COSY and TOCSY
BCMB/CHEM 8190
COSY for an AX Spin System
90x
d1 (recover)
90x (mix)
t1 (evolve)
t2 (observe)
Hamiltonian: H = -B0(1-A)IZA -B0(1-X)IZX + 2 J IZA · IZX
chemical shift
Basis set : (, ,  )
Using product operator transformation tables,
or Kanters’ POF procedures for MAPLE:
step1:=spinsystem([A,X]);
step2:=xpulse(step1,{A,X},Pi/2);
scalar coupling
Evolution Step Combines All parts of Hamiltonian
in Kanters’ POF Approach
> step3:=evolve(step2,{A,X}, t1);
Now the effect of another X pulse:
IXA + IXX
> 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 (IXA+ IXX+ IYA+ IYX). I is Y component
> step5:=observe(step4, {A,X}, t2,0);
Note: t1 must reach ~1/(2J) or sin terms make crosspeaks small
Useful Trigonometric Identities:
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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  +/- 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)));
Sequence has no quadrature in V1
• Can set transmitter rf to one side of spectrum,
but this reduces sensitivity
0
• 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
by setting second pulse to 90y,
and adding acquisitions to
imaginary part of memory (i sin(w))
Elementary Phase cycle for COSY
90, 1
90, 2
3
• Implement quadrature in t1
• Correct for T1 recover in t1 – would give axial peak
• Phase cycle:
1
x
x
-x
-x
2
x
y
x
y
3
+
+
-
memory
real, imag
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
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•
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•
•
t2
Consider MQ term from slide 4 and add x pulse
-2I1XI2Y –(I1X+I2X) -2I1XI2Z … auto-peak
-2I1YI2X –(I1X+I2X) -2I1ZI2X … 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
-Me-Galactose
2Q spectrum of -Me-Galactose:
90x

180y

90x
t1
90x
observe
OH
O
1
4
HO
Me
2 OH
3
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

t1
m
DIPSI-2
90x

t2
•  is a short delay to change transmitter power
• DIPSI-2 is an isotropic mixing sequence –
essentially a strong transverse field – Beff in rotating
frame is small and behavior highly second order
• m is mixing time
Isotropic Mixing
First order Hamiltonian: H = i -iIiZ + ij2JijIiZIjZ
Hamiltonian in small Beff: H = i -iIiZ + ij2JijIiIj
IiIj = IiXIjX + IiYIjY + IiZIjZ
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 B1 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
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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; J120, J230, J13=0; still
see 1-3 splitting and cross-peak.
• The magnitude of cross-peaks depends on the
topology of the spin system, magnitudes of all
couplings involved, efficiency of mixing
sequence, relaxation during m.
• Chose m 75-100 ms for long transfer, 30-50 ms
for one to two couplings.
TOCSY Transfers in Isoleucine
From H
O
H
H3C
NH
H
CH3
H
H
From HN
H , H -----, H1 -…-, H2 -.-,
H …….
3J
HNH = 10 Hz,
3J
3
HH = 12 Hz, JHCH3 = 7 Hz,
3J
geminal = -15 Hz,
From Cavanagh .. and Palmer
Example TOCSY for Lysine
H
+H3N
HN
O
H
H
H
H
• Mixing times of 48, 83, and 102 ms
• From Cavanagh, Fairbrother, Palmer and Skelton