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Magnetisation Transfer Schemes
P. K. MadhuDepartment of Chemical Sciences
Tata Institute of Fundamental ResearchHomi Bhabha Road
ColabaMumbai 400 005, India
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Sensitivity of NMR Spectroscopy
S/N∼ NγexcγdetB3/20 NST1/22
S/N signal-to-noise ratio
N number of spins
gyromagnetic ratio of excited spins
gyromagnetic ratio of detected spins
static magnetic field
NS number of scans
transverse relaxation time
γexc
γdet
B3/20
T1/22
sample concentration
isotope labeling
magnet size
measurement time
molecular weight
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Spin-1/2 nucleus
|α>
|β>
ΔE=(h/2π) γBFor 1H:γ=26.75 rad T-1s-1ΔE=2.65*10-25J for B=9.4 TkT= 4.14*10-21 J
ΔE/kT=6.4*10-5
Sensitivity of NMR Spectroscopy
Preferred Nβ
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Spin-1/2 nucleus
|α>
|β>
ΔE=(h/2π) γBFor 1H:γ=26.75 rad T-1s-1ΔE=2.65*10-25J for B=9.4 TkT= 4.14*10-21 J
ΔE/kT=6.4*10-5
Sensitivity of NMR Spectroscopy
Preferred Nβ
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2 million
1 million+16
1 million+64
1 million
1 million
1 million
1 million+128
ΔE
B0 (Tesla)
0 T 2.35 T 9.4 T 18.8 T
Energy Levels, Magnetic Field, and Relative Population
Spin-1/2 nucleus
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NMR Active Nuclei: Properties
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NMR Concentrations
Can the polarisation from an abundant spin, like 1H, betransferred to a rare spin, like 13C?
Polarisation Transfer
Sensitivity of NMR Spectroscopy: How to Increase?
Higher magnetic fields
Lower temperatures Cryoprobes/sample cooling
Hyperpolarised NMR Transfer of abundant population from some source to rare nuclei
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Selective Population Transfer (SPT)
Consider two proton spins, homonuclear 1H-1H spin system, weakly J coupled(having a large chemical-shift difference), forming an AX spin system
αα
αβ βα
ββ
A Xx
X
A
A
2 3
1
4 1,2 3,41,3 2,4
• • • •
• •• •
RF irradiation leading to saturationOf 1-3 transition
αα
αβ βα
ββ
A X
X
X
A
A
2 3
1
4
1,2
3,4
1,3 2,4
• • •
• • •• • 3-4 transition gets
a 50% increase
Population is transferred from one nuclues to the other
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Selective Population Inversion (SPI)
180 90
Soft pulse, transition selective
αα
αβ βα
ββ
A XX
X
A
A
2 3
1
4 1,2 3,41,3 2,4
• • • •
• •• •
Soft pulse, transition selective
αα
αβ βα
ββ
S
S
I
I
2 3
1
4
1,2
3,4
1,3
2,4
• •
• • • •• •
3-4 transition getsa two-fold increase
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Polarisation Transfer
Both SPT and SPI can lead to polarisation transfer, but we are onlydealing with homonuclear spin systems, not really interesting
SPT and SPI can identify scalar coupled spin systems in crowdeddpectral regions
But the real use of these are in heteronuclear spin systems
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SPI in Heteronuclear Spin Systems1,2 3,4
180, soft pulseon 1H
Overall 13C intensity:Before perturbation=2+2=4And after pertrubation=6+10=16Four-fold enhancement!
13C2,4
αα
αβββ
13C
1H
1H
βα• • • •• • • •
1
4
3
2
1,2
3,4
1,3
A X
• • • • •• • • • •
• • 13C1H
αα
αβββ13C
13C
1H
1H
βα• • • •• • • •
• • • • •• • • • •
• •
1
4
3
2
1,3 2,4
A X
13C1H
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SPI in Heteronuclear Spin Systems
By manipulating the polarisation of the protons, we have accomplished a four-fold enhancement for 13C signals, counting both positive andnegative signals
The factor of 4 comes from γH/γC ratio; it will be 10 for 1H to 15N polarisation transfer
This is all fine, but we have up and down signals, not quite interesting
2,4
1,2
3,4
1,3
A X
13C1H
Overall 13C intensity:Before perturbation=2+2=4And after pertrubation=6+10=16Four-fold enhancement!
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Echo Modulations
x
y
α
β
AX spin system, heteronuclear
18090
A
X
MAXα
MAXβx
y
MAXα
MAXβ
x
y
MAXα
MAXβ
x
y
α
β
MAXα
MAXβ
τ τ
Everything is refocussed, chemical shifts, RF and B0 inhomogeneities, andcoupling (scalar) effects- The spin-echo phenomenon
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Echo Modulations
x
y
α
β
AX spin system, homonuclear
18090
A
MAXα
MAXβx
y
MAXα
MAXβ
x
y
MAXβ
MAXα
x
y
MAXβ
MAXβ
τ τ
No J refocussing
φ
(2 ) 4 AXJφ τ π τ=The difference in angular frequency between the two components is 2πJAX
180
X τ τAX spin system, heteronuclear
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x
y
x
y
tD = 1 / 2JJ / 2
NO REFOCUSSING REFOCUSSINGBEFORE DECOUPLING BEFORE DECOUPLING
J-Modulation and Polarisation Transfer
13C magnetisation vectors,+5 and -3 in length in thexy plane
180
90
tp
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J-Modulation and Polarisation Transfer
180
90x
τ τ
A, 1H
τ=1/4J
X, 13C
13C signal of lengths -3 and 5 created along the z-axis
x
yMXAα
MXAβ
τ=J/4x
y
900x
180
180x
180xA
180xXx
τ=J/4x
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J-Modulation and Polarisation Transfer
We achieve polarisation transfer and signal enhancement, but:
•The proton 180 pulse has to be selective•Lack of generality•The need is to set up appropriate polarisation of all the protontransitions regardless of frequency/selectivity
Hence, we need a pulse sequence that generates anti-phaseproton transition for every 1H-13C spin pairs, but non-selectively
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INEPT
Insenstive nuclei enhanced by polarisation transfer
90x
τ τA, 1H
X, 13C
180x 90y
180x 90x
τ=1/4J
The idea is to create an antiphase doublet for the proton magnetisationand then a 90 pulse on 13C will create the (-3,5) carbon magnetisation
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x
y
z
90x
τA, 1H180x
τ
X, 13C
90y
180x 90x
90xA
Monitor the 1H magnetisation vectors
τ=J/4
x
yz
900
x
y
z180xA,X
τ=J/4
x
y
z
90yA
x
y
z
Anti-phase proton magnetisation and the subsequent90 on 13C creates the (-3,5) carbon vectors as earlierHere, we achieve uniform polarisation transfer
INEPT
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180xA
180x
X
δ δ
a b
90y
90x
c
12 ( )4
INEPTx z y
AX
A A XJ
δ⎯⎯⎯→ =
INEPT
2,4
1,3
13C
Factor of 4 as enhancement
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INEPT
Az
-Ay
-Ay cosπJδ
Ay cosπJδ
Ay cosπJδ
2AxXz sinπJδ
2AxXz sinπJδ
-2AxXz sinπJδ
Ay cos2 πJδ -2AxXz cosπJδ sinπJδ -2AxXz sinπJδ cosπJδ -Ay sin
2 πJδ
Ay cos2 πJδ -Ay sin
2 πJδ-4AzXz cosπJδ sinπJδ
Ay cos2 πJδ -4AzXy cosπJδ sinπJδ
-Ay sin2 πJδ
δ = 14J
0.5Ay -0.5Ay2AzSy
90x
δA, 1H
X, 13C
180x
δ
90y
180x 90x2πJAzXz
90Ax
180Ax
180Xx
2πJAzXz
90Ay
90Xx
δ = 14J
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INEPT
• Enhances polarisation– Basic building block in most pulse schemes
• Spectral editing– To select functional groups of our choice
• Establishes correlation between sets of coupled spins– Most important in multi-dimensional experiments
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INEPT
13C coupled
INEPT SpectrumINEPT
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-1:1-1: 0:1 -1: -1: 1:1
INEPT Spectral Patterns
CH3CH2CH
13C spectrum
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180xI
180x
S
δ δ
a b
90x
90x
c
Refocused NEPT
. 1( )4
ref INEPTx x
IS
I SJ
δ⎯⎯⎯⎯→ =
180xΔ/2 Δ/2
d
180x
Refocused INEPT
90x
For CH spin systems, the optimum value for Δ=1/2JCH
In case of CH, CH2, and CH3 groups, optimum value for Δ=1/3JCH
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Behaviour of CH, CH2 and CH3 Groups
Spectral Editing
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180x
90x
τ τθy
τ
180x
90x
I, 1H
S, 13C
Distortionless Enhancement by Polarisation Transfer
DEPT
The relative intensities of the mulitplet components in INEPT spectradiffer from the normal spectra, hence, DEPT
In DEPT, the θ pulse takes the role of Δ in INEPT, so the t delayis set to 1/2J and depending on the values of θ one gets variousfunctional group spectra
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DEPT45 experiment yields a positive peak for every carbon with attached protons: Ca at 16 ppm, Cb at 29 ppm, and Cd, Ce, and Cf at 128.5, 128.9, and 129 ppm, respectively. Note in the spectrum below that carbon in the CDCl3 solvent does not give a signal, since it has no attached protons
DEPT45
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Dept 90 yields only CH yields peaks; CH0, CH2, and CH3 are invisible. In our example we see only three lines due to Cd, Ce, and Cf in the aromatic range from 126 to 129 ppm.
DEPT90
-
With DEPT135 CH2 yields negative peaks, whereas CH and CH3 are positive. Thus, we see Ca, Cd, Ce, and Cf as positive peaks, while Cb is negative.
DEPT135
-
To distinguish the various multiplicity patterns in 13C NMR, three DEPT spectra are acquired
DEPT: Spectral Editing
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DEPT: Spectral Editing
CH3=FID(45)+FID(135)-0.707 FID(90)
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DEPT: Spectral Editing
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Major Relaxation Pathways
1. Dipole-dipole coupling
2. Scalar coupling
3. Chemical shift anisotropy
4. Chemical exchange
5. Paramagnetic interactions
6. Spin rotation
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NOE is the change in the intensity of an NMR resonance whenthe transitions of a dipolar coupled spin are perturbed (saturated/inverted)
The NOE enhancement of I spin upon saturating S spin is defined as
0
0
{ }II IS
Iη −=
Equilibrium I intensity
Perturbed spin
Observed spin
Nuclear Overhauser Effect
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αα (∗∗∗)
ββ (∗)
(∗∗∗) αβ
W1X
W1X
W1A
W1A
βα (∗)W2AX
NOE: Transition Probabilities
W0AX
W0AX and W2AX are determined by dipolar couplings andhave a distance dependence, r-6, and rotational correlationtime dependence, τc
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NOE and Molecular Motion
Relaxation
W2 W1 W0
Depends on the strength of the local (dipolar) fields fluctuating at that frequency, ω
Depends on the molecular motion at that frequency, ω
W0 transition will be predominant when the molecules tumble at ωA-ωX frequency, kHz, for large moleculesW1 for molecules tumbling at Larmor frequenciesW2 for molecules tumbling at twice the Larmor frequencies, small molecules, fast tumbling
Small molecules lead to positive NOEBig molecules lead to negative NOESomewhere in between null NOE
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W2AX - W0AX
2W1X + W2AX + W0AX ηA = = fA{X}
σAX = W2AX - W0AXρAX = 2W1X + W2AX + W0AX
ηA = σAX / ρAX= fA{X}
σAX = W2AX - W0AXρAX = 2W1X + W2AX + W0AX
ηA = σAX / ρAX= fA{X}
NOE: Some Expressions
Wn ∝ 1r6 J(nω)
J(nω) = τc1+(nωτc)2
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Steady-State NOE
ωτc1
ωτc=1.12
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Hb
Ha
Hc
HbHa Hc
_ =ηab ηac
C
NOE Difference Spectroscopy
13C
1H
Steady-state NOE
Knowing a reference distance, other distances may be calculated
ηab ∝ rab-6rac = rab * ( ηab / ηac ) -1/6
ηac ∝ rac-6
ηab ∝ rab-6rac = rab * ( ηab / ηac ) -1/6
ηac ∝ rac-6
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αα (∗∗)
ββ (∗∗)
(∗∗∗∗) αβ
W1X
W1X
W1A
W1A
βα ()W2AX
W0AX
180X90
selective inversion
Transient NOE
τm
τm
Inte
nsity
Monitor the magnetisation of the dipolarcoupled spin by inverting the other spinas a function of the mixing time. The initialrate of growth is proportional to r-6
Steady-state NOE could give ambiguous results in big molecules due to othermagnetisation transfer processes, such as, spin diffusion. Hence, transient NOEmuch more desirable and useful
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Nuclear Overhauser Effect
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Nuclear Overhauser Effect
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Nuclear Overhauser Effect
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Nuclear Overhauser Effect
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Nuclear Overhauser Effect
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• Useful to identify spins undergoing cross-relaxation
• Direct dipolar couplings provide primary means of cross relaxation
• Cross relaxation manifests in the form of cross peaks in the NOESY spectrum
Nuclear Overhauser Effect
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Overhauser being awarded the National Medal of Science, 1994
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"Overhauser proposed ideas of startling originality, so unusual that they initially took portions of the scientific community back, but of such depth and significance that they opened vast new areas of science."
The consequences of this discovery---known as the Overhauser Effect---for nuclear magnetic resonance, and through nuclear magnetic resonance for chemistry, biology and high-energy physics have been enormous. The idea, which has also had very practical consequences, was so unexpected that it was originally resisted vehemently by the authorities in the field. Not until its existence was demonstrated experimentally by Slichter and Carver in 1953 was it fully accepted. It has been said that one can judge the importance of a new discovery in physics by the number of other fields of science and engineering it impacts. From this point of view this contribution of Overhauser ranks among the highest.
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When first proposed as a contributed paper at an APS meeting in April 1953, the proposal was met with much skepticism by a formidable array of physics talent. Included among these were notables such as: Felix Bloch (recipient of 1952 Physics Nobel Prize), Edward M. Purcell (recipient of Nobel Prize 1952 with Bloch and session chair), Isidor I. Rabi (recipient of Physics Nobel Prize, 1944) and Norman F. Ramsey (recipient of Physics Nobel Prize, 1989). Eventually everyone was won over. In a letter dated 27 July 1953, Norman F. Ramsey stated the matter succinctly2,3:
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July 27, 1953Dear Dr. Overhauser:
You may recall that at the Washington Meeting of the Physical Society, when you presented your paper on nuclear alignment, Bloch, Rabi, Pearsall, and myself all said that we found it difficult to believe your conclusions and suspected that some fundamental fallacy would turn up in your argument. Subsequent to my coming to Brookhaven from Harvard for the summer, I have had occasion to see the manuscript of your paper.
After considerable effort in trying to find the fallacy in your argument, I finally concluded that there was no fundamental fallacy to be found. Indeed, my feeling is that this provides a most intriguing and interesting technique for aligning nuclei. After considerable argument, I also succeeded in convincing Rabi and Bob Pound of the validity of your proposal and I have recently been told by Pound that he subsequently converted Pearsall shortly before Pound left for Europe.
I hope that you will have complete success in overcoming the rather formidable experimental problems that still remain. I shall be very interested to hear of what success you have with the method.
Sincerely,Norman F. Ramsey
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April 20, 1993Dear Al:
I greatly appreciate your thoughtful remarks about the letter I wrote you forty years ago. Although I clearly remember surprising some of my friends by writing a very favorable referee report, I had forgotten that I also had written you a letter. You might be interested in how I came to get the matter straight and avoid the lifelong embarrassment of being responsible for the rejection of a great pioneering paper.
After the APS meeting I did not understand your paper and was thoroughly convinced by the vigorous arguments of Bloch, Rabi and others that a radio frequency field always produces heating. I was consequently annoyed when I was asked to referee the paper and therefore would have to find exactly what was wrong. I started my study with strong prejudices against you but I then remembered that in high school physics I had always had trouble remembering how a Servel (gas) refrigerator worked. I decided that I could not write a negative referee report until I understood once again how the Servel worked. By the time I understood that, I had lost my prejudice against your paper and on further study was convinced you were right. Incidentally the easiest way for me to remember how in principle a gas refrigerator can work without violating thermodynamics is to remember one could use the heat of the gas flame to operate a steam engine which in turn could operate a mechanical refrigerator.
Sincerely yours,Norman F. Ramsey
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NORMAL, NO NOE
INEPT
REFOCUSSED INEPT
REFOCUSSED INEPT AND
DECOUPLING
NORMAL DECOUPLING
FULL NOE
13C Chloroform Spectra
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INEPT
29Si with INEPT Scheme
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Enhancement via
NOE T1 of interest is that of observed nucleus
INEPT T1 of interest is that of proton
INEPT and NOE Transfers
INEPT
NOE
I=I0γAγX
I=I0(1 +γA2γX
)
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Signal strength available by direct observation in the presence of full NOE from protons and from polarisation transfer from protons to the heteronucleus
INEPT and NOE Transfers
Nucleus Maximum NOE Polarisation Transfer
31P 2.24 2.47
13C 2.99 3.98
29Si -1.52 5.03
15N -3.94 9.87
57Fe 16.48 30.95
103Rh -14.89 31.78
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• Time scales and molecular motions
Atomic fluctuations, vibrations. Influences bond length measurementsGroup motions. (covalently linked units) Molecular rotation, reorientation Relaxation, linewidths, correlation timesMolecular translation, diffusion DOSY NMRRotation of methyl groups. 2H NMRFlips of aromatic rings. 2H NMRDomain motions. 2H NMR
Chemical exchange, proline isomerization Chemical shiftsAmide exchange 15N-1H HSQCLigand binding Transferred NOE measurements
Dynamics and Relaxation
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s ns ps fsμsmsFastSlow Very slow
Slow Fast Very fast Ultra fast
MacroscopicDiffusion,Flow
Chemical exchange
Molecular rotations
Molecular vibrations
Motional Timescales
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Chemical Exchange
Motional process leading to formation or rupture of chemical bonds: Chemical exchange
The electronic structure is different in both the forms leading to differencechemical shifts and coupling constants when the exchange processtakes place: Detectable by NMR provided the process is on an appropriatetime scale
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Conformationalequilibrium
Chemicalequilibrium
Kex
KB
NMR and Dynamic Processes
This could be a chemical reaction, conformational equilibrium, exchange between the bound and free states of a ligand/protein complex, ligand binding of drugs to proteins.
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N H
O
N H
O
NMR: Measurement of Rate Constants
Inversion of NN-dimethylformamide
1 1Rate (s) >> or
δr - δb Δδ
1 1Rate (s) >> or
δr - δb Δδ
The two methyl groups exchange due to the double-bond nature of the amide bond.They give two distinct resonance lines as long as the rate of exchange is longerthan the relative difference in frequency of the two resonances
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Lets now start increasing the temperature. Since the rate depends on the ΔG of theinversion, and the ΔG is affected by T, higher temperature will make things go faster. What we see in the NMR looks like this:
At a certain temperature, called the coalecense temperature,the rate of the exchange between the two species becomescomparable to the difference in chemical shifts of the sites:
Past this point, the NMR measurement cannot distinguishbetween things in either site, because things are exchangingfaster than the difference in relative frequencies.
T TC
1 1Rate (s) ≤ or
δr - δb Δδ
1 1Rate (s) ≤ or
δr - δb Δδ
NMR: Measurement of Rate Constants
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Δδ * Rate > 1 Slow exchange
Δδ * Rate = 1 Transition
Δδ * Rate < 1 Fast exchange
NMR: Measurement of Rate Constants
Now, since we can estimate the temperature at which we have the transition taking place, we can get thermodynamic and kinetic data for the exchange process taking place.
If we did a very detailed study, we see that we have to take into account the populations of both sites (one site may be slightly favored over the other energetically), as well as the peak shape.
Assuming equally populated sites (equal energies) simple relationshipscould be obtained.
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NMR: Measurement of Rate Constants
From the Δδ value (in Hz) at the limit of slow exchange we estimate the rate constant at the coalecense temperature:
Since we have the coalecense temperature, we can calculate the ΔG‡ of the process:
With NMR we can measure rates from 10-2 to 108 s-1.
Kex = π * Δν / √2 = 2.22 * ΔνKex = π * Δν / √2 = 2.22 * Δν
ΔG‡ = R * TC* [ 22.96 + ln ( TC / Δν ) ]ΔG‡ = R * TC* [ 22.96 + ln ( TC / Δν ) ]
-
+
FreeBound
Ligand Conformation: Transfer NOE
Ligand binding to a receptor?
Eg. Drug binding to protein, helpful in the design of drugs providedthe chemical requirements of activity and conformational requirements of binding are known
Often the bound ligand-receptor form cannot be solved as theprotein could be very large.
Monitor the NOE rates!
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Ligand Conformation: Transfer NOE
*
*
HS
HI
When bound, the protons in the marked carbons will have an NOE interaction. It will be very hard to see it with the protein also having tons of other NOE correlations
HS
HI
*
*
H
H
*
*
HS
HI *
*
koff kunf
Usually, koff
-
bound L free L
protein
Ligand Conformation: Transfer NOE
Besides retaining NOE, sharp NMR spectral lines of the ligand could beobtained outside of the protein
The ligand cannot bind tightly to the receptor (we need constant exchange between bound and free ligand).
The koff rate has to be much smaller than the spin-lattice relaxation rate, otherwise the NOE dies before we can detect it.
Size of the receptor is not an issue.
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•Correlation experiments, homocorrelation/heterocorrelation•Assignments, connectivities•Single-quantum/multiple-quantum correlation
Correlation Experiments: Magnetisation Transfer
Magnetisation transfer
Coherent Incoherent
Mediated via dipolar couplings, NOE/ROE/chemical exchange
Mediated via scalar couplingsthrough one or more coherenttransfer steps
Essentially four building blocks: COSY, TOCSY, INEPT, and HMQC
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Building Blocks, Spin Echo Schemes
180xI
180xI
180x
S
τ τ
a b c dτ τ
a b c d
a b c d
I
S
180xDec. CS
Dec. SE
JIS SE
.Dec SEx xI I⎯⎯⎯→
. 142 ( )IS IS
J SEx y z JI I S τ⎯⎯⎯→ =
. cos( 2 ) sin( 2 )Dec CSx x I y II I Iτ τ⎯⎯⎯→ Ω + Ω
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Heteronuclear Multiple-Quantum Correlation, HMQC
HMQC building block which takes as input transverse I magnetisation and frequency labels it with S
Essentially HMQC does the following:
cos( )HMQCx x sI I t⎯⎯⎯→ Ω
t/2 t/2 ΔΔ
90x 90x
180x
a b c d e f
S
I
-
INEPT
180xI
180x
S
δ δ
a b
90y
90x
c
INEPT
12 ( )4
INEPTx z y
IS
I I SJ
δ⎯⎯⎯→ =
-
Refocused INEPT
180xI
180x
S
δ δ
a b
90y
90x
c
Refocused NEPT
. 1( )4
ref INEPTx x
IS
I SJ
δ⎯⎯⎯⎯→ =
180xδ δ
d
180x
-
Reverse INEPT
180xI
180x
S
δ δ
a c
90y
90x
b
Reverse INEPT
. 12 ( )4
rev INEPTz y x
IS
I S IJ
δ⎯⎯⎯⎯→ =
-
Reverse Refocused INEPT
180xI
180x
S
δ δ
a b
90y
90x
c
Reverse refocused INEPT
180xδ δ
d
180x
. . 1( )4
rev ref INEPTx x
IS
S IJ
δ⎯⎯⎯⎯⎯→ =
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Conclusions
•It is possible to manipulate the spin populations
•Transfer of polarisation possible from one nucleus to another
•Polarisation transfer mediated by J or dipolar coupling
•In the case of dipolar coupling, NOE, distance information is present
•These form the building blocks in experiments to determinethe structure of big molecules