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Residual Dipolar Couplings (RDCs). Biochem. 801 (Biochemical Applications of NMR). RDC applications validation of structures structure refinement (i.e. improvement of local and global accuracy) • determination of relative domain orientations • identification of multimerization state

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residual dipolar couplings rdcs

Residual Dipolar Couplings (RDCs)

Biochem. 801 (Biochemical Applications of NMR)


RDC applications

  • validation of structures
  • structure refinement (i.e. improvement of local and global accuracy)
  • • determination of relative domain orientations
  • • identification of multimerization state
  • • fast/improved backbone assignments (e.g. MARS program)
  • new information on CSA, bond lengths and geometry etc.
  • • structure determination of protein complexes
  • • analysis of inter-domain motion
  • evaluation of slow dynamics

Magnetic dipole-dipole coupling

Hamiltoniandipolar term (ensemble and time average):


Da and Dr scale with S (order parameter) not S2 => variations in S propagate only as a few percent in RDC since typical S2 values for structured regions are in the 0.85-0.95 range

dipolar coupling in principal axis frame
Dipolar Coupling in Principal Axis Frame

The magnitude of the residual dipolar coupling depends on the alignment tensor:

5 parameters

Da and Dr: magnitude and rhombicity

+ 3 Euler angles: orientation relative to the molecular frame

Knowing the alignment tensor (e.g. by least squares or SVD fitting to a known structure) RDCs can be back calculated and compared to experimental data

(in the principal axis frame)


|Axx| < |Ayy|< |Azz|

Four-fold degeneracy is inherent to the orientation of any 3D structure relative to a molecular alignment tensor, and derives from simple symmetry operations (180° rotations around Axx, Ayy and Azz).

cone localization degeneracy dipolar couplings restraints in nmr structure determination
Cone localization degeneracydipolar couplings restraints in NMR structure determination

The measured dipolar coupling limits the orientation of a bond vector to a narrow distorted cone on a unit sphere (taco shaped – due to the rhombicity of the alignment tensor).

It restricts the orientation relative to a ‘global’ alignment frame (not relative to other vectors)

two tensors remove degeneracy solution is the intersection of cones
Two tensors remove degeneracy (solution is the intersection of cones)

The 2 RDC cones for ubiquitin’s Gln 40 NH in bicelles w. and w/o CTAB

(Ramirez, B.E. and Bax, A. 1998. Modulation of the alignment tensor of macromolecules dissolved in a dilute liquid crystalline medium. J. Am. Chem. Soc.120: 9106–9107)


Alignment media

  • Bicelles (DMPC/DHPC) +CTAB or - SDS, DTPC/DHPC, DLPC/DHPC, DLPC/CHAPSO, DIODPC/CHAPSO, Dialkyl-PC stable at any pH, etc.
  • Filamentous bacteriophage particles (Pf1)
  • TMV (rod shaped viruses)
  • Bacteriophage (fd)
  • Purple membrane fragments
  • PEG/hexanol
  • CPBr/hexanol (Helfrich lamellar phases)
  • Compressed AA gels (neutral or charged) etc.
  • ----------------------------------------------------------------------------------------------------------
  • Rotation diffusion rate of protein/nucleic acid is generally unaffected (but should be checked anyway).
  • Broadening is usually from due to overalignment (weak binding), i.e. H-H dipolar broadening and can cause vanishing of INEPT transfer (dipolar cancels scalar contribution).
induced alignment
Induced Alignment

DMPC/DHPC bicelle surface may be additionally charged with CTAB(+) or SDS(-) to modulate the alignment tensor orientation, magnitude and rhombicity. Alternatively, charged tags may also be added to the macromolecule.

Zweckstetter, M. & Bax, A. (2000) . J. Am. Chem. Soc. 122: 3791–3792


Tunable Alignment Tensor Magnitude

  • 2H 1D NMR spectra:
  • Best indicator of an aligned sample homogeneity and stability is the linewidth of the water doublet in a 2H spectrum (preferably < 1Hz)
  • Bruker:
  • 1H 1D parameters (zg) / edasp / select 2H
  • replace 2H cable (back of preamp. box with the X-channel (15N or 13C) cable (on our older consoles)
  • Varian:
  • 1H 1D parameters (s2pul)
  • tn=‘lk’ (not ‘2H’ !)

2H quadrupolar splitting as a function of Pf1 phage concentration

Hansen MR, Mueller L & Pardi A (1998) Tunable alignment of macromolecules by filamentous phage yields dipolar coupling interactions. Nat. Struct. Biol. 5: 1065-1074.


Pf1 bacteriophage


anisotropy: the “cavities” in the gel are no longer random in shape, but will have a slightly oblate character

  • 6% gel density is close to optimal (higher - inhibits protein diffusion, lower – gel too fragile)
  • to recover the protein: mince, wash, concentrate

Predicted vs. calculated RDCs (positively and negatively charged stretched acrylamide gels, Pf1)

Note the different distributions of the RDC values measured for GB3 protein in various media, corresponding to independent alignment tensors


RDC experiments (details in hands-on sessions):

  • 1J HN: IPAP-HSQC, DSSE-HSQC, 3D HNCO (NH coupled)
  • 1J C‘Cα: 3D HNCO (CSA(C‘) ~ 500 MHz optimum)
  • 1J C‘N & 2J C‘HN: 2D HSQC, quantitative 3D TROSY-HNCO
  • 1J CαHα: 2D JCH-modulated ct-HSQC, (HA)CANH, HN(CO)CA
  • 1J CH(side-chain): 2D D CH-mod. HSQC, CCH-COSY, SPITZE-HSQC
  • 1H-1H: COSY, CT-COSY, HNHA, 3D SS-HMQC2 (long-range)
  • All 3D experiments can be performed in HIFI mode.
    • Accuracy of measured splitting: J = LW/SN
    • Required accuracy < 5% * Da
    • Bax, Kontaxis & Tjandra, Method Enzymol. 339, 127-174, 2001;
    • Chou & Bax JBNMR, 2001;
    • Delaglio et al. JMR 2001;
    • Wu & Bax, JACS, 2002;
dipolar couplings along a protein backbone
Dipolar couplings along a Protein Backbone

Measured as difference in splitting between aligned (left) and isotropic phase (right) DIS=(JIS+DIS) - JIS


HIFI version (1JNC’ from single 45º tilted plane)

P12 protein (149 aa.) ~45 hrs. for 3D vs. 15 hrs. for HIFI


Determination of alignment tensor

  • no structure needed!
  • one may use different observed or simulated (EHM) normalized sets of RDCs (CH, NH, CaC’, NC’, etc) to obtain a more accurate histogram
  • exclude residues with substantially lower order parameter than average

Extremes of the RDC histogram correspond to the alignment tensor components Dzz and Dopposite (Dxx or Dyy):

Dxx + Dyy + Dzz = 0 (traceless tensor), | Dzz | > | Dyy | , | Dzz | > | Dxx |

Da = ~ Dzz / 2, R = 2/3 ( 1 + Dopposite / Da ), 0 < R < 0.66

Dzz = 2Da, Dyy = - Da ( 1 + 3/2 R ), Dxx = - Da ( 1 - 3/2 R )


Relative magnitude of RDCs in proteins [Hz]



If an RDC set is scaled to the NH RDCs (using bond lengths and gyr. ratios) => its XPLOR force constant should be scaled by the square of the ratio of its exp. error to that of the NH set


Example of structure refinement with RDCs (HTLV NTD)

Cornilescu, C.C., Bouamr, F., Yao, X., Carter C. and Tjandra, N. (2001) Structural Analysis of the N-Terminal Domain of the Human T-Cell Leukemia Virus Capsid Protein. J. Mol. Biol. 306: 783–797.


Docking of multimers, protein-protein

and protein-DNA/RNA complexes

  • - conjoined rigid body/torsion angle molecular dynamics (XPLOR‑NIH) to ensure preservation of the correct peptide geometry when applying RDC and distance constraints simultaneously.
  • in the case of homo-multimers the X-PLOR non‑crystallographic symmetry (NCS) potential term is needed to maintain identical structure of the monomeric subunits
  • the coordinates of an initial complex structure can be obtained by a rigid body minimization protocol by using RDCs and less than a dozen intermolecular NOEs.

Quaternary Structure, Protein-Protein and Protein-DNA/RNA Complexes

Classic way:

Asymmetric isotope labeling (and perdeuteration for large proteins) combined with NMR isotope filtering and editing techniques are used commonly to solve protein complex structures

“Newer” way:

Use RDCs and a limited number of intersubunit NOEs to accurately dock the complexes

At5g22580 homodimer docking

(a) 13C inter (red) intra (black) NOEs

(b) 1DNH monomeric

(c) 1DNH dimeric

conformational differences between x ray and solution e g cam
Conformational differences between X-ray and solution (e.g. CaM)


Q=25 %

Chou, Li, Klee & Bax, Nature Struct. Biol., 2001

use same rdcs to calculate refine and cross validate structure
Use same RDCs to calculate, refine and cross-validate structure

NOEs vary with less than 0.5 A between X-ray (blue) and RDC refined (red) structures

Chou, Li, Klee & Bax, Nature Struct. Biol., 2001


Rapid Identification of Structural Distortions Induced by Crystal Packing in X-ray Structures of Proteins Using Residual Dipolar Couplings


The 4 regions of significant distortions arising from crystal packing

A and B - blue; C and D - magenta


Structure Validation:

Q = rms(Dcalc - Dobs) / rms(Dobs)


Aligning a molecule in at least 5 different media can provide fundamental information on CSA tensors

  • residual dipolar couplings (D), alignment tensor (Aii)
  • residual chemical shifts (Dd) / chemical shielding anisotropy (dii)
  • quality factor (Q)



A) CSA tensor in the alignment tensor frame

B) geometry of CSA tensors relative to the peptide plane

rapid structure determination molecular fragment replacement mfr
Rapid Structure Determination:Molecular Fragment Replacement (MFR)

Use Long Range Information in the assembly process

Fragments must share one common alignment frame so that the relative orientation can be inferred


0, 180x, 180y, 180z can be resolved by coordinate overlap

protein structure by mfr
Protein Structure by MFR

Delaglio, F., Kontaxis, G., and Bax, A. “Protein structure determination using molecular fragment replacement and NMR dipolar couplings”, J. Am. Chem. Soc. 122: 2142–2143, (2000)

Kontaxis, G., Delaglio F., and Bax, A. “Molecular fragment replacement approach to protein structure determination by chemical shift and dipolar homology database mining”, Meth. Enzymol. 394, 42-78 (2005)


Dynamics by RDCs

  • RDCs report the average of a bond vector, integrated over the entire timescale of the measurement (ms)
  • Motion of a bond vector relative to the molecular alignment frame scales the size of the RDC relative to a static average orientation
  • RDC approach to studying dynamics is most robust for large-amplitude processes

A 3D GAF motional model

(G. Bouvignies et. al, PNAS, vol. 102 no. 39, 13885–13890, 2005)


GAF distributions of γ motions

In the β-sheet of Protein G an alternating pattern of dynamics along the peptide sequence is found to form a long-range network across the β-strands, reminiscent of a standing wave.

The extracted motional modes significantly improve the prediction of experimentally measured scalar couplings across hydrogen bonds throughout the molecule.

The residues exhibiting the highest level of flexibility coincide precisely with

the sites participating in the interaction of protein G with its physiological partner, the antigen-binding domain of IgG.

(G. Bouvignies et. al, PNAS, vol. 102 no. 39, 13885–13890, 2005)



  • Residual dipolar couplings:
  • provide precise long‑range orientational constraints
  • complement intramolecular NOE constraints for backbone fold
  • replace many intermolecular NOEs traditionally needed to dock complexes
  • are structural quality indicators (structure validation)
  • indicate the quality (correctness) of the relative orientation of the subunits within a complex
  • can be used for automatic NMR assignments (MARS)
  • can be used to distinguish oligomeric states (by predicting alignment from molecular shape in the steric case with PALES)
  • clearly identify which structure obtained by crystallography is representative of the solution conformation
  • provide an accurate and simple means of identifying crystal packing defects in protein X-ray structures
Recommended reading:
  • Tjandra, N. and Bax, A. (1997). Direct measurement of distances and angles in biomolecules by NMR in a dilute liquid crystalline medium. Science 278: 1111–1114.
  • Tjandra, N., Omichinski, J.G., Gronenborn, A.M., Clore, G.M. & Bax (1997) Use of dipolar 1H-15N and 1H-13C couplings in the structure determination of magnetically oriented macromolecules in solution. Nature Struct. Biol. 4, 732-738.
  • Ottiger, M. and Bax, A. (1998). Characterization of magnetically oriented phospholipid micelles for measurement of dipolar couplings in macromolecules. J. Biomol. NMR 12: 361–372.
  • Ottiger M & Bax A (1998) Determination of relative N-HN, N-C’, Cα-C’ and Cα-Hα effective bond lengths in a protein by NMR in a dilute liquid crystalline phase. J. Am. Chem. Soc. 120: 12334-12341.
  • Clore GM, Gronenborn AM & Bax A (1998) A robust method for determining the magnitude of the fully asymmetric alignment tensor of oriented macromolecules in the absence of structural information. J. Magn. Reson. 133: 216-221.
  • Clore GM, Starich MR & Gronenborn AM (1998) Measurement of residual dipolar couplings of macromolecules aligned in the nematic phase of a colloidal suspension of rod-shaped viruses. J. Am. Chem. Soc. 120; 10571-10572.
  • Hansen MR, Mueller L & Pardi A (1998) Tunable alignment of macromolecules by filamentous phage yields dipolar coupling interactions. Nat Struct Biol 5: 1065-1074.
  • Clore, G.M., Starich, M.R., and Gronenborn, A.M. (1998) Measurement of residual dipolar couplings of macromolecules aligned in the nematic phase of a colloidal suspension of rod-shaped viruses. J. Am. Chem. Soc. 120: 10571–10572.
  • Ramirez, B.E. and Bax, A. (1998) Modulation of the alignment tensor of macromolecules dissolved in a dilute liquid crystalline medium. J. Am. Chem. Soc. 120: 9106–9107.
  • Cornilescu, G., Marquardt, J.L., Ottiger, M., and Bax, A. (1998) Validation of protein structure from anisotropic carbonyl chemical shifts in a dilute liquid crystalline phase. J. Am. Chem. Soc. 120: 6836–6837.
  • G. A. Mueller, W. Y. Choy, D. W. Yang, J. D. Forman-Kay, R. A. Venters & L. E. Kay (2000) Global Folds of Proteins with Low Densities of NOEs Using Residual Dipolar Couplings: Application to the 370 Residue Maltosedextrin Binding Protein, J. Mol. Biol., 300, 197.
  • Cornilescu, G. and Bax, A. (2000) Measurement of proton, nitrogen, and carbonyl chemical shielding anisotropies in a protein dissolved in a dilute liquid crystalline phase. J. Am. Chem. Soc. 122: 10143–10154.
  • Clore, G.M. (2000) Accurate and rapid docking of protein-protein complexes on the basis of intermolecular nuclear Overhauser enhancement data and dipolar couplings by rigid body minimization. Proc. Natl. Acad. Sci. U.S.A. 97, 9021-9025.
  • Sass, H.-J., Musco, G., Stahl, S. J., Wingfield, P. T. & Grzesiek, S. (2000). Solution NMR of proteins within polyacrylamide gels: diffusional properties and residual alignment by mechanical stress or embedding of oriented purple membranes. J Biomol NMR 18, 305-311.
  • Bewley, C.A. and Clore, G.M. (2000) Determination of the relative orientation of the two halves of the domain-swapped dimer of cyanovirin-N in solution using dipolar couplings and rigid body minimization. J. Am. Chem. Soc. 122: 6009–6016.
  • Meiler, J., Peti, W., and Griesinger, C. (2000). DipoCoup: A versatile program for 3D-structure homology comparison based on residual dipolar couplings and pseudocontact shifts. J. Biomol. NMR17: 283–294.
  • Zweckstetter, M. and Bax, A. 2000. Prediction of sterically induced alignment in a dilute liquid crystalline phase: Aid to protein structure determination by NMR. J. Am. Chem. Soc. 122: 3791–3792.
  • Sass, H. J., Musco, G., Stahl, S. J., Wingfield, P. T. & Grzesiek, S. (2001) An easy way to include weak alignment constraints into NMR structure calculations. J Biomol NMR 21, 275-280.
  • Chou, J.J., Gaemers, S., Howder, B., Louis, J.M., and Bax, A. (2001) A simple apparatus for generating stretched polyacrylamide gels, yielding uniform alignment of proteins and detergent micelles. J. Biomol. NMR 21: 377–382.
  • Chou, J.J., Kaufman, J.D., Stahl, S.J., Wingfield, P.T., and Bax, A. (2002) Micelle-Induced Curvature in a Water-Insoluble HIV-1 Env Peptide Revealed by NMR Dipolar Coupling Measurement in Stretched Polyacrylamide Gel. J. Am. Chem. Soc. 124, 2450-2451.
  • Clore, G.M. & Schwieters, C.D. (2003) Docking of protein-protein complexes on the basis of highly ambiguous intermolecular distance restraints derived from 1HN/15N chemical shift mapping and backbone 15N-1H residual dipolar couplings using conjoined rigid body/torsion angle dynamics. J. Am. Chem. Soc. 125, 2902-2912.
  • Clore GM, Schwieters CD (2004 ):Amplitudes of protein backbone dynamics and correlated motions in a small a/b protein: correspondence of dipolar coupling and heteronuclear relaxation measurements. Biochemistry, 43:10678-10691.
  • Lindorff-Larsen K, Best RB, DePristo MA, Dobson CM, Vendruscolo M (2005) Simultaneous determination of protein structure and dynamics. Nature, 433:128-132.


  • A. Grishaev and A. Bax: (2005).Weak alignment NMR: a hawk-eyed view of biomolecular structure. Cur. Opinion Struct. Biol. 15, 563-570.
  • Bax, A. (2003) Weak alignment offers new NMR opportunities to study protein structure and dynamics. Prot. Science, 12, 1-16.
  • Prestegard, J. H.; Al-Hashimi, H. M.; Tolman, J. R. Q. Rev. Biophys. 2000, 33, 371-424.
  • de Alba, E. & Tjandra, N. (2002) Prog. Nucleic Magn. Reson. Spectrosc. 40, 175-197.
  • Lipsitz, R.S. & Tjandra, N. (2004) Residual Dipolar Couplings in NMR Structure Analysis. Annu Rev Biophys Biomol Struct 2004, 33:387-413


  • Measuring RDCs in proteins: