Abstract folding space analysis based on helices

Classified Dynamic Programming in RNA Structure Analysis

Analysis of the folding space of RNA generally suffers from its exponential size. With classified Dynamic Programming algorithms, it is possible to alleviate this burden and to analyse the folding space of RNA in great depth. Key to classified DP is that the search space is partitioned into classes based on an on-the-fly computed feature. A class-wise evaluation is then used to compute class-wide properties, such as the lowest free energy structure for each class, or aggregate properties, such as the class' probability. In this paper we describe the well-known shape and hishape abstraction of RNA structures, their power to help better understand RNA function and related methods that are based on these abstractions.

Simulation of Folding Kinetics for Aligned RNAs

Studying the folding kinetics of an RNA can provide insight into its function and is thus a valuable method for RNA analyses. Computational approaches to the simulation of folding kinetics suffer from the exponentially large folding space that needs to be evaluated. Here, we present a new approach that combines structure abstraction with evolutionary conservation to restrict the analysis to common parts of folding spaces of related RNAs. The resulting algorithm can recapitulate the folding kinetics known for single RNAs and is able to analyse even long RNAs in reasonable time. Our program RNAliHiKinetics is the first algorithm for the simulation of consensus folding kinetics and addresses a long-standing problem in a new and unique way.

Helix-Based RNA Landscape Partition and Alternative Secondary Structure Determination

RNA is a versatile macromolecule with the ability to fold into and interconvert between multiple functional conformations. The elucidation of the RNA folding landscape, especially the knowledge of alternative structures, is critical to uncover the physical mechanism of RNA functions. Here, we introduce a helix-based strategy for RNA folding landscape partition and alternative secondary structure determination. The benchmark test of 27 RNAs involving alternative stable structures shows that the model has the ability to divide the whole landscape into distinct partitions at the secondary structure level and predict the representative structures for each partition. Furthermore, the predicted structures and equilibrium populations of metastable conformations for the 2'dG-sensing riboswitch reveal the allosteric conformational switch on transcript length, which is consistent with the experimental study, indicating the importance of metastable states for RNA-based gene regulation. The model delivers a starting point for the landscape-based strategy toward the RNA folding mechanism and functions.

Towards an understanding of RNA structural modalities: a riboswitch case study

A riboswitch is a type of RNA molecule that regulates important biological functions by changing structure, typically under ligand-binding. We assess the extent that these ligand-bound structural alternatives are present in the Boltzmann sample, a standard RNA secondary structure prediction method, for three riboswitch test cases. We use the cluster analysis tool RNAStructProfiling to characterize the different modalities present among the suboptimal structures sampled. We compare these modalities to the putative base pairing models obtained from independent experiments using NMR or fluorescence spectroscopy. We find, somewhat unexpectedly, that profiling the Boltzmann sample captures evidence of ligand-bound conformations for two of three riboswitches studied. Moreover, this agreement between predicted modalities and experimental models is consistent with the classification of riboswitches into thermodynamic versus kinetic regulatory mechanisms. Our results support cluster analysis of Boltzmann samples by RNAStructProfiling as a possible basis for de novo identification of thermodynamic riboswitches, while highlighting the challenges for kinetic ones.

Computational approaches for alternative and transient secondary structures of ribonucleic acids

Transient and alternative structures of ribonucleic acids (RNAs) play essential roles in various regulatory processes, such as translation regulation in living cells. Because experimental analyses for RNA structures are difficult and time-consuming, computational approaches based on RNA secondary structures are promising. In this article, we review computational methods for detecting and analyzing transient/alternative secondary structures of RNAs, including static approaches based on probabilistic distributions of RNA secondary structures and dynamic approaches such as kinetic folding and folding pathway predictions.

Swellix: a computational tool to explore RNA conformational space

Background

The sequence of nucleotides in an RNA determines the possible base pairs for an RNA fold and thus also determines the overall shape and function of an RNA. The Swellix program presented here combines a helix abstraction with a combinatorial approach to the RNA folding problem in order to compute all possible non-pseudoknotted RNA structures for RNA sequences. The Swellix program builds on the Crumple program and can include experimental constraints on global RNA structures such as the minimum number and lengths of helices from crystallography, cryoelectron microscopy, or in vivo crosslinking and chemical probing methods.

Results

The conceptual advance in Swellix is to count helices and generate all possible combinations of helices rather than counting and combining base pairs. Swellix bundles similar helices and includes improvements in memory use and efficient parallelization. Biological applications of Swellix are demonstrated by computing the reduction in conformational space and entropy due to naturally modified nucleotides in tRNA sequences and by motif searches in Human Endogenous Retroviral (HERV) RNA sequences. The Swellix motif search reveals occurrences of protein and drug binding motifs in the HERV RNA ensemble that do not occur in minimum free energy or centroid predicted structures.

Conclusions

Swellix presents significant improvements over Crumple in terms of efficiency and memory use. The efficient parallelization of Swellix enables the computation of sequences as long as 418 nucleotides with sufficient experimental constraints. Thus, Swellix provides a practical alternative to free energy minimization tools when multiple structures, kinetically determined structures, or complex RNA-RNA and RNA-protein interactions are present in an RNA folding problem.

Electronic supplementary material

The online version of this article (10.1186/s12859-017-1910-7) contains supplementary material, which is available to authorized users.

Random versus Deterministic Descent in RNA Energy Landscape Analysis

Identifying sets of metastable conformations is a major research topic in RNA energy landscape analysis, and recently several methods have been proposed for finding local minima in landscapes spawned by RNA secondary structures. An important and time-critical component of such methods is steepest, or gradient, descent in attraction basins of local minima. We analyse the speed-up achievable by randomised descent in attraction basins in the context of large sample sets where the size has an order of magnitude in the region of ~10⁶. While the gain for each individual sample might be marginal, the overall run-time improvement can be significant. Moreover, for the two nongradient methods we analysed for partial energy landscapes induced by ten different RNA sequences, we obtained that the number of observed local minima is on average larger by 7.3% and 3.5%, respectively. The run-time improvement is approximately 16.6% and 6.8% on average over the ten partial energy landscapes. For the large sample size we selected for descent procedures, the coverage of local minima is very high up to energy values of the region where the samples were randomly selected from the partial energy landscapes; that is, the difference to the total set of local minima is mainly due to the upper area of the energy landscapes.

New insights from cluster analysis methods for RNA secondary structure prediction

A widening gap exists between the best practices for RNA secondary structure prediction developed by computational researchers and the methods used in practice by experimentalists. Minimum free energy predictions, although broadly used, are outperformed by methods which sample from the Boltzmann distribution and data mine the results. In particular, moving beyond the single structure prediction paradigm yields substantial gains in accuracy. Furthermore, the largest improvements in accuracy and precision come from viewing secondary structures not at the base pair level but at lower granularity/higher abstraction. This suggests that random errors affecting precision and systematic ones affecting accuracy are both reduced by this 'fuzzier' view of secondary structures. Thus experimentalists who are willing to adopt a more rigorous, multilayered approach to secondary structure prediction by iterating through these levels of granularity will be much better able to capture fundamental aspects of RNA base pairing. WIREs RNA 2016, 7:278-294. doi: 10.1002/wrna.1334 For further resources related to this article, please visit the WIREs website.

Thermodynamic matchers for the construction of the cuckoo RNA family

RNA family models describe classes of functionally related, non-coding RNAs based on sequence and structure conservation. The most important method for modeling RNA families is the use of covariance models, which are stochastic models that serve in the discovery of yet unknown, homologous RNAs. However, the performance of covariance models in finding remote homologs is poor for RNA families with high sequence conservation, while for families with high structure but low sequence conservation, these models are difficult to built in the first place. A complementary approach to RNA family modeling involves the use of thermodynamic matchers. Thermodynamic matchers are RNA folding programs, based on the established thermodynamic model, but tailored to a specific structural motif. As thermodynamic matchers focus on structure and folding energy, they unfold their potential in discovering homologs, when high structure conservation is paired with low sequence conservation. In contrast to covariance models, construction of thermodynamic matchers does not require an input alignment, but requires human design decisions and experimentation, and hence, model construction is more laborious. Here we report a case study on an RNA family that was constructed by means of thermodynamic matchers. It starts from a set of known but structurally different members of the same RNA family. The consensus secondary structure of this family consists of 2 to 4 adjacent hairpins. Each hairpin loop carries the same motif, CCUCCUCCC, while the stems show high variability in their nucleotide content. The present study describes (1) a novel approach for the integration of the structurally varying family into a single RNA family model by means of the thermodynamic matcher methodology, and (2) provides the results of homology searches that were conducted with this model in a wide spectrum of bacterial species.

An implementation of the Gillespie algorithm for RNA kinetics with logarithmic time update

In this paper I outline a fast method called KFOLD for implementing the Gillepie algorithm to stochastically sample the folding kinetics of an RNA molecule at single base-pair resolution. In the same fashion as the KINFOLD algorithm, which also uses the Gillespie algorithm to predict folding kinetics, KFOLD stochastically chooses a new RNA secondary structure state that is accessible from the current state by a single base-pair addition/deletion following the Gillespie procedure. However, unlike KINFOLD, the KFOLD algorithm utilizes the fact that many of the base-pair addition/deletion reactions and their corresponding rates do not change between each step in the algorithm. This allows KFOLD to achieve a substantial speed-up in the time required to compute a prediction of the folding pathway and, for a fixed number of base-pair moves, performs logarithmically with sequence size. This increase in speed opens up the possibility of studying the kinetics of much longer RNA sequences at single base-pair resolution while also allowing for the RNA folding statistics of smaller RNA sequences to be computed much more quickly.

Profiling small RNA reveals multimodal substructural signals in a Boltzmann ensemble

As the biomedical impact of small RNAs grows, so does the need to understand competing structural alternatives for regions of functional interest. Suboptimal structure analysis provides significantly more RNA base pairing information than a single minimum free energy prediction. Yet computational enhancements like Boltzmann sampling have not been fully adopted by experimentalists since identifying meaningful patterns in this data can be challenging. Profiling is a novel approach to mining RNA suboptimal structure data which makes the power of ensemble-based analysis accessible in a stable and reliable way. Balancing abstraction and specificity, profiling identifies significant combinations of base pairs which dominate low-energy RNA secondary structures. By design, critical similarities and differences are highlighted, yielding crucial information for molecular biologists. The code is freely available via http://gtfold.sourceforge.net/profiling.html.

Analysing RNA-kinetics based on folding space abstraction

BACKGROUND

RNA molecules, especially non-coding RNAs, play vital roles in the cell and their biological functions are mostly determined by structural properties. Often, these properties are related to dynamic changes in the structure, as in the case of riboswitches, and thus the analysis of RNA folding kinetics is crucial for their study. Exact approaches to kinetic folding are computationally expensive and, thus, limited to short sequences. In a previous study, we introduced a position-specific abstraction based on helices which we termed helix index shapes (hishapes) and a hishape-based algorithm for near-optimal folding pathway computation, called HiPath. The combination of these approaches provides an abstract view of the folding space that offers information about the global features.

RESULTS

In this paper we present HiKinetics, an algorithm that can predict RNA folding kinetics for sequences up to several hundred nucleotides long. This algorithm is based on RNAHeliCes, which decomposes the folding space into abstract classes, namely hishapes, and an improved version of HiPath, namely HiPath2, which estimates plausible folding pathways that connect these classes. Furthermore, we analyse the relationship of hishapes to locally optimal structures, the results of which strengthen the use of the hishape abstraction for studying folding kinetics. Finally, we show the application of HiKinetics to the folding kinetics of two well-studied RNAs.

CONCLUSIONS

HiKinetics can calculate kinetic folding based on a novel hishape decomposition. HiKinetics, together with HiPath2 and RNAHeliCes, is available for download at http://www.cyanolab.de/software/RNAHeliCes.htm.

Adaptation and modification of three CRISPR loci in two closely related cyanobacteria

An RNA-based screen was performed to reveal a possible evolutionary scenario for the CRISPR-Cas systems in two cyanobacterial model strains. Following the analysis of a draft genome sequence of Synechocystis sp PCC6714, three different CRISPR-Cas systems were characterized that have different degrees of relatedness to another three CRISPR-Cas systems in Synechocystis sp PCC6803. A subtype III-B system was identified that is extremely conserved between both strains. Strong signals in northern hybridizations and the presence of different spacers (but identical repeats) indicated this system to be active, despite the absence of a known endonuclease candidate gene involved in the maturation of its crRNAs in the two strains. The other two systems were found to differ significantly from each other, with different sets of repeat-spacer arrays and different Cas genes. In view of the otherwise very close relatedness of the two analyzed strains, this is suggestive of an unknown mechanism involved in the replacement of CRISPR-Cas cassettes as a whole. Further RNA analyses revealed the accumulation of crRNAs to be impacted by environmental conditions critical for photoautotropic growth. All six systems are associated with a gene for a possible transcriptional repressor. Indeed, we identified one of these genes, sll7009, as encoding a negative regulator specific for the CRISPR1 subtype I-D system in Synechocystis sp PCC6803.

Bellman's GAP--a language and compiler for dynamic programming in sequence analysis

Motivation: Dynamic programming is ubiquitous in bioinformatics. Developing and implementing non-trivial dynamic programming algorithms is often error prone and tedious. Bellman’s GAP is a new programming system, designed to ease the development of bioinformatics tools based on the dynamic programming technique.

Results: In Bellman’s GAP, dynamic programming algorithms are described in a declarative style by tree grammars, evaluation algebras and products formed thereof. This bypasses the design of explicit dynamic programming recurrences and yields programs that are free of subscript errors, modular and easy to modify. The declarative modules are compiled into C++ code that is competitive to carefully hand-crafted implementations.

This article introduces the Bellman’s GAP system and its language, GAP-L. It then demonstrates the ease of development and the degree of re-use by creating variants of two common bioinformatics algorithms. Finally, it evaluates Bellman’s GAP as an implementation platform of ‘real-world’ bioinformatics tools.

Availability: Bellman’s GAP is available under GPL license from http://bibiserv.cebitec.uni-bielefeld.de/bellmansgap. This Web site includes a repository of re-usable modules for RNA folding based on thermodynamics.

Contact:robert@techfak.uni-bielefeld.de

Supplementary information:Supplementary data are available at Bioinformatics online