Biomedical subjects
Publications and source records attributed to P F Stadler.
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.
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.
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/
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 current implementation of the Neo-Darwinian model of evolution typically assumes that the set of possible phenotypes is organized into a highly symmetric and regular space equipped with a notion of distance, for example, a Euclidean vector space. Recent computational work on a biophysical genotype-phenotype model based on the folding of RNA sequences into secondary structures suggests a rather different picture. If phenotypes are organized according to genetic accessibility, the resulting space lacks a metric and is formalized by an unfamiliar structure, known as a pre-topology. Patterns of phenotypic evolution-such as punctuation, irreversibility, modularity--result naturally from the properties of this space. The classical framework, however, addresses these patterns by exclusively invoking natural selection on suitably imposed fitness landscapes. We propose to extend the explanatory level for phenotypic evolution from fitness considerations alone to include the topological structure of phenotype space as induced by the genotype-phenotype map. We introduce the mathematical concepts and tools necessary to formalize the notion of accessibility pre-topology relative to which we can speak of continuity in the genotype-phenotype map and in evolutionary trajectories. We connect the factorization of a pre-topology into a product space with the notion of phenotypic character and derive a condition for factorization. Based on anecdotal evidence from the RNA model, we conjecture that this condition is not globally fulfilled, but rather confined to regions where the genotype-phenotype map is continuous. Equivalently, local regions of genotype space on which the map is discontinuous are associated with the loss of character autonomy. This is consistent with the importance of these regions for phenotypic innovation. The intention of the present paper is to offer a perspective, a framework to implement this perspective, and a few results illustrating how this framework can be put to work. The RNA case is used as an example throughout the text.
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.
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.
Neurofibromatosis type 1 (NF1) is an autosomal dominant genetic disorder affecting one in 3,500 individuals. The mutation rate in the NF1 gene is one of the highest known for human genes. Compared to other methods, the protein truncation test (PTT) provides improved efficiency in detecting NF1 mutations which are dispersed throughout the gene which spans 350 kilobases of genomic DNA. We have applied the PTT and subsequent sequence analysis of cloned cDNA to identify mutations in NF1 patients. We report here the identification of two novel (W336X and Q315X), and one recurrent (R304X) mutation located in exon 7 and show that all three premature termination codons lead to skipping of exon 7 in a proportion of the transcripts derived from the mutated allele. Possible mutation-induced alterations of the RNA secondary structure and their impact on skipping of exon 7 of the NF1 gene are explored and discussed.
The effect of recombination on genotypes can be represented in the form of P-structures, i.e., a map from the set of pairs of genotypes to the power set of genotypes. The interpretation is that the P-structure maps the pair of parental genotypes to the set of recombinant genotypes which result from the recombination of the parental genotypes. A recombination fitness landscape is then a function from the genotypes in a P-structure to the real numbers. In previous papers we have shown that the eigenfunctions of (a matrix associated with) the P-structure provide a basis for the Fourier decomposition of arbitrary recombination landscapes. Here we generalize this framework to include the effect of genotype frequencies, assuming linkage equilibrium. We find that the autocorrelation of the eigenfunctions of the population-weighted P-structure is independent of the population composition. As a consequence we can directly compare the performance of mutation and recombination operators by comparing the autocorrelations on the finite set of elementary landscapes. This comparison suggests that point mutation is a superior search strategy on landscapes with a low order and a moderate order of interaction p < n/3 (n is the number of loci). For more complex landscapes 1-point recombination is superior to both mutation and uniform recombination, but only if the distance among the interacting loci (defining length) is minimal. Furthermore we find that the autocorrelation on any landscape is increasing as the distribution of genotypes becomes more extreme, i.e., if the population occupies a location close to the boundary of the frequency simplex. Landscapes are smoother the more biased the distribution of genotype frequencies is. We suggest that this result explains the paradox that there is little epistatic interaction for quantitative traits detected in natural populations if one uses variance decomposition methods while there is evidence for strong interactions in molecular mapping studies for quantitative trait loci.
A class of autocatalytic reaction networks based on template-dependent ligation and higher-order catalysis is analysed. Apart from an irreversible ligation reaction we consider only reversible aggregation steps that provide a realistic description of molecular recognition. The overall dynamics can be understood by means of replicator equations with highly non-linear interaction functions. The dynamics depends crucially on the total concentration c0 of replicating material. For small c0, in the hyperbolic growth regime, we recover the familiar dynamics of second-order replicator equations with its wealth of complex dynamics ranging from multi-stability to periodic and strange attractors as well as to heteroclinic orbits. For large c0, in the parabolic growth regime, product inhibition becomes dominating and we observe a single globally stable equilibrium tantamount to permanent coexistence. In an intermediate parameter range we sometimes observe a behavior that is reminiscent of 'survival of the fittest'. Independently replicating species (Schlögl's model) and the hypercycle are discussed in detail.
We study analytically the steady-state regime of a network of n error-prone self-replicating templates forming an asymmetric hypercycle and its error tail. We show that the existence of a master template with a higher noncatalyzed self-replicative productivity a than the error tail ensures the stability of chains in which m < n-1 templates coexist with the master species. The stability of these chains against the error tail is guaranteed for catalytic coupling strengths K on the order of a. We find that the hypercycle becomes more stable than the chains only if K is on the order of a2. Furthermore, we show that the minimal replication accuracy per template needed to maintain the hypercycle, the so-called error threshold, vanishes as square root of n/K for large K and N < or = 4.
The distinction between continuous and discontinuous transitions is a long-standing problem in the theory of evolution. Because continuity is a topological property, we present a formalism that treats the space of phenotypes as a (finite) topological space, with a topology that is derived from the probabilities with which one phenotype is accessible from another through changes at the genotypic level. The shape space of RNA secondary structures is used to illustrate this approach. We show that evolutionary trajectories are continuous if and only if they follow connected paths in phenotype space.
Many properties of organisms show great robustness against mutations. Whether this robustness is an evolved property or intrinsic to genetic systems is by and large unknown. An evolutionary origin of robustness would require a rethinking of key concepts in the field of molecular evolution, such as gene-specific neutral mutation rates, or the context-independence of deleterious mutations. We provide evidence that mutational robustness of the genome of RNA viruses to mutational changes in secondary structure has evolved. J. Exp. Zool. ( Mol. Dev. Evol.) 285:119-127, 1999.
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.
The dynamics of a network of autocatalytically replicating species in a continuously stirred tank reactor can be described by a replicator equation in the limit of small flux rates.
Novel species are introduced into a network of interacting replicators either (i) as mutants of members of the network (ii) as unrelated immigrants. We consider the meta-population dynamics of such a system. In the first case the appearance of mutants leads to a slow growth of the replicator network, proportional to the logarithm of the number of mutation events. Surprisingly, replicators evolved by mutant incorporation are always permanent, despite the fact that permanence is in general a very rare phenomenon. In the second case, on the other hand, immigrants lead to frequent break-downs on the entire network and hence to complete extinction. In both cases individual species are short-lived and the distribution of survival times is exponential.
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.
The theory of autocatalytic binary ligation is reviewed within the context of a consistently applied Michaelis-Menten quasi-steady-state approximation to obtain explicit analytical results describing time-course data from experiments. A detailed protocol for the step-wise elucidation of a minimal set of experimental parameters is outlined. The kinetic equations are then generalized to cases of self- and cross-catalysis among an arbitrary number of different templates and applied to experiments involving just two templates. Depending on the values of various kinetic parameters such systems can display exclusionary Darwinian selection corresponding to an exponential growth law, selective coexistence or coexistence of all species characteristic of a parabolic growth law; the intermediate behaviour arises as a property of the full mechanism analysed here. Our results are applicable to the classical case of self-replicating nucleic acids and their analogues as well as to newly discovered self-replicating peptides.