The complexity of multiple sequence alignment with SP-score that is a metric

AbstractThis paper analyzes the computational complexity of computing the optimal alignment of a set of sequences under the sum of all pairs (SP) score scheme. We solve an open question by showing that the problem is NP-complete in the very restricted case in which the sequences are over a binary alphabet and the score is a metric. This result establishes the intractability of multiple sequence alignment under a score function of mathematical interest, which has indeed received much attention in biological sequence comparison

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

Peptide vocabulary analysis reveals ultra-conservation and homonymity in protein sequences

A new algorithm is presented for vocabulary analysis (word detection) in texts of human origin. It performs at 60%–70% overall accuracy and greater than 80% accuracy for longer words, and approximately 85% sensitivity on Alice in Wonderland, a considerable improvement on previous methods. When applied to protein sequences, it detects short sequences analogous to words in human texts, i.e. intolerant to changes in spelling (mutation), and relatively contextindependent in their meaning (function). Some of these are homonyms of up to 7 amino acids, which can assume different structures in different proteins. Others are ultra-conserved stretches of up to 18 amino acids within proteins of less than 40% overall identity, reflecting extreme constraint or convergent evolution. Different species are found to have qualitatively different major peptide vocabularies, e.g. some are dominated by large gene families, while others are rich in simple repeats or dominated by internally repetitive proteins. This suggests the possibility of a peptide vocabulary signature, analogous to genome signatures in DNA. Homonyms may be useful in detecting convergent evolution and positive selection in protein evolution. Ultra-conserved words may be useful in identifying structures intolerant to substitution over long periods of evolutionary time

SVIM: Structural Variant Identification using Mapped Long Reads

Motivation: Structural variants are defined as genomic variants larger than 50bp. They have been shown to affect more bases in any given genome than SNPs or small indels. Additionally, they have great impact on human phenotype and diversity and have been linked to numerous diseases. Due to their size and association with repeats, they are difficult to detect by shotgun sequencing, especially when based on short reads. Long read, single molecule sequencing technologies like those offered by Pacific Biosciences or Oxford Nanopore Technologies produce reads with a length of several thousand base pairs. Despite the higher error rate and sequencing cost, long read sequencing offers many advantages for the detection of structural variants. Yet, available software tools still do not fully exploit the possibilities. Results: We present SVIM, a tool for the sensitive detection and precise characterization of structural variants from long read data. SVIM consists of three components for the collection, clustering and combination of structural variant signatures from read alignments. It discriminates five different variant classes including similar types, such as tandem and interspersed duplications and novel element insertions. SVIM is unique in its capability of extracting both the genomic origin and destination of duplications. It compares favorably with existing tools in evaluations on simulated data and real datasets from PacBio and Nanopore sequencing machines. Availability and implementation: The source code and executables of SVIM are available on Github: github.com/eldariont/svim. SVIM has been implemented in Python 3 and published on bioconda and the Python Package Index. Supplementary information: Supplementary data are available at Bioinformatics online

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

Multiple sequence alignment based on set covers

We introduce a new heuristic for the multiple alignment of a set of sequences. The heuristic is based on a set cover of the residue alphabet of the sequences, and also on the determination of a significant set of blocks comprising subsequences of the sequences to be aligned. These blocks are obtained with the aid of a new data structure, called a suffix-set tree, which is constructed from the input sequences with the guidance of the residue-alphabet set cover and generalizes the well-known suffix tree of the sequence set. We provide performance results on selected BAliBASE amino-acid sequences and compare them with those yielded by some prominent approaches