1. At this point, we have used COSY and TOCSY to connect spin
systems. i.e. if there are 8 arginines in the protein, we would aim
to find 8 arginine patterns. Overlap or missing signals may
hamper us in this initial goal.
The next step is to use NOESY experiments to sequentially link the amino acid spin systems together.
The nuclear Overhauser enhancement provides data on internuclear distances. These can be more directly correlated with molecular structure.

2. Consider 2 protons, I and S, not J-coupled but close in space
W1 is the normal transition - gives rise to a peak in the spectrum bb
W1I
W1s
W2 flip flip
W0 flip flop ba ab
W1I
W1S aa
W1 requires frequencies or magnetic field fluctuations near the
Larmor precession frequency i.e. 108 or 109 (100 MHz to 1000 MHz).
W2 requires frequencies at wI + ws, or to a good approximation, 2wI.
Wo requires frequencies at wI-ws, or to a good approximation.
So what fields are present that can cause this relaxation?

3. Spectral Density 2 - Rotational correlation time tc
small molecules tumble more quickly
large molecules tumble more slowly
rotational correlation time [in ns]
approx. equal to 0.5  molecular mass [in kDa]
1 kDa = 1000 atomic mass units

4. For a small molecule, tc is small (~0
For a small molecule, tc is small (~0.3ns) and the product wtc is << 1
In this extreme narrowing limit, rotational motions include 2wo (i.e.
fast motions) and W2 is preferred.
In large molecules (PROTEINS!), the tumbling is slow and wtc > 1.
Wo connects energy levels of similar energy so only low frequencies
are required. Therefore this is the preferred mechanism in large
molecules. It is known as cross-relaxation.

5. In the 2D NOESY experiment, an additional mixing time is
added to the basic COSY sequence. The result is a build up
of magnetisation from one nucleus to a close neighbour.
90o
90o
90o t2 t1
Mixing time
(magnetisation components of interest lie along -z)
Cross relaxation now occurs to nearby nuclei.

6. The NOE operates ‘through space’, it does not require the nuclei to be chemically bonded. The build-up is proportional to the separation of the two nuclei
nuclear separation
If we calibrate this function by measuring a known distance in the
protein and the intensity of the NOE, we can write
where k is a
proportionality
constant

7. The power of the NOESY experiment is that the intensity of an
NOE peak will be related to the nuclear separation.
Strong NOE crosspeaks Å
Weak NOE crosspeaks Å
Extending the mixing time will permit nuclei separated by 5Å - not
all spin systems will give a detectable peak though. So the absence of
a peak does not preclude close approach. Similarly a weaker
crosspeak does not always prove a larger internuclear distance. *
Therefore tend to be cautious and define distance ranges.
Strong ( Å), medium ( Å), weak ( Å).
Since this works through space we can use the NOE to connect spin
systems that we assigned with the COSY and TOCSY spectra.