NMR: Relaxation Measurements. How to measure relaxation rates? T 1 : Longitudinal or spin-lattice...
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Transcript of NMR: Relaxation Measurements. How to measure relaxation rates? T 1 : Longitudinal or spin-lattice...
![Page 1: NMR: Relaxation Measurements. How to measure relaxation rates? T 1 : Longitudinal or spin-lattice relaxation. M z is restored, the system goes back to.](https://reader033.fdocuments.in/reader033/viewer/2022052214/56649d945503460f94a7b4f6/html5/thumbnails/1.jpg)
NMR: Relaxation Measurements
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How to measure relaxation rates?
T1: Longitudinal or spin-lattice relaxation. Mz is restored, the system goes back to equilibrium.
T2: Transverse or spin-spin relaxation. Transverse magnetization Mx,y vanishes, the observable signal disappears.
For measurements pulsed methods should be used
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In principle we could calculate T2 according to
Dn1/2 = 1/pT2
from the width of the Lorentzian lineshape of the signals in our spectrum. But...
T2-Measurement
This value is strongly depends on the inhomogeneity of our B0-field.
We are rather interested in the 'pure' spin-spin relaxation component (which, in contrast to the B0-field, is a molecular property)!
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Homogeneous and inhomogeneous linewidth• However, transverse relaxation can also proceed due to
statistical (and static) inhomogeneities in the precession frequency ω0. T
• Resulting rate of Free Induction Decay is denoted as
• The first contribution is the same for all molecules and thus defines the homogeneous linewidth.
• The last contribution defines the inhomogeneous linewidth. • It is quite common that
• There are methods of getting rid of the inhomogeneous linewidth!
w
DNMRspectrum
2
*2
11TT
2*
2 TT
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Spin echo• Large inhomogeneous linewidth means very fast dephasing of the spin• However, dephased magnetization can be focused back by pulses• Let us consider pulse sequence π/2x - τ - π x
• Explanation: let us divide system into isochromates having the same frequency ω0. Their offsets are Δω=ω0–ω. At certain time they all have different phases
• But at t=2τ all have the same phase – there is an ‘echo’!
p/2 p echo
0 t 2tt
X´
Y´
t=0 j=0
X´
Y´
j=Dwt
X´
Y´
j=p–Dwt+Dw(t–t)
X´
Y´
t=2t j=p
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Carr-Purcell method• Spin echo not only allows one to get rid of the inhomogeneous broadening but
also to measure T2. To do this, however, the pulse sequence should be modified because the repetition rate of the echo experiment is <1/T1 (quite low)
• Luckily, the whole echo decay can be measured while applying one pulse sequence (C-P). Let us apply the sequence π/2x - τ - πx – 2τ - πx – 2τ - …
• At t=2τ we will have the first echo (negative phase). Then spins start dephasing again, the next πx-pulse again focuses them (positive phase!). Thus, there are echoes at times 2τ, 4τ, 6τ, 8τ,… amplitudes decay with T2.
• Drawback: if the pulses are not set precisely, mistakes are accumulated with time. It is better to use CPMG sequence: π/2x - τ - πy - 2τ - πy - 2τ - …
Y´
X´
Y´
X´
Y´
X´
Y´
X´
Y´
X´ X´
Y´
X´
Y´
X´
Y´
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T2-Measurement
Spin-echo sequence
t180o90o
tT2
I(t)=I(0)exp(-2t/T2)
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T2-Measurement
Spin-echo sequence
t180o90o
t T2
Before 90o After 180o
Before acquisition
Before 180oAfter 90o
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T2-Measurement
The spin-echo experiment:
Compensates for the component of T2 that origins from field inhomogeneity
The relaxation can be measured selectively Important dynamic properties of the molecule can
be extracted that way
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T2-Measurement
The experiment is repeated a number of times with increasing delays t.
I (t)=I (0)exp(-2t/T2)
I (t)
t
I (0)
T2 is obtained from a plot of I(t) against t:
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Inversion-recovery technique
• Determination of T1 is often quite important as well• Standard method is inversion-recovery• First we turn the spin(s) by pulse (usually π/2 or π) and then look how system
goes back to equilibrium (recovers Z-magnetization). If the pulse is a π-pulse magnetization will be inverted (maximal variation of magnetization) and then recovered
• Equation for Mz is as follows:
• The kinetic trace (t-dependence) gives T1-time• To detect magnetization at time t in NMR one more π/2-pulse is applied,
sequence is then πx - t (variable) - πx/2 - measurement• For broad lines spin echo is used for detection, the pulse sequence is then πx
- t (variable) - πx/2 - τ - πx - τ - measurement • Both sequences should be repeated many times at different delays t
100 /exp))0(()( TtMMMtM zz 1
–1
t
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T1-Measurement
Inversion recorvery
t
180o 90o t = 0
t >> T1
t = ln(2)T1
Mz(t)=Mo[1-2exp(-t/T1)]
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Inversion-Recovery
Mz(t)=Mo[1-2exp(-t/T1)]
t
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Inversion-Recovery
Mz(t)=Mo[1-2exp(-t/T1)]
>> t T1 = t ln(2)T1
t
Mz
+1
-1
0
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t = ln(2)T1
zero observable signal
Fast T1-Measurement
Inversion recorvery
t
180o 90o
For a quick estimation of T1: directly search for the time t, which results in zero intensity (tzero) and calculate T1 from this:
T1 = tzero/ln(2)
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NMR: NMR spectrometer
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Magnet (probe, sample)
Console (transmitter,receiver, interface)
Computer (pulse-programming, data processing)
Probe
What you see of it
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Inside a Magnet
1 Bore tube2 Filling port (N2)3 Filling port (He)4 Outer housing5 Vacuum chambers/ radiation shields6 Nitrogen reservoir7 Vacuum valve8 Helium reservoir9 Magnet coil
Shimming coils (not shown here) are also very important:One should resolve tiny splittings!!! Homogeneity of the order of 10–
9 is necessary for NMR
What you (usually) don’t see of it
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Tesla and MegaHertz
The strength of a magnetic field is meassured in Tesla (for strong fields) or Gauss (for weaker fields). 1 Tesla corresponds to 10000 Gauss. The earth magnetic field is about 0.5 Gauss.
The strength of an NMR magnet is usually given in terms of its 1H resonance frequency in MHz:
Tesla 2.3 8.4 11.7
14.1
16.5
17.6
21.1
MHz 100 360 500 600 700 750 900
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Why go for stronger fields?
Another reason is resolution: It is always better to work with AX-systems and only zz-parts of the scalar couplings spectra are much simpler and better resolved
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Signal-To-Noise Ratio S/N
S/N or the signal-to-noise ratio is a measure for the sensitivity of the NMR experiment:
S/N ~ n g5/2 B03/2 (NS)1/2
MHz 500 600 700 750 900
S/N 1.0 1.3 1.7 1.8 2.4
reso-lutio
n
1.0 1.2 1.4 1.5 1.8
Relative sensitivity and resolution of our spectrometer
Number of spins Number of scans
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NMR probe
Locates the sample at homogeneous field;
RF curcuit and coil for irradiating the sample and detecting its subsequent response;
Additional functions (sample rotations, T stabilization, field gradients)
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Transmitter, receiver, amplifiers Transmitter section: produces RF irradiation; consists of RF-
synthesizer, pulse gates and RF amplifierS(t)=Acos(ωt+φ(t))
φ(t) can be rapuidly switched
Receiver section: preamplifier, quadrature reciever (comparison of the signals with a reference wave to get rid of fast oscillations)
Mx(t)=M0cos(ω0t) M0cos(Ω0t) where Ω0=ω0–ωref going from 300 MHz to 1 MHzThe procedure does not distinguish positive and negative Ω0 receiver supplies two signals:
SA(t)=M0cos(Ω0t) and SB(t)=M0sin(Ω0t) full information is retained but phasing is necessary
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Hardware (Summary)
Magnet (Dewar, coil, shims)
Probe
Transmitter, receiver, amplifiers
Acquisition computer (ADC)
Sensitivity
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NMR: NOE
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NMR: NOENOE=Nuclear Overhauser Effect
Overhauser effect (EPR and NMR meet): NMR enhancement after pumping EPR transitions; works on dipolar relaxation of electron and nucleus
NOE also works using dipolar relaxation of two nucleiApplications are quite different: not mainly enhancing
NMR signals but rather measuring distances between spins
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NMR: NOE
RF
RF
RF
A B
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regular spectrum
NOE, small molecule
NOE, large molecule
Nuclear Overhauser Effect
RF
RF
RF
A B
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describes the change in intensity of a signal due to the NOE
Nuclear Overhauser Effect
eq
eq
M
)M(Mη
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Energy Level Diagram
W1A
W1A
W1B
W1B
A0 = B0 = D
W0
W2
baab
bb
aa
With population differencesfor the A and B transitionsin the undisturbed system:
W0 and W2 involve simultan-eous transitions of spins Aand B.Spins relax together in this mechanism.When spin A is off-equilibrium spin B will feel it.Difference of W0 and W2 is important
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A
A
A
A
W2 > W0
small molecules
W0 > W2
large molecules
W1A
W1A
W1B
W1B
A0 = B0 = D
A = 1.5 D
A = 0.5 D
W2
W0
A
A
A = A0 = DB = 0
Nuclear Overhauser Effect
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Nuclear Overhauser EffectIn practice we find the NOE ranging from +0.5 for small up to -1.0 for large moleculesSign of NOE depends on whether W0 (minus) or W2 (plus) is dominating
0.5
0.0
-0.5
-1.0
0.01 0.1 1.0 10 100
w0tcfasttumbling
slowtumbling
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tc = rotational correlation time (size of molecule)
r = distance between the two corresponding atoms
Distances from NOEs
tc
r6 ~
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tc
r6
ref
=tc
ref. r6
ref
tc tcref
refr = rref 6
Distances from NOEs
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Application for NOEs
• Information about short 1H-1H-distances in molecules (< 5Å)
• Translated into distance-constraints applied in Molecular Simulations
• Main source of structural information in NMR
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• Information about short 1H-1H-distances in molecules (< 5Å)
• Translated into distance-constraints applied in Molecular Simulations
• Main source of structural information in NMR
• It will be explained how it works
Application for NOEs
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NMR: 2D-NMR
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NMR: 2D-NMRWhy is 1D (just NMR spectrum) not enough?
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1-Dimensional NMR
1D FT-NMR(simplest case)
preparation - detection
S(t)FT
S(w)
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A 1D-Spectrum of a Protein
For large proteins it is really hard to assign NMR signals and to obtain quantitative information from the spectra!Too many peaks Spectrum is a mess!
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2-dimensional NMR
2D FT-NMR
Preparation - evolution - mixing - detection
t2 – direct domain; t1 – indirect domain
t1 tm t2
S(t1,t2)FT1, FT2
S(w1,w2)
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A 2D-Spectrum of a Protein
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A Signal of a 2D Spectrum
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Contour plot of the same Signal
Compare: Topographical map (lines of equal height)
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Now let us see how it worksHow to get to this second dimension???
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t1
The size of the signal depends onthe evolution in t1: the signal is said to be 'modulated' with w1
For simplicity we look at a single frequency wwhich is the same in t1 and in t2 (no mixing)!
t2=0
FT (t2)
t2
The Second Time Domain
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t2=0
FT (t2)
t2 t1 FT (t1)
w2
w1
The Second Time Domain
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The SCOTCH Experiment
Spin COherence Transfer in (photo) CHemical reactions
Reaction A B with a proton at wA in A which resonates at wB in B. hn
t1 t2light
The corresponding pulse sequence
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t1 t2light
The proton's magnetization is in t1
modulated with the frequency wA. After the light pulse, the same proton evolves with wB.
Subsequent FT of the both time domains results in a 2D spectrum with a peak at wA in F1 and wB in F2:
The SCOTCH Experiment
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t1 t2light
The proton's magnetization is in t1
modulated with the frequency wA. After the light pulse, the same proton evolves with wB.
If A would not completely be converted to B by the light pulse, we would be able to observe a diagonal peak ofA as well:
The SCOTCH Experiment
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Preparation - evolution - mixing - detection
t1 tm t2
In the mixing period the frequency modulationof one nucleus is transferred to another one!
General scheme of 2D NMR experiment
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No mixing (tm = 0): Only diagonal peaks!Boring case
Mixing (tm > 0): We get cross correlated peaks (cross peaks)!Interesting case
The Mixingperiod
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Some 2D NMR experiments: COSY and NOESY
SY = SpectroscopY (always in NMR)COSY = COrrelation SYNOESY = NOE SY
For both techniques there are also hetero-nuclear versions (for instance, proton-carbon, proton-nitrogen)
One can use other methods to obtain cross-peaks and acquire specific information on the spin system
One can go from 2D-NMR to 3D-NMR and even further
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COSY experiment
COSY: J-coupling (through bond connectivities of neigh-boring atoms, max. ~3 bonds)
t1 t2
π/2 π/2
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COSY experiment
COSY: J-coupling (through bond connectivities of neigh-boring atoms, max. ~3 bonds)
t1 t2
How does it work?
Effect of the chemical shift:I1x I1xcos(ω1t)+I1ysin(ω1t)
Effect of J-coupling with spin 2:I1x I1xcos(J12t)+I1yI2zsin(J12t)
Why I1yI2z term?
y
x
β α
y
x
β α
x-component changes in the usual way; y-component is given by the population difference of the α- and β-states of spin 2, which is I2z
π/2 π/2
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COSY experiment
COSY: J-coupling (through bond connectivities of neigh-boring atoms, max. ~3 bonds)
t1 t2
How does it work?
I1z I1x I1y I1y I1x
x-magnetization stays on spin 1The efficiency of this pathway issin(ω1t1)cos(J12t1)sin(ω1t2)cos(J12t2)Diagonal peak will appear in the COSY-spectrum
π/2y t1 π/2y t2
π/2 π/2
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COSY experiment
COSY: J-coupling (through bond connectivities of neigh-boring atoms, max. ~3 bonds)
t1 t2
How does it work?
I1z I1x –2I1xI2z 2I1zI2x I2x
x-magnetization went from spin 1 to spin 2The efficiency of transfer issin(ω1t1)sin(J12t1) sin(ω2t2)sin(J12t2)Cross-peak will appear in the COSY-spectrumCross-peak is the direct evidence for J-coupling
π/2y J12 π/2y J12
Gain is two-fold:(1) Spectral resolution is increased because peaks become resolved in 2D;(2) Knowledge on additional coherence pathways can be obtained.
π/2 π/2
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COSY experiment
COSY: J-coupling (through bond connectivities of neigh-boring atoms, max. ~3 bonds)
t1 t2Result for more than 2 spins
When the spins are scalar coupled cross-peak will appearIn 2D peaks, which overlap in 1D-spectrum, become resolved
ω1→ω 2→
Ω1 Ω2 Ω3 Ω4
π/2 π/2
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NOESY experiment
NOESY: dipolar couplings (through Space, NOEs give distances)
tm t2Cross-peaks come not from J but from NOE during the mixing period
t1
How does it work?
I1z –I1y –I1y –I1z –I2z I2y -I2x
x-magnetization went from spin 1 to spin 2The efficiency of transfer is different from the COSY casesin(ω1t1)sin(J12t1) sin(ω2t2)sin(J12t2)Cross-peak will appear in the NOESY-spectrumCross-peak gives information on NOE distance between the spins
π/2x t1 π/2x NOE π/2x t2
π/2 π/2 π/2
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Some 2D NMR experiments: COSY and NOESY
SY = SpectroscopY (always in NMR)COSY = COrrelation SYNOESY = NOE SY
For both techniques there are also hetero-nuclear versions (for instance, proton-carbon, proton-nitrogen)
One can use other methods to obtain cross-peaks and acquire specific information on the spin system
One can go from 2D-NMR to 3D-NMR and even further
![Page 61: NMR: Relaxation Measurements. How to measure relaxation rates? T 1 : Longitudinal or spin-lattice relaxation. M z is restored, the system goes back to.](https://reader033.fdocuments.in/reader033/viewer/2022052214/56649d945503460f94a7b4f6/html5/thumbnails/61.jpg)
INEPT experiment not yet 2D, but often used in 2DNMR signal is proportional to the γ-ratio
4 times higher signals for protons than for 13C; even 10 higher than for 15N
Possible improvement is polarization transfer 1H→X-spin
NOE is not (always) the best solution: coherent mechanisms work better
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INEPT experiment not yet 2D, but often used in 2DNMR signal is proportional to the γ-ratio
4 times higher signals for protons than for 13C; even 10 higher than for 15N
Possible improvement is polarization transfer 1H→X-spin
NOE is not (always) the best solution: coherent mechanism and proper pulsing work better
INEPT=Insensitive Nuclei Enhanced by Polarization Transfer
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INEPT experiment: explanation
All spins are along x
τ
t2
τ
π/2 π π/2
π/2 π π/2
1H
X
INEPT: transferring polarization from proton to X-nucleus
y
x
β α
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INEPT experiment: explanation
For τ=1/4J the angle between spins is 90-degree
τ
t2
τ
π/2 π π/2
π/2 π π/2
1H
X
INEPT: transferring polarization from proton to X-nucleus
y
x
β α
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INEPT experiment: explanation
Components are flip by protons pulseTheir colors are exchanged by X-nucleus pulse
τ
t2
τ
π/2 π π/2
π/2 π π/2
1H
X
INEPT: transferring polarization from proton to X-nucleus
y
x
βα
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INEPT experiment: explanation
Spins are along y for τ=1/4J
The last proton pulse results in one component positive and one negativeReminder: first both were positive
τ
t2
τ
π/2 π π/2
π/2 π π/2
1H
X
INEPT: transferring polarization from proton to X-nucleus
y
x
βα
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INEPT experiment: explanationResulting populations
Now the final pulse for X-nucleus does the detectionGain is given by the ratio of gammasGain can be further increased when NMR of X is detected via protons
τ
t2
τ
π/2 π π/2
π/2 π π/2
1H
X
INEPT: transferring polarization from proton to X-nucleus
Pulsing really makes possible many nice tricks with the spins
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The rest of 2D-NMR will be given by Prof. Robert Kaptein
The rest is:(i) Other methods;(ii) Their applications to proteins.