98
B. BERSCH et al.
sion angle; unfortunately, the magnitude of some 3J between heteronuclei is less
than a few Hz and can hardly be measured with precision. On the other hand, the
information provided by the coupling constants can directly be used at the structure refinement stage, by defining a penalty function for the coupling constants
themselves rather than the inferred dihedral angles (Mierke and Kessler 1992),
thus eliminating any explicit conversion.
Two classes of methods have been devised for the experimental determination:
the first one is based on the modulation of the intensity of a cross-peak by scalar
coupling (quantitative J correlation). In this approach, the intensity of a cross
peak (modulated by sin (nJt)) is compared to that of a diagonal peak (modulated
by cos (nJt)). The alternative relies on the frequency separation of the two doublet peaks in an additional dimension (E.COSY, see Biamonti et al 1994 for a
review) or in separate spectra (S3E, Meissner et al 1997).
Conformationally flexible molecules give rise to average coupling constants
weighted by their probability distribution. When an angle is measured from several couplings, inconsistencies are frequently attributed to internal flexibility,
especially for side-chain torsion angle (Xl> X2 ... ). Models of various complexity,
including either a discrete superposition of staggered conformations or a continuous probability (Dzakula et al. 1992) have been proposed. The improvement
brought by the larger number of degrees of freedom should however carefully be
questioned to avoid overinterpretation of the data.
Coupling constants have been recently added to other structural restraints for
NMR structure determination. Their incorporation offers a reliable means of
improving the accuracy of protein structure (Garrett et al. 1994), but, contrary to
nOe, they do not contain any long range information which is fundamental for
finding the global fold of a protein.
3.3
Relaxation
Once the spins have been perturbed by radio-frequency pulses, the magnetizations (or the coherences) recover to their equilibrium states by an irreversible
process called relaxation. Relaxation is caused by time-dependent magnetic
fields that originate from the random thermal motions present in the sample.
Fluctuating magnetic fields at a nucleus may derive from the interaction with
other spins (dipolar relaxation) or from a modulation of its own chemical shielding (CSA relaxation). In a phenomenological description of relaxation, the longitudinal magnetization recovers exponentially with a time constant TJ (spin lattice
relaxation) and the transverse coherences vanish with a time constant T2 (spinspin relaxation). Long TJ values prevent the use of short recycling delays, when
multiple scans are acquired, leading to long acquisition times. On the other hand,
short T2 values (in other words, broad resonances) strongly limit the spectral resolution. Unfortunately, large macromolecules with slow overall tumbling rates
share these two drawbacks. However, the spin-spin relaxation can be reduced by
using complete or partial deuteriation of the molecule (LeMaster 1990).
B. BERSCH et al.
sion angle; unfortunately, the magnitude of some 3J between heteronuclei is less
than a few Hz and can hardly be measured with precision. On the other hand, the
information provided by the coupling constants can directly be used at the structure refinement stage, by defining a penalty function for the coupling constants
themselves rather than the inferred dihedral angles (Mierke and Kessler 1992),
thus eliminating any explicit conversion.
Two classes of methods have been devised for the experimental determination:
the first one is based on the modulation of the intensity of a cross-peak by scalar
coupling (quantitative J correlation). In this approach, the intensity of a cross
peak (modulated by sin (nJt)) is compared to that of a diagonal peak (modulated
by cos (nJt)). The alternative relies on the frequency separation of the two doublet peaks in an additional dimension (E.COSY, see Biamonti et al 1994 for a
review) or in separate spectra (S3E, Meissner et al 1997).
Conformationally flexible molecules give rise to average coupling constants
weighted by their probability distribution. When an angle is measured from several couplings, inconsistencies are frequently attributed to internal flexibility,
especially for side-chain torsion angle (Xl> X2 ... ). Models of various complexity,
including either a discrete superposition of staggered conformations or a continuous probability (Dzakula et al. 1992) have been proposed. The improvement
brought by the larger number of degrees of freedom should however carefully be
questioned to avoid overinterpretation of the data.
Coupling constants have been recently added to other structural restraints for
NMR structure determination. Their incorporation offers a reliable means of
improving the accuracy of protein structure (Garrett et al. 1994), but, contrary to
nOe, they do not contain any long range information which is fundamental for
finding the global fold of a protein.
3.3
Relaxation
Once the spins have been perturbed by radio-frequency pulses, the magnetizations (or the coherences) recover to their equilibrium states by an irreversible
process called relaxation. Relaxation is caused by time-dependent magnetic
fields that originate from the random thermal motions present in the sample.
Fluctuating magnetic fields at a nucleus may derive from the interaction with
other spins (dipolar relaxation) or from a modulation of its own chemical shielding (CSA relaxation). In a phenomenological description of relaxation, the longitudinal magnetization recovers exponentially with a time constant TJ (spin lattice
relaxation) and the transverse coherences vanish with a time constant T2 (spinspin relaxation). Long TJ values prevent the use of short recycling delays, when
multiple scans are acquired, leading to long acquisition times. On the other hand,
short T2 values (in other words, broad resonances) strongly limit the spectral resolution. Unfortunately, large macromolecules with slow overall tumbling rates
share these two drawbacks. However, the spin-spin relaxation can be reduced by
using complete or partial deuteriation of the molecule (LeMaster 1990).