MOTIVATION: The task of designing optimized messenger RNA (mRNA) sequences has received much attention in recent years, thanks to breakthroughs in mRNA vaccines during the COVID-19 pandemic. Because most previous work aimed to minimize the minimum free energy (MFE) of the mRNA in order to improve stability and protein expression, which only considers one particular structure per mRNA sequence, millions of alternative conformations in equilibrium are neglected. More importantly, we prefer an mRNA to populate multiple stable structures and be flexible among them during translation when the ribosome unwinds it. RESULTS: Therefore, we consider a new objective to minimize the ensemble free energy of an mRNA, which includes all possible structures in its Boltzmann ensemble. However, this new problem is much harder to solve than the original MFE optimization. To address the increased complexity of this problem, we introduce EnsembleDesign, a novel algorithm that employs continuous relaxation to optimize the expected ensemble free energy over a distribution of candidate sequences. EnsembleDesign extends both the lattice representation of the design space and the dynamic programming algorithm from LinearDesign to their probabilistic counterparts. Our algorithm consistently outperforms LinearDesign in terms of ensemble free energy, especially on long sequences. Interestingly, as byproducts, our designs also enjoy lower average unpaired probabilities (which correlates with degradation) and flatter Boltzmann ensembles (more flexibility between conformations). AVAILABILITY AND IMPLEMENTATION: Our code is available on: https://github.com/LinearFold/EnsembleDesign.

MOTIVATION: RNA design is the search for a sequence or set of sequences that will fold to desired structure, also known as the inverse problem of RNA folding. However, the sequences designed by existing algorithms often suffer from low ensemble stability, which worsens for long sequence design. Additionally, for many methods only a small number of sequences satisfying the MFE criterion can be found by each run of design. These drawbacks limit their use cases. RESULTS: We propose an innovative optimization paradigm, SAMFEO, which optimizes ensemble objectives (equilibrium probability or ensemble defect) by iterative search and yields a very large number of successfully designed RNA sequences as byproducts. We develop a search method which leverages structure level and ensemble level information at different stages of the optimization: initialization, sampling, mutation, and updating. Our work, while being less complicated than others, is the first algorithm that is able to design thousands of RNA sequences for the puzzles from the Eterna100 benchmark. In addition, our algorithm solves the most Eterna100 puzzles among all the general optimization based methods in our study. The only baseline solving more puzzles than our work is dependent on handcrafted heuristics designed for a specific folding model. Surprisingly, our approach shows superiority on designing long sequences for structures adapted from the database of 16S Ribosomal RNAs. AVAILABILITY AND IMPLEMENTATION: Our source code and data used in this article is available at https://github.com/shanry/SAMFEO.

MOTIVATION: The secondary structure of RNA is of importance to its function. Over the last few years, several papers attempted to use machine learning to improve de novo RNA secondary structure prediction. Many of these papers report impressive results for intra-family predictions but seldom address the much more difficult (and practical) inter-family problem. RESULTS: We demonstrate that it is nearly trivial with convolutional neural networks to generate pseudo-free energy changes, modelled after structure mapping data that improve the accuracy of structure prediction for intra-family cases. We propose a more rigorous method for inter-family cross-validation that can be used to assess the performance of learning-based models. Using this method, we further demonstrate that intra-family performance is insufficient proof of generalization despite the widespread assumption in the literature and provide strong evidence that many existing learning-based models have not generalized inter-family. AVAILABILITY AND IMPLEMENTATION: Source code and data are available at https://github.com/marcellszi/dl-rna. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: RNA secondary structure prediction is widely used to understand RNA function. Recently, there has been a shift away from the classical minimum free energy methods to partition function-based methods that account for folding ensembles and can therefore estimate structure and base pair probabilities. However, the classical partition function algorithm scales cubically with sequence length, and is therefore prohibitively slow for long sequences. This slowness is even more severe than cubic-time free energy minimization due to a substantially larger constant factor in runtime. RESULTS: Inspired by the success of our recent LinearFold algorithm that predicts the approximate minimum free energy structure in linear time, we design a similar linear-time heuristic algorithm, LinearPartition, to approximate the partition function and base-pairing probabilities, which is shown to be orders of magnitude faster than Vienna RNAfold and CONTRAfold (e.g. 2.5 days versus 1.3 min on a sequence with length 32 753 nt). More interestingly, the resulting base-pairing probabilities are even better correlated with the ground-truth structures. LinearPartition also leads to a small accuracy improvement when used for downstream structure prediction on families with the longest length sequences (16S and 23S rRNAs), as well as a substantial improvement on long-distance base pairs (500+ nt apart). AVAILABILITY AND IMPLEMENTATION: Code: http://github.com/LinearFold/LinearPartition; Server: http://linearfold.org/partition. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Predicting the secondary structure of an ribonucleic acid (RNA) sequence is useful in many applications. Existing algorithms [based on dynamic programming] suffer from a major limitation: their runtimes scale cubically with the RNA length, and this slowness limits their use in genome-wide applications. RESULTS: We present a novel alternative O(n3)-time dynamic programming algorithm for RNA folding that is amenable to heuristics that make it run in O(n) time and O(n) space, while producing a high-quality approximation to the optimal solution. Inspired by incremental parsing for context-free grammars in computational linguistics, our alternative dynamic programming algorithm scans the sequence in a left-to-right (5'-to-3') direction rather than in a bottom-up fashion, which allows us to employ the effective beam pruning heuristic. Our work, though inexact, is the first RNA folding algorithm to achieve linear runtime (and linear space) without imposing constraints on the output structure. Surprisingly, our approximate search results in even higher overall accuracy on a diverse database of sequences with known structures. More interestingly, it leads to significantly more accurate predictions on the longest sequence families in that database (16S and 23S Ribosomal RNAs), as well as improved accuracies for long-range base pairs (500+ nucleotides apart), both of which are well known to be challenging for the current models. AVAILABILITY AND IMPLEMENTATION: Our source code is available at https://github.com/LinearFold/LinearFold, and our webserver is at http://linearfold.org (sequence limit: 100 000nt). SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Predicting the secondary structure of RNA is a fundamental task in bioinformatics. Algorithms that predict secondary structure given only the primary sequence, and a model to evaluate the quality of a structure, are an integral part of this. These algorithms have been updated as our model of RNA thermodynamics changed and expanded. An exception to this has been the treatment of multi-loops. Although more advanced models of multi-loop free energy change have been suggested, a simple, linear model has been used since the 1980s. However, recently, new dynamic programing algorithms for secondary structure prediction that could incorporate these models were presented. Unfortunately, these models appear to have lower accuracy for secondary structure prediction. RESULTS: We apply linear regression and a new parameter optimization algorithm to find better parameters for the existing linear model and advanced non-linear multi-loop models. These include the Jacobson-Stockmayer and Aalberts & Nandagopal models. We find that the current linear model parameters may be near optimal for the linear model, and that no advanced model performs better than the existing linear model parameters even after parameter optimization. AVAILABILITY AND IMPLEMENTATION: Source code and data is available at https://github.com/maxhwardg/advanced_multiloops. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Prediction of RNA tertiary structure from sequence is an important problem, but generating accurate structure models for even short sequences remains difficult. Predictions of RNA tertiary structure tend to be least accurate in loop regions, where non-canonical pairs are important for determining the details of structure. Non-canonical pairs can be predicted using a knowledge-based model of structure that scores nucleotide cyclic motifs, or NCMs. In this work, a partition function algorithm is introduced that allows the estimation of base pairing probabilities for both canonical and non-canonical interactions. Pairs that are predicted to be probable are more likely to be found in the true structure than pairs of lower probability. Pair probability estimates can be further improved by predicting the structure conserved across multiple homologous sequences using the TurboFold algorithm. These pairing probabilities, used in concert with prior knowledge of the canonical secondary structure, allow accurate inference of non-canonical pairs, an important step towards accurate prediction of the full tertiary structure. Software to predict non-canonical base pairs and pairing probabilities is now provided as part of the RNAstructure software package.

MOTIVATION: There are numerous examples of RNA-RNA complexes, including microRNA-mRNA and small RNA-mRNA duplexes for regulation of translation, guide RNA interactions with target RNA for post-transcriptional modification and small nuclear RNA duplexes for splicing. Predicting the base pairs formed between two interacting sequences remains difficult, at least in part because of the competition between unimolecular and bimolecular structure. RESULTS: Two algorithms were developed for improved prediction of bimolecular RNA structure that consider the competition between self-structure and bimolecular structure. These algorithms utilize two novel approaches to evaluate accessibility: free energy density minimization and pseudo-energy minimization. Free energy density minimization minimizes the folding free energy change per nucleotide involved in an intermolecular secondary structure. Pseudo-energy minimization (called AccessFold) minimizes the sum of free energy change and a pseudo-free energy penalty for bimolecular pairing of nucleotides that are unlikely to be accessible for bimolecular structure. The pseudo-free energy, derived from unimolecular pairing probabilities, is applied per nucleotide in bimolecular pairs, and this approach is able to predict binding sites that are split by unimolecular structures. A benchmark set of 17 bimolecular RNA structures was assembled to assess structure prediction. Pseudo-energy minimization provides a statistically significant improvement in sensitivity over the method that was found in a benchmark to be the most accurate previously available method, with an improvement from 36.8% to 57.8% in mean sensitivity for base pair prediction. AVAILABILITY AND IMPLEMENTATION: Pseudo-energy minimization is available for download as AccessFold, under an open-source license and as part of the RNAstructure package, at: http://rna.urmc.rochester.edu/RNAstructure.html CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Abstract Motivation: Many RNA molecules function without being translated into proteins, and function depends on structure. Pseudoknots are motifs in RNA secondary structures that are difficult to predict but are also often functionally important. Results: TurboKnot is a new algorithm for predicting the secondary structure, including pseudoknotted pairs, conserved across multiple sequences. TurboKnot finds 81.6% of all known base pairs in the systems tested, and 75.6% of predicted pairs were found in the known structures. Pseudoknots are found with half or better of the false-positive rate of previous methods. Availability: The program is available for download under an open-source license as part of the RNAstructure package at: http://rna.urmc.rochester.edu. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics online.

TurboFold, an iterative algorithm for estimating the common secondary structures of multiple RNA homologs, is presented. The algorithm is motivated by and has structure and attributes analogous to the turbo decoding algorithm in communications. Instead of solving the joint problem of aligning and folding multiple RNA sequences, TurboFold uses an iterative process to fold a collection of RNA homologs. Beneficial information from inter-sequence comparisons is incorporated by using feedback from iteration to iteration in the form of pseudo-prior probabilities for base pairing which are incorporated in the computation of base pairing probabilities. As a result Turbo Fold retains several of the advantages of join alignment and folding while maintaining a per iteration computational complexity comparable to single sequence RNA folding. Experimental evaluation of the algorithm, performed over six ncRNA families, demonstrates that TurboFold achieves high accuracy, offering better performance than available alternatives for estimating RNA base pairing probabilities.

MOTIVATION: With recent advances in sequencing, structural and functional studies of RNA lag behind the discovery of sequences. Computational analysis of RNA is increasingly important to reveal structure-function relationships with low cost and speed. The purpose of this study is to use multiple homologous sequences to infer a conserved RNA structure. RESULTS: A new algorithm, called Multilign, is presented to find the lowest free energy RNA secondary structure common to multiple sequences. Multilign is based on Dynalign, which is a program that simultaneously aligns and folds two sequences to find the lowest free energy conserved structure. For Multilign, Dynalign is used to progressively construct a conserved structure from multiple pairwise calculations, with one sequence used in all pairwise calculations. A base pair is predicted only if it is contained in the set of low free energy structures predicted by all Dynalign calculations. In this way, Multilign improves prediction accuracy by keeping the genuine base pairs and excluding competing false base pairs. Multilign has computational complexity that scales linearly in the number of sequences. Multilign was tested on extensive datasets of sequences with known structure and its prediction accuracy is among the best of available algorithms. Multilign can run on long sequences (> 1500 nt) and an arbitrarily large number of sequences. AVAILABILITY: The algorithm is implemented in ANSI C++ and can be downloaded as part of the RNAstructure package at: http://rna.urmc.rochester.edu.

BACKGROUND: The prediction of secondary structure, i.e. the set of canonical base pairs between nucleotides, is a first step in developing an understanding of the function of an RNA sequence. The most accurate computational methods predict conserved structures for a set of homologous RNA sequences. These methods usually suffer from high computational complexity. In this paper, TurboFold, a novel and efficient method for secondary structure prediction for multiple RNA sequences, is presented. RESULTS: TurboFold takes, as input, a set of homologous RNA sequences and outputs estimates of the base pairing probabilities for each sequence. The base pairing probabilities for a sequence are estimated by combining intrinsic information, derived from the sequence itself via the nearest neighbor thermodynamic model, with extrinsic information, derived from the other sequences in the input set. For a given sequence, the extrinsic information is computed by using pairwise-sequence-alignment-based probabilities for co-incidence with each of the other sequences, along with estimated base pairing probabilities, from the previous iteration, for the other sequences. The extrinsic information is introduced as free energy modifications for base pairing in a partition function computation based on the nearest neighbor thermodynamic model. This process yields updated estimates of base pairing probability. The updated base pairing probabilities in turn are used to recompute extrinsic information, resulting in the overall iterative estimation procedure that defines TurboFold.TurboFold is benchmarked on a number of ncRNA datasets and compared against alternative secondary structure prediction methods. The iterative procedure in TurboFold is shown to improve estimates of base pairing probability with each iteration, though only small gains are obtained beyond three iterations. Secondary structures composed of base pairs with estimated probabilities higher than a significance threshold are shown to be more accurate for TurboFold than for alternative methods that estimate base pairing probabilities. TurboFold-MEA, which uses base pairing probabilities from TurboFold in a maximum expected accuracy algorithm for secondary structure prediction, has accuracy comparable to the best performing secondary structure prediction methods. The computational and memory requirements for TurboFold are modest and, in terms of sequence length and number of sequences, scale much more favorably than joint alignment and folding algorithms. CONCLUSIONS: TurboFold is an iterative probabilistic method for predicting secondary structures for multiple RNA sequences that efficiently and accurately combines the information from the comparative analysis between sequences with the thermodynamic folding model. Unlike most other multi-sequence structure prediction methods, TurboFold does not enforce strict commonality of structures and is therefore useful for predicting structures for homologous sequences that have diverged significantly. TurboFold can be downloaded as part of the RNAstructure package at http://rna.urmc.rochester.edu.

BACKGROUND: To understand an RNA sequence's mechanism of action, the structure must be known. Furthermore, target RNA structure is an important consideration in the design of small interfering RNAs and antisense DNA oligonucleotides. RNA secondary structure prediction, using thermodynamics, can be used to develop hypotheses about the structure of an RNA sequence. RESULTS: RNAstructure is a software package for RNA secondary structure prediction and analysis. It uses thermodynamics and utilizes the most recent set of nearest neighbor parameters from the Turner group. It includes methods for secondary structure prediction (using several algorithms), prediction of base pair probabilities, bimolecular structure prediction, and prediction of a structure common to two sequences. This contribution describes new extensions to the package, including a library of C++ classes for incorporation into other programs, a user-friendly graphical user interface written in JAVA, and new Unix-style text interfaces. The original graphical user interface for Microsoft Windows is still maintained. CONCLUSION: The extensions to RNAstructure serve to make RNA secondary structure prediction user-friendly. The package is available for download from the Mathews lab homepage at http://rna.urmc.rochester.edu/RNAstructure.html.

We propose an algorithm for estimating the common secondary structure, alignment, and posterior base pairing probabilities for two RNA sequences. A definition of structural alignment is presented based on a novel concept of matched helical regions that generalizes the common secondary structure and alignment constraints used in prior work. A probabilistic framework for scoring structural alignments is developed based on a pseudo free energy model. Utilizing the model, maximum a posteriori probability estimates of secondary structure and alignment, and a posteriori probabilities for base pairing are computed using an efficient dynamic programming algorithm. Experimental results demonstrate that the proposed method offers significant improvements in structure and alignment prediction accuracy in comparison with single sequence thermodynamic methods for secondary structure prediction and purely sequence based alignment.

We propose an iterative probabilistic algorithm for estimation of RNA secondary structure using sequence data from two homologous sequences. The method is intended to exploit intersequence correlations "encoded" in the form of probabilistic models for alignment and for common secondary structure. In analogy with turbo-decoding in digital communications, we formulate a maximum a posteriori probability objective function for joint structural prediction and sequence alignment using iterations over individual structural and sequential alignment models with soft-input soft-output estimators. As a preliminary step toward realizing this methodology, we present results obtained from incorporating (hard) constraints based on posterior sequence alignment probabilities in joint secondary structure prediction. Through experimental evaluations over available databases of known secondary structure, we demonstrate that this results in a significant decrease in computation time while simultaneously providing a marginal increase in structural prediction accuracy.

BACKGROUND: Joint alignment and secondary structure prediction of two RNA sequences can significantly improve the accuracy of the structural predictions. Methods addressing this problem, however, are forced to employ constraints that reduce computation by restricting the alignments and/or structures (i.e. folds) that are permissible. In this paper, a new methodology is presented for the purpose of establishing alignment constraints based on nucleotide alignment and insertion posterior probabilities. Using a hidden Markov model, posterior probabilities of alignment and insertion are computed for all possible pairings of nucleotide positions from the two sequences. These alignment and insertion posterior probabilities are additively combined to obtain probabilities of co-incidence for nucleotide position pairs. A suitable alignment constraint is obtained by thresholding the co-incidence probabilities. The constraint is integrated with Dynalign, a free energy minimization algorithm for joint alignment and secondary structure prediction. The resulting method is benchmarked against the previous version of Dynalign and against other programs for pairwise RNA structure prediction. RESULTS: The proposed technique eliminates manual parameter selection in Dynalign and provides significant computational time savings in comparison to prior constraints in Dynalign while simultaneously providing a small improvement in the structural prediction accuracy. Savings are also realized in memory. In experiments over a 5S RNA dataset with average sequence length of approximately 120 nucleotides, the method reduces computation by a factor of 2. The method performs favorably in comparison to other programs for pairwise RNA structure prediction: yielding better accuracy, on average, and requiring significantly lesser computational resources. CONCLUSION: Probabilistic analysis can be utilized in order to automate the determination of alignment constraints for pairwise RNA structure prediction methods in a principled fashion. These constraints can reduce the computational and memory requirements of these methods while maintaining or improving their accuracy of structural prediction. This extends the practical reach of these methods to longer length sequences. The revised Dynalign code is freely available for download.

BACKGROUND: Non-coding RNAs (ncRNAs) have a multitude of roles in the cell, many of which remain to be discovered. However, it is difficult to detect novel ncRNAs in biochemical screens. To advance biological knowledge, computational methods that can accurately detect ncRNAs in sequenced genomes are therefore desirable. The increasing number of genomic sequences provides a rich dataset for computational comparative sequence analysis and detection of novel ncRNAs. RESULTS: Here, Dynalign, a program for predicting secondary structures common to two RNA sequences on the basis of minimizing folding free energy change, is utilized as a computational ncRNA detection tool. The Dynalign-computed optimal total free energy change, which scores the structural alignment and the free energy change of folding into a common structure for two RNA sequences, is shown to be an effective measure for distinguishing ncRNA from randomized sequences. To make the classification as a ncRNA, the total free energy change of an input sequence pair can either be compared with the total free energy changes of a set of control sequence pairs, or be used in combination with sequence length and nucleotide frequencies as input to a classification support vector machine. The latter method is much faster, but slightly less sensitive at a given specificity. Additionally, the classification support vector machine method is shown to be sensitive and specific on genomic ncRNA screens of two different Escherichia coli and Salmonella typhi genome alignments, in which many ncRNAs are known. The Dynalign computational experiments are also compared with two other ncRNA detection programs, RNAz and QRNA. CONCLUSION: The Dynalign-based support vector machine method is more sensitive for known ncRNAs in the test genomic screens than RNAz and QRNA. Additionally, both Dynalign-based methods are more sensitive than RNAz and QRNA at low sequence pair identities. Dynalign can be used as a comparable or more accurate tool than RNAz or QRNA in genomic screens, especially for low-identity regions. Dynalign provides a method for discovering ncRNAs in sequenced genomes that other methods may not identify. Significant improvements in Dynalign runtime have also been achieved.

MOTIVATION: Function derives from structure, therefore, there is need for methods to predict functional RNA structures. RESULTS: The Dynalign algorithm, which predicts the lowest free energy secondary structure common to two unaligned RNA sequences, is extended to the prediction of a set of low-energy structures. Dot plots can be drawn to show all base pairs in structures within an energy increment. Dynalign predicts more well-defined structures than structure prediction using a single sequence; in 5S rRNA sequences, the average number of base pairs in structures with energy within 20% of the lowest energy structure is 317 using Dynalign, but 569 using a single sequence. Structure prediction with Dynalign can also be constrained according to experiment or comparative analysis. The accuracy, measured as sensitivity and positive predictive value, of Dynalign is greater than predictions with a single sequence. AVAILABILITY: Dynalign can be downloaded at http://rna.urmc.rochester.edu