Asymptotics of RNA shapes.

RNA shapes, introduced by Giegerich et al. (2004), provide a useful classification of the branching complexity for RNA secondary structures. In this paper, we derive an exact value for the asymptotic number of RNA shapes, by relying on an elegant relation between non-ambiguous, context-free grammars, and generating functions. Our results provide a theoretical upper bound on the length of RNA sequences amenable to probabilistic shape analysis (Steffen et al., 2006; Voss et al., 2006), under the assumption that any base can basepair with any other base. Since the relation between context-free grammars and asymptotic enumeration is simple, yet not well-known in bioinformatics, we give a self-contained presentation with illustrative examples. Additionally, we prove a surprising 1-to-1 correspondence between pi-shapes and Motzkin numbers.     

Complete probabilistic analysis of RNA shapes

Background  

Soon after the first algorithms for RNA folding became available, it was recognised that the prediction of only one energetically optimal structure is insufficient to achieve reliable results. An in-depth analysis of the folding space as a whole appeared necessary to deduce the structural properties of a given RNA molecule reliably. Folding space analysis comprises various methods such as suboptimal folding, computation of base pair probabilities, sampling procedures and abstract shape analysis. Common to many approaches is the idea of partitioning the folding space into classes of structures, for which certain properties can be derived.     

On realizing shapes in the theory of RNA neutral networks

It is known (Reidys et al., 1997b. Bull. Math. Biol. 59(2), 339-397) that for any two secondary structures S,S' there exists an RNA sequence compatible with both, and that this result does not extend to more than two secondary structures. Indeed, a simple formula for the number of RNA sequences compatible with secondary structures S,S' plays a role in the algorithms of Flamm et al. (2001. RNA 7, 254-265) and of Abfalter et al. (2003. Proceedings of the German Conference on Bioinformatics, ) to design an RNA switch. Here we show that a natural extension of this problem is NP-complete. Unless P=NP, there is no polynomial time algorithm, which when given secondary structures S1,...,S(k), for k4, determines the least number of positions, such that after removal of all base pairs incident to these positions there exists an RNA nucleotide sequence compatible with the given secondary structures. We also consider a restricted version of this problem with a "fixed maximum" number of possible stars and show that it has a simple polynomial time solution.     

RNAshapes: an integrated RNA analysis package based on abstract shapes

We introduce RNAshapes, a new software package that integrates three RNA analysis tools based on the abstract shapes approach: the analysis of shape representatives, the calculation of shape probabilities and the consensus shapes approach. This new package is completely reimplemented in C and outruns the original implementations significantly in runtime and memory requirements. Additionally, we added a number of useful features like suboptimal folding with correct dangling energies, structure graph output, shape matching and a sliding window approach.     

Ecological connectivity shapes quasispecies structure of RNA viruses in an Antarctic lake

RNA viruses exist as complex mixtures of genotypes, known as quasispecies, where the evolution potential resides in the whole community of related genotypes. Quasispecies structure and dynamics have been studied in detail for virus infecting animals and plants but remain unexplored for those infecting micro‐organisms in environmental samples. We report the first metagenomic study of RNA viruses in an Antarctic lake (Lake Limnopolar, Livingston Island). Similar to low‐latitude aquatic environments, this lake harbours an RNA virome dominated by positive single‐strand RNA viruses from the order Picornavirales probably infecting micro‐organisms. Antarctic picorna‐like virus 1 (APLV1), one of the most abundant viruses in the lake, does not incorporate any mutation in the consensus sequence from 2006 to 2010 and shows stable quasispecies with low‐complexity indexes. By contrast, APLV2‐APLV3 are detected in the lake water exclusively in summer samples and are major constituents of surrounding cyanobacterial mats. Their quasispecies exhibit low complexity in cyanobacterial mat, but their run‐off‐mediated transfer to the lake results in a remarkable increase of complexity that may reflect the convergence of different viral quasispecies from the catchment area or replication in a more diverse host community. This is the first example of viral quasispecies from natural aquatic ecosystems and points to ecological connectivity as a modulating factor of quasispecies complexity.     

Consensus shapes: an alternative to the Sankoff algorithm for RNA consensus structure prediction

MOTIVATION: The well-known Sankoff algorithm for simultaneous RNA sequence alignment and folding is currently considered an ideal, but computationally over-expensive method. Available tools implement this algorithm under various pragmatic restrictions. They are still expensive to use, and it is difficult to judge if the moderate quality of results is because of the underlying model or to its imperfect implementation. RESULTS: We propose to redefine the consensus structure prediction problem in a way that does not imply a multiple sequence alignment step. For a family of RNA sequences, our method explicitly and independently enumerates the near-optimal abstract shape space, and predicts as the consensus an abstract shape common to all sequences. For each sequence, it delivers the thermodynamically best structure which has this common shape. Since the shape space is much smaller than the structure space, and identification of common shapes can be done in linear time (in the number of shapes considered), the method is essentially linear in the number of sequences. Our evaluation shows that the new method compares favorably with available alternatives. AVAILABILITY: The new method has been implemented in the program RNAcast and is available on the Bielefeld Bioinformatics Server. CONTACT: jreeder@TechFak.Uni-Bielefeld.DE, robert@TechFak.Uni-Bielefeld.DE SUPPLEMENTARY INFORMATION: Available at http://bibiserv.techfak.uni-bielefeld.de/rnacast/supplementary.html     

Dissecting the protein-RNA interface: the role of protein surface shapes and RNA secondary structures in protein-RNA recognition

Protein-RNA interactions are essential for many biological processes. However, the structural mechanisms underlying these interactions are not fully understood. Here, we analyzed the protein surface shape (dented, intermediate or protruded) and the RNA base pairing properties (paired or unpaired nucleotides) at the interfaces of 91 protein-RNA complexes derived from the Protein Data Bank. Dented protein surfaces prefer unpaired nucleotides to paired ones at the interface, and hydrogen bonds frequently occur between the protein backbone and RNA bases. In contrast, protruded protein surfaces do not show such a preference, rather, electrostatic interactions initiate the formation of hydrogen bonds between positively charged amino acids and RNA phosphate groups. Interestingly, in many protein-RNA complexes that interact via an RNA loop, an aspartic acid is favored at the interface. Moreover, in most of these complexes, nucleotide bases in the RNA loop are flipped out and form hydrogen bonds with the protein, which suggests that aspartic acid is important for RNA loop recognition through a base-flipping process. This study provides fundamental insights into the role of the shape of the protein surface and RNA secondary structures in mediating protein-RNA interactions.     

Abstract

Abstract

This study contains a definition of the Redbird Focus of the Chouteau Aspect, in north central Nebraska, and attempts to relate it to the problem of Ponca prehistory. The four excavated sites of this focus, near the mouth of the Niobrara River (25HT2, 25HT3, 25KX4, and 25KX9), are small open villages of circular earth lodges. Unexcavated camp sites are also identified on the lower Niobrara River and on the middle reaches of the Elkhorn River. The remains from these sites are similar to those of the Lower Loup and La Roche foci, but they are sufficiently distinct to warrant designating them as a new focus. Trade goods at 25KX9 date it at about A.D. 1700, but the other sites lack trade goods. Redbird is estimated to date between A.D. 1600 and 1700, or perhaps somewhat later. Shelltempered pottery in two of the sites implies contemporaneity with the Oneota Aspect, perhaps the Orr Focus, which is identified as the remains of the protohistoric Iowa Indians. Site location, settlement patterns and size, burial data, and the dating of the focus intimates that it is attributable to the Ponca Indians. Conflicting data must be resolved before this identification is verified.     

Abstract

<正>Marx and Dialectics of Nature Marx,concentrating his research work on economics,had no systematic writings on the dialectics of nature,but if we lump together all his ideas concerning the dialectics of nature presented in his various works and letters,a comprehensive dialectic outlook on nature will emerge.The doctrine of dialectics of nature is the joint creation of Marx and Engles resulting from their close coorperation,although Engles did     

Abstract

I n April 1900 the specimen in question was received from Miss Una A. Ware, of Dalkey, 17 miles north of Adelaide, in the "Mallee Scrub" of dwarf Eucalyptus. It consisted of a fully-developed Battarea from base to pileus, with a solid, heavy, tuber-like mass attached. The specimen was shown on 1st May, 1900, at a meeting of the Royal Society of South Australia (Trans, xxiv. p. 171). A few days later spores were abundantly shed, and the specimen bedded in sand and covered with a boll-glass, and for nearly a month it continued to develope in height. It was again shown to the R. Society of South Australia on 6th June, when the following dimensions were noted
Peridium whitish when fresh, irregularly hemispherical and smooth, except some slight irregular furrows.
The specimen was handed to Dr. M. Holtze, F.L.S., Director of the Adelaide Botanic Garden, and is there preserved in the Herbarium. No other specimen has been recently found, but it has been suggested that it may belong to Battarea phalloides , Dicks. The other Australian species known are B. Maelleriana , kalchb., from Yorke's Peninsula, and B. Tepperiana , Ludw., from N.W. Victoria.
Total height from base to summit. 235mm.
Pileus, diameter…. 42 mm
Stipes, at summit…. 12 mm
Stipes, 75 mm. below the summit. 20 mm