BCMB/CHEM 8190

One can collect similar spectra but some tricks are required
13 C solution, sat’d glucose, 8 min 13 C CP-MAS, 30 mg cellulose, 9 min

z
θ
θ r
B
0
µ
1 r
µ
2 x φ y
E = ( µ
0
/4 π )(( µ
1
· µ
2
)/r 3 – 3( µ
1
· r )( µ
2
· r )/r 5 ) r = i r x
+ j r y
+ k r z
= i r sin θ cos φ + j r sin θ sin φ + k r cos θ

µ = ( γ h/2 π )( i I x
+ j I y
+ k I z
) = ( γ h/2 π )f( I z
, I
+,-
)
H
D
= ( µ
0
/4 π )(( µ
1
· µ
2
)/r 3 – 3( µ
1
· r )( µ
2
· r )/r 5 )
H
D
= ( µ
0
γ
1
γ
2 h 2 )/(16 π 3 r 3 )(A + B + C + D + E + F)
A,B,C .. Grouped by type of operator, 0,1,2 Quantum
A = - I z1
I z2
(3cos 2 θ - 1), B = (1/4)( I
+1
I
-2
+ I
-1
I
+2
) (3cos 2 θ - 1)
………..
E = -(3/4)( I
+1
I
+2
)sin 2 θ exp(-2i φ ), F = ……..

To First Order Only I z1
I z2
Term is Important
A doublet would result – much like scalar coupling but large: as much as -60,000 Hz for a 13 C1 H pair.
Splittings are angle dependent – ranging from
-60,000 to +30,000. In a solid all possibilities superimpose: The result is a powder pattern
Points at 90º on a sphere are most abundant
D

H = H
CSA
+ H
D
+ H
Q
...
All share the following property:
Solution: < 3 cos 2 θ '– 1 > = 0
Solids: (3 cos 2 θ ' – 1) ≠ 0
CSA powder pattern

Magic Angle Spinning
• All interactions can be written in terms of Y 2
0
( θ ) = (3cos 2 ( θ )–1)/2
• Y 2
0
( θ ) can be transformed to another frame using Wigner Rotation elements: Y 2
0
( θ ) = Σ
2 m=-2
D 2 m0
( θ ’’, φ ’’) Y 2 m
( θ ’, φ ’)
• D 2 m0
( θ ’’, φ ’’) = (4 π /5) Y 2 m
( θ ’’, φ ’’)
• With rapid averaging over φ ’’, all terms except Y 2
0
( θ ’’) go to zero
• Selecting θ ’’ = 54.7
° , all interactions, regardless of θ ’ value, are zero
• (3cos 2 ( θ )–1) = (3cos 2 ( θ ’)–1) <3cos 2 (54.7
° )–1> = 0 Z
θ ’’
θ ’
Dipolar couplings
CSA
Quadrupolar couplings
= 0
φ
’’
θ
X Y

θ
B o

What is this peak?
(10 minute spectra)
13 C

Spinning Sidebands are Frequently Seen
When rotation rate is not >> anisotropies
Resonance position is modulated by rotation
Sidebands at the spinning frequency are produced
There are tricks that remove these:
TOSS – Total Suppression of Spinning Sidebands
180º pulses during rotor cycle dephases sideband magnetization but preserves center band magnetization

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
B
0 q
15 N r
1 H
D=
C r 3
⟨
3cos
2
θ − 1
2
⟩ I
NZ
I
HZ
Brackets denote averaging – goes to zero without partial orientation

B
0
Inducing Order Using Liquid Crystalline Media

Isotropic
J
Aligned
J + D

Polyacrylamide Gels another alignment medium
Yizhou Liu, J. Prestegard (2010)
J. Biomol NMR , 47 : 249-258.

ρ x z
ρ z φ z
θ x y
.
.
.
3cos 2
2
1
[
.
.
.
cos
i cos
j
. . .
. . .
. . .
. . .
.
]
[
.
.
3cos
k cos
l
kl
]

S xx
S xy
..
S yx
S yy
..
.. .. ..
= A
S x’x’
S y’y’
S z’z’
A -1

Strategy for Protein Fold Determination
• Express 15 N labeled protein
• Identify secondary structure 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
15 N Labeling Only

Data Used in ACP Fold Determination
A. Dipolar couplings in α -helices
Helix 1
Amide Couplings
(N i
-H N i
)
I3
E4
E5
V7
K8
I10
I11
G12
E13
Q14
L15
Amide-Alpha Couplings
(H N i
– H
α i
)
R6
V7
K9
L15
(H N i
– H
α i±1
)
Amide/Amide Couplings
(H N i
- H N i+1
)
1.4
0.4
3.4
-1.0
0.8
2.0
-0.3
2.1
2.1
0.0
-1.9
3.0
-3.5
4.5
0.0
Couplings (Hz)
Helix 2
L37
D38
T39
V40
-2.6
1.6
-0.3
-2.6
L37
L42
V43
M44
L46
V43
N
-L42
α
M44
N
-A45
α
D38
T39
V40
0.4
0.0
3.5
2.0
-2.0
2.0
-2.0
2.0
2.0
2.0
Helix 3
Q66
A67
I69
D70
N73
G74
H75
8.2
7.7
6.8
6.1
7.4
5.5
7.7
Q66
A68
H75
N73
0.0
-8.5
-9.0
2.0

Orientation Maps for Three ACP Helices

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
N-15-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,
14:333-343.
• 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
φ
ψ
X Y
Coupled HSQC
Soft HNCA-E.Cosy
HNCO

Soft HNCA – E.COSY
Weisemann, Ruterhans, Schwalbe, Schleucher Bermel,
Griesinger, J. Biomol. NMR, 4, 231-240, 1994

Soft HNCA E-COSY Spectra of 15 N-Labeled
13 C Natural Abundance Rubredoxin
C α chemical shift, C α i
to C α i-1
connectivity, 3 J-H N H α coupling, C α -H α , H N H α and H α i-1
H N dipolar coupling

Multiple Peptide Segments Oriented to
Superimpose Order Frames Yield Structures
Simultaneous assignment and structure determination of rubredoxin. Overlays X-ray structure to 1.6Å. Tian, Valafar, & Prestegard, (2001) J Am Chem Soc
123 :11791-11796

More Recent 15 N1 H Depositions use a J-modulation Experiment:
Also can be used for 15 N13 C’, 15 N13 C α
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 T
2
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:
223-231

Example of Validation and Refinement (MTH1743)
Q=
[ ( ∑ (
(
D obs
∑ D
− D
2 obs
)
1 / 2 calc
)
2
)
1 / 2 ]

X-ray Structures fit RDCs Better than
NOE-Based NMR Structures neSG
BeR31
CsR4
CtR107
GmR137 15844 2k5p 3cwi
HR3646E** 16250 2khn 3fia
MbR242E 16368 2kko
PfR193A 16385 2kl6
3gw2
3idu peg polyacrylamide gel peg phage
SgR42
SoR77 bmrb pdb nmr pdb xray alignment media #residues nmr Q xray Q RMSD*
15702 2k2e 3cpk phage 150 0.52
0.28
1.39
15317 2jr2
16097 2kcu
2ota
3e0h peg (and peg+ctab) phage (and peg)
68
158
0.37
0.44
0.32
0.30
0.52
1.84
15604 2jz2
15456 2juw
3c4s
2qti peg polyacrylamide gel
70 0.38
0.21
1.37
110
100
114
58
72
0.53
0.36
0.36
0.42
0.26
0.29
0.29
0.30
0.23
0.21
1.06
1.05
0.86
0.58
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.
Q=
[ (
∑
( D obs
− D
(
∑ D 2 obs
)
1 / 2 calc
)
2
)
1 / 2 ]

Structure Refinement Using RDCs
Write RDCs in principal alignment frame:
D = (D a
/r 3 ){(3cos 2 θ – 1)/r 3 + (3/2)Rsin 2 θcos(2 φ )}
Write error function in terms of D meas
and D calc
E
RDC
= (D meas
– D calc
) 2
Seek minimum in E
RDC
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
Anneal, no RDC
Anneal, with RDC
Refine, no RDC
Refine, with RDC
Average RMSD to X-ray
(best of 10)
4.4
3.4
2.5(2.0)
2.0(1.6)
RMSD of the ensemble
4.2
2.7
1.4
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