3J Scalar Couplings 3JHN-H

•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:

3JN = 9.4 cos2( - 60 ) - 1.1 cos( - 60 ) + 0.4

3J = 9.5 cos2( - 60 ) - 1.6 cos( - 60 ) + 1.8

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12

-200 -100 0 100 200

Series1

Sometimes 3J has no unique solution and extra information is required! CS, NOE, Ramachandran plot!

Measurement of CouplingsProblem: large linewidth, no splitting

quantitative J experiments

J is calculated from an intensity ratio

IPAP-HSQC

Measure 1JHN-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

B0 Dependence of Splittings Indicates Dipolar Contributions

Incomplete averaging of the dipolar interaction due to partial alignment in the magnetic field

IS=h*IS/rIS3(3cos2IS-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 B0

2, 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

Induced Alignment

Phospholipid

‘Bicelles’

colloidal

Phage particles

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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=JIS+DIS

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 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

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 Mininguse 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