Partition function and base pairing probabilities of RNA heterodimers

Background: RNA has been recognized as a key player in cellular regulation in recent years. In many cases, non-coding RNAs exert their function by binding to other nucleic acids, as in the case of microRNAs and snoRNAs. The specificity of these interactions derives from the stability of inter-molecular base pairing. The accurate computational treatment of RNA-RNA binding therefore lies at the heart of target prediction algorithms. Methods: The standard dynamic programming algorithms for computing secondary structures of linear single-stranded RNA molecules are extended to the co-folding of two interacting RNAs. Results: We present a program, RNAcofold, that computes the hybridization energy and base pairing pattern of a pair of interacting RNA molecules. In contrast to earlier approaches, complex internal structures in both RNAs are fully taken into account. RNAcofold supports the calculation of the minimum energy structure and of a complete set of suboptimal structures in an energy band above the ground state. Furthermore, it provides an extension of McCaskill's partition function algorithm to compute base pairing probabilities, realistic interaction energies, and equilibrium concentrations of duplex structures

Target prediction and a statistical sampling algorithm for RNA-RNA interaction

It has been proven that the accessibility of the target sites has a critical influence for miRNA and siRNA. In this paper, we present a program, rip2.0, not only the energetically most favorable targets site based on the hybrid-probability, but also a statistical sampling structure to illustrate the statistical characterization and representation of the Boltzmann ensemble of RNA-RNA interaction structures. The outputs are retrieved via backtracing an improved dynamic programming solution for the partition function based on the approach of Huang et al. (Bioinformatics). The $O(N^6)$ time and $O(N^4)$ space algorithm is implemented in C (available from \url{http://www.combinatorics.cn/cbpc/rip2.html})Comment: 7 pages, 10 figure

LinearCoFold and LinearCoPartition: Linear-Time Algorithms for Secondary Structure Prediction of Interacting RNA molecules

Many ncRNAs function through RNA-RNA interactions. Fast and reliable RNA structure prediction with consideration of RNA-RNA interaction is useful. Some existing tools are less accurate due to omitting the competing of intermolecular and intramolecular base pairs, or focus more on predicting the binding region rather than predicting the complete secondary structure of two interacting strands. Vienna RNAcofold, which reduces the problem into the classical single sequence folding by concatenating two strands, scales in cubic time against the combined sequence length, and is slow for long sequences. To address these issues, we present LinearCoFold, which predicts the complete minimum free energy structure of two strands in linear runtime, and LinearCoPartition, which calculates the cofolding partition function and base pairing probabilities in linear runtime. LinearCoFold and LinearCoPartition follows the concatenation strategy of RNAcofold, but are orders of magnitude faster than RNAcofold. For example, on a sequence pair with combined length of 26,190 nt, LinearCoFold is 86.8x faster than RNAcofold MFE mode (0.6 minutes vs. 52.1 minutes), and LinearCoPartition is 642.3x faster than RNAcofold partition function mode (1.8 minutes vs. 1156.2 minutes). Different from the local algorithms, LinearCoFold and LinearCoPartition are global cofolding algorithms without restriction on base pair length. Surprisingly, LinearCoFold and LinearCoPartition's predictions have higher PPV and sensitivity of intermolecular base pairs. Furthermore, we apply LinearCoFold to predict the RNA-RNA interaction between SARS-CoV-2 gRNA and human U4 snRNA, which has been experimentally studied, and observe that LinearCoFold's prediction correlates better to the wet lab results

Topology of RNA-RNA interaction structures

The topological filtration of interacting RNA complexes is studied and the role is analyzed of certain diagrams called irreducible shadows, which form suitable building blocks for more general structures. We prove that for two interacting RNAs, called interaction structures, there exist for fixed genus only finitely many irreducible shadows. This implies that for fixed genus there are only finitely many classes of interaction structures. In particular the simplest case of genus zero already provides the formalism for certain types of structures that occur in nature and are not covered by other filtrations. This case of genus zero interaction structures is already of practical interest, is studied here in detail and found to be expressed by a multiple context-free grammar extending the usual one for RNA secondary structures. We show that in $O(n^6)$ time and $O(n^4)$ space complexity, this grammar for genus zero interaction structures provides not only minimum free energy solutions but also the complete partition function and base pairing probabilities.Comment: 40 pages 15 figure

Exact Learning of RNA Energy Parameters From Structure

We consider the problem of exact learning of parameters of a linear RNA energy model from secondary structure data. A necessary and sufficient condition for learnability of parameters is derived, which is based on computing the convex hull of union of translated Newton polytopes of input sequences. The set of learned energy parameters is characterized as the convex cone generated by the normal vectors to those facets of the resulting polytope that are incident to the origin. In practice, the sufficient condition may not be satisfied by the entire training data set; hence, computing a maximal subset of training data for which the sufficient condition is satisfied is often desired. We show that problem is NP-hard in general for an arbitrary dimensional feature space. Using a randomized greedy algorithm, we select a subset of RNA STRAND v2.0 database that satisfies the sufficient condition for separate A-U, C-G, G-U base pair counting model. The set of learned energy parameters includes experimentally measured energies of A-U, C-G, and G-U pairs; hence, our parameter set is in agreement with the Turner parameters

RNA-RNA interaction prediction based on multiple sequence alignments

Many computerized methods for RNA-RNA interaction structure prediction have been developed. Recently, $O(N^6)$ time and $O(N^4)$ space dynamic programming algorithms have become available that compute the partition function of RNA-RNA interaction complexes. However, few of these methods incorporate the knowledge concerning related sequences, thus relevant evolutionary information is often neglected from the structure determination. Therefore, it is of considerable practical interest to introduce a method taking into consideration both thermodynamic stability and sequence covariation. We present the \emph{a priori} folding algorithm \texttt{ripalign}, whose input consists of two (given) multiple sequence alignments (MSA). \texttt{ripalign} outputs (1) the partition function, (2) base-pairing probabilities, (3) hybrid probabilities and (4) a set of Boltzmann-sampled suboptimal structures consisting of canonical joint structures that are compatible to the alignments. Compared to the single sequence-pair folding algorithm \texttt{rip}, \texttt{ripalign} requires negligible additional memory resource. Furthermore, we incorporate possible structure constraints as input parameters into our algorithm. The algorithm described here is implemented in C as part of the \texttt{rip} package. The supplemental material, source code and input/output files can freely be downloaded from \url{http://www.combinatorics.cn/cbpc/ripalign.html}. \section{Contact} Christian Reidys \texttt{[email protected]}Comment: 8 pages, 9 figure