102
B. BERSCH et aI.
(such as infrared, Raman ... ), NMR provides the resolution for monitoring each
individual site in a protein (see Englander et al 1996 for a review).
Exchange rate constants are measured by dissolving a protonated protein in
D20 and following the disappearance of the J H signals by means of any quick correlation experiment. Many experimental procedures are available to alter these
rates: denaturant can be added to the solution to partially unfold the protein, pH
can be rapidly changed in order to slow exchange and trap some kinetic information (protein folding). All these experiments provide information on the dynamics of the protein on a time scale ranging from seconds to hours.
3.5
Structural Constraints from Anisotropic Rotational Diffusion
and Dipolar Coupling Constants
In liquid state NMR it is normally assumed that the molecule of interest undergoes rapid isotropic tumbling in an isotropic environment. In some cases, an
anisotropic behavior of the molecule can yield new structural information as
some experimental parameters become orientation-dependent. Examples are
heteronuclear relaxation data, which can be related to anisotropic rotational diffusion, and residual dipolar couplings, induced by a partial alignment of the molecule in the magnetic field. This information can be used as additional experimental constraints in structure calculations or at least give some insights into the
relative orientation of individual chemical bonds or structural elements (such as
regions of secondary structure, loops, domains ... ).
3.5.1
Determination of the Anisotropic Rotational Diffusion Tensor
In the case of anisotropic rotational reorientation of the molecule, the overall
reorientation is no longer determined by one global rotational time constant 'tc
but by a molecular rotational diffusion tensor D, which is defined by the Euler
angles a,~ and y as well as the relative amplitudes of the tensorial components
Dm Dyy and Dzz (Woessner 1962). In this case, the spin relaxation becomes
dependent on the orientation of the interaction vector with respect to this tensor.
It is therefore possible to characterize the rotational diffusion of the molecule
by analysing heteronuclear relaxation rates of spins not experiencing significant
internal motion contributions to their relaxation. In practice this latter criterion
is achieved by analysing the ratio R2/RJ which becomes independant of the order
parameter S2 in the fast internal motion limit. Non-linear least-squared fitting
has been used to determine the rotational diffusion (i.e. the principle values and
the orientation of the rotational diffusion tensor) of a number of molecules in a
series of recent studies.
However, in many studies of the global dynamics of molecules of known structure, an axially symmetric tensor was either assumed, or shown, using statistical
significance tests, to provide an adequate description of the rotational diffusion.
It has nevertheless recently been pointed out that two orthogonal solutions are
simultaneously present if the axially symmetric model is used to describe a fully
B. BERSCH et aI.
(such as infrared, Raman ... ), NMR provides the resolution for monitoring each
individual site in a protein (see Englander et al 1996 for a review).
Exchange rate constants are measured by dissolving a protonated protein in
D20 and following the disappearance of the J H signals by means of any quick correlation experiment. Many experimental procedures are available to alter these
rates: denaturant can be added to the solution to partially unfold the protein, pH
can be rapidly changed in order to slow exchange and trap some kinetic information (protein folding). All these experiments provide information on the dynamics of the protein on a time scale ranging from seconds to hours.
3.5
Structural Constraints from Anisotropic Rotational Diffusion
and Dipolar Coupling Constants
In liquid state NMR it is normally assumed that the molecule of interest undergoes rapid isotropic tumbling in an isotropic environment. In some cases, an
anisotropic behavior of the molecule can yield new structural information as
some experimental parameters become orientation-dependent. Examples are
heteronuclear relaxation data, which can be related to anisotropic rotational diffusion, and residual dipolar couplings, induced by a partial alignment of the molecule in the magnetic field. This information can be used as additional experimental constraints in structure calculations or at least give some insights into the
relative orientation of individual chemical bonds or structural elements (such as
regions of secondary structure, loops, domains ... ).
3.5.1
Determination of the Anisotropic Rotational Diffusion Tensor
In the case of anisotropic rotational reorientation of the molecule, the overall
reorientation is no longer determined by one global rotational time constant 'tc
but by a molecular rotational diffusion tensor D, which is defined by the Euler
angles a,~ and y as well as the relative amplitudes of the tensorial components
Dm Dyy and Dzz (Woessner 1962). In this case, the spin relaxation becomes
dependent on the orientation of the interaction vector with respect to this tensor.
It is therefore possible to characterize the rotational diffusion of the molecule
by analysing heteronuclear relaxation rates of spins not experiencing significant
internal motion contributions to their relaxation. In practice this latter criterion
is achieved by analysing the ratio R2/RJ which becomes independant of the order
parameter S2 in the fast internal motion limit. Non-linear least-squared fitting
has been used to determine the rotational diffusion (i.e. the principle values and
the orientation of the rotational diffusion tensor) of a number of molecules in a
series of recent studies.
However, in many studies of the global dynamics of molecules of known structure, an axially symmetric tensor was either assumed, or shown, using statistical
significance tests, to provide an adequate description of the rotational diffusion.
It has nevertheless recently been pointed out that two orthogonal solutions are
simultaneously present if the axially symmetric model is used to describe a fully