![Structure of heme b ((protoporphyrin IX, (A)), heme c (B) and heme a (C). Reprinted with permission from [15], 2008, Royal Society of Chemistry.](https://www.researchgate.net/publication/366199098/figure/fig1/AS:11431281106856318@1670859601879/Structure-of-heme-b-protoporphyrin-IX-A-heme-c-B-and-heme-a-C-Reprinted-with_Q320.jpg)
![Schematic representation of the iron out-of-plane displacement of the heme group in deoxy-myoglobin and deoxyhemoglobin. Reprinted with permission from [52], 1993, Elsevier.](https://www.researchgate.net/publication/366199098/figure/fig2/AS:11431281106839486@1670859602028/Schematic-representation-of-the-iron-out-of-plane-displacement-of-the-heme-group-in_Q320.jpg)
![UV-Vis absorption spectra of oxidized and reduced cytochrome c. Reprinted with permission from [66], 2012, Elsevier.](https://www.researchgate.net/publication/366199098/figure/fig3/AS:11431281106817500@1670859602121/UV-Vis-absorption-spectra-of-oxidized-and-reduced-cytochrome-c-Reprinted-with-permission_Q320.jpg)
![Representation of out-of-plane (right) and in-plane deformations (left) associated with the lowest-wavenumber normal mode of different symmetries in a D 4h symmetry. Reprinted with permission [70], 1997, American Chemical Society.](https://www.researchgate.net/publication/366199098/figure/fig4/AS:11431281106839489@1670859603052/Representation-of-out-of-plane-right-and-in-plane-deformations-left-associated-with_Q320.jpg)
![Structure of (A) Pa-cyt 551 (PDB code 351c) and (B) Ne cyt 552 (PDB code 1A56). The amino acid residues colored in red in the depicted sequences indicate point mutations. Reprinted with permission from [47], 2008, American Chemical Society.](https://www.researchgate.net/publication/366199098/figure/fig5/AS:11431281106817503@1670859603148/Structure-of-A-Pa-cyt-551-PDB-code-351c-and-B-Ne-cyt-552-PDB-code-1A56-The-amino_Q320.jpg)
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Citation: Schweitzer-Stenner, R.
Heme–Protein Interactions and
Functional Relevant Heme
Deformations: The Cytochrome c
Case. Molecules 2022,27, 8751.
https://doi.org/10.3390/
molecules27248751
Academic Editors: Gianantonio
Battistuzzi and Carlo
Augusto Bortolotti
Received: 20 October 2022
Accepted: 29 November 2022
Published: 9 December 2022
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4.0/).
molecules
Review
Heme–Protein Interactions and Functional Relevant Heme
Deformations: The Cytochrome c Case
Reinhard Schweitzer-Stenner
Department of Chemistry, Drexel University, Philadelphia, PA 19104, USA; rs344@drexel.edu;
Tel.: +1-215-895-2268
Abstract:
Heme proteins are known to perform a plethora of biologically important functions. This
article reviews work that has been conducted on various class I cytochrome c proteins over a period of
nearly 50 years. The article focuses on the relevance of symmetry-lowering heme–protein interactions
that affect the function of the electron transfer protein cytochrome c. The article provides an overview
of various, mostly spectroscopic studies that explored the electronic structure of the heme group in
these proteins and how it is affected by symmetry-lowering deformations. In addition to discussing a
large variety of spectroscopic studies, the article provides a theoretical framework that should enable
a comprehensive understanding of the physical chemistry that underlies the function not only of
cytochrome c but of all heme proteins.
Keywords:
cytochrome c; structure and function; electronic structure; heme–protein interactions;
symmetry-lowering deformations; redox potential; electron transfer
1. Introduction
The family of heme proteins plays a peculiar and very prominent role among the
multitude of proteins identified and characterized thus far. They perform a diverse set of
biochemical functions, such as ligand binding and transfer (myoglobin, hemoglobin [
1
,
2
],
cytoglobin [
3
,
4
], neuroglobin [
5
]), electron transfer (coenzyme Q, cytochrome c, cytochrome
c oxidase, reaction centers) [
6
–
9
] and enzymatic reactions of various types (horseradish
peroxidase, guanylate cyclase, cytochrome P450 and lignin peroxidase as canonical rep-
resentatives of the peroxidases, cyclases, mono-oxygenases and ligninases) [
10
,
11
]. These
proteins differ in terms of their secondary structure composition and adopted tertiary (and
sometimes quaternary) structures, but they have very similar actives sites in common,
namely iron porphyrines, which differ mostly in regard to their peripheral substituents.
Three representative examples are shown in Figure 1. Hemo- and myoglobin contain proto-
porphyrin IX (heme b, Figure 1) as an active site that exhibits an asymmetric arrangement
of methyl, propionic acid and vinyl groups, each of which interacts non-covalently with the
respective protein moiety [
12
]. In both cases, the imidazole group of the so-called proximal
histidine coordinates with the heme iron. The sixth coordination site can be occupied by
external ligands such as O
2
, CO, NO, OH, CN and H
2
O, depending on the iron’s oxidation
state. Another prominent representative of the heme group family is heme c, which can be
found in all proteins of the highly diverse cytochrome c family (Figure 1) [
13
,
14
]. In these
proteins, the two vinyl groups of protoporphyrin IX are covalently linked to cysteins via
thioether bridges. In most cases, the two cysteins belong to a highly conserved CxxCH
motif, where x represents a variety of amino acid residues. The terminal histidine of the
motif coordinates with the heme iron. In some cases, this motif contains more than two
x-residues. In rare cases, only a single thioether bridge is formed. In class I cytochrome c
proteins, the sixth ligand is provided by the sulfur atom of a methionine side chain, and
the heme group is located near the N-terminal. The canonical mitochondrial cytochrome c
is a member of this family. Classes of cytochrome c differ in terms of their secondary and
Molecules 2022,27, 8751. https://doi.org/10.3390/molecules27248751 https://www.mdpi.com/journal/molecules
Molecules 2022,27, 8751 2 of 34
tertiary structures and the number of incorporated heme groups. The third type of heme
group, shown in Figure 1, is heme a, a functional group in, e.g., cytochrome c oxidase [
8
].
Here, one of the methyl groups of heme b is oxidized to a formyl group. One of the vinyl
substituents is replaced by a hydroxyethylfarnesyl group. There are two heme a groups in
cytochrome c oxidase, termed heme a and a3. Together with Cu
B
, the latter constitute a
binuclear center which catalyzes the reduction of O
2
. The axial coordinates of heme a in
cytochrome c oxidase are provided by two histidines, while the resting state of heme a3 is
pentacoordinate, with an imidazole side chain as the axial ligand.
Figure 1.
Structure of heme b ((protoporphyrin IX, (
A
)), heme c (
B
) and heme a (
C
). Reprinted with
permission from [15], 2008, Royal Society of Chemistry.
The biological function of proteins is frequently linked to structural changes. A promi-
nent example is oxygen binding to hemoglobin, which triggers a change in the tertiary
structure of the respective subunit [
2
,
16
]. This produces a mismatch between the two
quaternary structures that reduces the Gibbs energy difference between them. Consecu-
tive oxygen binding thus produces a switch between a low-affinity T and a high-affinity
R-state [
17
–
22
]. By comparison, structural changes induced by the reduction in/oxidation
of the heme iron in mitochondrial cytochrome c are moderate and mostly involve changes
in the Fe-S(M) bond length, inter-residue hydrogen bonding and water orientations in
the heme pocket [
23
–
29
]. However, the situation is different when the protein binds to
anionic surfaces, such as the inner membrane of the mitochondria, in that this causes
a conformational change which involves the replacement of the methionine ligand by
the imidazole side chain of a histidine and, thus, a significant decrease in the reduction
potential [13,14,30–34]. In this state, the protein acquires some moderate peroxidase activ-
ity [
35
]. On the contrary, structural changes involving interactions between cytochrome c
and cytochrome c oxidase and the subsequent redox reactions in the latter are moderate
and rather local [8,36,37].
While function-related alterations in the structure of heme protein have been the
focus of research activities since the necessary experimental tools became available (X-ray
diffraction and, later, multidimensional NMR, resonance Raman and circular dichroism
spectroscopy), changes in the porphyrin macrocycle have been given little attention for a
longer period of time. In spite of the asymmetric arrangement of the peripheral substituents
and a plethora of heme–protein contacts, the macrocycle of, e.g., hemes b and c were
generally assumed to be planar and to exhibit a D
4h
symmetry [
38
–
40
]. This seemed to be
justifiable in view of its aromatic character and the assumed lack of electronic substituent–
macrocycle interactions. The only deviation from the rule was the so-called iron out-of-
plane displacement of pentacoordinate heme groups, with its metal in the reduced state
(Fe
2+
) [
41
]. A binding of a second axial ligand was generally assumed to eliminate this
displacement [
2
,
42
]. The schematic representation of this deformation in Figure 2shows
Molecules 2022,27, 8751 3 of 34
that it was assumed to involve solely the metal atom. However, X-ray structures of both
oxidation states of mitochondrial cytochrome c proteins [
26
] and of the two subunit types of
oxygenated hemoglobin clearly reveal that this view is by far too simplistic [
43
]. In the latter,
the heme group maintains some of the domed structure that it assumes in the deoxygenated
ferrous state of the protein. In both redox states of yeast iso-1-cytochrome c, the heme group
exhibits a high degree of non-planarity (vide infra). Further evidence of a deviation from
an ideal D
4h
symmetry comes from nuclear magnetic (NMR) and electron paramagnetic
resonance data (EPR), which, for cytochrome c, are clearly diagnostic of a highly asymmetric
spin distribution and rhombic deformations of the metal’s crystal field [
44
–
47
]. Resonance
Raman dispersion and visible circular dichroism spectroscopy clearly revealed the presence
of electronic-deformation-inducing and vibronic perturbations [48–51].
Figure 2.
Schematic representation of the iron out-of-plane displacement of the heme group in
deoxy-myoglobin and deoxyhemoglobin. Reprinted with permission from [52], 1993, Elsevier.
In a biophysical context, the question arises as to whether these symmetry-lowering
deformations of the heme group are functionally relevant. While several lines of evidence
pointed in this direction for model porphyrins in solution [
53
], the functional significance,
particularly that of out-of-plane deformations, have only been revealed more recently by
the work of Bren, Walker and their respective associates [
47
,
54
–
56
]. This review puts their
accomplishments into the broader context. For the sake of brevity and readability, I will
focus on cytochrome c, which has been a laboratory fundamental for biophysical research
since the pioneering work of Theorell and Åkesson in the 1940s of the last century. In this
context, the review will focus mostly on class I cytochromes [
57
]. In what follows, Section 2
starts with a simple quantum mechanical model that describes the electronic structure of the
heme groups in the presence of symmetry-lowering perturbations. In Section 3, the early
EPR results are described and interpreted in terms of the symmetry of the metal’s ligand
Molecules 2022,27, 8751 4 of 34
field. It will be shown that EPR is a suitable tool for probing the in-plane deformations of
the heme group. In Section 4, the review turns to resonance Raman spectroscopy and shows
how this technique can be utilized to determine the in-plane and out-of-plane deformations
of the heme group. In Section 5, I focus on the normal mode structure decomposition
method, by means of which Shelnutt and coworkers obtained out-of-plane deformations
from the crystal structures of heme proteins (cf. [
58
] and references therein). Section 6
of the article discusses the work of Bren and colleagues, who explored the relationship
between the heme deformations, NMR chemical shifts and redox potentials of cytochrome
c derivatives (cf. [
59
] and references cited therein). The Summary and Outlook brings this
review to a close.
2. Protein-Induced Symmetry-Lowering Perturbations
In what follows, I use an ideal porphyrin macrocycle in a D
4h
symmetry as a reference
system. The most general form of the time-independent Schrödinger equation can be
written as:
b
H|ψi(r,q)i=Ei|ψi(r,q)i(1)
where the Hamiltonian
b
H
contains the electronic and vibrational kinetic and potential
energy.
|ψi(r,q)i
denotes the ith eigenfunctions, which depend on a set of electronic and
nuclear coordinates, which I denote collectively as rand q. The latter can be identified with
the the normal coordinates of the system.
For a zeroth-order approach, I invoke the crude Born–Oppenheimer approximation,
which allows us to separate electronic and vibrational wavefunctions and express the former
for the equilibrium geometry of the heme macrocycle. Hence, the electronic Schrödinger
equation can be written as:
b
Hel ψel,i(r,q0)i=Eel ,iψel,i(r,q0)i(2)
where q
0
represents the set of normal coordinates at equilibrium, and the subscript el
indicates that only electronic contributions are taken into account.
The classical four-orbital model of Gouterman describes the electronic structure of
the porphyrin macrocycle in terms of two HOMOS of A
1u
and A
2u
symmetry (in what
follows, I will use capital letters to denote symmetries (irreducible representations of point
groups,) while lower-case letters indicate a specific molecular orbital) and a LUMO of E
g
symmetry (Figure 3). In a zeroth-order reference system, the two HOMOs are accidentally
degenerate, but the configuration interaction lifts this degeneracy by a substantial amount.
The model ignores the d-orbitals of the central iron atom, which are mostly discussed in
the context of crystal or ligand field theories. As shown in Sections 2–4, such a separation
is inconsistent with EPR and particularly with NMR data. In order to formulate a more
holistic approach, I first remind the reader of the ligand field theory for Fe
2+
and Fe
3+
symmetry, which is illustrated in Figure 4. In an octahedral ligand field, the five d orbitals,
which are degenerate in the absence of zero-field splitting, split into two groups of E
g
(higher energy) and T
2g
symmetry (lower energy). The splitting energy
∆0
depends on
the strength of the ligand field. If the symmetry is lowered to D
4h
, further orbital splitting
occurs, though to a different extent. The higher-lying e
g
-orbital splits into its
dz2
(A
1g
) and
dx2−y2
(B
1g
) components, while the lower-lying t
2g
-orbital splits into
dπ
(
dxz
,
dyz
,E
g
) and
dxy
(B
2g
). The respective hierarchy depends on the ligand field. Figure 4shows the energy
level diagram generally obtained for ligand fields in class I cytochrome c derivatives. The
dz2
-orbital exhibits the highest energy. The twofold degenerate
dπ
-orbitals are higher in
energy than dxy.
Molecules 2022,27, 8751 5 of 34
Figure 3. Frontier orbitals of a metal porphyrin in D4h symmetry. The orbitals 3a1u,3a2u and 3egare
filled with electrons. The antibonding orbital 4e
g
is the LUMO. While 3a
1u
and 3a
2u
always lie at
higher energies than 3e
g
, the hierarchy of the former depends on peripheral substituents and axial
ligands. In an idealized reference system, they are assumed to be accidentally degenerate. Reprinted
with permission from [60], 2003, American Chemical Society.
Figure 4.
Energy diagram and orbital occupancy of a ferric iron in a strong ligand field that stabilizes
a low spin configuration. For the sake or readability, the influence of the distortions that lower the
symmetry from cubic to rhombic are only shown for the occupied orbitals. Note that the depicted
hierarchy assumes that the d
π
-orbitals exhibit higher energies than the d
xy
-orbital. This is generally
the case for the most prominent cytochrome c derivatives. HALS denotes a highly axial low-spin
heme iron. Rhombic deformations of the heme core are discussed in detail in the text. Reprinted with
permission from [47], 2008, American Chemical Society.
Molecules 2022,27, 8751 6 of 34
As I will show below, iron d-orbitals can mix with porphyrin orbitals in the presence
of the out-of-plane deformations of the latter. In the D
4h
symmetry assumed thus far, the e
g
-
orbitals of the macrocycle and the heme iron can mix. Regarding to the former, the occupied
3e
g
and the unoccupied 4e
g
-orbitals (LUMO) fall into this category [
47
]. Among the d-
orbitals, the
dπ
pair exhibits E
g
symmetry. NMR data provided evidence of some mixing of
3e
g
(Figure 3) and
dπ
, which produce spin density in the pyrrole rings of the macrocycle.
On the contrary, interactions between
dπ
and the 4e
g
LUMO are negligible [
47
,
54
] Based
on these findings, the classical four-orbital model of the porphyrin ring should be slightly
extended to yield the following basis set of electron configurations:
ψ1i=23a2
1u, 3a2
2u,(3eg−dπ)4,(dπ+3eg)3,d2
xy i
ψ2i=23a2
1u, 3a2
2u,(3eg−dπ)4,(dπ+3eg)4,d1
xy i
ψ3i=23a2
1u, 3a2
2u,(3eg−dπ)3,(dπ+3eg)4,d2
xy i
ψ4i=23a1
1u, 3a2
2u,(3eg−dπ)4, 4e1
g,(dπ+3eg)3,d2
xy i
ψ5i=23a2
1u, 3a1
2u,(3eg−dπ)4, 4e1
g,(dπ+3eg)3,d2
xy i
ψ6i=23a1
1u, 3a2
2u,(3eg−dπ)3, 4e1
g,(dπ+3eg)4,d2
xy i
ψ7i=23a2
1u, 3a1
2u,(3eg−dπ)3, 4e1
g,(dπ+3eg)4,d2
xy i
ψ8i=23a1
1u, 3a2
2u,(3eg−dπ)4, 4e1
g,(dπ+3eg)4,d1
xy i
ψ9i=23a2
1u, 3a1
2u,(3eg−dπ)4, 3e1
g,(dπ+3eg)4,d1
xy i
(3)
Here, the notations 3e
g−dπ
and 3e
g
+
dπ
simply indicate an out-of-phase and in-phase
combination of the two orbitals. The superscript in front of the ket indicates that all these
states are doublets. The states have been numbered so that they line up with the expected
increase in their eigenenergies. Quartet states, which involve the transition of an electron
from
dπ
into
dz2
or
dx2−y2
can be expected to have an energy too high to be thermally
populated at room temperature.
It should be noted that this model is still somewhat simplistic for two reasons. First,
it ignores the mixture of the metal d- with
π
-orbitals of the axial ligands. In the case of
cytochrome c, we thus neglect the mixing with the imidazole
π
-orbitals and the lone pair of
methionine sulfur (vide infra), which can have a measurable influence on the eigenenergies
of
|ψ2i
and
|ψ3i
[
56
,
59
,
61
]. Secondly, it ignores the influence of spin orbit coupling, which
mixes the
dπ
- and
dxy
-orbitals [
44
]. Within the basis set defined by
|ψ1i. . .
.
|ψ9i
, the
electronic Hamiltonian can be written as follows:
H=
E100000000
0E20000000
0 0 E3000000
000 E4δ45/2 0 0 0 0
000δ45/2 E50000
0 0 0 0 0 E6δ67/2 0 0
0 0 0 0 0 δ67/2 E70 0
0 0 0 0 0 0 0 E8δ89/2
0 0 0 0 0 0 0 δ89/2 E9
(4)
where the diagonal elements are the eigenenergies of the wave functions of Equation (3) in
the absence of the configurational interactions (CI)
δ
. The different subscripts of
δ
indicate
that CI might be different for configurations with differentelectron occupations of 3e
g−dπ
,
3e
g
+
dπ
or
dxy
. Owing to the block character of the Hamiltonian matrix, diagonalization is
straightforward and leads to the following new basis set. Here, one must be mindful of the
fact that the matrix elements of configuration interactions are two-electron integrals. Hence,
Molecules 2022,27, 8751 7 of 34
they couple (a
2u
,e
gx
) with (a
1u
,e
gy
), and vice versa. With this in mind, and by neglecting the
very high lying states |ψ7i–|ψ9i, one obtains the following new basis set:
|g0xi=|ψ1xi=2(dxz +3egx )3i
g0yi=ψ1yi=2(dyz +3egy )3i
|g1i=|ψ2i=2(dπ+3eg)4,d1
xy i
|g2xi=|ψ3xi=2(3egx −dxz )3,(dxz +egx )4i
g2yi=ψ3yi=2(3egy −dyz )3,(dyz +egy)4i
Q0
xi=sinν·23a1
2u, 4e1
gx ,(dπ+3eg)3i+cosν·23a1
1u, 4e1
gy,(dπ+3eg)3i
Q0
yi=cosν·23a1
2u, 4e1
gy,(dπ+3eg)3i − sinν·23a1
1u, 4e1
gx ,(dπ+3eg)3i
B0
xi=cosν·23a1
2u, 4e1
gx ,(dπ+3eg)3i − sinν·23a1
1u, 4e1
gy,(dπ+3egx)3i
B0
yi=sinν·23a1
2u, 4e1
gy,(dπ+3eg)3i+cosν·23a1
1u, 4e1
gx ,(dπ+3eg)3i
(5)
For the sake of brevity, I use only the not fully occupied and excited orbitals in the
notation for the electron configurations of the considered states. The mixing parameter
ν
relates to the coupling energy matrix element as follows:
ν=1
2arctan2·δ45
E5−E4(6)
Apparently, if E
4
=E
5
(i.e., 3a
1u
and 3a
2u
are accidentally degenerate),
νij
=
π
/4 [
20
]. In
the literature, this state is often chosen as a reference state [
62
]. Any lifting of the degeneracy
is then ascribed to an A1g-type perturbation [16].
The absorption spectra of cytochrome c and other heme proteins (Figure 5) contain
a very intense band in the region between 410 and 430 nm and a weak band in the 550
nm region. The former is called Soret or B-band, and the latter is a superposition of
the so-called
α
- and
β
-band, which are termed Q
0
and Q
v
in the spectroscopic literature.
These two bands are clearly resolved in the spectrum of ferrocytochrome c but merge
into a single, broad optical band in the spectrum of the oxidized protein. However, as
shown by Dragomir et al., they are still distinguishable in the respective circular dichroism
spectrum [
49
]. The B-band is generally assigned to a
g0x,yi →Bx,yi
transition, whereas the
Q
0
-band is understood to result from
g0x,yi →Qx,yi
. Both transitions are electronically
dipole-allowed (vide infra). The much weaker intensity of the Q
0
-band results from the
configurational interaction between the states
|ψ6(|ψ7)
and
|ψ8(|ψ9)
in Equation (3) [
62
].
The Q
v
-band results from vibronic coupling between
Bx,yi
and
Qx,yi
, which involves the
excitation of vibrational states in
Qx,yi
[
63
]. The B-band has a vibronic side band B
v
, which
overlaps with the B
0
-band. It mostly originates from Franck–Condon-type transitions into
the first vibrational state of totally symmetric porphyrin modes [64,65].
Traditionally, within the framework of the four-orbital model, the electronic transitions
|ψ1i →|ψ4i
and
|ψ1i →|ψ5i
are described as A
1g
(a
1u2
,a
2u2
)
→
E
u
(a
1u1
,e
g1
,a
2u2
) and A
1g
(a
1u2
,
a
2u2
)
→
E
u
(a
1u2
,e
g1
,a
2u1
). Both singlet transitions are electronically allowed. If one considers
the above extended electronic configuration instead, the ground state is a doublet and trans-
forms in the same manner as E
g
in D
4h
. The symmetry of the excited-state configuration
could be written as E
g×
E
g
=A
1u
+A
2u
+B
1u
+B
2u
. Since the ground state transforms in
the same manner as E
g
, the electronic transition dipole moment has E
u
symmetry, as in the
case of the four-orbital model.
Molecules 2022,27, 8751 8 of 34
Figure 5.
UV–Vis absorption spectra of oxidized and reduced cytochrome c. Reprinted with permis-
sion from [66], 2012, Elsevier.
Now, I consider a more realistic scenario, where an electronic perturbation term
b
VΓ
el
is
added to the Schrödinger equation 2, which is now written as [67,68]:
b
Hel,0 +b
VΓ
el ψ00
i(r,q)=E00
iψ00
i(r,q)(7)
where
Γ
denotes the symmetry of an irreducible representation in D
4h
. Hence, it is assumed
that the perturbing potential can be deconstructed into the symmetries of this point group.
The matrix representation of the Hamiltonian is the following:
Hel =
Eg0x+VB1gVB2gVB1g0 0 0 0 0 0
VB2gEg0y−VB1g0−VB1g0 0 0 0 0
VB1g0Eg1x+VB1gVB2g0 0 0 0 0
0−VB1gVB2gEg1y−VB1g0 0 0 0 0
0000Eg20 0 0 0
00000EQ0x+VB1gVB2gVB1gVB2g+VA2g
00000VB2gEQ0y−VB1gVB2g−VA2g−VB1g
00000VB1gVB2g−VA2gEB0x+VB1gVB2g
00000VB2g+VA2g−VB1gVB2gEB0y−VB1g
(8)
Apparently, the matrix of the Hamiltonian contains only perturbations of gerade sym-
metry, which lead to the in-plane deformation of the heme macrocycle. Owing to the mixing
of the 3e
g
porphyrin orbitals with the threefold occupied
dπ
orbital, the electronic ground
state configuration exhibits E
g
symmetry, which is typical of many low-spin ferric sys-
tems [
47
,
53
]. This allows the matrix elements of
VΓ
,
Γ=B1g
,
B2g
to contain non-vanishing
matrix elements in the ground state. This will be of relevance for the discussion of the EPR
results on the oxidized cytochrome.
The matrix elements of
VΓ
of the excited states
Q0
ii,B0
ii
,
i=x
,
y
deserve some further
comments. The four-orbital model dictates that the electronic perturbations of A
1g
,B
1g
,B
2g
and A
2g
symmetry can mix the Q- and B-states, since E
u×
E
u
=A
1g
+B
1g
+B
2g
+A
2g
.While
B
1g
and B
2g
deformations can produce intrastate (between the two Q- and the two B-states,
respectively) and interstate coupling (between the Q- and B-states), A
2g
perturbations solely
mix the Q- and B-states [
16
,
69
]. This scheme seems to become invalidated for this basis set,
described in Equation (5), since the excited-state configuration no longer transforms in the
manner of E
u
.However, if one considers only the perturbations that affect the electronic
Molecules 2022,27, 8751 9 of 34
structure of the macrocycle, the matrix elements of
VΓ
can be simplified as follows. In a
first step, the expressions for the Q and B can be rewritten as follows:
Qxi=sinν·3a1
2u, 4e1
gx i+cosν·3a1
1u, 4e1
gyi·2(dπ+3eg)3i
Qyi=cosν·3a1
2u, 4e1
gyi − sinν·3a1
1u, 4e1
gx i·2(dπ+3eg)3i
Bxi=cosν·3a1
2u, 4e1
gx i − sinν·3a1
1u, 4e1
gyi·2(dπ+3eg)3i
Byi=sinν·3a1
2u, 4e1
gy,i+cosν·3a1
1u, 4e1
gx i·2(dπ+3eg)3i
(9)
Now, the matrix elements of VΓhave the forms:
hQiVΓQji=−sin 2νhQ0
iVΓB0
ji
hBiVΓBji=sin 2νhQ0
iVΓB0
ji
hQiVΓBji=cos 2νhQ0
iVΓB0
ji
(10)
where
Q0
xi,Q0
yi
,
B0
xi,B0
yi
represent the four canonical electron configurations of the four-
orbital model in the absence of A
1g
-type deformations. This state is generally characterized
as 50:50 mixing. The subscripts iand jrepresent xand y. The mixed heme-iron orbital
function does not appear in Equation (10) because of their orthonormality.
If the electronic perturbation affects the porphyrin-iron orbital as well, one can proceed
as follows. The eigenfunctions of the Hamiltonian in Equation (8) can be obtained by
diagonalizing the two blocks formed by the sub-space states
|g0xi,|g0yi
,
|g1xi,|g1yi
and
|Qxi,|Qyi
,
|Bxi,|Byi
, respectively. Alternatively, if the interstate coupling is weak, one
can diagonalize two-dimensional blocks formed by the degenerate states and treat the
remainder of the Hamiltonian matrix with Rayleigh–Schrödinger perturbation theory. For
both procedures, one would assume that the considered perturbations affect only the four
porphyrin orbitals of the excited-state configuration (cf. Equations (9) and (10)). Next, one
would consider the excited-state subset of the obtained eigenfunctions, which are now
augmented by the above excluded porphyrin-iron orbital.
|Q0
ii=∑
jαQQ,ijQjidjz +3egji+αQ B,ijBjidjz +3egj i
i
|B0
ii=∑
jαBB,ijBjidjz +3egji+αB Q,ijQjidjz +3egj i(11)
where
αQQ,ij
(i,j=x,y) are the eigenvectors of the new eigenstates. Equation (11) reflects the
fact that in D
4h
symmetry, the 3e
g
+
dπ
orbital and the four excited electronic porphyrin
states share the same coordinate system with x and y along the Fe-N bonds and z perpen-
dicular to the heme plane. Some of the symmetry-lowering perturbations considered in
Equation (9) (i.e., those of B
2g
and A
2g
symmetry) cause a rotation of the coordinate system.
I omit the multiplicity in Equation (11), since the exact electron configuration depends on
the hierarchy of the two dπ+3egorbitals.
Let us now consider contributions to V
Γ
, which affect only the
dπ+
3
eg
orbital. In this
case, it is sufficient to consider the following two-dimensional basis set:
ψFeP
1xi=dxz +3egx i
ψFeP
1yi=dyz +3egy i(12)
Molecules 2022,27, 8751 10 of 34
Note that Equation (12) is formulated for the coordinate system of the unperturbed
porphyrin. The matrix of the Hamiltonian accounting for the perturbing potential can thus
be written as:
VFeP = VB1g
FeP VB2g
FeP
VB2g
FeP −VB1g
FeP !(13)
I will discuss the relevance of the above formalism when I present the EPR, NMR
circular dichroism and resonance Raman data below. Here, I only indicate that B
1g
-type
perturbations split the Q- as well as the B-band transition. A
2g
and B
2g
perturbations can do
the same if they occur together. Moreover, B
1g
perturbations lift the degeneracy of
ψFeP
xi
and ψFeP
yi.
Thus far, I have solely discussed how an asymmetric potential produced by ligands
and the protein environment can affect the electronic structure of the entire heme group. As
Zgierski and Pawlikowski pointed out nearly 40 years ago, electronic perturbations must
be distinguished from vibronic perturbations [
68
], which will be discussed in more detail
below. They must be further distinguished from symmetry-lowering deformations of the
heme group, which will be briefly discussed below.
The current discussion of heme (porphyrin) deformations relies on the normal-mode-
based concept developed by Shelnutt, Jentzen and coworkers nearly 25 years ago [
58
,
70
–
73
].
It is called normal coordinate structural decomposition (NCD). These authors mostly focused
on out-of-plane deformations, but, clearly, it is equally suitable for in-plane deformations. A
similar approach was earlier introduced by Schweitzer-Stenner, Dreybrodt and their associated
colleagues for the interpretation of the depolarization ratio dispersion of resonance Raman
bands (vide infra) [
74
]. Until the work of Shelnutt and Jentzen appeared, these authors focused
entirely on in-plane deformations.
The NCD approach is based on the assumption that any deformation of the heme group
that is not excessively large can be understood as a linear combination of deformations
along normal coordinates:
δqtotal =∑
Γ
∑
i
dΓ
iδqΓ
i(14)
where idenotes the considered normal coordinate, and
Γ
is the irreducible representation
in an ideal D
4h
symmetry. A 24-atom porphyrin macrocycle has 21 out-of-plane and 45
in-plane modes. The symmetries of the former are A
1u
,B
1u
,B
2u
,A
2u
and E
g
, whereas
in-plane modes can be classified in terms of A
1g
,B
1g
,B
2g
,A
2g
and E
u
.At first glance, the
large number of normal coordinates might discourage a decomposition based on Equation
(14) owing to the large number of options that such a large basis set can be expected to
offer. However, a closer look at the origin of these distortions reveals that options are rather
restricted. A distortion along the normal coordinates of a given symmetry in the electronic
ground state can be calculated as follows [75]:
∆Γ
g=∑
k(Γ)
hg|∂Hel,0 (r,q)
∂qΓ
k
|gi
(Ωg
k)2(15)
The denominator contains the expectation value of the vibronic coupling operator for
the kth mode of symmetry
Γ
in D
4h
and wavenumber
Ωg
k
in the electronic ground state
|g>. Equation (15) reveals that the individual displacement along a given normal mode
scales with the inverse of the square of its wavenumber in the ground state. Hence, only
low-wavenumber modes contribute significantly to the deformations of the macrocycle of
a given symmetry. Regarding out-of-plane modes, considering the lowest wavenumber vi-
bration of a representation often suffices to describe the heme (porphyrin) deformation [
76
].
In the framework of the canonical four-orbital model, the ground state transforms in
the manner of A
1g
. However, the mixture of d
xz
/d
yz
orbitals with 3e
g
produces a ground
state of E
g
symmetry. In D
4h
symmetry, the B
1g
and B
2g
modes can induce Jahn–Teller (JT)-
Molecules 2022,27, 8751 11 of 34
type coupling that produce Jahn–Teller distortions of the same symmetry. Apparently, A
1g
-
modes can produce distortions as well, but obviously, they would not alter the symmetry
of the macrocycle.
Apparently, JT coupling in the electronic ground state should predominantly involve
heme vibrations with an amplitude at the pyrrole nitrogens (in-plane modes do not involve
the metal). As shown below, the low-wavenumber modes of the A
1g
-, B
1g
- and B
2g
-modes
meet this requirement.
The above considerations apply to the first part of the electronic Hamiltonian (i.e.,
b
Hel,0
) described in Equation (8), which transforms as A
1g
in D
4h
. Hence, the symmetry of
the vibrations determines the symmetry of the vibronic coupling operator. However, if we
consider the second term in Equation (8), the corresponding matrix elements are [16,63]:
VΓxΓ0
el,gg =hg∂VΓ
el /∂qkΓ0gi(16)
Group theoretically, all the combinations of
Γ
and
Γ
’for which the product representa-
tion is gerade are allowed. This includes the combination
Γ
=
Γ
’=E
u
. Following Ziergski
and Pawlikowski, I term the derivative in Equation (16) as a vibronic perturbation [
68
]. In
the presence of out-of-plane electronic perturbations (
Γ
=A
1u
,B
1u
,B
2u
,A
2u
and E
g
), all the
out-of-plane modes can, in principle, contribute to the matrix element in Equation (16). The
respective deformations scale, again, with the inverse of the square of their wavenumber
in the electronic ground state, so that only low-wavenumber modes can be expected to
contribute significantly to the total deformation of the heme group.
Figure 6exhibits the deformations associated with the lowest-wavenumber modes
of A
1g
,B
1g
,B
2g
,E
u
,A
1u
,A
2u
,B
1u
,B
2u
and E
g
symmetry. I neglect the respective A
2g
-mode
because of its relatively high wavenumber [
40
,
77
]. I follow Jentzen et al. by using the
following terminology for these deformations: breathing (A
1g
), stretching (B
2g
) translation
(E
u
), propellering (A
1u
), doming (A
2u
), saddling (B
2u
), ruffling (B
1u
) and waving (E
g
) [
70
].
For B
1g
, I prefer the term rhombic so as to connect it to the interpretation of the EPR results
(vide infra) [44].
Figure 6.
Representation of out-of-plane (right) and in-plane deformations (left) associated with
the lowest-wavenumber normal mode of different symmetries in a D
4h
symmetry. Reprinted with
permission [70], 1997, American Chemical Society.
Molecules 2022,27, 8751 12 of 34
3. EPR on Ferricytochrome c
Over the last 60 years, a large number of papers have reported results of the EPR
measurements of heme proteins, in general, and cytochrome c derivatives, in particular.
This is not the place for a comprehensive review of this vast amount of literature. Here, I
focus on some representative papers that elucidate the deformations of the metal’s ligand
field in the cytochrome c derivatives.
I start with the classical study of Salmeen and Palmer on beef heart ferricytochome
c [
44
]. Since both the reduced and oxidized state of the metal are low-spin, only the latter
has an unpaired electron and can be explored by EPR. The authors measured the EPR
spectrum at 20 K with the X-band frequency. Their measurements revealed three different
values for the elements of the diagonal g-tensor, namely 1.24, 2.24. and 3.06. The indicated
anisotropy strongly suggests that the influence of axial and rhombic deformations do not
only split the low-lying
2
T
2g
state (t
2g5
) of the octahedral symmetry into three Kramers
doublets. In a first step, the authors proposed an energy scheme in which axial distortions
lower the symmetry to D
4h
(or C
4h
, if the two ligands are different) and split the t
2g
-orbitals
(Figure 4). Salmeen and Palmer deduced from their data a higher-lying d
xy
(B
2g
)-orbital
and a lower-lying twofold degenerate set of d
xz
- and d
yz
-orbitals, which would produce a
2
B
2g
ground state. However, at the end of their paper, they revised their energy hierarchy
in light of the results of the semi-empirical calculations of Zerner et al. [
78
] that put the two
d
π
-orbitals above d
xy
to produce an
2
E
g
ground state (vide supra), as shown in Figure 4. In
addition to axial and rhombic distortions, the authors considered the spin-orbit coupling of
the three occupied orbitals, which, to some extent, allowed them to theoretically reproduce
the experimental g-tensor values.
In a later study, Brautigan et al. showed that g-tensor values are indicative of rhombic
deformations in horse heart and yeast iso-1 oxidized cytochrome c [
46
]. The main purpose
of their study was the evaluation of the crystal field as a function of pH. In the oxidized
state, cytochrome c can adopt five to six different conformations if the pH is changed
between 1 and 12 [
57
,
79
–
84
]. Since these changes are associated with changes in the sixth
axial ligand (M80), the g-values of these conformations are substantially different.
I now turn to a more recent study of Andersson and colleagues, who used EPR to probe
the heme iron environment in the cytochrome c of Pseudimonas aeruginosa (Pa c
551
) and
Nitrosomonas europaea (Ne c
552
), which are both class I cytochrome c proteins. In addition
to the respective wild types, several mutants were investigated, which were expected
to affect the methionine ligand of the heme group. The two proteins are monomeric,
with a high helical content and positive reduction potentials (Figure 7). Pa c
551
donates
electrons to cytochrome cd
1
in nitrite and nitrate respiration, making its function analogous
to that of the mitochondrial cytochrome c discussed thus far. Ne c
552
is an electron donor
for cytochrome oxidase and a diheme peroxidase, whereas it accepts electrons from the
tetraheme cytochrome c
554
. The mutant studies aimed to explore the influence of N64 and
its neighbors on Pa c
551
.Both proteins differ regarding their respective position 50, i.e., G
in Ne c-552 and N in Pa c
552
.The authors’ mutation replaced the G with an N in the former
and the N with a G in the later.
The EPR spectra of these cytochromes (Figure 8) have in common that they all indicate
three g-values diagnostic of a metal environment that is subject to rhombic deformations.
Figure 4depicts the energy scheme according to which the data were interpreted. It
illustrates the lowering of the symmetry from octahedral to tetragonal and then to rhombic
(D
4h
). The axial strain in the tetragonal field splits the lower-lying t
2g
-orbital into the
higher-lying d
xz
/d
yz
- and the lower d
xy
-orbital by an energy
∆
. With regard to the rhombic
deformation that lifts the degeneracy between d
yz
and d
xz
(interaction energy V), the
authors followed Walker [
53
] in that they distinguished between two types of heme–ligand
complexes. Spectra with a large g
max
signal (type I) are diagnostic of highly anisotropic
low-spin hemes (HALS: highly axial low-spin). Type II depicts g
max
values below 3.2,
a small anisotropy and a more significant rhombic deformation (cf. the V/
∆
values in
Figure 4). The V/
∆
value derived from the g-values of Pa c-551 is 0.37, which puts it closer
Molecules 2022,27, 8751 13 of 34
to type II than type I. For the respective N64V mutant, the ratio is 0.55, which is closer to
the type II realm, thus indicating a stronger rhombic field. N interacts with the methionine
61 ligand
. This interaction is abrogated in the mutant. Ne c-552 has a V/
∆
value of 0.24,
which assigns it to type I. The deletion of N64 significantly increases this ratio to 0.5, moving
it closer to type II. Interestingly, a replacement of the adjacent valine does not cause any
significant changes in the energy ratio. These values should be compared with the ratio
of 0.58 obtained for horse heart cytochrome c, which makes it a clear type II protein with
strong rhombic deformation. A G50N replacement with V65 deletion for Ne c-552 keeps
the protein in the type I realm (V/
∆
= 0.23). A N50G replacement combined with a V65
insertion is also inconsequential regarding the V/
∆
-value. Interestingly, the authors could
not obtain any correlation between the changes in the V/∆and the orientation of M61.
Figure 7.
Structure of (
A
) Pa-cyt
551
(PDB code 351c) and (
B
) Ne cyt
552
(PDB code 1A56). The amino
acid residues colored in red in the depicted sequences indicate point mutations. Reprinted with
permission from [47], 2008, American Chemical Society.
A subsequent study of this group mutations of the Hydrogenhobacter thermophilus
cytochrome c
552
and Pseudomonas aeruginosa c
551
aimed to explore the influence of mutations
in the respective CxxCH region on the EPR spectrum [
84
]. These mutations were known to
change the ruffling deformation of the heme. The results did not reveal any clear correlation
between ruffling and V/
∆
. The wild types and their mutants were all found to lie closer to
the type I region, with minimal variations in its value.
Molecules 2022,27, 8751 14 of 34
Figure 8.
EPR spectra of (
A
) Pa cyt
551
, (
B
)cyt
551
N64V, (
C
) Pa cyt
551
N64Q, (
D
) Pa cyt
551
N50G/V65ins,
(
E
) Ne cyt
551
cloned, (
F
) Ne cyt
551
N64
∆
, (
G
)cyt
551
NeG50N/V65
∆
and (
H
) Ne cyt
551
V65
∆
in 50 mM
HEPES buffer (pH 7.5), recorded at 10.0 K. The dashed lines represent simulated EPR envelopes. The
asterisk indicates the Cu
2+
signal (g ~ 2) resulting from an impurity. Experimental conditions can be
inferred from the paper of Zoppellaro et al., from which this figure was reprinted with permission
from [47], 2008, American Chemical Society.
Taken together, all the EPR studies discussed above are indicative of a rhombic heme
environment. The low-spin character of the electron configuration puts the unpaired
electron into the higher-lying d
π
-orbital, which, according to Zoppellaro et al., is d
yz
[
47
].
As discussed below, ruffling deformations cause an upshift of d
xy
, but in class I cytochromes,
this change does not cause it to become the higher-lying orbital. Only in the presence of
very strong
π
-electron-accepting ligands can the d
xy
-orbital be destabilized to such an
extent [
53
]. While the rhombicity of low-spin ferric complexes has been well established
by multiple EPR experiments, its origin and influences on functional properties (ligand
binding, electron transfer) is rarely discussed in the literature. As pointed out by Walker, the
symmetry of the heme depends on the orientation of the two axial ligands (Figure 9) [
53
].
If they are both planar and oriented parallel to each other, the effective symmetry is D
2h
.
If they are perpendicular to each other, the symmetry is D
2d
. The methionine side chain
is not truly planar, but its SH bond lines up with one of the Fe-N lines in both the R and
the S configurations (Figure 9). This would correspond to a D
2d
symmetry. The latter
case of symmetry lowering involves a perturbation of B
1u
symmetry, which eliminates
the inversion center and corresponds to a ruffling deformation. This would not cause
the rhombic environment of the heme iron. A much better candidate is static JT coupling
(vide infra). The prime candidate is the low-wavenumber mode
ν24
of B
1g
symmetry
Molecules 2022,27, 8751 15 of 34
(Figure 6), which has been found at 228 cm
−1
in the resonance Raman spectrum of horse
heart ferri-cytochrome c [
40
]. This mode involves out-of-phase stretching vibrations of the
N-C
α
bond, with significant amplitudes of the four nitrogens (Figure 6). This mode would
be ideal for lifting the degeneracy of the mixed (3e
g−
d
π
) and (d
π−
3e
g
) orbitals. It would
cause a rhombic deformation along the normal coordinate of
ν24
and produce a ligand
field that has a B
1g
component. This symmetry-lowering effect would be present even if
there were no other protein-induced heme perturbations. This is obviously not the case. In
principle, the projection of the methionine ligand in both R and S onto the heme (Figure 10)
lowers its symmetry to C
s
by means of B
1g
and E
u
perturbations [
85
]. As shown below, the
two thioether bridges of heme c are instrumental in imposing a ruffling deformation onto
the heme group, but it is likely that they produce in-plane deformations as well (vide infra).
Figure 9.
Schematic representation of heme axial M orientations (ball and stick format) and corre-
sponding heme methyl 1H NMR chemical shift patterns observed in cytochromes c. The plane of the
axial H-residue is shown as a bold black stick. (
A
) M orientation in PA cyt
551
(R), (
B
) M orientation
in mitochondrial cytochromes c (S), (
C
) illustration of M fluxionality with M sampling, with the
conformations shown in panels (
A
) and (
B
). The sticks below the structures represent the respective
methyl shift pattern. Reprinted with permission from [47], 2008, American Chemical Society.
4. Absorption, Circular Dichroism and Resonance Raman Dispersion Spectroscopy
The resonance Raman, absorption and circular dichroism spectra of chromophores are
interrelated, since the underlying physical processes all involve vibronic coupling, i.e., the
change in the electronic Hamiltonian by nuclear vibrations along normal coordinates. For
porphyrins, this leads to a breakdown of the Born–Oppenheimer approximation, which
particularly affects resonance Raman scattering in the Q-band region due to complex mul-
timode mixing effects [
48
,
69
,
86
]. The canonical adiabatic Albrecht theory of resonance
Raman scattering, though widely popular, insufficiently accounts for the resonance excita-
tion profiles in the Q-band region [69].
Detailed theoretical descriptions of the relationship between absorption, circular
dichroism and resonance Raman scattering have been provided in earlier review articles,
to which the interested reader is herewith referred [
63
,
87
]. Here, I confine myself to a more
qualitative discussion. As mentioned earlier, the optical absorption spectra of both redox
states of mitochondrial cytochrome c can be understood in terms of electronic transitions
from the ground state into the excited electronic states of Q and B (Equations (6) and (10)).
The lower-lying Q-state transition is much less intense due to the intensity borrowing of the
B-state from the Q-state transition by a configuration interaction. If the two ground-state
orbitals 3a
1u
and 3a
2u
were to be accidentally degenerate, the effective oscillator strength of
the Q-band would be zero or very weak. Its apparent integrated molar absorptivity is a
measure of de-mixing, where the ν-parameter in Equation (10) departs from π/4 [62]. For
ferrocytochrome c, it is approximately 0.13 [
48
]. The so-called Q
v
-band, which is clearly
resolved on the high-energy side of the Q
0
-band in the spectrum of ferrocytochrome c,
Molecules 2022,27, 8751 16 of 34
stems predominantly from vibronic coupling between the Q- and B-states [
88
]. In the first
order, this can be accounted for by time-independent Rayleigh–Schrödinger perturbation
theory which leads to:
|Qj, 1ki=|Qj0, 1ki+
hBi, 0k|∂b
Hel
∂qΓ
k
·qΓ
k|Qj, 1ki
EBi−EQj−ΩQ
k
|Bi, 0ki(17)
This is the so-called Herzberg Teller expansion. It describes the mixing of the first
excited state of the k-th vibration in the excited Q-states with the respective vibrational
ground state of the excited electronic B-states. The subscripts iand jrepresent x and
y. E
Bi
and E
Qj
are the eigenenergies of the B
i
- and Q
j
-states in the unit of cm
−1
in the
absence of vibronic coupling. The vibronic coupling operator has already been introduced
in
Equation (15)
.
ΩQ
k
is the wavenumber of the kth vibrational mode in the excited Q-state,
which is generally not identical to the wavenumber in the electronic ground state [
48
,
69
,
75
].
The numbers 1 and 0 in the bras denote vibrational quantum numbers. It should be noted
that, for the sake of brevity, coupling with the higher-lying vibrational B-states has been
omitted in Equation (17).
Herzberg–Teller coupling, as described in Equation (17), transfers oscillator strength
from the
|g, 0ki →|Bi
, 0
ki
to the
|g, 0ki →|Bi
, 1
ki
transition, which, in spite of the large
energy difference between the Q- and B-states, becomes significant owing to the large
oscillator strength underlying the B-band transition. In D
4h
symmetry, all the in-plane
modes except for the E
u
-modes can contribute to the vibronic side band of the Q transition.
As shown by Levantino et al., the dominant contributions arise from high-wavenumber
A2g-type modes owing to their large vibronic coupling strength [88].
In principle, Herzberg–Teller coupling also contributes to transitions into the
|Bi, 1ki
states, but intensity borrowing from
|Qi, 0ki
is insignificant because of the weak oscillator
strength of the Q-band transitions. The (not spectroscopically) resolved vibronic side band
of the B-band transition is governed by intrastate Franck–Condon and, to a lesser extent, by
Jahn–Teller coupling [
67
,
86
,
89
]. While the former requires A
1g
symmetry in D
4h
, the latter
involves modes of B
1g
and B
2g
symmetry. If the B-state displacement along the respective
normal modes is small (as it is for large aromatic ring systems), one can again employ
Raleigh–Schrödinger perturbation theory to obtain:
|Bi, 1ki=|Bi, 1ki0+1
ΩB
k
hBi∂Hel /∂qΓ
kBji · 0g
kih0g
kqΓ
k|1ki−|2g
kih2g
kqΓ
k1g
ki(18)
This approach follows Garozzo and Galluzi in that it keeps the vibrational function of
the ground state and treats the displacement of the excited state along the coordinate q
k
as
intrastate coupling between B-state components [
90
]. As shown earlier, the A
1g
-, B
1g
- and
B
2g
-modes can contribute to the vibronic coupling matrix element in Equation (18). For A
1g
,
this is Franck–Condon-type coupling, whereas the B
1g
- and B
2g
-modes produce Jahn–Teller
coupling. A similar approach can be used for the Q-band. However, owing to the weak
transition dipole moment of the corresponding transition, the respective contributions to
the Q
v
-band are weak. The situation is quite different for resonance Raman scattering in
the Q-band region (vide infra) [69,91].
How do symmetry-lowering perturbations affect the absorption spectrum? Owing
to large width of the spectroscopic bands, the spectral resolution is low, which makes the
identification of these perturbations difficult. For ferrocytochrome c, this problem can be
circumvented by measuring the Q-band absorption at low temperatures (10 K) in glyc-
erol/water mixtures [
88
]. The corresponding spectra of horse heart and yeast cytochrome c
are shown in Figure 10. The Q
0
-band of horse heart cytochrome c is visibly split. Different
vibronic contributions (Equation (17)) to the Q
v
-band are thus resolved, and identifiable
components can be reproduced by doublets of Voigtian bands. The splitting is less pro-
nounced for yeast cytochrome c, but its existence is still inferable from the asymmetric
Molecules 2022,27, 8751 17 of 34
shape of the Q
0
-band (Figure 10, lower panel). The spectral analysis of Levantino et al.
yielded Q
0
-band splittings of 116 and 77 cm
−1
for the horse heart and yeast cytochrome c,
respectively [
88
]. Earlier measurements of Q-band splitting yielded values between 100
and 120 cm
−1
for other reduced mitochondrial cytochrome c derivatives (tuna, chicken,
bovine, porcine). This splitting is clearly diagnostic of removal of the degeneracy of Q
0x
and Q
0y
. The asymmetry of the band profile reflects the different transition dipole moments
of the two components.
Figure 10.
Q- and Qv-band region of the absorption spectra of horse heart (
a
) and yeast ferrocy-
tochrome c (
b
) recorded at 10 K in a water-glycerol mixture. The spectral decomposition takes into
account the observed splitting of vibronic transitions. The vibronic side band contributions can
be assigned to vibrations of the heme macrocyle. The residual displayed on top of both figures
reflects the quality of the performed fitting. Taken from Levantino et al. with permission [
88
], 2005,
AIP Publishing.
In an earlier study, Manas et al. attributed the splitting to the influence of the (rather
strong) electric field that the protein and the peripheral substituents produce in the heme
plane [
92
]. The first-order effect of an electric field whose vector does not exactly coincide
with a C
m
-Fe-C
m
line causes different blueshifts of the eigenenergies of Q
x0
and Q
y0
by
means of a quadratic Stark effect and, thus, the removal of the x,y degeneracy. However,
while this effect is significant for the B-state (vide infra), owing to the large transition dipole
moment, it is insufficient for reproducing the Q-band splitting. Based on electrostatic
calculations, Manas et al. suggested that the splitting is instead caused by the quadrupole
moment of the electric field. As argued by Levantino et al., the coupling matrix element ac-
counting for such an effect can be described as the intrastate electronic coupling of the type
<Q0
xVB1gQ0
xi=−<Q0
yVB1gQ0
yi
, where
VB1g
is an electronic perturbation potential of
Molecules 2022,27, 8751 18 of 34
the type introduced in Equation (7) [
88
]. While this type of electronic perturbation can split
the Q-state, it does not account for the different transition dipole moments of
|Qxi
and
Qyi
. To arrive at a consistent description of band splitting and asymmetry, Levantino et al.
considered interstate coupling in the presence of asymmetric perturbations. This led them
to the following set of equations for the eigenenergies in second order:
EQx =E0
Q+(VA1g
QxBx+VB1g
QxBx)2+ (VB2g
QxBy+VA2g
QxBy)2
E0
Q−E0
B
(19)
EQy =E0
Q+(VA1g
QyBy−VB1g
QyBx)2+ (VB2g
QyBx−VA2g
QyBx)2
E0
Q−E0
B
(20)
Equations (19) and (20) implicate that Q-band splitting requires the simultaneous pres-
ence of A
1g
and B
1g
and/or A
2g
and B
2g
perturbations. In the framework of the four-orbital
model, intrastate and interstate electronic coupling are not independent (cf. Equation (10)).
Levantino et al. found that, for horse heart cytochrome c, the
VB1g
QiQi
value that emerged
from their analysis of the Q-band profile was very close to the one derived from an esti-
mation of quadrupole coupling by Manas et al. This led them to the conclusion that the
Q-band splitting does indeed predominantly result from the quadrupole moment of the
electric field in the heme plane, which they estimated to be predominantly produced by the
charges on the two ligands and the propionic acid substituents.
In addition to the electronic contributions described above, a quantitative reproduction
of the Q-band profiles in Figure 10 requires the consideration of vibronic perturbations,
which are briefly described as follows. As shown by Zgierski and colleagues, vibronic
perturbations can be accounted for by using the Hamiltonian in Equation (7) for the vibronic
coupling operator [16,68,93]:
∂b
Hel
∂qk
=∂b
Hel,0
∂qk
+∑
Γ
∂b
VΓ
∂qk
(21)
While the first term of the r.h.s. transforms as the representation of q
k
, the second
(vibronic perturbation) term transforms as the product
Γk×Γ
.Hence, the symmetry of the
vibronic coupling operators reads as a sum of D
4h
symmetry representations. To illustrate
the significance of vibronic perturbations, let us consider a B
1g
-mode. This could contribute
to Jahn–Teller coupling between the Q- and B-states, respectively. It would be accounted
for by the matrix element in Equation (18), which would transform in the manner of B
1g
.
In the presence of B
1g
-type perturbations (vide supra), B
1g ×
B
1g
=A
1g
symmetry would
be admixed with the coupling operator, which would add Franck–Condon activity to the
considered mode qk.
The significance of vibronic perturbations can best be illustrated by a closer look at the
visible circular dichroism spectra. Figure 11 (left) depicts the CD and absorption spectra
of oxidized horse heart cytochrome c in the B-band (Soret band) region. The CD profile
can be described as a negative couplet. In the framework of the four-orbital model, its very
existence is indicative of a split between B
x
and B
y
, with opposite rotational strengths of the
respective electronic transitions [
49
]. The corresponding spectra of reduced cytochromes
are slightly more complex (Figure 11, right). Schweitzer-Stenner used a vibronic coupling
model to reproduce the shape of three couplets and the corresponding absorption bands
depicted for three different mitochondrial cytochrome cs [
50
]. The author found that while
the contribution of vibronic perturbations to the B-band splitting is small (41 cm−1added
to 505 cm
−1
for horse heart and cow and 12 cm
−1
to 380 cm
−1
for yeast), the situation
is quite different for ferricytochrome c, where the vibronic perturbations add 390 cm
−1
to
126 cm−1
for the horse heart, 127 cm
−1
to 186 cm
−1
for cow, and 25 cm
−1
to 217 cm
−1
for yeast. While B
x
lies at lower energies than B
y
in the oxidized proteins, it is at higher
Molecules 2022,27, 8751 19 of 34
energies in ferrocytochrome c. Vibronic perturbations have an even more pronounced
influence on the vibronic side bands of B
x
and B
y
. The underlying reason is reflected in the
vibronic coupling matrix elements:
hBx|∂b
Hel
∂qk
|Bxi=hBx|∂b
Hel,0
∂qA1g
k
+∂b
VB1g
el
∂qA1g
k
|Bxi
hBy|∂b
Hel
∂qk
|Byi=hBy|∂b
Hel,0
∂qA1g
k
−∂b
VB1g
el
∂qA1g
k
|Byi
(22)
where B
1g
-type vibronic perturbations add coupling strength to one side band and reduce
it for the other one. As a consequence, the vibronic side bands of B
x
- and B
y
can appear
rather different in the presence of the B
1g
perturbations of the heme group. It should be
noted, in the context, that this influence of vibronic perturbations on the shape of the
absorption bands was discussed more than 30 years ago by Bersuker and Stavrov [
94
].
Their contribution was mostly ignored in the porphyrin/heme protein literature. More
recently, Schweitzer-Stenner et al. [
65
] invoked the above vibronic coupling scheme to
explain the dispersion of the ratio of polarized absorption observed for the single crystals
of myoglobin cyanide by Eaton and Hochstrasser [95].
Figure 11.
Circular dichroism (
upper
figures) and Soret band absorption (
lower
figures) of oxidized
(
left
) and reduced horse heart cytochrome c (
right
). The solid lines result from a fit of a vibronic
coupling model with the corresponding band profiles. Details of the theory can be inferred from [
50
].
Reprinted with permission from [50], 2008, American Chemical Society.
I finish this chapter with a discussion of how electronic and vibronic perturbations
affect resonance Raman scattering. As mentioned above, absorption and resonance Raman
scattering are interrelated in that the Franck–Condon, Jahn–Teller and Herzberg–Teller
active modes are also resonance-Raman-active. On the most elementary level, this can
be explained by inserting the expansion in Equations (17) and (18) into the Kramers–
Heisenberg–Dirac equation. The interested reader can infer details from earlier review
articles [
63
]. In an ideal D
4h
symmetry, the modes of A
1g
,B
1g
,B
2g
and A
2g
are resonance-
Raman-active. While bands assignable to the A
1g
-modes dominate spectra taken with
B-band excitation, non-symmetric and antisymmetric modes dominate spectra taken in the
Q-band region. In D
4h
symmetry, these modes can be identified by their depolarization
ratios, i.e., 0.125 for A
1g
-modes, 0.75 for B
1g
and B
2g
and infinite for A
2g
-modes, independent
of the excitation wavelength [
77
,
96
]. The experimental values were indeed found to be
close to these expectation values for Ni(II) porphine. The situation is completely different
for cytochrome c. Figure 12 shows the depolarization ratio and the normalized scattering
intensity of the
ν4
-mode of horse heart ferrocytochrome c as a function of the excitation
wavenumber. While the value of 0.14 in the pre-resonance region of the B-band is close
to the D
4h
-value, it increases towards the Q-band region to rather high values of ca. 20.
Molecules 2022,27, 8751 20 of 34
In other words, the band becomes inverse-polarized between the respective Q
0
and Q
1
position, where the data exhibit local minima. The solid lines in the two figures result
from a self-consistent fit, which is described in detail in [
48
]. The depolarization dispersion
could only be reproduced by a vibronic coupling mixture of A
1g
,B
1g
and A
2g
symmetry.
Schweitzer-Stenner et al. interpreted the result as indicative of symmetry-lowering vibronic
perturbations of B
1g
and A
2g
symmetry. An analysis of the depolarization ratio and exci-
tation profiles of other Raman active modes led to a similar conclusion. Tthe validity of
these data was questioned by Hu et al. based on a comparison of the polarized Raman
spectra of isotopically substituted hemes in ferrocytochrome c [
40
]. The spectra were
measured at cryogenic temperatures. The authors claimed that the reported deviations
of depolarization ratios from the D
4h
expectation values solely reflect the overlap of the
bands originating from the macrocycle and peripheral substituents. In response to
Hu et al.,
Schweitzer-Stenner performed a more detailed spectral analysis of ferrocytochrome spectra,
which reproduced the previously reported depolarization dispersion of ν4[97].
Figure 12.
Depolarization ratio dispersion (
left
) and resonance excitation profiles (
right
) of the
oxidation marker A
1g
-type mode
ν4
of horse heart ferrocytochrome c. The solid lines in the figures
result from fits of a vibronic coupling model that considers symmetry-lowering perturbations and
multimode mixing. Details can be inferred from [
48
]. Resonance positions of Raman excitation are
indicated at the top of the figures with regard to the occupation of vibrational states. The figure was
reprinted with permission from reference [48], 1991, Wiley & Sons.
Contrary to the oxidized cytochrome c case, there cannot be any JT-induced distortion
in the reduced state owing to the
1
A
1g
-type electronic ground state. However, the occurrence
of B
1g
-deformation can easily be understood as being caused by the two axial ligands (vide
supra). While the depolarization ratio of
ν4
clearly reveals an antisymmetric contribution
to its Raman tensor, the deformations of A
2g
symmetry by a vibronic perturbation of the
same symmetry is unlikely to be dominant because of the comparatively high wavenumber
of the lowest A
2g
-mode (243 cm
−1
, compared with 168 cm
−1
(B
1g
) and 144 cm
−1
(B
2g
)
for Ni(II)-octaethylporphyrine). A much more sensible interpretation can be provided if
one invokes a combination of out-of-plane deformations based on the group theoretical
reasoning below. To this end, I rewrite Equation (21) as follows:
∂b
Hel
∂qk
=∂b
Hel,0
∂qk
+∑
Γ
∂VΓ
∂qk
=∂b
Hel,0
∂qk
+∑
l
∂2b
Hel,0
∂qk∂qΓ
l
·δQΓ
l+1
2∑
l
∑
m
∂3b
Hel,0
∂qk·∂qΓ
l·∂qΓ0
m
·δQΓ
l·δQΓ0
m(23)
where the second term in Equation (21) is replaced by a second-order Taylor expansion of
the vibronic coupling operator with respect to the normal coordinate deformations
δ
Q. The
second derivative of the expansion transforms in the manner of the product representation
Molecules 2022,27, 8751 21 of 34
Γk×Γl.
It accounts for the contribution of all the in-plane deformations to the vibronic
coupling operator. The third derivative transforms in the manner of the triple-product
representation
Γk×Γl×Γm0
.It can be used to describe the influence of the combination
of two out-of-plane deformations. As discussed in more detail below, the dominant out-of-
plane deformations of the heme group in cytochrome c are ruffling and saddling (Figure 5).
Since the corresponding symmetries are B
1u
and B
2u
, the product symmetry for an A
1g
-
mode would be A
2g
.The assignment of the antisymmetric contribution to the Raman tensor
of
ν4
to this combination of out-of-plane deformations is consistent with the occurrence of
a similarly large antisymmetric contribution to the
ν4
-mode of Ni-octaethyltetraphenyl-
porphyrin [
75
], which is predominantly saddled, with some minor contributions of ruffling
deformations [
98
] and with far less pronounced contributions in the case of other heme
proteins, such as myoglobin and hemoglobin [71].
As stated above, the heme of reduced cytochrome c cannot be subject to JT distortions
of the ground state. Since such a distortion is supposed to exist in ferricytochrome c, one
would expect a more pronounced deviation from the D
4h
-values of the depolarization ratio,
particularly with excitation wavelengths in the pre-resonance and resonance regions of the
B-band. Figure 13 exhibits the depolarization ratios of
ν4
(A
1g
, 0.125) and
ν10
(B
1g
, 0.75) of
oxidized horse heart cytochrome c as a function of the excitation wavenumber in the region
between Q and B. The data cover the resonance region of the respective Q
v
excitation (at
19,500 cm
−1
). With 442 nm (22,624 cm
−1
) excitation, the depolarization for
ν4
and
ν10
are
0.2 and 0.58, well above and below their respective D
4h
-values, respectively. As shown
by Alessi et al., these values are diagnostic of the substantial B
1g
-deformation of the heme
macrocycle, which by far exceeds the one in ferrocytochrome c [
51
]. Deformations of this
symmetry add B
1g
symmetry to the Raman tensor of
ν4
via the second term in the Taylor
expansion of Equation (23). For B
1g
-modes, however, the corresponding perturbation
term transforms in the manner of B
1g ×
B
1g
=A
1g
, which leads to a reduction in the
depolarization ratio from the D
4h
-value of 0.75. It should be noted that a similar dominant
B
1g
-deformation was obtained earlier for the low-spin ferric state of myoglobin cyanide,
which also has an 2Egground state, but not for the other myoglobin derivatives [65].
Figure 13.
Depolarization ratio dispersion of the oxidation marker
ν4
(
left
) and the spin marker
ν10
(
right
) of horse heart ferricytochrome c in the pre-resonance regions of the Q
v
- and B-bands obtained
at the indicated pH values. Reprinted with permission from [51], 2001, Wiley & sons.
Taken together, the combined analysis of (low-temperature) optical absorption, B-Band
circular dichroism and the resonance Raman data unambiguously shows that the heme
macrocycle of ferri- and ferrocytochrome c is subject to in-plane B
1g
(rhombic) and out-of-
plane B
1u
(ruffling) and B
2u
(saddling) deformations. In line with the results of EPR studies
(vide supra), the B
1g
deformation in the oxidized protein, which can be predominantly
ascribed to a rhombic distortion along the
ν24
coordinate, lifts the degeneracy of the d
π
orbitals, as well as that of the 3e
g
orbitals, of the heme macrocycle. The mixture of the two
Molecules 2022,27, 8751 22 of 34
orbitals confers spin density onto the heme macrocycle and produces an
2
E
g
ground state
of the heme group (macrocycle + iron). Additional symmetry-lowering deformations of the
heme group in both redox states are conferred onto the heme by electronic perturbations
produced by the charges on the two ligands and the two propionic acid charges Contrary
to the assumption of Manas et al., it is not certain that both propionic acid substituents are
protonated. The work of Bowler and coworkers [
99
] indicates that one of the two groups
has exceptionally high pK values.
While this chapter focused on the deformations produced by the in-plane components
of electronic and vibronic perturbations, out-of-plane deformations were briefly discussed
after they were inferred from the antisymmetric contributions to the Raman tensor of the
totally symmetric
ν4
-mode. They will be dealt with in greater detail in the subsequent
sections of this paper.
5. Out-of-Plane Deformations Inferred from the Crystal Structures of Cytochrome c
Th exploration and determination of the (mostly) out-of-plane deformations of metal
porphyrins in solution and in heme proteins have been pioneered by Jentzen and Shel-
nutt [
58
,
70
,
71
,
97
]. While work on model porphyrins indicated the functional relevance of
these deformations, it took some time and the work of Bren and coworkers to show that
they affect the redox potentials, electron transfer kinetics and ligand binding properties. In
this section, I review the results of the structural analysis of cytochrome c derivatives. The
work of Bren and coworkers is described in the subsequent section.
Equation (14) describes the total porphyrin deformation in which the contributions of
all the symmetries are added up. Generally, Jentzen et al. distinguished between deforma-
tions of different symmetries. They showed that a minimal basis set of low-wavenumber
modes is frequently sufficient to reproduce a certain type of deformation. Figure 14 shows
the results of their analysis of yeast ferrocytochrome c and some of its mutants. Note
that C102T yeast cytochrome c is generally considered as the wild type. The indicated
mutation just prevents the formation of protein dimers via the disulfide bridges between
C102 residues. Ruffling is the dominant deformation (0.8 Å), followed by a negative sad-
dling deformation (
−
0.3 Å). Waving is small but still significant (0.2 Å). Note that it is the
coexistence between ruffling and saddling that explains the antisymmetric contribution
to the Raman tensor of the
ν4
-mode [
48
,
51
]. The investigated mutants are all in the heme
pocket close to the M80 ligand, which can be expected to change the interactions between
the residues (Y67F, N52I), as well as the interactions between the water molecules in the
heme pocket [
100
]. However, in contrast to what one might expect, these substitutions have
very limited influences on the distribution of the out-of-plane deformations. This result
should be contrasted with the ones observed in the resonance Raman and low-temperature
absorption studies of some of these mutants, which reveal substantial changes in in-plane
deformations, particularly B
1g
deformations [
101
]. A different picture arises if one compares
the out-of-plane deformations of different mitochondrial cytochrome c proteins (Figure 14,
right column). Compared with horse heart cytochrome c, the reduced tuna cytochrome
exhibits less ruffling and more saddling. A comparison of the mitochondrial cytochromes
with the cytochrome c’ and cytochrome c
2
derivatives reveals major differences. For three
representatives of the former, particularly for cytochrome c’ of R. molischianum, Jentzen
et al. observed a dominance of saddling deformation. Among the three investigated forms
of cytochrome c
2
, only the heme group of R. rubrum depicts noticeable out-of-plane defor-
mations (mostly ruffling). The authors also investigated the crystal structures of oxidized
cytochrome c proteins and found them to be akin to the ones in the reduced state [
71
]. As
shown above, this is obviously not true for in-plane deformations, which affect the oxidized
protein more than the reduced one.
Molecules 2022,27, 8751 23 of 34
Figure 14.
Bar diagram representing the out-of-plane deformations of the heme group in yeast
ferrocytochrome and the indicated mutants. The diagram, at the top, exhibits the deformations of
the C102T mutant, which is generally considered as the wild type. This mutation solely serves the
purpose of avoiding disulfide bridging between proteins. The figure was taken from [
70
] and slightly
modified, with permission from Ref. [70], 1997, American Chemical Society.
Some light is shed on what might be deemed as the structural determinants of out-
of-plane deformations by the out-of-plane deformations of the four heme groups of cy-
tochrome c
3
from D. gigas,D. vulgaris,D. desulfuricans and Desulfomicrobium baculatum
(Figure 15). Hemes 1 and 2 are predominantly subject to ruffling. The contribution of
saddling varies between the proteins. Contributions from doming and waving are minor
but not insignificant. The picture is totally different for most of the investigated heme 3
and heme 4 chromophores, where saddling is the dominant out-of-plane deformation. An
exception from the rule is the heme 4 of Desulfomicrobium baculatum, which is predomi-
nantly ruffled. Jentzen et al. explained the latter finding based on differences between
the protein segments flanked by the two cysteins covalently linked to the heme group,
which is of the CxxC type for heme 4 but encompasses four residues in heme 4 in the other
investigated cytochrome c
3
species. However, the picture provided by the entire dataset is
equivocal in that hemes 1 and 3 both contain the classical CxxC segment of mitochondrial
cytochrome c but exhibit rather different out-of-plane deformations. The contributions
of the two thioether linkages and the amino acid residues between the two cysteins are
illuminated in context of NMR studies on the various cytochrome c derivatives, which are
described in the next section.
Molecules 2022,27, 8751 24 of 34
Figure 15.
Bar diagrams representing the indicated out-of-plane deformations of the four heme
groups of the indicated cytochrome c
3
proteins. References to the respective X-ray structures and the
papers in which they were published can be inferred from the caption of Figure 7in Jentzen et al. [
71
],
from which the figure was taken with permission, 1998, Elsevier.
Differences between cytochrome c and other heme proteins are worth mentioning.
Deoxyhemoglobin A is mostly subject to doming, which was originally described as iron
out-of-plane displacement [
71
]. This deformation is reduced in the oxygenated state. In
oxidized hemoglobin, the heme group is slightly distorted along nearly all the out-of-plane
deformations. The hemes in peroxidases, such as the classical horseradish peroxidase, are
dominantly saddled [71].
6. Out-of-Plane Deformations Probed by NMR Spectroscopy
Nowadays, NMR spectroscopy is generally employed using the two- and three-
dimensional versions to probe the structures of proteins in solution. With regard to proteins
such as cytochrome, NMR has been shown to compete with the canonical X-ray structure
analysis, which relies on the availability of protein crystals [
23
,
81
]. Here, I focus (mostly)
on the one-dimensional
1
H and
13
C NMR of heme groups in cytochrome c derivatives. The
applicability of these techniques results from modifications of the chemical shifts owing
to the presence of single-occupied molecular orbitals that Bren termed SOMO [
59
]. In the
framework of the classical four-orbital model, where the heme and metal orbitals are well
separated, the unpaired electron of a low-spin ferric heme resides solely in the d
π
or the d
xy
orbital. However, as described above, the mixing of 3e
g
and d
π
orbitals confers spin density
onto the porphyrin macrocycle in the electronic ground state. As shown below, ruffling
deformations provide another mode of porphyrin–metal orbital mixing that can modify
the spin density of the heme group.
Molecules 2022,27, 8751 25 of 34
As outlined by Bren [
59
], paramagnetic systems such as Fe
3+
-hemes give rise to a
so-called hyperfine shift:
δh f =δobs −δdia (24)
where
δobs
is the experimentally observed chemical shift of a nucleus interacting with an
unpaired electron, while
δdia
is the corresponding shift expected of the diamagnetic system.
The hyperfine shift is generally ascribed to three additive sources, i.e., the Fermi contact
shift, the sign of which reflects the z-component of the spin of the SOMO electron (positive
or negative), pseudocontact shift, which reflects paramagnetic anisotropy, and a ligand-
centered pseudocontact shift. The pseudocontact shift is a rather convoluted function of
the nuclear coordinates and the magnetic susceptibility tensor of the heme–ligand complex.
Details can be found in the very enlightening paper of Banci et al. [54].
Before I discuss the relationship between out-of-plane deformations and chemical
shifts, I would like to draw the reader’s attention to the influence of the axial ligands, in
particular methionine. As mentioned above, the orientation of both the methionine and
the imidazole side chains lowers the symmetry of the heme group by inducing in-plane
deformations. In the oxidized state, a JT distortion along the
ν24
-coordinate must be added
to the picture. The perturbation Hamiltonian in Equation (13) represents an interaction
that causes the mixing of the two iron-porphyrin states, which can be described as a linear
combination of the wavefunction in Equation (13):
ψ0
FeP,1 i=cosβ·dxz +3egx i+sinβ·dyz +egy i
ψ0
FeP,2 i=cosβ·dyz +3egyi − sinβ·dxz +egx i(25)
where
β
is the angle of rotation of the x,ycoordinate system, which diagonalizes the Hamil-
tonian in Equation (13). Equation (25) is equivalent to the one presented by
Banci et al.,
with a slightly different notation [
54
]. Karplus and Fraenkel showed that the rational angle
β
determines not only the energy splitting between the x- and y-polarized states (that
follows, of course, from elementary quantum mechanics) [
102
] but also the spin density
distribution of the heme carbons. As delineated by Banci et al., the hyperfine shifts of
protons and
13
Cs are different for oxidized horse heart cytochrome c in that the signals of
the methyl protons shift downfield, while those of carbon shift upfield. The temperature
dependence of the paramagnetic contribution to the chemical shift generally does not obey
Curie’s law in that it does not reach zero at an infinite temperature and exhibits positive as
well as negative slopes.
Before entering a discussion on how out-of-plane deformations change the chemical
shift of theme nuclei, the influence of the methionine ligand is briefly discussed. Figure 16
shows the downfield region of the
1
H NMR spectra of five different ferric cytochrome c
derivatives: Pa-cyt
551
(A), mitochrondrial horse heart cytochrome c (B), Hydrogenobacter
thermophilus (Ht) cyt
551
,Pa-cyt
551
in a solution containing 20% CD
3
OD (D), and Ht-cyt
551
,
also in a binary mixture of water and deuterated methanol. Here, I focus on a comparison of
spectra A–C, which differ in the sequence of methyl proton signals. All these signals exhibit
the same chemical shift in the absence of any electronic anisotropy. The differences between
the spectra of A and B were assigned to two different orientations of the methionine side
chain (termed A and B by Zhong et al. (Figure 17) [
61
]. The notation was later replaced
by R and S (vide supra)). The spectrum of Ht cyt
551
is diagnostic of a dynamic equilibrium
between R and S. Zhong et al. assigned the latter to the absence of hydrogen bonding
involving the methionine side chain and structural effects caused by the Q64 side chain.
Molecules 2022,27, 8751 26 of 34
Figure 16.
Downfield regions of the
1
H NMR spectra of the following oxidized cytochromes: (
A
): Pa
cyt
551
in aqueous solution, (
B
): horse heart cytochrome c, (
C
): Ht cyt c
552
in aqueous solution, (
D
): Pa
cyt
551
in a solution containing 20 vol% CD
3
OD, (
E
): Ht cyt
55s
in a solution containing 20 col% CD
3
OD.
Experimental details are provided in the paper of Zhong et al., from which the figure was taken [
61
]
(open access). The numbering 5,3 represents two overlapping signals.
Figure 17.
Left: (
a
) Temperature dependence of the three assigned
β
-pyrrole
13
C shifts of Pa cyt
551
WT
(black squares) compared with those of the two peaks with ambiguous assignments (blue diamonds,
red triangles). (
b
) Temperature dependence of the seven assigned
α
-pyrrole
13
C shifts of Pa cyt
551
WT
(black circles) compared with those of the two peaks with ambiguous assignments (blue diamonds,
red triangles). Right: Changes in the indicated chemical shifts caused by the indicated mutations
of Ht cyt
552
, plotted as a function of the axial energy terms determined by EPR experiments. (
a
)
13
C
shifts of pyrrole carbons. The HH shift of the H17 side chain is shown for comparison. (
b
)
13
C shifts
of the methyl and meso carbons, (
c
)
1
H shifts of meso and methyl groups compared with the shift of
CH3end group of M71. Reprinted with permission from [103], 2013, American Chemical Society.
Molecules 2022,27, 8751 27 of 34
The influence of heme ruffling on heme group chemical shifts was investigated by
Kleingardner et al. by employing the mutants of PA cyt
551
and Ht cyt
551
[
103
]. Regarding the
former, they measured the NMR spectra of an F7A mutant whose mutations are known to
increase the ruffling deformation without significantly affecting the deformation along the
other out-of-plane coordinates. For Ht cyt
551
, they investigated the mutants M13V, K22M
and the respective double mutant. All these mutations were shown to increase ruffling.
Figure 17 (left) shows the Curie plots for the paramagnetic shifts of the isotopically labeled
(
13
C)
α
- and
β
-carbons of wild-type PA cyt
551
.Most of the plots approach values above zero for
T ->
∞
, which is indicative of hyper-Curie behavior. It reflects the fact that higher-lying excited
electronic states (i.e., (dxy)1(dπ−eg)4) can become populated at room temperature.
A comparison of the investigated wild types and mutants revealed the following
picture. In the PA cyt
551
F7A mutant (increased ruffling), the average heme methyl shifts
(H and
13
C) were found to increase, while the shifts of the pyrrole carbons decreased. In Ht
cyt
551
, the same mutation decreased the ruffling. As a consequence, the respective chemical
shift exhibited the opposite behavior.
Figure 17 (right) shows the plots of the average
13
C and H shifts of the Ht cyt
551
derivatives as a function of the decreasing axial energy term
∆
/
λ
, inferred from the EPR
experiments.
∆
denotes the energy splitting between the t
2g
- and e
g
-orbitals caused by
the lowering of the symmetry of the metal’s ligand field from octahedral to tetragonal,
whereas
λ
denotes the (thus far not explicitly considered) spin–orbit coupling energy.
Can et al.
deduced from EPR experiments on the same protein that an increase in ruffling
results in a decrease in
∆
[
84
]. Hence, the abscissa in Figure 17 can be read as representing
heme ruffling. The data depicted therein clearly show how the chemical shifts of low-spin
oxidized hemes can be utilized to probe heme ruffling. Overall, the data demonstrate that
ruffling significantly affects the unpaired spin distribution of the macrocycle, which is an
indicator of mixing between heme and iron orbitals.
Details regarding the ways in which ruffling changes the spin delocalization over
pyrrole carbons, methyl carbons and methyl protons can be inferred from the very thorough
study of Kleingardner et al. [
101
]. The authors also provided a detailed deconstruction of
paramagnetic shifts into individual contributions. Here, I focus on how ruffling changes
the mixing between heme iron and porphyrin orbitals. In the chosen D
4h
reference system,
ruffling transforms as B
1u
.Thus, on the orbital level, ruffling can mix the d
xy
-orbital (B
1g
)
of the metal with the 3a
2u
-orbital of the macrocycle, since A
2u ×
B
1g
=B
1u
. Taking this
orbital mixing into account, one must augment the set of electronic states described in
Equation (5)
. Here, one must take into account the fact that, contrary to the mixing of the
d
π
- and 3a
2u
-orbitals, the mixing of d
xy
and 3a
2u
occurs in the lower D
2d
symmetry, where
both orbitals exhibit D2d symmetry and transform in the manner of B2.
|g0xi=|ψ1xi=2(3ex−dxz )4,(dxz +3ex)3,(3b2−dxy )2,(dxy +3b2)2i
g0yi=ψ1yi=2(3ey−dyz )4,(dyz +3ey)3,(3b2−dxy )2,(dxy +3b2)2i
|g1i=|ψ2i=2(3ey−dyz)4,(dπ+3e)4,(3b2−dxy )2,(dxy +3b2)1i
|g2i=|ψ3i=2(3e−dπ)4,(dπ+3e)4,(3b2−dxy )1,(dxy +3b2)2i
|g3xi=|ψ4xi=2(3ex−dxz )3,(dxz +ex)4,(3b2−dxy )2,(dxy +3b2)2i
g3yi=ψ4yi=2(3egy −dyz )3,(dyz +ey)4,(3b2−dxy)2,(dxy +3b2)2i
.
Q0
xi=sinν·2(3b2−dxy )1, 4e1
x,(dπ+3e)3i+cosν·3b1
1, 4e1
y,(dπ+3e)3i
Q0
yi=cosν·2(3b2−dxy )1, 4e1
y,(dπ+3e)3i − sinν·3b1
1, 4e1
x,(dπ+3e)3i
B0
xi=cosν·2(3b2−dxy)1, 4e1
x,(dπ+3e)3i − sinν·3b1
1, 4e1
y,(dπ+3e)3i
B0
yi=sinν·2(3b2−dxy)1, 4e1
y,(dπ+3e)3i+cosν·3b1
1, 4e1
x,(dπ+3e)3i
(26)
Molecules 2022,27, 8751 28 of 34
Note that, for the sake of brevity, only the unpaired orbitals are listed in the description
of the Q
0
- and B
0
-states. The admixture of d
xy
- into b
2
-orbitals lowers the energy of the
ground state, while states with (d
xy
+b
2
) orbitals move closer to (d
π
+3e). This makes
the thermal occupation of the state |g
1
>more likely. The lowering of the ground-state
energy leads to the experimentally observed redshift of the optical spectrum of the ruffled
metalporphyrins [73].
While we are focused on the effect of ruffling, here, it should be noted that saddling
(B
2u
) perturbations can mix d
xy
- with 3a
1u
(B
1
in D
2d
)-orbitals, thus leading to the further
destabilization of the former. Doming has A
2u
symmetry and can therefore mix
dz2
- and
3a
2u
-orbitals (B
2
in D
2d
). This is irrelevant for low-spin ferric complexes, but it becomes
relevant in all high-spin systems, irrespective of whether they are in the ferric or ferrous state.
How do all these perturbations affect the redox potential and the electron transfer
properties of cytochrome c derivatives? I start with the discussion of heme ruffling. The
respective deformation lowers the symmetry of the macrocycle from D
4h
to D
2d.
For
ferricytochrome c, the ground state |g
0
> exhibits
2
E-symmetry. The symmetry of the first
excited state |g
1
> becomes
2
A
2
, which is lower in energy than it is in D
4h
, since ruffling
destabilizes d
xy
, so that less energy is required to move an electron to d
π
. I ignore quartet
states in this discussion. In the case of ferrocytochrome c, the ground state symmetry is
1
A
1g
, which becomes
1
A in D
2d
, since there is no hole through which the symmetry can be
affected. The first excited state which involves an electron transfer from
dπ
to
dz2
transforms
in the manner
1
E
g
in D
4h
and Ein D
2d.
Electron transfer can be expected to involve an
electron that occupies the higher-lying d
π
-orbital (most likely d
yz
). Hence, from a group
theoretical point of view, ruffling should not affect the ionization energy of ferrocytochrome
c in the zeroth order, since neither ruffling nor saddling can mix d
π
with the occupied
porphyrin orbitals in a D
4h
reference frame. However, the situation is different in D
2d
,
where the d
π
-orbitals and the third-highest porphyrin orbitals transform as E. Since the
direct product of the two orbitals can be written as A
1
+A
2
+B
1
+B
2
, practically any
deformation with a one-dimensional representation can mix the two orbitals. Within the
D
4h
reference system, such a first-order effect can be ascribed to the matrix elements of
vibronic coupling operators of the type
∂b
VΓ/∂qΓ0
k
. Any combination of ungerade electronic
perturbations and vibrational modes will allow for the mixing of E
g
orbitals. Taken together,
this group theoretical reasoning suggests that ruffling or any other out-of-plane deformation
destabilizes the reduced state, because the amount of energy gained by filling the hole
in the states |g
0
>and |g
1
>is decreased more than the energy required to remove an
electron from the ground state of the reduced heme. Therefore, the reduction potential
decreases, which is in line with experimental observations of Bren and coworkers [
86
,
103
].
DFT calculations backed by NMR results arrived at a similar conclusion in that their results
suggest a destabilization of all ‘t
2g
’-orbitals by ruffling, though to a different extent [
56
]. As
one would expect from the above reasoning, the effect is dominant for dxy.
As outlined above, electronic B
1g
perturbation causes a split of the (d
xz
+3e
gx
)- and
(d
yz
+3e
gy
)-orbitals and, thus, of the E
g
ground state of the oxidized protein. If one chooses
D
2d
as the reference system (i.e., taking into account the influence of ruffling), the two
orbitals are denoted as (d
xz
+3e
x
) and (d
yz
+3e
y
). Together, they exhibit Esymmetry. The
electronic perturbation now exhibits B
1
symmetry and reduces the symmetry of the heme
from D
2d
to D
2
. In this new point group, the above orbitals should be written as (d
xz
+3b
2
)
and (d
yz
+3b
3
). This splitting can be substantial. In horse heart cytochrome c, for instance,
it amounts to nearly 60% of the axial field splitting (ca. 440 cm
−1
). Thus, the higher-lying
state (generally, the (dyz +3b3)-containing |g0y > state) lies 220 cm−1above the level of the
unperturbed D
4h
symmetry. The first excited electronic state |g
1
> exhibits B
2
symmetry in
D
2d
. Rhombic perturbation cannot mix |g
0
> and |g
1
>. In the reduced state, the ground
state is a singlet of A
1
symmetry, while the first excited state exhibits Esymmetry (vide
supra), which splits into B
2
and B
3
in D
2
. Any occupation of this state at room temperature
should be very low. As a consequence, neither the electronic B
1
nor B
2
perturbations of
Molecules 2022,27, 8751 29 of 34
a heme in D
2d
symmetry affects the ground state of the reduced heme. Altogether, these
perturbations thus destabilize the oxidized state, thus increasing the redox potential.
Vibronic perturbation can affect the electronic states differently. As one can read from
Equation (17), vibronic perturbation along a normal coordinate q
k
can practically affect all
the electronic states in the presence of an electronic perturbation of the same symmetry,
since the respective operator transforms in the manner of A
1g
in D
4h
. Even though the
respective matrix elements can be on-diagonal in the pure electronic basis set, they are
off-diagonal in a vibronic basis, since the operator
∂b
VΓ/∂qΓ0
k
has to be multiplied with
the operator
b
qΓ0
k
, which reflects the mixing of the vibrational states (which can involve
several states for normal modes of low wavenumbers). Hence, the energy contribution is
second-order. Since the matrix elements of
∂b
VΓ/∂qΓ0
k·b
qΓ0
k
can be in the range of, or even
exceed, the vibrational wavenumbers, these perturbations cannot be treated with Rayleigh–
Schrödinger perturbation theory. Obviously, these perturbations lead to the breakdown of
the Born–Oppenheimer approximation. The most prominent vibronic perturbation that
affects the ground state is that of B
1
symmetry, and this causes a JT distortion of the ground
state of ferricytochrome as long its symmetry is
2
E. As the above electronic perturbation is
of the same symmetry, it adds to the splitting of the ground state and, thus, a destabilization
of the oxidized state, thus increasing the redox potential.
I complement this section by briefly mentioning that the results of the combined
NMR and DFT studies suggest that ruffling deformations decrease the electronic coupling
between cytochrome c and its redox partners [
59
]. As one expects from the canonical
Marcus theory, this reduces the rate of the electron transfer. The reduction in the coupling
energy results from a decrease in the unpaired electron spin density and, thus, a higher
delocalization of the electron density of the iron atom. This is an interesting result in that it
suggests that the mixing of d
π
with 3e
g
is, to some extent, neutralized by the mixing of d
xy
with 3a2u.
7. Summary and Outlook
It was the goal of this review article to provide an overview of the protein- and
ligand-induced perturbations that affect the heme group of cytochrome c type proteins.
For a long period of time, the electronic structures of the heme macrocycle and of the
central iron atom were discussed independently. The four-orbital model of Gouterman
was based on optical absorption data, while the heme iron was explored through EPR
and Mössbauer spectroscopy. While the very early EPR studies of cytochrome c and other
heme proteins revealed that the ligand field of the heme iron has a rhombic symmetry
absorption, the resonance Raman data were generally interpreted within the framework
of a heme macrocycle exhibiting D
4h
symmetry, even though the depolarization ratio
dispersions clearly showed that this notion is incorrect. As a matter of fact, the invalidity of
the high-symmetry approach had already become apparent from the NMR experiments
of Wüthrich and colleagues, which revealed how the orientation of the methionine ligand
affects the spin distribution of the heme macrocycle. The more recent works of Walker, Bren
and coworkers must be credited not only for arriving at a more comprehensive picture
of the electronic structure of the cytochrome derivatives but also for demonstrating that
symmetry-lowering deformations are biologically relevant.
While the work of Bren and coworkers focused on out-of-plane deformations, which
were well characterized on a quantitative level by the pioneering work of Jentzen and
Shelnutt, this review argued that in-plane deformations deserve some consideration as well.
This article invoked group theoretical arguments to provide a comprehensive understand-
ing of the electronic (vibronic) structure of the heme group in cytochrome c derivatives.
An emphasis was placed on elucidating the relationships between electronic-perturbing
potentials and the induced heme distortions.
Finally, I would like to briefly refer to the paper of Galianto et al. that has not
been discussed thus far [
104
]. These authors made use of nuclear resonance vibrational
spectroscopy to explore vibrational spectra involving the motions of the heme iron, which
Molecules 2022,27, 8751 30 of 34
elude traditional spectroscopy methods, such as Raman and IR. The main result of this
study was that the normal modes are actually not restricted to the heme group but involve,
in particular, vibrations of the CxxCH linker and the iron ligands. These vibrations cover the
region between 250 and 500 cm
−1.
It is very likely that the vibrational dynamics revealed
by this study are of great relevance, helping to foster a thorough understanding of the
respective electron transfer processes.
This article focused on cytochrome c, but various studies of other heme proteins
revealed the influences of in-plane and out-of-plane deformations on, e.g., peroxidase
activity and ligand binding. However, a full and comprehensive account of the ways in
which heme deformations tune biological activities still has yet to be developed.
Funding:
The research of my own research group at Drexel University was supported by a grant
from the National Science Foundation (MCB-0328749).
Data Availability Statement: Not applicable.
Conflicts of Interest: The author declares no conflict of interest.
References
1.
Antonini, E.; Brunori, M. Hemoglobin and Myoglobin in Their Reactions with Ligands. In Frontiers of Biology; Elsevier: Amsterdam,
The Netherlands, 1971.
2.
Perutz, M.F. Mechanisms of Cooperativity and Allosteric Regulation in Proteins. Q. Rev. Biophys.
1989
,22, 139–237. [CrossRef]
[PubMed]
3.
Yoshizato, K.; Thuy, L.T.T.; Shiota, G.; Kawada, N. Discovery of Cytoglobin and Its Roles in Physiology and Pathology of Hepatic
Stellate Cells. Proc. Japan Acad. Ser. B Phys. Biol. Sci. 2016,92, 77–97. [CrossRef] [PubMed]
4.
Tejero, J.; Kapralov, A.A.; Baumgartner, M.P.; Sparacino-Watkins, C.E.; Anthonymutu, T.S.; Vlasova, I.I.; Camacho, C.J.; Gladwin,
M.T.; Bayir, H.; Kagan, V.E. Peroxidase Activation of Cytoglobin by Anionic Phospholipids: Mechanisms and Consequences.
Biochim. Biophys. Acta-Mol. Cell Biol. Lipids 2016,1861, 391–401. [CrossRef] [PubMed]
5.
Ascenzi, P.; di Masi, A.; Leboffe, L.; Fiocchetti, M.; Nuzzo, M.T.; Brunori, M.; Marino, M. Neuroglobin: From Structure to Function
in Health and Disease. Mol. Aspects Med. 2016,52, 1–48. [CrossRef] [PubMed]
6.
Trumpower, B.L.; Gennis, R.B. Energy Transduction by Cytochrome Complexes in Mitochondrial and Bacterial Respiration: The
Enzymology of Coupling Electron Transfer Reactions to Transmembrane Proton Translocation. Annu. Rev. Biochem.
1994
,63,
675–716. [CrossRef]
7.
Therien, M.J.; Bowler, B.E.; Selman, M.A.; Gray, H.B.; Chang, I.-J.; Winkler, J.R. Long-Range Electron Transfer in Heme Proteins.
Adv. Chem. 1991,228, 191–199. [CrossRef]
8.
Michel, H.; Behr, J.; Harrenga, A.; Kannt, A. Cytochrome c Oxidase. Structure and Spectroscopy. Annu. Rev. Biophys. Biomol.
Struct. 1998,27, 329–356. [CrossRef] [PubMed]
9.
Deisenhofer, J.; Michel, H. The Photosynthetic Reaction Centre from the Purple Bacterium Rhodopseudomonas Viridis. Biosci.
Rep. 1989,9, 383–419. [CrossRef]
10.
Poulos, T.L. Peroxidase and Cytochrome P450 Structures. In Porphyrin Handbook; Kadish, K.M., Smith, K.M., Guilard, R.G., Eds.;
Academic Press: San Diego, CA, USA, 2000; Volume 4, pp. 189–218. ISBN 0123932009.
11.
Gajhede, M.; Schuller, D.; Henricksen, A.; Smith, A.; Poulos, T. Crystal Structure Determination of Classical Horseradish
Peroxidase at 2.15A Resolution. Nat. Struct. Biol. 1997,4, 1032–1039. [CrossRef]
12.
Gelin, B.R.; Lee, A.W.M.; Karplus, M. Hemoglobin Tertiary Structural Change on Ligand Binding Its Role in the Co-Operative
Mechanism. J. Mol. Biol. 1983,171, 489–559. [CrossRef]
13.
Alvarez-Paggi, D.; Hannibal, L.; Castro, M.A.; Oviedo-Rouco, S.; Demicheli, V.; Tórtora, V.; Tomasina, F.; Radi, R.; Murgida, D.H.
Multifunctional Cytochrome c: Learning New Tricks from an Old Dog. Chem. Rev. 2017,117, 13382–13460. [CrossRef]
14.
Hannibal, L.; Tomasina, F.; Capdevila, D.A.; Demicheli, V.; Tórtora, V.; Alvarez-Paggi, D.; Jemmerson, R.; Murgida, D.H.; Radi, R.
Alternative Conformations of Cytochrome c: Structure, Function, and Detection. Biochemistry 2016,55, 407–428. [CrossRef]
15.
Bowman, S.E.J.; Bren, K.L. The Chemistry and Biochemistry of Heme c: Functional Bases for Covalent Attachment. Nat. Prod.
Rep. 2008,25, 1118–1130. [CrossRef]
16.
Schweitzer-Stenner, R. Allosteric Linkage-Induced Distortions of the Prosthetic Group in Haem Proteins as Derived by the
Theoretical Interpretation of the Depolarization Ratio in Resonance Raman Scattering. Q. Rev. Biophys.
1989
,22, 381–479.
[CrossRef]
17.
Schweitzer-Stenner, R.; Wedekind, D.; Dreybrodt, W. Detection of the Heme Perturbations Caused by the Quaternary R—-T
Transition in Oxyhemoglobin Trout IV by Resonance Raman Scattering. Biophys. J. 1989,55, 703–712. [CrossRef]
18. Friedman, J.M. Structure, Dynamics, and Reactivity in Hemoglobin. Science 1985,228, 1273–1280. [CrossRef] [PubMed]
19.
Eaton, W.A.; Henry, E.R.; Hofrichter, J.; Mozzarelli, A. Is Cooperative Oxygen Binding by Hemoglobin Really Understood? Rend.
Lincei 2006,17, 147–162. [CrossRef]
Molecules 2022,27, 8751 31 of 34
20.
Schweitzer-Stenner, R.; Wedekind, D.; Dreybrodt, W. The Influence of Structural Variations in the F- andFG-Helix of the
β
-Subunit
Modified OxyHb-NES on the Heme Structure Detected by Resonance Raman Spectroscopy. Eur. Biophys. J.
1989
,17, 87–100.
[CrossRef] [PubMed]
21.
Szabo, A.; Karplus, M. A Mathematical Model for Structure-Function Relationships in Hemoglobin. Biochem. Biophys. Res.
Commun. 1972,46, 855–860. [CrossRef] [PubMed]
22.
Herzfeld, J.; Stanley, H.E. A General Approach to Co-Operativity and Its Application to the Oxygen Equilibrium of Hemoglobin
and Its Effectors. J. Mol. Biol. 1974,82, 231–265. [CrossRef] [PubMed]
23.
Banci, L.; Bertini, I.; Huber, J.G.; Spyroulias, G.A.; Turano, P. Solution Structure of Reduced Horse Heart Cytochrome C. J. Biol.
Inorg. Chem. 1999,4, 21–31. [CrossRef] [PubMed]
24.
Banci, L.; Bertini, I.; Reddig, T.; Turano, P. Monitoring the Conformational Flexibility of Cytochrome c at Low Ionic Strength by
1H-NMR Spectroscopy. Eur. J. Biochem. 1998,256, 271–278. [CrossRef]
25.
Louie, G.V.; Brayer, G.D. High-Resolution Refinement of Yeast Iso-1-Cytochrome c and Comparisons with Other Eukaryotic
Cytochromes C. J. Mol. Biol. 1990,214, 527–555. [CrossRef]
26.
Berghuis, A.M.; Brayer, G.D. Oxidation State-Dependent Conformational Changes in Cytochrome C. J. Mol. Biol.
1992
,223,
959–976. [CrossRef]
27.
Bushnell, G.W.; Louie, G.V.; Brayer, G.D. High-Resolution Three-Dimensional Structure of Horse Heart Cytochrome C. J. Mol.
Biol. 1990,214, 585–595. [CrossRef] [PubMed]
28.
Battistuzzi, G.; Borsari, M.; Cowan, J.A.; Ranieri, A.; Sola, M. Control of Cytochrome c Redox Potential: Axial Ligation and Protein
Environment Effects. J. Am. Chem. Soc. 2002,124, 5315–5324. [CrossRef]
29.
De Biase, P.M.; Paggi, D.A.; Doctorovich, F.; Hildebrandt, P.; Estrin, D.A.; Murgida, D.H.; Marti, M.A. Molecular Basis for the
Electric Field Modulation of Cytochrome c Structure and Function. J. Am. Chem. Soc.
2009
,131, 16248–16256. [CrossRef] [PubMed]
30.
Hong, Y.; Muenzner, J.; Grimm, S.K.; Pletneva, E.V. Origin of the Conformational Heterogeneity of Cardiolipin-Bound Cytochrome
C. J. Am. Chem. Soc. 2012,134, 18713–18723. [CrossRef]
31.
Pandiscia, L.A.; Schweitzer-Stenner, R. Coexistence of Native-Like and Non-Native Cytochrome c on Anionic Lipsomes with
Different Cardiolipin Content. J. Phys. Chem. B 2015,119, 12846–12859. [CrossRef]
32.
Milorey, B.; Schweitzer-Stenner, R.; Kurbaj, R.; Malyshka, D. PH-Induced Switch between Different Modes of Cytochrome c
Binding to Cardiolipin-Containing Liposomes. ACS Omega 2019,4, 1386–1400. [CrossRef] [PubMed]
33.
Sinibaldi, F.; Milazzo, L.; Howes, B.D.; Piro, M.C.; Fiorucci, L.; Polticelli, F.; Ascenzi, P.; Coletta, M.; Smulevich, G.; Santucci,
R. The Key Role Played by Charge in the Interaction of Cytochrome c with Cardiolipin. J. Biol. Inorg. Chem.
2017
,22, 19–29.
[CrossRef] [PubMed]
34.
Hanske, J.; Toffey, J.R.; Morenz, A.M.; Bonilla, A.J.; Schiavoni, K.H.; Pletneva, E.V. Conformational Properties of Cardiolipin-Bound
Cytochrome C. Proc. Natl. Acad. Sci. USA 2012,109, 125–130. [CrossRef] [PubMed]
35.
Kagan, V.E.; Tyurin, V.A.; Jiang, J.; Tyurina, Y.Y.; Ritov, V.B.; Amoscato, A.A.; Osipov, A.N.; Belikova, N.A.; Kapralov, A.A.; Kini,
V.; et al. Cytochrome C Acts As A Cardiolipin Oxygenase Required for Release of Proapoptotic Factors. Nat. Chem. Biol.
2005
,1,
223–232. [CrossRef] [PubMed]
36.
Hildebrandt, P.; Vanhecke, F.; Buse, G.; Soulimane, T.; Mauk, A.G. Resonance Raman Study of the Interactions between
Cytochrome c Variants and Cytochrome c Oxidase. Biochemistry 1993,32, 10912–10922. [CrossRef] [PubMed]
37.
Weber, C.; Michel, B.; Bosshard, H.R. Spectroscopic Analysis of the Cytochrome c Oxidase-Cytochrome c Complex: Circular
Dichroism and Magnetic Circular Dichroism Measurements Reveal Change of Cytochrome c Heme Geometry Imposed by
Complex Formation. Proc. Natl. Acad. Sci. USA 1987,84, 6687–6691. [CrossRef] [PubMed]
38.
Spiro, T.G. Resonance Raman Spectroscopy as a Probe of Heme Protein Structure and Dynamics. Adv. Protein Chem.
1985
,37,
111–159. [CrossRef]
39.
Hu, S.; Smith, K.M.; Spiro, T.G. Assignment of Protoheme Resonance Raman Spectrum by Heme Labeling in Myoglobin. J. Am.
Chem. Soc. 1996,118, 12638–12646. [CrossRef]
40.
Hu, S.; Spiro, T.G.; Morris, I.K.; Singh, J.P.; Smith, K.M. Complete Assignment of Cytochrome c Resonance Raman Spectra via
Enzymatic Reconstitution with Isotopically Labeled Hemes. J. Am. Chem. Soc. 1993,115, 12446–12458. [CrossRef]
41.
Perutz, M.F.; Ladner, J.E.; Simon, S.R.; Ho, C. Influence of Globin Structure on the State of the Heme. I. Human Deoxyhemoglobin.
Biochemistry 1974,13, 2163–2173. [CrossRef]
42. Perutz, M.F. Stereochemistry of Cooperative Effects in Haemoglobin. Nature 1970,228, 726–734. [CrossRef]
43. Shaanan, B. Structure of Human Oxyhaemoglobin at 2·1resolution. J. Mol. Biol. 1983,171, 31–59. [CrossRef]
44.
Salmeen, I.; Palmer, G. Electron Paramagnetic Resonance of Beef-Heart Ferricytochrome C. J. Chem. Phys.
1968
,48, 2049–2052.
[CrossRef]
45.
Senn, H.; Billeter, M.; Wüthrich, K. The Spatial Structure of the Axially Bound Methionine in Solution Conformations of Horse
Ferrocytochrome c and Pseudomonas Aeruginosa Ferrocytochrome c 551 by 1H NMR. Eur. Biophys. J.
1984
,11, 3–15. [CrossRef]
[PubMed]
46.
Brautigan, D.L.; Feinberg, B.A.; Hoffman, B.M.; Margoliash, E.; Peisach, J.; Blumberg, W.E.; Peisach, J.; Blumberg, W.E. Multiple
Low Spin Forms of the Cytochrome c Ferrihemochrome. J. Biol. Chem. 1977,252, 574–582. [CrossRef]
Molecules 2022,27, 8751 32 of 34
47.
Zoppellaro, G.; Harbitz, E.; Kaur, R.; Ensign, A.A.; Bren, K.L.; Andersson, K.K. Modulation of the Ligand-Field Anisotropy in a
Series of Ferric Low-Spin Cytochrome c Mutants Derivd from Pseudomonas Aeruginosa Cytochrome c-551 and Nitrosomonas
Europaea Cytochrome c -552: A Nuclear Magnetic Resonance and Electron Paramagnetic Resonance. J. Am. Chem. Soc.
2008
,130,
15348–15360. [CrossRef]
48.
Schweitzer-Stenner, R.; Bobinger, U.; Dreybrodt, W. Multimode Analysis of Depolarization Ratio Dispersion and Excitation
Profiles of Seven Raman Fundamentals from the Haeme Group in Ferrocytochrome C. J. Raman Spectrosc.
1991
,22, 65–78.
[CrossRef]
49.
Dragomir, I.; Hagarman, A.; Wallace, C.; Schweitzer-Stenner, R. Optical Band Splitting and Electronic Perturbations of the Heme
Chromophore in Cytochrome c at Room Temperature Probed by Visible Electronic Circular Dichroism Spectroscopy. Biophys. J.
2007,92, 989–998. [CrossRef]
50.
Schweitzer-Stenner, R. Internal Electric Field in Cytochrome C Explored by Visible Electronic Circular Dichroism Spectroscopy. J.
Phys. Chem. B 2008,112, 10358–10366. [CrossRef] [PubMed]
51.
Alessi, M.; Hagarman, A.M.; Soffer, J.B.; Schweitzer-Stenner, R. In-Plane Deformations of the Heme Group in Native and
Nonnative Oxidized Cytochrome c Probed by Resonance Raman Dispersion Spectroscopy. J. Raman Spectrosc.
2011
,42, 917–925.
[CrossRef]
52.
Stavrov, S.S. The Effect of Iron Displacement out of the Porphyrin Plane on the Resonance Raman Spectra of Heme Proteins and
Iron Porphyrins. Biophys. J. 1993,65, 1942–1950. [CrossRef] [PubMed]
53.
Walker, F.A. Magnetic Spectroscopic (EPR, ESEEM, Mössbauer, MCD and NMR) Studies of Low-Spin Ferriheme Centers and
Their Corresponding Heme Proteins. Coord. Chem. Rev. 1999,185, 471–534. [CrossRef]
54.
Banci, L.; Bertini, I.; Luchinat, C.; Pierattelli, R.; Shokhirev, N.V.; Walker, F.A. Analysis of the Temperature Dependence of the 1H
and 13C Isotropic Shifts of Horse Heart Ferricytochrome C: Explanation of Curie and Anti-Curie Temperature Dependence and
Nonlinear Pseudocontact Shifts in a Common Two-Level Framework. J. Am. Chem. Soc. 1998,120, 8472–8479. [CrossRef]
55.
Michel, L.V.; Ye, T.; Bowman, S.E.J.; Levin, B.D.; Hahn, M.A.; Russell, B.S.; Elliott, S.J.; Bren, K.L. Heme Attachment Motif Mobility
Tunes Cytochrome c Redox Potential. Biochemistry 2007,46, 11753–11760. [CrossRef] [PubMed]
56.
Liptak, M.D.; Wen, X.; Bren, K.L. NMR and DFT Investigation of Heme Ruffling: Functional Implications for Cytochrome C. J.
Am. Chem. Soc. 2010,132, 9753–9763. [CrossRef] [PubMed]
57. Theorell, H.; Åkesson, Å. Studies on Cytochrome c. III. Titration Curves. J. Am. Chem. Soc. 1941,63, 1818–1820. [CrossRef]
58.
Shelnutt, J.A.; Song, X.Z.; Ma, J.G.; Jia, S.L.; Jentzen, W.; Medforth, C.J. Nonplanar Porphyrins and Their Significance in Proteins.
Chem. Soc. Rev. 1998,27, 31–41. [CrossRef]
59.
Bren, K.L. Going with the Electron Flow: Heme Electronic Structure and Electron Transfer in Cytochrome C. Isr. J. Chem.
2016
,56,
693–704. [CrossRef]
60.
Cheng, R.J.; Chen, P.Y.; Lovell, T.; Liu, T.; Noodleman, L.; Case, D.A. Symmetry and Bonding in Metalloporphyrins. A Modern
Implementation for the Bonding Analyses of Five- and Six-Coordinate High-Spin Iron(III)-Porphyrin Complexes through Density
Functional Calculation and NMR Spectroscopy. J. Am. Chem. Soc. 2003,125, 6774–6783. [CrossRef]
61.
Zhong, L.; Wen, X.; Rabinowitz, T.M.; Russell, B.S.; Karan, E.F.; Bren, K.L. Heme Axial Methionine Fluxionality in Hydrogenobacter
thermophilus Cytochrome C552.Proc. Natl. Acad. Sci. USA 2004,101, 8637–8642. [CrossRef]
62.
Gouterman, M. Study of the Effects of Substitution on the Absorption Spectra of Porphin. J. Chem. Phys.
1959
,30, 1139–1161.
[CrossRef]
63.
Schweitzer-Stenner, R. Polarized Resonance Raman Dispersion Spectroscopy on Metalporphyrins. J. Porphyr. Phthalocyanines
2001,5, 198–224. [CrossRef]
64.
Stallard, B.R.; Callis, P.R.; Champion, P.M.; Albrecht, A.C. Application of the Transform Theory to Resonance Raman Excitation
Profiles in the Soret Region of Cytochrome-C. J. Chem. Phys. 1984,80, 70–82. [CrossRef]
65.
Schweitzer-Stenner, R.; Cupane, A.; Leone, M.; Lemke, C.; Schott, J.; Dreybrodt, W. Anharmonic Protein Motions and Heme
Deformations in Myoglobin Cyanide Probed by Absorption and Resonance Raman Spectroscopy. J. Phys. Chem. B
2000
,104,
4754–4764. [CrossRef]
66.
Schweitzer-Stenner, R.; Soffer, J.B. Optical Spectroscopy. In Comprehensive Biophysics; Egelman, E.H., Ed.; Elsevier: Amsterdam,
The Netherlands, 2012; Volume 1, ISBN 9780080957180.
67.
Shelnutt, J.A. The Raman Excitation Spectra and Absorption Spectrum of a Metalloporphyrin in an Environment of Low Symmetry.
J. Chem. Phys. 1980,72, 3948–3958. [CrossRef]
68.
Zgierski, M.Z.; Pawlikowski, M. Depolarization Dispersion Curves of Resonance Raman Fundamentals of Metalloporphyrins
and Metallophthalocyanines Subject to Asymmetric Perturbations. Chem. Phys. 1982,65, 335–367. [CrossRef]
69.
Unger, E.; Bobinger, U.; Dreybrodt, W.; Schweitzer-Stenner, R. Vibronic Coupling in Ni(II) Porphine Derived from Resonant
Raman Excitation Profiles. J. Phys. Chem. 1993,97, 9956–9968. [CrossRef]
70.
Jentzen, W.; Unger, E.; Song, X.Z.; Jia, S.L.; Turowska-Tyrk, I.; Schweitzer-Stenner, R.; Dreybrodt, W.; Scheldt, W.R.; Shelnutt,
J.A. Planar and Nonplanar Conformations of (Meso-Tetraphenylporphinato)Nickel(II) in Solution as Inferred from Solution and
Solid-State Raman Spectroscopy. J. Phys. Chem. A 1997,101, 5789–5798. [CrossRef]
71.
Jentzen, W.; Ma, J.G.; Shelnutt, J.A. Conservation of the Conformation of the Porphyrin Macrocycle in Hemoproteins. Biophys. J.
1998,74, 753–763. [CrossRef]
72.
Hobbs, J.D.; Shelnutt, J.A. Conserved Nonplanar Heme Distortions in Cytochromes C. J. Protein Chem.
1995
,14, 19–25. [CrossRef]
Molecules 2022,27, 8751 33 of 34
73.
Haddad, R.E.; Gazeau, S.; Pécaut, J.; Marchon, J.C.; Medforth, C.J.; Shelnutt, J.A. Origin of the Red Shifts in the Optical Absorption
Bands of Nonplanar Tetraalkylporphyrins. J. Am. Chem. Soc. 2003,125, 1253–1268. [CrossRef]
74.
Schweitzer-Stenner, R.; Dreybrodt, W. Excitation Profiles and Depolarization Ratios of Some Prominent Raman Lines in Oxy-
haemoglobin and Ferrocytochrome c in the Pre-resonant and Resonant Region of the Q-band. J. Raman Spectrosc.
1985
,16, 111–123.
[CrossRef]
75.
Schweitzer-Stenner, R.; Stichternath, A.; Dreybrodt, W.; Jentzen, W.; Song, X.Z.; Shelnutt, J.A.; Nielsen, O.F.; Medforth, C.J.; Smith,
K.M. Raman Dispersion Spectroscopy on the Highly Saddled Nickel(II)-Octaethyltetraphenylporphyrin Reveals the Symmetry of
Nonplanar Distortions and the Vibronic Coupling Strength of Normal Modes. J. Chem. Phys. 1997,107, 1794–1815. [CrossRef]
76.
Jentzen, W.; Unger, E.; Karvounis, G.; Shelnutt, J.A.; Dreybrodt, W.; Schweitzer-Stenner, R. Conformational Properties of Nickel(II)
Octaethylporphyrin in Solution. 1. Resonance Excitation Profiles and Temperature Dependence of Structure-Sensitive Raman
Lines. J. Phys. Chem. 1996,100, 14184–14191. [CrossRef]
77.
Li, X.Y.; Czernuszewicz, R.S.; Kincaid, J.R.; Stein, P.; Spiro, T.G. Consistent Porphyrin Force Field. 2. Nickel Octaethylporphyrin
Skeletal and Substituent Mode Assignments from 15N, Meso-D4, and Methylene-D16 Raman and Infrared Isotope Shifts. J. Phys.
Chem. 1990,94, 47–61. [CrossRef]
78.
Zerner, M.; Gouterman, M.; Kobayashi, H. Porphyrins—VIII. Extended Hückel Calculations on Iron Complexes. Theor. Chim.
Acta 1966,6, 363–400. [CrossRef]
79.
Soffer, J.B.; Schweitzer-Stenner, R. Near-Exact Enthalpy-Entropy Compensation Governs the Thermal Unfolding of Protonation
States of Oxidized Cytochrome C. J. Biol. Inorg. Chem. 2014,19, 1181–1194. [CrossRef]
80.
Döpner, S.; Hildebrandt, P.; Resell, F.I.; Mauk, A.G. Alkaline Conformational Transitions of Ferricytochrome c Studied by
Resonance Raman Spectroscopy. J. Am. Chem. Soc. 1998,120, 11246–11255. [CrossRef]
81.
Assfalg, M.; Bertini, I.; Dolfi, A.; Turano, P.; Mauk, A.G.; Rosell, F.I.; Gray, H.B. Structural Model for an Alkaline Form of
Ferricytochrome C. J. Am. Chem. Soc. 2003,125, 2913–2922. [CrossRef] [PubMed]
82.
Berners-Price, S.J.; Bertini, I.; Gray, H.B.; Spyroulias, G.A.; Turano, P. The Stability of the Cytochrome c Scaffold as Revealed by
NMR Spectroscopy. J. Inorg. Biochem. 2004,98, 814–823. [CrossRef] [PubMed]
83.
Blouin, C.; Guillemette, J.G.; Wallace, C.J.A. Resolving the Individual Components of a PH-Induced Conformational Change.
Biophys. J. 2001,81, 2331–2338. [CrossRef]
84.
Can, M.; Zoppellaro, G.; Andersson, K.K.; Bren, K.L. Modulation of Ligand-Field Parameters by Heme Ruffling in Cytochromes c
Revealed by Epr Spectroscopy. Inorg. Chem. 2011,50, 12018–12024. [CrossRef] [PubMed]
85.
Schweitzer-Stenner, R.; Dreybrodt, W. Investigation of Haem—Protein Coupling and Structural Heterogenity in Myoglobin and
Haemoglobin by Resonance Raman Spectroscopy. J. Raman Spectrosc. 1992,23, 539–550. [CrossRef]
86.
Shelnutt, J.A.; O’Shea, D.C. Resonance Raman Spectra of Copper Tetraphenylporphyrin: Effects of Strong Vibronic Coupling on
Excitation Profiles and the Absorption Spectrum. J. Chem. Phys. 1978,69, 5361–5374. [CrossRef]
87.
Schweitzer-Stenner, R.; Hagarman, A.; Verbaro, D.; Soffer, J.B. Conformational Stability of Cytochrome C Probed by Optical
Spectroscopy. Methods Enzymol. 2009,466, 109–153. [CrossRef] [PubMed]
88.
Levantino, M.; Huang, Q.; Cupane, A.; Laberge, M.; Hagarman, A.; Schweitzer-Stenner, R. The Importance of Vibronic Pertur-
bations in Ferrocytochrome c Spectra: A Reevaluation of Spectral Properties Based on Low-Temperature Optical Absorption,
Resonance Raman, and Molecular-Dynamics Simulations. J. Chem. Phys. 2005,123, 54508. [CrossRef]
89.
Schweitzer-Stenner, R. Using spectroscopic tools to probe porphyrin deformation and porphyrin-protein interactions. J. Porphyrins
Phthalocyanines. 2011,15, 312–337. [CrossRef]
90.
Garozzo, M.; Galluzzi, F. A Comparison between Different Approaches to the Vibronic Theory of Raman Intensities. J. Chem.
Phys. 1976,64, 1720–1723. [CrossRef]
91.
Zgierski, M.Z.; Shelnutt, J.A.; Pawlikowski, M. Interference between Intra- and Inter-Manifold Couplings in Resonance Raman
Spectra of Metalloporphyrins. Chem. Phys. Lett. 1979,68, 262–266. [CrossRef]
92.
Manas, E.S.; Wright, W.W.; Sharp, K.A.; Friedrich, J.; Vanderkooi, J.M. The Influence of Protein Environment on the Low
Temperature Electronic Spectroscopy of Zn-Substituted Cytochrome. J. Phys. Chem. B 2000,104, 6932–6941. [CrossRef]
93.
Zgierski, M.Z. Depolarization Dispersion Curves of Some Raman Fundamentals in Ferrocytochrome c and Oxyhaemoglobin. J.
Raman Spectrosc. 1988,19, 23–32. [CrossRef]
94.
Bersuker, I.B.; Stavrov, S.S. Structure and Properties of Metalloporphyrins and Hemoproteins: The Vibronic Approach. Coord.
Chem. Rev. 1988,88, 1–68. [CrossRef]
95.
Eaton, W.; Hochstrasser, R.M. Single-Crystal Spectra of Ferrimyoglobin Complexes in Polarized Light. J. Chem. Phys
1958
,49,
985–995. [CrossRef]
96.
Spiro, T.G.; Strekas, T.C. Resonance Raman Spectra of Heme Proteins. Effects of Oxidation and Spin State. J. Am. Chem. Soc.
1974
,
96, 338–345. [CrossRef]
97.
Schweitzer-Stenner, R. Revisited Depolarization Ratio Dispersion of Raman Fundamentals from Heme c in Ferrocytochrome c
Confirms That Asymmetric Perturbations Affect the Electronic and Vibrational Structure of the Chromophore’s Macrocycle. J.
Phys. Chem. 1994,98, 9374–9379. [CrossRef]
98. Shelnutt, J.A. The Porphyrin Handbook; Kadish, R., Ed.; Academic Press: San Diego, CA, USA, 2000; Volume 7.
99.
Lei, H.; Bowler, B.E. Humanlike Substitutions to
Ω
-Loop D of Yeast Iso-1-Cytochrome c Only Modestly Affect Dynamics and
Peroxidase Activity. J. Inorg. Biochem. 2018,183, 146–156. [CrossRef]
Molecules 2022,27, 8751 34 of 34
100.
Blouin, C.; Wallace, C.J.A. Protein Matrix and Dielectric Effect in Cytochrome C. J. Biol. Chem.
2001
,276, 28814–28818. [CrossRef]
101.
Schweitzer-Stenner, R.; Levantino, M.; Cupane, A.; Wallace, C.; Laberge, M.; Huang, Q. Functionally Relevant Electric-Field
Induced Perturbations of the Prosthetic Group of Yeast Ferrocytochrome c Mutants Obtained from a Vibronic Analysis of
Low-Temperature Absorption Spectra. J. Phys. Chem. B 2006,110, 12155–12161. [CrossRef]
102.
Karplus, M.; Fraenkel, G.K. Theoretical Interpretation of Carbon-13 Hyperfine Interactions in Electron Spin Resonance Spectra. J.
Chem. Phys. 1961,35, 1312–1323. [CrossRef]
103.
Kleingardner, J.G.; Bowman, S.E.J.; Bren, K.L. The Influence of Heme Ruffling on Spin Densities in Ferricytochromes c Probed by
Heme Core 13C NMR. Inorg. Chem. 2013,52, 12933–12946. [CrossRef] [PubMed]
104.
Galninato, M.G.I.; Kleingardner, J.G.; Bowman, S.E.J.; Alp, E.E.; Zhao, J.; Bren, K.; Lehnert, N. Heme-protein vibrational couplings
in cytochrome c provide a dynamic link that connects the heme-iron and the protein surface. Proc. Natl. Acad. Sci. USA
2012
,108,
8896–8900. [CrossRef] [PubMed]
