Residual Dipolar Couplings
BCMB/CHEM 8190
Reviews
• Prestegard, A-Hashimi & Tolman, Quart. Reviews
Biophys. 33, 371-424 (2000).
• Bax, Kontaxis & Tjandra, Methods in Enzymology,
339, 127-174 (2001)
• Prestegard, Bougault & Kishore, Chemical
Reviews, 104, 3519-3540 (2004)
• Lipsitz & Tjandra, Ann. Rev. Biophys. Biomol.
Struct., 33, 387-413 (2004)
• Fushman et al., Prog. NMR Spect. 44, 189-214
(2004)
• Hu & Wang, Ann Rpts NMR Spect, 58,231-303
(2006)
• Bailor et al., Nature Protocols, 2, 1536-1546
(2007)
The Dipolar Interaction Between Two Spins
B0
θ
1H
r
15N
C 3cos2θ − 1
INZIHZ
D= 3
r
2
Brackets denote averaging –
goes to zero without partial orientation
Inducing Order Using Liquid Crystalline Media
B0
Measurement of Dipolar Couplings –
Coupled HSQC
Isotropic
J
Aligned
J+D
Polyacrylamide Gels
another alignment medium
Yizhou Liu, J. Prestegard (2010)
J. Biomol NMR, 47: 249-258.
Order Matrix Analysis
z
ρx
ρz
φz
θ
x
3 cos2 θ − 1
2
⋅
=
⋅
⋅
⎡cos φi cos φj
⎢
⋅
⎢
⎢
⋅
⎢
⋅
⎣
y
⋅ ⋅ ⋅⎤ ⎡3 cos ρk
⋅ ⋅ ⋅⎥ ⎢
⎥×⎢
⋅ ⋅ ⋅⎥ ⎢
⎥ ⎢
⋅ ⋅ ⋅⎦ ⎣
cos ρl − δkl ⎤
⎥
⋅
⎥
⎥
⋅
⎥
⋅
⎦
Finding a Principal Order Frame
Sxx Sxy ..
Syx Syy ..
.. .. ..
Sx’x’
=
A
A-1
Sy’y’
Sz’z’
Strategy for Protein Fold Determination
• Express 15N labeled protein
• Identify secondary elements
• Assign backbone resonances
•Orient protein in LC medium
•Collect residual dipolar data
• Orient individual elements
• Assemble protein fold
Dipolar Interaction Vectors
In an Idealized α-Helix
15N
Labeling Only
Data Used in ACP Fold Determination
A. Dipolar couplings in α-helices
Couplings (Hz)
Helix 2
Helix 1
Helix 3
Amide Couplings
(Ni-HNi)
I3
E4
E5
V7
K8
I10
I11
G12
E13
Q14
L15
1.4
0.4
3.4
-1.0
0.8
2.0
-0.3
2.1
2.1
0.0
-1.9
L37
D38
T39
V40
-2.6
1.6
-0.3
-2.6
Q66
A67
I69
D70
N73
G74
H75
8.2
7.7
6.8
6.1
7.4
5.5
7.7
Amide-Alpha Couplings
(HNi – Hαi)
R6
V7
K9
L15
3.0
-3.5
4.5
0.0
L37
L42
V43
M44
L46
V43N-L42α
M44N-A45α
0.4
0.0
3.5
2.0
-2.0
2.0
-2.0
Q66
A68
H75
0.0
-8.5
-9.0
D38
T39
V40
2.0
2.0
2.0
N73
2.0
(HNi – Hαi±1)
Amide/Amide Couplings
(HNi - HNi+1)
B. NOEs and distances used to position helices in POSE:
I3 HN - F50 Hα, V7 HN - F50 Hξ, V7 Hα - F50 Hξ, V7 methyl - A68 HN, I3 methyl - N73 HN
6Å
8Å
8Å
8Å
8Å
Orientation Maps for Three ACP Helices
ACP Dipolar Fold vs. NOE Structure
Fowler, et al., (2000) J Mol Biol 304(3):447-460.
Some Experiments for RDC Data Acquisition
• Tolman JR, Prestegard JH: Measurement of one-bond amide N15-H-1 couplings. JMR, 1996, 112:245-252
• Ottiger M, Delaglio F, Bax A, Measurement of couplings using
IPAP JMR 1998,131: 373-378.
• Wang YX, Marquardt JL, Wingfield P, Stahl SJ, Lee-Huang S,
Torchia D, Bax A: Measurement of H-1-N-15, H-1-C-13 ', and
N-15-C-13 ' dipolar couplings. JACS, 1998, 120:7385-7386.
• Yang DW, Venters RA, Mueller GA, Choy WY, Kay LE:
TROSY-based HNCO pulse sequences. JBNMR 1999, 14:333343.
• Liu, Y. and J.H, Prestegard. Measurement of one and two bond
N-C couplings in large proteins by TROSY-based J-modulation
experiments. JMR 2009, 200:109-118.
• Delaglio F, Wu ZR, Bax A: Homonuclear proton couplings
from regular 2D COSY spectra. JMR 2001, 149:276-281.
Measurable Dipolar Couplings in a Dipeptide
Define an Order Frame
Z
O
C
φ
N
H
H
C
ψ
C
O
H
N
X
Coupled HSQC
Soft HNCA-E.Cosy
HNCO
Y
Soft HNCA – E.COSY
Weisemann, Ruterhans, Schwalbe, Schleucher Bermel,
Griesinger, J. Biomol. NMR, 4, 231-240, 1994
Soft HNCA E-COSY Spectra of 15NLabeled 13C Natural Abundance
Rubredoxin
Cα chemical shift, Cαi to Cαi-1 connectivity, 3J-HNHα
coupling, Cα-Hα, HNHα and Hαi-1HN dipolar coupling
Multiple Peptide Segments Oriented to
Superimpose Order Frames Yield Structures
Proof of principle: rubredoxin structure overlays X-ray structure to 1.6Å
Tian, Valafar, & Prestegard. (2001)J Am Chem Soc 123:11791-11796
More Recent 15N-1H Depositions use a J-modulation Experiment:
Also can be used for 15N-13C’, 15N-13Cα
Data shown are on a 70kDa protein
Liu, Y. and J.H, Prestegard. 2009. J Magn Reson. 200(1): 109-118.
Rdc = -0.792 Hz
•
•
•
•
Rdc = -1.294 Hz
Rdc = 0.572 Hz
Cross-peaks overlap HSQC peaks exactly
Time requirements are similar to TROSY/HSQC
Based on TROSY detection for application to larger proteins
Fit gives T2 estimate – used to eliminate data on loops
Analysis of Residual Dipolar Couplings
• Schwieters CD, Kuszewski JJ, Tjandra N, et al.
XPLOR-NIH, J. Magn. Res. 160 (1): 65-73 JAN 2003
• Meiler J, Blomberg N, Nilges M, Griesinger C, Residual dipolar
couplings as restraints in structure elucidation
JBNMR 2000, 16: 245-252.
• Rohl CA, Baker D: Backbone structure from residual dipolar
couplings using rosetta. JACS, 2002, 124:2723-2729.
• Delaglio F, Kontaxis G, Bax A: Structure from molecular
fragment replacement and dipolar couplings. JACS, 2000,
122:2142-2143.
• Valafar H, Prestegard J. 2004, J. Mag. Res., 167, 228-241
http://www.ccrc.uga.edu/web/CarbResource/Software/
• Dosset, Hus, Marion & Blackledge (2001), JBNMR, 20: 223231
Example of Validation and Refinement (MTH1743)
⎡ (∑ ( Dobs − Dcalc ) 2 )1 / 2 ⎤
Q=⎢
⎥
2 1/ 2
(
D
)
⎢⎣
⎥⎦
∑ obs
exp RDC vs calc RDC for 1jsb
Q-factor = 0.23
10
10
5
5
0
-15
-10
-5
0
-5
-10
-15
ex p RDC
5
calc RDC
calc RDC
exp RDC vs calc RDC for refined structure after sa
Q-factor = 0.33
10
0
-15
-10
-5
0
-5
-10
-15
ex p RDC
5
10
X-ray Structures fit RDCs Better than
NOE-Based NMR Structures
neSG
BeR31
CsR4
CtR107
GmR137
HR3646E**
MbR242E
PfR193A
SgR42
SoR77
bmrb
15702
15317
16097
15844
16250
16368
16385
15604
15456
pdb nmr
2k2e
2jr2
2kcu
2k5p
2khn
2kko
2kl6
2jz2
2juw
pdb xray alignment media #residuesnmr Q
xray Q
RMSD*
3cpk
phage
150
0.52
0.28
1.39
68
0.37
0.32
0.52
2ota
peg (and peg+ctab
3e0h
phage (and peg)
158
0.44
0.30
1.84
3cwi
peg
70
0.38
0.21
1.37
3fia
polyacrylamide gel
110
0.53
0.29
1.06
3gw2
peg
100
0.36
0.29
1.05
3idu
phage
114
0.36
0.30
0.86
3c4s
peg
58
0.42
0.23
0.58
2qti
polyacrylamide gel
72
0.26
0.21
0.91
* PSVS analysis listed structured regions (obtained via PROCHECK)
1st NMR model compared to X-Ray structure for all analysis
** It was difficult to compare the xray and nmr structures for this protein.
⎡ (∑ ( Dobs − Dcalc ) 2 )1 / 2 ⎤
Q=⎢
⎥
2 1/ 2
(∑ Dobs )
⎢⎣
⎥⎦
Structure Refinement Using RDCs
Write RDCs in principal alignment frame:
D = (Da/r3){(3cos2θ – 1)/r3 + (3/2)Rsin2θcos(2φ)}
Write error function in terms of Dmeas and Dcalc
ERDC = (Dmeas – Dcalc)2
Seek minimum in ERDC to refine structure –
Need to float alignment axes during search
Refinement with RDCs can Improve Quality
CtR107 with and without RDCs
Cyan, X-ray
Red, best refined with RDC
Gray, best refined without RDC
Refinement detail
Average RMSD
to X-ray
(best of 10)
RMSD of the
ensemble
Anneal, no RDC
4.4
4.2
Anneal, with RDC
3.4
2.7
Refine, no RDC
2.5(2.0)
1.4
Refine, with RDC
2.0(1.6)
1.4
Alignment carried out by superimposing backbone atoms
of residues 19 to 26, 30 to 39, 59 to 61, 69 to 71, 88 to 90,
97 to 102, 111 to 122, 132 to 134 and 149 to 152