Large RNA molecules often carry multiple functional domains whose spatial arrangement is an important determinant of their function. Pre-mRNA splicing, furthermore, relies on the spatial proximity of the splice junctions that can be separated by very long introns. Similar effects appear in the processing of RNA virus genomes. Albeit a crude measure, the distribution of spatial distances in thermodynamic equilibrium therefore provides useful information on the overall shape of the molecule can provide insights into the interplay of its functional domains. Spatial distance can be approximated by the graph-distance in RNA secondary structure. We show here that the equilibrium distribution of graph-distances between arbitrary nucleotides can be computed in polynomial time by means of dynamic programming. A naive implementation would yield recursions with a very high time complexity of O(n^11). Although we were able to reduce this to O(n^6) for many practical applications a further reduction seems difficult. We conclude, therefore, that sampling approaches, which are much easier to implement, are also theoretically favorable for most real-life applications, in particular since these primarily concern long-range interactions in very large RNA molecules.
Given a random RNA secondary structure, $S$, we study RNA sequences having fixed ratios of nuclotides that are compatible with $S$. We perform this analysis for RNA secondary structures subject to various base pairing rules and minimum arc- and stack-length restrictions. Our main result reads as follows: in the simplex of the nucleotide ratios there exists a convex region in which, in the limit of long sequences, a random structure a.a.s.~has compatible sequence with these ratios and outside of which a.a.s.~a random structure has no such compatible sequence. We localize this region for RNA sec…
An RNA sequence is a word over an alphabet on four elements $\{A,C,G,U\}$ called bases. RNA sequences fold into secondary structures where some bases match one another while others remain unpaired. Pseudoknot-free secondary structures can be represented as well-parenthesized expressions with additional dots, where pairs of matching parentheses symbolize paired bases and dots, unpaired bases. The two fundamental problems in RNA algorithmic are to predict how sequences fold within some model of energy and to design sequences of bases which will fold into targeted secondary structures. Predicting…
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 sequence…
RNA structure prediction is a challenging problem, especially with pseudoknots. Recently, there has been a shift from the classical minimum free energy-based methods (MFE) to partition function-based ones that assemble structures using base-pairing probabilities. Two examples of the latter group are the popular maximum expected accuracy (MEA) method and the ProbKnot method. ProbKnot is a fast heuristic that pairs nucleotides that are reciprocally most probable pairing partners, and unlike MEA, can also predict structures with pseudoknots. However, ProbKnot's full potential has been largely ove…
Background: RNA exhibits a variety of structural configurations. Here we consider a structure to be tantamount to the noncrossing Watson-Crick and \pairGU -base pairings (secondary structure) and additional cross-serial base pairs. These interactions are called pseudoknots and are observed across the whole spectrum of RNA functionalities. In the context of studying natural RNA structures, searching for new ribozymes and designing artificial RNA, it is of interest to find RNA sequences folding into a specific structure and to analyze their induced neutral networks. Since the established inverse…
The design of multi-stable RNA molecules has important applications in biology, medicine, and biotechnology. Synthetic design approaches profit strongly from effective in-silico methods, which can tremendously impact their cost and feasibility. We revisit a central ingredient of most in-silico design methods: the sampling of sequences for the design of multi-target structures, possibly including pseudoknots. For this task, we present the efficient, tree decomposition-based algorithm. Our fixed parameter tractable approach is underpinned by establishing the P-hardness of uniform sampling. Model…
Boltzmann machines are energy-based models that have been shown to provide an accurate statistical description of domains of evolutionary-related protein and RNA families. They are parametrized in terms of local biases accounting for residue conservation, and pairwise terms to model epistatic coevolution between residues. From the model parameters, it is possible to extract an accurate prediction of the three-dimensional contact map of the target domain. More recently, the accuracy of these models has been also assessed in terms of their ability in predicting mutational effects and generating …
Dual graphs have been applied to model RNA secondary structures. The purpose of the paper is two-fold: we present new graph-theoretic properties of dual graphs to validate the further analysis and classification of RNAs using these topological representations; we also present a linear-time algorithm to partition dual graphs into topological components called {\it blocks} and determine if each block contains a {\it pseudoknot} or not. We show that a block contains a pseudoknot if and only if the block has a vertex of degree $3$ or more; this characterization allows us to efficiently isolate sma…
In this paper we study properties of topological RNA structures, i.e.~RNA contact structures with cross-serial interactions that are filtered by their topological genus. RNA secondary structures within this framework are topological structures having genus zero. We derive a new bivariate generating function whose singular expansion allows us to analyze the distributions of arcs, stacks, hairpin- , interior- and multi-loops. We then extend this analysis to H-type pseudoknots, kissing hairpins as well as $3$-knots and compute their respective expectation values. Finally we discuss our results an…
Many non-coding RNAs are known to play a role in the cell directly linked to their structure. Structure prediction based on the sole sequence is however a challenging task. On the other hand, thanks to the low cost of sequencing technologies, a very large number of homologous sequences are becoming available for many RNA families. In the protein community, it has emerged in the last decade the idea of exploiting the covariance of mutations within a family to predict the protein structure using the direct-coupling-analysis (DCA) method. The application of DCA to RNA systems has been limited so …
We consider a certain abstract of RNA secondary structures, which is closely related to RNA shapes. The generating function counting the number of the abstract structures is obtained by means of Narayana numbers and 2-Motzkin paths, through which we provide an identity related to Narayana numbers and Motzkin polynomials. Furthermore, we show that a combinatorial interpretation on 2-Motzkin paths leads to the correspondence between 1-Motkzin paths and RNA shapes, which facilitates probing further classifications or abstractions of the shapes. In this paper, we classify the shapes with respect t…
Non-coding RNA structure and function are essential to understanding various biological processes, such as cell signaling, gene expression, and post-transcriptional regulations. These are all among the core problems in the RNA field. With the rapid growth of sequencing technology, we have accumulated a massive amount of unannotated RNA sequences. On the other hand, expensive experimental observatory results in only limited numbers of annotated data and 3D structures. Hence, it is still challenging to design computational methods for predicting their structures and functions. The lack of annota…
Using structural and evolutionary information to detect and correct pyrosequencing errors in non-coding RNAs
RNA分子中序列-结构关系的分析对于进化研究是必不可少的，但对于具体的应用，如测序技术中的纠错方法也是必不可少的。突变和构象景观的大小与数据量相结合，需要有效的算法来计算序列结构特性。更具体地说，我们的目标是计算哪些突变增加了给定结构和RNA家族序列的可能性。在本文中，我们介绍RNApyro，一个有效的线性时间和空间内外算法，计算精确的突变概率下的二级结构和进化的限制，作为一个多个序列比对的共识结构。我们开发了一个评分计划结合经典的堆积碱基对能量的新型等排尺度，并应用我们的技术来纠正点的错误，在5s和16 s rRNA序列。我们的研究结果表明，RNApyro是一个很有前途的算法，以补充现有的工具，在NGS纠错管道。
