Analytical description of finite size effects for RNA secondary structures

The ensemble of RNA secondary structures of uniform sequences is studied analytically. We calculate the partition function for very long sequences and discuss how the cross-over length, beyond which asymptotic scaling laws apply, depends on thermodynamic parameters. For realistic choices of parameters this length can be much longer than natural RNA molecules. This has to be taken into account when applying asymptotic theory to interpret experiments or numerical results.Comment: 10 pages, 13 figures, published in Phys. Rev.

RNA denaturation: excluded volume, pseudoknots and transition scenarios

A lattice model of RNA denaturation which fully accounts for the excluded volume effects among nucleotides is proposed. A numerical study shows that interactions forming pseudoknots must be included in order to get a sharp continuous transition. Otherwise a smooth crossover occurs from the swollen linear polymer behavior to highly ramified, almost compact conformations with secondary structures. In the latter scenario, which is appropriate when these structures are much more stable than pseudoknot links, probability distributions for the lengths of both loops and main branches obey scaling with nonclassical exponents.Comment: 4 pages 3 figure

Zero Temperature Properties of RNA Secondary Structures

We analyze different microscopic RNA models at zero temperature. We discuss both the most simple model, that suffers a large degeneracy of the ground state, and models in which the degeneracy has been remove, in a more or less severe manner. We calculate low-energy density of states using a coupling perturbing method, where the ground state of a modified Hamiltonian, that repels the original ground state, is determined. We evaluate scaling exponents starting from measurements of overlaps and energy differences. In the case of models without accidental degeneracy of the ground state we are able to clearly establish the existence of a glassy phase with $\theta \simeq 1/3$.Comment: 20 pages including 9 eps figure

Statistical mechanics of RNA folding: importance of alphabet size

We construct a minimalist model of RNA secondary-structure formation and use it to study the mapping from sequence to structure. There are strong, qualitative differences between two-letter and four or six-letter alphabets. With only two kinds of bases, there are many alternate folding configurations, yielding thermodynamically stable ground-states only for a small set of structures of high designability, i.e., total number of associated sequences. In contrast, sequences made from four bases, as found in nature, or six bases have far fewer competing folding configurations, resulting in a much greater average stability of the ground state.Comment: 7 figures; uses revtex

Translocation of structured polynucleotides through nanopores

We investigate theoretically the translocation of structured RNA/DNA molecules through narrow pores which allow single but not double strands to pass. The unzipping of basepaired regions within the molecules presents significant kinetic barriers for the translocation process. We show that this circumstance may be exploited to determine the full basepairing pattern of polynucleotides, including RNA pseudoknots. The crucial requirement is that the translocation dynamics (i.e., the length of the translocated molecular segment) needs to be recorded as a function of time with a spatial resolution of a few nucleotides. This could be achieved, for instance, by applying a mechanical driving force for translocation and recording force-extension curves (FEC's) with a device such as an atomic force microscope or optical tweezers. Our analysis suggests that with this added spatial resolution, nanopores could be transformed into a powerful experimental tool to study the folding of nucleic acids.Comment: 9 pages, 5 figure

Statistical mechanics of secondary structures formed by random RNA sequences

The formation of secondary structures by a random RNA sequence is studied as a model system for the sequence-structure problem omnipresent in biopolymers. Several toy energy models are introduced to allow detailed analytical and numerical studies. First, a two-replica calculation is performed. By mapping the two-replica problem to the denaturation of a single homogeneous RNA in 6-dimensional embedding space, we show that sequence disorder is perturbatively irrelevant, i.e., an RNA molecule with weak sequence disorder is in a molten phase where many secondary structures with comparable total energy coexist. A numerical study of various models at high temperature reproduces behaviors characteristic of the molten phase. On the other hand, a scaling argument based on the extremal statistics of rare regions can be constructed to show that the low temperature phase is unstable to sequence disorder. We performed a detailed numerical study of the low temperature phase using the droplet theory as a guide, and characterized the statistics of large-scale, low-energy excitations of the secondary structures from the ground state structure. We find the excitation energy to grow very slowly (i.e., logarithmically) with the length scale of the excitation, suggesting the existence of a marginal glass phase. The transition between the low temperature glass phase and the high temperature molten phase is also characterized numerically. It is revealed by a change in the coefficient of the logarithmic excitation energy, from being disorder dominated to entropy dominated.Comment: 24 pages, 16 figure

Understanding the errors of SHAPE-directed RNA structure modeling

Single-nucleotide-resolution chemical mapping for structured RNA is being rapidly advanced by new chemistries, faster readouts, and coupling to computational algorithms. Recent tests have shown that selective 2'-hydroxyl acylation by primer extension (SHAPE) can give near-zero error rates (0-2%) in modeling the helices of RNA secondary structure. Here, we benchmark the method using six molecules for which crystallographic data are available: tRNA(phe) and 5S rRNA from Escherichia coli, the P4-P6 domain of the Tetrahymena group I ribozyme, and ligand-bound domains from riboswitches for adenine, cyclic di-GMP, and glycine. SHAPE-directed modeling of these highly structured RNAs gave an overall false negative rate (FNR) of 17% and a false discovery rate (FDR) of 21%, with at least one helix prediction error in five of the six cases. Extensive variations of data processing, normalization, and modeling parameters did not significantly mitigate modeling errors. Only one varation, filtering out data collected with deoxyinosine triphosphate during primer extension, gave a modest improvement (FNR = 12%, and FDR = 14%). The residual structure modeling errors are explained by the insufficient information content of these RNAs' SHAPE data, as evaluated by a nonparametric bootstrapping analysis. Beyond these benchmark cases, bootstrapping suggests a low level of confidence (<50%) in the majority of helices in a previously proposed SHAPE-directed model for the HIV-1 RNA genome. Thus, SHAPE-directed RNA modeling is not always unambiguous, and helix-by-helix confidence estimates, as described herein, may be critical for interpreting results from this powerful methodology.Comment: Biochemistry, Article ASAP (Aug. 15, 2011

The Vienna RNA Websuite

The Vienna RNA Websuite is a comprehensive collection of tools for folding, design and analysis of RNA sequences. It provides a web interface to the most commonly used programs of the Vienna RNA package. Among them, we find folding of single and aligned sequences, prediction of RNA–RNA interactions, and design of sequences with a given structure. Additionally, we provide analysis of folding landscapes using the barriers program and structural RNA alignments using LocARNA. The web server together with software packages for download is freely accessible at http://rna.tbi.univie.ac.at/

Discriminatory power of RNA family models

Motivation: RNA family models group nucleotide sequences that share a common biological function. These models can be used to find new sequences belonging to the same family. To succeed in this task, a model needs to exhibit high sensitivity as well as high specificity. As model construction is guided by a manual process, a number of problems can occur, such as the introduction of more than one model for the same family or poorly constructed models. We explore the Rfam database to discover such problems

R-Coffee: a web server for accurately aligning noncoding RNA sequences

The R-Coffee web server produces highly accurate multiple alignments of noncoding RNA (ncRNA) sequences, taking into account predicted secondary structures. R-Coffee uses a novel algorithm recently incorporated in the T-Coffee package. R-Coffee works along the same lines as T-Coffee: it uses pairwise or multiple sequence alignment (MSA) methods to compute a primary library of input alignments. The program then computes an MSA highly consistent with both the alignments contained in the library and the secondary structures associated with the sequences. The secondary structures are predicted using RNAplfold. The server provides two modes. The slow/accurate mode is restricted to small datasets (less than 5 sequences less than 150 nucleotides) and combines R-Coffee with Consan, a very accurate pairwise RNA alignment method. For larger datasets a fast method can be used (RM-Coffee mode), that uses R-Coffee to combine the output of the three packages which combines the outputs from programs found to perform best on RNA (MUSCLE, MAFFT and ProbConsRNA). Our BRAliBase benchmarks indicate that the R-Coffee/Consan combination is one of the best ncRNA alignment methods for short sequences, while the RM-Coffee gives comparable results on longer sequences. The R-Coffee web server is available at http://www.tcoffee.org