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Supporting information for
Perspective: Revisiting the Field Dependence of TROSY Sensitivity
Koh Takeuchi1,2, Haribabu Arthanari 3,4, Gerhard Wagner4*
1
Molecular Profiling Research Center for Drug Discovery, National institute of Advanced Industrial Science and
Technology, Tokyo 135-0064, Japan
2
PRESTO, Japan Science and Technology Agency, Tokyo 135-0064, Japan
3
Department of Cancer Biology, Dana Farber Cancer Institute, Boston, MA02115
4
Department of Biological Chemistry and Molecular Pharmacology, Harvard Medical School, Boston, MA 02115
*Email requests to: [email protected]
phone 617-432-3213
fax 617-432-4383
Calculation of transverse relaxation rates
The transverse relaxations of decoupled spin I (𝑅2𝐼 ) were calculated based on standard expressions (Peng and Wagner
1992) as follows,
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𝑅2𝐼 = ∑𝑛𝑗 𝑝𝐼𝑆
[(4𝐽(0) + 3(𝐽(𝜔𝐼 ) + 𝐽 (|𝜔𝐼 − 𝜔𝑆𝑗 |) + 6𝐽(𝜔𝐼 ) + 6𝐽 (𝜔𝐼 + 𝜔𝑆𝑗 ) ] + 𝛿𝐼2 [(4𝐽(0) + 3(𝐽(𝜔𝐼 )] (1)
𝑗
𝜇0 𝛾𝐼 𝛾𝑆𝑗 ℏ
) 3
2√2 𝑟𝐼𝑆
𝑝𝐼𝑆𝑗 = −(
𝜇0
)𝛾 𝐵 ∆𝜎𝐼
3√2 𝐼 0
𝛿𝐼 = −(
(2)
𝑗
(3)
∆𝜎𝐼 is the difference between the axial and the perpendicular principal components of the axially symmetric chemical
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shift tensors. Spectrum densities were estimated using equation 4
J(ω) = 2τc / (5 x (1+ (τc ω)2) (4)
where ω is substituted by the Larmor frequencies of the spins 1H and 15N, or sum or difference of those.
The TROSY (𝑅2𝐼𝑇 ) transverse relaxation of spin I were calculated as described in (Pervushin et al. 1997),
𝑅2𝐼𝑇 = 𝑅2𝐼 − |𝐶𝑝𝐼𝑆 𝛿𝐼 [4𝐽(0)]| (5)
C = (3 cos 2 Θ −1) (6)
where Θ is the angle between the tensor axes of the DD and CSA interaction. For calculation of transverse relaxation
rates, the dipole-dipole interactions with directly bonded nuclei as well as nuclei within defined distances and chemical
shift anisotropies were taken into consideration to mimic the typical proton density in a protein. For the estimation of
the dipole-dipole interactions for 1HN and
15
NH in a uniformly 2HC15N-labeled protein, the typical distances in an
α-helix region were used with distance cut-off criteria as follows: < 4.5 Å for 1H-1H and 1H-2H pairs and < 2.1 Å for
H-15N pairs. These are sequential 1HNi-1HNi+1 distance (2.8 Å), 1HNi-1H Ni+2 distance (4.2 Å), intra residue 1H Ni-2Hαi
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distance (2.2 Å), sequential 1HNi-2Hαi+1 distance (3.5 Å), 1HNi-2Hαi+2 distance (4.4 Å) , 1HNi-2Hαi+3 distance (3.4 Å),
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HNi-2Hαi+3 distance (4.2 Å), intra residue 1HNi-2Hβi distance (2.5 Å), and sequential 1HNi-2Hβi+1 distance (3.0 Å) for
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H-1H and 1H-2H pairs. Contributions from remote protons that are more than 4 residues away in the a.a. sequences are
not considered here. A single value for the CSA was included in the calculation for this estimate although this value
may vary for different residue, structural environments and likely to be asymmetric (15NH: -160ppm, 1HN: 16
ppm) (Yao et al. 2010), and Θ was set to 17°. For the estimation of the DD interactions for
13
Caro, alternate 13C-12C
labeling with 3-13C pyruvate is assumed (Milbradt et al. 2015) and the T2 of of the Phe  position was calculated. In the
alternate 13C-12C labeling with 3-13C pyruvate, 13C would be in the β and  positions for Phe, therefore, 13C-13C dipole
interactions between these positions were considered as well as the intra residual 13C-1H dipole interactions. These are
13
C-13Cβ (2.5 Å), 13C-1H (1.09 Å), 13C-1H (2.14 Å, 3.85 Å), 13C-1Hζ (3.38 Å), and 13C-1Hβ (2.56 Å, 3.24 Å). CSA
was also included in the calculation (13Caro: -184ppm), and Θ was set to 90°.
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Supplemental Figure 1. Effect of Rex on the field dependent signal height of 15N-detected (left) and 1H-detected (right)
amide resonances. The solid and broken lines are for signals without and with Rex contribution to the relaxation,
respectively. The Rex corresponds to 0.05 ppm and 0.01 ppm for 15N and 1H resonances, respectively. The 1D Signal
height of TROSY (red) and conventional decoupled non-TROSY (cyan) relative to the signal height of TROSY
resonances at 500 MHz. The signal height for the non-TROSY resonances are doubled. The perdeuterated protein with
rotational correlation time of 20 ns is assumed.
References:
Milbradt AG, Arthanari H, Takeuchi K, Boeszoermenyi A, Hagn F, Wagner G (2015) Increased resolution of aromatic cross peaks
using alternate 13C labeling and TROSY J Biomol NMR 62:291-301
Peng JW, Wagner G (1992) Mapping of spectral density functions using heteronuclear NMR relaxation measurements J Magn Res
98:308-332
Pervushin K, Riek R, Wider G, Wuthrich K (1997) Attenuated T2 relaxation by mutual cancellation of dipole-dipole coupling and
chemical shift anisotropy indicates an avenue to NMR structures of very large biological macromolecules in solution Proc
Natl Acad Sci U S A 94:12366-12371
Yao L, Grishaev A, Cornilescu G, Bax A (2010) Site-Specific Backbone Amide 15N Chemical Shift Anisotropy Tensors in a Small
Protein from Liquid Crystal and Cross-Correlated Relaxation Measurements Journal of the American Chemical Society
132:4295-4309
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