3j scalar couplings 3 j hn-h the 3 j coupling constants are related to the dihedral angles by the...
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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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-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
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