BCMB/CHEM 8190

COSY for an AX Spin System d1 (recover)
90x t1 (evolve)
90x (mix) t2 (observe)
Hamiltonian: H = -
γ
B
0
(1-
σ
A
) I
ZA
-
γ
B
0
(1-
σ
X
) I
ZX
+ 2
π
J I
ZA
· I
ZX chemical shift scalar coupling
Basis set : (
αα
,
αβ
,
βα ββ
)
Using product operator transformation tables, or Kanters’ POF procedures for MAPLE:
¾ step1:=spinsystem([A,X]);
¾ step2:=xpulse(step1,{A,X},Pi/2);

Evolution Step Combines All parts of Hamiltonian in Kanters’ POF Approach
> step3:=evolve(step2,{A,X}, t1);

Now the effect of another X pulse:
I
XA
+ I
XX
> step4:= xpulse(step3, {A,X}, Pi/2); some of the above are not observable (MQ,Z) – only retain observables some X observables were modulated by properties of A in t1 – crosspeaks some X observables were modulated by properties of X in t1 - autopeaks

Observe: take the trace of result with Mx and My operators (
I
XA
+ I
XX
+ I
YA
+ I
YX
). I is Y component
> step5:=observe(step4, {A,X}, t2,0);
Note: t1 must reach ~1/(2J) or sin terms make crosspeaks small

• sin(A)cos(B) = ½[sin(A+B) + sin(A-B)]
• cos(A)sin(B) = ½[sin(A+B) - sin(A-B)]
• sin(A)sin(B) = ½[cos(A-B) - cos(A+B)]
• cos(A)cos(B) = ½[cos(A+B) + cos(A-B)]
Previous expressions evolve at ω +/π J

Transforming these in t1 and t2 Gives a series of
Absorptive and Dispersive peaks at ν +/- J/2
> spec1:= evalc(Re(FT(FT(step5,0,t2,v2 ),0,t1,v1)));

0
Sequence has no quadrature in V1
• Can set transmitter rf to one side of spectrum, but this reduces sensitivity
• Cos(w) = 1/2 (exp(iw) + exp(-iw))
Sin(w) = -i/2 (exp(iw) – exp(-iw)) two opposite rotating components
•Solution: collect a second set set of data with sin modulation in t1: accomplished by setting second pulse to 90y, and adding acquisitions to imaginary part of memory (i sin(w))

Elementary Phase cycle for COSY
90,
φ
1 90,
φ 2 φ 3
• Implement quadrature in t1
• Correct for T1 recover in t1 – would give axial peak
• Phase cycle:
φ 1 φ 2 φ 3 memory x x + real, imag x
-x
-x y x y
-
-
+ imag, real real, imag imag, real

Another problem: Dispersive and
Twisted Auto-Peaks (or Cross-Peaks)
• Long tails make crosspeaks close to diagonal hard to see
• One solution: magnitude spectrum – but lines are still broad

Double-Quantum Filtered COSY
90x 90x 90x t1 t2
• Consider MQ term from slide 4 and add x pulse
• -2I
1X
I
2Y
• -2I
1Y
I
2X
>(I
>(I
1X
1X
+I
+I
2X
2X
) → -2I
) → -2I
1X
1Z
I
I
2Z
2X
… auto-peak
… cross-peak
• Note: both are absorptive (still antiphase)
• Phase cycling needed to remove other pathways
• Resonances from single lines (solvent) removed

Example of 2Q-Filtered COSY
β -Me-Galactose

2Q spectrum of β -Me-Galactose:
90x 180y 90x t1 90x observe
τ τ
OH
O
HO
4
3
OH
2
1
Me
OH
Solvent lines removed
No auto peaks

TOCSY – Total Correlation Spectroscopy
• Cross-peaks for all members of spin system – can often see these in un-cluttered spectral region
90x 90x τ
Δ m
Δ
90x
• Δ is a short delay to change transmitter power
• DIPSI-2 is an isotropic mixing sequence – essentially a strong transverse field – B eff in rotating frame is small and behavior highly second order
• τ m is mixing time

Isotropic Mixing
• First order Hamiltonian: H = Σ i
• Hamiltonian in small B eff
: H = Σ i
• I i
⋅
I j
= I iX
I jX
+ I iY
I jY
+ I iZ
I jZ
ω i
I iZ
ω i
I iZ
+ Σ i ≠ j
π 2J ij
I iZ
I jZ
+ Σ i ≠ j
π 2J ij
I i
⋅
I j
• The additional operators mix all coupled spin states
• Cartesian product operators no longer have nice one-toone inter-conversion rules
• Could be done with simple B
1 field but complex pulse sequences work better and suppress relaxation effects:
• DIPSI-2 (Shaka) uses super cycles R R R R
• R=320º 410º 290º 285º 30º 245º 375º 265º 370º

Practical Considerations for TOCSY
• Both cross-peaks and auto-peaks are in-phase and can be phased absorptive
• Cross-peaks do not necessarily indicate direct coupling – but show virtual coupling as in second order spectra; J
12
≠ 0, J
23 see 1-3 splitting and cross-peak.
≠ 0, J
13
=0; still
• The magnitude of cross-peaks depends on the topology of the spin system, magnitudes of all couplings involved, efficiency of mixing sequence, relaxation during τ m
.
• Chose τ m
75-100 ms for long transfer, 30-50 ms for one to two couplings.

TOCSY Transfers in Isoleucine
From H α
O
H
α
H
3
C
H
γ1
H
β
NH
CH
3
H
γ
2
From HN
H α , H β -----, H γ 1 -…-, H γ 2 -.-,
H δ …….
3
3
3
J
J
J
HNH α
H α H β
= 10 Hz,
= 12 Hz, 3 J
= -15 Hz,
HCH3
= 7 Hz, geminal
From Cavanagh .. and Palmer

Example TOCSY for Lysine
+H
3
N
H
δ
HN
H
ε
H
γ H
β
H
α
O
• Mixing times of 48, 83, and 102 ms
• From Cavanagh, Fairbrother, Palmer and Skelton