Small-angle X-ray scattering: a bridge between RNA secondary structures and three-dimensional topological structures

Abstract

Whereas the structures of small to medium-sized well folded RNA molecules often can be determined by either X-ray crystallography or NMR spectroscopy, obtaining structural information for large RNAs using experimental, computational, or combined approaches remains a major interest and challenge. RNA is very sensitive to small-angle X-ray scattering (SAXS) due to high electron density along phosphate-sugar backbones, whose scattering contribution dominates SAXS intensity. For this reason, SAXS is particularly useful in obtaining global RNA structural information that outlines backbone topologies and, therefore, molecular envelopes. Such information is extremely valuable in bridging the gap between the secondary structures and three-dimensional topological structures of RNA molecules, particularly those that have proven difficult to study using other structure-determination methods. Here we review published results of RNA topological structures derived from SAXS data or in combination with other experimental data, as well as details on RNA sample preparation for SAXS experiments.

Introduction

It was recognized in the 1980s that small-angle X-ray scattering (SAXS) data contain information about the overall shape of biomacromolecules in solution [1,2]. Applications of SAXS for biomolecule studies exploded after the third generation of synchrotron became operational and a number of critical computer programs and software tools became available. Over the years, those software tools have been developed to mine and interpret this information such as to reconstruct the low-resolution molecular envelopes of several macromolecules or to extract structural parameters mostly for proteins or protein complexes (Figure 1) [3^•,4,5,6^••,7,8^•,9,10]. In almost the same way, SAXS has also been applied to determine dimensional and physical parameters of RNAs (Figure 1), such as radius of gyration (R_g) [11], maximum particle diameter (D_max), molecular weight, Porod volume (V_p) [12^••], and molecular compactness [13^•, 14]. There are a number of excellent reviews on the fundamental physics of SAXS [2,15], computational tools and their applications [5,6^••,9,16^•]. There are also several reviews covering various aspects of applications of SAXS to study RNA [17,18^•,19,20]. This current review specifically focuses on the application of SAXS for determining RNA 3D topological structures.

Figure 1.

A schematic illustration of useful information that can be extracted from SAXS data. (a). Guinier plot from which one can obtain radius of gyration and approximate molecular weight; (b) & (c) Kratky and Porod plots to characterize dynamics and folding [12^••]; (d) Pair distance distribution function (PDDF) to derive maximum dimension, D_max and weighted distance distribution tally; (e) Refining RNA structure by restraining global dimension [56^•]; (f) generating global molecular shapes [6^••]; (g) calculating conformational ensembles.

The sugar-phosphate backbone of RNA makes it more electron-rich and, therefore, a stronger scatterer of X-rays than protein (Figure 2). In the analysis of experimental SAXS data, RNA has the following advantageous features compared to its protein counterpart: (a) Secondary structures of RNAs based on predictions [21,22] and/or experimental determination [23] are usually known prior to structure determination; (b) RNA structure tends to be relatively modular with a limited variety of structural elements and motifs [24^••]; and (c) RNA is usually non-spherical in overall shape [25^••]. In essence, RNA tertiary structures can be generally understood as being “packed” predominantly with A-form duplexes, which are linked by “single-stranded” linkers in junctions [26^••,27^••,28^••], interrupted by asymmetrical internal loops/bulges or “capped” with terminal structured or non-structured loops. The junctions themselves are prevalent structural elements, where intricate interactions among the junction residues dictate overall folding of RNAs [26^••,27^••,28^••]. Major structural features such as long duplexes, which have a cross-sectional diameter of ~22 Å, can be readily recognized in a SAXS-derived molecular envelope, such as in the Varkud satellite (VS) ribozyme [29^••]. Consequently, SAXS has been utilized as a valuable low-resolution technique to determine the 3D topological structures of large RNAs.

Figure 2.

A schematic illustration of contributions to the SAXS profiles from nucleobases (blue) and sugar-phosphate backbone (red) of a tRNA^phe. The electron-rich sugar-phosphate backbone dominates the shape of the SAXS profile [62].

Constructing global structures of RNA

It is recently recognized that RNA 3D structure and folding pathways are encoded in RNA secondary structure [30^••,31] and that RNA coarse structures may simplistically be viewed as a collection of duplexes that are branched out at junctions for multi-domain RNA [28^••]. The RNA conformation space, which consists of all possible global arrangements of duplexes, is restricted to a subspace due to covalent linkages imposed by linkers at junctions [28^••,30^••,31]. This subspace is further reduced to a few possible conformers because of preferential folding patterns of various types of junctions and tertiary interactions [26^••,27^••,28^••,30^••]. Thus, in principle, one might be able to identify a correct fold based on secondary structural information, given an approximate global shape and a few tertiary contacts.

The first RNA whose molecular shape was outlined using SAXS was a tRNA in 1964 by J. Witz [32]. In this study the tRNA was depicted as a boomerang-shaped molecule composed of two double-helices connected by a sharp kink. This model approximately agreed with the later-determined L-shaped high-resolution structure of the tRNA^phe [33]. Around the year 2000, several software programs were developed for the reconstruction of biomacromolecular shapes from SAXS data. Among these is the most popular ab-initio 3D-shape reconstruction software, DAMMIN [6^••]. The program’s algorithm is to search through a defined volume of densely packed beads (dummy atoms) and find a model(s) that best fits the experimental data using simulated annealing [6^••]. The initial search space is usually a bead-filled sphere whose diameter is defined by D_max. The search calculation is usually performed several tens of times with random number seeding, and accepted sets of values are used to compute an average shape.

The first RNA 3D-shape generated by ab-initio reconstruction was the free Thermus flavus 5S ribosomal RNA (rRNA) at 13 Å resolution, and a putative 5S rRNA atomic model was also presented [34]. The calculated molecular envelope of the 5S rRNA based on the SAXS data was remarkably similar to that in crystal structures, even though the proposed putative atomic model was not completely correct [34]. More widespread use of SAXS for RNA shape reconstruction did not start until the late 2000s [25^••,29^••,35,36,37^•,38,39.40^••,41^•]. For many RNAs, the 3D molecular shapes determined using ab-initio reconstruction have been highly valuable since they are often the only source of 3D structural information available and are sufficient to answer some key biological questions.

SAXS-aided divide-and-conquer strategies have also been employed to solve rather complex global topological structures of RNA. The first example of this approach is the VS ribozyme, a 160-nucleotide (nt) RNA consisting of multiple double-helices, junctions, and hairpins. In this pioneering and very clever work, Lipfert el al. used SAXS and a divide-and-conquer approach to define the locations of the various domain segments within the molecular envelope (Figure 3) [29^••]. The topological structure of VS ribozyme is consistent with previous results of chemical accessibility probing [42] and later activity studies [43]. Such a strategy appears to be generally applicable in many other cases. Another example is the HIV-1 5' untranslated region (5' UTR), in which nucleotides 1-334 were divided into three segments and studied using SAXS and computational modeling [36]. This structure revealed that the primer binding site (PBS) folds into an L-shape, similar to tRNA, thus providing a structural basis for interaction with tRNA-binding cellular factors.

Figure 3.

Two examples of applying the “divide-and-conquer” strategy and SAXS to derive three-dimensional topological structures of large RNAs. (a) Varkud satellite (VS) ribozyme; [29^••] (b) HIV-1 5' untranslated region (5' UTR) RNA [36]. In the VS ribozyme case, it was the first demonstration of the strategy to delineate the three-dimensional fold of an RNA using SAXS and the secondary structure information.

Global shape analysis using SAXS has become a useful tool to study conformation “switching” of riboswitch RNAs [25^••,44,45]. Riboswitches are structural elements of mRNA involved in regulation of gene expression. Binding of their cognate ligands is believed to induce global conformational changes besides local structural change in binding pockets. However, a recent systematic study of aptamer domains of eight different riboswitches reveals considerable diversity amongst the range of conformation changes taking place in the ligand binding domains [25^••,44]. Those changes, revealed by SAXS envelope shapes, range from distinct global conformation switching, such as in the thiamine pyrophosphate (TPP) and cyclic diguanylate (c-di-GMP) riboswitches, to a complete lack of switching such as in the flavin mononucleotide (FMN) riboswitch [44]. Combined with thermodynamic data, these studies used SAXS to unveil a wide spectrum of ligand-interaction modes in response to the environment. In these cases, SAXS becomes indispensable, and is in fact particularly useful when crystal structures of riboswitches in their apo form often are not available.

RNA structure-function relationship

Structure-function relationship studies of large RNAs often only rely on secondary structure information or three-dimensional structures of smaller RNA fragments. Previous research on the HIV-1 Rev response element (RRE) RNA, which plays a key role in viral recognition of its own mRNA for nuclear export, is a good example. The secondary structure of RRE [46-49] and the detailed local structural contacts between the viral Rev protein and the high-affinity binding site of RRE [50] have been known for more than a decade. In addition, the second Rev binding site was also discovered [51]. However, because of lack of binding specificity of either sites, neither two pieces of the local structural information alone could resolve the long-standing mystery—the structural basis for specific viral RNA recognition. This long-standing mystery can only be solved with the knowledge of the overall 3D topological structure of the whole RRE RNA where the relative positions of the two binding sites are known. A recent study using SAXS corroborated with biological assays resolved the mystery [52^••]. The shape-reconstruction of the RRE RNA resulted in an uncanny “A”-shaped molecular envelope, where the two known Rev binding sites are about 55 Å apart, a distance coinciding with that of the two arginine rich motifs (ARMs) in the Rev dimer [53,54] (Figure 4). The structural model and the specific mode of binding were validated by experiments using SAXS as well as both in vitro and in vivo assays. It was shown that the specificity of viral RNA recognition is achieved through a dual “lock-and-key” mechanism between the two binding sites on RRE and the two ARMs of a Rev dimer.

Figure 4.

An illustration of a combined use of SAXS and in vitro and in vivo assays to study the structure-function relationship of the HIV-1 Rev response element (RRE) RNA [52^••]. (a) an illustration of the two-step molecular shape derivation; (b) an illustration of divide-and-identify of domain locations in the RRE RNA; (c) extending the central helix to confirm the global topology of RRE; (c) & (e) corroborating the in vitro and in vivo assay results with the topological structural information.

Besides its biological significance, the SAXS analysis of RRE as a case study illustrates several useful hints. First, large RNA structures often consist of modular structural segments [55^••]. But whether a specific RNA is made of modular building blocks can only be validated by experimental means, and SAXS might be useful approach. Second, the secondary structures of large RNAs and some local structural details of small RNA fragments are often known. However, information derived from the global topological structures of large RNAs may be necessary to answer fundamental biological questions. While high-resolution structures of large, full-length RNAs in their functional forms are still sought-after prizes, relatively accessible 3D topological structures determined by SAXS may be a useful alternative. Such topological structures can be critical to understanding known biochemical and local structural information about a system in a global structural context, as illustrated in the recent study [52^••].

Combined use of SAXS and NMR measurements for global structure determination

By nature of physics, SAXS provides global structural information whereas NMR provides local structural details. One might consider the combination of these two methods to be a “perfect marriage” for RNA structure determination [56^•,57^•]. The first demonstration of such an approach was determining the structure of a 30 kDa homodimeric tetraloop-receptor RNA complex [56^•] (Figure 1). In this study, the SAXS data and residual dipolar couplings (RDCs) were used to define the global shape and relative orientation between the two domains, respectively. The SAXS-refined structures had a slightly improved backbone root-mean-square deviation (RMSD) from the average of the ensemble, ~1.3 Å, as compared to ~1.8 Å for the non-SAXS-refined structures. More importantly, the SAXS data complemented the NMR restraints in defining the global shape of the dimer, and the impact on the global structure is noticeable with an RMSD between the two structures of about 3.2 Å [56^•]. The pair distance distribution functions (PDDF) of the SAXS-refined structures are more narrowly dispersed and better matched to the experimental values in real space, and the R_g value of the structure changes from 25.1 Å (before) to 23.0 Å after the SAXS refinement, agreeing well with the experimental value of 23.2 Å.

Since the chemical-shift assignments and RDCs of RNA imino groups as well as SAXS data are relatively easy to obtain, combined use of these data has become a useful approach for rapid ab initio global structure determination of RNA [37^•,41^•,58^•,59-62]. An example of this approach is the structure determination of the U2/U6 snRNA complex [37^•]: a conserved and essential component of the active spliceosome that interacts with the pre-mRNA substrate and protein splicing factors to promote splicing catalysis. Using a combined approach that integrates SAXS, NMR, and molecular modeling, the three-dimensional solution structure of the 111-nt U2/U6 complex was determined that best fits both SAXS and NMR data (Figure 5). The conformation of the coaxial stacking of Helix Ib on the U6 ISL is similar to that in the Domain V structure in group II introns [37^•]. This U2/U6 structure is the largest RNA solution structure determined using the combined approach. Previously, the same method was applied to determine the 3D topological structure of the 102-nt ribosome-binding structural element (RBSE) of the 3' UTR of turnip crinkle virus (TCV) genomic RNA using SAXS and NMR RDC data and software package G2G [41^•]. The RBSE RNA shares similarities with almost all of the structural elements and features of a tRNA (Figure 5). The RBSE structure represents a prototype structure of a new class of RNA and provides a structural basis for understanding its involvement in viral translation/replication processes. In general, since RNA is mostly made of duplexes, more than 70% of total residues in an RNA structure, as well as backbones of duplexes, differ from each other on average within only 1 Å RMSD [60]. The resolution of the structures determined using only RDCs of imino groups and SAXS as a global constraint, as discussed in this review, could be better than 3.5 Å [60].

Figure 5.

Illustration of combined use of SAXS and NMR measurements to determine three-dimensional structures of U2/U6 snRNA [37^•] (a) and TCV RNA [41^•] (b). On the left are the secondary structures that are color-coded the same as in the three-dimensional models. The central panels are the fits to the experimental SAXS and NMR RDC data. The grey beads in (a) and mesh in (b) are molecular envelopes that are superimposed with the ensembles of NMR structures. (c) the 102-nt TCV RNA shares the identical folding topology with tRNA, even though the two RNAs have different sequences and sizes.

Conformation space of RNA

RNAs are inherently dynamic biomolecules and undergo conformational changes in response to a diverse set of cellular signals and environmental cues, such as recognition of proteins, nucleic acids, and metabolites, changes in physiochemical conditions, chemical reactions, and thermal and mechanical triggers [63^••,64]. RNA conformational changes occur through complex and often multilayered motions at different temporal and spatial scales. These changes can be rapid, local, small-scale atomic fluctuations around an average structure, or involve slow, global, large-scale rearrangements of molecular machinery [64]. Such motions are not random; they are linked to the topological constraints encoded at the secondary structural level, dominated, if not fully determined, by intra- and intermolecular interactions, which in turn depend on the three-dimensional structure [30^••]. RNA dynamics form the basis for the functional complexity of a vast universe of non-coding RNAs performing regulation and guide roles in multiple cellular processes [63^••], as witnessed in the past two decades [65]. Detailed characterization of the structural-dynamical properties of RNAs is crucial for a deeper understanding of their wide variety of functions and in rational RNA-targeted drug design [66].

The number of potential conformers in which a structured RNA molecule such as RRE may exist can be very large. This is made possible in part by structural features such as bulges, internal loops and junctions that serve as pivot points of flexibility [63^••,67^••]. Not only may multiple conformations coexist, but they may also change with time [68,69]. Therefore, a description of large RNAs with a single conformation may not be sufficient for understanding their behavior. Furthermore, for cases in which a large number of RNA conformations exists, consideration of each of them individually would be a task of scope beyond all possibility of realization, given such potentially large conformation space. This brings us at once to the necessity of adopting a statistical point of view.

When characterizing a heterogeneous and flexible system using experimental observables such as SAXS, the simplest approach is to use the SAXS-restrained ensemble of structures, where the scattering intensity is calculated as

$$I(q)=\sum _i{w}_i{I}_i(q)$$

Where w_i is the weight of ensemble member i, taken as 1/N_e here, and I_i(q) is the contribution to the scattering intensity from ensemble member i. If the surface-bound solvent contribution is omitted, the I_i(q) of an individual member i can be calculated using the Debye formula [70]:

$$I_i(q)=\sum _j^n\sum _k^n{f}_j(q)f_k(q)\frac{\text{sin}(q{r}_{jk})}{q{r}_{jk}}$$

where n is the number of atoms in the molecule, f_j(q) and f_k(q) are the form factors for atoms j and k, respectively, q is the momentum transfer and r_jk is the distance between atoms j and k. There are three computation programs that calculate conformation space using SAXS data [71^•,72^••,73^••]. In the Xplor-NIH, simulated annealing under restraints of various pseudo-potential functions, including a nucleic-acid database function, is used to calculate ensembles that best fit experimental SAXS data. The population weights can be set equal or different for conformation subsets [71^•]. The program was first applied to sample the conformation space of a Dickenson DNA dodecamer [71^•] and later applied to characterize the conformation space of the HIV-1 RRE RNA [52^••]. The Ensemble Optimization Method (EOM) [72^••] uses a metaheuristic algorithm to search for ensembles that best fit experimental data [74^••,75,76^•,77]. The Minimal Ensemble Search (MES) uses a high-temperature molecular dynamics (MD) simulation to search conformation space by a genetic algorithm [73^••,77]. In all of these methods, duplexes are considered rigid, whereas linkers, junctions, and loops serve as pivot points of flexibility [31,63^••]. Using the ensemble approach, Pérard et al. found that collective motions dominate the flexibility of the full-length internal ribosome entry site (IRES) of the hepatitis C virus genome, suggesting that a large-scale conformation change could take place when forming the initiation complex [76^•] (Figure 6). In the case of RNase P, the crystal structure of the free RNA in the RNase P is significantly different from that observed in the ternary complex, and the RNase P RNA in solution can only be described by an ensemble of four conformations that could best fit SAXS data (Figure 6) [75].

Figure 6.

Characterizing RNA conformation space using SAXS. (a) SAXS-filtered MD-simulated ensemble of the HCV IRES RNA [76^•]. An ensemble of five can best fit the experimental SAXS data; (b) In the case of RNase P it requires an ensemble of three to best fit experimental SAXS data [75]; (c) SAXS-filtered ensembles of models generated using a nucleic acid simulation tool (NAST) [95].

With the exception of rRNAs in ribosomes, overall structures or molecular shapes of kilobase-sized RNAs are relatively unknown, and it is of a great interest to demonstrate if those kilo-base sized RNA transcripts are largely linear—like what we often see conceptually in biologists’ presentations—or form complex 3D folds. A recent study by Gupal et al. [74^••] investigated the global folds of three large RNA transcripts (975-, 1523- and 2777-nt long) under two different buffer conditions: Tris-EDTA or an assembly buffer that contained Mg²⁺. Using SAXS, together with cryo-EM and the ensemble MD calculations, they showed: (1) under neither condition are the RNAs linear; and (2) Mg²⁺ promotes folding of the RNAs into a prolate geometry [74^••] (Figure 6). This study provides the first peek into the global three-dimensional shapes of kilobase-long RNA transcripts.

Practical considerations for RNA sample preparation

RNA molecules exhibit some unique behavior in solution. Thus it is informative to provide a more detailed account regarding RNA sample preparation for SAXS experiments. The first consideration is sample homogeneity. Typically, RNA samples used for SAXS experiments are usually produced using in vitro transcription by the T7 polymerase, purified by polyacrylamide gel electrophoresis (PAGE) under denaturing conditions, and then refolded. While this purification method works for small RNAs with simple structural elements (e.g., a single hairpin), larger RNAs with more complex folds often cannot be refolded into their native states once they have been denatured. This is true for the RRE RNA, where the refolded RNA under various folding conditions exhibits multiple bands on a native gel [52^••]. Such a sample containing a mixture of conformers may complicate SAXS data analysis and interpretation. Whenever possible, purification using size exclusion chromatography under a native condition is highly recommended.

Another important consideration is buffer selection and background subtraction. While phosphate buffer systems are convenient for NMR spectroscopy because they generate no proton NMR signals, these buffers should be avoided in SAXS experiments due to high background scattering and the promotion of free-radical formation. Organic buffer systems (e.g., Tris, HEPES), on the other hand, are highly recommended because they contribute very little to background scattering and also serve as radical scavengers to reduce radiation damage.

One critical aspect of processing SAXS data is the subtraction of the background scattering produced by the solvent. As water itself is a scatter of X-rays, SAXS of very dilute biomacromolecules is detected against a very strong background of water. The scattering profile for the biomacromolecule can then be calculated using the equation below:

$${\mathrm{I}}^{\text{solute}}(q)={\mathrm{I}}^{\text{sample}}(q)-\alpha {\mathrm{I}}^{\text{buffer}}(q)$$

For this reason, it is critical that the buffer used to measure the background scattering exactly matches that of the sample. In our experiments, first the wide angle X-ray scattering (WAXS) profile was obtained using the above equation and tuning the value of α to eliminate the water peak around 2.0 AÅ⁻¹. Then, the resulting WAXS profile was used as a guide for the SAXS background subtraction by tuning the value of α in the SAXS subtraction and overlaying the resulting SAXS profile with the WAXS profile at the overlapping q range (i.e., 0.1-0.28 Å⁻¹). The final scattering data were obtained by piecing the resulting SAXS and WAXS profiles together to achieve scattering q values of 0.006 < q < 2.3Å⁻¹ [41,60,62].

Lastly, RNAs are heavily charged polyanions and strongly interact with cations, water molecules, and sometimes anions (including themselves), repulsively or attractively, depending on the ionic conditions and types of counter ions in solution [62,78^••]. The interactions among macromolecules are referred to as the structure factor, s(q), and may have an effect on the quality of the SAXS data and skew interpretation. More specifically, s(q) is the ratio of the scattering under a given condition relative to that under an “ideal” condition, where the macromolecules do not interact with each other (i.e., monodispersed) (Figure 7) [79,80]. A non-uniform structure factor leads to non-linearity in the Guinier region. A linear plot in the Guinier region is critical for extracting accurate dimension- and mass-related information, such as R_g and molecular weight. In the absence of interactions, s(q)=1; when attractive interactions exist that cause aggregation (Figure 7), s(q) > 1 at q close to 0; and when repulsive interactions exist, s(q) < 1 at q close to 0 (Figure 7 ).

Figure 7.

(a) A curve-up scattering profile of RNA, indicative of high order aggregation; (b) A curve-down scattering profile, indicative of repulsive interaction among RNA molecules in low-salt conditions [62].

Commonly used software tools

The wide application of SAXS for characterizing biological molecules is not possible without a suite of indispensable software tools. The tools were originally developed for proteins and protein complexes but are largely applicable for RNA and RNA containing complexes as well. In this section, we provide a brief review of computation software tools and packages that are commonly used.

Software Primus [81], developed by Svergun’s group in early 2000, is widely used for data averaging and for extracting R_g and I₀ at the initial stage of SAXS data processing and analysis. Often, one can also accomplish the same task by programming using a commercial program package Igor Pro (Wavemetrics, Lake Oswego, OR, USA). For extracting some basic structural parameters from SAXS data, such as pair-distance-distribution-function (PDDF), maximum dimension (D_max) as well as R_g, the program GNOM is widely used [7]. Two programs on web-based servers, SAXS MoW (http://www.if.sc.usp.br/~saxs/) and Scatter (http://www.bioisis.net/tutorial), have been used to calculate molecular weights. Programs and packages DAMMINDI [6^••], DAMMIF [8^•] and MOSA [6^••] are widely used for ab initio shape reconstruction. Programs BUNCH, SASREF and CORAL in the ATSAS package [82] or Xplor-NIH [83] are widely used for rigid body modeling using SAXS. Programs of the EOM [72], MES [73] methods and Xplor-NIH are widely used for ensemble calculations to characterize RNA conformation space using SAXS data. The latter can also take combined data of both NMR measurements and SAXS to calculate ensembles [52^••,71^•] or to refine structures [37^•,41^•,56^•,60]. Often, coordinates of a structure are known, and one needs to compare the SAXS profile of the structure with the experimentally measured SAXS profile of the same molecule. Programs CRYSOL [84], FoXS [85] and Xplor-NIH are widely used for that purpose. The latter two can also accurately calculate the profile of wide-angle X-ray scattering (WAXS).

Conclusions and outlook

Our understanding of the roles of RNA in cellular processes has undergone a tremendous expansion over the past two decades. In contrast, our knowledge about RNA 3D structures and structure-function relationships is still very limited. Significant progress has been made, such as mapping the secondary structure of the entire HIV-1 genomic RNA, which is similar to rRNA in size. However, the “gap” between RNA secondary and tertiary structures is enormous. SAXS has become an ideal tool to bridge this gap, as has been illustrated in this review. As synchrotron beams become more accessible to users, and with sensitive in-house scattering instruments now commercially available, we expect a much broader application of SAXS in RNA structural biology. Besides what has been discussed in this review, the future directions of applying SAXS to RNA research may include: 1) time-resolved SAXS to study dynamics of RNA folding and conformation space [86^•,87-89], 2) studying RNA-protein complexes [90-92] and 3) determining 3D topological structures of large RNAs using RNA secondary structures and SAXS data as input. The latter is feasible since RNA secondary structure encodes 3D structure and folding pathway [30^••,31]. With global shape restraints and a few long-range contacts, topological structures of RNA may be computed.

The rapid development of X-ray free electron laser (XFEL) technology and its applications may revolutionize biological research, including RNA structural biology [93^••]. An XFEL beam is approximately one billion times brighter than the latest third-generation synchrotron sources, and pulses on a femtosecond time-scale. The time-resolved “snap shot” SAXS using XFEL has been demonstrated in a protein case to observe molecular motions on a much shorter time scale [94^••]. In particular, on the femtosecond time scale, any events that occur at the diffusion limit, ~10⁻⁹ sec., is steady still. Even photosynthesis processes that occur at a sub-picosecond time scale can be captured. Thus, the brilliance of XFEL and its femtosecond time frame potentially make it possible to image a single molecule in action (true molecular movies) in the very near future.

Highlights.

• SAXS is used to determine global topological structures of RNA

• SAXS is used to study structure-function relationship of RNA

• SAXS is used to study conformation space of RNA