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

Markov Chain-based Sampling for Exploring RNA Secondary Structure under the Nearest Neighbor Thermodynamic Model

We study plane trees as a model for RNA secondary structure, assigning energy to each tree based on the Nearest Neighbor Thermodynamic Model, and defining a corresponding Gibbs distribution on the trees. Through a bijection between plane trees and 2-Motzkin paths, we design a Markov chain converging to the Gibbs distribution, and establish fast mixing time results by estimating the spectral gap of the chain. The spectral gap estimate is established through a series of decompositions of the chain and also by building on known mixing time results for other chains on Dyck paths. In addition to th…

Uniform generation of RNA pseudoknot structures with genus filtration

In this paper we present a sampling framework for RNA structures of fixed topological genus. We introduce a novel, linear time, uniform sampling algorithm for RNA structures of fixed topological genus $g$, for arbitrary $g>0$. Furthermore we develop a linear time sampling algorithm for RNA structures of fixed topological genus $g$ that are weighted by a simplified, loop-based energy functional. For this process the partition function of the energy functional has to be computed once, which has $O(n^2)$ time complexity.

Shapes of interacting RNA complexes

Shapes of interacting RNA complexes are studied using a filtration via their topological genus. A shape of an RNA complex is obtained by (iteratively) collapsing stacks and eliminating hairpin loops. This shape-projection preserves the topological core of the RNA complex and for fixed topological genus there are only finitely many such shapes.Our main result is a new bijection that relates the shapes of RNA complexes with shapes of RNA structures.This allows to compute the shape polynomial of RNA complexes via the shape polynomial of RNA structures. We furthermore present a linear time uniform…

RNA二级结构中发夹结构和碱基对的统计分析

Statistical Analysis of Hairpins and BasePairs in RNA Secondary Structures

该研究推导了RNA二级结构中发夹结构和碱基对数量的统计特性，并证明了其分布趋于双变量正态分布。

Statistics of topological RNA structures

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…

Uniform generation of RNA-RNA interaction structures of fixed topological genus

Interacting RNA complexes are studied via bicellular maps using a filtration via their topological genus. Our main result is a new bijection for RNA-RNA interaction structures and linear time uniform sampling algorithm for RNA complexes of fixed topological genus. The bijection allows to either reduce the topological genus of a bicellular map directly, or to lose connectivity by decomposing the complex into a pair of single stranded RNA structures. Our main result is proved bijectively. It provides an explicit algorithm of how to rewire the corresponding complexes and an unambiguous decomposit…