Utility of ¹H NMR Chemical Shifts in Determining RNA Structure and Dynamics

Abstract

The development of methods for predicting NMR chemical shifts with high accuracy and speed is increasingly allowing use of these abundant, readily accessible measurements in determining the structure and dynamics of proteins. For nucleic acids, however, despite the availability of semi-empirical methods for predicting ¹H chemical shifts, their use in determining the structure and dynamics has not yet been examined. Here, we show that ¹H chemical shifts offer powerful restraints for RNA structure determination, allowing discrimination of native structure from non-native states to within 2–4 Å, and <3 Å when ignoring highly flexible residues. Theoretical simulations shows that while ¹H chemical shifts can provide valuable information for constructing RNA dynamic ensembles, large uncertainties in the chemical shift predictions and inherent degeneracies lead to higher uncertainties as compared to residual dipolar couplings.

There has been a long-standing effort directed towards extracting the rich structural and dynamic information contained within NMR isotropic chemical shifts^1–6. Recent advances in semi-empirical methods for predicting chemical shifts based on protein structure with high accuracy and speed are allowing protein structure determination with chemical shifts as the sole input experimental restraint^7–10. Isotropic chemical shifts are also time-averaged over all motions occurring at timescales faster than milliseconds and therefore provide a sensitive probe of dynamics occurring over a wide range of timescales^11,12. They have successfully been used to predict protein S² NMR order parameters^13,14, in constructing dynamic ensembles of proteins¹⁵ including intrinsically disordered proteins^16–19, and in evaluating molecular dynamics (MD) simulations of proteins^20–22.

Chemical shifts have long been recognized to be sensitive reporters of nucleic acid structure, but are seldom used in structure determination or dynamics characterization²³. This is despite the availability of semi-empirical methods for predicting ¹H chemical shifts based on nucleic acid structure with high speed and accuracy. In particular, the program SHIFTS²⁴ developed by Case and co-workers, and NUCHEMICS²⁵ developed by Wijmenga and co-workers, have been shown to predict sugar (H1’, H2’, H3’, H4’, H5’ and H5’’) and nucleobase (H2, H5, H6 and H8) ¹H chemical shifts for a panel of diverse nucleic acid structures with an overall root-mean-square deviation (RMSD) ranging between 0.16–0.28 ppm. These predictions compare favorably with protein ¹H chemical shift predictions (RMSD ranging between 0.15–0.6 ppm)^26–28 and suggest that ¹H chemical shifts may be used to define the structure and dynamic properties of nucleic acids in a manner analogous to what has been done with proteins.

The use of chemical shift as new abundant source of structure and dynamic information is arguably more important for nucleic acids as compared to proteins. NMR structure determination of nucleic acids traditionally suffers from a shortage in accessible inter-proton NOE-derived distance restraints that can be applied towards structure characterization. This problem is compounded by a high degree of flexibility, particularly in RNA, which can complicate the interpretation of NOE-derived distances. Here, we examine the utility of ¹H chemical shifts in determining the structure and dynamic ensembles of RNA. Our results suggest that ¹H chemical shifts can immediately be used in RNA structure validation and in evaluating the quality of RNA dynamic ensembles. However, our results suggest that additional improvements in chemical shift predictions are required in order to allow their use as primary data in generating ensembles.

METHODS AND MATERIALS

Predicting RNA ¹H Chemical Shifts

We used a panel of 18 RNA structures (1IDV, 1JU7, 1L1W, 1N8X, 1NC0, 1OW9, 1XHP, 1Z2J, 1ZC5, 2FDT, 2JTP, 2JYM, 2KOC, 2KYD, 2L1V, 2L3E, 2L5Z and 2QH2) to evaluate ¹H chemical shift predictions using SHIFTS and NUCHEMICS. This panel represents RNA structures that have been determined by NMR after SHIFTS and NUCHEMICS (2002–2011) were developed and parameterized and for which ¹H chemical shift assignments were also available in the Biological Magnetic Resonance Bank (BMRB)²⁹ (http://www.bmrb.wisc.edu/). Four additional structures (2QH3, 2QH4, 1YMO, 2JWV) were not included due to undocumented or incomplete chemical shift referencing. However, including these structures had little to no impact on the results presented here.

Molecular dynamics simulations

MD simulations of an RNA duplex (PBID:2KYD)³⁰, UUCG tetra-loop (PBID:2KOC)³¹, asymmetrical internal loop (PDBID:2L3E)³² and pre-quenosine-1 (preQ₁) riboswitch (PDBID:2L1V)^33,34 were performed at 300 and 500 K using GROMACS 4.5.1³⁵ and the AMER94³⁶ nucleic acid forcefield. Structures were subjected to 100 steps of steepest descent minimization and subsequently solvated with TIP3 water³⁷ in an triclinic box and charge neutralized using sodium counterions. Harmonic restraints with a force constant of 1000 kJ mol⁻¹ nm⁻² were placed on the heavy atoms and simulated at 300 K for 1.4 ns. The harmonic restraints were then gradually released over 200 ps. Starting from the equilibrated coordinates, two 4 ns trajectories were generated at 300 and 500 K, respectively. Coordinates were saved every 2 ps.

Replica-exchange molecular dynamics (REMD) simulations³⁸ were used to generate a broad conformational pool for the HIV-1 TAR apical loop from which sets of non-overlapping reference ensembles could be constructed (see below). Initial coordinates were obtained using Rosetta FARNA³⁹, a de novo structure determination program for nucleic acids. Starting from the primary sequence, UAUCGAGCCUGGGAGCUCGAUA, 1000 candidate structures were generated with base pairing restraints between residues U1 and A22, A2 and U21, U3 and A20, C4 and G19, G5 and C18, A6 and U17, G7 and C16, and C8 and G15. The conformation with the lowest energy was used as the initial coordinates for the REMD simulations. The initial structure was subjected to 100 steps of steepest descent minimization and then solvated with TIP3 water³⁷ in an octahedron box and charge neutralized using sodium counterions. Harmonic restraints with a force constant of 1000 kJ mol⁻¹ nm⁻² were placed on the heavy atoms and simulated at 300 K for 1.4 ns. The harmonic restraints were then gradually released over 200 ps. Starting from the equilibrated coordinates at 300 K, 15 additional apical loop replicas were prepared by slowing heating the system to 303, 306, 309, 312, 315, 319, 322, 325, 329, 332, 335, 339, 342, 346 and 350 K. REMD simulations were then initiated from these 16 replicas. Exchanges were attempted every 2 ps and coordinates were saved every 2 ps. Production trajectories 90 ns in length were generated. The 45,000 conformations were used as the representative conformational pool for the TAR apical loop.

Weighted chemical shift RMSD

To investigate the impact of the accuracy of chemical shifts predictions on the ability of ¹H chemical shifts to resolve the difference between related RNA conformations, we defined a weighted chemical shift RMSD (CS^RMSD) that takes into account the correlation between measured and predicted chemical shifts calculated from the NMR structure. The weighted CS^RMSD is calculated using:

$$\frac{1}{L_{CS}}{\sum }_{i=1}^{L_{CS}}{\sum }_j^N{R}_j^2{({\delta }_{\mathit{\text{meas}}}-{\delta }_{\mathit{\text{pred}}})}^2$$ (1)

where $R_j^2$ is the square of the Pearson correlation coefficient for a given proton type j and calculated from the average NMR structure. Using this equation, proton types that exhibit higher correlations between measured and predicted chemical shifts in the average NMR structure contribute more to the CS^RMSD and vice versa.

Selection Algorithm for Generating Ensembles

Ensembles were constructed using chemical shifts, residual dipolar coupling (RDC) and chemical shift+RDC data using the sample and select (SAS) approach as described previously^40,41. The ensembles were selected by minimizing, using Monte Carlo procedures (see below), the cost function,

$${\chi }^2=K_{CS}{\chi }_{CS}^2+K_{RDC}{\chi }_{RDC}^2$$ (2)

where

$${\chi }_{CS}^2=\frac{1}{L_{CS}}\sum _{i=1}^{L_{CS}}{({\delta }_i^{\mathit{\text{pred}}}-{\delta }_i^{\mathit{\text{meas}}})}^2$$

and

$${\chi }_{CS}^2=\frac{1}{L_{RDC}}\sum _{k=1}^{L_{RDC}}{(D_k^{\mathit{\text{pred}}}-D_k^{\mathit{\text{meas}}})}^2$$

Here, χ² is the total cost function to be minimized; χ²_CS and χ²_RDC are the chemical shift and RDC components of χ², respectively; K_CS and K_RDC are coefficients that determine the contribution of each component to χ²; δ_i^pred and δ_i^meas are the predicted and measured chemical shifts for the i^th proton averaged over the N structures in an ensemble (see below), while D_k^pred and D_k^meas are the predicted and measured RDCs averaged over the N members of the ensemble, with k an index that runs over the bond vectors; L_CS and L_RDC are the total number of chemical shifts and RDCs, respectively. For selections using chemical shifts only, K_CS=1 and K_RDC=0. For selections using RDCs only, K_CS=0 and K_RDC=1. For selections carried out using a combination of chemical shifts and RDCs, K_CS was varied until χ²_CS and χ²_RDC were near specified thresholds (see below) while K_RDC=1. Each selection cycle was initiated from N randomly selected conformers. A Monte Carlo (MC) simulated annealing scheme was then used to minimize the cost function χ² in Eq. (2) over the set of N-member ensembles. This is done by selecting at random one of the N conformers in the ensemble, suggesting a replacement for it from the pool of all generated conformers, and accepting or rejecting based on the regular Metropolis MC probability⁴². Simulations were initiated at a high “temperature” (a parametric, effective temperature), where the MC acceptance probability was high (0.99), and slowly decreased until the MC acceptance probability reached 10⁻⁵. At a given effective temperature, 10⁵ MC steps were carried out. The effective temperature was then decreased according to the exponential schedule T_n+1 =0.92 T_n.

The next two paragraphs describe procedures to generate two types of ensembles central to our study: the dynamical ensemble and the reference ensemble. The “dynamical ensemble” of structures is a set of structures that was selected using available chemical shift and/or RDC data. The “reference ensemble” addresses the problem of checking that the SAS-generated structures in the dynamical ensemble are drawn from the same distribution as that from which the chemical shift data was measured.

Generating TAR apical loop dynamical ensembles

Five ensembles were constructed with N=1, 2, 4, 6 and 8 members. At each N value, a number of M independent selection cycles were carried out with the simulated annealing scheme described above, initiated each of the M times with N random structures. Subsequently, all the N*M conformers were combined to form a super—ensemble, the “dynamical” ensemble. For N = 2, 4, 6 and 8 members, M = 80, 40, 26 and 20 selection cycles were carried out, respectively, so as to ensure that the total number of conformers selected were approximately equal. For N=1, the algorithm selects each of the M times, a unique structure that minimizes the cost function.

Generating TAR apical loop reference ensembles

The reference ensemble approach is used to test the ability of our chemical shift based selection algorithm to generate the dynamical ensembles above. This is important because, in the absence of single-molecule data, experimentally it is difficult to gauge the distribution of variables from bulk that typically report averages only. In this approach a known ensemble is computationally constructed and then synthetic experimental data back-calculated from the ensemble. The ‘experimental’ data is then used as an input to construct dynamical ensembles. The dynamical ensembles are then compared with the reference ensemble to assess their similarity. To generate the reference ensembles a random reference conformer is selected from the conformational pool and then a set of conformers that are within a given RMSD cutoff are randomly selected and pooled together in the reference ensemble with the reference structure at its center. For the TAR apical loop, we generated three sets of reference ensembles. The three sets of ensembles differ in the RMSD cutoff used to generate them. Specifically, ensembles with RMSD cutoff of 2, 3 and 4 Å were generated. At each cutoff value, 7 independent reference ensembles were generated from 7 independent reference structures. Thus, in total, 21 reference ensembles were generated for the TAR apical loop and each ensemble consisted of 100 conformers. To generate synthetic ‘experimental’ datasets, ¹H chemical shifts were then calculated by averaging over each of the 21 reference ensembles using SHIFTS. To simulate the presence of errors in the dataset when carrying out chemical shift based selections, ¹H chemical shifts were calculated for pool conformers using NUCHEMICS; for the set of 18 benchmark RNAs studied here the RMSD between SHIFTS and NUCHEMICS chemical shifts ~ 0.24 ppm, which is comparable to the uncertainty in NUCHEMICS predictions (~0.30 ppm; see below). Using SHIFTS chemical shifts to generate the reference datasets and then NUCHEMICS chemical shifts to select ensembles therefore effectively simulates the presence ~ 0.24 ppm error in predictions. This approach to simulate errors in numerical data is similar to that used by Vendruscolo and coworkers in their study validating the use of chemical shifts to characterize the dynamical ensemble of the protein RNase A¹⁵.

Comparing Ensembles

To examine how well the generated dynamical ensembles reproduce the target, i.e., the reference ensembles, we employed the S-matrix method⁴³. In this approach one directly compares the distributions of the two ensembles. Specifically, we defined the elements of matrix S = {s_ij} as a distribution overlap measure by

$$s_{ij}=|{\rho }_r^{ij}-{\rho }_d^{ij}|,$$

where ${\rho }_r^{ij}$ and ${\rho }_d^{ij}$ are the normalized distribution of the inter-atomic distance between atoms i and j in the reference and dynamical ensemble, respectively. s_ij ranges between 0 and 2 and is 0 if and only if ${\rho }_r^{ij}={\rho }_d^{ij}$. We constructed S-matrices using the C1’ atoms and utilized a bin-size of 0.5 Å to discretize ρ^ij. Ensembles were compared on the basis of the average s_ij = 〈s_ij〉_A.

RESULTS AND DISCUSSION

Accuracy of ¹H RNA chemical shift predictions

We first examined the accuracy with which RNA ¹H chemical shifts can be predicted using SHIFTS and NUCHEMICS based on an RNA structure. We note that, to our knowledge, SHIFTS ¹H chemical shift predictions have never been evaluated for RNA. For these benchmark studies, we used a panel of 18 RNA structures determined by NMR for which ¹H chemical shift assignments (H1’, H2, H5, H6 and H8) are available at the Biological Magnetic Resonance Bank (http://www.bmrb.wisc.edu/). This data set represents RNAs for which ¹H chemical shifts and NMR structures were deposited in the BMRB and PDB respectively following the introduction of SHIFTS and NUCHEMICS. Thus, they were not used in the development of SHIFTS and NUCHEMICS. In all cases, the ¹H chemical shifts were not used as restraints in RNA structure determination. Four additional data sets were excluded due to undocumented or incomplete chemical shift referencing (note however that including those data sets had little impact on the overall results but generally led to a deterioration in the chemical shift predictions). RNAs with modified bases were excluded because they cannot be handled by either SHIFTS or NUCHEMICS.

We used SHIFTS and NUCHEMICS to compute ¹H chemical shifts based on the NMR structure for our panel of 18 RNA structures. These structures are mainly stem-loop RNAs containing a diverse set of apical loops, ranging from four to twelve bases in size, and internal bulges of varying sequence and type. Most structures contain either single or multiple non-canonical base-pairs, and the set contains one pseudoknot riboswitch structure.

The ¹H chemical shifts were computed for every conformer in the NMR bundle. We then computed the root-mean-square-difference (RMSD) between the measured and predicted chemical shifts (CS^RMSD) for each conformer. Shown in Figure 1 are the lowest CS^RMSD values obtained over the bundle of NMR conformers for each RNA structure examined. The overall SHIFT and NUCHEMICS CS^RMSD ranged between 0.26–0.54 ppm and 0.22–0.64 ppm with mean values of 0.35 and 0.34 ppm, respectively (Fig. 1). Similar CS^RMSD were observed when examining the agreement for individual proton types, and ranged between 0.32–0.37 ppm and 0.29–0.41 ppm with mean values of 0.32 and 0.29 ppm, respectively (Fig. S1 and Table S1). The overall and individual CS^RMSD compare well with the agreement originally reported for SHIFTS (0.28 ppm)²⁴. For NUCHEMICS, both the overall and individual CS^RMSD reported here are larger than those reported originally (0.16 ppm)²⁵. This is mostly likely due to the fact that the reported CS^RMSD was calculated from the same dataset used to fit the chemical shift prediction model. The Pearson correlation coefficient for individual proton types ranged between 0.47 and 0.76 and 0.61–0.80, respectively, with notably weaker correlations for H1’ (Fig. S1 and Table S1). These R values are similar to those reported originally for SHIFTS²⁴ (no R values for individual protons were not reported for NUCHEMICS²⁵).

Figure 1.

Measured vs. predicted chemical shift in RNA database. Root mean square difference (CS^RMSD) between experimental and (A) NUCHEMICS and (B) SHIFTS predicted chemical shifts prior to (red) and post (blue) minimization of input structure. In cases where multiple conformers exist we report the results for the structure that gives the lowest CS^RMSD after minimization.

Despite the small magnitude of the CS^RMSD observed for individual proton types, on average they span ~ 18 % of the total chemical shift range for the H1’, H2, H5, H6 and H8 protons²⁵ (Table S1). Note that this uncertainty not only include intrinsic errors in chemical shift predications, it also includes any errors in the NMR structures, and uncertainty due to internal motional averaging, which is ignored in our analysis. While the three structures (PDBID: 2KOC, 2FDT, 1XHP) that yield the best agreement using NUCHEMICS (CS^RMSD = 0.19, 0.19 and 0.21 ppm respectively) also have the largest numbers of RDCs constraints per residue (~2.2 as compared to ~0.91 across all structures), a similar trend is not observed for SHIFTS. However, the overall CS^RMSD did decrease from 0.35 to 0.32 ppm and from 0.34 to 0.27 ppm for SHIFTS and NUCHEMICS respectively when subjecting the NMR structures to energy minimization prior to chemical shift prediction using the Generalized Born Surface Area (GBSA) implicit solvent model⁴⁰. This improvement is observed across all RNA structures and suggests that some uncertainty in the NMR structure does contribute to the observed CS^RMSD.

The agreement between measured and predicted ¹H chemical shifts is likely also affected by motional averaging, which is not accounted for during the calculation of ¹H chemical shifts. For example, for pseudoknot preQ RNA, the poor CS^RMSD value (0.64 ppm) improves when using the X-ray structure (0.36/0.38 pm when using SHIFTS/NUCHEMICS respectively) or when excluding highly flexible residues (0.32 ppm when residues with a root-mean-square-fluctuation (RMSF) > 2.0 Å are excluded). However, we did not observe improved agreement when averaging the predicted CS data over the entire NMR bundle of structures (CS^RMSD = 0.37 ppm and 0.35 ppm for SHIFTS and NUCHEMICS respectively).

Resolving power of ¹H chemical shifts

Next, we examined how well ¹H chemical shifts can be used to resolve differences between competing RNA conformations. In particular, we attempted to access whether predicted ¹H chemical shifts, despite the demonstrated limitations of the chemical shifts predictors (see above), possessed sufficient resolving power to distinguish native-like from non-native RNA structure. For these studies, we used experimental ¹H chemical shifts for four RNAs in our panel that contain representative RNA motifs and whose structure was determined with the use of RDCs. These include (i) a 32-nt RNA duplex structure (“duplex”) containing a canonical A-form helix determined with a large number of RDC and residual chemical shift anisotropy (RCSA) data³⁰, (ii) a 14-nt hairpin containing a UUCG tetraloop (“tetraloop”) for which a high resolution NMR structure has recently been reported based on an unprecedented amount of NMR input experimental data: nuclear Overhauser effect (NOE) derived-distances, torsion-angle dependent homonuclear and heteronuclear scalar coupling constants, cross-correlated relaxation rates and RDCs³¹, (iii) a 35-nt RNA containing an asymmetrical internal loop and flanked by two helices (“internal loop”) and determined using NOE derived-distances and RDCs, and (iv) a 36-nt preQ₁ riboswitch RNA structure determined with the aid of RDCs that contains a pseudoknot motif (“pseudoknot”)^33,34. These structures fit the ¹H chemical shifts with variable agreement (the best CS^RMSD = 0.30/0.28, 0.28/0.21, 0.33/0.31 and 0.64/0.56 ppm for duplex, tetraloop, internal loop and pseudoknot). The four RNAs have a similar density of ¹H experimental chemical shifts (~2.8, 2.6, 2.6 and 2.8 chemical shifts per residue for duplex, 14-mer, internal loop and pseudoknot respectively).

We examined how well the agreement between the measured and predicted ¹H chemical shifts can be used to distinguish between related RNA conformations. For each of the four RNA structures, we generated a broad distribution of 8,000 conformations spanning native and denatured conformations by carrying out high temperature MD simulations (see Methods). This pool of conformations superimposes with the native structure with an average heavy atom RMSD of 6.0 ± 4.2, 3.5 ± 2.6, 7.7 ± 4.6 and 5.6 ± 3.0 Å for the duplex, tetraloop, bugle-loop and psuedoknot, respectively. ¹H chemical shifts were then calculated for each conformer within each pool using SHIFTS and NUCHEMICS. For each conformer the CS^RMSD value was then computed as the average of the CS^RMSD for each proton type and then compared to the heavy atom root-mean-square deviation between the conformer and the native, i.e. average, NMR conformation (structure^RMSD).

The value of CS^RMSD generally decreases with decreasing structure^RMSD particularly for structure^RMSD > 4 Å (Fig. 2A). These data suggest that the CS data can resolve RNA structures to within 4 Å. The continued decrease of CS^RMSD for structure^RMSD < 4 Å for UUCG suggests an even stronger structure resolving power. This is likely due to the compact nature and well-known high stability of the UUCG structure³¹ in which fluctuations away from the native structure tend to involve coordinated movements of several bases that can lead to large changes in ring current effects and therefore the predicted chemical shifts. By contrast, motions in duplex, internal loop and pseudoknot may preserve aspects of stacking interactions and therefore affect the predicted chemical shifts to a lesser extent.

Figure 2.

Resolving structure using ¹H chemical shifts. (A) Correlation between SHIFTS (red) and NUCHEMICS (black) CS^RMSD and structure^RMSD for the A-form duplex, UUCG tetraloop, hTR internal loop, and pseudoknot. CS^RMSD and structure^RMSD are calculated over conformational pool consisting of native-like and unfolded conformers (see text). Plot where made by binning data along structure^RMSD. Bin widths were 0.50 Å. Averages and error were calculated over data in each bin. (B) Correlation plots between measured and predicted SHIFTS and NUCHEMICS chemical shifts for the A-form duplex, UUCG tetraloop, internal loop and pseudoknot. In each case, the chemical shifts shown are those calculated from conformer with lowest CS^RMSD, which is indicated on each plot. (C) Structural overlay of the average NMR structure with conformers with the lowest SHIFT and NUCHEMICS unweighted (left) and weighted (right) CS^RMSD. The NMR, SHIFTS, and NUCHEMICS structures are shown in blue, red and black, respectively. The structure^RMSD between the structures is indicated below each.

Further analysis suggests that ¹H chemical shifts can resolve RNA structure to < 4 Å resolution. Out of the broad conformational pool that was generated for our four target RNAs, the conformation that best satisfies the measured ¹H chemical shifts according to SHIFTS/NUCHEMICS (i.e. conformation that yields the lowest CS^RMSD) superimposes with the native structures with structure^RMSD of 2.3/1.9, 1.4/1.4, 3.3/3.7 and 2.9/3.7 Å for duplex, tetraloop, internal loop and psuedoknot, respectively (Fig. 2B and C). Although less agreement is observed for internal loop and pseudoknot, the structure^RMSD improves significantly when excluding highly flexible residues (SHIFTS/NUCHEMICS structure^RMSD reduces to 2.9/3.0 Å and 2.3/2.6 Å, respectively). Similar results were obtained when using a weighted CS^RMSD in selecting conformations which weighs more heavily proton types data that exhibits stronger correlations between measured and predicted chemical shifts (Fig. 2C). Therefore, even when accounting for the inherent error in the chemical shifts predictions, we were able to resolve the RNA structure to 2–4 Å and this improves to <3 Å when neglecting highly flexible residues. Taken together, our results strongly suggest that ¹H chemical shifts can already be implemented as powerful restraints in RNA structure determination. This is despite the demonstrated limitations of the empirical methods employed by SHIFTS and NUCHEMICS to predict chemical shifts.

Use of ¹H chemical shifts in constructing RNA dynamical ensembles

In solution, chemical shifts are time-averaged over all conformations that are sampled at timescales faster than milliseconds. Studies on protein systems have established the ability to extract this dynamics information from measured chemical shift data. We therefore examined whether ¹H chemical shifts can facilitate the determination of dynamic ensembles (see Methods) of RNA using the SAS approach⁴⁰, which we previously used to construct ensembles of RNA with the use of RDCs only⁴¹. Here, upon increasing N, we seek to find those dynamic ensembles that satisfy the time-averaged ¹H chemical shifts with the minimum value of N. This is because, while increasing N improves the minimization of the cost function, therefore seemingly increasing the accuracy, we do not wish to go beyond the inherent finite accuracy of chemical shift predictors. This therefore gives us the smallest N that produces accuracy within the threshold of 0.24 ppm (see below). In this approach, N conformers are randomly selected from a pool typically generated using MD simulations, and the agreement between measured and predicted ¹H chemical shift data is computed. Next, one conformer is randomly replaced with another conformer from the pool, and the agreement with measured ¹H chemical shift data is re-examined and the newly selected conformer is either accepted or rejected based on the Metropolis criteria. Using such a MC based approach, several iterations are carried out until convergence is reached, defined as achieving agreement between measured and calculated data to within the specified error (see below).

We examined the utility of ¹H chemical shifts in constructing RNA dynamic ensembles using simulated chemical shift and a known target reference ensemble. We used replica-exchange molecular dynamics (REMD) simulations³⁸ to generate a broad conformation pool for the TAR apical loop. The TAR apical loop has previously been shown to undergo complex motions at multiple timescales and therefore provides a good model system for testing this approach⁴⁴. We then generated 21 reference ensembles that feature different levels of dynamics by randomly selecting a reference conformer from the 45,000 membered pool and then randomly selecting 100 conformers that are within 2, 3 and 4 Å of the reference conformer. In so doing we generated a total of 21 reference ensembles (see Methods). For each reference ensemble, ‘experimental’ ensemble-averaged H1’, H2, H5, H6 and H8 chemical shifts were computed using SHIFTS. Selections on the other hand were carried out using NUCHEMICS predicted shifts. This corresponds to ~0.24 ppm prediction error, as judged based on comparison of the average CS^RMSD between SHIFTS and NUCHEMICS for the 18 benchmark RNAs studied herein (see Methods). One bond C-H RDCs were also computed assuming a fixed alignment tensor determined experimentally in Pf-1 phage. The RDCs were noise corrupted by adding Gaussian white noise with standard deviation of 2.0 Hz corresponding to the uncertainty in RDC measurements in elongated RNA⁴⁵. In order to minimize overlap between reference ensembles, we skewed the conformational pool by replicating underrepresented conformers prior to the selection of dynamical ensembles.

In all cases, convergence was achieved for the chemical shift based selections at N=2 (CS^RMSD = 0.13, 0.11 and 0.10 ppm for the 2, 3 and 4 Å reference ensembles; Table 1). We found that increasing the value of N for chemical shift selections did not lead to significant improvements in the chemical shift predictions (Table 1). By comparison, N~8 was required to achieve convergence for RDC and chemical shift+RDC selections; the RDC^RMSD for the 2, 3 and 4 Å ensemble was 1.71, 1.72 and 1.72, and 1.73, 1.73 and 1.66 Hz, respectively. We next investigated whether the chemical shift ensembles were able to recapitulate the reference ensembles RDCs. For the N=2 ensemble the RDC^RMSD = 15.8, 14.1, and 14.1 Hz for the 2, 3 and 4 Å ensembles, respectively, and increasing N did not result in any significant improvement in RDC agreement (Table 1). The chemical shift ensembles therefore were unable to satisfy the RDCs to within the 2.0 Hz error thresholds; a similar trend was observed when back-predicting RDCs from ensemble constructed using experimental chemical shift (data not show). In contrast, the RDC ensembles predicted the chemical shifts to within the 0.24 ppm threshold (CS^RMSD = 0.25, 0.24 and 0.23 for the 2, 3 and 4 Å ensembles, respectively), suggesting that though chemical shifts based dynamical ensembles may not themselves attain the required accuracy, chemical shifts maybe used to validate or invalidate dynamical ensembles generated using other input structural data (e.g. RDCs).

Table 1.

Back-predicting chemical shifts and RDCs from chemical shift based dynamical ensembles. Shown are the RMSD and Pearson correlation coefficient (R) between chemical shifts calculated from the reference ensembles and those calculated from the 2, 3 and 4 Å chemical shift based dynamical ensembles. For comparison, the RMSD and R between RDCs calculated from the reference ensembles and those calculated from the chemical shift based dynamical ensembles are also shown.

	CS: RMSD (ppm)/R			RDC: RMSD (Hz)/R
N	2 Å	3 Å	4 Å	2 Å	3 Å	4 Å
1	0.24/0.97	0.25/0.97	0.26/0.97	25.5/0.77	28.1/0.73	25.9/0.78
2	0.13/0.99	0.11/0.99	0.10/0.99	15.8/0.89	14.1/0.91	14.1/0.91
4	0.10/0.99	0.09/0.99	0.08/0.99	15.4/0.89	12.6/0.92	13.2/0.92
6	0.09/0.99	0.08/0.99	0.08/0.99	14.7/0.90	12.2/0.92	12.5/0.92
8	0.09/0.99	0.08/0.99	0.07/0.99	14.4/0.90	11.3/0.92	12.3/0.92

To further interrogate the chemical shift dynamical ensembles, we used the S-matrix method (Methods) to determine their structural similarity with the reference ensembles. We observed that for N=2 the 〈s_ij〉_A was 0.88, 0.78 and 0.84 for the 2, 3 and 4 Å reference ensembles (Table 2). Increasing N did not result in any significant enhancement in the overlap between the chemical shift and reference ensembles (Table 2). By comparison, the 〈s_ij〉_A for randomly selected ensembles were 1.06, 0.93 and 0.78, indicating that there was better correspondence between chemical shift based dynamical ensemble and reference ensembles than randomly selected dynamical ensembles and reference ensembles. However, the RDC, as well as the, chemical shift+RDC ensembles, exhibited much better overlap with the reference ensembles; for the N=8, 〈s_ij〉_A for 2, 3 and 4 Å ensembles was 0.44, 0.44 and 0.43, and 0.44, 0.41 and 0.39, respectively.

Table 2.

Overlap between chemical shifts based dynamical ensembles and reference ensembles. Shown are the 〈s_ij〉_A between chemical shift based dynamical ensembles and the 2, 3 and 4 Å reference ensembles for N=1, 2, 4, 6 and 8. For N=8, 〈s_ij〉_A between the reference ensemble and RDC and chemical shift+RDC based dynamical ensembles are included. For comparison, the 〈s_ij〉_A between randomly selected ensembles and the reference ensembles are included.

N	2 Å	3 Å	4 Å
1	1.47	1.59	1.56
2	0.88	0.78	0.84
4	0.76	0.64	0.65
6	0.75	0.61	0.56
8a	0.75/0.44/0.44	0.59/0.44/0.41	0.53/0.43/0.39
random	1.06	0.93	0.78

^afor comparison 〈S_ij〉_A for the RDC and chemical shift+RDC ensemble are also listed

Taken together, although the chemical shift-based dynamical ensembles exhibited greater resemblance to the reference ensembles than the randomly constructed ensembles, they were unable to achieve the same degree of overlap as the RDC and chemical shift+RDC, and consequently were unable to adequately predict the reference ensemble RDCs. These effects can be attributed to the comparatively larger error threshold used to define convergence for chemical shifts (threshold is ~22% of chemical shift total range) as compared to RDCs (threshold is ~2.5% of the RDC range). Indeed, repeating the simulations with zero error resulted in chemical shift dynamical ensembles that exhibited enhanced overlap with the reference ensembles, and thus, better predicted reference ensembles RDCs (data not shown). The ability of a chemical shift dynamical ensemble to recover the reference ensemble is therefore limited by the accuracy of chemical shifts predictions. Currently, SHIFTS and NUCHEMICS predict ¹H chemical shifts to within ~ 0.30 ppm, slightly higher than the 0.24 ppm error threshold used to determine convergence in the theoretical simulations. Significant improvement in the accuracy of the ¹H chemical shift predictions will be needed in order to construct accurate dynamical ensembles of RNAs based solely on chemical shift data.

Conclusions

NMR structure determination of nucleic acids has traditionally been challenging due to the paucity of inter-proton NOE-derived distance restraints, extended nature of the structures, and high degree of flexibility. There has been a long-standing quest to measure different sources of structural information, and indeed, the measurement of RDCs has revolutionized the ability to determine the structure and dynamics of nucleic acids. There is now renewed interest in utilizing NMR chemical shifts to solve RNA structure, as they are the most accessible and accurately measured NMR observable. In this report we demonstrated that ¹H chemical shifts can be used to resolve RNA structure, allowing discrimination of native structure from non-native states. We show using SHIFTS and NUCHEMICS, which on average predict ¹H chemical shifts to within 0.30 ppm, that ¹H chemical shifts can be used to resolve with to within 2–4 Å, and <3 Å when neglecting highly flexible residues. ¹H chemical shifts can immediately be used for RNA structure validation. In time, as more accurate ¹H chemical shift prediction methods emerge the resolution limit should decrease well below 4 Å. When combined with improvements in RNA structure prediction, we can anticipate that methodologies such as CS-ROSETTA will evolve that allow high-resolution RNA structure determination based on chemical shift data alone.

We also investigated whether ¹H chemical shifts could be used to generate accurate dynamical ensembles of RNAs. Using theoretical simulation on the hexa-nucleotide HIV-1 TAR apical loop our results indicate that though dynamical ensembles constructed using ¹H chemical shifts exhibited greater structural overlap with known reference ensembles than randomly constructed dynamical ensembles, they failed to achieve the same degree of overlap as the corresponding RDC dynamical ensembles. This result hinted to an inherent degeneracy in the chemical shifts dynamical ensembles and in fact, we observe that the chemical shift based dynamical ensembles were unable to reproduce the RDCs back-calculated from the reference ensembles. Here again, more accurate ¹H chemical shifts prediction methods should enable more accurate dynamical ensembles to be generated, as should the incorporation of chemical shifts from other nuclei e.g. ¹³C, ¹⁵N and ³¹P.