9,953 research outputs found
Evolutionary Dynamics and Optimization: Neutral Networks as Model-Landscapes for RNA Secondary-Structure Folding-Landscapes
We view the folding of RNA-sequences as a map that assigns a pattern of base
pairings to each sequence, known as secondary structure. These preimages can be
constructed as random graphs (i.e. the neutral networks associated to the
structure ). By interpreting the secondary structure as biological
information we can formulate the so called Error Threshold of Shapes as an
extension of Eigen's et al. concept of an error threshold in the single peak
landscape. Analogue to the approach of Derrida & Peliti for a of the population
on the neutral network. On the one hand this model of a single shape landscape
allows the derivation of analytical results, on the other hand the concept
gives rise to study various scenarios by means of simulations, e.g. the
interaction of two different networks. It turns out that the intersection of
two sets of compatible sequences (with respect to the pair of secondary
structures) plays a key role in the search for ''fitter'' secondary structures.Comment: 20 pages, uuencoded compressed postscript-file, Proc. of ECAL '95
conference, to appear., email: chris @ imb-jena.d
RNA secondary structure design
We consider the inverse-folding problem for RNA secondary structures: for a
given (pseudo-knot-free) secondary structure find a sequence that has that
structure as its ground state. If such a sequence exists, the structure is
called designable. We implemented a branch-and-bound algorithm that is able to
do an exhaustive search within the sequence space, i.e., gives an exact answer
whether such a sequence exists. The bound required by the branch-and-bound
algorithm are calculated by a dynamic programming algorithm. We consider
different alphabet sizes and an ensemble of random structures, which we want to
design. We find that for two letters almost none of these structures are
designable. The designability improves for the three-letter case, but still a
significant fraction of structures is undesignable. This changes when we look
at the natural four-letter case with two pairs of complementary bases:
undesignable structures are the exception, although they still exist. Finally,
we also study the relation between designability and the algorithmic complexity
of the branch-and-bound algorithm. Within the ensemble of structures, a high
average degree of undesignability is correlated to a long time to prove that a
given structure is (un-)designable. In the four-letter case, where the
designability is high everywhere, the algorithmic complexity is highest in the
region of naturally occurring RNA.Comment: 11 pages, 10 figure
Expected degree for RNA secondary structure networks
Consider the network of all secondary structures of a given RNA sequence,
where nodes are connected when the corresponding structures have base pair
distance one. The expected degree of the network is the average number of
neighbors, where average may be computed with respect to the either the uniform
or Boltzmann probability. Here we describe the first algorithm, RNAexpNumNbors,
that can compute the expected number of neighbors, or expected network degree,
of an input sequence. For RNA sequences from the Rfam database, the expected
degree is significantly less than the CMFE structure, defined to have minimum
free energy over all structures consistent with the Rfam consensus structure.
The expected degree of structural RNAs, such as purine riboswitches,
paradoxically appears to be smaller than that of random RNA, yet the difference
between the degree of the MFE structure and the expected degree is larger than
that of random RNA. Expected degree does not seem to correlate with standard
structural diversity measures of RNA, such as positional entropy, ensemble
defect, etc. The program {\tt RNAexpNumNbors} is written in C, runs in cubic
time and quadratic space, and is publicly available at
http://bioinformatics.bc.edu/clotelab/RNAexpNumNbors.Comment: 25 pages, 5 figures, 5 table
RNA secondary structure prediction from multi-aligned sequences
It has been well accepted that the RNA secondary structures of most
functional non-coding RNAs (ncRNAs) are closely related to their functions and
are conserved during evolution. Hence, prediction of conserved secondary
structures from evolutionarily related sequences is one important task in RNA
bioinformatics; the methods are useful not only to further functional analyses
of ncRNAs but also to improve the accuracy of secondary structure predictions
and to find novel functional RNAs from the genome. In this review, I focus on
common secondary structure prediction from a given aligned RNA sequence, in
which one secondary structure whose length is equal to that of the input
alignment is predicted. I systematically review and classify existing tools and
algorithms for the problem, by utilizing the information employed in the tools
and by adopting a unified viewpoint based on maximum expected gain (MEG)
estimators. I believe that this classification will allow a deeper
understanding of each tool and provide users with useful information for
selecting tools for common secondary structure predictions.Comment: A preprint of an invited review manuscript that will be published in
a chapter of the book `Methods in Molecular Biology'. Note that this version
of the manuscript may differ from the published versio
Parametrized Stochastic Grammars for RNA Secondary Structure Prediction
We propose a two-level stochastic context-free grammar (SCFG) architecture
for parametrized stochastic modeling of a family of RNA sequences, including
their secondary structure. A stochastic model of this type can be used for
maximum a posteriori estimation of the secondary structure of any new sequence
in the family. The proposed SCFG architecture models RNA subsequences
comprising paired bases as stochastically weighted Dyck-language words, i.e.,
as weighted balanced-parenthesis expressions. The length of each run of
unpaired bases, forming a loop or a bulge, is taken to have a phase-type
distribution: that of the hitting time in a finite-state Markov chain. Without
loss of generality, each such Markov chain can be taken to have a bounded
complexity. The scheme yields an overall family SCFG with a manageable number
of parameters.Comment: 5 pages, submitted to the 2007 Information Theory and Applications
Workshop (ITA 2007
RNA secondary structure prediction using large margin methods
The secondary structure of RNA is essential for its biological role. Recently, Do, Woods, Batzoglou, (ISMB 2006) proposed a probabilistic approach that generalizes SCFGs using conditional maximum likelihood to estimate the model parameters. We propose an alternative approach to parameter estimation which is based on an SVM-like large margin method
Reconstructing phylogeny from RNA secondary structure via simulated evolution
DNA sequences of genes encoding functional RNA molecules (e.g., ribosomal RNAs) are commonly used in phylogenetics (i.e. to infer evolutionary history). Trees derived from ribosomal RNA (rRNA) sequences, however, are inconsistent with other molecular data in investigations of deep branches in the tree of life. Since much of te functional constraints on the gene products (i.e. RNA molecules) relate to three-dimensional structure, rather than their actual sequences, accumulated mutations in the gene sequences may obscure phylogenetic signal over very large evolutionary time-scales. Variation in structure, however, may be suitable for phylogenetic inference even under extreme sequence divergence. To evaluate qualitatively the manner in which structural evolution relates to sequence change, we simulated the evolution of RNA sequences under various constraints on structural change
Nature of the glassy phase of RNA secondary structure
We characterize the low temperature phase of a simple model for RNA secondary
structures by determining the typical energy scale E(l) of excitations
involving l bases. At zero temperature, we find a scaling law E(l) \sim
l^\theta with \theta \approx 0.23, and this same scaling holds at low enough
temperatures. Above a critical temperature, there is a different phase
characterized by a relatively flat free energy landscape resembling that of a
homopolymer with a scaling exponent \theta=1. These results strengthen the
evidence in favour of the existence of a glass phase at low temperatures.Comment: 7 pages, 1 figur
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