NOE background 5

Evaluation of the transition probabilities W requires knowledge of the respective relaxation mechanism.

- for dipole - dipole relaxation between two spins:

3 gI2 gS2 h2 ?c

W1I =

20 4pr6 1 + wI2 tc2

1 gI2 gS2 h2 ?c

W0 =

10 4pr6 1 + (wI - wS )2 ?c2

3 gI2 gS2 h2 ?c

W2 =

5 4pr6 1 + (wI + wS )2 ?c2

For protons: NOE proportional to ?IS , the dipolar relation or “cross relaxation rate” between the spins:

g4 h2 6 ?c

?IS = W2 - Wo = ( 1/10) - ?c

4pr6 1 + w2 ?c2

NOE depends on : 1) distance i.e. it is proportional to r -6 . The intensity can be converted into

distances only for constant tc, RIGID molecules

2) wtc = frequency and correlation time = molecular tumbling, motion

small molecules = wtc << 1 “extreme narrowing limit “ , W2 dominant => positive NOE

large molecules = wtc >> 1 => negative NOE, relaxation mainly over energy conserving Wo

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