Diverse RNA pseudoknots exist for short stems only

RNA secondary structure prediction including pseudoknotted structures of arbitrary types is a well-known NP-hard problem of computational biology. By limiting the possible types of pseudoknots the problem can be solved in polynomial time. According to the empirical thermodynamic parameters, the formation of a stem starts to decrease free energy of the structure only after the formation of the third stack of base pairs. Thus, the short stems may be unstable and provide a limited contribution to the overall free energy of a folded RNA molecule. Therefore, detailed analysis of stems in pseudoknots could facilitate reducing pseudoknots complexity. In this paper, we show that the pseudoknots from experimentally determined RNA spatial structures are primarily formed by short stems of 2-3 base pairs. The short stems tend to avoid hairpins and prefer internal loops that indicates that they could be energetically insignificant. An exclusion of short stems reduces the diversity of pseudoknots to two basic types which are H-knots and kissing loops.

Random matrix theory and ribonucleic acid (RNA) folding

This article discusses a series of recent applications of random matrix theory (RMT) to the problem of RNA folding. It first provides a schematic overview of the RNA folding problem, focusing on the concept of RNA pseudoknots, before considering a simplified framework for describing the folding of an RNA molecule; this framework is given by the statistic mechanical model of a polymer chain of L nucleotides in three dimensions with interacting monomers. The article proceeds by presenting a physical interpretation of the RNA matrix model and analysing the large-N expansion of the matrix integral, along with the pseudoknotted homopolymer chain. It extends previous results about the asymptotic distribution of pseudoknots of a phantom homopolymer chain in the limit of large chain length.

An efficient algorithm for planar drawing of RNA structures with pseudoknots of any type

An RNA pseudoknot is a tertiary structural element in which bases of a loop pair with complementary bases are outside the loop. A drawing of RNA secondary structures is a tree, but a drawing of RNA pseudoknots is a graph that has an inner cycle within a pseudoknot and possibly outer cycles formed between the pseudoknot and other structural elements. Visualizing a large-scale RNA structure with pseudoknots as a planar drawing is challenging because a planar drawing of an RNA structure requires both pseudoknots and an entire structure enclosing the pseudoknots to be embedded into a plane without overlapping or crossing. This paper presents an efficient heuristic algorithm for visualizing a pseudoknotted RNA structure as a planar drawing. The algorithm consists of several parts for finding crossing stems and page mapping the stems, for the layout of stem-loops and pseudoknots, and for overlap detection between structural elements and resolving it. Unlike previous algorithms, our algorithm generates a planar drawing for a large RNA structure with pseudoknots of any type and provides a bracket view of the structure. It generates a compact and aesthetic structure graph for a large pseudoknotted RNA structure in O([Formula: see text]) time, where n is the number of stems of the RNA structure.