On the decomposition of $k$-noncrossing RNA structures

Pseudoknot RNA Structures with Arc-Length $\ge 3$

In this paper we study $k$-noncrossing RNA structures with arc-length $\ge 3$, i.e. RNA molecules in which for any $i$, the nucleotides labeled $i$ and $i+j$ ($j=1,2$) cannot form a bond and in which there are at most $k-1$ mutually crossing arcs. Let ${\sf S}_{k,3}(n)$ denote their number. Based on a novel functional equation for the generating function $\sum_{n\ge 0}{\sf S}_{k,3}(n)z^n$, we derive for arbitrary $k\ge 3$ exponential growth factors and for $k=3$ the subexponential factor. Our main result is the derivation of the formula ${\sf S}_{3,3}(n) \sim \frac{6.11170\cdot 4!}{n(n-1)...(n…

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…

通过竞争结构生成与结构分解识别不可设计RNA结构

Undesignable RNA Structure Identification via Rival Structure Generation and Structure Decomposition

本文针对RNA设计中的不可设计结构识别问题，提出数学定理和高效算法，并在Eterna100谜题上验证了15个不可设计结构，为RNA折叠与设计提供新见解。

Memory efficient RNA energy landscape exploration

Energy landscapes provide a valuable means for studying the folding dynamics of short RNA molecules in detail by modeling all possible structures and their transitions. Higher abstraction levels based on a macro-state decomposition of the landscape enable the study of larger systems, however they are still restricted by huge memory requirements of exact approaches. We present a highly parallelizable local enumeration scheme that enables the computation of exact macro-state transition models with highly reduced memory requirements. The approach is evaluated on RNA secondary structure landscapes…

Fast, approximate kinetics of RNA folding

In this paper, we introduce the software suite, Hermes, which provides fast, novel algorithms for RNA secondary structure kinetics. Using the fast Fourier transform to efficiently compute the Boltzmann probability that a secondary structure S of a given RNA sequence has base pair distance x [resp. y] from reference structure A [resp. B], Hermes computes the exact kinetics of folding from A to B in this coarse-grained model. In particular, Hermes computes the mean first passage time from the transition probability matrix by using matrix inversion, and also computes the equilibrium time from the…