3J Scalar Couplings 3 J HN-H  The 3 J 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: 3 J N  = 9.4 cos 2 (  - 60 ) cos(  - 60 ) J  = 9.5 cos 2 (  - 60 ) cos(  - 60 ) Sometimes 3 J has no unique solution and extra information is required! CS, NOE, Ramachandran plot!

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

IPAP-HSQC Measure 1 J HN-N by combining an InPhase and an AntiPhase HSQC

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

B 0 Dependence of Splittings Indicates Dipolar Contributions Incomplete averaging of the dipolar interaction due to partial alignment in the magnetic field  IS =h*  I  S /r IS 3 (3cos 2  IS -1) Angular dependance allows the measurement of angles and relative orientations, which has not been possible in NMR Contains information about angles !

Field induced Alignment Dipolar Contribution to J Splitings Proportional to B 0 2, but effects are very small Few Hz in molecules with a large magnetic anisotropy e.g. 2gat.pdb ‘Artificial’ Alignment required D IS is measured as the different splitting between different B 0 fields

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

NMR in LC Phases

NMR in Liquid Crystals

Dipolar couplings along a Protein Backbone Measured as difference in splitting between aligned (left) and isotropic phase (right)  IS =J IS +D IS

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)

Motion along a Cone dipolar 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

Two Tensors! almost unique solution (intersection of cones)

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

Dipolar Homology Mining use measured DC to search for matching overlapping peptide fragments

Molecular Fragment Replacement 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 Use ‘Long Range Information in the Assembly Process

Assemble a Protein Structure

Protein Structure by MFR