troduction to Electron Spin Resonance (ESR), Nov 1 st 2006 An Introduction to Electron Spin Resonance (ESR). Part 2. Pulse methods and distance measurements. Boris Dzikovski, ACERT, Cornell University • An introduction to pulsed ESR: technical considerations. • Important instrumentation differences between pulsed and cw ESR. • Introduction to typical pulse ESR experiments: COSY, SECSY, ELDOR, DQC • Examples of pulsed ESR experiments on biological systems. • Peaceful coexistence/symbiotic relations between pulse and CW ESR. • ENDOR – ESR detected NMR. • Summary
Transcript
An introduction to Electron Spin Resonance (ESR), Nov 1st 2006
An Introduction to Electron Spin Resonance (ESR).Part 2. Pulse methods and distance measurements.
Boris Dzikovski, ACERT, Cornell University
• An introduction to pulsed ESR: technical considerations.• Important instrumentation differences between pulsed
and cw ESR.• Introduction to typical pulse ESR experiments: COSY,
SECSY, ELDOR, DQC• Examples of pulsed ESR experiments on biological
systems.• Peaceful coexistence/symbiotic relations between pulse
and CW ESR.• ENDOR – ESR detected NMR.• Summary
What is special about ESR, in particular spin-label ESR? (e.g. compared to NMR)
ESR is much more sensitive per spin (than NMR).
In time domain experiments ESR’s time-scale is nanoseconds (NMR’s is milliseconds).
The spin-label spectrum is simple, and can focus on a limited number of spins.
ESR spectra change dramatically as the tumbling motion of the probe slows, thereby providing great sensitivity to local “fluidity”.
In NMR nearly complete averaging occurs, so only residual rotational effects are observed by T1 and T2.
Multi-frequency ESR permits one to take “fast-snapshots” using very high-frequencies and “slow-snapshots” using lower frequencies to help unravel the complex dynamics of bio-systems.
Pulsed ESR methods enable one to distinguish homogeneous broadening reporting on dynamics vs. inhomogeneous broadening reporting on local structure.
An introduction to Electron Spin Resonance (ESR), Nov 1st 2006
Why pulse ESR? And why CW ESR still survives?
Look back at the Bloch equations in the rotating frame:
In an ideal pulse experiment we either irradiate spins (apply B1) or record the signal,hence, in the recording phase we do not care about B1:
1
20
20
)(
)(
)(
0
'
'
'
'
'
'
T
MM
dt
dM
T
MM
dt
dM
T
MM
dt
dM
zzz
y
x
y
xy
x
PULSE vs. CW
In Fourier Transfer Spectroscopy one records signal when B1 is zero. For CW one sees frequency modulation noise of the carrier. We also do not care about field modulation… Hard pulses: B1> spectral range
If one uses Hard Pulses, the pulse excitation can be used for all spins at once. For narrow lines a CW spectrometer measures baseline most of the time – such a waste of time… A FT spectrometer measures signal all the time. However, FT requires a broader band spectrometer. And the noise goes as a square root of the bandwidth…
CW FT
VS.
Sensitivity issue: one rotates all spins into the X-Y plane and detects total magnetization. In CW one usually rotates only a small fraction of the possible magnetization into X-Y plane, to avoid saturation effects.
However: the dead-time problem in pulsed ESR. Dead time is finite time when the spectrometer relaxes to zero-power levels. It is not an issue in solution NMR, but a problem in solid state NMR and EPR.
Pulse ESR can isolate interactions and detect correlations that are not observable by CW methods. The additional information about weakly coupled spins and relaxation properties of the spin system that can be obtained by manipulating the spins with sequences of MW pulses explains the efforts put into the development of new pulse methods.
Time resolution (response time) of ~ 10 ns is much better than in CW ESR
FT ESR has clear advantage vs CW
If spectral width < 100 MHz (35 G) line width < 3 MHz (1 G)
Typical systems organic radicals in solution exchange narrowed lines or conduction electrons proton-free single crystals
disordered solids only IF
high local symmetry (cubic, tetrahedral)
virtually no hyperfine couplings (silica glass)
pathological cases (fullerenes, Mn2+
central lines)
A short review of basic pulse experiments (ESR and/or NMR)
1. Free Induction Decay (FID): much of NMR and occasionally in ESR. In the 90-FID pulse sequence, net magnetization is rotated down into the X'Y' plane with a 90o pulse.
)exp()cos(sin)(
)exp()sin(sin)(
200
200
T
tMtM
T
tMtM
y
x
By using the Bloch equations:/2 RF pulse
signal
The complex signal which is proportional to My-iMx as called an FID and is described as:
)exp(])(exp[)(2
0 T
ttitV
Pulse:
Relaxation:T1 process
T2 process
FID from 1mM TEMPO in decane
One-shot S/N
Receiver on
In phase receiver response
Quadrature receiver response
FID for T1 measurements
Pulse sequence:
FID amplitudeFID
t Two /2 pulses
One measures the FID amplitude of the second pulse as a function of the time between pulses, the signal intensity is proportional to )]
1T
texp([1
In practice, it is more convenient to measure T1 from a - /2 pulse sequence
called Inversion Recovery Pulse Sequence:
/2
FID amplitude )]1
T
texp(2[1
tWe measure FID stepping t….
2. Spin echo
Pulse sequence:/2
t t
Second pulse Refocusing
It is not so simple as it seems. What we see as T2 is actually the dephasing time T2*,
a combination of the real T2 relaxation and the relaxation due to inhomogeneous field on the sample and hence a variety of Larmor frequencies experienced by spins: (T2
*)-1= T2-1+ (T2(inhomogenious))-1
Can we measure T2 from FID?
The first nuclear spin echo observed by E. Hahn in 1950.
The first electron spin echo reported by R. Blume in 1958.
(a-c) the "race-track" echo, (d-f) the "pancake" echo
A brief history of spin echoes, with cartoons!
From the website of Zürich pulse ESR group
Spin Echo: -irradiated quartz
In phase receiver response
Quadrature receiver response
/2- sequence Spin echo
T2 is usually determined by measuring the decay of the two-pulse echo as
a function of the pulse interval t:
when the spread due to inhomogeneity is refocused along the Y-axis: Mx
’(2t)=0 My
’(2t)=
The Carr-Purcell-Meiboom-Gill (CPMG) sequence is derived from the Hahn spin echo and equipped with a "built-in" procedure to self-correct pulse accuracy error
0)
2exp(
2
MT
t
We do not reverse true relaxation
-If the first inversion pulse applied is shorter (e.g. 1750) than a 1800 pulse, a systematic error is introduced in the measurement. The echo will form above the XY plane.
To correct that error, instead of sampling the
echo immediately, a third delay is introduced, during which, the magnetization evolve slightly above the XY plane
If the second inversion pulse, also shorter than 1800 (1750), is applied, as the magnetization
is already above the plane, this shorter inversion pulse will put the magnetization exactly in the XY plane. At the end of the last delay, the echo will form exactly in the XY plane self correcting the pulse error!
Stimulated (three-pulse) echo
The equilibrium Z-magnetization is transferred to transverse magnetization by the first /2 pulse
During free evolution of length , the magnetization dephases
The second /2 pulse rotates the magnetization vectors into the XZ plane
During time T, the transverse magnetization decays
At time t=T + , the third /2 pulse transfers the Z-magnetization pattern again to transverse magnetization, which forms an echo at time t = T + 2 along the +Y-axis. The dotted curve represents the locus of the magnetization vector tips, the open arrow is the stimulated echo
Fourier-Transform ESR, Basic pulse sequences in 2D ESR
COSY
SECSY
2D FT ELDOR
preparation mixing detection
Corresponds to 2D-NOESY in NMR
-15 -10 - 5 0 5 10 15 , MHz
e= 2.84MHz/Gauss
5G
Relationship between spectral coverage and B1
5G of B1 implies a /2 pulse length of approximately 18ns.
2/2 2/1 tBe
Populations and coherencesEnsemble of isolated spins S=1/2. A single spin is in a general superposition state:
c
c
The expectation value of an operator Q:
C
C
QQ
QQCCQQ )( **
Which is QccQccQccQcc **** ,a quadratic product of C and C
**
**** )(
CCCC
CCCCCC
C
C}{
QTrQ If then
The approach becomes useful if many independent spins involved. The ensemble average instead of ...)( 332211
QQQaverageQobs
becomes }...){()( 332211
QTraverageQobs
...)(ˆ 3322111NOperator
Is known as density operator }ˆ{
QTrQ
, which means cc
Take a look at the matrix of the density operator:
**
**
CCCC
CCCC
The diagonal elements are called
populations of states and The off-diagonal elements
are called coherences
A coherence between two energy eigenstates r and s defined as:
srsrrs ˆ
In high magnetic field, the two energy eigenstates have well-defined values of the angular momentum in the magnetic field direction:
sMsS
rMrS
sz
rz
ˆ
ˆThe order prs of coherence is defined as prs = Mr-Ms
The populations and coherences may be identified as the coefficients of the shift and projection operators in the expression of density operator
SSSS ˆˆˆˆˆ
ZSS ˆ1̂
2
1ˆ , YX SiSS ˆˆˆ
Physical interpretation of the populations
Since their sum is always equal to one, only the difference has physical significance
……and indicates net longitudinal spin polarization (in the direction of the field)
-the phase of the (-1)-quantum coherence is the same as transverse magnetization with respect to the x-axis-the amplitude is the net transverse polarization.
What about +1 coherence? Forget about it!
Physical interpretation of the coherences (which are complex numbers): Coherence requires (1) the existence of spins with transverse polarization (superposition state); (2) the transverse polarization must be partially aligned
See Malcolm Levitt. Spin Dynamics
The density operator allows the state of the entire spin-1/2 ensemble to be specified using just four numbers. What are the numbers?
For one important point in time, thermal equilibrium:
1. The coherences between the states are all zero: rs(eq)=0 for rs2. The populations of the energy states obey the Boltzmann distribution
s Bs
Breqrr Tk
Tk
}/exp{
}/exp{
Define Boltzmann factor B TkB B/0
BTk
BTk
B
B
2
1expexp
2
1expexp
hence
High – temperature approximation:
BTk
BTk
B
B
2
11exp
2
11exp
zSBB
Beq ˆ
2
11̂
2
1
4
1
2
10
04
1
2
1
)(ˆ
Thermal equilibrium density operator – the starting pointfor subsequent calculations
Effect of MW pulses on populations and coherences
Strong /2 pulse
Spin density operator before the pulse zSBeq ˆ2
11̂
2
1)(ˆ
After the pulse
2ˆˆ
2ˆ
2
1
2ˆ1̂
2ˆ
2
1
2ˆ)(ˆ
2ˆ
2ˆ
xzxxxxx RSRBRRReqR
1̂2
1ySB ˆ
2
1
B
Beq
4
1
2
10
04
1
2
1
)(̂(/2)x
2
1
4
14
1
2
1
2ˆ
Bi
Bi The pulse (1)equalizes the populations
(2) Converts the population difference into coherences
Strong pulse zxzxxx SBRSRBReqR ˆ2
11̂
2
1ˆˆˆ2
11̂
2
1ˆ)(ˆˆˆ
B
Beq
4
1
2
10
04
1
2
1
)(̂()x
B
B
4
1
2
10
04
1
2
1
ˆ The pulse exchange the populations of the two states, generating an inverted population distribution
Sandwich relation for angular momentum operators
sinˆcosˆˆˆˆzyxyx llRlR
X,Y and Z are cyclic permutable in this relation……..
Spin ½ Rotation Operators
The operator for a rotation about the x-axis through the angle is given by: xx SiR ˆexp)(
21
21
21
21
cossin
sincos)(
i
iRx
21
21
21
21
cossin
sincos)(yR
21
21
exp0
0exp)(
i
iRz
Larger spin systems:
zzz
yyy
xxx
SSS
SSS
SSS
21
21
21
ˆˆˆ
ˆˆˆ
ˆˆˆ
The total angular momentum defined as follows:
z
z
z
z
S
S
S
S
ˆ
0ˆ
0ˆ
ˆ
The four Zeeman product states are eigenstates of the total z- angular momentum operator:
M=+1
M=0
M=0
M=-1
ˆ
A general quantum state of the spin ½ pair: cccc
Density operator
****
****
****
****
**** ,,,ˆ
cccccccc
cccccccc
cccccccc
cccccccc
cccc
c
c
c
c
2S1xS2z
2S1yS2z
2S1zS2x
2S1zS2y
2S1xS2x
2S1yS2x
2S1yS2y
2S1xS2y
2S1zS2z
For coupled spin systems instead of rotating single angular momentum operators, one must rotate their products
baaz
bbbz
aabbaa SSDQSSASSASISI ,2,2,,
Two spin system (hints on how to handle)
Thermal equilibrium:
B
B
eq
1000
0100
0010
0001
4
1̂ ZZ SSB 21ˆˆ
4
11̂
4
1
Individual spin states
01
10
2
1xS
01
10
2
1
iS y
10
01
2
1zS give coherences as direct products
0001
0010
0100
1000
4
1
01
10
2
1
01
10
2
121 ii
SS yx
11
11
11
11
1001
0010
0100
1000
11
11
11
11
8
1
2ˆˆˆ2
2ˆ
21
ii
ii
ii
ii
ii
ii
ii
ii
iRSSR xyxx
zxSSi 21
ˆˆ210
01
2
1
01
10
2
12
0010
0001
1000
0100
2
1
/2 pulse
12
1
2
10
2
110
2
12
101
2
1
02
1
2
11
4
1
iBiB
iBiB
iBiB
iBiB
Action of the /2 pulse on multiple-quantumcoherences:
Multiple QC transformed into single
It can help to think of pulse experiments in terms of coherence-transferpathway diagrams
+1
0
−1
+1
0
−1
•An electronic spin transitionis labeled by the ‘p’ index,which can have values −1, 0, or +1.•If two spins are coupled, thep index can take on larger (>+1) or smaller (<−1) values, as in DQC where products of transition operators may be excited.•The different coherences are combined in various ways to display SECSY, COSY, and ELDOR experiments. The ways always start at p=0 and come to p=-1•Solid pathways report on inhomogeneous, dotted pathways on homogeneous broadening.
+1
0
−1
COSY
SECSY
ELDOR/EXCSY
preparation mixingdetection
Sc+
Sc+
Sc+
Sc-
Sc-
Sc-
Other ways of thinking about the pulse spectrum
•Sometimes, the dotted coherence path is called the FID-like path and thesolid coherence path is called the echo-like path.•The echo-like path tends to re-focus the coherence and reduce the inhomogeneousbroadening of the resonance line.•The FID-like path does not have this refocusing character (no transfer of coherencefrom plus to minus or vice versa).•In order to separate out a particular coherence we generally use a phase-cyclingprocedure which consists of repeating the experiment with pulses applied alongdifferent axes in the rotating frame of the spin system.•By taking suitable combinations of the spectra produced by these pulse sequences,we can selectively enhance those terms of the spin Hamiltonian in which we areinterested.
A pulse applied along the x-axis becomes A pulse applied along the y-axis
If the appropriate phase shift is applied to the pulse
x
y
z
x
z
y(π/2)x
xy
z
(π/2)y
y
zx
From presentation by G. Jeschke
Sc- signal has lower inhomogeneous broadening...
…than the Sc+ signal
221
22 )(2 tt
C
GIB
CGeSS
-1.5 -1.0 - 0.5 0.0 0.5 1.0 1.5 t, s
-15 -10 - 5 0 5 10 15 , MHz
Time domain spectrum Fourier Transform spectrum
One dimensional pulse experiment
dtetsS ti
)()(
dteSts ti
)(2
1)(
Easy answer (specific goal):simulate and fit 2D-FT-ESR spectra
16-PC in pure DPPC vescicles
General goal: 2D methods capabilities to study biological systems
Example of a two dimensional Fourier Transform Spectrum
t1 T td
t2
Preparation Mixing
Detection
/2 /2 /2
t1 T td
t2
Preparation Mixing
Detection
/2 /2 /2
t1 T td
t2
Preparation Mixing
Detection
/2 /2 /2
Time domain representation Frequency domain representation
),()},({),( 212121)2()1(
212211 ttsedtedtttsFFS titi
),(4
1)},({),( 2121221
1)2(1)1(21
2211
SededSFFtts titi
True Fourier Transform Spectroscopy...
2D-ELDOR of 1mM TEMPONE in water/glycerol
... in aqueous samples at room temperature at 95GHz!
The active sample volume was
about 500 nl.
Spin-labeled Gramicidin A in Oriented Membrane (DPPC)
•Slow motional nitroxyl spectrum at 7oC.•Orientation selection at 95 GHz (3.2 mm)
The COSY experiment measures the transfer of coherence from oneESR allowed transition to another. Its time scale is usually limited tot1 + t2 < T2
SECSYThe SECSY experiment is a spin echo implementation of the COSYidea. Instead of the FID detected after a COSY experiment, the echospectrum is recorded. SECSY measures the variation of the phasememory time across the ESR spectrum since the second pulserefocuses hyperfine and resonance offsets.
ELDORBy including a mixing time in this three pulse sequence and transferringcoherences to the z axis, this experiment is sensitive to processes thatoccur on the T1 time scale which is usually longer than the T2 time scaleaccessible to COSY. Spectra are usually displayed in SECSY format.
DQCThis experiment measures distances between dipolar coupled electronspins.
Ld Logel
2D-ELDOR, A POWERFUL TOOL FOR STUDYING MEMBRANE DYNAMICS OVER LARGE TEMPERATURE AND COMPOSITION RANGES
• Antiphase coherences, which can be converted to DQC, can be prepared by the effect of coupling terms in Spin-Hamiltonian.
• The simplest case is the evolution caused by the secular part of dipolar coupling
)2/sin()2/cos()(
)2/sin()2/cos()(
atIatAtA
atAatItI
aaSaSa
aaSaSa
bz
az
bz
az
• Manipulating with SQCs I, A, and DQC, DQ in various ways led to several pulse sequences for distance measurements.
In DQC, signals unrelated to dipolar coupling are suppressed by phase-cycling
•Let us consider the 6-pulse DQC sequence, which we use the most often.
DQC ESR
The 6-pulse DQC Sequence
2 1 0-1-2
Signal is recorded vs. t tp - t2
tm tp + t2 and tDQ both fixed
2tp 2tDQ 2t2
2 2
2
p
2211
2211
1111
1111
AADQDQAA
AADQDQAA
AADQDQAA
AADQDQAA
1I
2 I
1 I
2211
2211
1111
1111
AADQDQAA
AADQDQAA
AADQDQAA
AADQDQAA
2 I
1I
1 I
The coherence pathways for the 6-pulse DQC sequence
in-phase,
antiphase,
double quantum ba SSDQ
bz
aa SSA 2
aa SI
• DQC ESR is well-suited for measuring distances over a broad range.
17 GHz DQC ESR has been applied to measure distances
• from 14 Å (small rigid biradicals)
• to 70 Å (RNAs),
with the likelihood of both limits being improved.
• large distances can be measured in spin-labeled proteins, using just small amounts.
Biological Applications of DQC ESR
Example: spin labeled Gramicidin A (GASL)
3/2 re
dipolar, MHz,
2/][]Å[
102.53
4
MHzr dipolar
Å.930Interspin distance=
)1cos3(1 2223
Bejk
DD gr
H
ALIGNED MEMBRANE:
Dipolar frequency, MHz
0
30
45
Magic
60
75
90
There is no averaging over all orientations of the membrane normal relative to B0. BUT: a tilt of the interspin vector will manifest itself as partial averaging.
n
Dipolar pulse spectroscopy offers a good opportunity to determine the orientation of interspin vectors and, hence, whole embedded molecules in the in the membrane
Equilibrium of gramicidin conformations in the membrane by dipolar pulse ESR
Double helical dimer (DHD)
20.0Å
Monomer 31.1Å
-40 -20 0 20 40F
dip, MHz
In a mismatching membrane gramicidin does not form channels, but exists in some non-channel conformation which could be either double helical or monomeric.The non-channel form(s) tend to aggregate.
Dipolar signal from aggregates due to many distances possible is poorly resolved, weak, and often beyond detection; this complicates identification of particular form.Solution of the problem:We use double-labeled Gramicidin with an addition of 20:1 by unlabeled GA, making the interspin distance a fingerprint of a distinct conformation.
DLPC
DPPC
C
CSS
C
N
O
S
N
O
S CH3
O
O
+ Protein-SH
Side-chain R1MTSSL
289 of CheA from T. maritima
P3
P4
P5
CheA, X-Ray Structure of CheA289 construct
Cysteine residue labeling by MTS (methanethiosulfonate) reagent and the corresponding side-chain, R1, introduced into the protein.
The details of the structure of WT CheA are not known, however the structure of its subdomains and that of CheW has been solved by X-ray crystallography and NMR. Pulsed ESR dipolar spectroscopy (PDS) has been applied to establish how CheW binds to CheA289, for which the X-ray structure was determined.
Site-directed Spin-labelling (SDSL)
PDS requires one to introduce nitroxide reporter groups, which in our case was MTSSL that forms a covalent bond with cysteine, introduced by site-directed mutagenesis.
A number of single and double cysteine mutants of CheA or 289 CheA were engineered for pulsed ESR study. CheA complexes with labeled or unlabeled CheW in various combinations have been used.
CheW: S15,S80,S72
Mutated Residues
579
568
646
553
579
568
646
553
553
553
646
568
579
579
646
568
80 15
72
289 CheA CheW
21Å
31Å32Å
28Å36Å
35.5Å
25Å
18.5Å27.5Å
Average Intra-Protein Spin Distances
Histidine Kinase, CheA is a dimer and binds two CheW. Thus, there are four electron spins. This is a complication, which was overcame by carefully selecting spin-labeling sites such that the distances of interest were significantly shorter than the rest, thereby making their measurement straightforward.
15
7280
Spin-labeling Sites and the Distances
CheA289: N553C, E646C, S579C, D568C
Intra-domain and inter-domain distances, Å.
Mutated site
15 72 80 553 568 579 646
15 27&29(a) 18.2 37 54.5 61 43.7
72 X 24.5&30(a) 27 49 46 32.5
80 X X 26 47 54.5 39.5
553 X X X 23.5 34.5 32
568 X X X X 32.5 35.5
579 X X X X X 28
646 X X X X X X
15
80
553
646
579
72
568
?
NO locationC location
15
80
553
646
579
72
568
?
NO locationC location
A cartoon depicting the “triangulation” grid of sparse large distance constraints from ESR for CheA P5 domain (blue) and CheW (red). Small spheres represent volumes occupied by the nitroxide groups. The increase in the number of constraints (which are fairly accurate distances) will tend to reduce the uncertainty in the position of the backbone.
“Triangulation”
Metric matrix, g is constructed from D
gij = ½ (di02+dj0
2-dij2)
Any atom as origin(0)
gij = Σk=x,y,z xik· xjk = Σk=x,y,z wik·wjk·λk
(w : eigenvector of gij; λ : eigenvalue of gij)
xjk = λk½ wjk
....
.
.
.
333231
232221
131211
ddd
ddd
ddd
D
D is the matrix of distances dik between nitroxides i an k
Quick Solution: Metric Matrix Distance Geometry
Thus (x, y, z) coordinates of all atom found.
The echo intensity is recorded as a function of t.In the absence of dipolar interaction, a pulse at frequency 2 has no impact on echo intensity at frequency 1. Dipolar interaction causes oscillation in echo intensity with a period that is characteristic of the interspin distance.
M. Pannier, S. Veit, G. Jeschke, and H. W. Speiss, J. Magn. Reson. 142, 331 (2000).
4-pulse DEER, another pulse method for measuring interspin dostances
Excitation at spectralposition 2
Excitation at spectralposition 1
From presentation by Sandra Eaton, ACERT 8/7/04)
Why CW ESR is still alive? CW NMR died many years ago…
-Simpler recording, simpler interpretation and simulation.
-Higher sensitivity in many cases
-Most pulse ESR experiments need low measuring temperatures
imposed by the short T2 relaxation time, especially for transition metal ions. On the
contrary, CW EPR spectra can be recorded at room temperature for a large number of spin systems, including radicals and transition metal ions
Pulse and CW ESR are not rivals but rather complementary methods.
Distance measurement by ESR: numbers and orders of magnitude…
Magnitude of dipolar coupling as a function of interspin distance
r (Å) D (gauss) D (MHz) 5 222 622 10 28 78 15 8.2 23 20 3.5 9.8 40 0.43 1.2 60 0.13 0.36
The CW lineshape at the rigid limit is a convolution of the “no broadening spectrum” with Pake: dtPFPF )()(*
The Fourier transform of the convolution of F and P is equal to the product of the Fourier transforms of F and P
3
22
2
3)(
r
gergD
r is in cm
3
410786.2)(
rgaussD
r is in Å, g assumed 2
3
78000)(
rMHzD
Resolved Splittings of CW Spectra
3300 3360 3420 3480 3540
900
00
H
0, GConsistent with a distance of 7.5Å
• Analysis by computer simulation of lineshapes• For shorter distances may need to include exchange as well as dipolar
interaction • In favorable cases may be able to define the relative orientations of the
interspin vector and hyperfine axes for two labels. • Usually assumes that relative orientations of magnetic axes for two centers
are well defined • Analysis of data at two microwave frequencies may be required to obtain
definitive results.
Human Carbonic Anhydrase II(examples from presentation by Sandra Eaton, ACERT 8/7/04)
A174
I59N67
V121
C206
1 23
4
5 67
89
10
Zn
Selected distances in HCA II
67-206121-20667-12159-174
Half-Field TransitionsDipolar interaction between two spins shifts the triplet state ms = 1 energy levels relative
to the ms = 0 level, and causes the normally forbidden transition probability between the ms
= -1 and ms = +1 levels to become non-zero. This transition occurs at half the magnetic
field required for the allowed transitions (at constant microwave frequency), and hence is called the “half-field” transition.
26
2)1.9)(5.05.19(
ns transitioallowed ofintensity integrated
signal field-half ofintensity integrated intensity relative
r
R is interspin distance in Å is MW frequency GHz
Fourier Convolution/Deconvolution
• Assume ~ random distribution of relative orientations or interspin vector and hyperfine axes.
• Fourier convolve spectrum of singly-labeled sample with broadening function to match spectrum of doubly-labeled samples
OR • Divide Fourier transform of doubly-labeled spectrum
by Fourier transform of singly-labeled spectrum to obtain broadening function
• Calculate the interspin distance from the "average" broadening.
M. D. Rabenstein and Y.-K. Shin, Proc. Natl. Acad. Sci (US) 92, 8329 (1995).H.-J. Steinhoff et al., Biophys J. 73, 3287 (1997).
3200 3300 3400M agnetic F ie ld (gauss)
2 0 4 0
0 . 0 0
0 . 2 0
0 . 4 0
0 . 6 0
2 0 4 0
D ata point
0 .00
0 .50
A
B
C
D
H C AII59-174
x 4
Fourier Deconvolution
r = 8 – 9 Å Note that the baseline for the deconvoluted function is close to zero for the subtracted spectrum.
After subtraction
Sum of singly-labeled
Doubly-labeled
Simulation and Fourier Deconvolution
x1.6
3200 3250 3300 3350M agnetic F ie ld (gauss)
3200 3250 3300 3350M agnetic F ie ld (gauss)
A
B
C
0 20 40D ata poin t
0.00
D
H C AII121-206
r = 16 – 18 Å
First integral
DEER measurement of distance between spin labels in carbonic anhydrase
H C AII121-206
H C AII67-206
0.0 0.2 0.4 0.6 0.8
tim e (s)
r = 18 Å (70%) 24 Å 30%)
r = 20 ± 1.8 Å
Distances (Å) Between Spin Labels on Carbonic Anhydrase Determined from EPR Spectra
Doubly spin-labeled variant
Distance between -carbonsa
Half-field transition
Fourier Deconvo-
lution
Lineshape Simulation
DEER
HCAII67-121 8.8 7 7-8 -
HCAII59-174 5.4 8 8.5-9 9-10 -
HCAII121-206 10.9 - 16-18 17-19b 18 (70%)
24 (30%)
HCAII67-206 17.9 - 17-20 20 1.8
aDistance between carbons of native amino acids at the sites where substitution with cysteine was performed, calculated from the X-ray crystal structure, cAssuming 100% doubly-labeled protein.
Persson et al., Biophys. J. 80, 2886 (2001).
Electron-nuclear double resonance (ENDOR)
The observation of the nuclear spin spectrum is realized by the simultaneous irradiation of an electron spin transition and a nuclear spin transition, a technique named Electron-Nuclear Double Resonance (ENDOR). The dramatic resolution enhancement achieved by ENDOR results to a large extent from the fact that two resonance conditions have to be fulfilled simultaneously: one for the electron spin transition (EPR) and one for the nuclear spin transition (NMR).
One stays in ESR resonance (MW) keeping ESR lines saturated and sweeps rf field…ESR-detected NMR: ESR signal vs rf fieldAt the NMR resonance an increase in relaxation lifts saturation and produces ESR signal…ENDOR is much more sensitive than NMR (NB: splitting and population difference in ESR and NMR)
BRUKER reference
The double resonance technique can highly simplify a spectrum since everyadditional nucleus with spin I multiplies the number of lines by (2I+1) …. But only
adds two lines to the ENDOR spectrum
Too bad: a Huge number of hyperfine lines in ESR
Nice and clean ENDOR spectra!
Even worse: the hf structure is totallyunresolved
ENDOR: resolution enhancement
BRUKER reference
Useful references for cw and pulse ESR
Wertz and Bolton. Electron paramagnetic resonance.
Carrington and MacLachlan. Magnetic resonance in chemistry.
Slichter (Good general background on NMR and ESR)Principles of magnetic resonance, 3rd Ed.
Schweiger and Jeschke (pulse ESR/EPR)Principles of pulse electron paramagnetic resonance
Berliner (Ed.) (Biological applications of resonance techniques >20vv.)Biological Magnetic Resonance, Spin Labeling (vv. 1, 2, 8),
Distance measurements (v. 19)
Poole (Experimental methods, mostly cw)Electron spin resonance: A comprehensive treatise onexperimental techniques
