An Introduction to Electron Spin Resonance (ESR)
Boris Dzikovski, ACERT, Cornell University
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The application field
The basic ESR experiment.
Some theoretical background.
Nitroxide spin labels.
Some examples for extraction of parameters of
molecular dynamics from ESR spectra
• Site directed spin labeling (SDSL)
• ESR distance measurements
An introduction to Electron Spin Resonance (ESR), November 7, 2007
ESR is a spectroscopic technique that detects
chemical species that have unpaired electrons :
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Transition metal ions and complexes Mn2+, Cu2+, Gd 3+ etc.
Simple inorganic compounds: O2 , NO, NO2 ….
Short-lived intermediate radicals OH, H, F etc. in kinetics study
Defects in crystals
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Electrons trapped in radiation damaged sites
Stable organic radicals
Triplet states
Biological applications:
Paramagnetic cofactors: iron sulfur, copper proteins
Free radicals of biological origin and their spin-trapping
products
• Spin-labeling
An introduction to Electron Spin Resonance (ESR), November 7, 2007
Energy-level diagram for two spin states as a function of applied field H.
This represents the simplest ESR transition (e.g.,
free electrons).
“Allowed” EPR transitions occur when Ms = 1
(Ms is the magnetic spin quantum number of the
spin state).
The equation describing the absorption (or
emission) of microwave energy between two spin
states is
E = hu = gbH
where:
H
E is the energy difference between the two spin
states
h is Planck’s constant
u is the microwave frequency
g is the Zeeman splitting factor (2.0023 for free
electron)
b is the Bohr magneton
H is the applied magnetic field.
An introduction to Electron Spin Resonance (ESR), November 7, 2007
Relaxation
Evolution of a spin system is described
by Bloch equations:
Mx’, My’ Mz – magnetization components in the
rotating frame
0=eH0 – the Larmor Frequency
 e = 1.76  107 rad /( s  G )
T1- spin-lattice or longitudinal relaxation time
T2- spin-spin or traverse relaxation time
When properly integrated, the Bloch equations will yield the X', Y', and Z
components of magnetization as a function of time.
Stationary solution in the rotating frame gives a lorentzian line F ( H ) =
Gaussian line F ( H ) =
ESR linewidth:
T2
1
 1   2T22 ( H  H 0 ) 2
T2
1
exp(   2T22 ( H  H 0 ) 2 ) = inhomogeneous broadening
2
2
1
= k  e H
T2'
1
1
1
=

T2' T2 2T1
k=1
Lorentz
k =  ln 2 Gauss
An introduction to Electron Spin Resonance (ESR), November 7, 2007
ESR and NMR are very different methods!
electron
proton
ratio
Rest mass
me =9.1094*10-28 g
mp =1.6726*10-24 g
5.446*10-4
Charge
e=-4.80286*10-10ESU
e=4.80286*10-10ESU
-1
Angular momentum
h/4
h/4
1
Magnetic dipole
moment
mS=-ge meS
mS=-gN mNS
ge= 2.002322
me=eh/4mec =
9.274*10-21 erg/G
gN= 5.5856
mN=eh/4mNc =
5.0504*10-24 erg/G
1836.12
Frequency: Factor 1000 larger in EPR ! (GHz instead of MHz)
Coupling strength: Factor 1 000 000 larger in EPR ! (MHz instead of Hz)
Relaxation Times: Factor 1000 000 smaller in EPR ! (ns instead of ms)
= much higher techniqual requirements, but unique sensitivity to molecular motion
Sensitivity : Factor 1 000 000 better than in NMR !! (1nM instead of 1mM )
An ideal case, though
An introduction to Electron Spin Resonance (ESR), November 7, 2007
The Basic ESR Experiment (conventional ESR)
Source
Circulator
electromagnet
Modulation coils
Detector
Resonator (cavity)
An introduction to Electron Spin Resonance (ESR), November 7, 2007
The Basic ESR Experiment (conventional ESR)
Unlike NMR a large proportion of machines are still 'cw'.
That is they do not use pulsed detection methods
•ESR is done from 1 to 300+GHz [30mT-10T or 30cm-1mm], up to 2000+ GHz
Machines are classified according to their source frequency :
Commonly used X-band at 9.5 GHz
L (1.5), S (3.0), C (6.0), Ku (17), K (23), Q (36), V (50), W (95), D(140), G(180)
•Field modulation is used to encode the spectrum [1st derivative lineshape]
•Use microwave transmission lines
•Do spectroscopy with a few microwatts to a few milliwatts of power
•Solid state [Gunn diode or DRO] or tube [klystron] sources
•Temperatures from 4K (heme and non-heme iron) to 310K+ (in vivo/vitro)
• Sensitivity : Increases as (frequency)2, but limited by sample size, field
homogeneity and component construction problems.
Practically (at X-band): detect 1011 spins,
a detectable concentration of ~10-9M.
An introduction to Electron Spin Resonance (ESR), November 7, 2007
Field modulation
An introduction to Electron Spin Resonance (ESR), November 7, 2007
A commercial 9GHz system
An introduction to Electron Spin Resonance (ESR), November 7, 2007
Commercial 95GHz
Spectrometer (3T)
An introduction to Electron Spin Resonance (ESR), November 7, 2007
The g-factor:
E = hu = gbH
The field at each spin influenced by local magnetic fields, not just the external field :
Heft = H + Hlocal so Heff = (1-s)H = (g/ge)H
-This field is induced by H, and so depends on the external field H
-g is an effective Zeeman factor, shifted from the electron g-factor, ge
-The shift in g is akin to the chemical shift of NMR
-The local induced field comes from the orbital motion of electrons, spin-orbit
coupling mixes J, L and S and shifts g, the shift can can be g<2 or g>2.
g is thus characteristic of different electronic structures and is also known as
the
Landé splitting factor:
Light atoms, i.e.'organic' and first row transition metals with a single unpaired
electron
can have g close to 2.0
Heavier atoms, and molecules or atoms with more than one unpaired electron can
have g-values very different from 2
An introduction to Electron Spin Resonance (ESR), November 7, 2007
g-values for some biologically important paramagnetic compounds
Flavin semiquinone, ubiquinone,
ascorbate, etc
Nitroxide spin labels and traps
sulphur radicals : S-S, S-H
MoV (in aldehyde oxidase)
Cu2+
Fe3+ (low spin)
Fe3+ (high spin)
g-value
2.0030 2.0050
2.0020 2.0090
2.02 - 2.06
1.94
2.0 - 2.4
1.4 - 3.1
2.0 - 10
An introduction to Electron Spin Resonance (ESR), November 7, 2007
A - the hyperfine splitting
The unpaired electron, which gives us the EPR spectrum,
is very sensitive to local fields in its surroundings.
Local fields arising from magnetic nuclei are
permanent and independent of H.
Interaction with neighboring nuclear magnetic dipoles gives the
nuclear hyperfine interaction and hyperfine splitting A
Corresponds to the NMR coupling constant J
A splittings are independent of the external field.
For several equivalent nuclei n, (2nMIM + 1) transitions are
observed for a nucleus M with a spin I
The relative intensities are given by Pascal's triangle for I = ½
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
An introduction to Electron Spin Resonance (ESR), November 7, 2007
I=1/2, 2I+1=2
I=1, 2I+1=3
An introduction to Electron Spin Resonance (ESR), November 7, 2007
Organic radicals in the liquid phase
Cyclooctatetraen anion
Butadien ion in liquid NH3
Pyrazine anion
Na+ is the counterion
Observation of the
1:8:28:56:70:56:28:8:1
spectrum shows that eight
protons are equivalent
Two sets of equivalent
protons: 2 and 4
K+ is the counterion
The figures are taken from the textbook by Wertz&Bolton
An introduction to Electron Spin Resonance (ESR), November 7, 2007
Anisotropy in g and A
Many measurements are made in the solid state in EPR spectroscopy.
The ability of EPR to obtain useful information from amorphous (glassy) and
polycrystalline (powders) as well as from single crystal materials has attracted
much biology and biochemistry research
Usually : gX, gY, gZ are not all equal, so g is anisotropic. Same for AX, AY, AZ.
For EPR the local symmetry at an unpaired electron center is
categorised as :
•Cubic. If x = y = z is cubic (cubal, octahedral, tetrahedral) No
anisotropy in g and A.
•Uniaxial (Axial). If x = y, and z is unique.
Linear rotation symmetry (at least 3-fold). Two principal values
each for g and A. For an arbitrary orientation:
2
g = g 2 sin 2   g II2 cos 2 
•Rhombic. Three unequal components for g and A
For an arbitrary orientation:
2
2
2
g 2 = g XX
sin 2  cos 2   gYY
sin 2  sin 2   g ZZ
cos 2 
An introduction to Electron Spin Resonance (ESR), November 7, 2007
gx=2.0091, gy=2.0061, gz=2.0023
The field shift between the X- and Z- orientations is
H=h/gxb- h/gz b  hg/4b~11G
An introduction to Electron Spin Resonance (ESR), November 7, 2007
gx=2.0091, gy=2.0061, gz=2.0023
I=1/2, Ax= 6.2, Ay = 6.3, Az=33.6
An introduction to Electron Spin Resonance (ESR), November 7, 2007
gx=2.0091, gy=2.0061, gz=2.0023
I=1, Ax= 6.2, Ay = 6.3, Az=33.6
An introduction to Electron Spin Resonance (ESR), November 7, 2007
Powder and glass spectra
S=1/2, I=0, gx=gy<>gz Axially symmetric g-factor
Hr =

h
h 2
=
[ g II cos 2   g 2 sin 2  ]1/ 2
g eff b
b
is the angle between a given symmetry axis and the
magnetic field direction
The given solid angle W is defined to be the ratio of the surface area A to the
total surface area on the sphere: W= A/4r2
sin 
dW=2r2sind/4r2= sind/2
P( H )dH  sin d P ( H ) 
b ( g II2 cos 2   g 2 sin 2  ) 3 / 2
P( H ) 
h
( g II2  g 2 ) cos 
b
1
P( H ) 
h H r3 ( g II2  g 2 ) cos 
An introduction to Electron Spin Resonance (ESR), November 7, 2007
dH / d
Axial Lineshape
Rhombic Lineshape
An introduction to Electron Spin Resonance (ESR), November 7, 2007
EPR Middle-Earth
An introduction to Electron Spin Resonance (ESR), November 7, 2007
ESR signals around us
Toothpaste
Human hair
Q-band ESR spectrum of molecular
oxygen at reduced pressure
EPR dosimetry:
5000
10000
15000 G
The rotational angular momentum,
which is quenched in the liquid or
solid phases couples strongly to the
electronic spin and orbital angular
momenta…
Determination of the accumulated radiation
dose by ESR of tooth enamel
An introduction to Electron Spin Resonance (ESR), November 7, 2007
Nitroxide spin labels
CH3
CH3
N
O
CH3
CH3
N
O
O
N
H3C
H3C
O
H
The g- and A-tensor frame for a
nitroxide radical
An introduction to Electron Spin Resonance (ESR), November 7, 2007
gx=2.0091, gy=2.0061, gz=2.0023
I=1, Ax= 6.2, Ay = 6.3, Az=33.6
9.4 GHz
An introduction to Electron Spin Resonance (ESR), November 7, 2007
Angular averaging in the case of S=1/2, I=1, gx=2.0089,
gy=2.0061, gz=2.0027, Ax= 5.2, Ay = 5.2, Az=31.0, X-Band
component I=+1
is spread over A- hg/4b
component I=0
is spread over hg/4b
component -1
is spread over A+ hg/4b
The figures are from the monograph by Kuznetsov
An introduction to Electron Spin Resonance (ESR), November 7, 2007
High field EPR spectroscopy is the g-resolved spectroscopy,
the regions corresponding different orientations of the magnetic
axis relative to the external magnetic field do
not overlap
An introduction to Electron Spin Resonance (ESR), November 7, 2007
gx=2.0091, gy=2.0061, gz=2.0023
I=1, Ax= 6.2, Ay = 6.3, Az=33.6
170 GHz
An introduction to Electron Spin Resonance (ESR), November 7, 2007
Nitroxyl tumbling correlation time
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:
An introduction to Electron Spin Resonance (ESR), November 7, 2007
Nitroxyl Lineshapes
As the tumbling correlation time
decreases, the extent of averaging of
anisotropic features increases and the
spectrum approaches the 3-line signal
that is characteristic of rapid tumbling.
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
B(mI ) = A  B mI  C m I
Rotation correlation times between 10-11
and 10-6 are detectable by ESR
X-band
An introduction to Electron Spin Resonance (ESR), November 7, 2007
2
Calculation of tumbling times in the case of fast isotropic tumbling
The parameters B and C are related to peak-to-peak amplitudes, I(mI) by:
1  I ( 0)
I(0) 
B= 


2  I(1)
I(1) 

1  I(0)
I(0)
C= 

 2
2  I(1)
I(1)

The high-field line has mI = -1.
Tumbling correlation times are calculated from B and C using

 4Bo 
 1 
2




 = B

b 


 3g ob  15 
 Bo 
Where
 =
1
1
g o = (g x  g y  g z )
3
b ( g z  0.5( g x  g y ))

and
Bo =
b=
 2  b 2  1 
 

 = C


8

B
 3g ob   o 

g ob
2
(A z  0.5(A x  A y ))
3
Bo is the peak-to-peak width of the center line
Hyperfine values (A) are in radians/s
The calculation assumes isotropic tumbling
An introduction to Electron Spin Resonance (ESR), November 7, 2007
1
Sample Calculation
OH
4-OH-TEMPO (tempol) in 9:1 glycerol:water
gx = 2.0094, gy = 2.0059, gz = 2.0023
N
O
Ax = 2 18x106, Ay = 2 22.5x106, Az = 2 103x106 rad/s
I(+1) = 13.5, I(0) = 16.4, I(-1) = 3.4 (arbitrary units)
Bo = 3.52 Gauss
= 9.2449x109 s-1
b = 9.274x10-21 erg/G
h=6.626x10-27 erg s
= 2.1x10-9 s from B or  = 2.3x10-9 s from C
The disagreement is an indication of the approximate nature of this calculation.
Determination of microviscosity:
 =
V
kT
(Stocks-Einstein)
Extremely useful in oversaturated/overcooled disperse systems.
Example: testing photographic materials
An introduction to Electron Spin Resonance (ESR), November 7, 2007
g- and A- tensors are sensitive to the local polarity
gx
gy
gz
giso
Ax Ay Az
Aiso
OH
Toluene
N
O
2.00986
Water/glyc 2.00878
2.00626 2.00222 2.00617 6.2 7.0 34.3 15.6
2.00604 2.00215 2.00565 6.9 7.9 37.4 17.4
TEMPO in Emulsion: toluene/SDS/water
An introduction to Electron Spin Resonance (ESR), November 7, 2007
TEMPO in the LQ phase of DLPC
Partially A-resolved
g-resolved spectra
An introduction to Electron Spin Resonance (ESR), November 7, 2007
Orientational resolution of HF ESR for nitroxide spin labels
One of the main virtues of HF ESR over ESR at conventional microwave frequency is the
excellent orientational resolution for nitroxide spin labels. At HF, once motion is discernable in
the spectrum, one can discern about which axis the motion occurs.
Spin labeled fatty acids in solid cyclodextrins
O
O
NO
O
OH
C
NO
C
O
OH
O
C O
NO
An introduction to Electron Spin Resonance (ESR), November 7, 2007
Z-rotation vs. slow motion
Averaging effective tensor
components
(gxx+ gyy)/2, (gxx+ gyy)/2, gzz
(Axx+ Ayy)/2, (Axx+ Ayy)/2 Azz
Averaging real tensor components
gxx, gyy, gzz, Axx, Ayy, Azz
An introduction to Electron Spin Resonance (ESR), November 7, 2007
X-rotation
Averaging effective tensor
components
gxx,, (gyy+ gzz)/2, (gyy+ gzz)/2,
Axx, (Ayy+ Azz)/2, (Ayy+ Azz)/2
An introduction to Electron Spin Resonance (ESR), November 7, 2007
Diffusion tilt angle
Y-rotation
Averaging effective tensor
components
(gxx+ gzz)/2, gyy, (gxx+ gzz)/2,
(Axx+ Azz)/2, Ayy, (Axx+ Azz)/2
An introduction to Electron Spin Resonance (ESR), November 7, 2007
Lipid spin labels
DPPTC
16-PC
CH3
_
O
P
CH2
O
+
CH2
O
CH2
N
ym
zR
O
O
C
O C
N
ym
CH3
H3C
CH2
O
O
CH3
CH3
C
CSL
xm
_
O
O
+N
O
P
O
CH2
O
zm
xm
CH2
O
Side view
zm
O
N
O
Upper view
O
CH
CH2
O
O
C
O
C
CH2
zd
O
N
O
zd
ym
xm
zR
O
N
O
Z-ordering
X-ordering
Y-ordering
An introduction to Electron Spin Resonance (ESR), November 7, 2007
N
O
ESR is one of the most powerful tools in lipid research
Phase state of lipids
Interaction of lipid with proteins, formation of lipoproteids, boundary lipid
etc.
Domains in model and biological membranes
Diffusion studies in the membrane phase
Polarity profiles in membranes
Membrane permeation profiles for oxygen and paramagnetic ions
An introduction to Electron Spin Resonance (ESR), November 7, 2007
ESR on aligned membranes
Spin-labeled gramicidin A in DPPC, 220 C
Aligned membrane
Vesicles
Simulation of angular dependent spectra is much freer of ambiguity, compared to
vesicles
Application of aligned membranes allows extracting information on relative
orientation of diffusion and magnetic axes, which can not be obtained from vesicles
An introduction to Electron Spin Resonance (ESR), November 7, 2007
Spin labeled Gramicidin A in DPPC at 170 GHz
An introduction to Electron Spin Resonance (ESR), November 7, 2007
MOMD: microscopic order – macroscopic disorder.
An important case in biology
All orientations of the membrane normal relative to the magnetic field
are averaged in vesicles:
gx=2.0091, gy=2.0061, gz=2.0023
I=1, Ax= 6.2, Ay = 6.3, Az=33.6
N
O
9 GHz
170 GHz
n
n
OH
O
NO
C
O
O
NO
C
O
X
Z
For a macroscopically disordered sample the orientation of the nitroxide
moiety manifests itself as a result of anisotropic molecular motion
around the principal axis of the molecular frame
Spin labeling. Peptides and proteins
Nitroxides are introduced into proteins as reporter groups to provide information
about local environment, overall tumbling rate of the protein or/and segmental
mobility, accessibility of the labeling site for polar/non-polar molecules, distance
measurements to other spin labels, co-factors, membrane surface….
O
O
R
N
OH
+
O
DCC
HO
R
N
N O
O
N
Labeling of the hydroxyl group
O
O
MTSL spin label is cysteine specific.
NO
NO
Protein
SH
+
CH3
SO2
S
CH2
Protein
S
S
CH2
SDSL = site directed spin labeling is introducing cysteines into the protein
molecule by point mutations with following MTSL labeling.
Cysteine mapping of the protein molecule.
An introduction to Electron Spin Resonance (ESR), November 7, 2007
T4 lysozyme – an example of successful EPR mapping
Multifrequency approach: high field EPR (250 GHz) spectra are
insensitive to the slow overall tumbling motion of the protein and
indicative of the internal motion
The 9 GHz spectra significantly affected by the overall tumbling and
less sensitive to the internal dynamics.
An introduction to Electron Spin Resonance (ESR), November 7, 2007
Multifrequency Analysis
Time scale
R (s-1)
Note: τR = (6R)-1
An introduction to Electron Spin Resonance (ESR), November 7, 2007
Oxygen Accessibility
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).
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 the
a-helical structure of this
segment of the protein.
W. L. Hubbell, H. S. Mchaourab, C. Altenbach, and M. A. Lietzow,
Structure 4, 779-783 (1996).
An introduction to Electron Spin Resonance (ESR), November 7, 2007
ESR distance measurements
Dipole-dipole interaction between two spins: Wdipolar =
H DD = g j g j mB2 (
S j  Sk
3
jk
r

3( S j  rjk )( Sk  rjk )
5
jk
r
)
H DD
m1 m 2

3( m1  r )( m 2  r )
r5
r3
1
= 3 g e2 m B2 (3 cos 2   1)
rjk
Proportional to (interspin distance)-3 angular dependent splitting.
Averaging over all orientations gives the Pake Doublet:
An introduction to Electron Spin Resonance (ESR), November 7, 2007
Some modern pulse EPR techniques (DQC, DEER) can cancel out all interactions
resulting in an EPR spectrum except the dipole interaction in spin pairs
Example: spin labeled Gramicidin A
 = 2 e  / r 3
5.2  104
=  dipolar[ MHz ] / 2
3
r [ Å]
Interspin distance= 30.9 Å
dipolar, MHz,
An introduction to Electron Spin Resonance (ESR), November 7, 2007
DQC-EPR ruler:
5'
(O*N) -U 3'
G-C
C-G
A-U
G-C
C-G
U-A
G-C
A-U
U-A
G-C
G-C
C-G
C-G
U-A
A-U
C-G
G-C
C-G
G-C
U-A
G-C
U-A
U-A
C-G
3' U-(N*O)
5'
Å 10
20
30
40
50
60
70
80
90
100
DQC RULER
Location of mobile domains in a protein complex
using DQC-ESR:
An introduction to Electron Spin Resonance (ESR), November 7, 2007