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Magnetisation Transfer Schemes

P. K. MadhuDepartment of Chemical Sciences

Tata Institute of Fundamental ResearchHomi Bhabha Road

ColabaMumbai 400 005, India

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

Spin-1/2 nucleus

|α>

|β>

ΔE=(h/2π) γBFor 1H:γ=26.75 rad T-1s-1

ΔE=2.65*10-25J for B=9.4 TkT= 4.14*10-21 J

ΔE/kT=6.4*10-5


Preferred Nβ <<Nα

NβNα=e−∆EkT =e

−γhBkt

Hence, the energy required to reorient the spins is dwarfed bythe thermal energy, little tendency for the spins to become orderedin the lower energy level

Spin-1/2 nucleus

|α>

|β>

ΔE=(h/2π) γBFor 1H:γ=26.75 rad T-1s-1

ΔE=2.65*10-25J for B=9.4 TkT= 4.14*10-21 J

ΔE/kT=6.4*10-5


Preferred Nβ <<Nα

Nα−NβNα+Nβ

= ∆E2kT

NβNα=e−∆EkT ≈ 1− ∆E

2kT

3.2*10-5 (one in 31000)

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

NMR Active Nuclei: Properties

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

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

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

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

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

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!

Echo Modulations

x

y

α

β

AX spin system, heteronuclear

18090

A

X

MAXα

MAXβ

x

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

Echo Modulations

x

y

α

β

AX spin system, homonuclear

18090

A

MAXα

MAXβ

x

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

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


180

90x

τ τ

A, 1H

τ=1/4J

X, 13C

13C signal of lengths -3 and 5 created along the z-axis

x

yMX

Aα

MXAβ

τ=J/4x

y

900x

180

180x

180xA

180xX

x

τ=J/4x


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

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

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

z180x

A,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

180x

A

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

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

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

INEPT

13C coupled

INEPT SpectrumINEPT

-1:1-1: 0:1 -1: -1: 1:1

INEPT Spectral Patterns

CH3CH2CH

13C spectrum

180x

I

180x

S

δ δ

a b

90x

90x

c

Refocused NEPT

. 1( )4

ref INEPTx x

IS

I SJ

δ⎯⎯⎯⎯→ =

180x

Δ/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

Behaviour of CH, CH2 and CH3 Groups

Spectral Editing

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

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

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


CH3=FID(45)+FID(135)-0.707 FID(90)

Major Relaxation Pathways

1. Dipole-dipole coupling

2. Scalar coupling

3. Chemical shift anisotropy

4. Chemical exchange

5. Paramagnetic interactions

6. Spin rotation

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

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

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

W2AX - W0AX

2W1X + W2AX + W0AX

ηA = = fA{X}

σAX = W2AX - W0AX

ρAX = 2W1X + W2AX + W0AX

ηA = σAX / ρAX= fA{X}

σAX = W2AX - W0AX

ρAX = 2W1X + W2AX + W0AX

ηA = σAX / ρAX= fA{X}

NOE: Some Expressions

Wn ∝ 1r6 J(nω)

J(nω) = τc1+(nωτc)2

Steady-State NOE

ωτc<<1

ωτc>>1

ωτc=1.12

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-6

rac = rab * ( ηab / ηac ) -1/6

ηac ∝ rac-6

ηab ∝ rab-6

rac = rab * ( ηab / ηac ) -1/6

ηac ∝ rac-6

αα (∗∗)

ββ (∗∗)

(∗∗∗∗) αβ

W1X

W1X

W1A

W1A

βα ()W2AX

W0AX

180X

90

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

• 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


Overhauser being awarded the National Medal of Science, 1994

"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.

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:

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

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

NORMAL, NO NOE

INEPT

REFOCUSSED INEPT

REFOCUSSED INEPT AND

DECOUPLING

NORMAL DECOUPLING

FULL NOE

13C Chloroform Spectra

INEPT

29Si with INEPT Scheme

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

)

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

• 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

s ns ps fsμsmsFastSlow Very slow Slow Fast Very fast Ultra fast

MacroscopicDiffusion,Flow

Chemical exchange

Molecular rotations

Molecular vibrations

Motional Timescales

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

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.

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

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


Δδ * Rate > 1 Slow exchange

Δδ * Rate = 1 Transition

Δδ * Rate < 1 Fast exchange


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.


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!


*

*

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<kunf, hence,if koff is faster than T1, therelaxation time, the NOEinformation will stay putwith the ligand even Outside of the protein

As the ligand dissociates from the protein, it adoptsanother conformation in a jiffy

bound L free L

protein


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.

•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

Building Blocks, Spin Echo Schemes

180x

I

180x

I

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

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

180x

I

180x

S

δ δ

a b

90y

90x

c

INEPT

12 ( )4

INEPTx z y

IS

I I SJ

δ⎯⎯⎯→ =

Refocused INEPT

180x

I

180x

S

δ δ

a b

90y

90x

c

Refocused NEPT

. 1( )4

ref INEPTx x

IS

I SJ

δ⎯⎯⎯⎯→ =

180x

δ δ

d

180x

Reverse INEPT

180x

I

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

180x

I

180x

S

δ δ

a b

90y

90x

c

Reverse refocused INEPT

180x

δ δ

d

180x

. . 1( )4

rev ref INEPTx x

IS

S IJ

δ⎯⎯⎯⎯⎯→ =

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