3J Scalar Couplings 3JHN-HaThe 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 ) + 1.8Sometimes 3J has no unique solution and extra information is required! CS, NOE, Ramachandran plot!

Chart3

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Sheet3

Measurement of CouplingsProblem: large linewidth, no splittingquantitative J experimentsJ is calculated from an intensity ratio

IPAP-HSQCMeasure 1JHN-N by combining an InPhase and an AntiPhase HSQC

J-Correlation through H-Bondsubq.pdbH-N-C andH-N O=CCorrelationse- density in the H-bond

B0 Dependence of Splittings Indicates Dipolar ContributionsIncomplete 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 NMRContains information about angles!

Field induced AlignmentDipolar Contribution to J SplitingsProportional to B02, but effects are very smallFew Hz in molecules with a large magnetic anisotropy e.g. 2gat.pdbArtificial Alignment requiredDIS is measured as the different splitting between different B0 fields

Induced AlignmentPhospholipidBicellescolloidalPhage particles--Surfaces may be additionally charged to modulate the alignmentsample stability can be a BIG problem

NMR in LC Phases

NMR in Liquid Crystals

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

Dipolar CouplingThe magnitude of the residual dipolar coupling depends on the alignment tensor:5 parametersDa/Dr: magnitude and rhombicity + 3 rotation angles: orientation relative to the .pdb frameKnowing 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 Conedipolar couplings can be used as restraints in NMR structure determinationThe 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 sphereIt restricts the orientaion relative to a global alignment framenot relative to other vectors

Two Tensors!almost unique solution (intersection of cones)

Dipolar HomologyArbitrary fragments from the .pdb are fitted to the collected dipolar couplingsThe dipolar agreement is used for the scoringThe best fragments are kept

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

Molecular Fragment ReplacementFragments must share one common alignment frame So the relative orientation can be inferredAmbiguities:0, 180x, 180y, 180z can be resolved by coordinate overlapUse Long Range Information in the Assembly Process

Assemble a Protein Structure

Protein Structure by MFR