1. 3J Scalar Couplings 3JHN-Ha • The 3J coupling constants are related to the dihedral angles • by the Karplus equation, which is an empirical relationship • obtained from molecules for which the crystal structure is known. • The equation is a sum of cosines, and depending on the type • of topology (H-N-C-H or H-C-C-H) we have different • parameters: • 3JNa = 9.4 cos2( f - 60 ) - 1.1 cos( f - 60 ) + 0.4 • 3Jab = 9.5 cos2( y - 60 ) - 1.6 cos( y - 60 ) + 1.8 Sometimes 3J has no unique solution and extra information is required! CS, NOE, Ramachandran plot!

2. Measurement of Couplings Problem: large linewidth, no splitting quantitative J experiments J is calculated from an intensity ratio

3. IPAP-HSQC Measure 1JHN-N by combining an InPhase and an AntiPhase HSQC

4. J-Correlation through H-Bonds H-N-C’ and H-N … O=C’ Correlations e- density in the H-bond ubq.pdb

5. B0 Dependence of Splittings Indicates Dipolar Contributions Incomplete averaging of the dipolar interaction due to partial alignment in the magnetic field DnIS=h*gIgS/rIS3(3cos2qIS-1) Angular dependance allows the measurement of angles and relative orientations, which has not been possible in NMR Contains information about angles!

6. Field induced Alignment • Dipolar Contribution to J Splitings • Proportional to B02, but effects are very small • Few Hz in molecules with a large magnetic anisotropy e.g. 2gat.pdb • ‘Artificial’ Alignment required DIS is measured as the different splitting between different B0 fields

7. Induced Alignment Phospholipid ‘Bicelles’ Surfaces may be additionally charged to modulate the alignment sample stability can be a BIG problem - - colloidal Phage particles

8. NMR in LC Phases

9. NMR in Liquid Crystals

10. Dipolar couplings along a Protein Backbone Measured as difference in splitting between aligned (left) and isotropic phase (right) DIS=JIS+DIS

11. Dipolar Coupling The magnitude of the residual dipolar coupling depends on the alignment tensor: 5 parameters Da/Dr: magnitude and rhombicity + 3 rotation angles: orientation relative to the .pdb frame Knowing the alignment tensor (e.g. by least squares fitting) DC can be simulated and compared to experimental data (in the principal axis frame)

12. Motion along a Conedipolar couplings can be used as restraints in NMR structure determination The measurement of a residual dipolar coupling limits the the orientation of a bond vector (relative to the alignment tensor) to a narrow cone on a unit sphere It restricts the orientaion relative to a ‘global’ alignment frame not relative to other vectors

13. Two Tensors!almost unique solution (intersection of cones)

14. Dipolar Homology Arbitrary fragments from the .pdb are fitted to the collected dipolar couplings The dipolar agreement is used for the scoring The best fragments are kept

15. Dipolar Homology Mininguse measured DC to search for matching overlapping peptide fragments

16. Molecular Fragment Replacement Use ‘Long Range Information in the Assembly Process Fragments must share one common alignment frame So the relative orientation can be inferred Ambiguities: 0, 180x, 180y, 180z can be resolved by coordinate overlap

17. Assemble a Protein Structure

18. Protein Structure by MFR