Electron Paramagnetic Resonance Theory EC

Electron Paramagnetic Resonance Theory EC
Wilfred R. Hagen
Introduction to
Biomolecular
Electron
Paramagnetic
Resonance
Theory
Paper:
EPR spectroscopy as a probe of metal centres in
biological systems (2006) Dalton Trans. 4415-4434
Book:
Biomolecular EPR Spectroscopy (2009)
Fred Hagen completed his
PhD on EPR of metalloproteins
at the University of Amsterdam
in 1982 with S.P.J. Albracht
and E.C. Slater.
E.C. Duin
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EPR, the Technique….
Spectral Simulations
• Molecular EPR spectroscopy is a method to look at the
structure and reactivity of molecules.
• The book ‘Biomolecular EPR spectroscopy’ comes with a
suite of programs for basic manipulation and analysis of EPR
data which will be used in this class.
• EPR is limited to paramagnetic substances (unpaired
electrons). When used in the study of metalloproteins not the
whole molecule is observed but only that small part where the
paramagnetism is located.
Isotropic Radicals
• This is usually the central place of action – the active site of
enzyme catalysis.
Simple Spectrum
Single Integer Signal
• Sensitivity: 10 μM and up.
Hyperfine Spectrum
GeeStrain-5
• Naming: Electron paramagnetic resonance (EPR), electron
spin resonance (ESR), electron magnetic resonance (EMR)
EPR File Converter
Visual Rhombo
EPR Editor
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1
Discovery
A Free Electron in a Magnetic Field
In 1944, E.K. Zavoisky discovered magnetic
resonance. Actually it was EPR on CuCl2.
E.K. Zavoisky’s first EPR system
First EMR on CuCl2.2H2O
4.76mT @ 133MHz
5
• An electron with spin S = ½ can have two orientations in a
magnetic field B0 labeled by mS = +½ or mS = −½.
• The unpaired electron will have a state of lowest energy when
the moment of the electron is aligned with the magnetic field
and a state of highest energy when aligned against the
magnetic field.
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A Free Electron in a Magnetic Field
EPR Theory
A Free Electron in Vacuo
Free, unpaired electron in space:
electron spin - magnetic moment
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• The energy of each orientation is the product of µ and B0. For
an electron µ = msgeβ, where β is a conversion constant
called the Bohr magneton and ge is the spectroscopic g-factor
of the free electron and equals 2.0023192778 (≈ 2.00).
Therefore, the energies for an electron with ms = +½ and ms =
-½ are, respectively: ½ geβB0 and -½ geβB0
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2
A Free Electron in a Magnetic Field
Spin-orbit Coupling
The electronic-Zeeman energies are E = mSgβB
Resonance condition: hν = geβB0
When the electron is bound to one, or more nuclei, then a virtual
observer on the electron would experience the nucleus (nuclei) as an
orbiting positive charge producing a second magnetic field, δB, at the
electron.
+½: E = +½geβB0
hν = geβ(Be + δB)
-½: E = -½geβB0
Since only the spectrometer value of B is known:
The electron can change orientation
by absorbing electromagnetic
radiation which energy should exactly
equal the state energy difference ΔE,
and this defines the resonance
condition:
hν = (ge + δg)βB = gβB
The quantity g = ge + δg contains the chemical information on the
nature of the bond between the electron and the molecule, the
electronic structure of the molecule.
∆𝐸 = ℎ𝜈 = 𝑔𝑒 𝛽𝐵0
The value of g can be taken as a fingerprint of the molecule.
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A Free Electron in a Magnetic Field
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Anisotropy
ℎ𝜈 = 𝑔𝑒 𝛽𝐵0
Two fundamental constants:
- Planck’s constant: h
- Bohr magneton: β
Two experimental parameters:
- Microwave frequency: ν
- Magnetic field: B0
Anisotropy: the fact that molecular
properties, such as δg are angular
dependent and reflect the 3D
electronic structure of the paramagnet.
A constant of proportionality: g-value
Property of matter, for the free electron: g = ge = 2.00232
Example: compound with axial paramagnetic anisotropy. This will
have a different dg-value for different orientations dependent on
the alignment of B0 along the z-axis or the y- or x-axes.
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Powder Spectrum
Angular Dependency of g-Value
A sample of realistic size
consists of randomly oriented
molecules, resulting in a socalled powder spectrum.
Inclusion of the angular terms into the resonance equation
gives:
ℎ𝜈 = 𝑔 𝜃, 𝜙 𝛽𝐵0
In the example of the compound
with axial paramagnetic
anisotropy, the spectrum has
axial EPR absorption.
A spin Hamiltonian that considers any arbitrary orientation
of B relative to g is given by:
𝐻 = 𝛽𝐵𝑇 ∙ 𝑔 ∙ 𝑆
(Higher chance of having the Bvector anywhere in the xy-plane
than parallel to the z-axis.)
With 𝑆 being the Pauli spin operator vector with individual
components 𝑆𝑥 , 𝑆𝑦 , and 𝑆𝑧 .
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Angular Dependency of g-Value
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Angular Dependency of g-Value
B can be aligned along any of the principle g tensor axes
and the individual components of B are defined in terms of
the polar angles (θ, φ).
Bx = B sinθ cosϕ, By = B sinθ sinϕ, and Bz = B cosθ
Filling in these values provides a more detailed matrix
representation of the spin Hamiltonian equation:
Defining the orientation of the magnetic field (a vector) with
respect to the coordinates of the molecule (and vice versa).
𝑔𝑥𝑥
𝐻 = 𝛽 ∙ 𝐵𝑥 𝐵𝑦 𝐵𝑧 ∙ 0
0
Two polar angles, θ and ϕ, where θ is the angle between the
vector B and the molecular z-axis, and ϕ is the angle between
the projection of B onto the xy-plane and the x-axis.
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0
𝑔𝑦𝑦
0
𝑆𝑥
0
0 ∙ 𝑆𝑦
𝑔𝑧𝑧
𝑆𝑧
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Angular Dependency of g-Value
Angular Dependency of g-Value
Combining with the polar angles equations for the
individual components of B:
For resonance absorption to occur:
𝐸1 − 𝐸2 = ℎ𝜈 = 𝑔 𝜃, 𝜙 𝛽𝐵0
𝐻 = 𝛽(𝐵𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜙 ∙ 𝑔𝑥𝑥 ∙ 𝑆𝑥 + 𝐵𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝜙 ∙ 𝑔𝑦𝑦 ∙ 𝑆𝑦 + 𝐵𝑐𝑜𝑠𝜃 ∙ 𝑔𝑧𝑧 ∙ 𝑆𝑧 )
As a result the value of g(θ, φ) now becomes:
The effect of the 𝑆𝑥 , 𝑆𝑦 , 𝑆𝑧 operators can be represented by
the 2 × 2 Pauli spin matrices quantized in units of ℏ as:
𝑆𝑥 =
1 0 1
,
2 1 0
𝑆𝑦 =
1 0
2 −𝑖
−𝑖
,
0
𝑆𝑧 =
𝑔 𝜃, 𝜙 =
1 1 0
2 0 −1
2 𝑠𝑖𝑛2 𝜃𝑐𝑜𝑠 2 𝜙 + 𝑔2 𝑠𝑖𝑛2 𝜃𝑠𝑖𝑛2 𝜙 + 𝑔2 𝑐𝑜𝑠 2 𝜃
𝑔𝑥𝑥
𝑦𝑦
𝑧𝑧
This equation gives the effective anisotropic g value for any
orientation (θ, φ) with respect to the applied magnetic field
B.
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Angular Dependency of g-Value
Angular Dependency of g-Value
For axial spectra: 𝑔𝑎𝑥 𝜃 =
The matrix of the Hamiltonian has the form:
1
𝑔𝑧𝑧 𝑐𝑜𝑠𝜃
𝐻=𝛽 𝐵
2 𝑔𝑥𝑥 𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜙 − 𝑖 𝑔𝑦𝑦 𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝜙
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2 𝑠𝑖𝑛2 𝜃 + 𝑔2 𝑐𝑜𝑠 2 𝜃
𝑔𝑥𝑦
𝑧
𝑔𝑥𝑥 𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜙 + 𝑖 𝑔𝑦𝑦 𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝜙
−𝑔𝑧𝑧 𝑐𝑜𝑠𝜃
The two resulting eigenvalues are:
1
2 𝑠𝑖𝑛2 𝜃𝑐𝑜𝑠 2 𝜙 + 𝑔2 𝑠𝑖𝑛2 𝜃𝑠𝑖𝑛2 𝜙 + 𝑔2 𝑐𝑜𝑠 2 𝜃
𝐸1 = − 𝛽𝐵 𝑔𝑥𝑥
𝑦𝑦
𝑧𝑧
2
1
2 𝑠𝑖𝑛2 𝜃𝑐𝑜𝑠 2 𝜙 + 𝑔2 𝑠𝑖𝑛2 𝜃𝑠𝑖𝑛2 𝜙 + 𝑔2 𝑐𝑜𝑠 2 𝜃
𝐸2 = 𝛽𝐵 𝑔𝑥𝑥
𝑦𝑦
𝑧𝑧
2
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Plot of the angle θ and the axial g-value versus the
resonance field (gz = 2.050 and gxy = 2.002, ν = 9500 MHz)
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5
Correlation Between Line Shape and Structure
Line Shape of EPR Spectra
Note: g// = gz and g = gxy
EPR symmetry
g and A tensors
Molecular point
symmetry
Isotropic
gxx = gyy = gzz
Axx = Ayy = Azz
Oh, Td, O, Th, T
Axial
gxx = gyy ≠ gzz
Axx = Ayy ≠ Azz
D4h, C4v, D4, D2d, D6h,
C6v, D6, D3h, D3d, C3v,
D3
Rhombic
gxx ≠ gyy ≠ gzz
Axx ≠ Ayy ≠ Azz
D2h, C2v, D2
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g-Value
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Correlation Between Line Shape and Structure
• Does the shape of the EPR signal, ‘isotropic’, ‘axial’, or
‘rhombic’ reflect the symmetry of a coordination site in a
metalloprotein?
ℎ𝜈 = 𝑔𝛽𝐵0
Two fundamental constants:
- Planck’s constant: h
- Bohr magneton: β
• Most of the time the answer is: No!
• Example: the Cu(II) spectrum of plastocyanin is virtually axial
(gx ≈ gy) even when recorded at higher frequency for
increased g-value resolution.
For X-band:
𝑔 = 0.7145
𝜈 (𝑀𝐻𝑧)
𝐵 (𝐺𝑎𝑢𝑠𝑠)
• Crystallographic analysis, however, reveals a highly distorted
tetrahedral site essentially with no symmetry at all!
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S=1/2 Systems
Hyperfine Interactions
Additional splitting can be observed in EPR
signals:
+½: E = +½geβB0
Hyperfine interaction
Interaction of the electron spin with the nuclear
spin of the metal ion nucleus
-½: E = -½geβB0
Super hyperfine interaction
Interaction of the electron spin with first
coordinate sphere ligands nuclei
∆𝐸 = ℎ𝜈 = 𝑔𝑒 𝛽𝐵0
Spin-spin interaction
Interaction of the electron spin with other
electron spins within 10 Å distance.
For X-band:
Resonance condition:
𝒈 = 𝟎. 𝟕𝟏𝟒𝟓
𝝂 (𝑴𝑯𝒛)
𝑩 (𝑮𝒂𝒖𝒔𝒔)
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What is this !?!
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Hyperfine Interactions
• Interaction of the electron spin (S = ½) with the nuclear spin
of the metal ion nucleus (I = ½)
• Four different situations: Four new energy levels
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Hyperfine Interactions
Quantum Mechanical Description
• With the four new energy
levels there are two field
positions where the
resonance conditions are
met: |Δms| = 1, |ΔmI| = 0
• For an isolated system with a single unpaired electron
and no hyperfine interaction the only relevant interaction
is the electronic Zeeman term, so the spin Hamiltonian is
𝐻𝑠 = 𝛽𝐵𝛽(𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜙 ∙ 𝑔𝑥𝑥 ∙ 𝑆𝑥 + 𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝜙 ∙ 𝑔𝑦𝑦 ∙ 𝑆𝑦 + 𝑐𝑜𝑠𝜃 ∙ 𝑔𝑧𝑧 ∙ 𝑆𝑧 )
A shorter way of writing this is
• The signal is in principle
split in two.
𝐻𝑠 = 𝛽𝐵 • 𝑔 • 𝑆
Solving this we get the equation we saw earlier for the
angular dependency of the g-value
• The original, unsplit, peak
would have been exactly
in the middle of the two
hyperfine lines.
𝑔 𝜃, 𝜙 =
2 𝑠𝑖𝑛2 𝜃𝑐𝑜𝑠 2 𝜙 + 𝑔2 𝑠𝑖𝑛2 𝜃𝑠𝑖𝑛2 𝜙 + 𝑔2 𝑐𝑜𝑠 2 𝜃
𝑔𝑥𝑥
𝑦𝑦
𝑧𝑧
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Quantum Mechanical Description
Quantum Mechanical Description
• A full quantum mechanical description of the
spectroscopic EPR event is not possible due to the
complexity of the systems under study.
• More terms can be added to the Hamiltonian when
needed.
• For hyperfine interactions Hs becomes
𝐻𝑠 = 𝛽𝐵 • 𝑔 • 𝑆 + 𝑆 • 𝐴 • 𝐼
• In Biomolecular EPR spectroscopy we use the concept
of the spin Hamiltonian. This describes a system with
an extremely simplified form of the Schrödinger wave
equation that is a valid description only of the lowest
electronic state of the molecule plus magnetic
interactions.
where A is the anisotropic hyperfine tensor.
• For multi-electron (high-spin) systems Hs becomes
𝐻𝑠 = 𝛽𝐵 • 𝑔 • 𝑆 + 𝑆 • 𝐷 • 𝑆
where D is the zero-field interaction.
𝐻𝑠 𝜓𝑠 = 𝐸𝜓𝑠
With: Hs, spin Hamiltonian; ys, the spin functions; E,
energy values of the ground state spin manifold.
• When both are present, both terms will have to be
added!
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Quantum Mechanical Description
Quantum Mechanical Description
• These simplified wave equations will sometimes, under
strict conditions, give analytical solutions.
• Using these assumptions the resonance condition
becomes
ℎ𝜐 = 𝑔𝛽𝐵0 + ℎ𝐴𝑚𝐼
• It is important to realize that a lot of the tools and
simulations software used in biomolecular EPR
spectroscopy can only be used when certain conditions
are met.
• In most systems we will encounter, we can use these
tools without any problem. There are specific cases,
however, where we cannot use these tools.
where A is called the Hyperfine Coupling Constant
and mI is the magnetic quantum number for the nucleus.
• This describes most hyperfine patterns we will
encounter.
• Exceptions can be found for example for Cu-ion spectra
(A-values of 30-200 Gauss) measured at lower
frequencies (L-band). In some Cu spectra the g and A
tensors are not linear.
• Other examples are Mn2+ spectra where D is small.
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Quantum Mechanical Description
Hyperfine Interactions
• Hyperfine interaction: 𝐻𝑠 = 𝛽𝐵 • 𝑔 • 𝑆 + 𝑆 • 𝐴 • 𝐼
• How to determine the hyperfine coupling constant A:
Interaction
with I = 1/2
• Assumption 1: the Zeeman interaction is much larger
(two orders of magnitude or more) than the hyperfine
interaction which can therefore be treated as a
perturbation of the larger Zeeman interaction.
• Assumption 2: Just like the Zeeman interaction, the
hyperfine interaction will be anisotropic. It is assumed
that g and A are collinear.
A
Interaction
with I = 1
A
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A
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Hyperfine Interactions
Hyperfine Interactions
• With the four new energy
levels there are two field
positions where the
resonance conditions are
met.
Bio ligand atom nuclear spins and their
EPR superhyperfine patterns
• The signal is in principle
split in two.
• The original, unsplit, peak
would have been exactly
in the middle of the two
hyperfine lines.
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Hyperfine Interactions
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Organic Radicals
• Effect of hyperfine splitting on anisotropic signals can be
very complex
• Organic radicals
• Measured in solution.
• Fast tumbling motions of the molecules averages the
axial anisotropy of the g-factors resulting in the
detection of only a narrow isotropic EPR signal with a
single g-value, ‘giso’.
• Line shape is pure isotropic.
• Bio transition metal nuclear spin and their hyperfine structure
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Hyperfine Interactions
Hyperfine Interactions
• Since there are 2I + 1 possible values of mI (mI = I, I-1,
…, 0, …,-I+1, -I), the hyperfine interaction terms splits
the Zeeman transition into 2I + 1 lines of equal intensity.
• Use a stick diagram or Pascal triangle to predict the
relative intensities of each line.
No interaction
I = ½ → 2 lines
I=1
→ 3 lines
I = 3/2 → 4 lines
I=2
→ 5 lines
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Hyperfine Interactions
Hyperfine Interactions
• Different patterns with lines with different intensities are
obtained when the unpaired electron interacts with more
than one nucleus with the same nuclear spin.
• Different patterns with lines with different intensities are
obtained when the unpaired electron interacts with more
than one nucleus with the same nuclear spin.
No interaction
No interaction
1x I = ½
1x I = 1
2x I = ½
2x I = 1
3x I = ½
3x I = 1
4x I = ½
4x I = 1
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Hyperfine Interactions
Organic Radicals: Localized
• Use a stick diagram or
Pascal triangle to
predict the relative
intensities of each line.
• Note that due to the fact that the OH proton is
exchangeable there is no interaction observed. However,
since only the α- and β-protons are contributing virtually
the same spectrum is generated by making a n-propyl
radical (CH3CH2CH2•) or a n-butanyl radical
(CH3CH2CH2CH2•).
• Interaction with 4 N atoms with I = 1 results in a
spectrum with 9 lines.
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Organic Radicals: Localized
Organic Radicals: Localized
• The unpaired electron density or spin density is close to
unity on one particular atom in the molecule.
• The unpaired electron will not interact to a significant
amount for nuclei further than two bonds away from the
atom with the unpaired electron.
• Example: ethanol radical HOCH2CH2•
• For this ethanol radical you would only expect to see
splittings from the protons of the two CH2 groups.
• These protons are termed α- and β-protons, counting
from the atom with the unpaired electron.
• Protons that are further away (e.g., the OH proton) will
be expected to give a negligible hyperfine coupling
constant.
• The EPR spectrum of the ethanol radical shows a triplet
of triplets
HO-C(Hβ)2-C(Hα)2•
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Organic Radicals: Delocalized
Benzyl Radical
• The unpaired electron in an orbital that can be
delocalized over the whole molecule or a large section.
• In delocalized radicals, hyperfine interaction affects spinactive nuclei attached to atoms in the α- and β-position
with respect to the unpaired electron.
• Nuclei in identical chemical environments are equivalent.
• Example: benzene radical anion.
• Due to the delocalization, the spin density is spread
around the whole molecule and all the protons interact
with the unpaired electron.
• In the benzene anion radical all six hydrogen atoms are
equivalent and they will cause a split of the EPR signal
into a septet.
• The electron is still delocalized but the HOMO has
different densities on the different C atoms
• The two ortho-protons are attached to carbons with the
same spin density and their chemical environment is the
same – hence they are equivalent and will split EPR
signal into a 1:2:1 triplet
• Meta-protons are also equivalent and yield triplet
splitting.
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Organic Radicals: Delocalized
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Benzyl Radical
• In the benzene anion radical all six hydrogen atoms are
equivalent and they will cause a split of the EPR signal
into a septet.
• The fast rotation across C-C bond linking the aromatic
ring to the methylene group makes the two protons H α
equivalent – hence triplet splitting from this group.
• The only para-proton will split the signal into a doublet.
• The EPR spectrum of benzyl radical should thus give a
triplet (Hα) of triplets (Hortho) of triplets (Hmeta) of doublets
(Hpara) resulting in 3×3×3×2 = 54 lines.
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How to Analyze Splitting Patterns
How to Analyze Splitting Patterns
ii. If the structure of the molecule is available, identify all
nuclei with a nuclear spin in the α- and β-position
relative to the unpaired electron. Use splitting diagrams
to reproduce the splitting pattern and use a Pascal
triangle and to determine the relative intensity of the
hyperfine lines for each environment.
• Four of the triplets around 338 mT and 339.7 mT overlap
hence the total number of lines in the spectrum is 48
rather than 54.
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55
How to Analyze Splitting Patterns
How to Analyze Splitting Patterns
i.
iii. To get to the first multiplet (multiplet A), take the
distance between the first two lines at the low field (e.g.,
left side) in the spectrum. Measure out this same
distance to detect if there are more lines that belong to
this multiplet. Keep in mind that that the multiplet might
not be symmetrical due to overlap with lines from other
multiplets.
Make sure the overall spectrum is symmetrical. If this is
not the case you are dealing with more than one
paramagnetic species. You have to look for measuring
conditions that allow the spectra to be measured with
different ratios. If that is possible you could try to isolate
each species by a series of subtractions. If this is not
possible you will have to try to insulate and analyze
both spectra separately.
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14
How to Analyze Splitting Patterns
How to Analyze Splitting Patterns
iv. To find the second multiplet, measure the distance from
the outermost line to the first line which does not form
part of multiplet A. This distance corresponds to the
hyperfine coupling constant of the next multiplet
(labelled B). Just as with multiplet A keep on measuring
the same distance towards higher field until all the lines
of multiplet B have been identified.
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59
How to Analyze Splitting Patterns
Solution vs. powder spectra
v. Since multiplet B has a larger hyperfine coupling
constant A than that of multiplet the hyperfine pattern of
multiplet A will be superimposed on each component of
multiplet B.
• With small molecules in dilute solutions fast tumbling
motions averages the anisotropy of the g-factor resulting in
the detection of a narrow isotropic EPR signal with one
apparent g-value, giso. In this case the splitting patterns will
all have their origin in this central isotropic signal.
• With large molecules like proteins that show slow tumbling,
or molecules in frozen or powder samples, all g-values will
be displayed. Now each peak will have its own splitting
pattern since the hyperfine interaction A is anisotropic.
• An average g value can be calculated gav = (gx + gy + gz)/3
for the ‘powder’ spectra. Note that the giso obtained at room
temperature and the gav obtained on frozen or powder
samples can differ slightly due to the influence of solvent at
ambient temperatures.
vi. Repeat steps 6-9 until all multiplets have been
identified. If you somehow get stuck on the left side also
start from the right side and try to get to the middle of
the spectrum.
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15
Hyperfine Splitting on Anisotropic Spectra
Type Identification - Metals
• The hyperfine splitting pattern will be the same for each
of the principle g-factors
• A is anisotropic and therefore the magnitude of the
splitting can differ significantly for the different g-factors
• In some cases the patterns on the different g-factors can
even overlap partly or completely making it much more
difficult to analyze these patterns.
• Which redox state is EPR active?
Metal Ion
Electron Configuration
Spin State
Fe2+
Fe3+
Ni1+
Ni2+
Ni3+
Cu1+
Cu2+
d6
d5
d9
d8
d7
d10
d9
S = 0 (ls) or S = 2 (hs)
S = 5/2 (hs)
S=½
S = 0 or S = 1
S=½
S=0
S=½
Prepare different samples:
1) as such
2) reduced (dithionite)
3) oxidized (ferricyanide)
• How many unpaired electrons? Different spin states!
61
Hyperfine Splitting on Anisotropic Spectra
63
Type Identification - Metals
• Has the metal a nuclear spin?
Atom
Resolved
hyperfine on
the gz peak for
the Cu nucleus
(I = 3/2)
V
Mn
Fe
Co
Ni
Cu
Mo
W
Unresolved
hyperfine on
the gxy peak
Isotope
50, 51
55
54, 56, 57, 58
59
58, 60, 61, 62
63, 65
92, 94, 95, 96, 97, 98, 100
180, 182, 183, 184, 186
Spin (abundance)
50V,
𝟓
𝟏
𝟕
𝟑
6 (0.25); 51V,
𝟕
𝟐
(99.75)
𝟐
𝟐
(2.119)
𝟐
𝟐 (1.14)
63Cu, 𝟑
65Cu, 𝟑
𝟐 (69.17);
𝟐 (30.83)
95Mo, 𝟓
97Mo, 𝟓
𝟐 (15.92);
𝟐 (9.55)
𝟏
𝟐 (14.3)
Is the signal going to be split into 2 I + 1 lines?
• In general: The spin–orbit coupling parameter is positive for
systems with less than half filled outer shells and negative for
those with more than half filled shells, which means that the
former have g<ge and the latter have g>ge.
62
64
16
Type Identification - Metals
Nickel
Ni1+, d9
Ni1+, d9
Methyl-coenzyme-M reductase
g>ge: gxyz = 2.252, 2.073, 2.064
Hyperfine structure due to Nligands detectable
65
Nickel
67
Type Identification - Nickel
Ni3+, d7
A
What if you are not certain about
the origin of the spectrum:
labeling studies with nuclear
isotopes
B
Hydrogenase.
The iron is low-spin Fe2+
C
The signal is due to the nickel
D
g>ge: gxyz = 2.32, 2.24, 2.01
66
Spectra of hydrogenase
(A) growth was performed with
natural Ni (natural
abundance of 61Ni is
1.19%);
(B) growth in the presence of
61Ni (I = 3/2)
68
17
Type Identification - Nickel
The Microwave Frequency
• An increase in the strength of the
magnetic field B0 will result in a larger
separation of the two energy levels.
• As a result there will be an increased
population difference between the
ground and excited state resulting in
higher signal amplitude.
• To be able to meet the resonance
conditions the frequency will also
have to be increased according to
A
B
C
D
Methyl-coenzyme-M reductase
from Methanothermobacter
marburgensis
(C) natural Ni
(D) growth in the presence of
61Ni (86 %)
𝑔 = 0.7145
𝜈 (𝑀𝐻𝑧)
𝐵 (𝐺𝑎𝑢𝑠𝑠)
69
Cobalt
71
The Microwave Frequency
• Starting at 133 MHz just like NMR spectroscopy
researchers have been pushing to get better resolution
and better sensitivity.
• For both technical and fundamental reasons it turned out
that the optimum sensitivity in EPR is reached in the
8-12 GHz range and X-band is right there in the middle
of that range.
• There are cases, however, that the information obtained
at X-band frequencies is limited and a higher frequency
is needed.
Co+, d7, I = 7/2
g>ge
A
B
Methyltransferase from
M. marburgensis.
(A) Protein as isolated.
(B) Computer simulation.
gxyz = 2.2591, 2.2530, 2.00659
70
72
18
• EPR absorption lines can
have a width that is
independent of the used
frequency and the
corresponding resonance
field. As a consequence,
the resolution of two
partially overlapping lines
will increase with increasing
frequency.
• Note that there is a theoretical limit of maximal resolution
enhancement by frequency increase. In practical cases
the enhancement is usually less or in some cases there
is no enhancement at all.
• Comparison of a Vitamin B12
spectrum at X-band (9.5
GHz) and Q-band (35 GHz).
• In this example, the
superhyperfine lines are still
resolved at Q-band, but are
not overlapping with the gxand gy-peaks anymore. Now
the 8 hyperfine lines can be
detected without any
problems
X-band
1.89
The Microwave Frequency
2.3
The Microwave Frequency
250
275
300
325
350
375
400
425
Field (mT)
Q-band
73
75
The Microwave Frequency
The Microwave Frequency
• The Zeeman interaction is field dependent
• The linewidth is generally not field dependent (with the
exception of g-strain).
• The (super) hyperfine interactions are also independent
of the magnetic field.
• Therefore, changing the microwave frequency means
changing the relative weight of the B-dependent and Bindependent interactions and so the shape (and
information content) of the spectrum changes with
frequency.
• Note that by doing this, for example, the description of
the high-spin systems is no longer valid.
• Comparison of the MCRred1 spectrum at X-band (9.5
GHz) and W-band (90 GHz).
• Note that the linewidth does not change on a linear Gaussscale (both scales cover 3000 Gauss).
W-band
X-band
74
76
19
The Microwave Frequency
Identification of Ligands
• When the spectra are both plotted on the same g-scale is
seems like the linewidth is much smaller, and small
differences in g-values can be detected.
• In this example, the superhyperfine lines are not resolved
at W-band.
X-band
W-band
Free electron in dx2-y2 orbital
Free electron in dz2 orbital
77
Cobalt
Vanadium
Co+, d7, I = 7/2
g>ge
A
B
79
Methyltransferase from M.
marburgensis.
V4+
d1
I = 7/2
(A) Protein as isolated.
(B) Computer simulation
gxyz = 2.2591, 2.2530, 2.00659
The position of the 8 hyperfine
lines are indicated in the
figure. Each line, in turn, is
split due to interaction with a
N-ligand
78
Vanadium-containing
chloroperoxidase from the
fungus Curvularia inaqualis
80
20
Vanadium
Tungsten
W5+, d1
Spectrum is due to V4+
d1, I = 7/2
A
B
The spectrum is axial:
g// = 1.95 and g = 1.98 (g<ge)
(A) gxyz = 2.0488, 2.0122,
1.9635.
(B) Simulation of C based on
the natural abundance of
the tungsten isotopes:
I = 0: 180W, 0.14%; 182W,
26.4%; 184W, 28.4% and I
= 1/2: 183W, 14.4%.
Both lines are split into 8
hyperfine lines.
The hyperfine splitting A is very large and the hyperfine lines of
one peak will be on the other side of the other peak. This
causes an effect called overshoot: The orientation and shape
of these lines will change.
81
Molybdenum
A
B
Mo5+, d1
Formyl-methanofuran
dehydrogenase (FDH II) from
cells grown on tungstate.
83
Copper
Cu2+ in Cu(ClO4)2
d9, I = 3/2
Axial signal
(g>ge)
Methanobacterium wolfei formylmethanofuran dehydrogenase
(FDH I) isolated from cells grown
on molybdate
(A) Two signals with gxyz = 2.003,
1.989, 1.955 and gxyz = 2.00,
1.984, 1.941
(B) Cells grown in the presence
of 97Mo-molybdate (I = 5/2).
Note that we have g-values
above and below ge
82
84
21
Copper
S=1/2 Systems
B0
ΔE
Absorption
st
1 Derivative
Comparison of EPR spectra and structures for copper centres in
azurin. a, Type 1 (wildtype). b, Type 0 (C112D/M121L). c, Type 2
(C112D).
Resonance condition:
(Rosenzweig (2009) Nature Chemistry, 1, 684 – 685)
∆𝐸 = ℎ𝜈 = 𝑔𝑒 𝛽𝐵0
85
Iron-sulfur Clusters
High-Spin Systems
• A system with n unpaired electrons has a spin equal to S
= n/2. Such a system has a spin multiplicity:
ms = 2S + 1
• This value is equal to the number of spin energy levels.
• All the spin levels together are called the spin multiplet.
• An essential difference between S = ½ systems and
high-spin or S ≥ 1 systems is that the latter are subject to
an extra magnetic interaction namely between the
individual unpaired electrons.
• Unlike the electronic Zeeman interaction this interaction
is always present and is independent of any external
field. Another name for this interaction therefore is zerofield interaction.
[2Fe-2S]1+ S = ½
[2Fe-2S]2+ S = 0
20-70 K
[3Fe-4S]0 S = 2
[3Fe-4S]1+ S = ½
4-10 K
4-20 K
[4Fe-4S]1+ S = ½
[4Fe-4S]2+ S = 0
87
4-10 K
(HiPIP)
[4Fe-4S]2+ S = 0
[4Fe-4S]3+ S = ½
86
88
22
(non-)Kramers’ Systems
Half-Integer / Kramers’ systems
Systems with more than one unpaired electron
• The spin Hamiltonian becomes
𝐻𝑠 = 𝛽𝐵 • 𝑔 • 𝑆 + 𝑆 • 𝐷 • 𝑆
Half-integer / Kramers’ systems
• S = 3/2, 5/2, 7/2, 9/2
• All systems detectable in perpendicular-mode EPR
Integer / non-Kramers’ systems
• S = 1, 2, 3, 4
• Detection in parallel-mode EPR
• In biochemistry only relevant for S = 2 systems of
[3Fe-4S]0 and Heme-Fe2+
• The Ni2+ in MCR is S =1 but does not display a
spectrum
• Solving the wave equations it can be shown that in zero
field, the sub levels of a half-integer spin multiplet group
in pairs (Kramer pairs) and these pairs are separated by
energy spacings significantly greater than the X-band
microwave energy hν.
• These spacing are also called zero-field splittings, or
ZFS.
89
Examples for Fe3+/S = 5/2
Example 1: Fe3+ in
rubredoxins. The ion is
coordinated by the
thiolate groups of four
Cys residues.
Example 2: Fe3+ in the
heme group of KatG.
The ion is coordinated
by the four nitrogen
ligands from the heme
ring.
91
Energy Levels for S = 5/2 System
|mS = ±5/2>
Rubredoxin
(Photosystem II)
|mS = ±3/2>
|mS = ±1/2>
KatG
• The S = 5/2 multiplet forms three Kramers’ doublets that are
separated from the others by energies significantly larger than
the ≈ 0.3-cm-1 microwave quantum (X-band).
90
92
23
Energy Levels for S = 5/2 System
Half-Integer / Kramers’ Systems
ℎ𝜈 = 𝑔𝑒𝑓𝑓 𝛽𝐵
|mS = ±5/2>
• geff encompasses the real g-values plus the effect of the
zero-field interaction.
• Just like the g-value and A-values also the zero-field
interaction parameter can be anisotropic and have three
values Dx, Dy, and Dz.
|mS = ±3/2>
|mS = ±1/2>
• The degeneracy between the pairs is lifted in an external field.
• Since the zero field splitting is very large, the external fieldinduced splitting only allows for the occurrence of EPR
transitions within each (split) pair of levels.
Only intra-doublet transitions observed in EPR.
93
Energy Levels for S = 5/2 System
95
Half-Integer / Kramers’ Systems
ℎ𝜈 = 𝑔𝑒𝑓𝑓 𝛽𝐵
|mS = ±5/2>
• In contrast to g and A, however, the three Di’s are not
independent because Dx2 + Dy2 + Dz2 = 0, and so they
can be reduced to two independent parameters by
redefinition:
|mS = ±3/2>
|mS = ±1/2>
𝐷=
• There is no crossing over and mixing of the energy levels.
• For Kramers’ systems each Kramer pair can give rise to its own
resonance.
• Each of these can be described in terms of an effective S = ½
spectrum with three effective g-values.
94
3𝐷𝑧
2
and 𝐸 =
𝐷𝑥 −𝐷𝑦
2
• We can also define a rhombicity
𝜂=𝐸
𝐷
with 0 ≤ 𝜂 ≤ 1
3
96
24
Half-Integer / Kramers’ Systems
Rhombogram & Simulations
|mS = ±5/2>
• From the complete energy matrix it can be derived that
under the so-called weak-field limit (Zeeman
interaction << zero-field interaction) the three
elements of the real g-tensor, gx, gy, and gz, can be fixed
at 2.00 and that the shape of the EPR spectra, the
effective g-values, is a function of the rhombicity E/D.
10 K
–– spectrum
–– simulation
|mS = ±3/2>
Axial component(s)
E/D = 0.00
• The relationship of the effective g-values versus the
rhombicity can be plotted in two-dimensional graphs, socalled rhombograms.
Rhombic component
E/D = 0.03
|mS = ±1/2>
97
Rhombogram
Mn2+
4.5 K
|mS = ±5/2>
• The somewhat simplified description of the EPR spectra
of the different Fe3+ systems and iron-sulfur-cluster
containing proteins was possible due to the fact that they
all fall within the weak-field limit (Zeeman interaction <<
zero-field interaction).
• It is also possible that the zero-field interaction is much
weaker than the Zeeman interaction, and this “strongfield limit” hold for six-coordinate Mn2+, which is not only
biologically relevant as a site in some manganese
proteins, but also because this is a very common
contaminant of biological preparations.
|mS = ±3/2>
S = 3/2
S = 1/2
E/D = 0.315
99
|mS = ±1/2>
98
100
25
Mn2+
Mn2+
• The electronic spin state of Mn2+ is S = 5/2.
• Six energy states with the electron spin magnetic
quantum number, ms = 5/2, 3/2, 1/2. -1/2, -3/2, and -5/2
arise due to the Zeeman effect.
• Due to the nuclear spin magnetic quantum number, all
lines will be further split into six hyperfine lines, m = 5/2,
3/2, 1/2. -1/2, -3/2, and -5/2.
• Note that due to second-order effects the energy level
splitting by the Zeeman effect is not linear.
103
101
Mn2+
Mn2+
• The energy level diagram
predicts that the
spectrum is dominated by
the ms = +1/2 ↔ -1/2
transition and shows the
presence of six hyperfine
lines each split by a small
anisotropy induced by the
zero-field splitting.
• Pure cubic (e.g., octahedral) situation: D and E are zero,
g is isotropic, because of the high spin a new zero-field
energy term exists that produces EPR anisotropy.
• The zero-field splitting for Bǁz are shown.
102
Mn2+
d7
I = 5/2
(S = 5/2)
• In between the six hyperfine lines there are five pairs of weak
lines from forbidden ΔmI = ± 1 transitions with an order of
magnitude lower intensity than the main lines.
• This whole ms = ±1/2 spectrum is on top of a very broad,
rather structureless feature that is the sum of all the other five
Δms =1 transitions (e.g., ms = -3/2 ← -5/2).
104
26
Integer / non-Kramers’ Systems
S = 2 System
• Non-Kramers’ systems or integer systems are systems
with S = 1, 2, 3, 4.
• These systems are very seldom observed in biological
systems.
• One of the reasons is that just as in the Kramers’
systems the energy levels are organized in doublets
(and one singlet, |0).
• These doublets, however, are split even at zero field and
this splitting is generally greater than the energy of the
X-band radiation.
• This means that in most cases the signals cannot be
detected.
105
• For E ≠ 0, the signals become more rhombic and mixing
of the wave function takes place
• Signal can be detected in perpendicular-mode EPR:
|Δms| = 1 or in parallel-mode EPR |Δms| = 0
• Since the levels are already split at B0 = 0 the peaks will
be shifted to higher g-values.
107
S = 2 System
S = 2 System
• For E = 0, the effective g-values are gxyz = 0, 0, 4 (for
|±1 doublet) and gxyz = 0, 0, 8 (for |±2 doublet), purely
axial.
• This means that the signals are not detectable
• Due to several mechanisms the EPR signals are very
broad and deformed and not much information can be
obtained from the signals itself.
• For most systems however this zero-filed splitting is
larger than the microwave energy at X-band and no
signal will be detected.
106
108
27
S = 2 System
Spin-Spin Interaction
• In principle one could expect to see two signals for each
paramagnetic species present and both signal would be
split due to the spin-spin interaction.
• The distance of the split peaks would be dependent on
the distance between the two species in the molecule
• This would only happen when the g-tensors of both
species are linear.
• When the g-tensors are
not parallel, however,
the spectra will change
significantly.
• Example of the spectra detected for the S = 2 [3Fe-4S]0
cluster from hydrogenase from Allochromatium vinosum.
109
111
Hyperfine Interactions
Spin-Spin Interaction
Hyperfine interaction
Interaction of the electron spin with the
nuclear spin of the metal ion nucleus
A) [4Fe-4S]+ signal detected in
a ferredoxin from Bacillus
stearothermophilus.
B) Signal detected in a socalled 8Fe ferredoxin from
Clostridium pasteurianum.
In this sample two [4Fe-4S]+
clusters are present.
Spectrum B does not look like two overlapping signals.
A more complex signal is now detected. The broad
wings in the EPR spectrum (indicated by the arrows)
are typically found for two interacting clusters.
Super hyperfine interaction
Interaction of the electron spin with first
coordinate sphere ligands nuclei
Spin-spin interaction
Interaction of the electron spin with other
electron spins within 10 Å distance.
110
112
28
Spin-Spin Interaction
Spin-Spin Interaction
EPR spectrum of the Co2+
species by itself (gav ≈2.18)
B) EPR of the radical species
by itself (g = 2.0023)
C-E) The actual observed EPR
spectra for different types of
isomerases.
A)
• Adenosylcobalamin (coenzyme B12)-dependent
isomerases.
• Catalyze skeletal rearrangements via a radical
mechanism.
• The reaction starts with the generation of the 5’deoxyadenosyl radical and cob(II)alamin from enzymebound adenosylcobalamin by homolysis of the
coenzyme’s cobalt-carbon σ-bond in the presence of a
substrate molecule SH.
113
Spin-Spin Interaction
115
Spin-Spin Interaction
Different types of interactions dependent on the distance
between the two interacting paramagnets.
• Stereospecific hydrogen abstraction from the substrate
molecule by the 5’-deoxyadenosyl radical gives 5’deoxyadenosine and a substrate radical S•.
• At this point two paramagnetic species are present in the
enzyme, the Co2+ species and the S• radical species.
114
• Through-space dipole-dipole interaction: anisotropic
interaction that follows a 1/r3 dependence on the spacing
between the interacting centers
• Exchange interaction that depends on orbital overlap
and spin polarization effects: isotropic interaction, which
falls off approximately exponentially with the distance
between the partners.
116
29
Weakly Coupled Spin Systems
Strongly Coupled Spin Systems
• At distances greater than approximately 9 Å, the
exchange interaction creates a doublet splitting in
the EPR spectrum of each partner
• At distances greater than approximately 9 Å, the
exchange interaction creates a doublet splitting in the
EPR spectrum of each partner
• At closer distances, the exchange interaction mixes the
two spin systems, such that their g-values become
averaged and eventually converge to a triplet state at
interspin separations of <7 Å.
• At closer distances, the exchange interaction mixes
the two spin systems, such that their g-values
become averaged and eventually converge to a
triplet state at interspin separations of <7 Å.
117
119
Weakly Coupled Spin Systems
Strongly Coupled Spin Systems
• EPR spectrum of
hydroxyethylhydrazineinactivated ethanolamine
ammonia-lyase showing the
presence of features
corresponding to B12r and a
companion radical species
with absorption near g = 2.0.
Simulation of signals:
• For distances larger than 4-5 Å both
paramagnets can be considered point
dipoles.
• The zero-field splitting is described as a
traceless tensor with an axial, D, and a
rhombic, E, term. In the commonly used
point-dipole approximation, E ≡ 0.
• The principal axis of the zero-field
splitting normally contains the interspin
vector. In simulations, Euler rotations (θ)
are required to relate the axis system of
the zero-field splitting tensor to a
reference system, such as the g-axis of
Co2+.
• The signals from the low-spin Co2+ and the partner
radical were split by a combination of exchange and
dipole-dipole coupling. This can be detected as the
additional hyperfine splitting of the Co2+ signal.
• The amplitude of the signal of the radical centered at g
= 2.0 is off scale.
118
120
30
Strongly Coupled Spin Systems
Very Strongly Coupled Spin Systems
• When there is a strong coupling between the cobalt and
the radical species, the EPR spectra becomes a hybrid
of both the cobalt and the radical EPR signals and
exhibit an average g-value of ≈ 2.1 that arises from
coupling between a carbon centered radical (g = 2.0023)
with cob(II)alamin (gav ≈ 2.18).
• When there is a very strong coupling the EPR spectrum
does not resemble that of Co2+ or a radical species.
• However, it is still consistent with a rhombic triplet-state
species. A prominent half-field transition at around g = 4
can be detected (not shown).
• Note that the EPR spectrum covers a wide area.
• The close spacing of the unpaired electrons, together
with the spin delocalization within the allylic radical,
requires a higher level of treatment than the point-dipole
approximation.
123
• The signals are due to a ‘hybrid’ triplet spin system
comprising both paramagnets.
121
Strongly Coupled Spin Systems
Very Strongly Coupled Spin Systems
(C) Signal of the coupled
Co2+/radical species in
ethanolamine ammonia
lyase after reacting with
ethanolamine. The
interspin distance is 8.7 Å
and θ = 25°
(D) Coupled Co2+/radical
species in lysine-5,6aminomutase after reacting
with 4-thialysine. The
interspin distance is 7.0 Å
and θ = 43°.
(E) Coupled Co2+/radical species
in diol dehydratase after
reacting with 5’-deoxy-3’,4’anhydroadenosylcobalamin.
The interspin distance is 3.5 Å
and θ = 75°.
122
124
31
g-Strain
g-Strain
• We know from folding studies and from structural NMR
and X-ray studies that samples of proteins come with a
distribution of conformations.
• For EPR this means that the paramagnet in each
molecule has a slightly different structural surrounding
and thus a slightly different g-value.
• This structural inhomogeneity or g-strain is reflected in
the spectroscopy in the form of an inhomogeneous line
shape.
• This normally results in a change from a Lorentzian to
Gaussian line shape. An important consequence of this
g-value anisotropy is that the line width, W, is in general,
also isotropic.
125
• The most noticeable
difference is now that
the linewidth, plotted
on a g-scale does not
change when the
spectra are measured
at higher frequency.
• This effect is shown in the figure for the [4Fe-4S] cluster
detected in spinach-leaf ferredoxin. The line width is very
similar in the range of 35 to 3.3 GHz.
• At 1.1 GHz a broadening is detected due to unresolved
hyperfine coupling.
127
g-Strain
ENDOR
• Most of the time we do not have to worry about this, but
particularly in the EPR spectra of the iron-sulfur clusters
g-strain can have a big effect on the shape of the EPR
spectrum and therefore on the simulation and
interpretation of the EPR data.
• Nuclear hyperfine splitting might not always be resolved
but might be hidden in the EPR peaks.
• Techniques have been developed to detect these
interactions: Electron-Nuclear Double Resonance
(ENDOR), Electron Spin Echo Envelope Modulation
(ESEEM), and HYperfine Sublevel CORrElation
(HYSCORE) spectroscopies.
• In transition metal complexes and metalloproteins,
magnetic nuclei such as 1H, 2H, 13C, 14N, 15N, 17O, 31P
and 33S, in the vicinity (2-12 Å) of the paramagnetic
metal ion can be detected by these techniques.
• Identification of the presence of a particular ligand
nucleus, and under favorable circumstances metalligand nuclei distances and angles can be obtained.
128
126
32
ENDOR
ENDOR
• Energy level
diagram for an
S = ½, I = ½
spin system.
• The g-value
and hyperfine
coupling are
assumed to be
isotropic.
• The red lines show the allowed EPR transitions and the
stick EPR spectrum.
• The blue lines show the NMR (ENDOR) transitions and
the stick ENDOR spectrum.
129
• Using higher MW power, the E1 ↔ E3 transition becomes
saturated such that the spin population in both levels
equalizes (b), a situation that should be avoided in regular
CW EPR spectroscopy since the signal intensity will
decrease to almost zero.
• To restore the EPR signal intensity, a population difference
between the levels E1 and E3 needs to be created.
131
ENDOR
ENDOR
• The energy levels for an S = ½, I = ½ spin system
• Using low MW powers, resonance absorption occurs as,
for example, the EPR II transition frequency E1 ↔ E3 is
induced but rapid relaxation ensures that the excited
spins return quickly to the ground state leading to an
unsaturated EPR signal (a).
• Two mechanisms: One way is by ‘pumping’ the RF
transition E3 ↔ E4 (NMR I) using a saturating RF field
(c). An enhancement of the EPR absorption is detected if
the irradiated RF frequency is resonant with this
transition. This enhancement represents the first
ENDOR signal.
130
132
33
ENDOR
ENDOR
• In an alternative way, the RF transition E1 ↔ E2 (NMR II)
can be pumped (Fig. 39d). This also creates an
enhancement and represents the second ENDOR
resonance line.
133
C)
31P-ENDOR
spectra. Spectra were collected at the fields
and g-values indicated, and are shown alongside the
respective pulse-echo detected EPR spectra.
A cluster-31P distance of 6.6 Å was calculated
135
ENDOR
Pulsed ENDOR
A) EPR spectrum obtained for IspG upon incubation with
the substrate MEcPP and the reductant dithionite
B) Proposed structure for the reaction intermediate
• The Davies ENDOR sequence (πMW -πRF-π/2MW-τ-πMW-τecho) is the pulsed equivalent of a CW ENDOR
experiment.
• The effect of this sequence on the occupation of the
energy levels for the two-spin system (S = ½, I = ½) is
136
shown.
134
34
Pulsed ENDOR
ESEEM
• The first selective πMW pulse inverts the electron spin
populations in the E1 and E3 manifolds (a) inducing the
transition EPR II.
• This is followed by a πRF pulse that inverts the nuclear
spin populations upon resonance with an NMR transition
137
(NMR I, b).
Pulsed ENDOR
• Electron Spin Echo Envelope Modulation (ESEEM) is an
important technique for measuring the hyperfine
interaction parameters between electron spins and
nearby nuclear spins.
• From the analysis of the ESEEM signals detailed
information about electron spin density distribution,
distances and bonding angles is gained.
139
ESEEM
• With ESEEM the NMR frequencies are observed
indirectly through observation of the mixing of allowed
and (formally) forbidden EPR transitions as modulations
superimposed on a time-decaying spin-echo.
• Echo envelope modulation occurs when state mixing of
hyperfine levels occurs.
• Fourier transformation of the modulated time trace
results in spectra in the frequency domain containing the
nuclear frequencies.
• The remaining sequence consists of either the selective
(c) or non-selective (d) electron-spin echo detection
pulses.
138
140
35
2D-HYSCORE
2D-HYSCORE
• An extension of ESEEM is HYperfine Sub-level
CORrElation (2D-HYSCORE).
• This technique is essentially a two dimensional ESEEM
experiment in which correlation is transferred from one
electron spin manifold to another.
• HYSCORE allows one to take a complicated ESEEM
spectrum and extend the data into a second dimension.
• The nuclear coherence generated by the first two π/2
pulses undergoes free evolution during time t1 with
frequency ω12 (ω34). The mixing π pulse then transfers
populations in one ms manifold to the other and similarly
transfers the nuclear coherence between manifolds so
that it evolves with frequency ω34 (ω12) during time t2.
• The modulated time decay data is subsequently Fourier
transformed in both dimensions (i.e. t1 and t2) to produce
a 2D frequency-domain spectrum (with axes ν1 and ν2).
141
143
2D-HYSCORE
2D-HYSCORE
• The HYSCORE pulse sequence is a four-pulse MW
sequence in which an additional mixing π pulse is
inserted between the second and third π/2 pulse of the
three-pulse ESEEM Experiment.
• The two inter-pulse delays, t1 and t2, are varied
independently to produce a two-dimensional (2D) time
delay array.
• The nuclear frequencies from the different ms manifolds
are correlated and appear as cross-peaks at the
frequencies (ν1, ν2), (ν2, ν1), and (ν1, -ν2), (ν2, -ν1) in the
(+,+) and (+,-) quadrants of the 2D spectrum,
respectively.
• As strong cross peaks can only be observed between
NMR frequencies of the same nucleus, HYSCORE
spectra can be significantly simplified compared to threepulse ESEEM.
142
144
36
2D-HYSCORE
2D-HYSCORE
• Another advantage of HYSCORE spectroscopy is that
the frequencies from weakly-coupled nuclei (|aiso| < 2|νL|)
appear as cross-peaks in the (+, +) quadrant, whereas
strongly-coupled nuclei (|aiso| > 2|νL|) are observed in the
(+,–) quadrant (a). This facilitates spectral interpretation
for systems containing many interacting nuclei such as
metalloenzymes or proteins.
13C
and 17O HYSCORE Spectra
of the FeSA species in IspG
145
2D-HYSCORE
147
Summary
+½: E = +½geβB0
-½: E = -½geβB0
• For disordered systems with broad ESEEM features, the
correlation peaks broaden into ridges, as illustrated for
the two-spin system (S = ½, I = ½) with an axial
hyperfine tensor (b). The anisotropy of the dipolar
hyperfine interaction, T, can be determined from the
maximum curvature of the ridges away from the antidiagonal, labelled ωmax, and the magnitude of aiso can be
found from the ridge end points or from simulation.
146
Resonance condition:
∆𝐸 = ℎ𝜈 = 𝑔𝑒 𝛽𝐵0
For X-band:
𝒈 = 𝟎. 𝟕𝟏𝟒𝟓
𝝂 (𝑴𝑯𝒛)
𝑩 (𝑮𝒂𝒖𝒔𝒔)
148
37
Quantum Mechanical Description
Line Shape of EPR Spectra for High-Spin Systems
• Simplified Schrödinger wave equation
• Half-integer/non-Kramers:
S = 3/2, 5/2, 7/2, 9/2
𝐻𝑠 𝜓𝑠 = 𝐸𝜓𝑠
𝐻𝑠 = 𝛽𝐵 • 𝑔 • 𝑆 + 𝑆 • 𝐴 • 𝐼 + 𝑆 • 𝐷 • 𝑆 + … … …
Zeeman
interaction
Hyperfine
interaction
• Rhombograms will help with the identification of the spin
state, determination of which spin doublets are
detectable and determination of the E/D value.
Zero field
splitting
or
spin-spin
interaction
• Can sometimes be solved under a set of assumptions
• Solutions sometimes analytical, sometimes need for
numerical approach
• Cannot allows be solved
149
Line Shape of EPR Spectra for S = ½ Systems
151
Examples for Fe3+/S = 5/2
|mS = ±5/2>
• Four basic shapes.
Rubredoxin
(Photosystem II)
• When more than three
peaks are detected the
signal could be split due
to spin interaction or
there could be more than
one signal present.
|mS = ±3/2>
KatG
|mS = ±1/2>
150
152
38
Practical Aspects of EPR Spectrometry
Metal-Ion Type Identification
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
• Has the metal a nuclear spin?
Metal-Ion Type Identification
Optimal Measuring Conditions (T,P)
The X-band EPR Spectrometer
Spectrometer Parameters
Spin Intensity
Redox Titrations
Freeze-Quench Experiments
Simulation of EPR Spectra
EPR on Whole Cells/Cell Extract
Site-Directed Spin Labeling (SDSL) EPR
Atom
V
Mn
Fe
Co
Ni
Cu
Mo
W
Spin (abundance)
50V,
𝟓
𝟏
𝟕
𝟑
6 (0.25); 51V,
𝟕
𝟐
(99.75)
𝟐
𝟐
(2.119)
𝟐
𝟐 (1.14)
63Cu, 𝟑
65Cu, 𝟑
𝟐 (69.17);
𝟐 (30.83)
95Mo, 𝟓
97Mo, 𝟓
𝟐 (15.92);
𝟐 (9.55)
𝟏
𝟐 (14.3)
Is the signal going to be split into 2 I + 1 lines?
153
1) Metal-Ion Type Identification
• In general: The spin–orbit coupling parameter is positive for
systems with less than half filled outer shells and negative for
those with more than half filled shells, which means that the
former have g<ge and the latter have g>ge.
155
2) Optimal measuring Conditions (T, P)
• Which redox state is EPR active?
• There is a need to measure at lower temperatures!
Metal Ion
Electron Configuration
Spin State
Fe2+
Fe3+
Ni1+
Ni2+
Ni3+
Cu1+
Cu2+
d6
d5
d9
d8
d7
d10
d9
S = 0 (ls) or S = 2 (hs)
S = 5/2 (hs)
S=½
S = 0 or S = 1
S=½
S=0
S=½
Prepare different samples:
Isotope
50, 51
55
54, 56, 57, 58
59
58, 60, 61, 62
63, 65
92, 94, 95, 96, 97, 98, 100
180, 182, 183, 184, 186
• EPR frequencies (1-100 GHz) are in the microwave
range!
• Aqueous solutions will warm up in the EPR cavity at RT!
This effect is absent in frozen samples.
1) as such
2) reduced (dithionite)
3) oxidized (ferricyanide)
Do-it-yourself
microwave source
• How many unpaired electrons? Different spin states!
154
156
39
The Need for Lower Temperatures
Heisenberg Uncertainty Principle
• Due to the uncertainty principle the EPR spectra will
broaden beyond detection at higher temperatures. At
lower temperatures the spectra will sharpen up.
The energy difference between the
two energy level due to the Zeeman
splitting is very small, ~0.3 cm-1 for
X-band EPR.
• This sharpening up of the spectrum by cooling the
sample is, however, limited by a temperatureindependent process: inhomogeneous broadening.
Based on the Boltzmann
distribution
𝑛1 = 𝑛0 𝑒
−
• The protein or model molecules in dilute frozen solutions
are subject to a statistical distribution in conformations,
each with slightly different 3D structures and, therefore,
slightly different g-values, which manifest themselves as
a constant broadening of the EPR line independent of
the temperature.
∆𝐸
𝑘𝑇
it can be shown that only at low
temperatures there will be enough difference in the
population of the S = -½ level (n0) and the S = ½ level
(n1) to create a signal.
157
Spin-Lattice Relaxation
159
What to Do?
POWER
SATURATION
OPTIMAL
CONDITIONS
TEMPERATURE
BROADENING
EPR on metalloproteins:
• the relaxation rate decreases with decreasing
temperature; and
• the relaxation rate is anisotropic (i.e. is different for
different parts of the spectrum).
• Optimal measuring conditions (T,P) are determined by
the interplay of the Boltzmann distribution, the
Heisenberg uncertainty relation, the spin–lattice
relaxation rate, and the conformational distribution of
molecular structure.
When too much power is applied the signal will saturate:
Power saturation!
• How do I find the correct measuring condition?
1) Make a Curie Plot
2) Make Power Plots
158
160
40
Power Plots
Power Plot (Copper Perchlorate)
• The power in EPR is expressed in decibels (dB)
attenuation
• X-band microwave sources have a constant output that
is usually leveled off at 200 mW (= 0 dB):
P(dB) = −10 × log(0.2/P(W))
• logarithmic scale: every -10 dB attenuation means an
order-of-magnitude reduction in power.
• A good X-band bridge operates at power levels between
0 and -60 dB
161
163
Power Plots
Power Plot (Copper Perchlorate)
Relationship between the amplitude, gain and the power in
dB:
• The relaxation rate increases
with increasing temperature.
𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒
−𝑑𝐵
20 = constant
∙ 10
𝑔𝑎𝑖𝑛
• Therefore if a signal does not
saturate at a certain power at
a certain temperature it will
also not saturate at the same
power at a higher
temperature.
Both power and gain scales are logarithmic!
Need for low temperatures and high power, but this could
lead to power saturation!
Practical rule: the amplitude of a non-saturated EPR signal
does not change if a reduction in power by -1 dB is
compensated by an increase in gain by one step.
162
• The temperature behavior
or Curie behavior will be
different for different species.
164
41
Curie Plot (Copper Perchlorate)
Line Shape
In, normalized value for
the intensity;
I0, observed intensity;
𝐼𝑛 =
𝐼0 ∙ 𝑇 ∙ 10
−𝑑𝐵
𝑔𝑎𝑖𝑛
20
T, absolute temperature
in K;
dB, reading of the
attenuator;
gain, gain
165
Curie Plot
• The basic form of an EPR
peak is described by the
Lorentz distribution. The
Lorentzian line shape is
also frequently called the homogeneous line shape.
• In biological samples the paramagnet in each molecule
has a slightly different structural surrounding and thus a
slightly different g-value.
• This structural inhomogeneity is reflected in the form of
an inhomogeneous line shape in addition to the
Lorentzian shape.
• At low temperature the contribution from homogeneous
broadening is small and the line shape can be described
by the Gaussian distribution.
167
Line Shape
• At relatively high
temperature a Lorentzian
line shape will be
observed, while a
Gaussian line will be
observed at relatively low
temperatures
• The Gaussian shape will
be broader.
• Preference to measure at
the higher temperature
end of Curie plot
• Practice better signal-tonoise at the lower end.
166
168
42
Power Plots
EPR Spectrometer
• Note that there are different
ways to compose power plots.
• Plot A shows the signal intensity
vs. power (-dB) with no
correction.
• Plot B show the signal intensity
versus 𝑃 (in mW). In this case
there is a linear relationship as
long as the sample does not
saturate (indicated by the
straight line).
• Plot C uses the earlier described
method on slide 165.
Varian E4
Varian E3
Bruker ElexSys W-band
Bruker ElexSys X-band
169
171
X-Band EPR Spectrometer
3) The X-band EPR Spectrometer
• In 1944, E.K. Zavoisky discovered magnetic resonance.
Actually it was EPR on CuCl2.
E.K. Zavoisky’s first EPR system
170
172
43
X-Band EPR Spectrometer
Microwave
bridge
• The produced radiation is transferred by means of a
rectangular, hollow wave guide to an attenuator where the
200 mW can be reduced by a factor between 1 and 10 6.
173
175
174
• The output of the attenuator is transferred with a waveguide
to a circulator that forces the wave into the resonator/cavity.
• The entrance of the resonator is marked by the iris, a device
to tune the amount of radiation reflected back out of the
176
resonator.
• On the left is a monochromatic source of microwaves of
constant output (200 mW) and slightly (10%) tunable
frequency.
44
• The reflected radiation returns to the circulator and is
directed to the diode for the detection of microwave
intensity.
177
• A small amount of the 200 mW source output is directed
through the reference arm directly to the detector to produce
a constant working current.
• The reference arm contains a port that can be closed and a
179
device to shift the phase of the wave.
X-Band EPR Spectrometer
• Most EPR spectrometers are
reflection spectrometers.
• They measure the changes
(due to spectroscopic
transitions) in the amount of
radiation reflected back from
the microwave cavity
containing the sample.
• The detector should only detect
the microwave radiation
coming back from the cavity.
• Any remaining radiation that reflects back from the
detector is forced by the circulator into the upward
waveguide that ends in a wedge to convert the radiation
into heat.
178
180
45
Cavity/EPR Resonator
Cavity/EPR Resonator
• A microwave cavity is simply a
metal box with a rectangular or
cylindrical shape which resonates
with microwaves much as an
organ pipe resonates with sound
waves.
• The resonator is designed to set
up a pattern of standing
microwaves in its interior.
• Standing electromagnetic waves
have their electric and magnetic
field components exactly out of
phase - where the magnetic field
is maximum, the electric field is
minimum.
• Cavities are
characterized by their
Q or quality factor,
which indicates how
efficiently the cavity
stores microwave
energy.
• We can measure Q factors easily:
Q = (νres)/(Δν)
where νres is the resonant frequency of the cavity and Δν
is the width at half height of the resonance.
181
183
Cavity/EPR Resonator
Cavity/EPR Resonator
• Resonance means that the
cavity stores the microwave
energy; therefore, at the
resonance frequency of the
cavity, no microwaves will be
reflected back, but will remain
inside the cavity.
• In order for the microwaves to
enter the cavity one of its end walls
must have an opening: iris.
• The size of the iris controls the
amount of microwaves which will
be reflected back from the cavity
and how much will enter the cavity.
• Just before the iris is a small metal
plate (attached to the iris screw).
Moving this plate up or down
changes the amount of coupling.
• Only for one unique position is the
cavity critically coupled: all waves
enter the cavity, and no radiation is
reflected out.
• Energy can be lost to the side
walls of the cavity because
the microwaves generate
electrical currents in the side
walls of the cavity which in
turn generates heat.
182
184
46
Cavity/EPR Resonator
Tuning the Microwave Cavity and Bridge
• How do all of these properties of a cavity give rise to an
EPR signal? When the sample absorbs the microwave
energy, the Q is lowered because of the increased
losses and the coupling changes.
• Locate and center the “dip”
on the display.
• The cavity is therefore no longer critically coupled and
microwaves will be reflected back to the bridge, resulting
in an EPR signal.
• The pattern is a display of the
microwave power reflected from
the cavity and the reference
arm power as a function of the
microwave frequency.
• The dip corresponds to the microwave power absorbed
by the cavity and thus is not reflected back to the detector
diode.
• By centering the dip on the display monitor, the
microwave source is set to oscillate at the same
frequency as the cavity resonant frequency
185
187
Tuning the Microwave Cavity and Bridge
• Tune the signal (reference) phase. Adjust the Signal
Phase until the depth of the dip is maximized and looks
somewhat symmetric.
• Adjust the bias level. Adjust the Bias until the Diode
meter needle is centered.
• Critical coupling of the cavity. Power is increased and
the iris screw is adjusted to keep the diode current in the
center.
186
188
47
4) Spectrometer Parameters
Spectrum Settings
• Center Field and Sweep Width
• Gain
• For initial broad scans, a Sweep Width around 5000
Gauss is recommended. Set the Center Field value to
2600 Gauss. This means that the scan will start at 100
Gauss and stops at 5100 Gauss (2500 Gauss below and
2500 Gauss above the Center Field value).
• Use the full range of the
digitizer (a), coincides with
the screen display.
• If the receiver gain is too low
the effect of digitization will
be evident in the spectrum
(b)
• At too high gain the signals
will be clipped due to an
overload in the signal
channel (c).
• This scan will cover the complete area available with our
magnet where signals might be detectable.
189
191
Spectrum Settings
Microwave Bridge Parameters
• Points
• Microwave power level. The EPR signal intensity grows
as the square root of the microwave power in the
absence of saturation effects. When saturation sets in,
the signals broaden and become weaker. Several
microwave power levels should be tried to find the
optimal microwave power.
• Standard 1024 points. Can be increased to 4096 for
wide scans to keep the resolution.
• It is advisable, however, to rescan the interesting parts of
a wide scan.
• Subtractions are not possible if the amounts of points
between the two spectra are different.
190
192
48
Phase Sensitive Detection
Field Modulation
• Enhancement of the sensitivity of the spectrometer: less
noise from the detection diode and the elimination of
baseline instabilities due to the drift in DC electronics.
• With more magnetic field
modulation, the intensity of
the detected EPR signals
increases; however, if the
modulation amplitude is too
large (larger than the
linewidths of the EPR
signal), the detected EPR
signal broadens and
becomes distorted.
• A good compromise between signal intensity and signal
distortion occurs when the amplitude of the magnetic field
modulation is equal to the width of the EPR signal. Also, if we
use a modulation amplitude greater than the splitting between
two EPR signals, we can no longer resolve the two signals.
• The magnetic field at the site of the sample is modulated
(varied) sinusoidally at the modulation frequency. If there
is an EPR signal, the field modulation quickly sweeps
through part of the signal and the microwaves reflected
from the cavity are amplitude modulated at the same
frequency.
• Only the amplitude modulated signals are detected. Any
signals which do not fulfill these requirements (i.e, noise
and electrical interference) are suppressed.
193
195
Phase Sensitive Detection
Signal Channel Parameters
• For an EPR signal
which is approximately
linear over an interval
as wide as the
modulation amplitude,
the EPR signal is
transformed into a sine
wave with an
amplitude proportional to the slope of the signal.
• As a result the first derivative of the signal is measured.
• Modulation frequency: normally set to 100 kHz
• Modulation amplitude: You can start with 6 Gauss. The
larger this value the lower the value needed for the
Receiver Gain, which means less noise. Excessive field
modulation, however, broadens the EPR lines and does
not contribute to a bigger signal. As a rule-of-thumb this
value has to be smaller than the line width of your signal.
• Two new parameters: modulation amplitude, and
frequency.
194
196
49
Time Constant
Signal Averaging
• Very weak signals might get lost in the noise. You can
increase your signal to noise ratio by signal averaging. The
resultant signal to noise is proportional to N, where N is
the number of scans.
• To further improve the sensitivity, a time constant is
used to filter out more of the noise.
• Time constants filter out noise by slowing down the
response time of the spectrometer. As the time constant
is increased, the noise levels will drop. If we choose a
time constant which is too long for the rate at which we
scan the magnetic field, we can distort or even filter out
the very signal which we are trying to extract from the
noise. Also, the apparent field for resonance will shift. 197
• With a perfectly stable laboratory environment and
spectrometer, signal averaging and acquiring a spectrum
with a long scan time and a long time constant are
equivalent. Unfortunately perfect stability is impossible to
attain. Slow variations result in baseline drifts. For a slow
scan (>15 min) the variations can cause broad features in
the spectrum dependent on the sample concentration and
the gain used. If you were to signal average the EPR signal
with a scan time short compared to the variation time, these
baseline features could be averaged out.
199
Signal Channel Parameters
Spectrometer Parameters
• Time Constant and Conversion Time: If the Time
Constant is too large in comparison with the Conversion
Time (the rate at which the field is scanned) the signals we
want to detect will get distorted or will even be filtered out.
• Center Field, Sweep Width, Gain, Microwave power level:
sample dependent
• A longer Conversion Time, however, also improves the
signal to noise ratio in a different way: The signal channel
incorporates an integrating ADC (Analog to Digital
Converter) to transfer the analog EPR spectra to the digital
data acquisition system. An important side effect of using
the integration method for the conversion is that it
integrates the noise out of the signal.
• Modulation amplitude: normally set to 6 Gauss.
• Modulation frequency: normally set to 100 kHz
• With a sweep width off about 1000 Gauss a Conversion
Time of 163.84 msec and a Time Constant of 163.84 msec
can be used.
198
• Time Constant and Conversion Time: same value!
sweep width off 1000 Gauss; both 163.84 msec
• Number of X-Scans: normally set to 1
200
50
Signal Integration
5) Spin Intensity
• Also known as spin counting
• To calculate the amount of signal in a protein sample,
the spin intensity can be compared with that of a
standard with a known concentration (Copper
perchlorate: 10 mM)
• Since an EPR spectrum is a first derivative, we have to
integrate twice to obtain the intensity (I0 = area under the
absorption spectrum).
• In addition, corrections are needed for a number of
parameters, to ‘normalize’ the spectra. Only then a direct
comparison of double integral values of standard and
unknown is possible:
Step 1: select spectrum
201
Normalized Signal Intensity
𝐼𝑛 =
𝐼0 ∙ 𝑑2 ∙ 𝑇 ∙ 10
𝑔𝑝𝑎𝑣
203
Signal Integration
−𝑑𝐵
20
∙𝑓∙𝑎
where
In
I0
d
normalized double integral
observed intensity
distance between the starting and ending points (in
Gauss)
T
absolute temperature in K
dB reading of the attenuator
f
tube calibration factor
a
gain
and
𝑔𝑝𝑎𝑣 =
2
3
𝑔𝑥2
+𝑔𝑦2
3
+𝑔𝑧2
+
Step 2: select area to integrate
(shown is the first integral)
𝑔𝑥 +𝑔𝑦 +𝑔𝑧
9
202
204
51
Signal Integration
Signal Intensity???
Clostridium
pasteurianum
[2Fe-2S]2+
S = 9/2
(D < 0)
Step 3: get the value for the double integral
205
Comparison with ‘Spin’ Standard
𝐼𝑛 =
𝐼0 ∙ 𝑑2 ∙ 𝑇 ∙ 10
𝑔𝑝𝑎𝑣
𝐶𝑢 =
−𝑑𝐵
207
Signal Intensity???
• The effective spin-Hamiltonian suggests an easy way for
quantification of high-spin spectra: one simply applies
the double-integration procedure to the effective Seff =
1/2 spectrum as if it were a real S = 1/2 spectrum,
however, with a correction for the fractional population of
the relevant doublet. (Most of the time not possible!)
20
∙𝑓∙𝑎
𝐼𝑛(𝑢) ∙ 𝐶𝑠𝑡
𝐼𝑛(𝑠𝑡)
• Keep measuring conditions the same: temperature,
modulation amplitude, sweep time, amount of points,
amount of scans (These are not averaged!)
• Measure samples on the same day!
• Correct for spin: S(S+1)
• Exception: For high spin ferric hemoproteins (D ≈ +10
cm−1) in X-band at T = 4.2 K the fractional population of
the |mS = ±1/2> doublet is very close to unity (0.999)
therefore, quantification of the spectrum does not require
a depopulation correction.
206
208
52
Signal Intensity ???
Redox Titrations
• When there is only a single paramagnetic species present
the intensity of this signal can be determined directly.
• When more than one species are present you have to look
for unique features, or the different components have to be
simulated and their intensities determined.
• Plots of the intensity vs. the potential are generated.
• The points in the plot can be fitted with the Nernst
equation:
𝑅𝑇
[𝑜𝑥]
𝐸 = 𝐸0 +
𝑙𝑛
𝑛𝐹
[𝑟𝑒𝑑]
Simulations will be needed to get the
signal intensity of a signal when
more than one signal is present, the
signal intensity is too low (too much
noise), or the baseline is not linear.
Spectrum
Simulation
Difference
R (gas constant) = 8.314 J K−1 mol−1; F (Faraday constant)
= 9.649×104 C mol−1; n is the number of moles of electrons
209
211
6) Redox Titrations
Redox Titrations
• With species that are only paramagnetic at a certain
redox potential it is possible to do a redox titration and
obtain the midpoint potential (Em) of the redox couple.
• This is particular useful if you are studying proteins that
are involved in electron transfer pathways.
• In these experiments the protein is titrated in both the
oxidative direction with ferricyanide and in the reductive
direction with dithionite. The potential can be measured
with a combination Ag/AgCl electrode,
• A mixture of redox dyes is added to stabilize the redox
potential outside the Em region
Heterodisulfide Reductase/Hydrogenase Complex:
• Found in the cytosol of some Methanogens
• Electrons from hydrogen are used to break down the
heterodisulfide CoB-S-S-CoM which allows the reuse of
both cofactors.
• A proton gradient is generated in this process
• Except for one, all clusters are involved in electron
transport.
210
212
53
Redox Titrations
7) Freeze-Quench Experiments
• To follow a reaction involving
paramagnetic species freezequench experiments can be
performed.
• In this experiment enzyme is
mixed with substrate and
other compounds and EPR
samples are made by rapid
mixing and freezing.
• Multiple samples have to be
made to get insight into the
formation/disappearance of an
EPR signal.
One unique cluster can either bind CoM or CoB
Labeling studies
with H33S-CoM
(33S: I = 3/2)
213
Redox Titrations
215
Role of IspG in Isoprene Synthesis
Cluster with bound
HS-CoM behaves like a
[4Fe-4S]2+/3+ cluster
(paramagnetic when
oxidized)
Em = -60 mV, pH 7.6, n = 1
214
216
54
Role of IspG in Isoprene Synthesis
• IspG contains a single
[4Fe-4S] cluster.
• The cluster is very
unstable.
• Cluster falls apart when
exposed to molecular
oxygen.
• Instability probably
caused by incomplete
coordination.
Freeze-Quench Experiments with IspG
Cys
Cys
Cys
Cys
217
Role of IspG in Isoprene Synthesis
• A transient isotropic signal is detected with maximal intensity
at 90 ms.
• A transient rhombic signal, FeSA, reaches maximal intensity
at 30 s.
• A second rhombic signal, FeSB, accumulates over time and
reaches maximal intensity at 4 min.
219
Freeze-Quench Experiments
FeSB
• The reaction is a reductive elimination of a hydroxyl
group involving 2 electrons.
• A [4Fe-4S] cluster can only donate 1 electron at-a-time.
• Formation of radical species expected.
FeSA
218
radical
species
220
55
ENDOR
8) Simulation of EPR spectra
• There are several reason why you might
want to simulate an EPR signal.
• For example to obtain the intensity of a
particular signal in a mixture of signals.
Spectrum
Simulation
A) EPR spectrum obtained for IspG upon incubation with
the substrate MEcPP and the reductant dithionite
B) Proposed structure for the reaction intermediate
Difference
221
223
222
224
2D-HYSCORE
13C
and 17O HYSCORE Spectra
of the FeSA species in IspG
56
Visual Rhombo
9) EPR on Whole Cells/Cell Extract
• CO2-reducing pathway
of methanogenesis,
which uses H2 and
CO2 as substrates.
• The reduction of CO2
to CH4 proceeds via
coenzyme-bound C1intermediates,
methanofuran (MFR),
tetrahydromethanopter
in (H4MPT), and
coenzyme M (HSCoM).
• Estimates of the effective g-values
CO2
Formylmethanofuran
Dehydrogenase
H2
Hydrogenase
MFR
CHO MFR
H4MPT
MFR
CHO H4MPT
CH H4MPT
H2
CH2 H4MPT
H2
CH3 H4MPT
Methyl-H4MPT:coenzyme M
Methyltransferase
H4MPT
CH3 S CoM
HS CoM + HS CoB
H2
Heterodisulfide
Reductase
Methyl-coenzyme M
Reductase
CoM S S CoB
CH4
225
227
EPR on Whole Cells
Simulation
• Overview of all
paramagnetic species
• Behavior under
different growth
conditions
• Estimates of the
amount of species
present (simulations
and integration)
Clostridium
pasteurianum
[2Fe-2S]2+
S = 9/2
(D < 0)
5K
20 K
70 K
2800
3000
3200
3400
3600
3800
Field (Gauss)
226
228
57
EPR on Whole Cells
2.4
2.3
2.2
2.1
2.0
The Technique
1.9
77 K
• Specific Cys residues are labeled with a spin label:
2,2,5,5-tetramethyl-1-oxyl-3-methyl
methanethiosulfonate (MTSL).
A: 80% H2/20% CO2
1
3
A
4
2
B: 80% N2/20% CO2
6
5
B
1)
2)
3)
4)
5)
6)
MCR (red2 form)
280
MCR (red1 form)
Hydrogenase (Ni-C form)
Heterodisulfide reductase
Hydrogenase (Ni-A form)
MCR (ox1 form)
290
300
310
320
330
340
350
360
Field (mT)
• Drawback: Cys residues have to be introduced in the
structure at the positions of interest. All other accessible
Cys residues need to be deleted.
229
231
Nitroxide Spin Labels
10) Site-Directed Spin Labeling (SDSL) EPR
Hyperfine Interactions: TEMPO
Provides specific information on the location and
environment of an individual residue within large and
complex protein structures.
A. Motion: Determine rotational mobility of label at
different protein sites.
B. Accessibility: An amino acid can be on the surface of a
protein and accessible to water, or it can be placed
inside the structure and is less accessible or not
accessible at all. An amino acid can also be deep in the
membrane space.
C. Distance: Measure the distance between 2 or more
amino acids in one system or between systems.
230
232
58
Nitroxyl Lineshapes
Nitroxyl Lineshapes
gx=2.0091, gy=2.0061, gz=2.0023
Freely
tumbling
The field shift between the X- and Z- orientations is
Weakly
immobilized
Strongly
immobilized
H=h/gx- h/gz   hg/4~11G
• Conventional X-band
EPR spectra are
sensitive to rotational
motion in the range 0.1
to ~100 nsec.
I=1: Ax= 6.2, Ay = 6.3, Az=33.6
• In the fast motional limit
(~0.1 nsec) three lines
of approximately equal
height are observed.
9.4 GHz
233
235
Thomas Stockner (2105) Biochm. Soc. Trans. 43:1023-1032
Nitroxyl Lineshapes
Nitroxyl Lineshapes
Freely
tumbling
Weakly
immobilized
Strongly
immobilized
In the motional narrowing region, the dependence of the
width of an individual hyperfine line on the nuclear spin
state (mI) can be expressed as
• In the motional
narrowing region the
three lines become
broader and since the
total intensity does not
change the line
amplitude decreases.
• These changes,
however, vary for each
of the three lines.
ΔB(mI) = A + B mI + C mI2
The dependence of the linewidth on the nuclear spin state
(mI) indicates that each line will have a different width. The
‘A’ term broadens all lines equally; the ‘C’ term broadens
the low-and high-field lines but does not affect the center
line (for which mI = 0); the ‘B’ term is negative and causes
the high-field (mI = -1) line to broaden and the low-field (mI
= 1) line to narrow.
234
236
59
Nitroxyl Lineshapes
Nitroxyl Lineshapes
• High field EPR
spectroscopy is the g170 GHz
resolved spectroscopy,
the regions corresponding
to different orientations of
the magnetic axis relative
to the external magnetic
field do not overlap.
• Note that using a different
frequency will change the
time scale of the
gx=2.0091, gy=2.0061, gz=2.0023
experiment.
As the molecule
tumbles, the smaller
splitting for mI = 0 is
averaged more
effectively than the
larger splittings, which
causes differences in
the linewidths of the
three hyperfine lines.
I=1, Ax= 6.2, Ay = 6.3, Az=33.6
237
Nitroxyl Lineshapes
A.
Freely
tumbling
Weakly
immobilized
Strongly
immobilized
239
• Strongly immobilized
corresponds to the slow
motion limit (>100
nsec). The spectrum is
very similar to the
‘powder’ or ‘rigid limit’
spectrum that is
obtained for any
nitroxide in the absence
of rotational motion and
for a dilute powder or
frozen solution
238
Motion
Attachment of the spin label to even a small unstructured
peptide can result in some degree of motional restriction,
and this restriction increases significantly in the presence of
local secondary structure.
240
60
Spin Label Mobility Based on EPR Spectra Line Shape
MTSL-15 AA peptide
The motion of the spin label side
chain is sensitive to tertiary contacts
and protein structure in the local
environment of the spin label.
A. dilute solution of MTSL fast
motional limit (~0.1 nsec)
B. attached to 15 AA peptide with
random coil structure
C. attached to same peptide with an
α-helical structure
D. No motion (slow motion limit,
>100 nsec) or in frozen solution
(C) Mobility map constructed as a plot of the inverse
second moment of the EPR spectrum (<H2>–1) versus
inverse central line width (ΔH0–1), which indicates the
correlation between the measured parameters and regions
of protein topology.
241
Spin Label Mobility Based on EPR Spectra Line Shape
243
Mobility Map
(A) motionally restricted spin label of a buried side chain of
a helix and (B) increased mobility of an exposed side chain
of the same helix forming β spectrin lipid-binding domain
The separation between the outer hyperfine extrema (2Apar)
and the peak-to-peak separation of the central line
width (ΔH0) provide a measure of label mobility.
Czogalla, A. (200&) Acta Biochim Polonica 54: 235-244
242
244
61
B.
Accessibility
Power Saturation Studies
An amino acid can be located on a solvent-exposed
surface, buried within a protein, or within a membrane
bilayer.
Three common reagents:
Oxygen
• small and hydrophobic
• generally found in the center of lipid bilayers of
membranes and in hydrophobic pockets of proteins
• Only present to a small extent in solution
Ni(II) ethylendiaminediacetate (NiEDDA)
• Neutral/Water soluble
Chromium Oxalate (CROX)
• Negative/Water soluble
245
247
Power Saturation Studies
Power Saturation Studies
• Under nonsaturating conditions, the amplitude of the
spectral lines are proportional to the incident microwave
power, increasing linearly with the square root of the
incident power, 𝑃 or P1/2.
The spin label is in a watersoluble environment. CROX
and NiEDDA prevent
saturation (in comparison
with the N2 curve), while O2
does have a much smaller
effect.
• Under saturation conditions the increase becomes less
than linear.
• When paramagnetic relaxation reagents interact with the
spin label, they enhance the relaxation rate and allow the
sample to absorb more power before becoming
saturated.
246
248
62
T4 lysozyme
C.
• Oxygen accessibility
and probe mobility
were measured as a
function of sequence
number for spin
labels attached to T4
lysozyme (T4L) and
cellular retinol binding
protein (CRBP).
• Measure the distance between 2 spin labels.
• This can be intramolecular distances between two labels
in the same monomer or intermolecular distances
between sites on different proteins.
• The correlation between the two parameters indicates
that the most mobile sites are also the most oxygen
accessible.
• The repeat period of about 3.6 for T4L is consistent with
249
the α-helical structure of this segment of the protein.
Depth Parameter
Distances
• Binding processes,
conformational changes
• In the range ~8-20 Å,
interactions between
the two paramagnets
give rise to distancedependent line
broadening in CW EPR.
251
Distances: Pulse EPR
DEER (Double Electron-Electron Resonance) is a pulse EPR technique
that measures the dipolar frequency between two spins. Deer can
cancel out all interactions resulting in an EPR spectrum except the
dipole interaction in spin pairs. The dipolar Pake pattern shown is an
FT of the DEER echo.
  2 e  / r 3
5.2  10 4
  dipolar[ MHz] / 2
r 3 [ Å]
Interspin distance= 30.9 Å
• [O2] is highest in the center of the membrane and lowest
at the surface. The opposite is true for the [NiEDDA].
• The natural log of this ratio yields Φ, a parameter with a
linear dependence on depth into the bilayer.
250
Example: spin labeled Gramicidin A
 dipolar, MHz,
252
63
Effect of Deuterium
Solutions
3) Three protons (I = ½) with A = 40 G
4) Three deuterium (I = 1) with A = 12.4 G.
253
255
Radicals
Unresolved Hyperfine Effects
1) Frequency = 9500 MHz
B-min = 3300 Gauss
B-max = 3500 Gauss.
g = 2, W = 3, A = 0
5) Proton 1: A = 20 G
Proton 2: A = 10 G
Proton 3: A = 5 G
2) I-spin = 2/2
A-value = 25 Gauss
A-value = 15 Gauss
A-value = 5 Gauss
A-value = 2 Gauss
As .the value of A come close to the line width of the signal, the
hyperfine lines start to cancel each other (A = 5, green line) or only a
small broadening of the signal is detectable which is called unresolved
hyperfine splitting (A = 2, purple line). The A = 0 spectrum is overlain
(dash/dot) for comparison
Just as in exercise 2, the splitting between the lines is very close to
the line width. (You can try a much smaller line width (like 1 or 0.5
Gauss) to show the complete hyperfine pattern
254
256
64
Hyperfine Patterns
Ethanol Radical
6) Frequency, 9500 MHz; B-min, 3300 Gauss; B-max, 3500 Gauss.
CH3CH•OH
Rh-diazo radical: Two N interactions with identical A.
For nitrogen 1: A-value = 10 G
For nitrogen 2: A-value = 10 G
MNP-C•: Interaction with 1 N (large A) and 1 H (smaller A)
For nitrogen: A-value = 15 G
For hydrogen: A-value = 4 G
7) Signal is split into four due to the three Hβ. There is an
additional split into two due to the single Hα.
257
Hyperfine Patterns
259
Hyperfine Patterns
DMPO-C•: Interaction with 1 H (large A) and 1 N (smaller A)
For nitrogen: A-value = 30 G
For hydrogen: A-value = 40 G
DMPO-N•: Similar interaction with 1 H (large A),
1 N (smaller A) and 1 N (even smaller A)
For hydrogen: A-value = 50 G
For nitrogen 1: A-value = 40 G
For nitrogen 2: A-value = 10 G
•
•
•
•
258
The first multiplet (A) induces a small two-fold split due to one I = ½
nucleus
The second (B) is a triplet due to two equal I = ½ nucleus
The third (C) is again a two-fold split due to one I = ½ nucleus
The fourth (D) is a triplet due to a I = 1 nucleus
260
65
Hyperfine Patterns
Simulations – Not Enough Orientations
9) B-min: 3100 gauss, B-max: 3700 gauss.
For Co: A-value = 50 G, for nitrogen: A-value = 20 G, for
hydrogen: A-value = 10 G
261
Dimethyl Nitroxyl Radical.
263
Simulations – Not Enough Orientations
• Frequency = 9766.13 MHz, B-min = 3380 gauss, B-max
= 3580 gauss.
• g = 2.005, W = 0.7, AN = 17.0 (1x), AH = 14.8 (6x)
• To get the pattern right AN needs to be just a bit larger
than AH
262
264
66
Cobalamin
X-band
2.3
2Fe Ferredoxin
1.89
Cp 2Fe Fd
Cp2Fe_spec
simulation
250
275
300
325
350
375
400
425
Field (mT)
Q-band
9630.00/3005/4005
Gxyz: 2.0115, 1.9605, 1.9270
gxyz =
Wxyz =
ACoxyz =
ANxyz =
W xyz: 9, 13.5, 12.5
3200
3300
3400
3500
3600
3700
3800
2.275, 2.220, and 2.006
25, 25, and 7.0
11, 11, and 111
18, 18, and 18
Field (Gauss)
265
Overshoot
267
Simulations
Overshoot
266
268
67
00
Hyperfine Interactions
Simulations
4 x S=1
In this structure the
interaction with four
nitrogen ligands (I = 1)
would result in 9
superhyperfine lines.
MCRox1
269
gxyz =
Wxyz =
ANxyz =
2.2305, 2.1665, and 2.1530.
3.5, 4.0, and 4.0
8.0, 9.7, and 9.7
MCRred1 gxyz =
Wxyz =
ANxyz =
2.2495, 2.0720, and 2.0625.
4.5, 3.5, and 5.0
8.8, 9.9, and 9.9
271
Simulations
3
2
4
1
5
10
9
6
7
3100
3200
8
3300
3400
270
Field (Gauss)
68
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