The evolution of 5S RNA secondary structures

We have applied the Pipas-McMahon algorithm based on free energy calculations to the search for a 5S RNA base-pair structure common to all known sequences. We find that a 'Y' shaped model is consistently among the structures having the lowest free energy using 5S RNA sequences from either eukaryotic or prokaryotic sources. Compaison of this 'Y' structure with models which have recently been proposed show these models to be remarkably similar, and the minor differences are explicable based on the technique used to obtain the model. That prokaryotic and eukaryotic 5S RNA can adopt a similar secondary structure is strong support for its resistance to change during evolution.     

Alternative secondary structures in the 5' exon affect both forward and reverse self-splicing of the Tetrahymena intervening sequence RNA

The natural splice junction of the Tetrahymena large ribosomal RNA is flanked by hairpins that are phylogenetically conserved. The stem immediately preceding the splice junction involves nucleotides that also base pair with the internal guide sequence of the intervening sequence during splicing. Thus, precursors which contain wild-type exons can form two alternative helices. We have constructed a series of RNAs where the stem-loop in the 5' exon is more or less stable than in the wild-type precursor, and tested them in both forward and reverse self-splicing reactions. The presence of a stable hairpin in ligated exon substrates interferes with the ability of the intervening sequence to integrate at the splice junction. Similarly, the presence of the wild-type hairpin in the 5' exon reduces the rate of splicing 20-fold in short precursors. The data are consistent with a competition between unproductive formation of a hairpin in the 5' exon and productive pairing of the 5' exon with the internal guide sequence. The reduction of splicing by a hairpin that is a normal feature of rRNA structure is surprising; we propose that this attenuation is relieved in the natural splicing environment.     

Multiple 5' terminal cap structures in late polyoma virus RNA.

Nuclear and cytoplasmic polyoma virus-specific RNA extracted from 32P-labeled mouse embryo cells late during productive viral infection was analyzed for the presence of 5' terminal capped structures by complete digestion with RNAases T1, T2 and A, followed by two-dimensional electrophoretic fractionation. Seven major cap I structures (m7 GpppNm1pN2p) were observed in both cases. These termini were further characterized by digestion with penicillium nuclease P1, followed by product analysis in a variety of alternative separate systems. Each structure had an individual combination of N1 and N2 nucleotides, where N1 was always a purine nucleotide but N2 was any nucleotide subject to the single exception that m7GpppGmpCp is found only in low yield. Four different cap II derivatives (m7GpppNm1pNm2pN3p) of four of the cap I structures were also detected in cytoplasmic RNA. None of the termini described derived from contaminating host cell RNA. All of these cap structures mapped on the polyoma viral DNA genome between 66 and 71 map units, a region distant from the 5' end of the bodies of two of the three late polyoma mRNAs. All the polyoma virus-specific cap structures, however, were present in each of the purified 16S, 18S and 19s late mRNAs. These data suggested that families of capped leader sequences of varying sizes are attached to the main body of each late polyoma mRNA species by a splicing mechanism.     

Statistics of RNA secondary structures

A statistical reference for RNA secondary structures with minimum free energies is computed by folding large ensembles of random RNA sequences. Four nucleotide alphabets are used: two binary alphabets, AU and GC, the biophysical AUGC and the synthetic GCXK alphabet. RNA secondary structures are made of structural elements, such as stacks, loops, joints, and free ends. Statistical properties of these elements are computed for small RNA molecules of chain lengths up to 100. The results of RNA structure statistics depend strongly on the particular alphabet chosen. The statistical reference is compared with the data derived from natural RNA molecules with similar base frequencies. Secondary structures are represented as trees. Tree editing provides a quantitative measure for the distance d_t, between two structures. We compute a structure density surface as the conditional probability of two structures having distance t given that their sequences have distance h. This surface indicates that the vast majority of possible minimum free energy secondary structures occur within a fairly small neighborhood of any typical (random) sequence. Correlation lengths for secondary structures in their tree representations are computed from probability densities. They are appropriate measures for the complexity of the sequence-structure relation. The correlation length also provides a quantitative estimate for the mean sensitivity of structures to point mutations. © 1993 John Wiley & Sons, Inc.     

Heterogeneity of 5S RNA species in tobacco chloroplasts

Summary Tobacco chloroplasts were found to contain three species of 5S RNA with different electrophoretic mobility. The nucleotide sequences of two species of the 5S RNA have been determined. The large 5S RNA species (5S RNA_L) is composed of 121 nucleotides and the small 5S RNA species (5S RNA_s) of 119 nucleotides. The 5S RNA_L contains and extra uridine residue at both 5 and 3ends of the 5S RNA_s.     

Conserved RNA secondary structures in Picornaviridae genomes

The family Picornaviridae contains important pathogens including, for example, hepatitis A virus and foot-and-mouth disease virus. The genome of these viruses is a single messenger-active (+)-RNA of 7200–8500 nt. Besides coding for the viral proteins, it also contains functionally important RNA secondary structures, among them an internal ribosomal entry site (IRES) region towards the 5′-end. This contribution provides a comprehensive computational survey of the complete genomic RNAs and a detailed comparative analysis of the conserved structural elements in seven of the currently nine genera in the family Picornaviridae. Compared with previous studies we find: (i) that only smaller sections of the IRES region than previously reported are conserved at single base-pair resolution and (ii) that there is a number of significant structural elements in the coding region. Furthermore, we identify potential cis-acting replication elements in four genera where this feature has not been reported so far.     

Theoretical basis for stabilizing messenger RNA through secondary structure design

RNA hydrolysis presents problems in manufacturing, long-term storage, world-wide delivery and in vivo stability of messenger RNA (mRNA)-based vaccines and therapeutics. A largely unexplored strategy to reduce mRNA hydrolysis is to redesign RNAs to form double-stranded regions, which are protected from in-line cleavage and enzymatic degradation, while coding for the same proteins. The amount of stabilization that this strategy can deliver and the most effective algorithmic approach to achieve stabilization remain poorly understood. Here, we present simple calculations for estimating RNA stability against hydrolysis, and a model that links the average unpaired probability of an mRNA, or AUP, to its overall hydrolysis rate. To characterize the stabilization achievable through structure design, we compare AUP optimization by conventional mRNA design methods to results from more computationally sophisticated algorithms and crowdsourcing through the OpenVaccine challenge on the Eterna platform. We find that rational design on Eterna and the more sophisticated algorithms lead to constructs with low AUP, which we term ‘superfolder’ mRNAs. These designs exhibit a wide diversity of sequence and structure features that may be desirable for translation, biophysical size, and immunogenicity. Furthermore, their folding is robust to temperature, computer modeling method, choice of flanking untranslated regions, and changes in target protein sequence, as illustrated by rapid redesign of superfolder mRNAs for B.1.351, P.1 and B.1.1.7 variants of the prefusion-stabilized SARS-CoV-2 spike protein. Increases in in vitro mRNA half-life by at least two-fold appear immediately achievable.     

Methylated constituents of heterogeneous nuclear RNA: presence in blocked 5' terminal structures.

A substantial portion of the hnRNA of mouse L cells contains internal residues of N6-methyl adenylate and blocked 5' terminal sequences which are apparently of the type m7G5' ppp5' YmpZp..., in which 7-methyl guanosine is joined by a 5'-5' pyrophosphate linkage to a 2'-0-methylated residue, Ym. These sequences are indistinguishable from those comprising one of the two classes of blocked 5' sequences found in mRNA, and are quite distinct from those comprising the other class. The remarkable similarity in 5' terminal methylated sequences of hnRNA and a major fraction of mRNA appears to extend even to the relative occurrence of each of the four 2'-0-methylated species in position Ym.     

Modeling RNA secondary structures. I. Mathematical structural model for predicting RNA secondary structures.

A mathematical model for analyzing the secondary structures of RNA is developed that is based on the connection matrix associated with the planar p-h graph. The classification of the elementary structures allows the introduction of the basis of structural space from which to build the global secondary structure. All admissible solutions belong to the configuration space and can be obtained directly from its basis.     

RNA secondary structures and their prediction

This is a review of past and present attempts to predict the secondary structure of ribonucleic acids (RNAs) through mathematical and computer methods. Related areas covering classification, enumeration and graphical representations of structures are also covered. Various general prediction techniques are discussed, especially the use of thermodynamic criteria to construct an optimal structure. The emphasis in this approach is on the use of dynamic programming algorithms to minimize free energy. One such algorithm is introduced which comprises existing ones as special cases. Issued as NRCC No. 23684.     

Metrics on RNA secondary structures.

Many different programs have been developed for the prediction of the secondary structure of an RNA sequence. Some of these programs generate an ensemble of structures, all of which have free energy close to that of the optimal structure, making it important to be able to quantify how similar these different structures are. To deal with this problem, we define a new class of metrics, the mountain metrics, on the set of RNA secondary structures of a fixed length. We compare properties of these metrics with other well known metrics on RNA secondary structures. We also study some global and local properties of these metrics.     

Conservation of RNA structures enables TNV and BYDV 5' and 3' elements to cooperate synergistically in cap-independent translation

The subgenomic RNA 2 of tobacco necrosis virus A (TNV sgRNA2) encodes the viral coat protein, is unpolyadenylated and presumably uncapped. Here, we show that TNV sgRNA2 is translated cap independently. This cap-independent translation requires the leader and a 140 nt element of the trailer both in wheat germ extract and in tobacco protoplasts. Similar to barley yellow dwarf virus (BYDV), the TNV 5′ and 3′ elements stimulate translation synergistically. Computer-aided phylogenetic analysis of the secondary structure of the TNV trailer revealed that the 3′ translation element is part of a major conserved stem–loop that contains similarities to structures in the BYDV 3′ translation element. These data suggest that the translation mechanisms of TNV sgRNA2 and BYDV RNA are related. To further characterize this relationship, we tested whether cooperativity exists between TNV sgRNA2 and BYDV 5′ and 3′ elements. We found that the TNV sgRNA2 5′ element stimulates translation synergistically with the BYDV 3′ element in vitro. This finding is the first evidence for conservation of structures that enable a 5′–3′ interaction stimulating cap-independent translation.     

Combinatorics of locally optimal RNA secondary structures

It is a classical result of Stein and Waterman that the asymptotic number of RNA secondary structures is $1.104366 \cdot n^{-3/2} \cdot 2.618034^n$ . Motivated by the kinetics of RNA secondary structure formation, we are interested in determining the asymptotic number of secondary structures that are locally optimal, with respect to a particular energy model. In the Nussinov energy model, where each base pair contributes $-1$ towards the energy of the structure, locally optimal structures are exactly the saturated structures, for which we have previously shown that asymptotically, there are $1.07427\cdot n^{-3/2} \cdot 2.35467^n$ many saturated structures for a sequence of length $n$ . In this paper, we consider the base stacking energy model, a mild variant of the Nussinov model, where each stacked base pair contributes $-1$ toward the energy of the structure. Locally optimal structures with respect to the base stacking energy model are exactly those secondary structures, whose stems cannot be extended. Such structures were first considered by Evers and Giegerich, who described a dynamic programming algorithm to enumerate all locally optimal structures. In this paper, we apply methods from enumerative combinatorics to compute the asymptotic number of such structures. Additionally, we consider analogous combinatorial problems for secondary structures with annotated single-stranded, stacking nucleotides (dangles).     

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.     

Base-pair probability profiles of RNA secondary structures

Dynamic programming algorithms are able to predict optimal andsuboptimal secondary structures of RNA. These suboptimal oralternative secondary structures are important for the biologicalfunction of RNA. The distribution of secondary structures presentin solution is governed by the thermodynamic equilibrium betweenthe different structures. An algorithm is presented which approximatesthe total partition function by a Boltzmann–weighted summationof optimal and suboptimal secondary structures at several temperatures.A clear representation of the equilibrium distribution of secondarystructures is derived from a two-dimensional bonding matrixwith base–pairing probability as the third dimension.The temperature dependence of the equilibrium distribution givesthe denaturation behavior of the nucleic acid, which may becompared to experimental optical denaturation curves after correctionfor the hypochromicities of the different base-pairs. Similarly,temperature-induced mobility changes detected in temperature-gradientgel electrophoresis of nucleic acids may be interpreted on thebasis of the temperature dependence of the equilibrium distribution.Results are illustrated for natural circular and synthetic linearpotato spindle tuber viroid RNA respectively, and are comparedto experimental data.