3J Scalar Couplings 3JHNHa

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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!
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Measurement of Couplings
Problem large linewidth, no splitting quantitativ
e J experiments J is calculated from an intensity
ratio
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IPAP-HSQC
Measure 1JHN-N by combining an InPhase and an
AntiPhase HSQC
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J-Correlation through H-Bonds
H-N-C and H-N OC 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
DnIShgIgS/rIS3(3cos2qIS-1) Angular dependance
allows the measurement of angles and relative
orientations, which has not been possible in
NMR Contains information about angles!
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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

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Induced Alignment
Phospholipid Bicelles
Surfaces may be additionally charged to modulate
the alignment sample stability can be a BIG
problem
- -
colloidal Phage particles
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NMR in LC Phases
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NMR in Liquid Crystals
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Dipolar couplings along a Protein Backbone
Measured as difference in splitting between
aligned (left) and isotropic phase (right)
DISJISDIS
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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)
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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
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Two Tensors!almost unique solution (intersection
of cones)
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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
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Dipolar Homology Mininguse measured DC to search
for matching overlapping peptide fragments
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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
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Assemble a Protein Structure
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Protein Structure by MFR