The use of residual dipolar coupling in studying proteins by NMR

Abstract

The development of residual dipolar coupling (RDC) in protein NMR spectroscopy, over a decade ago, has become a useful and almost routine tool for accurate protein solution structure determination. RDCs provide orientation information of magnetic dipole-dipole interaction vectors within a common reference frame. Its measurement requires a nonisotropic orientation, through a direct or indirect magnetic field alignment, of the protein in solution. There has been recent progress in the developments of alignment methods to allow the measurement of RDC and of methods to analyze the resulting data. In this chapter we briefly go through the mathematical expressions for the RDC and common descriptions of the alignment tensor, which may be represented using either Saupe order or the principal order matrix. Then we review the latest developments in alignment media. In particular we looked at the lipid-compatible media that allow the measurement of RDCs for membrane proteins. Other methods including conservative surface residue mutation have been invented to obtain up to five orthogonal alignment tensors that provide a potential for de novo structure and dynamics study using RDCs exclusively. We then discuss approximations assumed in RDC interpretations and different views on dynamics uncovered from the RDC method. In addition to routine usage of RDCs in refining a single structure, novel applications such as ensemble refinement against RDCs have been implemented to represent protein structure and dynamics in solution. The RDC application also extends to the study of protein-substrate interaction as well as to solving quaternary structure of oligomer in equilibrium with a monomer, opening an avenue for RDCs in high-order protein structure determination.

Fig. 1

Illustrations of relationships between RDC internuclei vector AB and an arbitrary molecular frame (a) and the alignment tensor frame (b). A protein molecule, carrying spin nuclei A and B, is represented using an ellipsoid. B₀ is the external field. Θ is the instantaneous angle between the internuclei vector AB and B₀. β_x,y,z specify the projection angles of B₀ onto each axis of a molecular frame. Polar angle θ; and azimuth angle ϕ are spherical coordinates of the vector AB in the alignment tensor frame

Fig. 2

Variation of alignment using stretched polyacrylamide gels (SAG) and bacteriophage Pf1, which has been embedded and aligned (along z′) at different angles relative to the long axis (z) of the sample. The gels were cast in an approximately ellipsoidal (squashed cylinder) geometry, with dimensions of 5, 7, and 10 mm along the x, y, and z axes, respectively. The gels were then dried, rehydrated, and stretched to fit within a 4.2 mm i.d. NMR tube. (Reprinted with permission from [31])

Fig. 3

Alignment tensor orientations relative to the ribbon backbone structure of GB3 for six mutants, all in liquid-crystalline Pf1 medium. The six tensors are for A – K19AD47K; B –K19ED40N; C – K19EK4A-C-His-tag; D – K19EK4A-N-His-tag; E – K19AT11K; F – K19EK4A. Diagonalized tensor elements, Dxx (red), Dyy (green), and Dzz (blue) have magnitudes proportional to the length of the corresponding lines. (Reprinted with permission from [30])

Fig. 4

Experimental order parameters, S, of NH bond vectors in GB3 derived from iterative Direct Interpretation of Dipolar Couplings (DIDC) using all six sets of RDCs. The red line marks the order parameters derived from ¹⁵N relaxation. Filled symbols represent residues for which the fully anisotropic model was required to get a satisfactory fit to the data, while, for open symbols, the isotropic internal motion model was able to fit the RDCs to within the experimental noise. (Reprinted with permission from [41])

Fig. 5

Structure ensemble of Ubiquitin. (a) Two members (shown in red and blue) of a typical ensemble from the two-member size calculation. (Reprinted with permission from [52].) (b) Backbone trace of 40 randomly chosen structures from the ensemble. Residues are colored by the amount of additional (slower than-τc) mobility as compared with the Lipari-Szabo order parameters. (Reprinted with permission from [70])

Fig. 6

Ensemble structural fitting to RDCs. Agreement between experimental and back-calculated RDCs for a one-state ensemble (left) and a three-state ensemble (right). Data include NH, NC′, and phenyl CH (the latter two are normalized to NH). RDCs are collected in positive and negative gels. (Reprinted with permission from [78])