An energy model that predicts the correct folding of both the tRNA and the 5S RNA molecules

DUETT quantitatively identifies known and novel events in nascent RNA structural dynamics from chemical probing data

MOTIVATION

RNA molecules can undergo complex structural dynamics, especially during transcription, which influence their biological functions. Recently developed high-throughput chemical probing experiments that study RNA cotranscriptional folding generate nucleotide-resolution 'reactivities' for each length of a growing nascent RNA that reflect structural dynamics. However, the manual annotation and qualitative interpretation of reactivity across these large datasets can be nuanced, laborious, and difficult for new practitioners. We developed a quantitative and systematic approach to automatically detect RNA folding events from these datasets to reduce human bias/error, standardize event discovery and generate hypotheses about RNA folding trajectories for further analysis and experimental validation.

RESULTS

Detection of Unknown Events with Tunable Thresholds (DUETT) identifies RNA structural transitions in cotranscriptional RNA chemical probing datasets. DUETT employs a feedback control-inspired method and a linear regression approach and relies on interpretable and independently tunable parameter thresholds to match qualitative user expectations with quantitatively identified folding events. We validate the approach by identifying known RNA structural transitions within the cotranscriptional folding pathways of the Escherichia coli signal recognition particle RNA and the Bacillus cereus crcB fluoride riboswitch. We identify previously overlooked features of these datasets such as heightened reactivity patterns in the signal recognition particle RNA about 12 nt lengths before base-pair rearrangement. We then apply a sensitivity analysis to identify tradeoffs when choosing parameter thresholds. Finally, we show that DUETT is tunable across a wide range of contexts, enabling flexible application to study broad classes of RNA folding mechanisms.

AVAILABILITY AND IMPLEMENTATION

https://github.com/BagheriLab/DUETT.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Folding and finding RNA secondary structure

Optimal exploitation of the expanding database of sequences requires rapid finding and folding of RNAs. Methods are reviewed that automate folding and discovery of RNAs with algorithms that couple thermodynamics with chemical mapping, NMR, and/or sequence comparison. New functional noncoding RNAs in genome sequences can be found by combining sequence comparison with the assumption that functional noncoding RNAs will have more favorable folding free energies than other RNAs. When a new RNA is discovered, experiments and sequence comparison can restrict folding space so that secondary structure can be rapidly determined with the help of predicted free energies. In turn, secondary structure restricts folding in three dimensions, which allows modeling of three-dimensional structure. An example from a domain of a retrotransposon is described. Discovery of new RNAs and their structures will provide insights into evolution, biology, and design of therapeutics. Applications to studies of evolution are also reviewed.

Inverse folding of RNA pseudoknot structures

Background

RNA exhibits a variety of structural configurations. Here we consider a structure to be tantamount to the noncrossing Watson-Crick and G-U-base pairings (secondary structure) and additional cross-serial base pairs. These interactions are called pseudoknots and are observed across the whole spectrum of RNA functionalities. In the context of studying natural RNA structures, searching for new ribozymes and designing artificial RNA, it is of interest to find RNA sequences folding into a specific structure and to analyze their induced neutral networks. Since the established inverse folding algorithms, RNAinverse, RNA-SSD as well as INFO-RNA are limited to RNA secondary structures, we present in this paper the inverse folding algorithm Inv which can deal with 3-noncrossing, canonical pseudoknot structures.

Results

In this paper we present the inverse folding algorithm Inv. We give a detailed analysis of Inv, including pseudocodes. We show that Inv allows to design in particular 3-noncrossing nonplanar RNA pseudoknot 3-noncrossing RNA structures-a class which is difficult to construct via dynamic programming routines. Inv is freely available at http://www.combinatorics.cn/cbpc/inv.html.

Conclusions

The algorithm Inv extends inverse folding capabilities to RNA pseudoknot structures. In comparison with RNAinverse it uses new ideas, for instance by considering sets of competing structures. As a result, Inv is not only able to find novel sequences even for RNA secondary structures, it does so in the context of competing structures that potentially exhibit cross-serial interactions.

Energetic signatures of single base bulges: thermodynamic consequences and biological implications

DNA bulges are biologically consequential defects that can arise from template-primer misalignments during replication and pose challenges to the cellular DNA repair machinery. Calorimetric and spectroscopic characterizations of defect-containing duplexes reveal systematic patterns of sequence-context dependent bulge-induced destabilizations. These distinguishing energetic signatures are manifest in three coupled characteristics, namely: the magnitude of the bulge-induced duplex destabilization (DeltaDeltaG(Bulge)); the thermodynamic origins of DeltaDeltaG(Bulge) (i.e. enthalpic versus entropic); and, the cooperativity of the duplex melting transition (i.e. two-state versus non-two state). We find moderately destabilized duplexes undergo two-state dissociation and exhibit DeltaDeltaG(Bulge) values consistent with localized, nearest neighbor perturbations arising from unfavorable entropic contributions. Conversely, strongly destabilized duplexes melt in a non-two-state manner and exhibit DeltaDeltaG(Bulge) values consistent with perturbations exceeding nearest-neighbor expectations that are enthalpic in origin. Significantly, our data reveal an intriguing correlation in which the energetic impact of a single bulge base centered in one strand portends the impact of the corresponding complementary bulge base embedded in the opposite strand. We discuss potential correlations between these bulge-specific differential energetic profiles and their overall biological implications in terms of DNA recognition, repair and replication.

Predicting RNA secondary structure by the comparative approach: how to select the homologous sequences

Background

The secondary structure of an RNA must be known before the relationship between its structure and function can be determined. One way to predict the secondary structure of an RNA is to identify covarying residues that maintain the pairings (Watson-Crick, Wobble and non-canonical pairings). This "comparative approach" consists of identifying mutations from homologous sequence alignments. The sequences must covary enough for compensatory mutations to be revealed, but comparison is difficult if they are too different. Thus the choice of homologous sequences is critical. While many possible combinations of homologous sequences may be used for prediction, only a few will give good structure predictions. This can be due to poor quality alignment in stems or to the variability of certain sequences. This problem of sequence selection is currently unsolved.

Results

This paper describes an algorithm, SSCA, which measures the suitability of sequences for the comparative approach. It is based on evolutionary models with structure constraints, particularly those on sequence variations and stem alignment. We propose three models, based on different constraints on sequence alignments. We show the results of the SSCA algorithm for predicting the secondary structure of several RNAs. SSCA enabled us to choose sets of homologous sequences that gave better predictions than arbitrarily chosen sets of homologous sequences.

Conclusion

SSCA is an algorithm for selecting combinations of RNA homologous sequences suitable for secondary structure predictions with the comparative approach.

HotKnots: heuristic prediction of RNA secondary structures including pseudoknots

We present HotKnots, a new heuristic algorithm for the prediction of RNA secondary structures including pseudoknots. Based on the simple idea of iteratively forming stable stems, our algorithm explores many alternative secondary structures, using a free energy minimization algorithm for pseudoknot free secondary structures to identify promising candidate stems. In an empirical evaluation of the algorithm with 43 sequences taken from the Pseudobase database and from the literature on pseudoknotted structures, we found that overall, in terms of the sensitivity and specificity of predictions, HotKnots outperforms the well-known Pseudoknots algorithm of Rivas and Eddy and the NUPACK algorithm of Dirks and Pierce, both based on dynamic programming approaches for limited classes of pseudoknotted structures. It also outperforms the heuristic Iterated Loop Matching algorithm of Ruan and colleagues, and in many cases gives better results than the genetic algorithm from the STAR package of van Batenburg and colleagues and the recent pknotsRG-mfe algorithm of Reeder and Giegerich. The HotKnots algorithm has been implemented in C/C++ and is available from http://www.cs.ubc.ca/labs/beta/Software/HotKnots.

Thermodynamic Parameters Based on a Nearest-Neighbor Model for DNA Sequences with a Single-Bulge Loop

All 64 possible thermodynamic parameters for a single-bulge loop in the middle of a sequence were derived from optical melting studies. The relative stability of a single bulge depended on both the type of bulged base and its flanking base pairs. The contribution of the single bulge to helix stability ranged from 3.69 kcal/mol for a TAT bulge to -1.05 kcal/mol for an ACC bulge. Thermodynamics for 10 sequences with a GTG bulge were determined to test the applicability of the nearest-neighbor model to a single-bulge loop. Thermodynamic parameters for the GTG bulge and Watson-Crick base pairs predict, DeltaH degrees, DeltaS degrees, and T(M)(50 microM) values with average deviations of 3.0%, 4.3%, 4.7%, and 0.9 degrees C, respectively. The prediction accuracy was within the limits of what can be expected for a nearest-neighbor model. This certified that the thermodynamics for single-bulge loops can be estimated adequately using a nearest-neighbor model.

Thermodynamic parameters for an expanded nearest-neighbor model for the formation of RNA duplexes with single nucleotide bulges

Thirty-four RNA duplexes containing single nucleotide bulges were optically melted, and the thermodynamic parameters deltaH degrees, deltaS degrees, deltaG degrees (37), and T(M) for each sequence were determined. Data from this study were combined with data from previous thermodynamic data [Longfellow, C. E., Kierzek, R., and Turner, D. H. (1990) Biochemistry 29, 278-85] to develop a model that will more accurately predict the free energy of an RNA duplex containing a single nucleotide bulge. Differences between purine and pyrimidine bulges as well as differences between Group I duplexes, those in which the bulge is not identical to either neighboring nucleotide, and Group II duplexes, those in which the bulge is identical to at least one neighboring nucleotide, were considered. The length of the duplex, non-nearest-neighbor effects, and bulge location were also examined. A model was developed which divides sequences into two groups: those with pyrimidine bulges and those with purine bulges. The proposed model for pyrimidine bulges predicts deltaG degrees (37,bulge) = 3.9 kcal/mol + 0.10deltaG degrees (37,nn) + beta, while the model for purine bulges predicts deltaG degrees (37,bulge) = 3.3 kcal/mol - 0.30deltaG degrees (37,nn) + beta, where beta has a value of 0.0 and -0.8 kcal/mol for Group I and Group II sequences, respectively, and deltaG degrees (37,nn) is the nearest-neighbor free energy of the base pairs surrounding the bulge. The conformation of bulge loops present in rRNA was examined. Three distinct families of structures were identified. The bulge loop was either extrahelical, intercalated, or in a "side-step" conformation.

Automatic RNA secondary structure prediction with a comparative approach

This paper presents an algorithm, DCFold, that automatically predicts the common secondary structure of a set of aligned homologous RNA sequences. It is based on the comparative approach. Helices are searched in one of the sequences, called the 'target sequence', and compared to the helices in the other sequences, called the 'test sequences'. Our algorithm searches in the target sequence for palindromes that have a high probability to define helices that are conserved in the test sequences. This selection of significant palindromes is based on criteria that take into account their length and their mutation rate. A recursive search of helices, starting from these likely ones, is implemented using the 'divide and conquer' approach. Indeed, as pseudo-knots are not searched by DCFold, a selected palindrome (p, p') makes possible to divide the initial sequence into two sequences, the internal one and the one resulting from the concatenation of the two external ones. New palindromes can be searched independently in these subsequences. This algorithm was run on ribosomal RNA sequences and recovered very efficiently their common secondary structures.

The energetics of small internal loops in RNA

The energetics of small internal loops are important for prediction of RNA secondary and tertiary structure, selection of drug target sites, and understanding RNA structure-function relationships. Hydrogen bonding, base stacking, electrostatic interactions, backbone distortion, and base-pair size compatibility all contribute to the energetics of small internal loops. Thus, the sequence dependence of these energetics are idiosyncratic. Current approximations for predicting the free energies of internal loops consider size, asymmetry, closing base pairs, and the potential to form GA, GG, or UU pairs. The database of known three-dimensional structures allows for comparison with the models used for predicting stability from sequence.

RNA pseudoknot prediction in energy-based models

RNA molecules are sequences of nucleotides that serve as more than mere intermediaries between DNA and proteins, e.g., as catalytic molecules. Computational prediction of RNA secondary structure is among the few structure prediction problems that can be solved satisfactorily in polynomial time. Most work has been done to predict structures that do not contain pseudoknots. Allowing pseudoknots introduces modeling and computational problems. In this paper we consider the problem of predicting RNA secondary structures with pseudoknots based on free energy minimization. We first give a brief comparison of energy-based methods for predicting RNA secondary structures with pseudoknots. We then prove that the general problem of predicting RNA secondary structures containing pseudoknots is NP complete for a large class of reasonable models of pseudoknots.

Factors affecting the thermodynamic stability of small asymmetric internal loops in RNA

Optical melting experiments were used to determine the thermodynamic parameters for oligoribonucleotides containing small asymmetric internal loops. The results show a broad range of thermodynamic stabilities, which depend on loop size, asymmetry, sequence, closing base pairs, and length of helix stems. Imino proton NMR experiments provide evidence for possible hydrogen bonding in GA and UU mismatches in some asymmetric loops. The stabilizing effects of GA, GG, and UU mismatches on the thermodynamic stability of internal loops vary depending on the size and asymmetry of the loop. The dependence of loop stability on Watson-Crick closing base pairs may be explained by an account of hydrogen bonds. Models are presented for approximating the free energy increments of 2 x 3 and 1 x 3 internal loops.

Thermodynamics of single mismatches in RNA duplexes

The thermodynamic properties and structures of single mismatches in short RNA duplexes were studied in optical melting and imino proton NMR experiments. The free energy increments at 37 degrees C measured for non-GU single mismatches range from -2.6 to 1.7 kcal/mol. These increments depend on the identity of the mismatch, adjacent base pairs, and the position in the helix. UU and AA mismatches are more stable close to a helix end, but GG mismatch stability is essentially unaffected by the position in the helix. Approximations are suggested for predicting stabilities of single mismatches in short RNA duplexes.

Prediction of sequentially optimal RNA secondary structures

A rigorous mathematical modeling of the RNA sequential folding process during transcription is proposed. It is based, at each transcription step, on a homogeneous markovian jump process, the state space of which is the set of structures constructible on the part of the RNA already transcribed. A theoretical formula permitting the computation of the structures probabilities at the end of the RNA transcription is derived. Successive approximations, aimed at reducing the size of the state space, permit the design of a prediction algorithm. The algorithm is tested on some structural RNAs (tRNA, 5S, 16S, hammerhead, ...), results are discussed and possible improvements are proposed.

Chemical and computer probing of RNA structure

Ribonucleic acids (RNAs) are one of the most important types of biopolymers. RNAs play key roles in the storage and multiplication of genetic information. They are important in catalysis and RNA splicing and are the most important steps of translation. This chapter describes experimental methods for probing RNA structure and theoretical methods allowing the prediction of thermodynamically favorable RNA folding. These methods are complementary and together they provide a powerful approach to determine the structure of RNAs. The three-dimensional (tertiary) structure of RNA is formed by hydrogen-bonding among functional groups of nucleosides in different regions of the molecule, by coordination of polyvalent cations, and by stacking between the double-stranded regions present in the RNA. The tertiary structures of only some small RNAs have been determined by high-resolution X-ray crystallographic analysis and nuclear magnetic resonance analysis. The most widely used approach for the investigation of RNA structure is chemical and enzymatic probing, in combination with theoretical methods and phylogenetic studies allowing the prediction of variants of RNA folding. Investigations of RNA structures with different enzymatic and chemical probes can provide detailed data allowing the identification of double-stranded regions of the molecules and nucleotides involved in tertiary interactions.

Statistical description of nucleic acid secondary structure folding

A simple statistical model describing the folding of nucleic acids is proposed. For long sequences the real configuration of the secondary structure is a quasi equilibrium state that cannot be characterised by minimal free energy. This is because the time required to achieve complete thermal equilibrium considerably exceeds the life-time of the molecule. The formation of the secondary structure is represented as a random walk process in the space of all possible molecular configurations. The quasi equilibrium structure is obtained by successive linking and disruptions of helix segments with probabilities determined by the rate constants of corresponding unimolecular reactions. The probabilities of configurations consisting of all possible compatible helices are calculated. Structures of some t-RNAs and ribosomal RNAs are analysed.

Identification of new eukaryotic tRNA genes in genomic DNA databases by a multistep weight matrix analysis of transcriptional control regions

A linear method for the search of eukaryotic nuclear tRNA genes in DNA databases is described. Based on a modified version of the general weight matrix procedure, our algorithm relies on the recognition of two intragenic control regions known as A and B boxes, a transcription termination signal, and on the evaluation of the spacing between these elements. The scanning of the eukaryotic nuclear DNA database using this search algorithm correctly identified 933 of the 940 known tRNA genes (0.74% of false negatives). Thirty new potential tRNA genes were identified, and the transcriptional activity of two of them was directly verified by in vitro transcription. The total false positive rate of the algorithm was 0.014%. Structurally unusual tRNA genes, like those coding for selenocysteine tRNAs, could also be recognized using a set of rules concerning their specific properties, and one human gene coding for such tRNA was identified. Some of the newly identified tRNA genes were found in rather uncommon genomic positions: 2 in centromeric regions and 3 within introns. Furthermore, the presence of extragenically located B boxes in tRNA genes from various organisms could be detected through a specific subroutine of the standard search program.

Prediction of alternative RNA secondary structures based on fluctuating thermodynamic parameters

In this paper we present a new method for predicting a set of RNA secondary structures that are thermodynamically favored in RNA folding simulations. This method uses a large number of 'simulated energy rules' (SER) generated by perturbing the free energy parameters derived experimentally within the range of the experimental errors. The structure with the lowest free energy is computed for each SER. Structural comparisons are used to avoid multiple generation of similar structures. Computed structures are evaluated using the energy distribution of the lowest free energy structures derived in the simulation. Predicted be graphically displayed with their occurring frequencies in the simulation by dot-plot representations. On average, about 90% of phylogenetic helixes in the known models of tRNA, Group I self-splicing intron, and Escherichia coli 16 S rRNA, were predicted using the method.

Comparison of binding of mixed ribose-deoxyribose analogues of CUCU to a ribozyme and to GGAGAA by equilibrium dialysis: evidence for ribozyme specific interactions with 2' OH groups

Dissociation constants at 15 degrees C were measured by equilibrium dialysis for the binding of rCrUrCrU, dCrUrCrU, rCdUrCrU, rCrUdCrU, and rCrUrCdU to the L-21 ScaI form of the self-splicing group I LSU intron from Tetrahymena thermophila. Substitution of deoxyribose for ribose in each of the middle two positions makes the free energy change for binding 1-2 kcal/mol less favorable, compared to about 0.3 kcal/mol less favorable for each of the terminal positions. Dissociation constants for binding of the same oligomers to rGGAGAA were measured by optical melting methods. Substitution of a single deoxyribose for ribose makes the free energy change for binding less favorable by 0.4-0.9 kcal/mol for this simple duplex formation. Comparison of the effects for binding to ribozyme and to rGGAGAA indicate that ribozyme-specific tertiary interactions dependent on the middle two 2' OH groups of rCrUrCrU add about 2 kcal/mol of favorable free energy for binding to L-21 ScaI. Comparisons are made with results from gel retardation studies [Pyle, A. M., McSwiggen, J. A., & Cech, T. R. (1990) Proc. Natl. Acad. Sci. U.S.A. 87, 8187-8191; Pyle, A. M., & Cech, T. R. (1991) Nature (London) 350, 628-631].

RNA pseudoknots downstream of the frameshift sites of retroviruses

RNA pseudoknot structural motifs could have implications for a wide range of biological processes of RNAs. In this study, the potential RNA pseudoknots just downstream from the known and suspected retroviral frame-shift sites were predicted in the Rous sarcoma virus, primate immunodeficiency viruses (HIV-1, HIV-2, and SIV), equine infectious anemia virus, visna virus, bovine leukemia virus, human T-cell leukemia virus (types I and II), mouse mammary tumor virus, Mason-Pfizer monkey virus, and simian SRV-1 type-D retrovirus. Also, the putative RNA pseudoknots were detected in the gag-pol overlaps of two retrotransposons of Drosophila, 17.6 and gypsy, and the mouse intracisternal A particle. For each sequence, the thermodynamic stability and statistical significance of the secondary structure involved in the predicted tertiary structure were assessed and compared. Our results show that the stem-loop structures in the pseudoknots are both thermodynamically highly stable and statistically significant relative to other such configurations that potentially occur in the gag-pol or gag-pro and pro-pol junction domains of these viruses (300 nucleotides upstream and downstream from the possible frameshift sites are included). Moreover, the structural features of the predicted pseudoknots following the frameshift site of pro-pol overlaps of the HTLV-1 and HTLV-2 retroviruses are structurally well conserved. The occurrence of eight compensatory base changes in the tertiary interaction of the two related sequences allow the conservation of their tertiary structures in spite of the sequence divergence. The results support the possible control mechanism for frameshifting proposed by Brierley et al. and Jacks et al.

Modeling RNA secondary structures. II. The geometric structural solution for tRNA

The set of admissible solutions of the configuration space of tRNA molecules is obtained after incorporating further restrictions based on the principles of local stability and homology as well as on geometric and energetic considerations.

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.

Phylogenetic analysis and evolution of RNase P RNA in proteobacteria

The secondary structures of the eubacterial RNase P RNAs are being elucidated by a phylogenetic comparative approach. Sequences of genes encoding RNase P RNA from each of the recognized subgroups (alpha, beta, gamma, and delta) of the proteobacteria have now been determined. These sequences allow the refinement, to nearly the base pair level, of the phylogenetic model for RNase P RNA secondary structure. Evolutionary change among the RNase P RNAs was found to occur primarily in four discrete structural domains that are peripheral to a highly conserved core structure. The new sequences were used to examine critically the proposed similarity (C. Guerrier-Takada, N. Lumelsky, and S. Altman, Science 246:1578-1584, 1989) between a portion of RNase P RNA and the "exit site" of the 23S rRNA of Escherichia coli. Phylogenetic comparisons indicate that these sequences are not homologous and that any similarity in the structures is, at best, tenuous.

Thermodynamic characterization of deoxyribooligonucleotide duplexes containing bulges

Ultraviolet absorption techniques were used to study the thermodynamics of duplex formation for a DNA decamer, d(GCGAAAAGCG).d(CGCTTTTCGC), and a series of related duplexes, each of which contains a bulged base centered in the A.T tract. Thermodynamic parameters were obtained from nonlinear least-squares fits of the melting curves and the concentration dependences of the melting temperatures. Duplexes containing a localized single-base bulge were found to be 3.5-4.6 kcal/mol less stable than the decamer at 37 degrees C. These results indicate that both the identity of the bulged base and the strand in which it is located may influence the amount by which the duplex is destabilized. Bulged bases located in the T-strand, d(CGCTTYTTCGC), in position Y, were observed to be slightly more destabilizing than those located in the A-strand, d(GCGAAXAAGCG), in position X. Bulged purines may be more destabilizing than bulged pyrimidines.

Structural elements in RNA

This chapter describes the RNA structural characteristics that have emerged so far. Folded RNA molecules are stabilized by a variety of interactions, the most prevalent of which are stacking and hydrogen bonding between bases. Many interactions among backbone atoms also occur in the structure of tRNA, although they are often ignored when considering RNA structure because they are not as well-characterized as interactions among bases. Backbone interactions include hydrogen bonding and the stacking of sugar or phosphate groups with bases or with other sugar and phosphate groups. The interactions found in a three-dimensional RNA structure can be divided into two categories: secondary interactions and tertiary interactions. This division is useful for several reasons. Secondary structures are routinely determined by a combination of techniques discussed in chapter, whereas tertiary interactions are more difficult to determine. Computer algorithms that generate RNA structures can search completely through possible secondary structures, but the inclusion of tertiary interactions makes a complete search of possible structures impractical for RNA molecules even as small as tRNA. The division of RNA structure into building blocks consisting of secondary or tertiary interactions makes it easier to describe RNA structures. In those cases in which RNA studies are incomplete, the studies of DNA are described with the rationalization that RNA structures may be analogous to DNA structures, or that the techniques used to study DNA could be applied to the analogous RNA structures. The chapter focuses on the aspects of RNA structure that affect the three-dimensional shape of RNA and that affect its ability to interact with other molecules.

Modification of the anticodon wobble position of tRNA(Ala) in vitro does not require 5' or 3' processing

Maturation of eukaryotic tRNA molecules requires nuclear processing as well as nuclear and cytoplasmic modification of specific nucleotides. Nucleotide modifications within the anticodon are found in the majority of all tRNAs and are among the last maturation events to occur in vivo. We show that 5' and 3' processing of SP6 polymerase-generated transcripts are not necessary for the in vitro modification of A----I in the anticodon of tRNA(Ala).

A novel repeated DNA sequence located in the intergenic regions of bacterial chromosomes

We report the discovery of a novel group of highly conserved DNA sequences located within the intergenic regions of the chromosomes of Escherichia coli, Salmonella typhimurium and other bacteria. These intergenic repeat units (IRUs) are 124-127 nucleotides long and have the potential to form stable stem-loop structures. The location of these sequences within the intergenic regions is variable with respect to known or putative signals for transcription and translation of the flanking genes. Some of the IRU sequences are transcribed, others are probably not. The structure and possible functions of these sequences are discussed in relation to palindromic units and other repeated DNA sequences in bacteria.

Speeding up the dynamic algorithm for planar RNA folding

The simplest dynamic algorithm for planar RNA folding searches for the maximum number of base pairs. The algorithm uses O(n3) steps. The more general case, where different weights (energies) are assigned to stacked base pairs and to the various types of single-stranded region topologies, requires a considerably longer computation time because of the partial backtracking involved. Limiting the loop size reduces the running time back to O(n3). Reduction in the number of steps in the calculations of the various RNA topologies has recently been suggested, thereby improving the time behavior. Here we show how a "jumping" procedure can be used to speed up the computation, not only for the maximal number of base pairs algorithm, but for the minimal energy algorithm as well.

Prediction of RNA secondary structure, including pseudoknotting, by computer simulation

A computer program is presented which determines the secondary structure of linear RNA molecules by simulating a hypothetical process of folding. This process implies the concept of 'nucleation centres', regions in RNA which locally trigger the folding. During the simulation, the RNA is allowed to fold into pseudoknotted structures, unlike all other programs predicting RNA secondary structure. The simulation uses published, experimentally determined free energy values for nearest neighbour base pair stackings and loop regions, except for new extrapolated values for loops larger than seven nucleotides. The free energy value for a loop arising from pseudoknot formation is set to a single, estimated value of 4.2 kcal/mole. Especially in the case of long RNA sequences, our program appears superior to other secondary structure predicting programs described so far, as tests on tRNAs, the LSU intron of Tetrahymena thermophila and a number of plant viral RNAs show. In addition, pseudoknotted structures are often predicted successfully. The program is written in mainframe APL and is adapted to run on IBM compatible PCs, Atari ST and Macintosh personal computers. On an 8 MHz 8088 standard PC without coprocessor, using STSC APL, it folds a sequence of 700 nucleotides in one and a half hour.

The equilibrium partition function and base pair binding probabilities for RNA secondary structure

A novel application of dynamic programming to the folding problem for RNA enables one to calculate the full equilibrium partition function for secondary structure and the probabilities of various substructures. In particular, both the partition function and the probabilities of all base pairs are computed by a recursive scheme of polynomial order N3 in the sequence length N. The temperature dependence of the partition function gives information about melting behavior for the secondary structure. The pair binding probabilities, the computation of which depends on the partition function, are visually summarized in a "box matrix" display and this provides a useful tool for examining the full ensemble of probable alternative equilibrium structures. The calculation of this ensemble representation allows a proper application and assessment of the predictive power of the secondary structure method, and yields important information on alternatives and intermediates in addition to local information about base pair opening and slippage. The results are illustrated for representative tRNA, 5S RNA, and self-replicating and self-splicing RNA molecules, and allow a direct comparison with enzymatic structure probes. The effect of changes in the thermodynamic parameters on the equilibrium ensemble provides a further sensitivity check to the predictions.

A highly conserved RNA folding region coincident with the Rev response element of primate immunodeficiency viruses

A series of unusual folding regions (UFR) immediately 3' to the cleavage site of the outer membrane protein (OMP) and transmembrane protein (TMP) were detected in the envelope gene RNA of the human immunodeficiency virus (HIV-1, HIV-2) and simian immunodeficiency virus (SIV) by an extensive Monte Carlo simulation. These RNA secondary structures were predicted to be both highly stable and statistically significant. In the calculation, twenty-five different sequence isolates of HIV-1, three isolates of HIV-2 and eight sequences of SIV were included. Although significant sequence divergence occurs in the env coding regions of these viruses, a distinct UFR of 234-nt is consistently located ten nucleotides 3' to the cleavage site of the OMP/TMP in HIV-1, and a 216-nt UFR occurs forty-six and forty-nine nucleotides downstream from the OMP/TMP cleavage site of HIV-2 and SIV, respectively. Compensatory base changes in the helical stem regions of these conserved RNA secondary structures are identified. These results support the hypothesis that these special RNA folding regions are functionally important and suggest that the role of this sequence as the Rev response element (RRE) is mediated by secondary structure as well as primary RNA sequence.

The revised genetic code

Recent findings on the genetic code are reviewed, including selenocysteine usage, deviations in the assignments of sense and nonsense codons, RNA editing, natural ribosomal frameshifts and non-orthodox codon-anticodon pairings. A multi-stage codon reading process is presented.

Electrostatic forces at helix-coil boundaries in DNA

The Tm of internal loop-forming (dA.dT)N domains in pBR322 DNA has been measured over a tenfold range of [Na+]. The slopes SN = dTm/d log [Na+] are linear and decrease in magnitude with decreasing loop size N, signaling a reduction in Na+ released during the transition of these domains to the coil state. Values of SN decrease linearly with increasing N-1 in accordance with the expectation of a simple model for the occurrence of a gradient of long-range electrostatic forces at helix-coil boundaries, and extrapolate almost precisely to the value of S infinity observed for (dA.dT) infinity. These results indicate (1) less counterion is released per phosphate residue from the finite loop than from the infinite-sized loop, and (2) the difference in binding is constant for each boundary formed and independent of the size of the loop within the range examined: approximately 350 base pair (bp) greater than N greater than 71 bp. The slope of the dependence of SN on N-1 indicates the region of higher charge density at the boundary extends at least 18 A into the coil and probably 40-50 A before dropping to a value characteristic of the unperturbed coil. The free energy for excess counterion binding at boundaries can be expressed by -delta G/RT = 10.47 log[Na+] + 5.234 When the loop entropy function in a statistical mechanical algorithm for the dissociation of DNA is weighted by this quantity, calculated Tm are seen to vary by only +/- 0.09 degrees C from observed.

Conformational comparisons among homologous bony fish 5S ribosomal RNAs

The reversible thermal melting of homologous 5S ribosomal RNAs of three bony fishes, rainbow trout (Salmo gairdneri), carp (Cyprinus carpio), and dog salmon (Onchorhynchus keta), were compared in aqueous salts (sodium chloride and/or divalent metal chlorides) by means of differential optical absorption at 260 and 280 nm, and c.d. at 265 nm. The melting parameters of the multiphasic melting process were conserved among the homologous RNAs, and it was shown that they did not depend on the methods of measurement but on concentrations of [Na+] and of [metal2+]. Other physicochemical methods, such as FT-IR absorption, gave the same melting profiles as the u.v. methods. The c.d. spectrum was homologous among the ribosomal RNAs. The melting is explained by changes in local structures in the 'consensus secondary structure model'. Also, stabilization of the secondary and tertiary structures by binding of Mg2+ and Ca2+, and the catalysed hydrolysis of the main chains by various divalent ions are discussed.

Thermodynamic and spectroscopic study of bulge loops in oligoribonucleotides

Thermodynamic parameters for bulge loops of one to three nucleotides in oligoribonucleotide duplexes have been measured by optical melting. The results indicate bulges Bn of An and Un have similar stabilities in the duplexes, GCGBmGCG + CGCCGC. The stability increment for a bulge depends on more than its adjacent base pairs. For example, the stability increment for a bulge is affected more than 1 kcal/mol by changing two nonadjacent base pairs or by adding terminal unpaired nucleotides (dangling ends) three base pairs away. Thus a nearest-neighbor approximation for helixes with bulges is oversimplified. Many of the non-self-complementary strands used in this study were observed to form homoduplexes. Such duplexes with GA mismatches were particularly stable.

Improved predictions of secondary structures for RNA

The accuracy of computer predictions of RNA secondary structure from sequence data and free energy parameters has been increased to roughly 70%. Performance is judged by comparison with structures known from phylogenetic analysis. The algorithm also generates suboptimal structures. On average, the best structure within 10% of the lowest free energy contains roughly 90% of phylogenetically known helixes. The algorithm does not include tertiary interactions or pseudoknots and employs a crude model for single-stranded regions. The only favorable interactions are base pairing and stacking of terminal unpaired nucleotides at the ends of helixes. The excellent performance is consistent with these interactions being the primary interactions determining RNA secondary structure.

String analysis and energy minimization in the partition of DNA sequences

Two approaches to the understanding of biological sequences are confronted. While the recognition of particular signals in sequences relies on complex physical interactions, the problem is often analysed in terms of the presence or absence of literal motifs (strings) in the sequence. We present here a test-case for evaluating the potential of this approach. We classify DNA sequences as positive or negative depending on whether they contain a single melted domain in the middle of the sequence, which is a global physical property. Two sets of positive "biological" sequences were generated by a computer simulation of evolutionary divergence along the branches of a phylogenetic tree, under the constraint that each intermediate sequence be positive. These two sets and a set of random positive sequences were subjected to pattern analysis. The observed local patterns were used to construct expert systems to discriminate positive from negative sequences. The experts achieved 79% to 90% success on random positive sequences and up to 99% on the biological sets, while making less than 2% errors on negative sequences. Thus, the global constraints imposed on sequences by a physical process may generate local patterns that are sufficient to predict, with a reasonable probability, the behaviour of the sequences. However, rather large sets of biological sequences are required to generate patterns free of illegitimate constraints. Furthermore, depending upon the initial sequence, the sets of sequences generated on a phylogenetic tree may be amenable or refractory to string analysis, while obeying identical physical constraints. Our study clarifies the relationship between experts' errors on positive and negative sequences, and the contributions of legitimate and illegitimate patterns to these errors. The test-case appears suitable both for further investigations of problems in the theory of sequence evolution and for further testing of pattern analysis techniques.

The complete nucleotide sequence of the Rattus norvegicus mitochondrial genome: cryptic signals revealed by comparative analysis between vertebrates

This paper reports the nucleotide sequence of rat mitochondrial DNA, only the fourth mammalian mitochondrial genome to be completely sequenced. Extensive comparative studies performed with similar genomes from other organisms revealed a number of interesting features. 1) Messenger RNA genes: the codon strategy is mainly dictated by the base compositional constraints of the corresponding codogenic DNA strand. The usage of the initiation and termination codons follows well-established rules. In general the canonical initiator, ATG, and terminators, TAA and TAG (in rat, only TAA), are always present when there is gene overlapping or when the mRNAs possess untranslated nucleotides at the 5' or 3' ends. 2) Transfer RNA genes: a number of features suggest the peculiar evolutionary behavior of this class of genes and confirm their role in the duplication and rearrangement processes that took place in the evolution of the animal mitochondrial genome. 3) Ribosomal RNA genes: accurate sequence analysis revealed a number of significant examples of complementarity between ribosomal and messenger RNAs. This suggests that they might play an important role in the regulation of mitochondrial translation and transcription mechanisms. The properties revealed by our work shed new light on the organization and evolution of the vertebrate mitochondrial genome and more importantly open up the way to clearly aimed experimental studies of the regulatory mechanisms in mitochondria.

On finding all suboptimal foldings of an RNA molecule

An algorithm and a computer program have been prepared for determining RNA secondary structures within any prescribed increment of the computed global minimum free energy. The mathematical problem of determining how well defined a minimum energy folding is can now be solved. All predicted base pairs that can participate in suboptimal structures may be displayed and analyzed graphically. Representative suboptimal foldings are generated by selecting these base pairs one at a time and computing the best foldings that contain them. A distance criterion that ensures that no two structures are "too close" is used to avoid multiple generation of similar structures. Thermodynamic parameters, including free-energy increments for single-base stacking at the ends of helices and for terminal mismatched pairs in interior and hairpin loops, are incorporated into the underlying folding model of the above algorithm.

Conserved structural domains in the 5'-untranslated region of picornaviral genomes: an analysis of the segment controlling translation and neurovirulence

A model of secondary structure common for the central part (ca. 400 nucleotides) of the 5'-untranslated regions (5'-UTR) of all the so far sequenced genomes of polioviruses, coxsackieviruses, and rhinoviruses was derived on the basis of evolutionary and thermodynamic considerations. According to the model, this part of the genome comprises three domains, which appear to be involved, at least in the poliovirus genome, in the control of viral neurovirulence and in vitro translation. Some salient features of this model were supported by investigating RNAs of five poliovirus and one coxsackievirus strains with respect to their accessibility to modifications with dimethyl sulfate and sensitivity to single-strand- and double-strand-specific nucleases. In contrast to the previous suggestion, no major changes in the conformation of the Sabin vaccine poliovirus type 3 5'-UTR due to the transition in position 472 were observed. The biological relevance of the conserved primary and secondary structure elements in the picornaviral 5'-UTRs is discussed.

The ordering of the nucleotides in DNA: computational problems in molecular biology

Viewing DNA, RNA and proteins as strings of letters, various algorithms designed for their optimal alignments or their secondary structures have been developed. The results emanating from such sequence editing algorithms are often not correlated with the physio-chemical computations for calculating the detailed atomic coordinates of these molecules. These two aspects are often viewed as separate research entities. Here I attempt to relate various computational aspects of modern molecular biology. In particular, I attempt putting these (along with complementary experimental data) in the framework of a very basic biological question--what fixes the order of the bases in the DNA.

Phosphoenolpyruvate:sugar phosphotransferase system of Bacillus subtilis: nucleotide sequence of ptsX, ptsH and the 5'-end of ptsI and evidence for a ptsHI operon

The nucleotide sequence of a 1689bp fragment of the Bacillus subtilis locus containing ptsX (a crr-like gene), ptsH (coding for HPr), and the 5'-end of ptsI (coding for Enzyme I) was determined. The deduced amino acid sequences of ptsH and the N-terminal part of ptsI were compared to those of Streptococcus faecalis and Escherichia coli. Transcription fusion demonstrated that ptsHI constitutes an operon. An open reading frame overlapping the main part of ptsH in the opposite sense was shown to be expressed in vivo, using protein fusions with beta-galactosidase. The deduced amino acid sequence of ptsX showed significant homology with that of Salmonella typhimurium glucose-specific Enzyme III. ptsX was preceded by an open reading frame whose amino acid sequence showed strong homology with the C-terminal part of E. coli Enzyme IIGlc.

Mutant U2 snRNAs of Xenopus which can form an altered higher order RNA structure are unable to enter the nucleus

We studied the nuclear targeting of U snRNAs by microinjection of wild-type and mutant U2 small nuclear RNA transcripts into the cytoplasm of Xenopus oocytes. It has previously been shown that a mutant U2 RNA (delta C) which does not bind certain common U snRNP proteins, some of which carry epitopes recognized by anti-Sm antisera, does not enter the nucleus. We show here that several mutant U2 RNAs which bind to Sm antigens do not enter the nucleus, demonstrating that this RNA-protein interaction is insufficient to produce a nuclear targeting signal. Computer predictions of the secondary structures of the RNAs, derived from minimal energy calculations, show that those which are unable to enter the nucleus have the potential to form an additional secondary structure interaction due to base complementarity between sequences near to their 5' and 3' ends. The data suggest that this structural feature inhibits nuclear targeting.

A new natural hGH variant--17.5 kd--produced by alternative splicing. An additional consensus sequence which might play a role in branchpoint selection

From a human pituitary cDNA library, we have cloned 3 distinct human growth hormone (hGH) cDNAs, coding respectively for the 22 K hGH, the 20 K variant, and a yet unknown 17.5 K variant. S1 mapping analysis using human pituitary RNA confirms the existence of at least four distinct hGH mRNAs originating from alternative acceptor sites at the second intron of the primary transcript. We have analysed the hGH gene sequence to explain the high frequency of alternative splicings which occur only at this location. In this study we propose CTTGNNPyPyPy as an additional consensus sequence guiding the selection of the branched nucleotide.