一种新的高水平RNA二级结构比较距离

An infinite class of unsaturated rooted trees corresponding to designable RNA secondary structures

An RNA secondary structure is designable if there is an RNA sequence which can attain its maximum number of base pairs only by adopting that structure. The combinatorial RNA design problem, introduced by Haleš et al. in 2016, is to determine whether or not a given RNA secondary structure is designable. Haleš et al. identified certain classes of designable and non-designable secondary structures by reference to their corresponding rooted trees. We introduce an infinite class of rooted trees containing unpaired nucleotides at the greatest depth, and prove constructively that their corresponding …

Designing RNA Secondary Structures is Hard

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…

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 sequence…

Algorithms for ranking and unranking the combinatorial set of RNA secondary structures

In this paper, we study the combinatorial set of RNA secondary structures of length $n$ with $m$ base-pairs. For a compact representation, we encode an RNA secondary structure by the corresponding Motzkin word. For this combinatorial set, we construct an AND/OR tree structure, find a bijection between the combinatorial set and the set of variants of the AND/OR tree, and develop algorithms for ranking and unranking the variants of the AND/OR tree. The developed ranking and unranking algorithms have polynomial time complexity $O(m^2 (n - m))$ for $m < n - 2 m$ and $O(m (n - m)^2)$ for $m > n - 2…

最大化堆积对数预测任意伪结点的RNA二级结构

Predicting RNA Secondary Structures with Arbitrary Pseudoknots by Maximizing the Number of Stacking Pairs

本文研究了预测RNA二级结构的计算问题。一般认为，允许伪结会使问题变得困难。现有的多项式时间算法是启发式算法，没有性能保证，只能处理有限类型的伪节点。在本文中，我们开始研究预测RNA二级结构的最大数量的堆叠对，同时允许任意的伪结。我们得到了两个近似算法的最坏情况下的近似比为1/2和1/3的平面和一般的二级结构，分别。对于$n$碱基的RNA序列，平面二级结构的近似算法在$O(n^3)$时间内运行，而一般情况下在线性时间内运行。此外，我们证明，允许伪结使它NP-难的最大化的堆叠对在一个平面的二级结构的数量。这一结果是在对比与最近的NP-难的结果，这些结果是基于优化一些一般的和复杂的能量函数。

使用一整套生物学相关的编辑操作来比较RNA结构是棘手的

Comparing RNA structures using a full set of biologically relevant edit operations is intractable

弧形注释序列可用于表示RNA的结构信息，并已广泛用于在序列和结构相似性方面比较RNA结构。在涉及弧注释序列和RNA结构比较的许多范例中（更多细节参见\cite{IGMA_BliDenDul08}），最重要的范例是通用编辑距离。在\cite{Evans99}中引入了计算两个非交叉弧注释序列之间的编辑距离的问题。引入的模型使用涉及单个字母或成对字母（从不单独考虑）的编辑操作，并且可以在多项式时间\cite{ZhangShasha:1989}中求解。为了解释其他可能的RNA结构进化事件，在\cite{jiangli}中引入了新的编辑操作，允许考虑一对中的两个或两个单独的字母;不幸的是，这是以计算易处理性为代价的。已经证明，使用一套完整的生物学相关编辑操作比较两个RNA二级结构是{ \sf \bf NP}-完全的。然而，在\cite{DBLP:conf/spire/GuignonCH05}中，作者使用了强组合限制，以比较两个RNA茎环与一套完整的生物学相关的编辑操作;这使他们能够设计一个多项式时间和空间算法，用于比较一般的二级RNA结构。在本文中，我们将从理论上证明，使用一套完整的生物相关的编辑操作来比较两个RNA结构，如果没有很强的组合限制，就无法完成。