Protein Structure and Dynamics by NMR in Solution
103
anisotropic system, representing the prolate and oblate approximations to the
real tensor (Blackledge et al. 1998).
Knowledge of the rotational diffusion tensor can be related to the size and the
shape of the molecule. Interestingly, numerous studies of rotational diffusion
using this method have derived values of the diffusion tensor components which,
while in general coaxial to the components of the inertia tensor of the protein,
imply the presence of a solvation layer of approximately one water molecule
thickness around the protein, when compared to hydrodynamic calculations
(Garcia de la Torre and Bloomfield 1981).
In addition, the rotational diffusion tensor determined from relatively rigid
regions of a molecule (normally secondary structure elements) can be incorporated into a Lipari-Szabo type analysis of local motion to characterize the local
mobility. This results in a much greater confidence in the results obtained as a
precise knowledge of the component of the auto-correlation function due to the
overall tumbling of the molecule is necessary in order for the model-free
approach to give realistic information concerning local motions.
3.5.2
Heteronuclear Relaxation Rate Constants as Structural Constraints
The ability to accurately characterize rotational diffusion anisotropy using heteronuclear relaxation rates has led to the observation that the R2/RJ ratio can also
provide a novel long-range constraint for NMR structure determination (Tjandra
et al. 1997). Such constraints no longer aim to describe relative atomic positions
of nuclei by means of the scalar coupling or the nOe, which are local interactions,
but the absolute orientation of many internuclear vectors (corresponding to
chemical bonds) with respect to a single reference tensor (i.e. a three dimensional reference system, see Fig. 7.1). This orientational information can be used
in the form of additional constraints during structure calculation (for a review,
see Clore and Gronenborn 1998). In addition, it allows the determination of the
relative orientation of one protein domain with respect to another, even if they
are several tens of A away. Internuclear nOes do not permit such a determination,
as no long-range order information is available and the errors tend to accumulate. Orientational constraints can also be obtained from the analysis of residual
dipolar couplings, which can be observed if the protein molecules become partially aligned within the magnetic field.
3.5.3
Residual Dipolar Couplings
Although theory shows that scalar J -couplings do not vary with the magnetic
field, several authors have recently reported a field dependence of an apparent Jcoupling constant. This unexpected observation arises from the superimposition
of a dipolar contribution to the true scalar coupling. This effect appears when the
protein has a slightly preferred orientation in a magnetic field: consequently, the
dipolar interaction - which depends upon the orientation of the internuclear vector in the applied field - does not vanish anymore to zero. Macromolecules may
103
anisotropic system, representing the prolate and oblate approximations to the
real tensor (Blackledge et al. 1998).
Knowledge of the rotational diffusion tensor can be related to the size and the
shape of the molecule. Interestingly, numerous studies of rotational diffusion
using this method have derived values of the diffusion tensor components which,
while in general coaxial to the components of the inertia tensor of the protein,
imply the presence of a solvation layer of approximately one water molecule
thickness around the protein, when compared to hydrodynamic calculations
(Garcia de la Torre and Bloomfield 1981).
In addition, the rotational diffusion tensor determined from relatively rigid
regions of a molecule (normally secondary structure elements) can be incorporated into a Lipari-Szabo type analysis of local motion to characterize the local
mobility. This results in a much greater confidence in the results obtained as a
precise knowledge of the component of the auto-correlation function due to the
overall tumbling of the molecule is necessary in order for the model-free
approach to give realistic information concerning local motions.
3.5.2
Heteronuclear Relaxation Rate Constants as Structural Constraints
The ability to accurately characterize rotational diffusion anisotropy using heteronuclear relaxation rates has led to the observation that the R2/RJ ratio can also
provide a novel long-range constraint for NMR structure determination (Tjandra
et al. 1997). Such constraints no longer aim to describe relative atomic positions
of nuclei by means of the scalar coupling or the nOe, which are local interactions,
but the absolute orientation of many internuclear vectors (corresponding to
chemical bonds) with respect to a single reference tensor (i.e. a three dimensional reference system, see Fig. 7.1). This orientational information can be used
in the form of additional constraints during structure calculation (for a review,
see Clore and Gronenborn 1998). In addition, it allows the determination of the
relative orientation of one protein domain with respect to another, even if they
are several tens of A away. Internuclear nOes do not permit such a determination,
as no long-range order information is available and the errors tend to accumulate. Orientational constraints can also be obtained from the analysis of residual
dipolar couplings, which can be observed if the protein molecules become partially aligned within the magnetic field.
3.5.3
Residual Dipolar Couplings
Although theory shows that scalar J -couplings do not vary with the magnetic
field, several authors have recently reported a field dependence of an apparent Jcoupling constant. This unexpected observation arises from the superimposition
of a dipolar contribution to the true scalar coupling. This effect appears when the
protein has a slightly preferred orientation in a magnetic field: consequently, the
dipolar interaction - which depends upon the orientation of the internuclear vector in the applied field - does not vanish anymore to zero. Macromolecules may