The folding of RNA species into complex secondary and tertiary structures is central to RNA's catalytic, regulatory, and information-carrying roles ¹. Pioneering approaches for elucidating RNA structure—including crystallography², electron microscopy³, and spectroscopy⁴—are technically complex and difficult to scale, motivating the development of computational algorithms for RNA structure prediction^5–7. Current algorithms have limited predictive power, particularly for long-range interactions such as pseudoknots (secondary structures involving intercalated stem loops).With the advent of massively parallel sequencing⁸, less laborious experimental techniques have been developed for the global interrogation of RNA secondary structures. These include methods relying on structure-specific chemical modifications^9–11, such as DMS-seq and SHAPE-seq, as well as methods involving digestion with structure-specific RNases^12–14, like PARS-seq and Frag-seq. Although these methods probe the extent to which individual bases participate in secondary structures, they do not directly query which specific pairs of bases or regions interact to form these structures. To address this, recent efforts have combined systematic mutagenesis and structure-specific probing to generate pairwise information for inferring RNA folds^15,16. However, despite considerable progress, the high-throughput determination of RNA secondary and tertiary structures remains a challenging problem.

Here we show that proximity ligation is a straightforward means of generating global pairwise data about RNA secondary and tertiary structure. Proximity ligation records the physical proximity of two nucleic acid termini through their ligation, and has been applied to detect DNA aptamer-bound proteins¹⁷, to probe protein-protein interactions via antibody-bound oligonucleotides¹⁸, and for targeted or global chromosome conformation capture (3C)^19,20. Proximity ligation has also been applied in conjunction with crosslinking and either affinity purification or immunoprecipitation to characterize snoRNA-rRNA interactions²¹ and Ago-mediated miRNA-target interactions²². However, these efforts have primarily focused on assessing specific trans interactions, rely on low-efficiency 254 nanometer UV crosslinking, and require time-consuming purification steps.

RPL (‘ripple’) globally assesses which pairs of regions are interacting to form intramolecular RNA structure (Fig. 1).Similar to 3C methods for DNA conformation, RPL uses digestion and re-ligation of RNA, but omits crosslinking, relying instead on the inherent spatial proximity of RNA nucleobases in secondary structural features (i.e. stem-loops). To generate RPL libraries, we performed RNase digestion in situ (or, for yeast, took advantage of endogenous single-stranded RNases), followed by treatment with exogenous T4 RNA Ligase I under non-denaturing conditions. These steps result in chimeric molecules formed from RNA strands intra-molecularly ligating across digested loops (Fig. 1a, inset). By deeply sequencing these resulting fragments and quantifying the relative abundance of specific intramolecular ligation junctions, we are able to create pairwise contact maps that reflect the short- and long-range stem-loop and pseudoknot interactions of intramolecular RNA secondary structures.

First we tested RPL in the budding yeast S. cerevisiae. To create libraries, we spheroplasted whole yeast cells for 1 h with zymolyase (dissolved in 1X PBS without DTT to allow endogenous RNases to remain active). We then treated the resulting slurries with T4 polynucleotide kinase (PNK) to convert 5′-hydroxyl to 5′-phosphate termini, and diluted and incubated these mixtures overnight in the presence of a single-stranded RNA ligase (T4 RNA Ligase I) under non-denaturing conditions. We then purified total RNA using acid guanidinium-phenol, and carried out a standard RNA-seq library preparation. Sequencing (Illumina) yielded 304 million (M) concatenated reads for a (+) ligase sample, and 342M concatenated reads for a (−) ligase control sample (Methods).

To identify candidate ligation junctions in these sequencing reads, we adapted an algorithm for identifying novel RNA isoforms from RNA-seq data²³, relaxing constraints on splice-site composition to more generally recognize intramolecular chimeric reads that map discontinuously to a single RNA sequence (Methods). To quantify the enrichment of candidate ligations in our samples, we first examined the distribution of spanned distances of intramolecular chimeric reads (i.e. gap sizes), per million reads, in both (+) and (−) ligase samples. Although the overall fraction of reads corresponding to candidate intramolecular ligation junctions is low, the (+) ligase sample is enriched for these across a broad range of spanned distances (0.28% in (+) ligase sample vs. 0.011% in (−) ligase sample; Supplementary Fig. 1).

Potential sources of technical artifacts in these data include the formation of chimeric molecules by reverse transcriptase (RT) template switching, systematic mapping artifacts, PCR-mediated duplicates and non-specific ligation events. To reduce the impact of RT template switching, we discarded candidate ligation junctions with >5 nucleotides (nt) microhomology, as well as those mapping to opposite strands. To remove PCR-mediated duplicates, we collapsed all reads with identical mapping coordinates and CIGAR alignment strings. To reduce the impact of systematic mapping artifacts caused by errors within our reference transcriptome (for example, gross deletions, un-annotated splice junctions), we conservatively discarded candidate ligation junctions containing the highest 1% of ligation counts, for each RNA species analyzed. Finally, to quantify the extent of nonspecific ligation, we performed an experiment in duplicate wherein human cells were taken through a modified version of the RPL protocol (Methods) and spiked into yeast slurries immediately before proximity ligation. The resulting data demonstrate marked enrichment for intraspecies, intramolecular chimeric reads (Supplementary Fig. 2).

We first analyzed RPL data in the context of the complex but extensively validated secondary structures of the yeast ribosomal RNAs (rRNAs). The yeast ribosome is comprised of the 60S large subunit (LSU), which includes the 3.4 kb 25S rRNA and short 5.8S and 5S rRNAs, and the 40S small subunit (SSU), which includes the 1.8 kb 18S rRNA. To assess whether RPL captures the proximity implied by secondary structure base-pairing, we tallied candidate ligation junctions in a 500 base-pair window centered on known base pairs of the established rRNA structures, effectively quantifying ligation probability as a function of distance (in linear sequence) from known base pairs (in secondary structure). We observe an enrichment of candidate ligation junctions immediately proximal (i.e. within 10 nt) to known base pairs in both the 5.8S/25S rRNAs (~9-fold; Fig. 1b) and 18S rRNA (~6-fold; Fig. 1c). Furthermore, in the case of the 5.8S/25S rRNAs, which contain many long-range base-pairing interactions, this enrichment is maintained even if we restrict analysis to candidate ligation junctions that span >100 bases in the linear sequence (Supplementary Fig. 3).

The observed signal is entirely dependent on the inclusion of ligase, and is not explained by sequencing errors, mapping artifacts or by proximity in sequence space (as opposed to structure space). As such, we conclude that it primarily derives from intramolecular ligation events between structurally proximal bases. Nonetheless, the signal shown in Fig. 1b,c is “noise-averaged” over all base pairs in these rRNA structures. Consistent with the stochastic nature of individual ligation events, we observe weaker enrichment when repeating our analysis with a randomly selected subset of 10, 25, or 50 paired bases in either the LSU or SSU rRNAs (Supplementary Fig. 4). The ligation junctions that we observe are also clearly affected by other biases, including the bias against G/C extremes routinely seen with Illumina sequencing, as well as more subtle base composition preferences at the ligation junction (Supplementary Fig. 5). We also observe that ligation junctions are enriched for single-stranded bases in the LSU and SSU rRNAs (Odds Ratio (OR) = 2.24; P < 2.2E-16, Fisher's Exact Test). This bias, and the noisiness of the raw data, is evident when ligation junctions are overlaid onto a known secondary structure (Fig. 2a).

Given these observations, we concluded that the signal of RPL likely arises from the combinatorial digestion and ligation of predominantly unpaired ribonucleotides across broken loop structures. Considering this, along with the stochastic, biased nature of individual ligation events, we speculated that our ability to resolve secondary structure would improve by calculating the frequency of ligation events between pairs of sliding windows (21 nt each), effectively capturing a combinatorial diversity of ligation events surrounding secondary structural elements. Concurrent with this, we adapted normalization methods developed for Hi-C matrices²⁴ to account for other one-dimensional biases (for example, sequence biases of RNA ligase and PCR) (Methods). We then visualized these normalized RPL scores, calculated for pairwise windows, by directly overlaying them onto known secondary structures. RPL scores broadly mirror the secondary structures of the 5.8S/25S LSU rRNAs (Fig. 1d, Fig. 2b; Supplementary Fig. 6a) as well as the SSU 18S rRNA (Supplementary Fig. 6b). Furthermore, we observe signal corresponding to distal tertiary structures, including long-range “pseudo-knots” in the LSU rRNAs (Fig. 1d, right inset)²⁵.

We next sought to evaluate the correspondence between proximity ligation events and the structures of non-ribosomal RNA transcripts. Because we are limited by sampling depth, we focused on well-characterized, abundant RNAs; specifically, the snoRNA snR86 (Fig. 3a), which guides uridylation of the LSU rRNA, the U1 spliceosomal RNA (snR19) (Fig. 3b), the RNA component of the signal recognition particle (SCR1) (Fig. 3c), and the U2 spliceosomal RNA homolog (LSR1) (Supplementary Fig. 7). In “contact probability maps” for these RNAs (based on the normalized RPL scores described above), we observe a striking anti-diagonal pattern, reminiscent of signal observed at known stems in the 5.8S/25S and 18S rRNAs. When comparing our contact probability maps to secondary structure predictions generated with INFERNAL²⁶ using covariance models taken from Rfam²⁷, our observations are consistent with conserved stems in both snR86 and snR19 (Fig. 3a,b). In RPL measurements for snR19, we also observed signal indicative of stem formation in the region comprising bases 320-510—MFE predictions suggest that this region can form a helix, raising the possibility that this structure is present endogenously.

We also analyzed RPL measurements in the context of a non-ribosomal RNA with a solved structure, the RNA subunit of the signal recognition particle (SCR1). Again, we observed broad agreement between RPL scores and regions containing paired bases (Fig. 3c), though we do find that certain expected long-range interactions (for example, folding between the molecule termini) are not seen. Further work will be needed to determine whether this is simply an artifact of insufficient depth-of-coverage, or is symptomatic of some other bias with respect to the classes of structural elements that proximity ligation can resolve.

Finally, our observations for LSR1 (Supplementary Fig. 7) are consistent with previous work employing cross-linking, affinity-purification, and proximity ligation of RNA²¹, which found ligation products supporting stem-formation between the two termini. In agreement with this cross-linking based approach, our data support the formation of both proximal (for example, stem formation at bases 1100 – 1150), and distal folds.

We next explored the value of RPL scores as a predictive tool for classifying pairs of interacting regions within a structured RNA. To show that RPL scores can be used in this manner, we examined their positive predictive value (PPV) at varying quantile thresholds for the gold-standard 5.8S/25S and 18S rRNAs (Fig. 4a,b). This is a challenging classification problem (92,392 true positive interacting windows out of 6,317,235 possible interacting windows for the LSU rRNAs (1.5%); 41,981 true positive interacting windows out of 1,620,900 possible interacting windows for the SSU rRNA (2.6%)). The highest RPL scores are strongly enriched for true positive interacting windows (LSU rRNA: PPV of 54% using the top 1% of RPL scores; SSU rRNA: PPV of 61% using the top 1% of RPL scores). Plotting PPV as a function of threshold illustrates the tradeoff with sensitivity (Fig. 4c,d). For example, at a sensitivity of 50%, RPL scores have a PPV of 43% for the LSU rRNA and 27% for the SSU rRNA, for predicting structurally interacting pairs of regions.

The high-throughput, unbiased identification of intermolecular RNA-RNA interactions is of strong interest in the RNA biology field. Recent work has shown that psoralen-mediated crosslinking may be used in tandem with anti-sense purification to capture trans RNA-RNA interactions²⁸. In principle, RPL should be able to provide complementary information, as interacting RNAs may form ligation products at a higher rate than non-interacting RNAs. Although we observed a modest enrichment for intermolecular yeast ligation junctions in the species mixing experiment (Supplementary Fig. 2), this enrichment in our yeast RPL experiment derives primarily from ligation products between the small and large ribosomal subunits (Supplementary Fig. 8). While no inter-subunit RPL scores approached those of strongly interacting intramolecular windows, it remains possible that a combination of methodological improvements to reduce background and deeper sequencing of RPL libraries may enable global surveys of trans RNA-RNA interactions (for example, the signal recognition particle-ribosome interaction; subunit interactions in the translating ribosome).

We next sought to adapt RPL to generate secondary structure information corresponding to RNAs in human cells. Most notably, we replaced the zymolyase treatment with a limited in situ digestion with exogenous single-stranded RNases A and T1. In analyzing the resulting data in the context of the well-studied human ribosomal RNAs, we again observed correlation of high RPL scores with known interacting regions (Supplementary Fig. 9). However, an RNase (−), ligase (−) control also demonstrated signal that correlated with secondary structure, albeit much more weakly and possibly reflecting endogenous nuclease and ligase activity (Supplementary Fig. 10). The possibility that endogenous enzymatic activity may contribute to the formation of chimeric RNAs is not novel; recent work using a cross-linking approach to characterize the miRNA interactome of C. elegans curiously found that expected ligation products could form in the absence of exogenous T4 RNA Ligase I²⁹.

We anticipate several directions for improving RPL. First, RPL libraries require deep sequencing to reliably map interacting regions, even for highly abundant RNA species. The sufficient sampling of lower-abundance RNA species of interest (for example, mRNAs) might be achieved by optimizing the enzymatic steps of the protocol, by adopting hybrid capture enrichment or subtraction, or simply by brute force deep sequencing.

Second, given the high predictive value^9,15,16,30 of in vivo structure probing methods (for example, DMS-seq, SHAPE-seq) in determining the pairedness of individual bases in secondary structures, a framework that integrates two-dimensional, lower-resolution RPL data with one-dimensional, higher-resolution structure probing data seems highly attractive. Ideally, computational predictions would be integrated at the same time, thereby taking advantage of three largely orthogonal approaches to maximize the accuracy of RNA structural predictions.

The current repertoire of high-throughput empirical assays for RNA secondary structure provides us with a deep, but ultimately one-dimensional window into the structural landscape of RNA molecules. In contrast, RPL globally captures information with respect to pairwise interactions within RNA secondary structures. Through its integration with complementary computational and experimental approaches, we anticipate that RPL will facilitate the high-throughput elucidation of RNA secondary structures in diverse organisms.