Calcium-Binding Protein Protocols Calcium-Binding Protein Protocols

Dipolar Couplings for Structure Refinement 303
unequal orientational probabilities, so that the magnetic dipole–dipole coupling
between each pair of 1 H and 15 N nuclei does not average to zero. The dependence
of the residual dipolar coupling on orientational order can be quantified
by employing the symmetric traceless molecular alignment tensor, A (10,18),
where A = 0 for an isotropic system. The alignment tensor is internal to and
moves with the protein. Hence, for a sample without significant relative domain
or internal motions, the transformation from the principal axes of each 1 H– 15 N
dipolar coupling tensor to the principal axes of the alignment tensor does not
depend on time or the details of the molecular motion. In contrast, 15 N–T 1, and
T 2 relaxation rates from isotropic solution depend upon the random motions
experienced by the internal molecular rotational diffusion, dipolar and chemical
shift tensors with respect to the fixed laboratory magnetic field. The time-dependent
motional details can be quantified using the spectral density function. For
the system of phospholipids employed in this work, the director of the liquid
crystalline phase is perpendicular to the axis of the laboratory magnetic field
(see Fig. 1) and the direct dipolar coupling constant for an isolated 15 N– 1 H spin
pair is given by:
1 DNH(Hz) = 1/2[S NHγ Nγ Hh(µ o/4π 2 )]{Azz (3 cos 2 θ–1)/2+0.5(A xx–A yy)(sin 2 θcos2φ)} (1)
where A ii are the magnitudes of the principal axes of the alignment tensor A and
θ and ϕ are the spherical polar coordinates that specify the orientation of the NH
internuclear vector in the principal axis system of the alignment tensor (10,19).
Ottiger and Bax (20) have suggested that whenever the generalized order
parameter (21), S NH, for internal motion is greater than about 0.89 (20), it is
possible to define an effective NH bond length = 0.104 nm with S NH = 1.
The degree of protein alignment depends on the concentration of additive
(bicelles, phage, or purple membrane) as well as upon the shape of the molecule.
Whenever the shape of the protein deviates from axial symmetry, the
rhombic term (A xx–A yy) in Eq. 1 is expected to assume increased significance.
However, it has also been proposed that it will become particularly significant
whenever the protein interacts electrostatically and asymmetrically with the
additive causing the molecular alignment (13). The use of residual dipolar
coupling-derived restraints has proven to be particularly useful for the structure
determination of an elongated molecule, such as the two linked cbEGF
domains in LDLR-AB, as described here.
2. Materials
1. A purified sample of an 15N enriched protein, in the concentration range approx
0.2–1.0 mM (see Notes 1 and 2).
2. An NMR spectrometer with a magnetic field strength sufficient to provide good
resolution and signal-to-noise ratio in a 2-D 15N– 1H correlated spectrum
of the sample.