RNA structures and folding: from conventional to new issues in structure predictions

Global epistasis on fitness landscapes

Epistatic interactions between mutations add substantial complexity to adaptive landscapes and are often thought of as detrimental to our ability to predict evolution. Yet, patterns of global epistasis, in which the fitness effect of a mutation is well-predicted by the fitness of its genetic background, may actually be of help in our efforts to reconstruct fitness landscapes and infer adaptive trajectories. Microscopic interactions between mutations, or inherent nonlinearities in the fitness landscape, may cause global epistasis patterns to emerge. In this brief review, we provide a succinct overview of recent work about global epistasis, with an emphasis on building intuition about why it is often observed. To this end, we reconcile simple geometric reasoning with recent mathematical analyses, using these to explain why different mutations in an empirical landscape may exhibit different global epistasis patterns—ranging from diminishing to increasing returns. Finally, we highlight open questions and research directions.

This article is part of the theme issue ‘Interdisciplinary approaches to predicting evolutionary biology’.

Improving RNA Branching Predictions: Advances and Limitations

Minimum free energy prediction of RNA secondary structures is based on the Nearest Neighbor Thermodynamics Model. While such predictions are typically good, the accuracy can vary widely even for short sequences, and the branching thermodynamics are an important factor in this variance. Recently, the simplest model for multiloop energetics—a linear function of the number of branches and unpaired nucleotides—was found to be the best. Subsequently, a parametric analysis demonstrated that per family accuracy can be improved by changing the weightings in this linear function. However, the extent of improvement was not known due to the ad hoc method used to find the new parameters. Here we develop a branch-and-bound algorithm that finds the set of optimal parameters with the highest average accuracy for a given set of sequences. Our analysis shows that the previous ad hoc parameters are nearly optimal for tRNA and 5S rRNA sequences on both training and testing sets. Moreover, cross-family improvement is possible but more difficult because competing parameter regions favor different families. The results also indicate that restricting the unpaired nucleotide penalty to small values is warranted. This reduction makes analyzing longer sequences using the present techniques more feasible.

RNA substructure as a random matrix ensemble

Combinatorial analysis of a certain abstraction of RNA structures has been studied to investigate their statistics. Our approach regards the backbone of secondary structures as an alternate sequence of paired and unpaired sets of nucleotides, which can be described by a random matrix model. We obtain the generating function of the structures using the Hermitian matrix model with the Chebyshev polynomial of the second kind and analyze the statistics with respect to the number of stems. To match the experimental findings of the statistical behavior, we consider the structures in a grand canonical ensemble and find a fugacity value corresponding to an appropriate number of stems.

The challenge of RNA branching prediction: a parametric analysis of multiloop initiation under thermodynamic optimization

Prediction of RNA base pairings yields insight into molecular structure, and therefore function. The most common methods predict an optimal structure under the standard thermodynamic model. One component of this model is the equation which governs the cost of branching, where three or more helical "arms" radiate out from a multiloop (also known as a junction). The multiloop initiation equation has three parameters; changing those values can significantly alter the predicted structure. We give a complete analysis of the prediction accuracy, stability, and robustness for all possible parameter combinations for a diverse set of tRNA sequences, and also for 5S rRNA. We find that the accuracy can often be substantially improved on a per sequence basis. However, simultaneous improvement within families, and most especially between families, remains a challenge.

Fine-grained parallelism accelerating for RNA secondary structure prediction with pseudoknots based on FPGA

PKNOTS is a most famous benchmark program and has been widely used to predict RNA secondary structure including pseudoknots. It adopts the standard four-dimensional (4D) dynamic programming (DP) method and is the basis of many variants and improved algorithms. Unfortunately, the O(N(6)) computing requirements and complicated data dependency greatly limits the usefulness of PKNOTS package with the explosion in gene database size. In this paper, we present a fine-grained parallel PKNOTS package and prototype system for accelerating RNA folding application based on FPGA chip. We adopted a series of storage optimization strategies to resolve the "Memory Wall" problem. We aggressively exploit parallel computing strategies to improve computational efficiency. We also propose several methods that collectively reduce the storage requirements for FPGA on-chip memory. To the best of our knowledge, our design is the first FPGA implementation for accelerating 4D DP problem for RNA folding application including pseudoknots. The experimental results show a factor of more than 50x average speedup over the PKNOTS-1.08 software running on a PC platform with Intel Core2 Q9400 Quad CPU for input RNA sequences. However, the power consumption of our FPGA accelerator is only about 50% of the general-purpose micro-processors.

A hybrid neural network system for prediction and recognition of promoter regions in human genome

This paper proposes a high specificity and sensitivity algorithm called PromPredictor for recognizing promoter regions in the human genome. PromPredictor extracts compositional features and CpG islands information from genomic sequence, feeding these features as input for a hybrid neural network system (HNN) and then applies the HNN for prediction. It combines a novel promoter recognition model, coding theory, feature selection and dimensionality reduction with machine learning algorithm. Evaluation on Human chromosome 22 was approximately 66% in sensitivity and approximately 48% in specificity. Comparison with two other systems revealed that our method had superior sensitivity and specificity in predicting promoter regions. PromPredictor is written in MATLAB and requires Matlab to run. PromPredictor is freely available at http://www.whtelecom.com/Prompredictor.htm.

Grass evolution inferred from chromosomal rearrangements and geometrical and statistical features in RNA structure

The grasses (Poaceae) represent a monophyletic lineage that arose about 70 million years ago. The lineage contains about 10,000 species that differ widely in morphology and physiology. Species show striking differences in genome size, a feature important in the context of conservation of gene content and order (synteny and colinearity) and in the extension of genomic information directly from one grass species to another using comparative approaches. Grass diversification has been a contentious issue, as the exact branching order of the various subfamilies has been difficult to establish with standard methods. This motivated an evolutionary study of deep phylogenetic relationships based on the structure of coding and non-coding RNA molecules and on chromosomal rearrangements. Phylogenetic relationships in the grass family were inferred directly from the structure of RNA using cladistic principles and considerations in statistical mechanics. Coded attributes describing topological and thermodynamic information embedded in RNA molecules were treated as linearly ordered multi-state characters and were polarized by fixing the direction of character transformation toward molecular order. Intrinsically rooted phylogenies derived from the structure of signal recognition particle (SRP) RNA, the mRNA encoded by the early nodulation gene enod40, the small subunit of ribosomal RNA (rRNA), and the internal transcribed spacer ITS1 of rRNA established an order for the diversification of major grass lineages, suggesting a sister relationship of the Pooideae and the PACCAD clade. This same conclusion was reached when large-scale chromosomal rearrangements derived from the comparative genetic mapping of cereal genomes were studied. Chromosomal complements aligned in the most parsimonious manner allowed identification and coding of characters depicting chromosomal translocations, insertions, and linkage block arrangements and the reconstruction of phylogenetic trees based on large-scale chromosomal structure. Congruent reconstruction of deep branching relationships using geometrical and statistical features of RNA structure and orthology and large scale chromosomal recombination events support assumptions of polarization in character argumentation, and fail to falsify the claim that extant grass chromosomes can be considered combinations of linkage blocks of an ancestor of the rice genome. Congruence also suggests that the universal tendency toward order in RNA and the search for the most parsimonious organization of be genome architecture appear to be mutually supported drivers of molecular evolution. The study clarifies the relationship of major clades in the grasses, shows that phylogenetic history can be reconstructed effectively from the combinatorial exchange of chromosomal linkage blocks, and reveals considerable phylogenetic signal embedded in the structure of signal polypeptide-coding mRNA molecules, describing an instance where mRNA structure is the subject of strong evolutionary constraint.

The 18S rDNA sequence of Synchytrium endobioticum and its utility in microarrays for the simultaneous detection of fungal and viral pathogens of potato

Resting spores extracted from wart (Synchytrium endobioticum)-infected potato tubers were used for DNA extraction and amplification of 18S rDNA. Analysis of the cloned, sequenced fragment revealed high similarity to members of the Chytridiomycota. Using this information, specific oligonucleotide probes were designed and arrayed onto glass slides for detection of the pathogen. Viral sequence information available in the databank was retrieved, or new viral sequences were generated, and used to design probes for specific detection of important quarantine viruses of potato. To determine the sensitivity and specificity of the oligonucleotide probes, total RNA from infected plants was reverse transcribed, labelled with Cyanine 5, and hybridised with the microarray. A significant number of the oligonucleotide probes exhibited high specificity to S. endobioticum, Andean potato latent virus, Andean potato mottle virus, Potato black ringspot virus, and Potato spindle tuber viroid. Hybridisation signals of sub-arrays within slides were reproducible (r = 0.79) with a high correlation coefficient of hybridisation repetitions (0.73). Our results demonstrate the potential of microarray-based hybridisation for identification of multiple pathogen targets, which will find application in quarantine laboratories, where parallel testing for diverse pathogens is essential.

Validation of automated docking programs for docking and database screening against RNA drug targets

The increasing awareness of the essential role of RNA in controlling viral replication and in bacterial protein synthesis emphasizes the potential of ribonucleoproteins as targets for developing new antibacterial and antiviral drugs. RNA forms well defined three-dimensional structures with clefts and binding pockets reminiscent of the active sites of proteins. Furthermore, it precedes proteins in the translation pathway; inhibiting the function of a single RNA molecule would result in inhibition of multiple proteins. Thus, small molecules that bind RNA specifically would combine the advantages of antisense and RNAi strategies with the much more favorable medicinal chemistry of small-molecule therapeutics. The discovery of small-molecule inhibitors of RNA with attractive pharmacological potential would be facilitated if we had available effective computational tools of structure-based drug design. Here, we systematically test automated docking tools developed for proteins using existing three-dimensional structures of RNA-small molecule complexes. The results show that the native structures can generally be reproduced to within 2.5 angstroms more than 50-60% of the time. For more than half of the test complexes, the native ligand ranked among the top 10% compounds in a database-scoring test. Through this work, we provide parameters for the validated application of automated docking tools to the discovery of new inhibitors of RNA function.

A permutation-based genetic algorithm for the RNA folding problem: a critical look at selection strategies, crossover operators, and representation issues

This paper presents a Genetic Algorithm (GA) to predict the secondary structure of RNA molecules, where the secondary structure is encoded as a permutation. More specifically, the proposed algorithm predicts which specific canonical base pairs will form hydrogen bonds and build helices, also known as stems. Since RNA is involved in both transcription and translation and also has catalytic and structural roles in the cell, determining the structure of RNA is of fundamental importance in helping to determine RNA function. We introduce a GA where a permutation is used to encode the secondary structure of RNA molecules. We discuss results on RNA sequences of lengths 76, 210, 681, and 785 nucleotides and present several improvements to our algorithm. We show that the Keep-Best Reproduction operator has similar benefits as in the traveling salesman problem domain. In addition, a comparison of several crossover operators is provided. We also compare the results of the permutation-based GA with a binary GA, demonstrating the benefits of the newly proposed representation.

Generalized topological spaces in evolutionary theory and combinatorial chemistry

The search spaces in combinatorial chemistry as well as the sequence spaces underlying (molecular) evolution are conventionally thought of as graphs. Recombination, however, implies a nongraphical structure of the combinatorial search spaces. These structures, and their implications for search process itself, are heretofore not well understood in general. In this contribution we review a very general formalism from point set topology and discuss its application to combinatorial search spaces, fitness landscapes, evolutionary trajectories, and artificial chemistries.

Randomness, Structural Uniqueness, Modularity and Neutral Evolution in Sequence Space of Model Proteins

The genotype-phenotype map for short chains of a protein-like hetero-polymer model has been characterised [9, 12]. Hydrophobic-Polar (HP) sequences on a square lattice, their structures and partition functions have been exhaustively enumerated and analysed. Homologous sequences folding uniquely into the same structure are interconnected by point mutations. These

Influence of mRNA self-structure on hybridization: computational tools for antisense sequence selection

Antisense targeting, an innovative technology based on preventing biosynthesis through sequence-specific hybridization of mRNA to synthetic oligodeoxynucleotides (ODNs), is used to selectively and transiently downregulate the expression of any gene product. Its potential applications are both investigative (neurobiology and related disciplines) and therapeutic (oncology, virology, genetic diseases), and several antisense-based drugs are currently undergoing clinical trials. However, the reported efficiencies vary and there is still a lack of clarity in the underlying mechanisms of action. A critical factor of antisense efficiency is the issue of target site selection, as both mRNA and ODN molecules exhibit a significant amount of highly heterogeneous self-structure and the region selected for targeting may well be sterically or energetically inaccessible. Because of the prohibitively large chain length, mRNA structural information is not accessible by X-ray crystallography or NMR, making a modeling approach indispensable. I outline how the latest molecular modeling techniques can be employed to establish the secondary (2D) and tertiary (3D) structures into which a given mRNA folds during and after transcription. The aim should be to integrate 2D prediction results achieved by (a) free-energy minimization, (b) kinetic folding simulations, (c) iterative population breeding by genetic algorithms, and (d) phylogenetic comparison techniques. These results can form the input of a 3D structure prediction paradigm based on constraint-satisfying programming, governed by experimental molecular mechanical constraints, and refined by molecular dynamics simulations. Finally, the automated docking (by simulated annealing) of ODN molecules to the mRNA structure can provide information about the accessibility of target mRNA regions for hybridization. To date, the great majority of studies that employ antisense as a tool select their target sequences more or less randomly. Although the wealth of molecular interactions that take place within a cell makes complete predictability unrealistic, the kind of information that can be extracted from such techniques is of relevance to every application of antisense technology, both investigative and therapeutic.

RNA as a drug target: methods for biophysical characterization and screening

RNA folds into complex structures that can interact specifically with effector proteins. These interactions are essential for various biological functions. In order to discover small molecules that can affect important RNA-protein complexes, a thorough analysis of the thermodynamics and kinetics of RNA-protein binding is required. This can facilitate the formulation of high-throughput screening strategies and the development of structure-activity relationships for compound leads. In addition to traditional methods, such as filter binding, gel mobility shift assay and various fluorescence techniques, newer methods such as surface plasmon resonance and mass spectrometry are being used for the study of RNA-protein interactions.

RNA shape space topology

The distinction between continuous and discontinuous transitions is a long-standing problem in the theory of evolution. Because continuity is a topological property, we present a formalism that treats the space of phenotypes as a (finite) topological space, with a topology that is derived from the probabilities with which one phenotype is accessible from another through changes at the genotypic level. The shape space of RNA secondary structures is used to illustrate this approach. We show that evolutionary trajectories are continuous if and only if they follow connected paths in phenotype space.

ConStruct: a tool for thermodynamic controlled prediction of conserved secondary structure

A tool for prediction of conserved secondary structure of a set of homologous single-stranded RNAs is presented. For each RNA of the set the structure distribution is calculated and stored in a base pair probability matrix. Gaps, resulting from a multiple sequence alignment of the RNA set, are introduced into the individual probability matrices. These 'aligned' probability matrices are summed up to give a consensus probability matrix emphasizing the conserved structural elements of the RNA set. Because the multiple sequence alignment is independent of any structural constraints, such an alignment may result in introduction of gaps into the homologous probability matrices that disrupt a common consensus structure. By use of its graphical user interface the presented tool allows the removal of such misalignments, which are easily recognized, from the individual probability matrices by optimizing the sequence alignment with respect to a structural alignment. From the consensus probability matrix a consensus structure is extracted, which is viewable in three different graphical representations. The functionality of the tool is demonstrated using a small set of U7 RNAs, which are involved in 3'-end processing of histone mRNA precursors. Supplementary Material lists further results obtained. Advantages and drawbacks of the tool are discussed in comparison to several other algorithms.

Acquisition of novel catalytic activity by the M1 RNA ribozyme: the cost of molecular adaptation

The ribonucleoprotein RNase P is a critical component of metabolism in all known organisms. In Escherichia coli, RNase P processes a vast array of substrates, including precursor-tRNAs and precursor 4. 5S RNA. In order to understand how such catalytic versatility is achieved and how novel catalytic activity can be acquired, we evolve the M1 RNA ribozyme (the catalytic component of E. coli RNase P) in vitro for cleavage of a DNA substrate. In so doing, we probe the consequences of enhancing catalytic activity on a novel substrate and investigate the cost this versatile enzyme pays for molecular adaptation. A total of 25 generations of in vitro evolution yield a population showing more than a 1000-fold increase in DNA substrate cleavage efficiency (kcat/KM) relative to wild-type M1 RNA. This enhancement is accompanied by a significant reduction in the ability of evolved ribozymes to process the ptRNA class of substrates but also a contrasting increase in activity on the p4.5S RNA class of substrates. This change in the catalytic versatility of the evolved ribozymes suggests that the acquired activity comes at the cost of substrate versatility, and indicates that E. coli RNase P catalytic flexibility is maintained in vivo by selection for the processing of multiple substrates. M1 RNA derivatives enhance cleavage of the DNA substrate by accelerating the catalytic step (kcat) of DNA cleavage, although overall processing efficiency is offset by reduced substrate binding. The enhanced ability to cleave a DNA substrate cannot be readily traced to any of the predominant mutations found in the evolved population, and must instead be due to multiple sequence changes dispersed throughout the molecule. This conclusion underscores the difficulty of correlating observed mutations with changes in catalytic behavior, even in simple biological catalysts for which three-dimensional models are available.

A dynamic programming algorithm for RNA structure prediction including pseudoknots

We describe a dynamic programming algorithm for predicting optimal RNA secondary structure, including pseudoknots. The algorithm has a worst case complexity of O(N6) in time and O(N4) in storage. The description of the algorithm is complex, which led us to adopt a useful graphical representation (Feynman diagrams) borrowed from quantum field theory. We present an implementation of the algorithm that generates the optimal minimum energy structure for a single RNA sequence, using standard RNA folding thermodynamic parameters augmented by a few parameters describing the thermodynamic stability of pseudoknots. We demonstrate the properties of the algorithm by using it to predict structures for several small pseudoknotted and non-pseudoknotted RNAs. Although the time and memory demands of the algorithm are steep, we believe this is the first algorithm to be able to fold optimal (minimum energy) pseudoknotted RNAs with the accepted RNA thermodynamic model.

Simulations of the molecular dynamics of nucleic acids

The growing amount of high quality molecular dynamics simulations generated using the latest methodological developments and force fields has led to a sharper understanding of the forces underlying the dynamics of biomolecular systems, as well as to stimulating insights into the structure and catalysis of nucleic acids. It is now clear that inclusion of long-range electrostatic interactions and of the aqueous and ionic environment is necessary for producing realistic and accurate simulations. Yet, many papers hint at a force field and protocol dependence of the results and thus contain the seeds for the future improvements that will be necessary for deepening our understanding of recognition phenomena and folding of nucleic acids.

Modern methods for probing RNA structure

Molecular biologists have been remarkably successful in dividing large RNAs into small functional modules manageable for NMR and X-ray studies. At the same time biophysical, biochemical and genetic tools in RNA structure determination have reached a level of sophistication, at which we start to see a glimpse of molecular dynamics and the mechanism of RNA mediated catalysis.

Neutral networks in protein space: a computational study based on knowledge-based potentials of mean force

BACKGROUND

Many protein sequences, often unrelated, adopt similar folds. Sequences folding into the same shape thus form subsets of sequence space. The shape and the connectivity of these sets have implications for protein evolution and de novo design.

RESULTS

We investigate the topology of these sets for some proteins with known three-dimensional structure using inverse folding techniques. First, we find that sequences adopting a given fold do not cluster in sequence space and that there is no detectable sequence homology among them. Nevertheless, these sequences are connected in the sense that there exists a path such that every sequence can be reached from every other sequence while the fold remains unchanged. We find similar results for restricted amino acid alphabets in some cases (e. g. ADLG). In other cases, it seems impossible to find sequences with native-like behavior (e.g. QLR). These findings seem to be independent of the particular structure considered.

CONCLUSIONS

Amino acid sequences folding into a common shape are distributed homogeneously in sequence space. Hence, the connectivity of the set of these sequences implies the existence of very long neutral paths on all examined protein structures. Regarding protein design, these results imply that sequences with more or less arbitrary chemical properties can be attached to a given structural framework. But we also observe that designability varies significantly among native structures. These features of protein sequence space are similar to what has been found for nucleic acids.