Lecture 11: INEPT, HSQC
Simultaneous spin echo
INEPT
1
H
1
3C or15N
1
1
H
3C or15N
1
4J
1 y
I
ii i
INEPT
1
H
1
3C or15N
1
1
H
3C or15N
1
4J
1 y
I
ii i
z
INEPT
1
H
1
3C or15N
1
1
H
3C or15N
1
4J
i\y
/5(e) =      +      cos^j^y - i«x sin     (2j^z) - |«2^
INEPT
1
H
1
3C or15N
1
1
H
3C or15N
1
4J
i\y
I
ii i
p(e) = -j^t - -«i (2j^^) - -«2-^
INEPT
11 1
WL -
X
lx
-2/1/2
lx
lz
y-2,ylzI2z
INEPT
P(g) = -*t - -«1 (2^y) + -«2^y
INEPT
P(g) = -*t - -«1 (2^y) + -K2^J/
INEPT
st
-2szyy
y
y
■> st —v st
-C2 ISzSTy ->
+s2 2sxyz —>
+c2y
y
-s2yx —>
| -c2cj 2szyy
\ +c2sj yx
I +s2cj 2j^x { +s2sj ^
| +c2cj
1 -c2sj 2^x^e -s2cj ^
-s2sj 2,yyyz
Relaxation with J-coupling
=>- = j?ix + \j?iy —>■ —\2j?i+j?2z different R2
• relaxation of       depends on 2^1+^ relaxation of 2s±+S2z depends on cross-correlated cross-relaxation (ingnored here) cf. cross-relaxation of A{Mlz) and A(M22> (NOE)
INEPT
<M+)
oc
4 ^
A/"7i72^ Bo 16fcB^
/
i?2
R2
\
\
Ri+(0o-n2 + 7T J)2     R2+ (u) — Q-2 — ttj)2
+
A/"7272^ Bo 16fcB^
/
i?2
i?2
V
+ (CO - n2 + 7TJ)2       ^ +        - Q2 - 7T^)2
anti-phase vs. in phase coherences
Phase cycling
Ii l
(j) = +90 °,    y :    p(g) = -jt - -Kl (2szyy) + -n2yy
11 1
(j) = -go °, -y :    p(g) =      + -Kl (2szyy) + -«2^/
difference :    ß(g) =      —  «i (2^^y)
Phase cycling
1
1
H
3C or15N
1
3C or15N
A/"7i72^ bq 16kBT
R2
R2
R\ + (jjj - Q2 + nJ)2    #2 + (<*> - ^2 -
INEPT vs. direct excitation
1
H
3C or15N
if//*
1H
13C or15N
, 1 Ay
r * 1431
1H
13C or15N
INEPT vs. direct excitation
INEPT (phase cycled): fc{Y(uj)} =
A/"7i72^ bq 16kBT
R2
R2
\
Direct excitation: U{Y(a>)} =
A/7272^ B0
16kBT
I
R2
R\ + (W - Q2 + 7T^)2   '   i?2 +        - ^2 - 7T^)2
R2
\
I1/12 ~ 4 for 13C
71/72 ~ 10 for 15N
Insensitive Nuclei Enhanced by Polarization Transfer
HSQC Spectroscopy
(Heteronuclear Single-Quantum Coherence)
1
H
1
3C or15N
COMPLEX EXPERIMENT
ANALYSIS FACILITATED BY SIMPLIFICATIONS
Using results of already analyzed building blocks (echoes) Ignoring components of 5 that cannot produce signal
HSQC Spectroscopy
Measured quantity: Mi_|_
(M2+ does not pass the frequency filters)
Only jxM^-\. and JvM^-\. have non-zero traces:
Tr{sy(Slx + \Sly)} = i
Directly measurable: JXl Jy (in-phase single-quantum of nucleus 1)
Evolve to measurable due to j coupling:
IJx&z, l^y&z (anti-phase single-quantum of nucleus 1)
Need 90° pulse + j coupling:
Jz (90° pulse),      IJz^z (populations, longitudinal polarization) .yx, yy, 2j?zy?x, 2-^z^y (single-quantum of nucleus 2) lJ?xyx, ISySTy, ISxSry, 2j?yyx (multiple-quantum)
Never measurable: Jt (unit matrix)
HSQC Spectroscopy
■
5f
1
3C or15N
1
1 y
x/y
I I -
i
BLOCK 1: INEPT
p(e) = \jt ~ 5«1 (ZSzfy) + ^2-Sy
HSQC Spectroscopy
1
H
1
3C or15N
I 4j I 4j I
x/y
g
i I
h
1 4j	ill	t2
	1	UV*VVV ™lr
BLOCK 2: DECOUPLING ECHO, INCREMENTED tx
p(e) = ^ -      (2^^y) + ^k2yy
p(f) = §J«Jt + 5«l (C2l2^^y - S212^^x)+5«2 (C21^/ ~ «21^)
HSQC Spectroscopy — Real
1
3C or15N
■
JSP
1 ■ ■	1 y ■ — ■	1 ■	1	t2 l ill
4j	<j i	4j	|4j	
X				I||lrf f ™r
t1
g
h
BLOCK 3: TWO 90° PULSES, PHASE x (13C or 15N)
p(f) = \st + \*>i {c2\2^zyy - s2i2szyx) +1«2 (c2l^y ~ «21^) p(g) = \st-\*>\ {c2\2^yyz - s2i2syyx)+^K2 (c2iyz - s2iyx)
HSQC Spectroscopy — Real
1
3C or15N
■
JSP
1 ■ ■	1 y ■ — ■	1 ■	1	t2 l ill
4j	<j i	4j	|4j	
X				I||lrf f ™r
t1
g
h
BLOCK 3: TWO 90° PULSES, PHASE x (13C or 15N)
p(f) = \st + \*>i (C2i2^zyy - s2i2yzyx) + \k2 (c2i^/ - s2iyx) ß(g) = —i«iC2i2^v^z+ unmeasurable (no more 90° pulses)
HSQC Spectroscopy — Real
■
_i   ± y
| 4j | 4j |
1
3C or15N
X
I l
5f
■ II
t1
g
BLOCK 4: SIMULTANEOUS ECHO
^(g) = —\k\C2\l^yyz-\- unmeasurable p(h) = ^/«iC2i^x+ unmeasurable
HSQC Spectroscopy — Real
13C or15N
KiC2lSx —>•
1
2«lC2iCi2 Sx
+i«ic2ic12cj
+2K1C21C12SJ 2j^^ r +9^1C21S12CJ ^/
HSQC Spectroscopy — Imaginary
13C or15N
BLOCK 3: TWO 90° PULSES, PHASE y (13C or 15N) p(f) = \^t + \&\ {c2\2^zyy - s2i2yzyx) + \k2 (c2i^y - s2i^r)
HSQC Spectroscopy — Imaginary
13C or15N
BLOCK 3: TWO 90° PULSES, PHASE y (13C or 15N)
p(f) = l^t + ^i (s2i2^zyy - s2i2j?zyx) + \k2 (c2i^y - s^i^x) ^(g) = — ^KiS2i2jfyyz-\- unmeasurable (no more 90° pulses)
HSQC Spectroscopy — Imaginary
13C or15N
BLOCK 4: SIMULTANEOUS ECHO
^(g) = —^KiS2i2^yyz-\- unmeasurable —>• ^(h) = ^k\S2isx-\- unmeasurable
HSQC Spectroscopy — Imaginary
13C or15N
+|K1S21C12CJ ^a; + 2«1S21C12SJ 2^y^ +o^ls21s12Cj -2«lS21s12sJ 2j^xj^
HSQC Spectroscopy — Hypercomplex
1
1
3C or15N
1
± y
H x/y
f g
i i
1 4j	ill	t2
	1	
h
t
±«ie,SÍ2*l^
+4«ie,fí2íiCl2Cj Jx +2«ie'^2íiCl2Sj 2^ +§/íielQ2íiSl2Cj ^
-5«ie,n2Í1«i2*j
HSQC Spectroscopy — Hypercomplex
1
H
1
3C or15N
j_
4j
i y
x/y
i i
ti
i i
fi \ g
h
t
1 4j	li	t2
	1	
16kBT
(
X
i?2 2 + O - ^2)2 1^2 i + TT J)2  ' R%1 + (u;-n1- ttJ)
R2A
-t<2
ß2,l
V
Decoupling in direct dimension
C22
2	ttJ
	
Decoupling in direct dimension
1
H
1
3C or15N
| 4j | 4j |
x/y
i
ti
1
4J
1
is
A/712 ft2 £0
8kBT    r\^ + {u- Q2)2 Ri x + (
-^2.2
Decoupling in direct dimension
VfJW"
1H
3C or15N
±    ± y
i 4j | 4j |
•t>i/*t>i <tV<t>i
I
ti
j_ j_ | 4j | 4j
<t>2
i
■i
GARP
=X,-X,X-X,X-X,X-X (|>2=X,X-X-X,X,X,-X-X
<h =y-y.y-y.y-y.y-y fe=x,x,x,x-x-x-x-x
signal multiplied by: 1 -1 -1,1,1 -1 -1,1
R2A
8kBT     r12 + (u- q2)2 R^1 + (u- Qi)
Decoupling in direct dimension
[ 2	ttJ
' wow	
1 ^2
1 ^2
Benefits of HSQC
• High sensitivity for 1JC or 1DN
(higher by (7i/72)5//2 than by the direct detection
• High resolution
Second dimension and less peaks in spectrum
(only 13C/15N-bonded protons and protonated 13C/15N visible)
• Important structural information 1H-13C and 1H-15N correlation
(it tells us which proton is attached to which 13C or 15N).
HOMEWORK: COSY
Section 11.3