The Physical Methods in Inorganic Chemistr

y

(Fall Term, 2004) (Fall Term, 2005) Department of Chemistry

National Sun Yat-sen University

無機物理方法（核磁共振部分）

Chapter 6

Nuclear Overhauser Effect (NOE) and NOESY

Population TransferIn population manipulations, the most commonly used technique is selective population transfer (SPT):

Nuclear Overhauser Effect (NOE)

N

SN

Sr

The distance between the two spins therefore can be determined by disturbing one of them and observing how other is affected.

Na23

electron

Nucleus-Electron OE: Mechanism

550

547

550

547

W2

W0

1000

995

100

99 =1+5=6

W2>>W0

999577

98520

=422+422=844

Nucleus-Electron OE: Mechanism

550

547

550

547

W2

W0

1000

995

100

99 =1+5=6

W2<<W0

580990

517107

=-410-410=-820

Nucleus-Nucleus OE (Nuclear OENOE): Mechanism

60

54

60

54

W2

W0

100

90

20

18 =2+10=12

W2>>W0

9058

2456

=32+32=64

Nucleus-Nucleus NOE: Mechanism

60

54

60

54

W2

W0

100

90

20

18 =2+10=12

W2<<W0

6490

5024

=-26-26=-52

Example: C-H NOE

Whenever a polarization or a transition of a spin is inverted or saturated, the polarization or transition of the other spins that are coupled to it will be affected.

Perturbation on a Spin (Saturation/Inversion) + Cross Relaxation

The Polarization of Another (Coupled) Spin Is Altered.

Depending on the relative magnitudes of W2 and W0, NOE factor can beLarger or smaller than 1 and can be both negative and positive.

w0 w2

Longitudinal Relaxation RatesAlso Affect NOE

)]2(6)(3)0([ 0016

,1 62

4220

JJJR

IIrII

60

54

60

54

W2

W0

100

90

20

18 =2+10=12

W2,W0, R1I, R1S all affect overall NOE.Here W2 > W0, R1I, R1S

9580

1934

=15+15=30

R1I

R1S

R1S

Positive NOE

Longitudinal Relaxation RatesAlso Affect NOE

)]2(6)(3)0([ 0016

,1 62

4220

JJJR

IIrII

60

54

60

54

W2

W0

100

90

20

18 =2+10=12

W2,W0, R1I, R1S all affect overall NOE.Here W2 > W0, R1I, but R1S>W2.

9690

1824

=6+6=12

R1I

R1S

R1S

No NOE

Longitudinal Relaxation RatesAlso Affect NOE

)]2(6)(3)0([ 0016

,1 62

4220

JJJR

IIrII

100

90

20

18 =2+10=12

W2,W0, R1I, R1S all affect overall NOE.Here W0> W2, but R1I>W0, R1S

9295

1922

=3-3=0!

60

54

60

54

W2

W0R1I

R1S

R1S

Negative NOE

)log( 0 c

logW

W2

W0

W1

-4 -3 -2 -1 0 1 2 3 4

Relaxation Rates and Motion

For slow motions,W0 is dominant and NOE tends tonegative.

Fast motion Slow motion

Homonuclear Steady State NOE

60

54

60

54

W2

W0

100

90

20

18 =2+10=12

NOE factor depends on W2, W0

9078

2436

=12+12=24

NOE Difference Spectrum(NOEdif)

Red: Saturated peakBlack: NOE affected peak

1D Homonuclear Transient NOE

A single spin is inverted and the spin system response isread using a 90° pulse after a “mixing” time delay of variable duration. In the transient mode, the NOE builds up due to cross-relaxation of nearby spins by the inverted spin as the entire spin system.

180o

100

9090

81

Neither have to be steadyNor have to be equilibrium

R1

R1

R1

90

81100

90

W2W0

98

8890

85

NOE: Essence

Whenever the polarization of one of two coupled spins deviates from its equilibrium value, the polarization of the other spin is affected by cross relaxations. The NOE factor (the extent that the polarization of the unperturbed spin is affected) depends on cross relaxation rates and longitudinal relaxation rates.

N

SN

Sr

A

B

When the distance between spins A and B is smaller than ~ 5 Å, NOE cross peaks are observable.

132

967 48510

1 25

3

4

6

7 8

910

1 25

3

4

67 8

910

132

967 48510

1D Homonucelar ROE

A single transition is inverted using a selective 180° pulse (along the x axis), and then a hard 90° x pulse is immediately applied to the spin system.This has the effect of placing the “inverted” magnetization along the -y axis while the rest of the magnetization is aligned along +y. Then, a low-power rectangular pulse is applied long the y-axis.This pulse is applied parallel to the magnetization (in the rotating frame) and effects no net rotation. Instead, it “locks” the magnetization along the y axis, and is referred to as a spin lock pulse. The magnetization is said to be spin locked becauseit doesn’t precess about B0, but the spins now precess aboutB1(the spin lock pulse). Therefore, under these conditions, the magnetization can be considered to being analogous to alignment along the z axis in the presence of B0 alone. Finally, the spins will relax towards a new equilibrium in the presence of B1; the characteristic time constant for this decay is called T1ρ forT1in the rotation frame.

180o90o

ROE Mechanism:All relaxation rates are changed

into rotating frame.

Rotating frame Note that both W2 and W0 promote ROE!

100

9090

81

98

9592

76Z

R1rho

R1rho

R1rho

90

90100

81

W2rho

W0,rho

Y

)]2(6)0([ 016 62

4220

JJ

IIr

NOEII

For homonuclear systems

)]2(3)0(2[ 016 62

4220

JJ

IIr

ROEII

Both W2 and W0 promote ROE

W2 promotes NOE while W0 blocks NOE

22152)(

c

cJ

I

NOEIS

IS

)]2(6)(3)0([ 0016

,1 62

4220

JJJR

IIrII

)]2(6)0([ 016 62

4220

JJ

IIr

NOEII

52

152

22)( c

c

cJ

cc

cJ

222 52

152)(

62

4220

12 II

c

r

ROEII

I

S

I

NOEIS

z

z

I

NOEIS

I

SIS

)0(

)0(

Some Applications of NOESY

Structure determination of biomacromolecules

Polymers

Sterochemistry

Hydration of biomolecules

)()cos()cos(

))sin()cos((

)sin()cos(

))sin()cos((

)sin()cos(

)()(

)erion transfmagnetizat(11

11

112

11

11

2

11

ZZSZIZ

SXSZ

IXIZ

SXSY

IXIYIt

YYZZ

SIatStI

tStS

tItI

tStS

tItI

SISI

m

X

Z

X

Sterochemistry

CORMA

Principle of CORMA

Example of CORMA

CORMA(COmplete Relaxation Matrix Analysis)

V(τm)=V0 exp(Rτm)

CORMA

NOESY of Poly(N-vinyl-carbazole): CHCl3, mixing time:450 ms, 500 MHz, 303 K

Detection of hydration water via observation of NOEs from water-protein --- G. Otting, E. Liepinsh, K. Wuthrich, Science 1991,254,974

BPTI 牛胰蛋白抑制劑

Residues : 58

Internal water : 4

Residence times:

Interior water:10-2-10-8s

Surface water:10-9s

Assignments of water-solute cross peak :

(a) Direct water-solute NOE

(hydration water-solute)

(b) Exchange-relayed NOE

(solute-solute)

(c) Chemical exchange

(bulk water-solute)

Non-labile

Labile

Labile

--- G. Otting, J. Progr. NMR. Spectrosc. 1997, 31 , 259

Glu1-190 ( mix=0.4 ms )

2

3

4

5

6

Significance to Structure Determination

rij=(1.78 Å)×(σkl/σij)1/6

Intensity:640Distance:1.78Å

Intensity:10Distance:3.56Å

A

B

C

D

E

F

C-terminal domain of rat Erp29 protein

C

R1

H

C

O

N

H

C

R2

H

C

O

N C C

R3

H H O

N

H

C

H

C

R4

O

N

H

C

H

C

R5

O

COSYNOESY NOESY

i i+1

i COSY NOESY (i+1) COSYNH-CαH iCαH-(i+1)NH

(i+1)NH-CαH

CTX II: 44-60

COSY