97 The steady state NOE resulting from this balance now does not relly depend on the distance between the two spins, only so far that the observation of any effect proves the distance to be shorter than ca 5-6 A. The intensity of the observed NOE can vary widely depending on the neighbourhood of other protons which act as a relaxation source. a few examples will show this(from: Sanders/Hunter, Modern NMr Spectroscopy, Oxford University press, Oxford 1987) two-spin system I-12 saturated 50% for small molecules(W2 dominating) saturated saturated -100% for large molecules(Wo -100% aturated There is no distance dependence for these steady-state NOes! linear three-spin system 1-12-1(r23=r12)* saturated 25% -11.5% 49.2% saturated 49.2% -11.5% only shown for positive NOEs, with W2>> Wo Generally, the NOEs are weaker, because they now have to compete with relaxation from two neighbouring protons. This can be seen esp for the first case, where 12 gets an NOE contribution from the saturated spin I, but now has two equally close neighbours causing T, relaxation(I' and 13) Since the NOE on 12 leads to an increased population difference for this spin, it causes itself(being
97 The steady state NOE resulting from this balance now does not relly depend on the distance between the two spins, only so far that the observation of any effect proves the distance to be shorter than ca. 5-6 Å. The intensity of the observed NOE can vary widely, depending on the neighbourhood of other protons which act as a relaxation source. A few examples will show this (from: Sanders / Hunter, Modern NMR Spectroscopy, Oxford University press, Oxford 1987): two-spin system I1 – I2 I 1 I 2 saturated 50 % for small molecules (W2 dominating) 50 % saturated saturated -100 % for large molecules (W0 dominating) -100 % saturated There is no distance dependence for these steady-state NOEs! linear three-spin system I1 – I2 – I3 (r23 = r12) * I 1 I 2 I 3 saturated 25 % -11.5 % 49.2 % saturated 49.2 % -11.5 % 25 % saturated *only shown for positive NOEs, with W2 >> W0 ! Generally, the NOEs are weaker, because they now have to compete with relaxation from two neighbouring protons. This can be seen esp. for the first case, where I2 gets an NOE contribution from the saturated spin I1 , but now has two equally close neighbours causing T1 relaxation (I1 and I3 ). Since the NOE on I2 leads to an increased population difference for this spin, it causes itself (being
not in the BOLtZMAnn equilibrium anymore)an NOE at spin 13, of opposite sign than the direct NOE caused by the decreased population difference of I linear three-spin system I-I-I([23=2 12) saturated 49.2% 18.6% 50% saturated 50% -0.4% 0.8% saturated for Wo>>Wo! In the last case, I and 1- are close together and relax each other very efficiently, while the Noe build-up from the more distant i is too slow to lead to a significant stady state NOE. This is often true,e.g,for CH2 groups, where the distance between the two methylene protons(ca. 1.78 A)is much shorter than to any other proton 2D NOESY Any quantitative interpretation of steady state NOEs requires knowledge of the arrangement of all protons relative to each other! Otherwise, instead of staedy state NOEs, the Noe build-up rate has to be determined, which depends on the interproton distance with r-6. It is also called the transient noE or kinetic noe While some variations of the id difference Noe experiment have been used to measure build-ip rates, the easiest way to do this is the 2D NOESY experiment t2 Like, e.g., the 2D COSY or TOCSY experiments, it starts with a H 90 pulse followed by aH indirect evolution time, at the end of which the following terms exist
98 not in the BOLTZMANN equilibrium anymore) an NOE at spin I3 , of opposite sign than the direct NOE caused by the decreased population difference of I1 . linear three-spin system I1 – I2 –––– I3 (r23 = 2 r12) * I 1 I 2 I 3 saturated 49.2 % -18.6 % 50 % saturated 50 % -0.4 % 0.8 % saturated *for W2 >> W0 ! In the last case, I1 and I2 are close together and relax each other very efficiently, while the NOE build-up from the more distant I3 is too slow to lead to a significant staedy state NOE. This is often true,e.g., for CH2 groups, where the distance between the two methylene protons (ca. 1.78 Å) is much shorter than to any other proton. 2D NOESY Any quantitative interpretation of steady state NOEs requires knowledge of the arrangement of all protons relative to each other! Otherwise, instead of staedy state NOEs, the NOE build-up rate has to be determined, which depends on the interproton distance with r –6 . It is also called the transient NOE or kinetic NOE. While some variations of the 1D difference NOE experiment have been used to measure build-ip rates, the easiest way to do this is the 2D NOESY experiment: Like, e.g., the 2D COSY or TOCSY experiments, it starts with a 1H 90° pulse followed by a 1H indirect evolution time, at the end of which the following terms exist: