q 2002 Elsevier Science Ltd. All rights reserved

Transcription

1 doi: /S (02) available online at on Bw J. Mol. Biol. (2002) 318, Towards Structural Genomics of RNA: Rapid NMR Resonance Assignment and Simultaneous RNA Tertiary Structure Determination Using Residual Dipolar Couplings Hashim M. Al-Hashimi 1 *, Andrey Gorin 2, Ananya Majumdar 1 Yuying Gosser 1 and Dinshaw J. Patel 1 1 Cellular Biochemistry and Biophysics Program, Memorial Sloan-Kettering Cancer Center New York, NY 10021, USA 2 Computer Science and Mathematics Division, Oak Ridge National Laboratory Oak Ridge, TN 37830, USA *Corresponding author We report a new residual dipolar couplings (RDCs) based NMR procedure for rapidly determining RNA tertiary structure demonstrated on a uniformly 15 N/ 13 C-labeled 27 nt variant of the trans-activation response element (TAR) RNA from HIV-I. In this procedure, the time-consuming nuclear Overhauser enhancement (NOE)-based sequential assignment step is replaced by a fully automated RDC-based assignment strategy. This approach involves examination of all allowed sequence-specific resonance assignment permutations for best-fit agreement between measured RDCs and coordinates for sub-structures in a target RNA. Using idealized A-form geometries to model Watson Crick helices and coordinates from a previous X-ray structure to model a hairpin loop in TAR, the best-fit RDC assignment solutions are determined very rapidly (, five minutes of computational time) and are in complete agreement with corresponding NOE-based assignments. Orientational constraints derived from RDCs are used simultaneously to assemble sub-structures into an RNA tertiary conformation. Through enhanced speeds of application and reduced reliance on chemical shift dispersion, this RDC-based approach lays the foundation for rapidly determining RNA conformations in a structural genomics context, and may increase the size limit of RNAs that can be examined by NMR. q 2002 Elsevier Science Ltd. All rights reserved Keywords: resonance assignments; residual dipolar couplings; ribonomics; structural genomics; HIV-I TAR Introduction Structural genomics and the quest for comprehensive information about biomolecular function through large-scale structure elucidation 1 has so far focused on the high-throughput determination of protein structures using X-ray crystallography, 2 NMR spectroscopy 3,4 and computational homology modeling. 5 However, RNAs play a fundamental role in gene processing and regulation, and adopt three-dimensional architecture and recognition elements with a complexity approaching that Abbreviations used: RDC, residual dipolar coupling; TAR, trans-activation response element; HIV-I, human immunodeficiency virus type I; NOE, nuclear Overhauser enhancement. address of the corresponding author: hashimi@sbnmr1.mskcc.org observed in proteins. 6,7 RNA constitutes a drug target, therapeutic agent, and catalytic enzyme used in a variety of chemical and biochemical applications. 7 9 For these reasons, launching a structural genomics program and the development of methods for high-throughput structure determination is as important for RNAs 10,11 as it is for proteins. Effort in protein structural genomics is focusing on experimental determination of novel protein folds, because an expansion in protein structural space is expected to pave the way for future determination of protein structures based on computational comparative homology technologies. 5 Similarly, methods for high-throughput RNA structure determination should focus on elements that would help advance the development of computational methods for predicting RNA /02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved

2 638 RDC-based Structure Determination of RNA structures. 12 While relatively robust computational methods exist for predicting RNA secondary structures from sequence, 13 RNA tertiary structures are more generally resistant to computational characterization. Tertiary interactions in RNA are often scarce, and energetically small compared to interactions stabilizing secondary structure, and are frequently mediated by divalent cations or backbone interaction groups that are very difficult to predict a priori. RNA structures can be determined experimentally using X-ray crystallography, but nucleic acids frequently fail to yield well-diffracting crystals or are affected by crystal-packing forces. On the other hand, NMR spectroscopy does not require crystallization, but application is limited to relatively small RNAs (, 60 nt). This, however, does not represent a major drawback, as an increasing number of regulatory RNAs that fall within the latter size limit are being characterized. 14 A more severe limitation to the NMR approach is the over-reliance on short-range (, 5Å) distance constraints derived from the measurement of nuclear Overhauser enhancements (NOEs). Structure determination using NOE-based methods often consumes several months of data acquisition and analysis, most of which is expended on assignment of resonances and NOEs. In particular, sequential assignments in nucleic acids continue to rely heavily on the observation of inter-residue NOEs between base and sugar protons in typically overcrowded spectra. The density of inter-proton distance constraints is also small, and short distance constraints are ineffective in defining extended RNA tertiary conformation. This is in stark contrast to the situation in proteins, where an overabundance of robust through-bond NMR experiments are available for rapidly establishing sequential connectivities, and the density of inter-proton distance constraints is high, many of which correspond to long-range NOEs that can effectively define a globular protein fold. Recent developments in NMR methodology involving the measurements of residual dipolar couplings (RDCs) in partially oriented systems provide novel long-range orientational constraints that can remedy many of the aforementioned limitations. So far, applications of RDCs in studies of nucleic acids have focused primarily on improving the accuracy and precision of structures determined by NMR. In one approach, 22,23 the measurement of five or more independent RDCs (D ) in sub-structures with known molecular geometry is used to determine five order matrix elements (S pq ) describing average sub-structure alignment: 24 D ¼ D int S pq ðcos a ij p cos aij q ÞS pq ð1þ where D int is a constant and cos a ij p are the direction cosines that define inter-nuclear vector orientation relative to an arbitrary sub-structure frame. Three of the order tensor elements can then be used to orient sub-structures relative to a common ordering frame, and hence relative to one another. Because this approach can be applied effectively in determining the alignment of remotely positioned sub-structures in modular biomolecules, it is particularly well suited for determining extended RNA tertiary conformation. 25,26 RNA structures are uniquely hierarchical, and are composed of a limited number of autonomously folding structural motifs. 27,28 These sub-structures can be identified readily using RNA secondary structure prediction programs, 13 and can often be modeled with reasonable accuracy using idealized geometries or using coordinates from previously determined homologous sub-structures. The recent structure determination of the ribosome has greatly expanded the available RNA structural database from which model homologous sub-structures can be derived. While relative sub-structure orientations can be determined rapidly using RDCs, this process remains limited by the time-consuming requirements for sequence-specific resonance assignments. Here, we introduce a new procedure based on order matrix analysis of RDCs that allows rapid and simultaneous sequence-specific resonance assignments and RNA structure determination. Application is demonstrated on a uniformly 15 N/ 13 C-labeled 27 nt hairpin-loop variant of the trans-activation response element (TAR) RNA found at the 5 0 -end of all premessenger RNA transcripts, 32 for which we have recently reported an RDC-based structural and dynamic analysis. 26 Results and Discussion Assignment of RNA sub-structures with known geometries using RDCs The use of RDCs in resonance assignments has been demonstrated recently in application to protein systems. In one study, RDC contributions were used to overcome limitations associated with chemical shift degeneracies 33 in the so-called molecular fragment replacement approach, 34 and in another study, 35 RDCs were used directly in the simultaneous resonance assignment and protein fold determination. The latter study relied on having a large number of independent RDCs measured between protein backbone nuclei that are constrained by only two degrees of freedom (f and c). Unfortunately, application of this method to nucleic acids is difficult, owing to the proportionally smaller number of independent RDCs that can be measured and the significantly larger degree of conformational freedom that must be overcome. Assuming model geometries for sub-structures in RNA can overcome the latter limitations. 11 When resonances are assigned correctly, and more

3 RDC-based Structure Determination of RNA 639 Figure 1. Resonance assignments in known sub-structures using correlated RDCs. The orientation of a given internuclear vector type (A or B) is shown as circles pointing along the surface of a sphere relative to an axially symmetric order tensor frame (S zz ). RDCs constrain inter-nuclear vector orientations along two continuous cones, shown using different colors for different RDC values. Misassignment of two inter-nuclear vectors having different corresponding RDC values leads to disagreement between RDCs and the assumed sub-structure geometry (A $ A 00 ). Misassignment of inter-nuclear vectors having similar RDCs does not lead to disagreement with an assumed geometry (A $ A 0 ). This degeneracy can be minimized by correlating (indicated by broken red lines) two different types of RDC (A,B $ A 0,B 0 ). than five independent RDCs measured, RDC values will agree with an accurately modeled substructure, allowing the determination of an order matrix that reproduces experimentally measured RDCs satisfactorily using equation (1). Conversely, misassignment of resonances can lead to disagreement. This can be appreciated when visualizing RDC constraints on inter-nuclear vector orientation. As shown in Figure 1 for an axially symmetric order tensor, inter-nuclear vectors (depicted as white circles on a surface of a globe) are constrained along two cones of allowed orientations relative to the order tensor frame (S zz ). The misassignment of spin-pairs effectively interchanges corresponding inter-nuclear vector orientations, and when these have different orientations and RDC values, this leads to disagreement between RDCs and the assumed geometry (Figure 1, A $ A 00 ). A measure of this agreement is given by the rmsd between measured RDCs and values calculated using best-fit order tensor parameters determined using equation (1). Due to the orientational degeneracy in RDCs, resonances can be misassigned without affecting agreement between RDCs and an assumed geometry (Figure 1, A $ A 0 ). Such limitations can be overcome by measuring RDCs in a different ordering medium, 23,36 or by establishing through-bond correlations among spin pairs between which RDCs are measured. Having groups of correlated RDCs reduces the likelihood of having such degeneracies (Figure 1 (A,B $ A 0,B 0 ). For example, in nucleic acids, inter-nuclear vectors in nucleotides will seldom all point along identical cones of orientations for different positions in an RNA structure. Even for regular A-form helices, the most common secondary structural element in RNA, variations in inter-nuclear vector orientations in a given residue type arise due to rotation of base-pairs about the helix axis across the first 11 residues in the double helix (, 338 per residue), due to variations in sequence (for example GC versus CG), and due to departures from coaxial helix alignment. This is the basis of the assignment strategy that we employ here for accelerating tertiary structure determination of RNA using NMR.

4 640 RDC-based Structure Determination of RNA Figure 2. (a) Secondary structure and molecular sub-structures in the 27-mer HIV-I TAR variant (six residue hairpin loop in wt-tar CUGGGA is replaced with the UUCG tetra-loop) used in this study. (b) Atom numbering in A U and G C Watson Crick base-pairs and a spin basis set (shown in red) between which independent RDCs can be measured and correlated in RNA. Correlations can be established among spin-pairs within a residue (intra-residue correlations) using through-bond scalar couplings and between base-paired residues (inter-residue correlations) using trans-hydrogen bondmediated scalar couplings (see Table 1). RDC basis set and intra-residue correlations Decomposition of our target TAR RNA into substructures is shown in Figure 2(a). Based on the secondary structure predicted using the program mfold version 3.1, 37 four contiguous sub-structures can be identified: two Watson Crick helices (designated stem 1 and 2), a UUCG hairpin loop, and a three residue UCU bulge. Continuous Watson Crick regions in helices can be modeled using idealized A-form geometries, while model coordinates for the hairpin loop can be obtained from a 2.8 Å resolution X-ray structure of a similar hairpin loop. 38 While no predefined conformation can be assumed for the bulge, this does not preclude determination of RNA tertiary conformation based on the alignment of the latter three sub-structures. A target spin basis set in RNA nucleotides that have many of the attributes needed for obtaining resonance assignments and determining tertiary structure using RDCs is shown in Figure 2(b) (shown in red). Independent RDCs can be measured accurately between many of these directly bonded spin-pairs [C8 H8 ( 1 D C8H8 ), C2 H2 ( 1 D C2H2 ), C5 H5 ( 1 D C5H5 ), C6 H6 ( 1 D C6H6 ), N3 H3 ( 1 D N3H3 ), N1 H1 ( 1 D N1H1 ), and C1 0 H1 0 ( 1 D C1 0 H10)], and NMR correlations among members of this spin basis set are possible using robust intra-residue correlation experiments. 21,39 RDCs can be measured very efficiently using simple variants of HSQC experiments (see Materials and Methods) as additional contributions to scalar coupling (J ) in an aligned state (J þ D ) relative to an isotropic state (J ). 17,18 Partial alignment for TAR was achieved using a phage ordering medium. 40,41 A total of 18/27 ( 1 D 0), 3/3 C1 0 H1 (1 D C2H2 ), 9/11 ( 1 D C8H8 ), 12/16 ( 1 D C5H5 ) and 7/16 ( 1 D C6H6 ) values could be measured with an average uncertainty estimated to be,1.5 Hz. The total acquisition time for these experiments under the conditions described in Materials and Methods (,1.2 mm TAR using a 500 MHz NMR spectrometer) was,five days. RDCs were recorded on a TAR sample dissolved in 2 H 2 O, and hence no 1 D NH values were measured. 26 Resonances belonging to our spin basis set can be intra-residue correlated using a suite of well established through-bond NMR experiments involving intra-base and base-sugar correlations. 21,39 Experiments used in application to TAR are summarized in Table 1. Correlations need to be established only for resonances having

5 RDC-based Structure Determination of RNA 641 Table 1. NMR experiments used in establishing intra and inter-residue correlations in nucleic acids Correlations Experiment AU-pairs GC-pairs Reference/source Intra-nucleotide Bid_hCNcH_py H6/C6 to H1 0 /C1 0 H6/C6 to H1 0 /C Bid_hCNcH_pu H8/C8 to H1 0 /C1 0 H8/C8 to H1 0 /C H8(C8)N9N3 A(H8) to A(N3,N9) G(H8) to G(N3,N9) 62 H2(C4)N9 A(H2) to A(N9) NA Majumdar et al., unpublished results H1(N1C2)N3 NA G(H1) to G(N1,N3) 62 H1(N1C6C4)N9 NA G(H1) to G(N9) 62 Inter-nucleotide HNN-COSY U(H3 N3) to A(N1) G(H1 N1) to C(N3) 42,43 H5NN U(H5 N3) to A(N1) NA Majumdar et al., unpublished results H2NN A(H2 N1) to U(N3) NA 63,64 H3(N3N1)lH2 U(H3) to A(H2) NA 46 H5(N3N1)H1 NA C(H5) to G(H1) 46 H6(N3N1)H1 NA C(H6) to G(H1) 46 H5(N3N1)H2 U(H5) to A(H2) NA Majumdar et al., unpublished results corresponding RDC values. Because correlations can be made with greater tolerance to spectral overlap compared to RDC measurement, all spins having corresponding RDC values could be correlated unambiguously in TAR over a total acquisition period of, three days. With these experiments, it was possible to group all RDC data belonging to individual residues. While intraresidue correlation of RDCs may be sufficient to allow both assignment and tertiary structure determination, it is now possible to establish interresidue correlations in nucleic acids in a fairly robust and rapid manner. Trans-hydrogen bond-mediated scalar couplings: a direct approach to inter-residue correlations in nucleic acids The discovery of trans-hydrogen bond-mediated scalar couplings provides a direct approach for establishing a variety of base-pair alignments in nucleic acids These experiments rely on magnetization transfer across the hydrogen bond (N d H N a ) mediated by trans-hydrogen bond scalar couplings ( 2h J NdNa ). Typically, in an HNN- COSY spectrum, the detection of a cross-peak between the hydrogen-bonded proton (H d ) and the acceptor nitrogen atom (N a ) signifies hydrogen bond formation between the corresponding donor and acceptor bases. For example, A U and G C base-pairs can be identified through U(H3):A(N1) and G(H1):C(N3) cross-peaks, respectively (Figure 2(b)). These provide a robust approach for establishing inter-residue correlations between our target spins and a means of discrimination between base-paired and single residue nucleotides. For example, in an A U pair, inter-nucleotide U(H3):A(N1) and intra-nucleotide A(H2): A(N1) correlations identify the U(H3) and A(H2) protons as belonging to a single A U linkage (Figure 2(b), Table 1). Alternatively, direct U(H3):A(H2) correlations (Table 1) may be obtained using more recently developed methodology. 46 Once an inter-nucleotide 1 H 1 H connection is established in this way, additional intra-nucleotide correlations on either base (e.g. U(H5,H6):U(H3), U(H5):U(H6) and A(H8):A(H2), see Table 1) are used to connect all of these basis set protons and their associated C H vectors into a single A U base-pair unit. Similarly, spins across G C base-pairs may be correlated using either a combination of G(H1):C(N3) and C(H5,H6):C(N3) spectra or direct G(H1):C(H5,H6) connectivities, followed by appropriate intraresidue correlations (e.g. G(H1):G(H8), C(H5):C(H6), Table 1). In application to TAR, 3 A U and 7 G C transhydrogen bond cross-peaks could be detected using a suite of trans-hydrogen bond NMR experiments listed in Table 1 and recorded over a period of, three days. Hence, all Watson Crick basepairs predicted in the TAR secondary structure (Figure 1) could be accounted for experimentally and inter-residue correlations among our target spins could be established unambiguously for all base-pairs. The seven residues for which no transhydrogen bonds could be detected were assumed to belong to either the bulge or hairpin loop. On the basis of these experiments, RDCs could be grouped to individual Watson Crick base-pairs or to single nucleotides deemed not to be involved in detectable hydrogen bond alignments, but sequence-specific assignments still need to be determined. Sequence-specific assignment of resonances in RNA Using idealized A-form geometries generated using the program Insight II, and a previous 2.8 Å resolution X-ray structure 38 to model Watson Crick helices and the hairpin loop, respectively, all allowed permutations of resonance assignments were examined for best-fit agreement with correspondingly measured RDCs. Candidate residues for assignments and permutations are shown

6 642 RDC-based Structure Determination of RNA Figure 3. The rmsds between measured RDCs and values calculated using best-fit order tensors for allowed assignment permutations for three sub-structures in TAR. Candidate residues and permutations are shown using differently colored circles (guanine), rectangles (cytosine), squares (adenine) and diamonds (uracil), which are linked for Watson Crick base-pairs determined using J NN - NMR. The rmsds are shown as histogram plots for (a) stem 1, using coordinates from an idealized A-form geometry. The 5040 resonance assignment permutations were examined involving the assignment of a total ten base-pairs (seven G C and three A U basepairs) and associated RDCs to six positions (four G C and two A U). (b) Stem 2, using coordinates from an idealized A-form geometry. The 540 resonance assignment permutations were examined involving the assignment of a total of ten base-pairs (seven G C and three A U base-pairs) and associated RDCs to four positions (three G C and one A U). (c) The hairpin loop, using coordinates from a previous X-ray structure. The 24 resonance assignment permutations were examined involving the assignment of a total of seven residues (four U, two C and one G) and associated RDCs to four positions (two U, one C and one G). schematically in Figure 3 using circles (guanine), rectangles (cytosine), squares (adenine) and diamonds (uracil), which are linked for experimentally determined base-pairs. For a given assignment permutation, the best-fit order tensor solution was calculated using all corresponding RDC data independently for stems 1 and 2, and the hairpin loop. Sub-structure-specific best-fit order tensors were then used to back calculate best-fit RDC values. The rmsd values between measured RDCs and best-fit back-calculated values for allowed assignment permutations are shown in Figure 3 as histogram plots. These calculations could be carried out for all three sub-structures in less than five minutes of computational time on an SGI Origin with an R10000 processor. The average rmsd values (stem 1 ¼ 7.9 Hz, stem 2 ¼ 7.1 Hz, and hairpin loop ¼ 4.3 Hz) are significantly larger than the estimated experimental uncertainty in measured RDCs (, 1.5 Hz), indicating that many of the allowed resonance assignment permutations lead to significant disagreement between RDCs and the assumed sub-structure geometry. For stem 1, a single solution with a uniquely small rmsd value of 1.8 Hz is obtained (Figure 3(a)), while two solutions with comparably small rmsd values (2.2 Hz and 2.3 Hz) are obtained for stem 2 (Figure 3(b)). A reasonably unique best-fit assignment solution having an rmsd value of 1.8 Hz is also obtained for the hairpin loop (Figure 3(c)). The five best-fit sequence-specific assignment solutions (lowest rmsd values) are shown in Figure 4 for stem 1 (Figure 4(a)), stem 2 (Figure 4(b)) and the hairpin loop (Figure 4(c)). Assignments determined using NOE methods are indicated by color-matching base-paired/single nucleotides and their corresponding position in the RNA secondary structure (Figure 4). For the three sub-structures, the best-fit assignment solutions (solutions 1a, 2a, and 3a ) are in complete agreement with the NOE assignments, as shown by the placement of residues into their colormatching positions. For stem 1, solution 1a has a

7 RDC-based Structure Determination of RNA 643 Figure 4. Sequence-specific assignment arrays determined using RDCs. Candidate residues/base-pairs for assignments are shown using circles (guanine), rectangles (cytosine), squares (adenine) and diamonds (uracil), and are linked for experimentally determined Watson Crick base-pairs. The total number of RDCs measured in a base-pair or single residue is shown inside individual symbols. Sequence-specific assignment solutions are shown as a function of the TAR secondary structure, which is represented as a series of color-coded wells. NOE-based assignments are indicated by color-matching base-pairs and residues with their corresponding wells in the secondary structure. The rmsd between measured and calculated RDCs is shown to the right of the assignment array. Five assignment solutions having the lowest rmsds are shown for (a) stem 1, (b) stem 2, and (c) the hairpin loop. Bulge residues U23 and U25 are colored light blue and purple, respectively. considerably lower rmsd (1.8 Hz) compared to the other four best-fit solutions (3.7 Hz 5.0 Hz) and solutions 1b and 1c simply represent exchange of assignments between neighboring residues. The latter can be expected because it leads to minimal changes in the orientation of inter-nuclear vectors in a given base-pair. On the other hand, solutions 1d and 1e have significantly higher rmsd values (5.0 Hz) and include residues that belong to stem 2. For the shorter stem 2, the two best-fit assignment solutions 2a and 2b have almost identical rmsd values (Figure 4(b), 2.1 Hz and 2.2 Hz, respectively) but differ considerably in assignments. However, solution 2b differs from all other solutions (2c e ) and, more importantly, includes residues that are assigned to stem 1 in all of the five best-fit solutions (Figure 4(a), solutions 1a e ). On the other hand, solutions 1a and 2a allocate the complete set of Watson Crick assignments to unique positions in stems 1 and 2, respectively. For the hairpin loop, the only guanine residue not involved in Watson Crick alignment G34 is assigned a priori (Figure 4(c), colored brown), but candidates for assignments include bulge residues U23, C24, and U25. While solution 3a (rmsd ¼ 1.8 Hz) is in agreement with the NOE assignments and has a smaller rmsd value compared to solutions 3b and 3c (2.3 Hz and 2.4 Hz, respectively), we illustrate an additional avenue for selecting assignments. Besides the low rmsd criterion, the derived principal order matrix parameter S zz, which defines the degree of alignment for a substructure, should be similar for two rigidly attached sub-structures. While we previously demonstrated that this assumption of rigidity does not hold for the two stems separated by a flexible bulge in TAR, 26 stem 2 should be attached rigidly to the directly linked hairpin loop. Notwithstanding the small number of RDCs measured in the hairpin loop, which limits the ability to accurately determine an S zz value, comparing the S zz values for solutions 3a (7.08(^0.35) ), 3b (3.96(^0.29) ), and 3c (4.28(^0.35) ), solution 3a has the best agreement with the S zz value for stem 2 (using solution 2a, 8.76(^0.16) ). With these sequence-specific assignments, the remaining cytosine residue can, by elimination, be assigned unambiguously to the bulge residue (C24), leaving two inter-changeable assignments for two uracil residues in the bulge (U23/U25).

8 644 RDC-based Structure Determination of RNA Figure 5. RDC assignment arrays using non-optimal data. (a) Using only 20% of RDCs that can be measured between C1 0 and H1 0 nuclei (stem 1 ¼ 2/12 and stem 2 ¼ 2/8). Only assignment solutions for stem 2 that are consistent with assignments in stem 1 are shown. (b) Where base-pairing is defined only between C19 G43 (orange residues) and C29 G36 (purple residues). Eight out of ten base-pairs (G17, C45, G18, C44, A20, U42, G21, C41, A22 and U40 in stem 1 and G26, C39, A27, U38, G28, C37, and C29) in stem 2 are included without defining their hydrogen bonding partners. A total of 259,299 and 72,000 assignment permutations were examined for stems 1 and 2, respectively. RDC-based sequential assignments with reduced reliance on intra and interresidue correlations While a detailed examination of the limits of applicability of this RDC-based sequential assignment strategy is beyond the scope of this work and is deferred for later publication (Gorin et al., unpublished results), we explored two important scenarios in the present application. One potentially significant advantage of this RDC-based approach over traditional NOE-based methods is the reduced reliance on adequate chemical shift dispersion for specific NOE reporter nuclei. Because RDCs were measured for only well resolved resonances in the 2D NMR experiments, only 65%, 80%, 20% and 90% of the total measurable 1 D 0, 1 C1 0 H1 D C5H5, 1 D C6H6, and 1 D C8H8 values, respectively, were measured in the two stems, and no RDC was measured for residue C19 in stem 1. While assignments could be established using this incomplete data set, we further examined if assignments could be determined when reducing the 1 D data (and hence requirements for C1 0 H1 0 C10 and H1 0 chemical shift resolution) to only 20% of the total measurable RDCs (stem 1 ¼ 2/12 and stem 2 ¼ 2/8) (Figure 5(a)). As shown in Figure 5(a), the correct assignments are determined for stem 1 and with a significant degree of confidence. While the correct assignments cannot be determined independently with similar confidence for the shorter stem 2, insisting on consistency with assignments for stem 1 alleviates the uncertainty, as shown in Figure 5(a), where only assignments for stem 2 that are compatible with the best-fit assignment solution in stem 1 are shown. Here, trans-hydrogen bond correlations were established for all Watson Crick base-pairs. This may not always be possible even for canonical base-pairs, due to departures from perfect canonical geometries (especially for terminal residues), insufficient chemical shift resolution and/or poor sensitivity in the NMR experiments, and some mismatched base-pair alignments (e.g. G U) lacking N H N hydrogen bonds cannot be detected easily using current NMR methods. We therefore

9 RDC-based Structure Determination of RNA 645 explored RDC-based assignments where base-pair alignment is defined explicitly for only two residues C19 G43 (orange residues) and C29 G36 (purple residues) and eight out of ten base-pairs were included without explicitly defining their hydrogen-bonding partners. The correct assignments can be determined with reasonable resolution, particularly for stem 1, where the bestfit solution differs by at least 0.4 Hz from the remaining four next to best-fit solutions (Figure 5(b)). To display results more completely, we do not filter assignment solutions for stem 2 for consistency with stem 1, but simply point out that the latter allows determination of the correct set of assignments for stem 2. Together, these results indicate that RDC-based sequential assignments is highly tolerant to inadequate chemical shift resolution and incomplete trans-hydrogen-bond correlations, and this may allow examination of larger RNAs than is possible currently using NOE methods alone. Determining RNA tertiary conformation The analysis used in examining assignment permutations simultaneously provides the three Euler angles needed to define relative substructure orientations. We have reported the RDCderived inter-helical conformation for TAR (average inter-helical angle ranging between 448 and 548). 26 The latter study also employed idealized A-form geometries for the two stems but more extensive experimental data that included 1 D 0, 1 C2 0 H2 D 0, 1 C3 0 H3 D and C4 0 H4 1 D 0 C5C6. We do not revisit this discussion, but point out that orientational solutions determined here are in excellent agreement with our previous findings (data not shown), and with previous structural studies of TAR. Here, the orientation of stem 2 relative to the hairpin loop, which was previously omitted from analysis, can be determined and compared with a high-resolution X-ray structure of a similar hairpin loop. 38 This is shown in Figure 6, where the orientation of stem 2 (in blue) relative to the loop (in green) determined by superimposing the centers of their orientational solutions (RDC- NMR) is compared with the 2.8 Å resolution X-ray structure of the TL1 loop in 16 S ribosomal RNA fragment (X-ray). 38 The orientation of the hairpin loop is superimposed for the two structures. Because the order tensor for TAR is close to axially symmetric and hence the S xx and S yy orientations are not well defined, the relative orientation of the two sub-structures about the S zz direction is not well defined (^458). However, this uncertainty and the degeneracy arising from allowed inversions about principal axes is minimized when insisting on proper chemical linkage between the two sub-structures (C29(stem2) U31(loop) and G36(stem 2) G34(loop)). On the other hand, the principal S zz orientation is well defined (^88) and the RDC alignment determined by superposition of the S zz axes is in excellent agreement with the X-ray structure (the difference in orientations,58 about the S yy direction) as can be seen from comparison of the backbone alignments. Figure 6. The alignment of stem 2 relative to the hairpin loop in TAR determined using RDCs is compared to the structure of a similar hairpin loop determined by X-ray crystallography. The orientation of the loops is superimposed in the two structures. The average RDC alignment differs by,58 from the X-ray structure.

10 646 RDC-based Structure Determination of RNA Geometry of sub-structures and limits of applicability For TAR, the assumption of idealized A-form geometry for the two Watson Crick stems appears to be a very good one, because the rmsd between measured and calculated RDCs approaches the experimental uncertainty in measuring RDCs. Agreement between RDCs and idealized RNA A-form geometries have been reported. 25,47 However, deviations from idealized A-form geometries can arise, and this can potentially limit the accuracy and applicability of our presented RDC procedure. For example, when using a family of 20 NOE-derived NMR geometries 51 as input coordinates for stem I, 5/20 structures yielded lowest rmsd values for the correct assignment solution, while 15/20 resulted in aberrations. Nevertheless, the two lowest rmsd values across the 20 structures (2.7 Hz and 3.2 Hz for models 9 and 1) corresponded to the correct set of assignments. The third best-fit solution corresponded to incorrect assignments, but also displayed a proportionally higher rmsd (3.8 Hz), and no competitive alternative assignment solutions were determined consistently with low rmsd values. This emphasizes the need to generally examine assignments against a large pool of candidate sub-structures. These candidate sub-structure geometries can be derived from homologous RNA sub-structures in the protein data bank, which has greatly expanded owing to the recent X-ray structure determination of the ribosome. This would allow application of RDC-based assignments with greater accuracy, and would simultaneously allow for the refinement of the local geometry of sub-structures, in analogy to the so-called molecular fragment replacement methodology developed by Bax and co-workers for protein systems. 34,50 While this may also allow for more general applicability to nonhelical motifs, such as bulge, loops, and junctions, structure determination as well as assignments of such motifs will likely necessitate additional NOEbased NMR data. In this regard, it is important to note that such residues tend to have better chemical shift dispersion compared to helical regions. Another approach to reduce assumptions about sub-structure conformation (for example in accommodating bent helices) would be to minimize the size of individual sub-structures. 48 For TAR, the correct resonance assignments (albeit with weaker resolution, see Figure S1 in the Supplementary Material) could be determined using RDCs when dividing stems 1 and 2 into sub-structures composed of only three base-pairs. Successful application using smaller fragments would benefit tremendously from the additional measurement of 1 D NH and other RDCs, which can be measured between our target nuclei, 49 and/or using different ordering media. 23,36 Such additional measurements of RDCs will be critically important for ensuring consistent measurement of RDCs for all residues in a sub-structure, because reduced RDC representation of residues can lead to severe ambiguities in the assignment process. Similarly, enhancing the distribution of measured RDCs will be important for overcoming potential assignment ambiguities arising from degeneracies in RDCs. For example, for a limiting case of having one idealized helix with S zz perfectly coincident with the helix axis and axial symmetry of alignment, RDCs measured for a given residue type will all have identical values and various assignment permutations will be indistinguishable using RDCs. Having said that, as long as more than five independent RDCs have been measured, all assignment permutations will also lead to determination of identical and accurate order tensor solutions, which can be used to determine the alignment of the helix. Therefore using our RDC procedure, an RNA tertiary structure could, in principle, be determined while still having some ambiguous resonance assignments. Although this limiting scenario will not be encountered frequently for folded RNAs, it argues that general applicability of our RDC procedure in resonance assignments may require some additional NOE data. Finally, the number of assignment permutations that need to be examined will rise significantly ( ) with increasing RNA size (.40), or when having a limited number of trans-hydrogen bond correlations, posing a computational challenge to implementation of our RDC-based procedure. We anticipate that a combination of parallel computing, optimization of the size of molecular fragments and protocols for reducing redundant assignment permutations (for example, excluding candidate residues from an assignment pool once they have been assigned to a substructure), should help to enhance computational efficiency to allow rapid application to larger RNAs. Conclusions The foundation of de novo determination of biomolecular structure by NMR has traditionally relied on establishing resonance assignments to allow interpretation of geometry-dependent interactions in terms of specific structural constraints. 55 Here, we have sought to reverse this tradition, and to exploit a priori structural information to expedite resonance assignments and structure determination. The current pace of progress in computational methods for predicting biomolecular structure, as well as the increasing number of biomolecular structures determined by X-ray and NMR, provides the impetus to integrate a priori structural information in NMR structure determination. 11 While we have presented an application for nucleic acids, this RDC-assignment approach is extendable to proteins for which structures have already been determined using X-ray or computational homology modeling. There is often the incentive to carry out resonance assignments for such proteins, because NMR can be used to

11 RDC-based Structure Determination of RNA 647 probe inter-molecular interactions and molecular dynamics. 11 For application to nucleic acids, sequential assignments using RDCs are almost entirely computer-automated, consuming less than five minutes of computational time for RNAs such as TAR (,27 nt), while the entire data collection and spectral analysis consumed less than two weeks. The advent of cryogenic probes coupled with higher magnetic fields can be expected to reduce data acquisition by a factor of,4. Tertiary structures determined using the presented RDC approach may lack some of the intricate details associated with high-resolution structures but, nevertheless, captures significantly important elements of RNA conformation pertinent to function. For example, the inter-helical angle in TAR determined using RDCs is,44 548, and this is known to undergo coaxial alignment upon complex formation with relevant targets. 52 High-resolution structures can be obtained through further refinement of best-fit sub-structures against RDCs and readily assignable NOE data. Bax and co-workers have demonstrated the feasibility of refining model protein structures based primarily on RDCs in cases where the model structure is reasonably similar to the final target. 50 Such a refinement approach will be critically important for allowing general structure determination of non-helical linking motifs, such as bulges, loops, and junctions. Variations in RDCs (RDC mapping) can be used to probe inter-molecular interactions, 56 thereby complementing information from chemical shift perturbations, which are often more difficult to interpret for RNA compared to proteins. Finally, both RDC-derived tertiary structure and dynamics 26 will provide an important database upon which RNA structure predication tools may be developed. We anticipate that such applications will be critical components of an RNA structural genomics program. Materials and Methods Sample preparation and NMR spectroscopy Uniformly 15 N/ 13 C-labeled TAR RNA was prepared using standard procedures as described. 57 NMR samples contained,1.2 mm uniformly 15 N/ 13 C-labeled TAR, 15 mm sodium phosphate (ph ), 25 mm sodium sulfate and 0.1 mm EDTA. A second NMR sample was prepared that also contained 22 mg/ml of Pf1 phage for inducing molecular alignment. 58 All NMR data were acquired on Varian Inova spectrometers operating at 1 H frequencies of 500 MHz and 600 MHz at 25 8C, equipped with actively shielded triple resonance z-gradient probeheads possessing a signal-tonoise ratio (standard ethyl benzene sample) of 800:1 and 1200:1, respectively. NOE-based resonance assignments were obtained using standard homonuclear and heteronuclear, 2D and 3D NMR experiments closely following a previously reported procedure 57 (see Table 1 for a list of experiments). The measurement of RDCs in TAR has been described. 26 Briefly, one bond 1 D CH splittings between C8 H8, C6 H6, C2 H2, and C1 0 H1 0 were measured using the 1 J CH -CT-CE-HSQC experiment, 59 and using IPAP versions of a regular HSQC without 1 H decoupling in the indirect ( 13 C) dimension. 60 C5 H5 splittings were measured using a regular CT-HSQC without 1 H decoupling in the indirect ( 13 C) dimension. In all cases, RDC values were calculated as the difference between splittings measured in the absence and presence of phage aligning medium. The random uncertainty in 1 D CH estimated from multiple measurements was, on average,,1.5 Hz. Sequence-specific assignments using RDCs Software for evaluating all allowed assignment permutations based on RDCs was written using Perl and Cþþ. This software requires three input informational batches: (1) coordinates of sub-structures; (2) sequence of sub-structures; and (3) RDC data. Coordinates for sub-structures need to be in PDB format. The sequence batch is a linear list of all residues in the RNA and need not follow any particular order. Residues known to be involved in H-bond alignments are specified in the sequence batch as A:U and G:C, and are distinguished from single residues deemed not to be involved in H-bond alignments as A, U, G and C. The data batch includes the atom types between which RDCs are measured. RDCs are listed as a series of data belonging to either a single residue or base-pair. A combinatorial assignment program (CAP) was written to collect the three informational batches from separate files and construct all possible permutations for assignments. Specifically, the CAP program matches the series of RDC measurements and corresponding inter-nuclear vectors provided in the PDB file for all allowed assignment permutations. For a given set of assignments, the best-fit order matrix elements are evaluated using a previously described singular value decomposition (SVD) procedure 22 and RDC values back-calculated using equation (1). The rmsd values between calculated and experimental RDC values are then evaluated for a given set of assignments. The CAP program outputs the rmsd values for a given set of assignments. This program includes additional features for accommodating gaps in the RDC data, and incorporating RDCs from two or more ordering media, and this will be presented in more detail elsewhere (Gorin et al., unpublished results). Determining the relative alignment of stem 2 and the hairpin loop using RDCs Order tensor frames were calculated independently for stem 2 and the hairpin loop using the program ORD- ERTEN_SVD. 22 Idealized A-form coordinates and the previous X-ray structure of the TL1 hairpin loop 38 were used as input coordinates for stem 2 and the hairpin loop, respectively. A total of 16 and seven RDCs were included in the calculations for stem 2 and the hairpin loop, respectively, using a total of the 100,000 reiterations. Input uncertainties for RDCs were on average 4 Hz, and were increased relative to experimental uncertainties (,1.5 Hz) to allow for possible departures from the assumed sub-structure geometry. Order tensor frames determined independently for stem 2 and the loop were superimposed using Insight II to carry out the rotations. Although this results in four allowed conformations that are related by inversions about principal axes, three of these could readily be discarded due to violations in linkage geometry (Figure 6).

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