Probing-directed identification of novel structured RNAs

ABSTRACT

Transcripts often harbor RNA elements, which regulate cell processes co- or post-transcriptionally. The functions of many regulatory RNA elements depend on their structure, thus it is important to determine the structure as well as to scan genomes for structured elements. State of the art ab initio approaches to predict structured RNAs rely on DNA sequence analysis. They use 2 major types of information inferred from a sequence: thermodynamic stability of an RNA structure and evolutionary footprints of base-pair interactions. In recent years, chemical probing of RNA has arisen as an alternative source of structural information. RNA probing experiments detect positions accessible to specific types of chemicals or enzymes indicating their propensity to be in a paired or unpaired state. There exist several strategies to integrate probing data into RNA secondary structure prediction algorithms that substantially improve the prediction quality. However, whether and how probing data could contribute to detection of structured RNAs remains an open question. We previously developed the energy-based approach RNASurface to detect locally optimal structured RNA elements. Here, we integrate probing data into the RNASurface energy model using a general framework. We show that the use of experimental data allows for better discrimination of ncRNAs from other transcripts. Application of RNASurface to genome-wide analysis of the human transcriptome with PARS data identifies previously undetectable segments, with evidence of functionality for some of them.

Introduction

RNAs perform diverse functions and are typically produced as single-stranded molecules, which fold intra-molecularly to form base-paired stem structures. Flood of novel classes of non-coding RNAs with well-defined secondary structure poses the problem of de novo identification of structured RNAs in long sequences.¹ Comparative methods are suitable to detect functional secondary structure,^2,3 as they detect evolutionary pressure on the secondary structure,⁴ or generate covariance models.⁵ But a suitable set of homologous sequences with moderate sequence divergence and sufficient number of compensatory substitutions is often not available. In these cases, we have to deal with single RNA sequences. High stability of secondary structure is an important feature of structured RNAs and could be inferred from sequence alone. Albeit this signal is not sufficient for a genome-wide screen,⁶ functional RNA elements have substantially lower free energy compared to genomic background or random control.⁷

We have recently developed the RNASurface approach to scan long sequences for structured RNA elements.⁸ The RNA world is made of a variety of functional RNAs, from small hairpins to complicated multidomain structures (e.g. T-boxes). Thus, the size of putative regulatory RNA elements may vary from tens to hundreds of nucleotides and their boundaries may remain unknown. As a consequence, sliding-window procedures estimate either structured RNA with genomic flanks, or only a part of the structure, yielding significant loss of the detection power.⁹ We suggested an alternative approach to infer segments of the optimal size and location. Our RNASurface algorithm efficiently estimates the strength of secondary structure (Z-score) of each segment in a RNA sequence and detects segments with a locally-optimal Z-score.⁸ This approach does not lose any structured segment, while still retaining specificity comparable to that of the sliding-window approaches (Fig. 1).

Figure 1.

Overview of the RNASurface approach. For each segment of RNA sequence up to a predefined size RNASurface effectively determines the Z-score and selects locally optimal segments with the Z-score below threshold. The heatmap visualizes Z-scores: each dot corresponds to a segment with the color reflecting its Z-score. Local peaks of the heatmap correspond to locally optimal structured segments.

Chemical probing of RNA is an alternative source of structural information. RNA footprinting detects positions accessible to specific types of attack by chemical reagents or nucleases and thus reveals which nucleotides tend to be in a double-stranded helix and which nucleotides tend to form unpaired loops. For example, SHAPE reagents (1M7 or NMIA) acylate the 2′ hydroxyl group of the ribose, reacting much more readily where the backbone is flexible, hence single-stranded, than where it is rigid, or Watson–Crick base-paired. This is thought to be because unconstrained nucleotides more often display rare conformations that enhance the nucleophilicity of the 2′ hydroxy group.¹⁰ First genome-scale experimental methodology for profiling of RNA structures, parallel analysis of RNA structure (PARS), relied on enzymes and was used to characterize the entire yeast transcriptome in vitro.¹¹ In this strategy deep-sequencing reads of double- or single-stranded regions of RNAs generated by RNase V1 and S1 nuclease, respectively, are compared. To date, genome-scale experiments with different methodologies were performed in yeast,¹¹ Arabidopsis,¹² human,^13,14 and mouse.¹⁵ The SHAPE-seq method can be potentially applied genome-wide but now data is available only for a limited number of RNA sequences.¹⁶

The information obtained in a typical RNA secondary structure probing experiment is the reactivity at each site. Reactivity captures complex properties of an RNA molecule and is correlated with paired/unpaired status of a nucleotide.¹⁷ Depending on an experiment, this correlation may be further blurred by noise in the data. Nevertheless, the experimentally determined reactivities contain information about propensity of a specific site to be paired. The reactivities can then be combined with a thermodynamic model of RNA folding to predict the optimal secondary structure.^18,19 An efficient way to do this is to transform reactivities into a pseudo-energy term of the RNA free energy model. It was also recently shown that incorporation of RNA probing data into ncRNA homology search allows one to improve the accuracy and efficiency of the latter.²⁰

More importantly, the emergence of whole-genome RNA probing data provides an opportunity not only to determine secondary structure of a single, given RNA molecule but to expand pipelines for genome-wide search for structured RNA elements. Here we present an extended version of the RNASurface algorithm that allows for incorporation of high-throughput RNA probing data of different sources into the computational pipeline to increase the signal/noise rate of detection of structured RNAs. The algorithm takes data of any source and transforms it into likelihood scores that reflect reactivity information content of paired/unpaired state of the nucleotide. We show that incorporation of probing data from SHAPE²¹ and PARS¹³ experiments significantly increases the power to discriminate functional structural RNAs from the genomic background.

Results

Computational pipeline to detect structured RNAs based on thermodynamic stability and probing data

We incorporate RNA probing data into the RNASurface computational pipeline to scan sequences for structured elements. The pipeline predicts structured RNA segments from raw probing data and sequence in several steps (Fig. 2). First, experimental reactivities that have a limited ability to distinguish paired and unpaired bases are transformed into likelihood scores that reflect the probabilistic information about the RNA structure on the basis of reactivities. Transformation of reactivities to unambiguous probabilistic scores allows incorporation of various sources of probing data. Next, we incorporate these likelihood scores as soft constraints into the RNASurface energy model. Finally, we estimate the statistical significance of RNA secondary structures (Z-score) using a novel approach and detect locally optimal structured RNAs. In order to analyze different sources of probing data, throughout the paper we apply the pipeline to chemical-based SHAPE data²¹ and genome-scale enzyme-based PARS data.¹³

Figure 2.

RNASurface pipeline overview. Raw data from probing experiment is processed and then incorporated into the RNASurface energy model as soft constraints. RNASurface estimates the statistical significance of secondary structures and detects locally optimal structured RNAs.

The likelihood approach allows one to derive probabilistic information from probing experiments

High-throughput RNA structure profiling technologies provide quantitative information on RNA pairing at a nucleotide resolution. This information is reflected in different reactivity distributions of base-paired and unpaired residues, as exemplified for sets of functional structured RNAs with the reference base status inferred from phylogenetic secondary structure (Figs. 3a and d; S1 Fig). To estimate the uncertainty of the base status in experiments, we analyze how accurately reactivity cutoff uncovers paired and unpaired bases.

Figure 3.

Properties of reactivities and their transformation to likelihood ratios. a. Distributions of SHAPE values observed for paired and unpaired nucleotides in a test SHAPE set (3 riboswitches, 5S rRNA and tRNA). b, ROC curve for the test set, SHAPE data. c. Paired/unpaired likelihood ratios: from the 2 fitted distributions in (a). Paired nucleotides are either inferred from phylogenetic secondary structures or determined by the RNAplfold program. d. Distributions of PARS values observed for paired and unpaired nucleotides in the test PARS set (4 classes of ncRNAs). e, ROC curve for test, PARS data. f. Paired/unpaired likelihood ratios from the 2 fitted distributions in (d). Paired nucleotides are either inferred from phylogenetic secondary structures or determined by the RNAplfold program.

ROC curves demonstrate that dividing bases into paired and unpaired on the basis on an arbitrary cutoff results in a moderate precision of structure determination for some classes of RNA (Figs. 3b and e). The accuracy measured by the area under the ROC curve (AUC) varies from 0.89 to 0.59 for SHAPE data, and from 0.72 to 0.48 for PARS data, suggesting that a cutoff on reactivity would be insufficient to distinguish paired and unpaired bases for all RNA classes. Possible explanation of the moderate prediction quality is that probing experiments measure more complex properties of RNA molecules, or noisy reality of experimental data, and thus reactivity only indirectly informs about paired/unpaired state of a nucleotide. We also note that the SHAPE method is substantially more accurate in general and this finding is consistent with nucleases providing lower resolution²² and possible non-uniform quality of PARS data. Probability to observe reactivity ${\displaystyle r}$ in a probing experiment is ${\displaystyle P(r|paired)}$ if nucleotide is paired and ${\displaystyle P(r|unpaired)}$ if nucleotide is unpaired. Probabilities ${\displaystyle P(r|paired)}$ and ${\displaystyle P(r|unpaired)}$ are specific for each probing experiment (Figs. 3a and d) and reflect its ability to discriminate between paired/unpaired bases. The simplest way to find ${\displaystyle P(r|paired) }$ and ${\displaystyle P(r|unpaired)}$ is to use the reactivity distributions of paired and unpaired bases of known structured RNAs (Figs. 3c and f). Information content of reactivity ${\displaystyle r}$ about structural properties of a nucleotide can be inferred as likelihood score of observed reactivity for nucleotide in paired compared to unpaired status

$${\displaystyle L\left(r\right)=log\frac{P(r|paired)}{P(r|unpaired)}}$$

This approach provides an opportunity to extract probabilistic information ${\displaystyle L\left(r\right)}$ of reactivity r from any source of data.²³ In practice, RNAs with known secondary structure could be unavailable for probing experiment. To overcome this limitation, nucleotides with high-confidence McCaskill probabilities may be used as a surrogate of real interactions. High base-pairing probabilities of partition function confidently predict interactions in diverse structured RNAs.²⁴ Therefore we estimate ${\displaystyle P(r|unpaired)}$ and ${\displaystyle P(r|paired)}$ using a high-confidence set of paired and unpaired bases predicted from the partition function. Replacement of known paired/unpaired bases by predicted ones in our examples on test ncRNAs shows only minor changes of paired/unpaired ratio curve (Figs. 3c and f), indicating validity of the replacement.

Extended thermodynamic model

Early “hard-constraints” methods predicted RNA secondary structure by constraining bases with evidence of chemical reactivity.²⁵ Moderate quality of base status prediction by thresholding log-ratio L (Figs. 3c and f) prompts us to use the recently developed “soft-constraints” approach.^18,26 Briefly, we assign to each base pair pseudo-energy term ${\displaystyle \Delta G_{ij}^{\prime }}$ that reflects its likelihood with respect to the probing data:

$${\displaystyle \Delta G_{ij}^{\text{'}}=RT\cdot \left(L_i+L_j\right),}$$

where ${\displaystyle L_i}$ represents the probing log-likelihood to observe reactivity in paired compared to unpaired state for position i in the RNA sequence.

The pseudo-energy term is added to the energy contribution of stacking interactions in the Zuker algorithm of optimal RNA folding, implemented in the core of RNASurface (Fig. 2, Energy model). Pseudo-MFE reflects tradeoff between thermodynamic stability of RNA molecule and its consistency with probing data. This energy model does not take into consideration pseudoknots that can lead to misinterpretation of probing data and relevant features of RNA molecule. On the other hand, model of “nested” secondary structures reflects main properties of RNA molecule,²⁷ allows time-efficient genome-wide analysis²⁸ and still distinguishes structured RNAs from other transcripts.⁷

Novel background model allows to discriminate structured RNAs from others

The Z-score of a sequence estimate deviation of a minimum free energy (MFE) from expected values of random sequences. The widely-used background model generating random sequences is well established and preserves the length and dinucleotide content,²⁹ although more sophisticated models exist depending of the context.³⁰ Incorporation of probing data modifies MFE (pseudo-MFE) and yields the problem of correct estimation of significance of pseudo-MFE. This requires simulating both sequence and probing data simultaneously. Here we use transcriptome-wide PARS data to construct and analyze background model of pseudo-MFE. To calculate pseudo-MFE we used likelihood scores inferred from high-confidence base pairs of functional RNAs (Fig. 3f). As attempts to shuffle the data did not result in an adequate background model, presumably because of the complex nature of probing data (Suppl. Discussion, S2 Fig), we construct background by sampling fragments from transcriptome, which contain low fraction of functional RNA elements. To this end, fragments of mRNA highly expressed in PARS were selected as a sample with low fraction of functional RNA elements. In this case background distribution contains pseudo-MFEs for fragments that are rarely functionally highly structured or unstructured and this reflects expected amount of formed structure under certain experimental conditions. We note that pseudo-MFE depends approximately linearly on MFE for randomly sampled segments of the human transcriptome and functional RNAs (Fig. 4a). Energy contribution of probing data to pseudo-MFE reflects its consistency with some stable structure. The majority of segments do not possess unique functional secondary structure, thus the linear term captures the background contribution of the structural ensemble reflected in probing data. Strong deviation of pseudo-MFE from the linear trend reflects non-random contribution of the experimental data. To capture this deviation, the energy is substituted by its linear approximation of the probing energy in the Z-score estimation (S3 Fig). Low probing-Z-scores reflect segments that are thermodynamically stable and consistent with probing data.

Figure 4.

Probing-Z-score of pseudo-MFE compared to Z-score of MFE for different classes of human ncRNAs and random segments of transcripts with the same length distribution. a. Pseudo-MFE depends approximately linearly on MFE and coverage. The coverage is defined as a fraction of bases in the sequence covered with at least 10 reads by both enzymes. Expressed transcripts are binned in 3 equal-sized classes by the coverage (low, medium and high). The inset shows the dependence of pseudo-MFE regression slope on coverage. b. Normalized Z-score for pseudo-MFE (probing Z-score) versus Z-score for randomly sampled segments of mRNAs. c. Boxplots for shift in the Z-score (Probing-Z-score - Z-score) for randomly sampled mRNA segments and structured ncRNA. d. Shifts in the Z-score for 3 classes of structured ncRNA; dashed gray line shows the linear regression for ncRNAs, black line, the regression for mRNA segments.

Nucleotides have different availability to probing reagents due to the ascertainment bias, which is not related to base-pairing state of nucleotides. For example, PARS data shows that some fragments have low coverage by both single- and double-stranded specific enzymes (S4 Fig. a). It indicates unavailability of a fragment to probing enzymes independently of base-paired states of nucleotides in this fragment (S4 Fig. a, b). Thus, we assign to each fragment its probing coverage as a fraction of nucleotides that is confidently probed. Empirical results with PARS show that contribution of the probing data linearly depends on the probing coverage (inset in Fig. 4a) indicating that fraction of probed nucleotides is an important determinant of pseudo-MFE. For example, if no bases are probed, then pseudo-MFE should equal to MFE. We thus build a linear regression that models the relationship between pseudo-MFE and 2 variables, MFE and probing coverage. Next, we calculate probing-Z-score for expected MFE derived from its regression by pseudo-MFE and coverage (Methods). As result, probing-Z-score is highly correlated (Spearman rho=0.81) with Z-score for a set of mRNA segments, and this dependence is unbiased from probing coverage (Fig. 4b), in contrast to the result obtained with regression by pseudo-MFE only (S4 Fig. d).

We compare Z-scores and probing-Z-scores for several classes of ncRNA (snoRNA (H/ACA), scaRNA, snRNA). In contrast to mRNA fragments, probing-Z-scores are lower than Z-scores for ncRNAs (Fig. 4c; p-value = 2.4 × 10⁻⁶, Wilcoxon test) with the average shift by 0.64 of the standard deviation. As considered ncRNAs already have low Z-scores (Fig. 4d), this moderate shift results in a significant increase in the predictive power (S5 Fig) indicating that these ncRNAs are structured and the probing data is in agreement with thermodynamically stable structures. Thus the probing data contributes to the demarcation of functional non-coding RNAs from the genomic background.

Transcriptome-wide screen

We performed a transcriptome-wide screen for structured RNAs using RNASurface with human PARS data from.¹³ We considered 558 transcripts that had the average coverage in both nuclease datasets exceeding 10 reads per position (S6 Fig.). We also run RNASurface on the same transcripts without using the probing data to assess their contribution. With the Z-score cutoff of −3, we identified 3587 structured RNA elements in PARS-constrained run and 3201 elements in unconstrained run. The lengths and z-scores of elements in the 2 runs showed similar distributions (Figs. 5a and 5b), hence confirming unbiased incorporation of experimental data.

Figure 5.

Properties of structured elements in experiment-constrained and unconstrained scan by RNASurface. a. Length distribution of structured elements. b. Z-score distribution of structured-element energies. c. Distribution of structured elements across mRNA regions, averaged over all transcripts. d. Relative enrichment of predicted structured segments in probing-constrained run compared to unconstrained run (upper panel) and coverage in probing constrained run (bottom panel) across the 5′ UTR, the coding region, and the 3′ UTR, averaged over all transcripts, aligned by the translational start and stop sites.

Five′UTRs were enriched with structured elements in both runs compared to 3′UTRs and CDSs (p = 1.06 × 10⁻¹⁰) and this result doesn't depend on Z-score threshold (S7 Fig). Contrary, regions around the translation start site tended to have a lower number of structures in the probing-constrained run compared to non-constrained run (p = 0.00075, Figs. 5c and 5d) indicating unfolded bases around start codon in vitro. This is consistent with the fact that secondary structures can function as a major regulatory mechanism in 5′ UTRs³¹ but nucleotides around the translation start site tend to be unpaired.³² This is in agreement with previous whole-genome computational predictions for human mRNAs.³³ Overall, the probing data emphasizes depletion of structured segments at the boundaries of coding regions.

Computational de novo screens for structural ncRNA usually work with multiple alignments and use stochastic context-free grammars (SCFG).^4,34 We compared our predictions with the Evofold program based on phylo-SCFG and having high prediction accuracy.⁴ Among 259 Evofold ncRNA candidates within the considered transcripts, 16% and 12% intersect RNASurface predictions on cutoff −3 in PARS-constrained and unconstrained run respectively. PARS-constrained predictions show a consistently higher overlap with Evofold hits compared to the results of the unconstrained run (Fig. 6a). Since many RNASurface predictions overlap with each other, we grouped intersected RNASurface predictions in clusters (so that intersecting predictions form clusters and clusters don't intersect with each other) and observed the same trend (S8 Fig). Among 273 probing-constrained and 295 unconstrained RNASurface clusters, we observed 9 structures that are found only in the probing-constrained run (gained predictions) and 5 structures that are found only in the unconstrained run (lost predictions).

Figure 6.

Comparison to Evofold predictions. a. The number of unique intersections between Evofold predictions and structured elements identified in the probing-constrained run (red line) and the unconstrained run (blue line). b. Evofold predicted structures color-coded according to the PARS score. Top: structures identified only in the probing-constrained run (gained), bottom: structures identified only in the unconstrained run (lost). AUC is the area under the ROC curve. Structures with the best (left) and worst (right) AUC are shown for gained and lost predictions. c. Boxplots of the PARS-score distribution for paired and unpaired bases (the structure is determined by Evofold) for gained and lost RNASurface predictions. d. ROC curves for gained and lost structures, reflecting the correspondence between the PARS probing data and Evofold structures considered as the reference.

To understand better the benefits of probing data, we mapped the PARS scores on secondary structures predicted by Evofold for gained and lost predictions and estimated, how accurately PARS uncovered paired and unpaired bases. Structures identified only in the probing-constrained run generally show a better correspondence between base status obtained in experiment and Evofold-predicted structure (Fig. 6b). The ROC curves demonstrate that dividing bases into paired and unpaired by a cutoff results in different levels of precision of structure determination for gained and lost structures (Fig. 6d). Moreover, paired bases have significantly higher PARS scores than unpaired ones in the case of gained structures (p-value = 0.013), but similar or even lower PARS scores in lost structures (Fig. 6c). The lost structures demonstrate a discrepancy between the probing data constraints and stable secondary structure and are thus filtered out, in contrast to gained predictions well supported by phylogenetic reconstruction.

Web-server

We also developed a web-server to detect locally optimal structured segments with RNASurface and to provide a heatmap visualization. The user uploads an RNA or DNA sequence with a range of optional parameters, which include the input of probing information. The probing information is available as 2 files with probabilities of score observation given the paired or unpaired status of bases. Alternatively, the user may supply raw scores, which are then transformed to probabilities. Additionally, the user may upload a custom track file in the BED format with interval-like features (genes, regulatory elements, non-coding RNAs etc.) to compare these features to the web-server output. This option makes possible to consider the results in a biological context.http://bioinf.fbb.msu.ru/RNASurface/

Discussion

All experimental methods report only partial information on the structure and even a perfect experiment does not reveal the actual base pairing patterns and structure itself. Incorporation of probing data assists computational strategies to improve modeling of the RNA structure, to predict RNA function and to screen genomes for functional RNAs.

We have developed a computational pipeline to detect structured RNAs, which combines a thermodynamic model and probing data. The approach is aimed to provide general framework for analysis of difference sources of genome-scale probing data, supplemented by user-friendly web-server. Reactivities from probing experiments are converted into likelihood scores that are incorporated into the RNASurface energy model. Transformation to likelihood scores allows to process reactivity profiles from different experiments. This is an attractive opportunity, because there exist several experiments without standard normalization of reactivities.³⁵ Since there exist difficulties to simulate experimental data of RNA sequence in silico, we use a class of mRNA fragments as a surrogate of sample without functional structures. We have noted that contribution of the probing data depends on the probing coverage, and thus have built a linear regression to model relationship between pseudo-MFE and MFE and coverage. Slope of linear regression reflects informational contribution of probing data and is unique for each experiment. Nucleotide is defined as unavailable, if its probing has been precluded by experimental artifacts, in contrast to the paired/unpaired status. Experimental artifacts include a low number of RNA molecules or a low resolution of nucleases because their steric radii do not allow access to many sites that are solvated.²² For example, fragments of low coverage for both enzymes in the PARS data indicate either inaccessibility to both enzymes or a low number of the target transcript. Overall, we recommend using the coverage as a parameter when normalizing energy, because all types of experiments have their limitations.

We show that experimental data allow for better discrimination of structured RNAs from the background by calculating the delta of Z-score: differences between Z-score and probing-Z-score are more pronounced for functional structured RNAs compared to mRNAs. The strength of this effect varies between classes (Fig. 3e). For example, the annotated secondary structure of C/D-box snoRNA differs substantially from the PARS profile in vitro. That may indicate that RNA molecules in solution may have secondary structures that are only partially determined by thermodynamics and may undergo conformational changes upon interaction with other RNAs and proteins. In particular, recent researches report widespread structural rearrangement in vivo compared to in vitro conditions¹⁴ with less thermodynamic contribution in the former case.

Using PARS data,¹³ we performed probing-directed transcriptome-wide screen for structured RNAs and compared the results with an unconstrained run. In both runs 5′UTRs of mRNAs were enriched in structured elements, and 3′UTRs had the same density of structured elements as expected by chance. Previous studies have shown that the structural content of 5′UTRs and 3′UTRs relative to coding regions varies from organism to organism. 5′UTRs and 3′UTRs were less structured than coding regions on average for Saccharomyces cerevisiae¹¹ and Arabidopsis thaliana,³⁶ whereas the opposite trend was observed for Drosophila melanogaster, Caenorhabditis elegans³⁷ and human mRNAs.¹³ Depletion of structure in 3′UTRs may be partially explained by properties of the PARS data: PARS protocol does not enable identification of RNA structural features close to the 3′ ends of transcripts. We also observed a local region with weak structural pairings at the start codon in the probing-constrained run but not in the unconstrained run (Figs. 5c and 5d). This is an interesting finding suggesting that probing-directed approach may allow to identify biologically relevant results: the absence of structures around starts and stops of translation may correspond to regulation of translation initiation, elongation or termination. RNASurface detects segments that are thermodynamically stable and consistent with probing data. The fact that it has relatively low intersection with deeply conserved structures according to Evofold may indicate that substantial fraction of structured segments does not show signs of evolutionary selection.

Probing-directed predictions demonstrate some differences with purely computational results. When a structure is lost in probing-directed analysis it means that a stable structure from the low energy spectrum and probing data are inconsistent, but it may happen due to other reasons. In accordance with the rugged folding landscape of RNA,³⁸ the PARS profile shows many nucleotides with high coverage of S1 and V1 nucleases, indicating the existence of multiple conformations. In this case, PARS reflects ensemble of conformations being inconsistent with any individual structure.

Here we apply experimental data to genome-wide identification of structured RNAs. This is only the first step toward global incorporation of experimental data to computational pipelines scanning genomes for structured RNAs. We believe that continued application and improvement of in vitro and in vivo methods is essential for identification and characterization of functional RNA structures.

Materials and methods

Probing data

We used SHAPE data²¹ downloaded from RNA Mapping Database³⁹ and PARS data from¹³ (native deproteinized data set). For PARS data merging of data from 2 replics produced structural information for >10,000 transcripts with at least 1 read per base. We filtered the transcripts so that the average coverage by reads from both enzymes was over 10 reads per position. This resulted in 558 transcripts (S5 Fig).

We selected a pool of test RNA sequences to obtain the distributions of reactivities. The SHAPE test dataset comprised of E.coli 5S rRNA, adenine, cyclic-di-GMP and glycine riboswitches and phenylalanine tRNA molecules; PARS test data set comprises of 3 available classes of ncRNAs (snoRNA H/ACA, snRNA, small Cajal body-specific RNA (scaRNA)). We selected these classes as their secondary structures were known and they consisted of at least 8 ncRNAs with the coverage above the threshold (S6 Fig. b). Secondary structures of ncRNA were predicted based on Rfam covariance models⁴⁰ using Infernal.⁵

We ran RNAplfold⁴¹ to separate nucleotides in test RNA sequences into 2 groups: nucleotides that were more likely to be paired (probability of being paired > 0.8) and more likely to be unpaired (probability < 0.2). The threshold p was selected arbitrarily, thresholds from p = 0.7 to p = 0.95 produced almost the same results (S9 Fig. a, b). Moreover, likelihood ratios are stable to the folding algorithm and probability threshold (S9 Fig. c, d). We fitted the distributions of SHAPE values with the generalized extreme value and exponential distributions for paired and unpaired bases, respectively¹⁹; and the PARS values, with normal distributions for paired and unpaired bases (S10 Fig). Based on inferred fitted distributions P(r|paired) of paired and P(r|unpaired) for unpaired bases, we estimated log-likelihood ${\displaystyle L_i}$ of base i.

Each base pair was assigned a pseudo-energy term ${\displaystyle \Delta G_{ij}^{\text{'}}}$ that reflected the pair likelihood with respect to the probing data:

$${\displaystyle \Delta G_{ij}^{\prime }=RT(log{L}_i+log{L}_j),}$$

where ${\displaystyle L_i}$ represents the probing log likelihood of position i in RNA sequence.

The RNA secondary structure was decomposed in a number of consecutive base pairs, forming stems, and unpaired stretches, forming loops. The free energy of stems was approximated by stacking interactions of its base pairs. Calculation of MFE was performed by Zucker-style dynamic programming, we modified this algorithm by adding the pseudo-energy term to stacking interactions for each base pair. This procedure was implemented in the dynamic programming calculation of MFE in RNASurface.

ROC curves

We varied the reactivity threshold from 0 to 5 for the SHAPE data and from −10 to 10 for the PARS data. For a given threshold, each nucleotide with SHAPE reactivity below the threshold or PARS score above the threshold was predicted to be paired and designated as test outcome positive. Sensitivity was defined as the proportion of correctly identified positive outcomes (i.e. paired in RFam structure). Specificity was defined as the proportion of correctly identified negative outcomes (i.e., unpaired in RFam structure). We calculated sensitivity (true positive rate) and 1—specificity (false positive rate) at each threshold and used this information to generate the ROC curves (Figs. 3b and e).

Z-score calculation

The Z-score of an RNA sequence with energy E was calculated as:

$${\displaystyle Z=\frac{E-\mu \left(l,d\right)}{\sigma \left(l,d\right)}}$$

where μ is the mean and σ is the standard deviation, which are dependent on the sequence length l and average dinucleotide frequencies d.

After introducing the additional term to MFE, we obtained a shifted value of MFE (called pseudo-MFE) that is the thermodynamic energy coupled with probing scores. To capture this bias, we constructed the linear regression between pseudo-MFE and MFE using a random set of segments from a set of sequences with high coverage:

$${\displaystyle pseudoMFE=a\cdot MFE+b}$$

We used mRNA sequences from the genome assuming that they posses only small fraction of functional secondary structure in general (but still may have some local structured regions) and hence could be used to build the background model. This approach can be used only if at least one long transcript covered with probing data is available for analysis. We constructed several regressions, for classes of segments with specific coverage thresholds (fraction of positions with PARS score) ranging from 0.1 to 1 (S11 Fig). As the regression slope linearly depended on the coverage, we introduced coverage as an additional variable:

$${\displaystyle a\left(cov\right)=a^{\prime }cov+c\prime }$$

Consequently, pseudo-MFE depends both on MFE and coverage:

$${\displaystyle pseudoMFE=a\left(cov\right)\cdot MFE+b=\left(a^{\prime }\cdot cov+c\prime \right)\cdot MFE+b=a^{\prime }\cdot MFE\cdot cov+c^{\prime }\cdot MFE+b}$$

After calculating regression coefficients a′, b and c′ we can derive MFE from pseudo-MFE. This transformed MFE is used to estimate the Z-score:

$${\displaystyle \text{MFE}=\frac{\text{pseudoMFE}-\text{b}}{\text{a}\prime \cdot \text{cov}+\text{c′}}}$$

In practice, regression coefficients are estimated by using 23000 vectors (MFE, pseudo-MFE, coverage) obtained from random sample of mRNA fragments from transcripts highly expressed in PARS. It should be noted, that coefficients are optimized separately for each experimental dataset. For other data set, they should be fitted based on the sample of RNA fragments.

Comparison with evofold

We used BedTools⁴² to intersect our structured elements and Evofold⁴ predictions. We considered 2 segments as intersecting if they intersected by at least 50% of length and we counted only unique Evofold predictions (Evofold structure covered by several segments was counted once). To estimate the consistency between PARS data and Evofold structures, we separated all bases in a structure into paired and unpaired ones. Next, we varied the reactivity threshold from −10 to 10 and for each threshold, a base with PARS score above the threshold was considered as paired and below the threshold, as unpaired. Bases paired in both tests were designated as true positive, bases unpaired in both tests, as true negative. Bases unpaired in a reference Evofold structure but defined as paired by PARS were designated as false positive, and paired in the reference structure but unpaired in PARS, as false negative. Next, these were used to calculate the specificity and sensitivity and to produce ROC curves. We also selected the best threshold for each structure (defined as providing the highest Matthews coefficient) and divided all bases in 4 structures in Fig. 6b into paired and unpaired ones. RNASurface predicted regions with their Z-score are available in S1 Table.

Conclusion

Currently, the most common way to survey genomes for structured RNA elements is to use comparative genomics approaches implemented in a number of algorithms. RNASurface uses only one genome sequence, which makes it applicable even when a suitable set of homologous sequences is not available. At the same time, genome-scale probing of RNA structure becomes increasingly popular, so we incorporated probing data into our pipeline. One important advantage of this approach is the ability to incorporate any type of experimental data (SHAPE,^16,21 PARS,¹³ DMS,¹⁴ etc.): we deal with probabilities of nucleotides of being paired/unpaired instead of relying on arbitrary normalized data from experiments. Incorporation of RNA probing data increases the signal/noise rate of structure prediction and detects a larger fraction of functional structures. Though at the moment high quality genome-wide RNA probing data for most organisms is not available, we believe that global interrogation of RNA structure will assist computational strategies to better model RNA structure, predict RNA function, and screen genomes for functional RNAs.

Disclosure of potential conflicts of interest

No potential conflicts of interest were disclosed.

Acknowledgments

We thank Mikhail Gelfand and Dmitri Pervouchine for insightful discussions and Dmitriy Vinogradov for useful discussion and support of computational infrastructure of the project.