Anisotropy in Protein NMR

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Anisotropy in Protein NMR

• Anisotropic Rotational Diffusion
• Anisotropic Susceptibility
• Chemical Shift Anisotropy

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Anisotropic Susceptibility
B0
ca
E -1/2 B0 Dc B0
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Dipolar Coupling
Dipolar Interaction
B0
HDD DABmax ? IAZ IBZ (3 cos2q -1) ?
B
?
DABmax -?0(h/2p) gA gB / (4p2r3AB)
Dipolar splitting
A
DAB DABmax ? P2 (cosq) ?
? P2 (cosq) ? Sij Sij cos ai cos aj
S Saupe matrix
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Dipolar Coupling
In the principal axis frame
DAB (ax, ay, az) DABmax ?Cx?2 cx ?Cy?2 cy
?Cz?2 cz -1 Where ?Ci?2 is the
probability of finding ith axis parallel to B0
Setting ?Ci?2 1/3 Aii , and expressing the
equation in polar coordinates DAB (?, ?) (3/
2) DABmax cos2q Azz sin2q cos2 ? Axx sin2q
sin2 ? Ayy
Defining Azz gt Ayy gt Axx , and using Ayy
Axx -Azz DAB (?, ?) (3/ 2) DABmax
P2(cosq? Azz 1/2 sin2q cos 2? (Axx - Ayy)
DAB (?, ?) DABa (3cos2q???
3/2 R sin2q cos 2??
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Anisotropic Susceptibility
E -1/2 B0 Dc B0
ddip (?,?) -C(B02) ?a (3cos2? -1) 3/2 ?r
(sin2? cos2?)
JNH ddip(NH) DFS
15N
HN b gt
HN a gt
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Residual Dipolar Coupling Measurement(susceptibil
ity anisotropy)

• Measure scalar (J) couplings as a function of
  magnetic fields.
• J-coupling is encoded as a modulation of the NMR
  signal intensity.
• Least square fit of the modulated signal
  provides
• a very accurate J-coupling value (0.02Hz).
• apparent T2.
• Any systematic offset.

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GATA-1 DNA Complex
Coordinate precision (Å) rms shift (Å)
SA SA dipolar SA .vs. SA
dipolar Protein backbone 0.760.13 0.680.15 1.
12 All protein atoms 1.290.13 1.210.15 1.25 DNA
0.620.16 0.650.10 0.39
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GATA-1 DNA Complex
Without Dipolar With Dipolar Most fav. R.
map 62 79 Bad contacts/100 res. 17 10
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Dipolar Coupling Refinement

• Define an external axis system
• Use harmonic potential for non-mobile residues
• E kdip (Dmeas - Dcalc)2
• Use half-open potential for any suspected
  mobile residues
• Dmeas lt 0 Dcalc lt Dmeas E 0
• Dcalc gt Dmeas E kdip (Dmeas -
  Dcalc)2
• Dmeas gt 0 Dcalc gt Dmeas E 0
• Dcalc lt Dmeas E kdip (Dmeas - Dcalc)2
• Estimate the alignment tensor (Da and Dr) using
  the distribution of measured dipolar coupling
• Adjust the force constant (kdip) such that the
  final dipolar RMS reflects the measurement error

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Potential for mobile residues
Dmeas lt 0
Dmeas gt 0
Edip
Edip
Dmeas
Dmeas
0
0
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Dipolar Coupling Q Factor

• Calculate a family of structures excluding the
  dipolar coupling type of interest.
• Calculate the distribution RMS of the dipolar
  coupling of interest
• RMSa SQRT( S Dmeas2 )
• Calculate the RMS between measured and predicted
  dipolar coupling values of interest based on the
  family of calculated structures
• RMSb SQRT( S ( Dmeas - Dpred )2 )
• Q factor
• Qdc RMSa / RMSa

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Structure comparison
W/o dipolar with dipolar Backbone RMSD 0.34
Å 0.17 Å All non-H RMSD 0.85 Å 0.79 Å Most fav.
Region of 90.9 2.6 95.8 1.4 Ramachandran Bad
contact per 100 4.2 2.8 4.5 1.7 residues

QNH factor 32 QCH factor 27
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Anisotropic Diffusion

• ? ? tc D?/D// Dy/Dx
• 82.4 12.0 60.5 6.87 1.37 1.12

c2
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Anisotropy in Protein NMR

• Anisotropic Rotational Diffusion
• Anisotropic Susceptibility
• Chemical Shift Anisotropy

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s22
C
O
C
N
H
s33
C
s11
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Chemical Shift Anisotropy
s22
s33
s11
s
s//
Isotropic (s11 s22 s33) / 3 Anisotropic
s// - s
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Chemical Shift Anisotropy
Cross correlation
Dipolar Chemical Shift Anisotropy ( D ) (
C )
Relaxation rates ( D C ) 2 ( D - C ) 2
1/T2 - ?
1/T2 ?
15N
HN b gt
HN a gt
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