Structural parameters affecting the kinetics of RNA hairpin formation.

There is little experimental knowledge on the sequence dependent rate of hairpin formation in RNA. We have therefore designed RNA sequences that can fold into either of two mutually exclusive hairpins and have determined the ratio of folding of the two conformations, using structure probing. This folding ratio reflects their respective folding rates. Changing one of the two loop sequences from a purine- to a pyrimidine-rich loop did increase its folding rate, which corresponds well with similar observations in DNA hairpins. However, neither changing one of the loops from a regular non-GNRA tetra-loop into a stable GNRA tetra-loop, nor increasing the loop size from 4 to 6 nt did affect the folding rate. The folding kinetics of these RNAs have also been simulated with the program 'Kinfold'. These simulations were in agreement with the experimental results if the additional stabilization energies for stable tetra-loops were not taken into account. Despite the high stability of the stable tetra-loops, they apparently do not affect folding kinetics of these RNA hairpins. These results show that it is possible to experimentally determine relative folding rates of hairpins and to use these data to improve the computer-assisted simulation of the folding kinetics of stem-loop structures.

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.

Prediction of locally stable RNA secondary structures for genome-wide surveys.

MOTIVATION: Recently novel classes of functional RNAs, most prominently the miRNAs have been discovered, strongly suggesting that further types of functional RNAs are still hidden in the recently completed genomic DNA sequences. Only few techniques are known, however, to survey genomes for such RNA genes. When sufficiently similar sequences are not available for comparative approaches the only known remedy is to search directly for structural features. RESULTS: We present here efficient algorithms for computing locally stable RNA structures at genome-wide scales. Both the minimum energy structure and the complete matrix of base pairing probabilities can be computed in theta(N x L2) time and theta(N + L2) memory in terms of the length N of the genome and the size L of the largest secondary structure motifs of interest. In practice, the 100 Mb of the complete genome of Caenorhabditis elegans can be folded within about half a day on a modern PC with a search depth of L = 100. This is sufficient example for a survey for miRNAs. AVAILABILITY: The software described in this contribution will be available for download at http://www.tbi.univie.ac.at/~ivo/RNA/ as part of the Vienna RNA Package.

Stochastic pairwise alignments.

MOTIVATION: The level of sequence conservation between related nucleic acids or proteins often varies considerably along the sequence. Both regions with high variability (mutational hot-spots) and regions of almost perfect sequence identity may occur in the same pair of molecules. The reliability of an alignment therefore strongly depends on the level of local sequence similarity. Especially in regions of high variability, many alignments of almost equal quality exist, and the optimal alignment is highly arbitrary. RESULTS: We discuss two approaches which deal with the inherent ambiguity of the alignment problem based on the computation of the partition function over all canonical pairwise alignments. The ensemble of possible alignments can be described by the probabilities P(ij) of a match between position i in the first and position j in the second sequence. Alternatively, we introduce a probabilistic backtracking procedure that generates ensembles of suboptimal alignments with correct statistical weights. A comparison between structure based alignments and large samples of stochastic alignments shows that the ensemble contains correct alignments with significant probabilities even though the optimal alignment deviates significantly from the structural alignment. Ensembles of suboptimal alignments obtained by stochastic backtracking can be used as input to any bioinformatics method based on pairwise alignment in order to gain reliability information not available from a single optimal alignment. AVAILABILITY: The software described in this contribution is available for downloading at http://www.tbi.univie.ac.at/~ulim/probA/

Exploring protein sequence space using knowledge-based potentials.

Knowledge-based potentials can be used to decide whether an amino acid sequence is likely to fold into a prescribed native protein structure. We use this idea to survey the sequence-structure relations in protein space. In particular, we test the following two propositions which were found to be important for efficient evolution: the sequences folding into a particular native fold form extensive neutral networks that percolate through sequence space. The neutral networks of any two native folds approach each other to within a few point mutations. Computer simulations using two very different potential functions, M. Sippl's PROSA pair potential and a neural network based potential, are used to verify these claims.

Design of multistable RNA molecules.

We show that the problem of designing RNA sequences that can fold into multiple stable secondary structures can be transformed into a combinatorial optimization problem that can be solved by means of simple heuristics. Hence it is feasible to design RNA switches with prescribed structural alternatives. We discuss the theoretical background and present an efficient tool that allows the design of various types of switches. We argue that both the general properties of the sequence structure map of RNA secondary structures and the ease with which our design tool finds bistable RNAs strongly indicates that RNA switches are easily accessible in evolution. Thus conformational switches are yet another function for which RNA can be employed.

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.

The hepatitis B virus pregenome: prediction of RNA structure and implications for the emergence of deletions.

The terminally redundant pregenomic RNA of human hepatitis B virus (HBV) comprises some 3,330 nucleotides and is a replicative intermediate in the production of the circular DNA genome. Deletions are known to arise in the HBV genome during the course of chronic infection and are sometimes associated with interferon therapy. These deletions are limited to small parts of the genome such as the 357-nucleotide pre-S1 region. Long RNA molecules such as the HBV pregenome have considerable structural flexibility and will undergo secondary structure shifts between energetically favourable states in a continuous and semi-random fashion. Since prediction of structure elements that are highly conserved in different forms of one RNA molecule is now feasible by computer modelling, we have analysed the whole HBV pregenome by two different RNA structure prediction algorithms and by new methods that exploit these algorithms. Significantly, the ends of pregenomic RNA were predicted to undergo both short-range and long-range interactions, which has relevance to our knowledge of the virus replicative cycle. By incorporating phylogenetic information relating to the 6 recognised genotypes of HBV, it was possible to highlight short secondary structures that may be common to all HBV strains. For example, although the pre-S1 region was predicted to undergo local folding of a loosely defined nature, most observed pre-S1 deletions mapped to all or part of an arm carrying a better-defined structure. The loss of such sequences may be mechanistically attributable to polymerase skipping during reverse transcription, and the possible advantages of such deletions are considered.

Prediction of RNA base pairing probabilities on massively parallel computers.

We present an implementation of McCaskill's algorithm for computing the base pair probabilities of an RNA molecule for massively parallel message passing architectures. The program can be used to routinely fold RNA sequences of more than 10,000 nucleotides. Applications to complete viral genomes are discussed.

RNA folding at elementary step resolution.

We study the stochastic folding kinetics of RNA sequences into secondary structures with a new algorithm based on the formation, dissociation, and the shifting of individual base pairs. We discuss folding mechanisms and the correlation between the barrier structure of the conformational landscape and the folding kinetics for a number of examples based on artificial and natural sequences, including the influence of base modification in tRNAs.

Concurrent neutral evolution of mRNA secondary structures and encoded proteins.

Messenger RNA sequences often have to preserve functional secondary structure elements in addition to coding for proteins. We present a statistical analysis of retroviral mRNA which supports the hypothesis that the natural genetic code is adapted to such complementary coding. These sequences are still able to explore efficiently the space of possible proteins by point mutations. This is borne out by the observation that, in stem regions of retroviral mRNA foldings, silent mutations on one strand are preferentially accompanied by conservative mutations on the other. Distances between amino acids based on physicochemical properties are used to quantify the conservation of protein function under the constraint of maintained RNA secondary structure. We find that preservation of RNA secondary structure by compensatory mutations is evolutionary compatible with the efficient search for new variants on the protein level.

Automatic detection of conserved base pairing patterns in RNA virus genomes.

Almost all RNA molecules--and consequently also almost all subsequences of a large RNA molecule-form secondary structures. The presence of secondary structure in itself therefore does not indicate any functional significance. In fact, we cannot expect a conserved secondary structure for all parts of a viral genome or a mRNA, even if there is a significant level of sequence conservation. We present a novel method for detecting conserved RNA secondary structures in a family of related RNA sequences. The method is based on combining the prediction of base pair probability matrices and comparative sequence analysis. It can be applied to small sets of long sequences and does not require a prior knowledge of conserved sequence or structure motifs. As such it can be used to scan large amounts of sequence data for regions that warrant further experimental investigation. Applications to complete genomic RNAs of some viruses show that in all cases the known secondary structure features are identified. In addition, we predict a substantial number of conserved structural elements which have not been described so far.

Complete suboptimal folding of RNA and the stability of secondary structures.

An algorithm is presented for generating rigorously all suboptimal secondary structures between the minimum free energy and an arbitrary upper limit. The algorithm is particularly fast in the vicinity of the minimum free energy. This enables the efficient approximation of statistical quantities, such as the partition function or measures for structural diversity. The density of states at low energies and its associated structures are crucial in assessing from a thermodynamic point of view how well-defined the ground state is. We demonstrate this by exploring the role of base modification in tRNA secondary structures, both at the level of individual sequences from Escherichia coli and by comparing artificially generated ensembles of modified and unmodified sequences with the same tRNA structure. The two major conclusions are that (1) base modification considerably sharpens the definition of the ground state structure by constraining energetically adjacent structures to be similar to the ground state, and (2) sequences whose ground state structure is thermodynamically well defined show a significant tendency to buffer single point mutations. This can have evolutionary implications, since selection pressure to improve the definition of ground states with biological function may result in increased neutrality.

Automatic detection of conserved RNA structure elements in complete RNA virus genomes.

We propose a new method for detecting conserved RNA secondary structures in a family of related RNA sequences. Our method is based on a combination of thermodynamic structure prediction and phylogenetic comparison. In contrast to purely phylogenetic methods, our algorithm can be used for small data sets of approximately 10 sequences, efficiently exploiting the information contained in the sequence variability. The procedure constructs a prediction only for those parts of sequences that are consistent with a single conserved structure. Our implementation produces reasonable consensus structures without user interference. As an example we have analysed the complete HIV-1 and hepatitis C virus (HCV) genomes as well as the small segment of hantavirus. Our method confirms the known structures in HIV-1 and predicts previously unknown conserved RNA secondary structures in HCV.

Oxygen and proton pathways in cytochrome c oxidase.

Cytochrome c oxidase is a redox-driven proton pump, which couples the reduction of oxygen to water to the translocation of protons across the membrane. The recently solved x-ray structures of cytochrome c oxidase permit molecular dynamics simulations of the underlying transport processes. To eventually establish the proton pump mechanism, we investigate the transport of the substrates, oxygen and protons, through the enzyme. Molecular dynamics simulations of oxygen diffusion through the protein reveal a well-defined pathway to the oxygen-binding site starting at a hydrophobic cavity near the membrane-exposed surface of subunit I, close to the interface to subunit III. A large number of water sites are predicted within the protein, which could play an essential role for the transfer of protons in cytochrome c oxidase. The water molecules form two channels along which protons can enter from the cytoplasmic (matrix) side of the protein and reach the binuclear center. A possible pumping mechanism is proposed that involves a shuttling motion of a glutamic acid side chain, which could then transfer a proton to a propionate group of heme alpha 3.

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.

From sequences to shapes and back: a case study in RNA secondary structures.

RNA folding is viewed here as a map assigning secondary structures to sequences. At fixed chain length the number of sequences far exceeds the number of structures. Frequencies of structures are highly non-uniform and follow a generalized form of Zipf's law: we find relatively few common and many rare ones. By using an algorithm for inverse folding, we show that sequences sharing the same structure are distributed randomly over sequence space. All common structures can be accessed from an arbitrary sequence by a number of mutations much smaller than the chain length. The sequence space is percolated by extensive neutral networks connecting nearest neighbours folding into identical structures. Implications for evolutionary adaptation and for applied molecular evolution are evident: finding a particular structure by mutation and selection is much simpler than expected and, even if catalytic activity should turn out to be sparse of RNA structures, it can hardly be missed by evolutionary processes.

An ESS-analysis for ensembles of prisoner's dilemma strategies.

The ESS (Evolutionary Stable Strategy) concept of Maynard Smith can be applied in its weak form to ensembles of competing PD ("Prisoner's Dilemma") strategies memorizing two to three of one's own and one's opponent's moves. The format of our study is: (1) games have very long duration; (2) Taylor-Jonker dynamics applies; (3) Effects of finite population size can be ignored. It is shown that in the case R greater than (T + S)/2 a set of strategies can be singled out which do not lose against any other strategy while co-operating with themselves. Such a set is uninvadable by other PD strategies if it constitutes more than half of the total population.