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Chem 526Chem 526

NMR for Analytical Chemists

Lecture 21Lecture 21

(Ch 4, Ch 6)

Class Schedule

HW9 due on Thursday• 11/17 Follow up of 2D Exps 3D Experiments Intro• 11/17 Follow up of 2D Exps, 3D Experiments Intro• 11/22 YOUR Presentation• 11/24 (No Class)• 11/29 Final Exam Prep Final Exam Dec 1 (Thr)

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Final Presentation• How it works?

– Density Operators– Explanation of Components

• How the spectrum looks like?How the spectrum looks like?– What are the two (three) axes?– What do the cross peaks represent?

• What kind of information can you extract from the spectrum?

• What is the advantage of this method?HMQC vs HSQC– HMQC vs HSQC

– NOESY vs TOCSY– Heteronuclear vs Homonuclear– 2D vs 3D

• Example of an application (Show at least two spectra &Explain) 20 mins +5 min Question time

Final Presentation on multidimensional NMR (ch 6-7) (Nov 22)

1H/1H homonuclear correlation (20 min presentation) COSY TOCSY (6.5) + DQF COSY Group 1

1H/(15N/13C) heteronuclear correlation HMQC (7.1.1.1) & HSQC (7.1.1) Group 2 HNCO, HNCOCA, HCANH (7.4) Group 3

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A 2D NMR experiment: Basic Scheme

Preparation MixingEvolution (t1) Acquisition (t2)

t

t2

FT t2

t2FT t1

ω1

ω2

diagonal peaks (ω1 = ω2)cross peaks (ω1 ≠ ω2)

Thanks to Hongyan & Jie

6.5 TOCSY

A train of composite pulse(DIPSI-2, WALTZ-16 etc)

● Eliminates chemical shifts ● Create strong coupling

Hmix = 2J’(IXSX + IYSY + IZSZ)

● Create strong coupling

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TOCSY Transfer

• Heff = 2J(IXSX + IYSY+IZSZ )

(0) = IX

[IXSX, IYSY] = [IYSY, IZSZ] =

[IZSZ, IXSX] = 0 & [(0), IXSX] = 0

IX – 2 JIZSZ IXcosJ + 2IYSZsinJ2IYSZ – 2 JIYSY 2IYSZ cosJ+ SXsinJ

[Q1]

[Q1] [Q2]

TOCSY vs. NOESY

• Magnetization transfer mechanism:

TOCSY: J-coupling (Through bond)

NOESY: NOE effect (Through space)

• 3D NOESY-TOCSY

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Cross Relaxation in NOESY

preparation evolution(t1) mixing acquisition(t2)

d I t

dtI t I tkz

k kz kj jzj k

( )( ) ( )

k kj

k j

I I a S az z II m z IS mm ( ) ( )

Solomon Equation

IS

NOE c

IS cr

202 4

2 602 240

16

1 4

Pulse sequence & Product Operator Analysis

CtItII zyt

y @)sin()cos( 11111111

BIAI y

x

z @@ 12

1

t1 t2 1 2

1 2 3 4

DtItItI z

Ix

zy @)cos()sin()cos( 1112

111111

tI zm)cos( 111

EtaItIK

kmkkzz

m @)cos()()cos( 111

1111

t1 t2m 1 2

P+1

0

-1

EDA B C F

EtaIK

kmkkz @)cos()( 11

11

FtaItaIK

kmkkymy @)cos()()cos()( 11

2111111

Fig. 1 pulse sequence and coherence level diagram for the NOESY experiment.

Cross peaks

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NOESY Spectrum

Axes:1H chemical shift

Cross peaks d(1HA-1HB) <5 Ao

Fig. 2 A expansion of a NOESY spectrum

Diagonal peaks (1HA, 1HB) when 1HA = 1HB

7.1 Sensitivity in Heteronuclear Correlation 2D NMR

• S/N ex det3/2[1 –exp(-R1exTc)]

H ~4C ~10N

Relative S/N

• Ex 1H Det 1H 32• Ex 1H Det 13C 4• Ex 13C Det 13C 1

Relative S/N

• Ex 1H Det 1H 330• Ex 1H Det 15N 10• Ex 15N Det 15N 1

[Q1]

[Q2]

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HMQC/2Y

I

Y

/2Y /2Y

σ(0) = IZ

H = SSZ + 2JIZSZ

S

Y Y

t1

↑ ↑ ↑

IX 2IYSZ

1 3 4↑2 ↑5 6↑

IX 2IYSZ

2IYSX

2IY(cSX +sSY) 2IY(-cSZ +sSY) IXcosSt1

X6: cosSt1{IXcosIt2+ IYsinIt2}Q6

t1 tmix

IX 2IYSZ

2IYSX

How do you select signals only from the DQ coherence

2IYSZ IX

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Basic HSQC

/2Y Y

I

S

Y

/2Y /2Y

t1

Cf. HMQC

HSQC/2X

Y

I

/2Y/2Y X

H = SSZ + 2JIZSZ

S

Y /2Y

t1

/2Y X

IZ – /2IX (Q1)(Q1) – 2JIZSZ2 (Q2)(Q2) – 3/2IY (Q3)(Q3) – 3/2SY 2IZSX

2IZSX – SSZt1 (Q4)

J2 = /2

Single Quantum Coherence

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HSQC/2X Y

I

/2Y /2Y X

H = SSZ + 2JIZSZ

S

J2 = /2

Y /2Y

t1

/2Y X

2IZSX – SSZt1 c2IZSX+ s(Q6)c2IZSX+ s(Q6) – /2IY -c2IXSX+ s(Q6) – /2SYc2IXSZ+ s(Q7) –2JIZSZ2 (Q8)

6.2 COSY with couplingI: 90Y – t1 – 90X – t2 –

I1Z – /2IY I1X

I1X –1I1Zt1 I1Xcos1t1 +I1Ysin1t1I1X 1I1Zt1 I1Xcos1t1 I1Ysin1t1

–2JI1ZI2Zt1 {I1Xcos(Jt1)+ 2I1YI2Z[Q1] }cost1+ {I1Ycos(Jt1) + [Q2] }sint1

– /2IX {I1Xcos(Jt1) -2I1ZI2Y[Q1]}cost1+ {I1Zcos(Jt1) + [Q3] }sint1

p+1

-10

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6.2 COSY with couplingI: 90Y – t1 – 90X – t2 –I1Z – /2IY I1X

I1X –1I1Zt1 I1Xcos1t1 +I1Ysin1t1–2JI1ZI2Zt1 {I1Xcos(Jt1)+ 2I1YI2Z[Q1] }cost1

+ {I1Ycos(Jt1) + [Q2] }sint1– /2IX {I1Xcos(Jt1) - 2I1ZI2Ysin(Jt1)}cost1

+ {I1Zcos(Jt1) + [Q3] }sint1

cos(Jt1)cost1 = {cos(Jt1+t1)+ cos(Jt1-t1)}/2

sin(Jt1)cost1 = {sin(Jt1+t1) - sin(t1 - Jt1)}/2

Absorbance

Dispersion

Problem of COSY?

Diagonal Peak DispersionCross Peak Absorbance

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6.3.1 DQF-COSY (p437-449)

Remove Dispersive Diagonal Peaks by Only Selecting Double Quantum Coherence

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t1 tmix

How do you select signals only from the DQ coherence

DQF-COSY with couplingI: 90X – t1 – 90X –90X+- t2 –

I1Z – /2IX -I1Y

-I1X –IZt1 -I1Ycost1 +I1Xsint1

1X Z 1 1Y 1 1X 1

–2JI1ZI2Zt1 {-I1Ycos(Jt1)+ 2I1XI2Z[Q1] }cost1+{I1Xcos(Jt1) - 2I1YI2Z[Q2] }sint1

– /2IX {-I1Zcos(Jt1) -2I1XI2Y sin(Jt1)}cost1+{I1Xcos(Jt1) + [Q4] }sint1

– /2IX {-I1Ycos(Jt1) -2I1XI2Zsin(Jt1)}cost1+{-I1Xcos(Jt1) + [Q4] }sint1

2I1XI2 = 1/2{(2I1XI2Y + 2I1YI2X) +(2I1XI2Y - 2I1YI2X)}

DQ ZQDQ – /2IX (2I1XI2Z + 2I1ZI2X)

–2JI1ZI2Zt2 sin(Jt2) (I1Y + I2Y)

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IY

-IX-IX

-IYcos +IXsin

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-IYcos +IXsin

Pulse Phase & Receiver Phase

<I+> =< IX> + i<IY> <I+> ={< IX> + i<IY>}e-i

Receiver Phase:

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Effects of Phase Shift in General Case

p IX qp q

I

p IX+ exp{-i(q-p)} q

p IX q

p IX+ exp{-i(q-p)} q

Q – P

0

Effects of Phase Shift =0 =/2 = =3/2

0

1

2

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Phase Shift of RF Pulse• U RF() = exp(-iI) ; = /2

= RZ()exp(-iIX) RZ-1()

U RF-1() = RZ()exp(iIX)RZ

-1()

URF()IZURF-1() =

RZ() exp(-iIX)RZ-1()IZRZ() exp(iIX) RZ

-1()

R ( ) ( iI )I (iI ) R 1( )= RZ() exp(-iIX)IZ exp(iIX) RZ-1()

= RZ()IYRZ-1()

= IY+

The Effects of Phase ShiftRZ

-1()pRZ () = RZ-1()|m+p><m|RZ ()

= exp(iIZ)|m+p><m|exp(-i IZ)= exp{i(m+p))|m+p><m|exp(-im)

p IX q

I e p{i (p q)}

exp{i(m p))|m p><m|exp( im)= exp{i(m+p-m)}|a><b| = exp(ip)|a><b|= exp(ip)p

p IX+ exp{i(p-q)} q

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Phase shift of RF Pulse

• U RF() = exp(-iI) ; = /2

= RZ()exp(-iIX) RZ-1()

URF() p URF-1()

=RZ() exp(-iIX)RZ-1() p RZ() exp(iIX)RZ

-1()

= RZ() exp(-iIX) p exp(iIX)RZ-1()exp(ip)

= RZ() (q ) RZ-1() exp(ip)

= q exp[i(p-q)]

Coherence Selection by Phase Cycle

UXRF()pUXRF-1() = q

URF()pURF-1() = qexp{-i(q-p)}

= qexp{-ip} (4.32)

UXRF()pUXRF-1() = p+1 + p+2

U RF() U RF-1() = [Q1]URF()pURF () = [Q1]

UXRF()pUXRF-1() = p + p+2

URF()pURF-1() = [Q2]

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3D NOESY-HSQC

Ii Ij Sj Ij(t1) (t2) (t3)

NOE JIS JIS

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3D Triple Resonance Experiments

3D Triple Resonance

• Bax Coworkers ~ 1990

• Target ~ 30 kDa

• With deuteration 60-1 MDa

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Naming of 3D Triple-Resonance Experiments

The spins frequency labeled in the t1-t3i d l b l dperiods are labeled as

HN, N, HA, CA, CO, HB, CB

The spins not frequency labeled are placed in parenthesesin parentheses

(HN)-N-(CO)-C-(CO)-(N)-HN

HNCAHN(CO)CA

Two Type of Experiments

“Out & Back”

(HN) N CA (N) HNOut transfer & Back transfer

“Straight-Through”

HNCA

Straight Through

HA (CA) N HN

H(CA)NH

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3D HNCA

4-9 Hz7 11 Hz

(1HN) 15N 13CA (15N) 1HN

7-11 Hz

A 1HN/13CA slice in HNCA for ubiquitin(15N = 121.6 ppm)

13CA

1HN

Q. How can you read the spectrum?

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Transfer Efficiency from 1HN to 13CA

A 1HN/13CA slice in HNCA for ubiquitin(15N = 121.6 ppm)

13CACA for G47

CA for K48

1HN for K48

1HN

Q. How can you read the spectrum?

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a

b

c

e

a)

b)

JNCJHN JNC JHN

b)

c)

e)

Application: HNCO2D 1H/13CO projection 3D 1H/13CO Slice at 15N shift of 119.7 ppm

Kay L.E. et al; J. Mag. Res. 89, 496-514 (1990)