2,018 research outputs found
Evolutionary models for insertions and deletions in a probabilistic modeling framework
BACKGROUND: Probabilistic models for sequence comparison (such as hidden Markov models and pair hidden Markov models for proteins and mRNAs, or their context-free grammar counterparts for structural RNAs) often assume a fixed degree of divergence. Ideally we would like these models to be conditional on evolutionary divergence time. Probabilistic models of substitution events are well established, but there has not been a completely satisfactory theoretical framework for modeling insertion and deletion events. RESULTS: I have developed a method for extending standard Markov substitution models to include gap characters, and another method for the evolution of state transition probabilities in a probabilistic model. These methods use instantaneous rate matrices in a way that is more general than those used for substitution processes, and are sufficient to provide time-dependent models for standard linear and affine gap penalties, respectively. Given a probabilistic model, we can make all of its emission probabilities (including gap characters) and all its transition probabilities conditional on a chosen divergence time. To do this, we only need to know the parameters of the model at one particular divergence time instance, as well as the parameters of the model at the two extremes of zero and infinite divergence. I have implemented these methods in a new generation of the RNA genefinder QRNA (eQRNA). CONCLUSION: These methods can be applied to incorporate evolutionary models of insertions and deletions into any hidden Markov model or stochastic context-free grammar, in a pair or profile form, for sequence modeling
Accurate reconstruction of insertion-deletion histories by statistical phylogenetics
The Multiple Sequence Alignment (MSA) is a computational abstraction that
represents a partial summary either of indel history, or of structural
similarity. Taking the former view (indel history), it is possible to use
formal automata theory to generalize the phylogenetic likelihood framework for
finite substitution models (Dayhoff's probability matrices and Felsenstein's
pruning algorithm) to arbitrary-length sequences. In this paper, we report
results of a simulation-based benchmark of several methods for reconstruction
of indel history. The methods tested include a relatively new algorithm for
statistical marginalization of MSAs that sums over a stochastically-sampled
ensemble of the most probable evolutionary histories. For mammalian
evolutionary parameters on several different trees, the single most likely
history sampled by our algorithm appears less biased than histories
reconstructed by other MSA methods. The algorithm can also be used for
alignment-free inference, where the MSA is explicitly summed out of the
analysis. As an illustration of our method, we discuss reconstruction of the
evolutionary histories of human protein-coding genes.Comment: 28 pages, 15 figures. arXiv admin note: text overlap with
arXiv:1103.434
Evolutionary Inference via the Poisson Indel Process
We address the problem of the joint statistical inference of phylogenetic
trees and multiple sequence alignments from unaligned molecular sequences. This
problem is generally formulated in terms of string-valued evolutionary
processes along the branches of a phylogenetic tree. The classical evolutionary
process, the TKF91 model, is a continuous-time Markov chain model comprised of
insertion, deletion and substitution events. Unfortunately this model gives
rise to an intractable computational problem---the computation of the marginal
likelihood under the TKF91 model is exponential in the number of taxa. In this
work, we present a new stochastic process, the Poisson Indel Process (PIP), in
which the complexity of this computation is reduced to linear. The new model is
closely related to the TKF91 model, differing only in its treatment of
insertions, but the new model has a global characterization as a Poisson
process on the phylogeny. Standard results for Poisson processes allow key
computations to be decoupled, which yields the favorable computational profile
of inference under the PIP model. We present illustrative experiments in which
Bayesian inference under the PIP model is compared to separate inference of
phylogenies and alignments.Comment: 33 pages, 6 figure
Evolutionary distances in the twilight zone -- a rational kernel approach
Phylogenetic tree reconstruction is traditionally based on multiple sequence
alignments (MSAs) and heavily depends on the validity of this information
bottleneck. With increasing sequence divergence, the quality of MSAs decays
quickly. Alignment-free methods, on the other hand, are based on abstract
string comparisons and avoid potential alignment problems. However, in general
they are not biologically motivated and ignore our knowledge about the
evolution of sequences. Thus, it is still a major open question how to define
an evolutionary distance metric between divergent sequences that makes use of
indel information and known substitution models without the need for a multiple
alignment. Here we propose a new evolutionary distance metric to close this
gap. It uses finite-state transducers to create a biologically motivated
similarity score which models substitutions and indels, and does not depend on
a multiple sequence alignment. The sequence similarity score is defined in
analogy to pairwise alignments and additionally has the positive semi-definite
property. We describe its derivation and show in simulation studies and
real-world examples that it is more accurate in reconstructing phylogenies than
competing methods. The result is a new and accurate way of determining
evolutionary distances in and beyond the twilight zone of sequence alignments
that is suitable for large datasets.Comment: to appear in PLoS ON
Probabilistic Phylogenetic Inference with Insertions and Deletions
A fundamental task in sequence analysis is to calculate the probability of a multiple alignment given a phylogenetic tree relating the sequences and an evolutionary model describing how sequences change over time. However, the most widely used phylogenetic models only account for residue substitution events. We describe a probabilistic model of a multiple sequence alignment that accounts for insertion and deletion events in addition to substitutions, given a phylogenetic tree, using a rate matrix augmented by the gap character. Starting from a continuous Markov process, we construct a non-reversible generative (birth–death) evolutionary model for insertions and deletions. The model assumes that insertion and deletion events occur one residue at a time. We apply this model to phylogenetic tree inference by extending the program dnaml in phylip. Using standard benchmarking methods on simulated data and a new “concordance test” benchmark on real ribosomal RNA alignments, we show that the extended program dnamlε improves accuracy relative to the usual approach of ignoring gaps, while retaining the computational efficiency of the Felsenstein peeling algorithm
Towards realistic benchmarks for multiple alignments of non-coding sequences
<p><b>Abstract</b></p> <p>Background</p> <p>With the continued development of new computational tools for multiple sequence alignment, it is necessary today to develop benchmarks that aid the selection of the most effective tools. Simulation-based benchmarks have been proposed to meet this necessity, especially for non-coding sequences. However, it is not clear if such benchmarks truly represent real sequence data from any given group of species, in terms of the difficulty of alignment tasks.</p> <p>Results</p> <p>We find that the conventional simulation approach, which relies on empirically estimated values for various parameters such as substitution rate or insertion/deletion rates, is unable to generate synthetic sequences reflecting the broad genomic variation in conservation levels. We tackle this problem with a new method for simulating non-coding sequence evolution, by relying on genome-wide distributions of evolutionary parameters rather than their averages. We then generate synthetic data sets to mimic orthologous sequences from the <it>Drosophila </it>group of species, and show that these data sets truly represent the variability observed in genomic data in terms of the difficulty of the alignment task. This allows us to make significant progress towards estimating the alignment accuracy of current tools in an absolute sense, going beyond only a relative assessment of different tools. We evaluate six widely used multiple alignment tools in the context of <it>Drosophila </it>non-coding sequences, and find the accuracy to be significantly different from previously reported values. Interestingly, the performance of most tools degrades more rapidly when there are more insertions than deletions in the data set, suggesting an asymmetric handling of insertions and deletions, even though none of the evaluated tools explicitly distinguishes these two types of events. We also examine the accuracy of two existing tools for annotating insertions versus deletions, and find their performance to be close to optimal in <it>Drosophila </it>non-coding sequences if provided with the true alignments.</p> <p>Conclusion</p> <p>We have developed a method to generate benchmarks for multiple alignments of <it>Drosophila </it>non-coding sequences, and shown it to be more realistic than traditional benchmarks. Apart from helping to select the most effective tools, these benchmarks will help practitioners of comparative genomics deal with the effects of alignment errors, by providing accurate estimates of the extent of these errors.</p
Tensor Decomposition Reveals Concurrent Evolutionary Convergences and Divergences and Correlations with Structural Motifs in Ribosomal RNA
Evolutionary relationships among organisms are commonly described by using a
hierarchy derived from comparisons of ribosomal RNA (rRNA) sequences. We propose that
even on the level of a single rRNA molecule, an organism's evolution is composed
of multiple pathways due to concurrent forces that act independently upon different
rRNA degrees of freedom. Relationships among organisms are then compositions of
coexisting pathway-dependent similarities and dissimilarities, which cannot be
described by a single hierarchy. We computationally test this hypothesis in
comparative analyses of 16S and 23S rRNA sequence alignments by using a tensor
decomposition, i.e., a framework for modeling composite data. Each alignment is
encoded in a cuboid, i.e., a third-order tensor, where nucleotides, positions and
organisms, each represent a degree of freedom. A tensor mode-1 higher-order singular
value decomposition (HOSVD) is formulated such that it separates each cuboid into
combinations of patterns of nucleotide frequency variation across organisms and
positions, i.e., “eigenpositions” and corresponding nucleotide-specific
segments of “eigenorganisms,” respectively, independent of a-priori
knowledge of the taxonomic groups or rRNA structures. We find, in support of our
hypothesis that, first, the significant eigenpositions reveal multiple similarities
and dissimilarities among the taxonomic groups. Second, the corresponding
eigenorganisms identify insertions or deletions of nucleotides exclusively conserved
within the corresponding groups, that map out entire substructures and are enriched
in adenosines, unpaired in the rRNA secondary structure, that participate in tertiary
structure interactions. This demonstrates that structural motifs involved in rRNA
folding and function are evolutionary degrees of freedom. Third, two previously
unknown coexisting subgenic relationships between Microsporidia and Archaea are
revealed in both the 16S and 23S rRNA alignments, a convergence and a divergence,
conferred by insertions and deletions of these motifs, which cannot be described by a
single hierarchy. This shows that mode-1 HOSVD modeling of rRNA alignments might be
used to computationally predict evolutionary mechanisms
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