Quantifying the effects of long-range 13C-13C dipolar coupling on measured relaxation rates in RNA

Selective stable isotope labeling has transformed structural and dynamics analysis of RNA by NMR spectroscopy. These methods can remove 13C-13C dipolar couplings that complicate 13C relaxation analyses. While these phenomena are well documented for sites with adjacent 13C nuclei (e.g. ribose C1′), less is known about so-called isolated sites (e.g. adenosine C2). To investigate and quantify the effects of long-range (> 2 Å) 13C-13C dipolar interactions on RNA dynamics, we simulated adenosine C2 relaxation rates in uniformly [U-13C/15N]-ATP or selectively [2-13C]-ATP labeled RNAs. Our simulations predict non-negligible 13C-13C dipolar contributions from adenosine C4, C5, and C6 to C2 longitudinal (R1) relaxation rates in [U-13C/15N]-ATP labeled RNAs. Moreover, these contributions increase at higher magnetic fields and molecular weights to introduce discrepancies that exceed 50%. This will become increasingly important at GHz fields. Experimental R1 measurements in the 61 nucleotide human hepatitis B virus encapsidation signal ε RNA labeled with [U-13C/15N]-ATP or [2-13C]-ATP corroborate these simulations. Thus, in the absence of selectively labeled samples, long-range 13C-13C dipolar contributions must be explicitly taken into account when interpreting adenosine C2 R1 rates in terms of motional models for large RNAs. Supplementary Information The online version contains supplementary material available at 10.1007/s10858-021-00368-8.


Introduction
RNAs are important macromolecules that function in a wide range of cellular roles (Cech and Steitz 2014;Mortimer et al. 2014;Sharp 2009). Despite being composed of only four ribonucleotide building blocks, RNAs are capable of adopting complex three-dimensional structures that impart functionality (Dethoff et al. 2012;Ganser et al. 2019). Moreover, RNAs are dynamic and can sample numerous conformations on various time scales that might be important for function (Zhao et al. 2017;Marušič et al. 2019). Solution nuclear magnetic resonance (NMR) spectroscopy is a highresolution biophysical technique that is well suited to probe these dynamic RNA structures. Three commonly measured dynamics parameters are the longitudinal (R 1 ) and transverse (R 2 ) relaxation rates and the heteronuclear Overhauser effect (hNOE) (Marušič et al. 2019;Palmer 2004;Wagner 1993).
The R 1 rate measures the return of the longitudinal magnetization to thermal equilibrium whereas R 2 measures the decay of transverse magnetization, and the hNOE measures the change in heteronuclear spin magnetization in response to saturating proton spins (Yamazaki et al. 1994;Peng and Wagner 1992;Abragam 1961).
RNA motions directly influence these R 1 , R 2 , and hNOE relaxation parameters (Marušič et al. 2019;Palmer 2004;Wagner 1993;Yamazaki et al. 1994;Peng and Wagner 1992;Abragam 1961;Spiess 1978;Hansen and Al-Hashimi 2007;Nirmala and Wagner 1988;Palmer et al. 1991). Depending on the probed nuclei, dipolar interactions and chemical shielding anisotropy (CSA) mechanisms contribute predominantly to R 1 and R 2 relaxation, and dipolar interactions to the hNOE. These three relaxation measurements can be fit to extract motional variables such as overall correlation time ( C ) and the square of the generalized order parameter (S 2 ) that describe fast (ps-ns) dynamics in RNA within a Model Free formalism (Spiess 1978;Lipari and Szabo 1982) or combined Model Free and reduced spectral density mapping implemented in ROTDIF (Berlin et al. 2013). Therefore, accurate R 1 , R 2 , and hNOE measurements are crucial for 1 3 obtaining precise dynamics information and drawing valid conclusions about RNA molecular recognition events.
These dynamic RNA motions are most often measured by using 13 C (Boisbouvier et al. 1999;Dayie et al. 2002) and 15 N (Dayie et al. 2002;Akke et al. 1997) nuclei as indirect probes. However, imino and amino 15 N nuclei experience solvent exchange and are only visible in structured regions, making non-protonated 15 N (e.g. purine N7) and protonated 13 C (e.g. adenosine C2) nuclei attractive probes. The latter sites are present in both the nucleobase and ribose moieties and therefore provide more coverage of RNA structure. Still, large 13 C-13 C scalar and dipolar couplings in uniformly 13 C/ 15 N labeled RNA can complicate analyses of these sites (Yamazaki et al. 1994;Kay et al. 1989;Alvarado 2014;Johnson et al. 2006;Nam et al. 2020;. Indeed, the effect of dipolar couplings on RNA relaxation has been studied for sites with adjacent 13 C nuclei (e.g. ribose C1′). These investigations demonstrate that dipolar interactions from attached 13 C atom(s) lead to deviations from monoexponential decay and discrepancies in the extracted R 1 rate for ribose C1′ (Alvarado 2014;Nam et al. 2020;, C2′ and C4′ (Johnson et al. 2006), as well as for pyrimidine C6 (Nam et al. 2020;. However, much less is known about isolated sites such as purine C8 or adenosine C2. We recently showed that purine C8 may experience non-negligible dipolar contributions to R 1 relaxation from non-adjacent coupling partners (Nam et al. 2020). The extent to which adenosine H2-C2 approximates an isolated spin pair remains unclear.
To investigate and quantify the effects of long-range (> 2 Å) 13 C-13 C dipolar coupling on RNA dynamics, we simulated adenosine C2 relaxation rates in uniformly [U-13 C/ 15 N]-ATP or selectively [2-13 C]-ATP labeled RNAs. Our simulations predict non-negligible 13 C-13 C dipolar contributions from adenosine C4, C5, and C6 to C2 R 1 rates in [U-13 C/ 15 N]-ATP labeled RNAs that increase with higher magnetic fields and molecular weights. To empirically test our simulations, we measured adenosine C2 relaxation in the 61 nucleotide (nt) human hepatitis B virus encapsidation signal ε (HBV ε) RNA (Flodell et al. 2006;Lee 1997;Knaus and Nassal 1993;Hirsch et al. 1990) labeled with [U-13 C/ 15 N]-ATP or [2-13 C]-ATP. To this end, we used our recently synthesized [2-13 C, 7-15 N]-ATP (Olenginski and Dayie 2020) as a selective adenosine 13 C2 labeled probe. We demonstrate that the removal of long-range 13 C-13 C dipolar coupling partners reveals discrepancies in measured adenosine C2 R 1 values between uniformly and selectively labeled samples. Moreover, R 1 measurements at lower temperature (mimicking increased molecular weight) revealed exacerbated R 1,C2 discrepancies, which further corroborates our simulations and argues that selective 13 C2 labeled probes obviates the need to account for the significant contributions to meausured R 1,C2 that arise from neighboring 13 C atom(s) in RNAs with a > C 20 ns. Our [2-13 C, 7-15 N]-ATP (Olenginski and Dayie 2020) also showed better spectroscopic properties than [U-13 C/ 15 N]-ATP, providing and additional advantage to using selectively labeled samples to measure RNA dynamics.

Data analysis
NMR spectra were processed and analyzed using TopSpin 4.0, NMRFx Processor, and NMRViewJ (Norris et al. 2016;Johnson and Blevins 1994). R 1 and R 1ρ relaxation rates were determined by fitting peak intensities to a monoexponential decay. Uncertainties in R 1 rates were estimated by propagating the error in peak intensities from duplicated delay points (indicated by " × 2" above). R 2 rates were corrected for the off-resonance ω 1 using Eqs. 7 and 8. Uncertainties in R 1ρ rates were determined by the RELAXFIT (Fushman et al. 1997) Matlab program. The steady-state 13 C{ 1 H} hNOE was obtained using (1 + η) (Peng and Wagner 1992;Palmer et al. 1991;Clore et al. 1990a, b;Weaver et al. 1988). Uncertainties in 13 C{ 1 H} hNOE values were estimated by propagating the error in peak intensities in duplicated experiments.

Effects of long-range dipolar couplings on adenosine C2 relaxation
Before quantifying the effects of dipolar couplings on RNA dynamics, it is informative to consider the various relaxation contributions to our targeted nuclei. The 13 C R 1 and R 2 rates of adenosine C2 (R 1,C2 and R 2,C2 ) are given by wherein the auto R 1,C2 ( R C C z ) and R 2,C2 ( R C C x,y ) rates and cross-relaxation ( R C H C z → C z ) are functions of the underlying spectral density function (Palmer 2004;Peng and Wagner 1992;Abragam 1961): R ex is the chemical exchange contribution to R 2 , D C,i and C C are the dipolar coupling ( 0 C i ℏ/4πr 3 ) and CSA ( C Δ C ∕ √ 3 ) constants, respectively, where i is the gyromagnetic ratio of spin i (where i can be 1 H, 13 C, or 15 N), r is the distance between the two spins, 0 is the permeability of free space, ℏ is Plank's constant divided by 2p, and Here, σ x = σ 33 − σ 11 , σ y = σ 33 − σ 22 and σ 11 , σ 22 , and σ 33 are the principal components of the chemical shielding tensor (Ying et al. 2006;Fushman et al. 1998) and J( ) is the spectral density function assuming isotropic tumbling. The auto-and cross-relaxation rates combine to give the steady-state 13 C{ 1 H} hNOE (η) (Peng and Wagner 1992;Palmer et al. 1991;Clore et al. 1990a, b;Weaver et al. 1988) where I sat and I eq are signal intensities of the 13 C resonances when the 1 H resonances are saturated or not.
We do not observe differences in the simulated R 2,C2 rates or steady-state 13 C{ 1 H} hNOE values ( Supplementary Fig.  S2), in agreement with previous studies (Yamazaki et al. 1994;Hansen and Al-Hashimi 2007;Nam et al. 2020). However, our simulations do predict discrepancies in R 1,C2 rates (Fig. 1a) between uniformly and selectively labeled samples (R 1,C2(uniform) and R 1,C2(selective) , respectively), an observation similar to that recently reported for purine C8 sites (Nam et al. 2020). Specifically, dipolar interactions result in overestimated R 1,C2(uniform) rates that increase with higher magnetic fields and molecular weights (Fig. 1a), as predicted by Eq. 3 (Supplementary Fig. S1a). Moreover, the percent difference in R 1,C2 (defined as [100*(R 1,C2(uniform) − R 1,C2(selective) )/R 1,C2(uniform) ]) is predicted to be as large as 80% at 1.2 GHz and a C of 100 ns (Fig. 1b). While RNAs of this size are rarely probed by NMR, the simulated discrepancies are still significant for smaller RNAs. As highlighted by our simulations, 13 C-13 C dipolar interactions dominate the discrepancy whereas N1 and N3 have almost no effect. Moreover, the 13 C-13 C contributions scale with atomic distance from C2, with C4 (2.2 Å) having the greatest effect followed by C6 (2.3 Å) and then C5 (2.7 Å) (Figs. 1a, inset and c).

Adenosine C2 R 1 measurements in uniformly and selectively labeled RNA
Our newly synthesized [2-13 C, 7-15 N]-ATP (Olenginski and Dayie 2020) removes unwanted 13 C-13 C and 13 C-15 N dipolar interactions and was therefore used along with commercially available [U-13 C/ 15 N]-ATP to empirically test our simulations. To this end, we measured adenosine R 1,C2 rates for [U-13 C/ 15 N]-ATP or [2-13 C, 7-15 N]-ATP labeled HBV ε (Fig. 2) at 800 MHz and 25 °C using TROSY-detected pulse sequences (Hansen and Al-Hashimi 2007;Lakomek et al. 2013;Weigelt 1998;Pervushin et al. 1997). In agreement with our simulations (Fig. 1a), R 1,C2(uniform) was significantly higher than R 1,C2(selective) for 6 of the 8 HBV ε adenosine residues (Fig. 3a). Explanations for why A29 and A55, in particular, differ from the other residues requires detailed structural information which is currently lacking. Nevertheless, our simulated and experimental trends show good agreement on the whole. That is, the average percent difference in measured R 1,C2 rates was 4.7% (Fig. 3b) compared to the simulated 5.4% (Fig. 2b) for an RNA with a C of 11 ± 1 ns at 800 MHz (measured from R 2 /R 1 (Fushman et al. 1994;Thakur et al. 2010)) ( Supplementary Fig. S3). While this discrepancy is small and can likely be ignored, our simulations suggest that this is no longer true as RNAs increase in size.
To experimentally verify that the discrepancy in R 1,C2 increases at higher molecular weights, we repeated our R 1,C2 measurements in [U-13 C/ 15 N]-ATP or [2-13 C, 7-15 N]-ATP labeled HBV ε at 5 °C to simulate an RNA with a higher molecular weight (larger C ). To maximize signalto-noise and minimize experimental time, we reduced the sweep-width and time-domain points while increasing the number of scans. Therefore, only 4 of 8 adenosine C2-H2 resonances were resolved ( Supplementary Fig. S4). Nevertheless, R 1,C2(uniform) was again observed to be significantly higher than R 1,C2(selective) for all 4 resolved HBV ε adenosine residues (Fig. 3a). Moreover, the average percent difference in measured R 1,C2 at 5 °C was significantly higher than those measured at 25 °C (Fig. 3b), in agreement with our simulations (Fig. 1b). Specifically, the average percent difference in measured R 1,C2 rates was 25.5% (Fig. 3b), compared to the simulated 15.6% (Fig. 1b) for an RNA with a C of 21 ± 1 ns at 800 MHz (measured from R 2 /R 1 (Fushman et al. 1994;Thakur et al. 2010)) ( Supplementary  Fig. S3).
Taken together, while relatively isolated, adenosine C2 experiences long-range 13 C-13 C dipolar couplings that can neither be wholly ignored nor circumvented with selective pulses in [U-13 C/ 15 N]-ATP labeled samples. That is, these dipolar contributions must be explicitly taken into account Adenosine C2 R 1ρ relaxation and steady-state 13 C{ 1 H} hNOE measurements in uniformly and selectively labeled RNA As previously described, R 1 , R 2 , and hNOE measurements are a prerequisite to a robust analysis of RNA ps-ns dynamics (Marušič et al. 2019;Palmer 2004;Wagner 1993;Lipari and Szabo 1982). We have already quantified the discrepancies that exist in adenosine R 1,C2 measurements derived from [U-13 C/ 15 N]-ATP labeling. While we did not observe such differences in the simulated adenosine R 2,C2 rates or steady-state 13 C{ 1 H} hNOE values ( Supplementary Fig. S2), we sought to experimentally verify this for completeness. We therefore measured adenosine R 2,C2 rates and 13 C{ 1 H} hNOE values for [U-13 C/ 15 N]-ATP or [2-13 C, 7-15 N]-ATP labeled HBV ε (Fig. 2) at 800 MHz and 25 °C using TROSYdetected pulse sequences (Hansen and Al-Hashimi 2007;Lakomek et al. 2013;Weigelt 1998;Pervushin et al. 1997). Observed R 1ρ rates contain contribution from both R 1 and R 2 relaxation, which are accounted for according to the relations (Hansen and Al-Hashimi 2007;Lakomek et al. 2013;Akke and Palmer 1996;Davis et al. 1994) (7) R 1 = R 1 (cos 2 ) + R 2 (sin 2 ) Here, 1 is the strength of the spin-lock field and Ω is the offset from the spin-lock carrier frequency. We used an R 1ρ experiment (Hansen and Al-Hashimi 2007;Lakomek et al. 2013;Akke and Palmer 1996;Peng et al. 1991;Korzhnev et al. 2002) to extract R 2 rates in HBV ε. In agreement with our simulations, adenosine R 2,C2 rates and steady-state 13 C{ 1 H} hNOE values did not differ significantly between uniformly or selectively labeled samples ( Supplementary  Fig. S5). For straightforward analysis, we will interpret dynamics data from our [2-13 C, 7-15 N]-ATP labeled sample.
As such, adenosine R 1,C2 and R 2,C2 rates measured in helical regions of HBV ε were all close to the mean, except for residues A13 and A21 (Fig. 4). Specifically, residue A13 shows high R 1,C2 and low R 2,C2 rates suggestive of increased internal motions (Fig. 4). Residue A21, on the other hand, has a high R 2,C2 rate indicative of possible R ex contributions (Fig. 4). In addition to R 1 and R 2 rates, accurate measurements of steady-state 13 C{ 1 H} hNOE values can provide further information on RNA dynamics (Marušič et al. 2019;Palmer 2004;Wagner 1993;Lipari and Szabo 1982). Consistent with adenosine R 1,C2 and R 2,C2 rates, residue A13 shows the highest hNOE value suggestive of increased internal motions (Fig. 4). All other adenosine C2 nuclei have hNOE values close to the mean indicative of helical residues (Fig. 4). Taken together, our [2-13 C, 7-15 N]-ATP label simplified probing of adenosine C2 spin  (Fushman et al. 1994;Thakur et al. 2010)]. The average percent difference in measured R 1,C2 rates at 5 °C was 25.5%, compared to the simulated 15.6% difference for an RNA with a C of 21 ± 1 ns [measured from R 2 /R 1 ratio (Fushman et al. 1994;Thakur et al. 2010)]. Taken together, our simulations and experimental measurements suggest that the discrepancy between R 1,C2(uniform) and R 1,C2(selective) increases with higher molecular weights relaxation measurements in HBV ε without the need for selective pulses (Emsley and Bodenhausen 1992;Kupče et al. 1995;Geen and Freeman 1991) or explicit spectral density modeling with assumed models of motion (Hansen and Al-Hashimi 2007). As an added benefit, 1 H-13 C TROSY spectra collected on selectively labeled HBV ε showed better signal-to-noise and narrower 1 H linewidths compared to its [U-13 C/ 15 N]-ATP counterpart ( Supplementary Fig. S6).

Conclusion
We investigated and quantified the effect of long-range 13 C-13 C dipolar couplings on adenosine C2 relaxation in [U-13 C/ 15 N]-ATP and [2-13 C, 7-15 N]-ATP labeled RNAs. Selective 13 C-labeling of adenosine C2 removed unwanted dipolar interactions with C4, C5, and C6 found in [U-13 C/ 15 N]-ATP. Theoretical simulations and experimental measurements revealed non-negligible overestimates in adenosine R 1,C2 rates derived from [U-13 C/ 15 N]-ATP labeled samples that increase with higher magnetic fields and molecular weights. The agreement between our experimental and simulated R 1,C2 rates and discrepancies at 25 °C support the predictions from our simulations. Moreover, R 1,C2 measurements at 5 °C (increased molecular weight) revealed exacerbated R 1,C2 discrepancies, which further confirms our simulations and argues that selective 13 C2 labeled probes simplify R 1,C2 measurements in RNAs with a C > 20 ns. It is important to note that auto-relaxation due to the 13 C-13 C dipolar interaction does not lead to deviation from the expected monoexponential relaxation and can be explicitely taken into account by using the appropriate spectral density function (Hansen and Al-Hashimi 2007). Therefore, elimination of these unwanted 13 C-13 C dipolar contributions permits the use of simple spectral density modeling, offering advantages in data analysis. We also observed better signal-to-noise and narrower 1 H linewidths in 1 H-13 C TROSY spectra collected on selectively labeled samples compared to its uniformly labeled counterpart. To take advantage of these benefits, our atom-selectively labeled [2-13 C, 7-15 N]-ATP was also used to measure 13 C R 2 relaxation rates and steady-state 13 C{ 1 H} hNOE values in HBV ε. These spin relaxation measurements provide a starting point to a robust understanding of HBV ε dynamics and suggest that residue A13 has increased flexibility whereas A21 may have R ex contributions.

Conflict of interest The authors declare no competing interests.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/. Fig. 4 Experimental adenosine C2 relaxation measurements for [2-13 C, 7-15 N]-ATP labeled HBV ε at 800 MHz and 25 °C. Adenosine R 1,C2 and R 2,C2 (calculated from R 1ρ,C2 using Eqs. 6 and 7) rates and steady-state 13 C{ 1 H} hNOE measurements are shown. Error bars represent ± s.d. and the mean relaxation parameters are shown with dashed lines with a shaded box representing ± s.d. above and below the mean. Residue A13 shows high R 1,C2 and hNOE suggestive of increased internal motions whereas A21 has a high R 2,C2 rate indicative of possible R ex