At this point, we have used COSY and TOCSY to connect spinsystems. i.e. if there are 8 arginines in the protein, we would aimto find 8 arginine patterns. Overlap or missing signals mayhamper 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.

W2 flip flip

W0 flip flop

Consider 2 protons, I and S, not J-coupled but close in space

W1s

W1I W1S

W1I

W1 is the normal transition - gives rise to a peak in the spectrum

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?

Spectral Density 2 - Rotational correlation time

c 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

For a small molecule, c is small (~0.3ns) and the product c is << 1In this extreme narrowing limit, rotational motions include 2o (i.e.fast motions) and W2 is preferred.

In large molecules (PROTEINS!), the tumbling is slow and c > 1. Wo connects energy levels of similar energy so only low frequenciesare required. Therefore this is the preferred mechanism in large molecules. It is known as cross-relaxation.

t2

90o90o

t1

90o

(magnetisation components of interest lie along -z)Cross relaxation now occurs to nearby nuclei.

Mixing time

In the 2D NOESY experiment, an additional mixing time isadded to the basic COSY sequence. The result is a build upof magnetisation from one nucleus to a close neighbour.

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

€

NOE ∝1

r6

nuclear separation

If we calibrate this function by measuring a known distance in theprotein and the intensity of the NOE, we can write

€

NOE = k1

r6

where k is aproportionalityconstant

The power of the NOESY experiment is that the intensity of an NOE peak will be related to the nuclear separation.

Strong NOE crosspeaks - 2.5 ÅWeak NOE crosspeaks - 2.5-3.5 ÅExtending the mixing time will permit nuclei separated by 5Å - notall spin systems will give a detectable peak though. So the absence ofa 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 (1.8-2.5Å), medium (1.8-3.5Å), weak (1.8-5.0Å).

Since this works through space we can use the NOE to connect spinsystems that we assigned with the COSY and TOCSY spectra.