Metastable secondary structures in ribosomal RNA molecular hysteresis in the acid-base titration of Escherichia coli ribosomal RNA

The metastable conformational states which underlie the hysteresis displayed by Escherichia coli ribosomal RNA in its pH titration in the acid range have been analyzed in terms of acid-stable RNA secondary structures. Sedimentation measurements show that the phenomenon is intramolecular, so that analysis of the hysteresis loops can, in principle, reveal details of molecular architecture. Hysteresis cycles obtained spectrophotometrically and potentiometrically were compared for RNA in solutions of different ionic strengths and ionic compositions. The effect is much smaller at lower ionic strength and disappears in the absence of magnesium ions. The curve followed upon addition of acid appears to reflect the equilibrium state of the system at each pH value. On the “base branch” of the loop, a slow absorbance change (complete in hours) was observed after the pH was raised by addition of a portion of base. This slow process is attributed to the annealing of “mismatched” multihelical regions of the ribosomal RNA. Certain regions, however, remain in metastable configurations for days and it is these long-lived non-equilibrium structures that underlie the hysteresis. Titration at 35 °C gave hysteresis loops of the same size and shape as at 20 °C; indeed, we found that the metastabilities are not removed even at 80 °C. Ultraviolet light absorbance difference spectra at 80 °C between solutions at the same pH, but on different branches of the cycle, give insight into the nature of the metastable conformation(s).Our experimental observations lead us to propose that the hysteresis is due to the formation at acidic pH of double-helical structures involving protonated guanine and adenine base pairs. The G.G pairs seem especially important to account for the very high thermal stability, as well as for the fact that the structures formed at a given pH value as acid is added dissociate only at higher pH values when the solution is titrated with base. Titrations of transfer RNA, along with literature data on 16 S rRNA primary structure, imply that the metastable regions in rRNA may consist of perhaps 10 to 15 base pairs.     

A new method to find a set of energetically optimal RNA secondary structures.

We present a computer method to determine nucleic acid secondary structures. It is based on three steps: 1) the search for all possible helical regions relied on a mathematical approach derived from the convolution theorem; it uses a tetradimensional complex vector representation of the bases along the sequence; 2) a 'tree' search for a set of minimum free energy structures, by the aid of an approximate energy evaluation to reduce the computer time requirements; 3) the exact calculation and refinement of the energies. A method to introduce the experimental data and reach an arrangement between them and the free energy minimization criterion is shown. In order to demonstrate the confidence of the program a test on four RNA sequences is performed. The method has computer time requirement proportional to N2, where N is the length of the sequence and retrieves a set of optimal free energy structures.     

A method for prediction of conserved RNA secondary structures

The RNA secondary structure prediction is a classical problem in bioinformatics. The most efficient approach to this problem is based on the idea of a comparative analysis. In this approach the algorithms utilize multiple alignment of the RNA sequences and find common RNA structure. This paper describes a new algorithm for this task. This algorithm does not require predefined multiple alignment. The main idea of the algorithm is based on MEME-like iterative searching of abstract profile on different levels. On the first level the algorithm searches the common blocks in the RNA sequences and creates chain of this blocks. On the next step the algorithm refines the chain of common blocks. On the last stage the algorithm searches sets of common helices that have consistent locations relative to common blocks. The algorithm was tested on sets of tRNA with a subset of junk sequences and on RFN riboswitches. The algorithm is implemented as a web server (http://bioinf.fbb.msu.ru/RNAAlign/).     

A method for finding optimal RNA secondary structures using a new entropy model (vsfold)

We are developing a program to calculate optimal RNA secondary structures. The model uses di-nucleotide pairing energies as with most traditional approaches. However, for long-range entropy interactions, the approach uses an entropy-loss model based on the accumulated sum of the entropy of bonding between each base-pair weighted inversely by the correlation of the RNA sequence (the Kuhn length). Stiff RNA forms very different structures from flexible RNA. The results demonstrate that the long-range folding is largely governed by this entropy and the Kuhn length.     

A new Motzkin class for joint RNA secondary structures

In general RNA prediction problem includes genetic mapping, physical mapping and structure prediction. The ultimate goal of structure prediction is to obtain the three dimensional structure of bimolecules through computation. The key concept for solving the above mentioned problem is the appropriate representation of the biological structures. Even though, the problems that concern representations of certain biological structures like secondary structures either are characterized as NP-complete or with high complexity, few approximation algorithms and techniques had been constructed, mainly with polynomial complexity, concerning the prediction of RNA secondary structures. In this paper, a new class of Motzkin paths is introduced, the so-called semi-elevated inverse Motzkin peakless paths for the representation of two interacting RNA molecules. The basic combinatorial interpretations on single RNA secondary structures are extended via these new Motzkin paths on two RNA molecules and can be applied to the prediction methods of joint structures formed by interacting RNAs.     

A method for rapid similarity analysis of RNA secondary structures

Background  

Owing to the rapid expansion of RNA structure databases in recent years, efficient methods for structure comparison are in demand for function prediction and evolutionary analysis. Usually, the similarity of RNA secondary structures is evaluated based on tree models and dynamic programming algorithms. We present here a new method for the similarity analysis of RNA secondary structures.     

G-ribo: a new structural motif in ribosomal RNA

Analysis of the available crystal structures of the ribosome and of its subunits has revealed a new RNA motif that we call G-ribo. The motif consists of two double helices positioned side-by-side and connected by an unpaired region. The juxtaposition of the two helices is kept by a complex system of tertiary interactions spread over several layers of stacked nucleotides. In the center of this arrangement, the ribose of a nucleotide from one helix is specifically packed with the ribose and the minor-groove edge of a guanosine from the other helix. In total, we found eight G-ribo motifs in both ribosomal subunits. The location of these motifs suggests that at least some of them play an important role in the formation of the ribosome structure and/or in its function.     

A method for aligning RNA secondary structures and its application to RNA motif detection

Background  

Alignment of RNA secondary structures is important in studying functional RNA motifs. In recent years, much progress has been made in RNA motif finding and structure alignment. However, existing tools either require a large number of prealigned structures or suffer from high time complexities. This makes it difficult for the tools to process RNAs whose prealigned structures are unavailable or process very large RNA structure databases.     

Conserved RNA secondary structures in viral genomes: a survey

SUMMARY: The genomes of RNA viruses often carry conserved RNA structures that perform vital functions during the life cycle of the virus. Such structures can be detected using a combination of structure prediction and co-variation analysis. Here we present results from pilot studies on a variety of viral families performed during bioinformatics computer lab courses in past years.     

Search for conservative secondary structures of RNA

We suggest a new algorithm to search a given set of the RNA sequences for conserved secondary structures. The algorithm is based on alignment of the sequences for potential helical strands. This procedure can be used to search for new structured RNAs and new regulatory elements. It is efficient for the genome-scale analysis. The results of various tests run with this algorithm are shown.     

Cloning and sequence analysis of the 18 S ribosomal RNA gene of tomato and a secondary structure model for the 18 S rRNA of angiosperms

Summary The gene of a cytoplasmic 18 S ribosomal RNA (18 S rDNA) of the dicotyledonous plant tomato (ycopersicon esculentum) cv. Rentita has been cloned, and its complete primary structure has been determined. The tomato 18 S rDNA is 1805 by long with a G+C content of 49.6%. Its sequence exhibits 94%–96% positional identity when it is colinearly aligned with the previously reported sequences of the 17–18 S rDNAs of the dicot soybean and the monocots maize and rice. A model of the secondary structure of the 18 S rRNA of angiosperms is presented and its genera-specific structural features are compared with a current eukaryotic 18 S rRNA consensus model.     

The secondary structures of the Xenopus laevis and human mitochondrial small ribosomal subunit RNA are similar

Extensive corrections of the nucleotide sequence of the Xenopus laevis mitochondrial small ribosomal subunit RNA gene [Roe et al. (1985) J. Biol. Chem. 260, 9759-9774] are reported. We found an additional fragment of 142 nucleotides and describe 25 nucleotide differences scattered in the gene. The nucleotide sequence the same gene of bovine mitochondrion. We propose a new secondary structure for the product of the X. laevis gene. Contrary to the finding of Roe et al., we observed the same general organization of stems and loops as for the human mitochondrial 12 S rRNA gene product. On the other hand, the structural homology observed between the mitochondrial and cytoplasmic small subunit rRNAs of X. laevis appears much lower. These results strongly suggest that animal vertebrate mitochondrial DNAs have followed the same evolutionary pathway.     

Moments of the Boltzmann distribution for RNA secondary structures

We here present a dynamic programming algorithm which is capable of calculating arbitrary moments of the Boltzmann distribution for RNA secondary structures. We have implemented the algorithm in a program called RNA-VARIANCE and investigate the difference between the Boltzmann distribution of biological and random RNA sequences. We find that the minimum free energy structure of biological sequences has a higher probability in the Boltzmann distribution than random sequences. Moreover, we show that the free energies of biological sequences have a smaller variance than random sequences and that the minimum free energy of biological sequences is closer to the expected free energy of the rest of the structures than that of random sequences. These results suggest that biologically functional RNA sequences not only require a thermodynamically stable minimum free energy structure, but also an ensemble of structures whose free energies are close to the minimum free energy.     

Investigation of the Bernoulli model for RNA secondary structures

Within this paper we investigate the Bernoulli model for random secondary structures of ribonucleic acid (RNA) molecules. Assuming that two random bases can form a hydrogen bond with probability p we prove asymptotic equivalents for the averaged number of hairpins and bulges, the averaged loop length, the expected order, the expected number of secondary structures of size n and order k and further parameters all depending on p. In this way we get an insight into the change of shape of a random structure during the process . Afterwards we compare the computed parameters for random structures in the Bernoulli model to the corresponding quantities for real existing secondary structures of large subunit rRNA molecules found in the database of Wuyts et al. That is how it becomes possible to identify those parameters which behave (almost) randomly and those which do not and thus should be considered as interesting, e.g., with respect to the biological functions or the algorithmic prediction of RNA secondary structures.     

On a six-dimensional representation of RNA secondary structures

In this paper, we proposed a 6-D representation of RNA secondary structures. The use of the 6-D representation is illustrated by constructing structure invariants. Comparisons with the similarity/dissimilarity results based on 6-D representation for a set of RNA secondary structures, are considered to illustrate the use of our structure invariants based on the entries in derived sequence matrices restricted to a selected width of a band along the main diagonal.     

On a seven-dimensional representation of RNA secondary structures

In this paper, we proposed a seven-dimensional (7D) representation of ribonucleic acid (RNA) secondary structures. The use of the 7D representation is illustrated by constructing structure invariants. Comparisons with the similarity/dissimilarity results based on 7D representation for a set of RNA 3 secondary structures at the 3′-terminus of different viruses, are considered to illustrate the use of our structure invariants based on the entries in derived sequence matrices restricted to a selected width of a band along the main diagonal.     

Recognition of the folding consensus in RNA secondary structures by the topological-filtering method.

Functionally homologous RNA sequences can substantially diverge in their primary sequences but it can be reasonably assumed that they are related in their higher-degree structures. The problem to find such structures and simultaneously satisfy as far as possible the free-energy-minimization criterion, is considered here in two aspects. Firstly a quantitative measure of the folding consensus among secondary structures is defined, translating each structure into a linear representation and using the correlation theorem to compare them. Secondly an algorithm for the parallel search for secondary structures according to the free-energy-minimization criterion, but with a filtering action on the basis of the folding consensus measure is presented. The method is tested on groups of RNA sequences different in origin and in functions, for which proposals of homologous secondary structures based on experimental data exist. A comparison of the results with a blank consisting of a search on the basis of the free energy minimization alone is always performed. In these tests the method shows its ability in obtaining, from different sequences, secondary structures characterized by a high-folding consensus measure also when lower free energy but not homologous structures are possible. Two applications are also shown. The first demonstrates the transfer of experimental data available for one sequence, to a functionally related and therefore homologous one. The second application is the possibility of using a topological probe in the search for precise structural motifs.     

The secondary structure of the protein L1 binding region of ribosomal 23S RNA. Homologies with putative secondary structures of the L11 mRNA and of a region of mitochondrial 16S rRNA.

An heterologous complex was formed between E. coli protein L1 and P. vulgaris 23S RNA. We determined the primary structure of the RNA region which remained associated with protein L1 after RNase digestion of this complex. We also identified the loci of this RNA region which are highly susceptible to T1, S1 and Naja oxiana nuclease digestions respectively. By comparison of these results with those previously obtained with the homologous regions of E. coli and B. stearothermophilus 23S RNAs, we postulate a general structure for the protein L1 binding region of bacterial 23S RNA. Both mouse and human mit 16S rRNAs and Xenopus laevis and Tetrahymena 28S rRNAs contain a sequence similar to the E. coli 23s RNS region preceding the L1 binding site. The region of mit 16S rRNA which follows this sequence has a potential secondary structure bearing common features with the L1-associated region of bacterial 23S rRNA. The 5'-end region of the L11 mRNA also has several sequence potential secondary structures displaying striking homologies with the protein L1 binding region of 23S rRNA and this probably explains how protein L1 functions as a translational repressor. One of the L11 mRNA putative structures bears the features common to both the L1-associated region of bacterial 23S rRNA and the corresponding region of mit 16S rRNA.