+
-
-
Fe FeB
1
-
-
-
NOR
-
-
NADH + H+
-
NO2
NAR
- - -
2NO + 2H+
+
551
DH
AP
N2 OR
2H NO3
-
NO2
NAD +
Cytoplasm (n-side)
Figure 4.2: A schematic picture of the denitrification in Escherichia coli.
nal electron acceptors in place of O2 , i.e. instead of reducing dioxygen
to water, nitrate is reduced to dinitrogen. The principle is very similar
to the respiration discussed in Chapter 3. In the denitrification the
electrons coming from the oxidation of food are reducing nitrate. The
energy released is used to pump protons across the bacterial inner
membrane, which drives the synthesis of ATP. The details of the two
processes are however quite different. An overview of the respiration
and the denitrification chains are shown in Figs. 2.3 and 4.2, respectively. The denitrification is less efficient compared to the respiration
of O2 , and occurs only when there is a lack of dioxygen and plenty of
nitrate or nitrite (NO−
2 ).
In the present thesis one step in the denitrification process has
been studied, the reduction of nitric oxide (NO) to nitrous oxide
(N2 O), see the central part in Fig. 4.1. Nitric oxide reductase (NOR)
catalyzes the reduction of two nitric oxide molecules to nitrous oxide
and water according to the overall reaction in eq. 4.1.
2N O(g) + 2H + + 2e− → N2 O(g) + H2 O(l)
(4.1)
For a long time there was a debate whether NO existed as a free
diffusable intermediate in the denitrification process, since the enzyme
catalyzing this reaction was yet to be found, or if nitrous oxide was
produced directly in the reduction of nitrite. The production of free
NO is of interest since NO is cytotoxic, e.g. by indirectly causing oxidation and nitration of proteins, lipids and DNA. Furthermore, NO
is able to inhibit a number of metalloproteins in the bacterial respiratory chains, e.g. cytochrome oxidase. At present NO is known to be
32
4.1 Energetics of proton and electron transfers
a free intermediate in the denitrification, and the enzyme catalyzing
the reduction of nitric oxide, nitric oxide reductase (NOR), has been
characterized. NOR is closely related to cytochrome oxidase, and thus
a member of the heme–copper oxidase family. A major difference between cytochrome oxidase and nitric oxide reductase is that the latter
does not pump protons [56].
Cytochrome oxidases and nitric oxide reductases (NOR) are believed to have a common ancestor due to their structural similarities [57]. It has even been argued that NOR is the ancestor of cytochrome oxidase, since higher concentrations of nitrogen oxides may
have appeared earlier than dioxygen in the atmosphere on earth. In
the last decade many structures of cytochrome oxidases have been
determined. In contrast no structure is available for nitric oxide reductase to date. However, it is known that both cytochrome oxidase
and nitric oxide reductase have a binuclear center, consisting of a
heme and a non–heme metal ion. In cytochrome oxidase the non–
heme metal is CuB , whereas in NOR it is a high–spin non–heme
iron [58, 59]. Several cytochrome oxidases have been shown to display nitric oxide reductase activity [60–62] and nitric oxide reductase
in Paracoccus denitrificans have been shown to reduce O2 [63]. In
Paper III the reduction of NO in a ba3 –type oxidase in Thermus
thermophilus has been investigated, which will be discussed in Section 4.2. In the following sections, 4.3 and 4.4, the reduction of NO
in a model system of NOR (Paper IV) and in a recently discovered
scavenging type1 of bacterial NOR (Paper V) are discussed. The
energetics of the electron and proton transfers in eq. 4.1 are treated
in the next section.
4.1
Energetics of proton and electron transfers
In the reduction of NO in the ba3 –type oxidase and in respiratory
NOR the electrons and protons are taken from different sources. The
electrons come from an electron carrier, e.g. cytochrome c, whereas
the protons are taken from the solution. To fully describe the reduction process in eq. 4.1 the energetics of the entering electrons and
protons have to be obtained. The procedure used in Paper III and
Paper IV is introduced in the present section. The ba3 –type oxidase
will be used as an example.
1 Not
energy conserving but protecting against “nitrosative stress”.
33
4 NO reduction
!"$#&%'%(*)
! ",+.-.%(/)
Figure 4.3: Cartoon of a ba3 –type cytochrome oxidase. The main midpoint
reduction potentials (Em ) for heme b and heme a3 are given relative SHE
(pH=7) [64].
In the ba3 –oxidase electrons enter at CuA and continue via heme b
to the binuclear center, consisting of heme a3 and CuB . The electron–
flow between the metal centers is shown in Fig. 4.3.
The energetics of the electron and proton transfers can in principle
be obtained by calculating the electron affinities (EA), and proton
affinities (PA), respectively, for an acceptor and a donor. However, the
energetics of these charge transfer reactions are difficult to estimate
accurately. A change in the charge of a system makes the calculations
sensitive to the description of the surroundings, and thus to the model
used. In a quantum chemical calculation the size of the system is
limited. Therefore, both the donor and the acceptor can often not be
included in the same model. Furthermore, how well the surroundings
are described may differ between the models of the donor and the
acceptor, which is difficult to control. The limitation in model size also
makes the description of the surroundings depend on the dielectric
continuum model. The latter corresponds to making the assumption
that the surroundings of the donor and acceptor are similar.
However, relative proton and electron affinities within the same
model are generally much more accurate due to a cancellation of
these errors. Therefore, experimental reduction potentials have been
used together with calculated relative electron affinities to estimate
the energetics of the electron transfers in the reduction process. The
34
4.1 Energetics of proton and electron transfers
energetics of the proton transfers will be discussed further below.
The main reduction potentials of heme b and heme a3 are 188
and 428 mV (SHE, pH=7), respectively [64], see also Fig. 4.3. Thus,
transferring an electron from heme b to heme a3 is exergonic by 5.5
kcal/mol. This electron transfer is assumed to correspond to an electron transfer from a ferrous heme b to heme–a3 –Fe(III)–OH2 CuB (I).
The calculated electron affinity of the electron acceptor, heme–a3 –
Fe(III)–OH2 CuB (I), is 114.1 kcal/mol. According to the reduction
potentials above, an electron transfer to this acceptor is exergonic by
5.5 kcal/mol. Thus, the electron affinity of the donor, heme b, is set
to 108.5 kcal/mol. This value is then used as a reference to evaluate
the energetics of electron transfers to other intermediates during the
catalytic cycle. Thus, by connecting the energetics of one known experimental electron transfer to the calculations, the energetics for all
other electron transfers during the catalytic cycle can be estimated.
The estimation of the energetics of the proton transfers is done in
a similar way, by calculating the relative proton affinities of intermediates during the catalytic cycle. However, there are no experimental
estimations of the energetics for the proton transfers. Instead the overall energy of the reaction taken from the reduction potential of NO is
used, see eq. 4.2.
2N O(g) + 2H + + 2e− → N2 O(g) + H2 O(l)
(4.2)
The reduction potential of eq. 4.2 is E0 =1.591 V (SHE, pH=0). A
correction has to be added to obtain the potential corresponding to
a physiologic6al pH of 7. This is done by using the Nernst equation,
which gives a correction of 0.414 V. The corrected reduction potential
is E00 (pH=7.0)=1.177 V.
The electrons are transferred from heme b, as discussed above.
Thus, the potential for the NO reduction has to be related to the
reduction potential of heme b (E00 (pH=7.0)=0.188 V, SHE), which
corresponds to eq. 4.3:
hemeb(ox) + e− → hemeb(red)
(4.3)
giving the total reaction in eq. 4.4.
2N O(g)+2hemeb(red) +2H + → N2 O(g)+H2 O(l)+2hemeb(ox) (4.4)
The reduction potential obtained for the overall reaction in eq. 4.4
is E(pH=7.0)=0.989 V (rel. heme b). Thus, ∆G for the overall reaction
is -45.6 kcal/mol, taking the electrons from heme b and the protons
from a solution with pH=7.
35
4 NO reduction
The following is now known: i) The energetics of all the reaction
steps forming and breaking bonds can be calculated. ii) The energetics
of the electron transfers can be obtained according to above. iii) The
relative proton affinity for the intermediates abstracting a proton from
the bulk can be calculated. iv) The energetics of the overall reaction
can be obtained as described above. Thus, the only unknown is the
energetics for the proton transfers from the bulk to the intermediates
in the reaction mechanism, and these will be determined by the overall
energy of the reaction. By doing this, a reference value for the proton
affinity of the bulk can be obtained, which can be used to evaluate
the energetics of other possible proton transfers.
4.2
NOR activity in a heme-copper oxidase
The reduction of nitric oxide to nitrous oxide and water in a ba3 –type
oxidase was investigated in Paper III, and the resulting reaction
mechanism will be discussed in the present section. NO reduction in
cytochrome oxidase is of interest for the comparison to the mechanism
with which O2 is reduced. The enzymes are structurally similar, but
whereas an O–O bond is cleaved in the O2 reduction, an N–N bond
is formed and an N–O bond is cleaved in the reduction of NO. Furthermore, the mechanism with which NO is reduced in cytochrome
oxidase may be similar to the one in nitric oxide reductase.
In Paper III four different mechanisms for the reduction of NO
were investigated. The energetically most favorable mechanism will
be discussed in the present section, see Fig. 4.4 for an overview. The
model used in the calculations can be seen in Fig. 4.5.
CuBII
CuBII
CuBI
CuBI
NO(g)
NO
FeII
NO(g)
O
O
N N
FeIII
FeII
H+
O
N N
HO
FeIII
e-
H2O(l)
CuBI
H 2O
CuBII
CuBI
HO
HO
FeII
FeIII
e -, H+
CuBII
N 2O
O
N N
FeII
FeII
HO
N2O(g)
Figure 4.4: Overview of the mechanism for the NO reduction in a ba 3 –type
cytochrome oxidase.
36
4.2 NOR activity in a heme-copper oxidase
N2O2
TS1
C
C
CC
CC
CN
Cu
C
O4
O3
0
2.2
N1
C
C
C
C
N
C
C
Fe
CuB
N1
O3
N2
O4
C
C
1.05
-0.58
-0.05
-0.12
-0.14
N1
C
C
1.94
C
C
N
Fe
N
C
C
N
C
C
C
C
C
C
N
spin
N
C
8
1.2 N2
C
C
N
C
O4
O3
N2
C
C
C
C
C
1.84 NC
C
N
C
C
C
Fe
C
N
C
C
N
C
C
C
C
C
C
C
N
C
C
C
N
N
N
C
CC
C
9
1.3
0.44
Fe
CuB
N1 -0.64
O3 -0.41
0.51
N2
0.19
O4
N
O
3.3
5
1.
23
spin
CC
C
1.36
C
C
N
9
1.1
N
Cu
N
C
C
C
N C
N
C
2.71
C
C
C
CN
96
1.
O
C
C
C
2.02
N
C
C
N
C
C
C
C
N
C
C
Figure 4.5: Optimized structures along the reaction path in a ba 3 –type
oxidase. In TS1 (left) the second nitric oxide enters the active site and
attacks the NO coordinated to the heme iron forming a hyponitrous acid
anhydride intermediate (right).
The first nitric oxide binds to the ferrous iron forming a nitrosyl
intermediate. In this reaction step iron becomes slightly oxidized, and
NO is reduced to a more nitroxyl anion character. In solution the nitroxyl anion is known to react with nitric oxide at a high rate [65].
The reduction of nitric oxide coordinating to the iron implies that
the electron is readily available upon reaction with a second NO. The
transition state for the formation of the N–N bond (TS1) is very early,
which can be seen in the long N–N distance in Fig. 4.5. The barrier
for this reaction step is 14.0 kcal/mol, see Fig. 4.6. The product is a
hyponitrous acid anhydride coordinated to the oxidized binuclear center. Hyponitrous acid anhydride, N2 O2−
2 , is stabilized by coordinating
with both negatively charged oxygens to the cupric CuB and N(1) to
the ferric heme iron, see Fig. 4.5. To form nitrous oxide one of the
N–O bonds has to be broken. However, breaking an N–O bond in the
hyponitrous acid anhydride intermediate would form a CuB (III)=O,
which is energetically very unfavorable. Thus, the N–O bond cannot
be broken until the hyponitrous acid anhydride intermediate becomes
protonated.
The procedure for estimating the energetics for the proton and
electron transfers has been discussed above in Section 4.3, and is
also described in Paper III. The most favored position to protonate
37
4 NO reduction
on the hyponitrous acid anhydride intermediate is O(3). However,
the proton transfer from the bulk to this position appeared to be
endergonic by 12.5 kcal/mol, which together with the intrinsic barrier
for breaking the N–O(H) bond give a total barrier of 28.1 kcal/mol.
The experimental turnover rate, 0.04 s−1 [60], corresponds to a barrier
of 19.5 kcal/mol. Thus, the barrier of 28.1 kcal/mol discussed above
is too high.
An electron transfer to the protonated hyponitrous acid anhydride
is exergonic by 5.3 kcal/mol, which reduces the ferric heme to a ferrous state. Furthermore, the total barrier for breaking the N–O(H)
bond is lowered to 17.3 kcal/mol (Fig. 4.6), which fits quite well with
the experimental barrier of 19.5 kcal/mol. The transition state for
the N–O(H) bond cleavage (TS2), which is the rate determining step
in the reaction mechanism, is shown in Fig. 4.7. The nitrous oxide
formed is only weakly coordinated to the ferrous iron, and will be
expelled from the active site in an exergonic step. A hydroxo group
bridging the binuclear center is then formed, which includes an electron transfer from the heme iron to CuB . The remaining part of the
reaction mechanism is an additional protonation and reduction followed by the water leaving the active site, which in total is a slightly
exergonic process, see Fig. 4.6.
The hyponitrous acid anhydride is a relatively stable intermediate,
see Fig. 4.6. It should therefore be possible to isolate the hyponitrous
TS1
13.7
-20
H+
CuI
CuI
FeII
NO
FeII
CuII O
HO
N N
-12.0
CuII O
O
N N
FeIII
-30
5.3
e-
17.3
0.5
-0.3
0
-10
TS2
14.0
10
Fe
III
-4.8
CuII O
HO
N N
-N2O
FeII
-22.1
CuII
HO N O
2
FeII
TS3
-28.5
-27.3
HO
FeII
-40
H+
1.2
e-
CuII
-39.7
CuI
HO
FeIII
-50
-37.2
CuI
H 2O
FeIII
-42.7
CuI
H 2O
FeII
-45.6
CuI
FeII
reaction coordinate
Figure 4.6: Calculated free energy profile for the reduction of NO in a
ba3 –oxidase.
38
4.2 NOR activity in a heme-copper oxidase
TS2
N
CC
C
C
C C
C
C
N
N
O3
18
2.
N C
O4
N2
N
C
1.29
C
2.2
5
1.
18
C
N
C
Cu
C
OC
2.04
C
CN
N1
1.94
C C
C
C
C C
N
C
C
N
C
C
Fe
C
N
C C
N
C C
C C
C
C
C
N
C
spin
Fe
CuB
N1
O3
N2
O4
-0.06
-0.64
-0.05
-0.06
C
C
N
C
C
Figure 4.7: Optimized transition state for the N–O bond cleavage (TS2) in
a ba3 -type oxidase. To cleave the N–O bond the hyponitrous acid anhydride
intermediate must first be protonated and reduced.
acid anhydride by starting the reaction with a mixed valence form of
the enzyme, i.e. CuA and heme b are oxidized and the binuclear center
is fully reduced. Only two electrons would then be available, and one
more electron is needed to break the N–O(H) bond according to the
study in Paper III. Thus, the experiment described above would
conclude if the predicted mechanism is the right one.
In similarity with the N–O bond cleavage discussed above, the
O–O bond cleavage in cytochrome oxidase, has also been shown to
depend on a proton at the binuclear center, forming a hydroxyl group
coordinating to CuB as the product [53, 54]. The activity for the NO
reduction in the ba3 –type of oxidase is quite low (0.04 s−1 ). Applying
a gradient across the membrane would make the already endergonic
protonation of the hyponitrous acid anhydride intermediate even more
unfavorable. Thus, it is unlikely that the reduction of NO in a cytochrome oxidase is able to pump protons. Some cytochrome oxidases catalyze the reduction of NO, whereas for example the bovine
cytochrome c oxidase does not. In the mechanism described above
the rate determining barrier depends on the energetics of the preceding proton and electron transfer. If the proton or electron affinity for
the hyponitrous acid anhydride is lower in the bovine compared to
the ba3 –oxidase, it would explain the absence of NOR activity in the
bovine enzyme.
39
4 NO reduction
4.3
Reduction of NO in model systems of
NOR
Even though the structure of the respiratory nitric oxide reductase has
not been determined to date, there are both experimental information
as well as a modeled structure of NOR. The model was obtained
by fitting the primary sequence of NorB to subunit I in cytochrome
oxidase (Pa. denitrificans) [57]. The structural features are similar to
a cytochrome oxidase, with almost superimposible transmembrane α–
helices and all conserved metal binding histidines in the corresponding
positions [57]. Furthermore, two glutamates are located as second shell
ligands to FeB , of which Glu211 has been shown to be essential for
the activity [66].
However, there are large uncertainties in the modeled structure.
In the modeled binuclear center the non–heme iron (FeB ) has a tetrahedral coordination, analogous to CuB in cytochrome oxidase. This
type of coordination is very uncommon for non–heme iron centers and
additional ligands are most likely involved to provide an octahedral
coordination of FeB .
In contrast to the model of NorB, a very common coordination of
mononuclear non–heme iron is the 2–His–1–Glu/Asp motif [67], with
the remaining sites filled by water forming an octahedral coordination.
Furthermore, an A–type flavoprotein in Moorella thermoacetica has
been shown to display NOR activity [68]. The active site consists of
a non–heme diiron site ligated by four histidines, two aspartates and
one glutamate.
The differences between the coordination for FeB obtained in the
model of NorB and the other non–heme iron enzymes discussed above,
implies that FeB most likely has an octahedral coordination. Therefore, two models of the binuclear center in NOR were constructed. One
with a tetrahedral coordination corresponding to the NorB model, and
one with an octahedral coordination. The intention of the study in
Paper IV was to investigate both the mechanism for the reduction
of NO in NOR, and furthermore what type of coordination of FeB
that is most likely.
Model A is based on the suggested FeB ligands and the common
coordination motifs generally found in non–heme iron enzymes. In
model A FeB is coordinated by three histidines, one glutamate and a
water molecule, see Figs. 4.8 and 4.9.
Model B has the same ligands as model A, but arranged in a tetrahedral coordination with the glutamate and water as second shell ligands. This coordination corresponds to the modeled structure of NorB
discussed above, see Fig. 4.10. An overview of the reaction mechanism
40
4.3 Reduction of NO in model systems of NOR
N2O2
TS1
C
C
N
C
C
C
C
C
C
N
C
FeB
N
C
C
N
C
C
N
C
0
2.2
C
C
N
Fe
C
C
C
N
C
C
C
O
O4
O2
N3
N1
1.95
C
C
C
C
C
N
C
C
C
C
C
C
9
1.3
C
C
C
N
C
C
N
FeB 4.04
Fe -1.03
0.13
N1
0.38
O2
N3
0.17
O4
1.27
C
C
C
N1
FeB
O
O
2
1.3
3
1.2
1.83
C
N3
N
C
2.00
9
O4
N C
C
Fe
N
C
spin
C
N
FeB 3.85
Fe -0.49
N1
0.65
O2
0.38
N3 -0.48
O4 -0.16
N
C
N
spin
O
C
O2
C
C
C
N
C
1.19
O
2.5
O
C
C
N
N C
N
C
C
N
C
C
C
C
C
C
N
Figure 4.8: Optimized structures along the reaction path in model A of
the binuclear center in NOR. In TS1 (left) the second nitric oxide enters
the active site and attacks the NO coordinated to the heme iron forming a
hyponitrous acid anhydride intermediate (right).
and the resulting free energy profiles for both models are shown in Fig.
4.11 and Fig. 4.12, respectively. The reaction mechanism of model A,
which will be discussed below, appeared to be energetically favored
compared to model B. Furthermore, there are many similarities to
the NO reduction in the ba3 –oxidase discussed in Section 4.2.
Heme b3 has an unusually low reduction potential in NOR and
has been proposed to be oxidized at physiological conditions [69].
The procedure for estimating the energetics for the proton and electron transfers occurring during the reaction mechanism has been discussed above in Section 4.3, and is also described in Paper IV. In the
calculations, the first step in the reaction mechanism is assumed to be
a reduction of the ferric heme b3 followed by the binding of NO. The
endergonic reduction of heme b3 makes the mixed–valence binuclear
center the resting state, see Fig. 4.12. Similar to the ba3 –oxidase the
binding of NO to heme b3 oxidizes the latter partly, whereas NO is
reduced to a more nitroxyl anion character. The second nitric oxide
attacks the one coordinating to the heme iron in an early transition
state, which can be seen in the long N–N distance of 2.20 Å, see Fig.
4.8. The total barrier for the reaction step (TS1) is 16.7 kcal/mol
(Fig. 4.12) and the product is a hyponitrous acid anhydride, N2 O2−
2 ,
coordinating in between the two irons, see Fig. 4.8.
To form nitrous oxide one N–O bond has to be cleaved in the
hyponitrous acid anhydride intermediate, see Fig. 4.9. The intrinsic
41
4 NO reduction
TS2
C
C
N
C
C
C
C
N
C
N
C
C
FeB
N
C
N
N C
spin
FeB 3.93
Fe -0.94
N1 -0.03
0.62
O2
0.11
N3
0.06
O4
O
C
O
O
O2
O4
0
2.3
1.1
6
N3
1.24
1.74
N1
C
C
C
N
C
C
C
C
C
C
C
C
C
N
1.94
Fe
N
C
N
C
C
C
C
C
C
C
N
Figure 4.9: Optimized transition state (TS2) for the cleavage of the N–
O bond in the hyponitrous acid anhydride intermediate in model A of the
binuclear center of NOR. The product is a ferrylic FeB and a nitrous oxide
coordinating to a ferrous heme b3 .
barrier for TS2 is 16.3 kcal/mol, which is in good agreement with
the experimental turnover rate corresponding to a barrier of 15.9
kcal/mol [61]. However, both the reduction of heme b3 and the formation of the hyponitrous acid anhydride are endergonic processes,
which makes the total barrier 21.3 kcal/mol, see Fig. 4.12. Regarding
the uncertainties in the model used, due to the absence of a determined structure of NOR, the agreement is considered satisfactory. In
contrast to the reduction of NO in the ba3 –oxidase the N–O bond
can be broken without additional protons and electrons. The reason
for this is that the non–heme iron can be oxidized to a ferrylic state,
whereas the formation of a CuB (III)=O species is energetically very
unfavorable. After the N–O bond has been cleaved a ferrylic FeB
(FeB (IV)=O) and a nitrous oxide coordinating to a ferrous heme b3
are formed in an endergonic reaction. Expelling the the nitrous oxide
leads to the formation of a µ–oxo bridged diferric binuclear center.
This reaction step is exergonic by as much as 45.3 kcal/mol, see Fig.
4.12. Reduction and protonation of the µ–oxo bridge and water leaving the active site are fairly thermoneutral processes, in agreement
with experiments [69, 70].
The free energy profiles of models A and B are shown in Fig.
4.12. The tetrahedral coordination and absence of negatively charged
ligands in model B makes FeB a strong electrophile. Thus, both the
42
4.3 Reduction of NO in model systems of NOR
N2O2
C
C
O
C
1.36
C
C
C
N
C
C
C
2.00
O2
1.
29
spin
C
C
C
N
C
N3
O
C
37
1.
Fe
N
C
O4
O
6
C
C
C
N
C
N
C
C
C
C
C
FeB 4.03
Fe -1.06
-0.05
N1
0.63
O2
0.07
N3
0.08
O4
C
N
C
C
C C
C
C
C
N
N
C
N
FeB
98
1.
C
N
1 .3
N1
spin
N
C
N
C
O
2.01
1.2
N3 9
C
N
8 FeB
1.9
O4
FeB 4.13
Fe -1.08
N1
0.05
O2
0.22
N3
O4
0.23
C
N
C
C
N
C
2.01
N
O
CC
C
C N C
C
C
N
N
O2
1.3
7
O
TS2
N1
2.00
C
C
Fe
C
C
C C
C
C
C
N
C
C
N
C
N
Figure 4.10: Optimized structures along the reaction path in model B of
the binuclear center in NOR. The hyponitrous acid anhydride intermediate (left) is formed without a barrier. In TS2 (right) the N–O bond in the
hyponitrous anhydride intermediate is cleaved forming an Fe B (II) coordinating an oxyl radical. Nitrous oxide is coordinating to the ferric heme b 3 .
hyponitrous acid anhydride (Fig 4.10) and the hydroxo–bridged structures are substantially more stabilized compared to model A, see Fig.
4.12. The consequence of this is a too high barrier for the N–O bond
cleavage (TS2) and also a too endergonic protonation of the hydroxyl
group bridging the ferric heme b3 and ferrous FeB .
In conclusion, the present study gives valuable information for
the coordination of FeB . A tetrahedral coordinated non-heme iron
has severe problems catalyzing the reduction of NO, and is thus not
FeBIII
FeBII
e-
FeBII
FeIII
FeII
FeBII
FeBII
FeBII
NO(g)
O
NO(g)
NO
O
N
N
FeIII
FeII
H2O(l)
H 2O
Fe
Fe
O
O
HO
III
FeBIV
FeBIII
III
Fe
H+
e -, H+
N 2O
FeII
III
N2O(g)
Figure 4.11: Overview of the mechanism for the NO reduction in respiratory NOR.
43
4 NO reduction
TS1
e-
20
+NO
6.6
10
0
FeB
-10
FeII
II
TS2
(+NO)
16.7
21.3
-N2O
3.5 1.4 5.0
-2.8
10
-8.8
30.7
-30
FeIII
FeBII
NO
FeII
-25.1
-33.5
-40
FeBIII
-50
O
-60
Model A: octahedral FeB
B
Model B: tetrahedral FeB
-N2O
FeBII
-20
A
8.9
FeB
O
O
N N
IV
H+
-36.4
-37.1
N 2O
-45.9
FeII
-56.6
FeIII
FeBIII
HO
FeBIII
-70
e-
O
FeIII
FeIII
-42.1
e-
H+
-H2O
-34.6
-41.1
FeBII
H 2O
-38.4
FeBII
FeIII
FeIII
-66.6
FeBII
HO
FeIII
reaction coordinate
Figure 4.12: Free energy profiles for the reduction of NO in models A and
B of the binuclear center in NOR.
likely. In addition a plausible reaction mechanism can be proposed
in a model with an octahedral coordination (model A). This model
has one negatively charged ligand and gives energetics in quite good
agreement with experiments.
4.4
Reduction of NO in a scavenging NOR
Nitric oxide is not only formed in the denitrification process but is
present throughout the biosphere. Prokaryotes not directly involved
in the denitrification are still likely to be exposed to NO produced by
denitrifying neighbors or as a host’s response to infection by pathogenic
bacteria [71, 72]. Thus, also non–denitrifiers most likely have defense
mechanisms to remove NO or to protect themselves against the toxic
effects. A class of enzymes called A–type flavoproteins (FprA), widespread among bacteria and archae, has been shown to display a NOR
activity similar to the one in respiratory NOR [73–76]. The reduction
of NO in FprA is not energy conserving, but has rather a scavenging
function, protecting the organism from nitrosative stress. Recently,
the crystal structure of an FprA in Moorella thermoacetica was determined, harboring a flavin mononucleotide (FMN) cofactor in close
contact with a high–spin non–heme diiron center [73], see Fig. 4.13.
44
4.4 Reduction of NO in a scavenging NOR
3
# *+#, , - . / 012
&')(
"! # $
3
%
Figure 4.13: The coordination of the diiron center in FprA in M. thermoacetica.
The mechanism for the reduction of NO at the diiron center in M.
thermoacetica was investigated in Paper V, and will be discussed in
the present section.
NO is reduced in the FprA active site with a mechanism which
has many similarities with the NO reduction in NOR discussed in
Section 4.3. The starting point in the calculations is a fully reduced
antiferromagnetically coupled diiron center. The relatively symmetric coordination of the two irons (Fig. 4.13) resulted in two reaction
TS1
18.2
20
TS2
16.5
15.0
10
0
-10
O
Fe(II)
H
-5.0
N
Fe(II)
O
-20
-40
-50
-N2O
TS3
O
-30
11.8
4.7
3.2
N
H
O
Fe(II)
O
Fe(II)
Fe(II)
H
O
O
Fe(IV) Fe(II)
N
OH
Fe(III)
H+
O
Fe(III) O Fe(III)
H
-60
-70
H+
e-
-36.8
H
O
Fe(III) O Fe(III)
H
-45.9
e-
-H2O
H
O
-48.6
H
O
Fe(III) Fe(II)
H 2O
H
O
Fe(III) O Fe(II)
H
Fe(II)
-62.1
H2 O
Fe(II)
H
O
Fe(II)
reaction coordinate
Figure 4.14: Free energy profile for the reduction of NO in FprA.
45
Fe(II)
4 NO reduction
N2O2
TS1
spin
spin
C
N
CC
O
C
1.93
FeA
N3
N1
O
C
C
N
C
2.08
O
C
N
C
N
C
N
C
C
C
CO
N
C
C
FeA
C
N3
N1
2.07
O
1.39
O
C
O
N
FeB
C
N
C
C N
C
C
O
N C
O
N
C
C
N
C
N
C
C
C
C
1.35
O2
O
C
O
N
C
O4
FeB
O
O
N C
O4
1.2
1
C
C
0
2.1
C
O
C
O2
3.
34
1.8
9
N
C
N
7
1.2
C
C
19
1.
N
N
C
C
FeA 4.30
FeB -4.07
N1
-0.24
O2 -0.04
N3
0.04
O4 -0.30
C
C
1.89
FeA 3.82
FeB -4.03
N1
0.34
O2
0.27
N3 -0.24
O4 -0.06
N
C
C
C
C
C
Figure 4.15: Optimized structures along the reaction path in FprA. The
second nitric oxide enters the active site and attacks the NO coordinated to
FeB (TS1, left) forming a hyponitrous acid anhydride intermediate (right).
mechanisms, which are almost mirror images of each other. The most
favored mechanism will be discussed below.
The first NO coordinates to FeB , which is partly oxidized. Consequently, NO is reduced to a more nitroxyl anion character, very
similar to the binding of NO to the ferrous hemes discussed in Sections 4.2 and 4.3. The bond to the ferrous non–heme high–spin iron
is weaker as compared to the ferrous heme, and the binding of NO is
slightly endergonic, see Fig. 4.14. The second NO will attack the one
coordinated to FeB forming a hyponitrous acid anhydride, see Fig.
4.15. The barrier for this reaction step is 18.2 kcal/mol, and the hyponitrous acid anhydride is 4.7 kcal/mol higher in energy compared
to the empty diiron center. In the next step the N–O bond is cleaved
forming nitrous oxide and a ferrylic FeA , see Fig. 4.16. N2 O does not
coordinate to FeB but is expelled from the active site. The barrier for
TS2 is 16.5 kcal/mol relative to the empty diiron center, quite close to
the experimental rate–determining barrier of 14.8 kcal/mol [73]. The
ferrylic FeA is quite unstable, and by distorting the geometry slightly
a µ–oxo bridged diferric diiron center is formed in a very exergonic
reaction step, see Fig. 4.14.
In the reduction process of the µ–oxo bridge the FMN cofactor is
oxidized. The energetics for these reaction steps is difficult to estimate
due to the incoming protons and electrons. However, the reduction potentials for the FMN cofactor have been determined experimentally,
46
4.4 Reduction of NO in a scavenging NOR
TS2
spin
C
FeA 4.13
FeB -4.30
-0.07
N1
0.44
O2
0.10
N3
0.07
O4
C
N
C
C
N
C
O
C
C
C O
N C Fe
A
C
C
C
2.22
N
FeB
N
C
C
C
C
O
N
C
O
O
O
O
N3
N1
1.1
9
1.95
1.7
9
O2
N
O4
1.26
1.82
C
N
C
C
C
N
C
C
N
C
C
Figure 4.16: The N–O bond in the hyponitrous acid anhydride intermediate, coordinating to the diiron center in FprA, is cleaved (TS2) forming a
ferrylic FeA and a nitrous oxide.
and are -0.117 V and -0.220 V (SHE, pH=7) for FMNox /FMNsq and
FMNsq /FMNred , respectively. The reduction potential for the reduction of NO (eq. 4.2) is 1.177 V (SHE, pH=7), and the overall reaction
is thus exergonic by 62.1 kcal/mol. The formation of the µ-oxo bridge
is exergonic by 36.8 kcal/mol according to the calculations. In addition, water leaving the active site is exergonic by 13.5 kcal/mol. Hence,
the reduction of the µ-oxo bridge to a water molecule coordinating to
the fully reduced diiron center is exergonic by 11.8 kcal/mol, see Fig.
4.14. It should be noted that the energetics of the individual steps for
the reduction of the µ-oxo bridge to water are somewhat uncertain.
In a mutational study on the FprA in M. thermoacetica a lowering
of kcat was observed when mutating the distal His25 to an apolar
phenylalanine. In Paper V the effect of this mutation on the barrier
of TS2 was investigated by removing His25 from the model shown in
Figs. 4.15 and 4.16. The barrier increased by 3.9 kcal/mol, which is
quite similar to the corresponding experimentally observed effect of
2.1 kcal/mol [73].
The reduction of NO has been proposed to go via a dinitrosyl
intermediate, which has been detected in diiron enzymes showing a
very low NOR activity [77, 78]. In the mechanism described above the
binding of a second NO would inhibit the reduction of NO by blocking
the second iron. Thus, it is possible that the dinitrosyl complex is an
inhibitor rather than a reactive intermediate during the reduction of
NO.
47
4 NO reduction
4.5
Summary
The mechanisms obtained for the reduction of nitric oxide in the
ba3 –oxidase, the model of respiratory NOR and in FprA are quite
similar. In all three cases a hyponitrous acid anhydride is formed
as an intermediate. Furthermore, in all cases a free NO is bound
during the N–N bond formation, and a large part of the barrier in
TS1 consists of entropy. Thus, the barriers for TS1 should be lower
at saturating conditions. The most obvious difference is the need for
protonating and reducing the hyponitrous acid anhydride in the ba3 –
oxidase, in order to break the N–O(H) bond. In the two diiron systems
the reaction mechanisms are in principle analogous, even if the details
differ. The binding of NO to the iron results in a partial reduction to a
more nitroxyl anion character. The transition state for the N–N bond
formation is very early in both the ba3 –oxidase and in the respiratory
NOR model, as can be seen in the 2.20 Å long N–N distance. Both
systems have the same heme model and the non–heme metal is only
weakly interacting in TS1, which makes the transition states very
similar. In FprA the corresponding distance is 1.93 Å and the barrier
is somewhat higher.
In both diiron systems the hyponitrous acid anhydride is stabilized by coordinating with one nitrogen and the adjacent oxygen to
the two irons. On the other hand, in both the ba3 –oxidase and in the
model of NOR with a tetrahedral coordination of FeB both oxygens
in hyponitrous acid anhydride coordinate to CuB and FeB , respectively. This type of coordination results in a stable hyponitrous acid
anhydride intermediate, which shows as the high barrier for the N–O
bond cleavage in the NOR model with a tetrahedral FeB . The transition state for breaking the N–O bond is quite early in FprA with
an N–O bond distance of 1.95 Å, whereas the corresponding distance
is 2.30 Å in the NOR model (A). In both cases a ferrylic non–heme
iron is an intermediate. In FprA the ferrylic iron is considerably more
stable compared to the corresponding intermediate in the respiratory
NOR model. The stability could depend on that the diiron center is
neutral in FprA, whereas in the respiratory NOR model the FeB has
only one anionic ligand. Forming an Fe(IV)=O during the reduction
of NO implies that FeB in respiratory NOR should have at least one
negative ligand.
In conclusion, the similarities of the mechanisms in the two diiron
systems are striking, and support the reaction mechanism proposed
for NO reduction in the model of respiratory NOR. Furthermore, the
formation of a ferrylic species as an intermediate during the catalytic
cycle would explain why there is an iron as the non–heme metal in
NOR instead of CuB as in cytochrome oxidase.
48
5
Myoglobin working as a
nitric oxide scavenger
Myoglobin (Mb) is known to work as an intracellular oxygen carrier
and reservoir, as discussed in Section 2.1. However, during the latest years a potential new function of myoglobin has been proposed.
Myoglobin may work as a nitric oxide dioxygenase (NOD), scavenging
nitric oxide [79, 80].
Cytochrome c oxidase, the terminal enzyme in the respiration
chain (Section 2.3), has been shown to be reversibly inhibited by
NO [81, 82] through competition with O2 for the binding site at the
binuclear center [83, 84]. Thus, myoglobin scavenging NO may be of
large importance to keep the respiration rate as high as possible,
maintaining the proton gradient and thereby the synthesis of ATP.
Furthermore, nitric oxide is known to react with superoxide (O•−
2 )
forming peroxynitrite (ONOO− ) at almost diffusion–controlled rate
[85]. Peroxynitrite is a strong oxidant and nitrating agent, reacting
with a number of biological substrates [86–89]. The scavenging function of myoglobin may therefore also be important for the protection
against oxidative and nitrating damage in the cell.
Myoglobin in the oxy–form has been shown to react with NO
producing nitrate, while oxidizing the heme from a ferrous to a ferric
state (metMb) [90]. Furthermore, metMb has been shown to scavenge
peroxynitrite in solution [91]. The structurally related hemoglobin
(Hb) and many other members of the hemoglobin superfamily also
display nitric oxide dioxygenase activity [90–92].
The investigation of the mechanism for the reaction between nitric
oxide and oxy–Mb is reported in Paper VI, and will be discussed in
49
5 Myoglobin working as a nitric oxide scavenger
O
O N
O
O
FeIII
His93
TS1
NO
O O
FeII
His93
N
TS2
O
O
FeIV
His93
TS3
H2O
O2
FeII
His93
metMb
red.
OH
FeIII
His93
O
N O
O
FeIII
His93
HNO3
Figure 5.1: The mechanism for the conversion of dioxygen and nitric oxide
to nitrate. In the reaction myoglobin is oxidized from a ferrous to a ferric
state and is then reduced by metMb reductase. The highlighted part of the
catalytic cycle has been investigated in Paper VI.
the present chapter. An overview of the reaction mechanism for the
nitric oxide dioxygenase activity in myoglobin is shown in Fig. 5.1.
The starting point in the study was dioxygen bound to a ferrous
myoglobin. O2 coordinating to a ferrous heme forms an open–shell
singlet state. The low–spin heme is in a ferric state antiferromagnetically coupled to a superoxide. It is the superoxide character that
activates dioxygen for the NO attack. A peroxynitrite intermediate is
formed without an enthalpy barrier, and the cis–form, shown to the
left in Fig. 5.2, was found to be most stable. The pure entropy barrier
of TS1 was estimated to be at most 10 kcal/mol, and the reaction
step is slightly exergonic, see Fig. 5.3. The isomerization of peroxynitrite occurs by cleaving the weak O–O bond homolytically, forming
a low–spin ferrylic heme and a nitrogen dioxide (NO•2 ). The transition
state for the O–O bond cleavage (TS2) is shown to the right in Fig.
5.2, and the barrier is 6.7 kcal/mol, see Fig. 5.3. The NO2 radical
formed is trapped inside the proximal pocket of myoglobin. Nitrogen
dioxide attacks the ferrylic heme and forms nitrate in a rebound type
of mechanism. The barrier for this reaction step is only 2.7 kcal/mol
and the transition state (TS3) is shown in Fig. 5.4. Due to the limited translational freedom inside the active site pocket the entropy
is particularly difficult to estimate in this reaction step. In the free
energies discussed above the entropy is calculated relative a complex
between the ferrylic heme and the NO2 radical. The harmonic oscillator, which is used to calculate the entropy, might not describe this
type of weak interaction very accurately. The exergonicity in the formation of nitrogen dioxide and the barrier height for the N–O bond
formation are therefore uncertain. If the NO2 radical is regarded as
free, its formation would be more exergonic and the barrier height
50
peroxynitrite
TS2
spin
spin
1.03
-
Fe
O1
O2
N3
O4
1.23
47 N3 O4
1.
1.48
O2
1.12
0.56
-0.36
-0.15
-0.07
O1
C
C
C
C
C
C
C 1.85
N
C
N
C
C
Fe
C
C
C
N
C
O2
O1
C
N
1.25
9 N3
O4
1.2
1.94
Fe
O1
O2
N3
O4
C
C C
C
C
C
C
N
N 1.71
C
Fe
C
C
C
N
N
C
C
C
C
C
C
C
C
C
C
C
C
N
C
C
N
Figure 5.2: Optimized structures along the reaction path in myoglobin. The
O–O bond in the peroxynitrite intermediate (left) is cleaved in TS2 (right)
forming nitrogen dioxide.
for the N–O bond formation would be raised compared to the free
energy profile shown in Fig. 5.3. The entropy effect in the formation
of nitrogen dioxide inside the proximal pocket should presumably be
in between a completely free NO2 radical and the reactant complex
used in the calculations. Even if the amount of entropy release in this
reaction step is uncertain, the barrier for TS3 should be similar or
lower than the barriers of the preceding steps. Thus, the conversion
of O2 and NO to nitrate should be fast.
The quantitative formation of nitrate reported suggests that a
very small amount of nitrogen dioxide escapes from the distal pocket
in myoglobin, and the reaction should thus be fast [90]. Furthermore,
no ferrylic heme has been detected, which implies that the reaction
occurs at a similar or higher rate compared to the preceding steps [90].
The overall reaction is exergonic by 37.2 kcal/mol.
According to the energetics discussed above myoglobin should be
an efficient NO scavenger. However, there are experimental data that
are difficult to explain with the free energy profile in Fig. 5.3. The
peroxynitrite intermediate has been observed in myoglobin by Herold
et al. at a pH above 8.5 [90]. The rate of decay corresponds to a
barrier of 14.0–14.3 kcal/mol for pH 8.5 and 9.5, respectively [90].
In the calculated free energy profile (Fig. 5.3) on the other hand,
the barrier for breaking the O–O bond is only 6.7 kcal/mol (TS2).
Furthermore, the experimental observations imply that there should
be a pH–effect on the barrier of TS2, increasing the barrier at high
pH resulting in an accumulation of the peroxynitrite intermediate. In
contrast no accumulation should occur according to the free energy
profile discussed above.
51
5 Myoglobin working as a nitric oxide scavenger
TS1
10
10
-1.6
0
TS2
5.2
6.7
-8.2
+NO
-10
-20
Fe
O N
O
O
Fe
NH3
NH3
O
O
TS3
-7.7
2.7
O
N
-30
O
O
N
O
O
Fe
Fe
NH3
NH3
O
-37.2
-40
reaction coordinate
Figure 5.3: The free energy profile for the isomerization of peroxynitrite
to nitrate in myoglobin.
In order to investigate these possible discrepancies further calculations were performed. Two possible changes in the heme environment
in myoglobin due to variations in pH were investigated using several
models in Paper VI. The first dependence on pH concerns the distal histidine in Mb, which has been proposed to swing out from the
active site pocket when protonated [93]. The second effect concerns a
hydrogen–bonding chain from the proximal histidine, via a serine, to
one of the heme propionates. The strength of the hydrogen–bonding
chain could be affected by pH, decreasing the Lewis acidity of the
heme iron at high pH. However, the change in the rate of decay of
the peroxynitrite intermediate at pH=8.5 does not fit very well with
the pKa of the distal histidine (pKa =5–6 [93]) nor the pKa of the
proximal histidine (pKa =10.5 [94]). However, in a study where peroxynitrite in solution was allowed to react with distal histidine mutants of myoglobin, the peroxynitrite intermediate was not detected
even at pH=9.5 [95]. Hence, according to this study the distal histidine seems to be important for the decay rate of peroxynitrite, and
the effect of its presence was therefore investigated. Furthermore, the
proximal histidine does not have to be deprotonated, but the decay
of the peroxynitrite intermediate could be affected by the strength of
the hydrogen–bonding chain to the propionate, which would have a
more complicated pH–dependence.
The model discussed above, which is shown in Fig. 5.2, represents
a low pH case (pH<5–6), with the distal histidine turned away from
the heme binding site toward the propionates. The low barrier of TS2
52
TS3
spin
1.22
0.68
-0.20
-0.39
-0.29
O2
1.
25
N3
2.1
6
Fe
O1
O2
N3
O4
O4
1.25
O1
C
C
C 1.67
N
C
C
C
C
C
N
C
C
Fe
C
C
C
N
C
N
C
C
C
C
C
C
N
Figure 5.4: Optimized transition state for the N–O bond formation in myoglobin. The NO2 radical attacks the Fe(IV)=O forming nitrate coordinating
to a ferric heme.
agrees well with the peroxynitrite intermediate not being observed at
a low pH. A high pH was modeled by incorporating the distal histidine
in the calculations (pH>5–6), which raised the barrier height of TS2
by only 1.5 kcal/mol. This is a modest effect compared to the experimentally observed barrier of around 14 kcal/mol. Thus, the presence
of a distal histidine cannot explain the experimental observations.
Furthermore, the effect of deprotonating the proximal histidine,
modeled as an imidazolate (pH>10, not shown in Fig. 5.4), was investigated. The deprotonation of the histidine can be regarded as
the extreme of the hydrogen–bonding chain from the histidine to the
heme propionate. The deprotonation raised the barrier of TS2 by only
0.6 kcal/mol. Thus, the modeled pH–dependence has only minor effects on the decay rate of the peroxynitrite intermediate. Furthermore,
the radical reaction mechanism described above does not involve any
charge separations, which is consistent with the small effects observed
in the calculated barrier for TS2 by the change in charge and polarity
of the surroundings. Instead, the pH dependence on the decay rate
fits better with nitrate leaving the metMb, which involves a separation of charges. Recently, Goldstein et al measured a decay rate
for metMb–NO3 [96], which was strikingly similar to the decay rate
for the peroxynitrite intermediate reported by Herold et al [90]. The
similar rates imply that it was actually the metMb–NO3 which was
observed by Herold et al. Furthermore, Goldstein et al have estimated
the lifetime of the peroxynitrite intermediate in myoglobin to <1µs.
The latter corresponds to a barrier height of <9 kcal/mol, which is
in quite good agreement with the calculated barrier of TS2 spanning
from 6.7 to 8.2 kcal/mol for the different models used in Paper VI.
53
6
Synthesis of prostaglandin
G2 in prostaglandin
endoperoxide H synthase
Prostaglandin H synthase (PGHS) is the key regulatory enzyme in
the biosynthesis of prostaglandins. Prostaglandins are diverse signal
molecules produced in many different cell types in the body, and play
a central role in inflammation, fever and pain. Furthermore, they are
involved in the regulation of blood clotting, ovulation, initiation of labor, wound healing, kidney function etc. [97]. Prostaglandin synthase
is best known for being the target of one of todays most commonly
used drugs, the pain–killer aspirin. The acetylsalicylic acid in aspirin
inhibits the production of prostaglandin G2 (PGG2 ) by an acetylation
of a serine, which blocks the substrate from entering the active site.
There are two isoenzymes of PGHS, PGHS–1 is proposed to have
housekeeping functions whereas PGHS–2 is associated with pathological processes [98]. PGHS has two catalytic domains responsible for
the enzymatic activities in the protein. A heme active site is located
at the surface of the enzyme and functions as a peroxidase (ROOH
→ ROH) [99], see Fig. 6.1. A cyclooxygenase active site is embedded
in the protein matrix [99] and catalyzes the dioxygenation of arachidonic acid (AA) producing prostaglandin G2 (PGG2 ), see Fig. 6.2.
This reaction occurs in a hydrophobic channel, which reaches from
the membrane binding domain into the globular domain of the protein, where the catalytically active Tyr385 is situated [99], see Fig.
6.1.
The reduction of peroxides by the heme group oxidizes the latter
from a ferric to a ferrylic state with a porphyrin radical cation (Com55
6 Synthesis of prostaglandin G2 in PGHS–1
ROOH
ROH
Tyr385
Ser530
O2 binding pocket
Tyr355
Arg120
Cytoplasm
Membrane
O2
Figure 6.1: Cartoon of PGHS–1, showing the key features of the peroxidase
and cyclooxygenase active sites. Dioxygen and arachidonic acid have been
proposed to migrate from the lipid membrane through a hydrophobic channel
to the cyclooxygenase active site.
pound I). The porphyrin is proposed to be reduced back to a ferrylic
state by oxidizing Tyr385 in the cyclooxygenase active site to a tyrosyl
radical [100]. A mechanism for the conversion of arachidonic acid to
PGG2 was proposed by Hamberg and Samuelsson in 1967 [101]. The
tyrosyl radical is proposed to abstract a hydrogen atom from C13 of
arachidonic acid (AA) and generate a protein bound arachidonyl radical, which has been observed under anaerobic conditions [102–105].
The formation of the arachidonyl radical initiates a chain of radical
reactions incorporating two dioxygens and results in the formation of
the PGG2 and the regeneration of the tyrosyl radical. An overview of
the proposed reaction mechanism is shown in Fig. 6.3. The feasibility of the mechanism for the conversion of arachidonic acid to PGG2
is addressed in Paper VII. The peroxidase activity has not been
studied and the tyrosyl radical was used as the starting point in the
investigation.
The substrate in PGHS, arachidonic acid, is a twenty–carbon,
four–fold unsaturated acid ((Z,Z,Z,Z)–5,8,11,14–eicosatetraenoic acid)
bound in an active site composed of around twenty amino acids. The
main model used in the calculations consists of the C7–C16 part of
the AA substrate, where the radical chemistry is believed to occur, see
56
11
O
9
O
11
13
O
O
9
7
2O2
peroxidase
15
HO2
15
HO
HO2C
CO2H
Arachidonic acid
(AA)
HO2C
Prostaglandin H2
(PGH2)
Prostaglandin G2
(PGG2)
Figure 6.2: The cyclooxygenase active site in PGHS converts arachidonic
acid to prostaglandin G2 (PGG2 ) in a dioxygenation, and a peroxidase
reduces PGG2 to prostaglandin H2 (PGH2 ).
Fig. 6.4. The parts of the arachidonic acid excluded from the model
have no chemical properties affecting the radical reactions taking
place on C8–C15. However, the hydrophobic channel in PGHS imposes steric effects on the substrate, which are of major importance
for the enantiomeric control of the synthesis of PGG2 . The effect on
the energetics for the chemical reaction by the protein surrounding
the substrate should however be small. Therefore, only the models
Tyr385
Tyr385
S
H O
O
HR H S
7
13
PGG 2
15
HR
(CH2)3CH3
(CH2)2COO-
AA
11
2
1
(CH2)3CH3
13
(CH2)2COO9
Tyr385
O
O
13
O
3
6
HSO
O2
O
O 11
15
O
15
(CH2)2COO-
(CH2)3CH3
(CH2)2COO-
4
5
O
O
O2
(CH2)3CH3
13
15
(CH2)3CH3
O
O
8
12
15
(CH2)3CH3
(CH2)2COO-
(CH2)2COO-
Figure 6.3: The proposed mechanism for the conversion of arachidonic
acid to prostaglandin G2 in PGHS.
57
6 Synthesis of prostaglandin G2 in PGHS–1
of the substrate and the catalytic active Tyr385 were included in the
calculations. The tyrosyl radical is modeled as a phenoxyl radical, and
it is only incorporated in the calculations when it takes part in the
reaction, i.e. in the hydrogen atom abstractions. For some of the steps
in the reaction sequence investigated in Paper VII, there are similar
gas phase reactions studied experimentally, e.g. for the addition of O2
to a pentadienyl and an allyl radical. In these cases corrections were
introduced to account for the deviations between the calculated and
experimental bond strengths. The corrections, of up to ∼4 kcal/mol,
were added to the calculated relative energies for the enzyme model
to obtain a more accurate free energy profile, for details see Paper
VII. The corrected energies are reported in the present chapter, and
the resulting free energy profile is shown in Fig. 6.5.
In the first reaction step the 13proS –hydrogen in arachidonic acid
is abstracted by the tyrosyl radical, and an arachidonyl radical delocalized over C11–C15 is formed. The transition state (TS1) is shown
to the left in Fig. 6.4. This reaction step is exergonic by 9.2 kcal/mol
and the barrier for the hydrogen atom transfer is 14.5 kcal/mol, see
Fig. 6.5. Thus, the backward reaction is slow and the step can be
assumed to be irreversible. In the second step dioxygen is proposed
to approach from the lipid bilayer through the channel ending at
the cyclooxygenase active site. O2 could in principle attack all three
carbons with high spin populations on the arachidonyl radical (C11,
C13 or C15). These competing reactions are discussed further below.
TS3
TS1
spin
C
C
C C
0.21
0.22
0.21
0.31
0.25
C
C
C
1.36 C C
O
1.37
13
C
11
C
C
15
1.25
C
15
13
C 1.36
1.4
1
C11
C13
C15
OPh
Ph
9
O1
8
C
C
1.36
11
1.
93
C
spin
O2
1.46
C
C8
C9
O1
O2
0.64
-0.14
0.41
0.08
Figure 6.4: The optimized structures of the hydrogen atom abstraction in
TS1, and the endoperoxide ring formation in TS3 in PGHS.
58
TS1
20
14.5
14.5
10
TS2
0
1
2
-20
-2.9
11.9
-9.2
-10
TS4
TS3
-0.6
8.6
-14.8
0.1
14.9
-9.9
TS5
4
3
~7
-23.5
TS6
5
-25.9
10.5
-30
-40
-36.4
-36.6
6
7
reaction coordinate
Figure 6.5: The calculated free energy profile for the dioxygenation of
arachidonic acid to prostaglandin G2 in PGHS. Corrections according to
gas phase experiments have been added, see Paper VII. The intermediates
corresponding to the numbers 1–7 are shown schematically in Fig. 6.3.
The dioxygen is believed to migrate to a small pocket in the vicinity
of C11 [99], which is proposed to control the stereochemistry of the
product, see Fig. 6.1. The barrier for the formation of the C11–O2
bond (TS2) is 8.6 kcal/mol and the reaction step is exergonic by 5.6
kcal/mol. A free O2 is bound in this reaction step, and a large part
of the barrier in TS2 consists of entropy. In the third reaction step
the peroxyl radical attacks C9 of the C8–C9 double bond and an endoperoxide ring is formed. The transition state (TS3) is shown to the
right in Fig. 6.4. The barrier of the reaction (TS3) is 11.9 kcal/mol
and the reaction step is endergonic by 4.9 kcal/mol, see Fig. 6.5.
In the fourth reaction step a cyclopentane ring is formed by the
radical on C8 attacking the C12–C13 double bond in an exergonic
reaction step, see Fig. 6.6. The bicyclic system of prostaglandin G2
is now ready with an allyl radical spanning C13–C15. The barrier of
this reaction is 10.0 kcal/mol (TS4) relative to the endoperoxide ring
intermediate. However, the total barrier is 14.9 kcal/mol relative to
the resting state, which is the peroxyl radical, see Fig. 6.5. In the fifth
reaction step a second O2 attacks C15 of the allyl radical forming a
peroxyl radical. In this reaction step O2 could in principle attack two
59
6 Synthesis of prostaglandin G2 in PGHS–1
TS4
TS6
spin
O
O
C C
C
8
C
spin
C8
0.75
C12 -0.31
C13 0.42
C15 0.28
C
C
C
C
O
1.
2.37 12 39
C
C
O1
O2
OPh
Ph
1.19
1.21
1.44O2
O1
13
C
15
1.
37
15 C
O
C
C
11
C
O
0.27
0.15
0.26
0.35
13
C
C
8
C
Figure 6.6: The optimized structures of the cyclopentane ring formation
in TS4, and the hydrogen atom abstraction in TS6 in PGHS.
of the allyl radical carbons (C13 or C15). Due to the formation of
the ring system in the previous reactions the substrate is shortened,
and the binding pocket for O2 is now well positioned directing O2
toward C15. The enthalpy barrier of this reaction is absent, but the
loss in entropy gives a barrier of approximately 7 kcal/mol. In the
final reaction step the tyrosyl hydroxyl hydrogen is abstracted back
by the peroxyl radical forming PGG2 , while regenerating the tyrosyl
radical, see Fig. 6.6. The overall reaction has a large driving force of
37 kcal/mol, see Fig. 6.5.
In the reaction mechanism TS1 and TS4 have very similar barrier heights, 14.5 and 14.9 kcal/mol, respectively. The experimental turnover rate corresponds to a rate–determining barrier of 14.8
kcal/mol, which is in good agreement with both barriers. However,
the difference in barrier height is too small compared to the uncertainty of the B3LYP method to discern which one is rate limiting.
In kinetic isotope experiments it was concluded that the hydrogen
atom abstraction in TS1 is the rate determining step on the basis of
the retention of tritium–labeled arachidonic acid. However, according
to the free energy profile in Fig. 6.5, the hydrogen atom abstraction
can be regarded as irreversible. Thus, the measured isotope effect
gives only information about the first reaction step, and cannot be
used to determine which step is rate limiting.
Several competing reaction steps, not leading to the main prostaglandin G2 product, have also been investigated. Experimentally it
60
has been shown that 95% of the arachidonic acid (AA) is converted
into prostaglandin G2 [106]. The remaining 5% of AA gives byproducts, where molecular oxygen adds not only to C11 but also to C15
of the arachidonyl radical (intermediate 3 in Fig. 6.3) followed by a
hydrogen abstraction from Tyr385. In these cases the cyclization reactions do not occur and the intermediates 4–6 in Fig. 6.3 are never
formed. The result is two different hydroperoxides called 11–HPETE
(hydro–peroxy–eicosa–tetra–enoic acid) and 15–HPETE. The other
competing reactions investigated in Paper VII are also concerned
with the attack of molecular oxygen to different radical intermediates formed along the reaction path. The calculated energetics are in
agreement with the formation of 11–HPETE and 15–HPETE, but can
neither explain why certain other possible byproducts are not formed,
nor the observed distribution among the products actually formed.
For example the attack by oxygen on C8 in intermediate 4, shown in
Fig. 6.3, is an irreversible reaction, but has not been observed as a
byproduct. It is therefore concluded that steric effects from the surrounding protein, not included in the model used in the calculations,
determine the selectivity between these different reaction paths.
61
7
Concluding Remarks
Nitric oxide was found to be an intermediate in denitrification only a
few decades ago, which led to the discovery of NO as a biomolecule.
In addition to being an intermediate in bacterial energy conservation,
NO is both a signal molecule and a toxic agent. In the present thesis
the reductions of nitric oxide in both cytochrome oxidase and respiratory nitric oxide reductase have been studied, and mechanisms have
been proposed. Furthermore, some insights in the coordination of the
non–heme iron in respiratory NOR have been gained. The forthcoming structure of respiratory NOR will be received with great interest.
Even though nitric oxide is an intermediate in denitrification, it
is toxic to all organisms. Apart from respiratory NOR, two strategies
for protecting the cell from NO has been studied. The scavenging
NOR (FprA) in non–denitrifying bacteria uses a mechanism which in
principle is analogous to the one proposed for respiratory NOR. It is
rather fascinating that two enzymes so structurally different seem to
reduce nitric oxide to nitrous oxide and water in very similar ways.
A second strategy to handle NO, possibly used by vertebrates, is by
the dioxygenation catalyzed by myoglobin.
The development of computer technology will lead to an increase
in computational power. In quantum chemistry this means that more
and larger systems can be treated. Covering more of the strategies
applied by nature to catalyze very complicated chemical reaction will
increase the knowledge and the possibility to see trends and similarities between different systems. Furthermore, it will give the basic
conditions for the development and improvement of biomimetic catalysts, which in the future hopefully will be used both in an efficient
production of chemicals and also to treat diseases caused by e.g. a
scarcity of enzyme activity.
63
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Acknowledgments
I have had a good time during the last five years that I have been
working in the “Theoretical Biochemistry” group here at Fysikum. I
have learned a lot and met a lot of good friends, and there are of
coarse many persons who I would like to thank.
My supervisors Margareta and Per, thank you both for your guidance
and support during my PhD, and for always taking time to discuss
small and big problems.
I sincerely want to thank my friend and former roommate Marcus for
always being a great discussion partner, and for giving me a helping
hand with this thesis.
All the present and former group members, thank you for creating
such a friendly and stimulating atmosphere, I will miss you all: Rajeev,
Marcus, Vladimir, Fredrik, Arianna, Kyung-Bin, Dan, Tomek, Sven,
Johannes, Valentin, Dimitri, Reto and Holger. Not to forget the people
outside the group, thank you Matteo, Pernilla and Satoru for all the
chats at lunch and coffee breaks.
I also owe a special thanks to Peter, not so much for convincing me
to become a quantum chemist or for our scientific discussions, as for
being a great friend.
All friends who have supported me throughout five long years even
though you don’t really know what I’m doing or why I’m doing it,
thank you all.
My family, thank you for your support and for all the times we spend
together.
Ella, thank you for always being there for me.
71