A local algorithm for DNA sequence alignment with inversions

Computing Nonoverlapping Inversion Distance Between Two Strings in Linear Average Time

Biological events like inversions are not automatically detected by the usual alignment algorithms. Alignment with inversions does not have a known polynomial time algorithm and Schöniger and Waterman introduced a simplification of the alignment problem with nonoverlapping inversions, where all regions will not be allowed to overlap. They presented an \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${ \cal O} ( {n^6} )$$ \end{document} algorithm to compute nonoverlapping inversion distance between two strings of length n. The time and space complexities were improved to \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${ \cal O} ( {n^3} )$$ \end{document} and \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $${ \cal O} ( {n^2} )$$ \end{document} later by Cho, Vellozo, and Ta. In this article, a linear space and linear average time algorithm to compute the inversion distance between two strings of the same length is presented. The recursive formula for this purpose is new to the best of our knowledge. The space costs of the algorithms to solve the same problem are quadratic in the literature, and thus our original algorithm is the first linear space and linear average time algorithm to solve the inversion distance problem.

Computational identification of micro-structural variations and their proteogenomic consequences in cancer

Motivation

Rapid advancement in high throughput genome and transcriptome sequencing (HTS) and mass spectrometry (MS) technologies has enabled the acquisition of the genomic, transcriptomic and proteomic data from the same tissue sample. We introduce a computational framework, ProTIE, to integratively analyze all three types of omics data for a complete molecular profile of a tissue sample. Our framework features MiStrVar, a novel algorithmic method to identify micro structural variants (microSVs) on genomic HTS data. Coupled with deFuse, a popular gene fusion detection method we developed earlier, MiStrVar can accurately profile structurally aberrant transcripts in tumors. Given the breakpoints obtained by MiStrVar and deFuse, our framework can then identify all relevant peptides that span the breakpoint junctions and match them with unique proteomic signatures. Observing structural aberrations in all three types of omics data validates their presence in the tumor samples.

Results

We have applied our framework to all The Cancer Genome Atlas (TCGA) breast cancer Whole Genome Sequencing (WGS) and/or RNA-Seq datasets, spanning all four major subtypes, for which proteomics data from Clinical Proteomic Tumor Analysis Consortium (CPTAC) have been released. A recent study on this dataset focusing on SNVs has reported many that lead to novel peptides. Complementing and significantly broadening this study, we detected 244 novel peptides from 432 candidate genomic or transcriptomic sequence aberrations. Many of the fusions and microSVs we discovered have not been reported in the literature. Interestingly, the vast majority of these translated aberrations, fusions in particular, were private, demonstrating the extensive inter-genomic heterogeneity present in breast cancer. Many of these aberrations also have matching out-of-frame downstream peptides, potentially indicating novel protein sequence and structure.

Availability and implementation

MiStrVar is available for download at https://bitbucket.org/compbio/mistrvar, and ProTIE is available at https://bitbucket.org/compbio/protie.

Contact

cenksahi@indiana.edu.

Supplementary information

Supplementary data are available at Bioinformatics online.

Homoplastic microinversions and the avian tree of life

BACKGROUND

Microinversions are cytologically undetectable inversions of DNA sequences that accumulate slowly in genomes. Like many other rare genomic changes (RGCs), microinversions are thought to be virtually homoplasy-free evolutionary characters, suggesting that they may be very useful for difficult phylogenetic problems such as the avian tree of life. However, few detailed surveys of these genomic rearrangements have been conducted, making it difficult to assess this hypothesis or understand the impact of microinversions upon genome evolution.

RESULTS

We surveyed non-coding sequence data from a recent avian phylogenetic study and found substantially more microinversions than expected based upon prior information about vertebrate inversion rates, although this is likely due to underestimation of these rates in previous studies. Most microinversions were lineage-specific or united well-accepted groups. However, some homoplastic microinversions were evident among the informative characters. Hemiplasy, which reflects differences between gene trees and the species tree, did not explain the observed homoplasy. Two specific loci were microinversion hotspots, with high numbers of inversions that included both the homoplastic as well as some overlapping microinversions. Neither stem-loop structures nor detectable sequence motifs were associated with microinversions in the hotspots.

CONCLUSIONS

Microinversions can provide valuable phylogenetic information, although power analysis indicates that large amounts of sequence data will be necessary to identify enough inversions (and similar RGCs) to resolve short branches in the tree of life. Moreover, microinversions are not perfect characters and should be interpreted with caution, just as with any other character type. Independent of their use for phylogenetic analyses, microinversions are important because they have the potential to complicate alignment of non-coding sequences. Despite their low rate of accumulation, they have clearly contributed to genome evolution, suggesting that active identification of microinversions will prove useful in future phylogenomic studies.

AGE: defining breakpoints of genomic structural variants at single-nucleotide resolution, through optimal alignments with gap excision

MOTIVATION

Defining the precise location of structural variations (SVs) at single-nucleotide breakpoint resolution is an important problem, as it is a prerequisite for classifying SVs, evaluating their functional impact and reconstructing personal genome sequences. Given approximate breakpoint locations and a bridging assembly or split read, the problem essentially reduces to finding a correct sequence alignment. Classical algorithms for alignment and their generalizations guarantee finding the optimal (in terms of scoring) global or local alignment of two sequences. However, they cannot generally be applied to finding the biologically correct alignment of genomic sequences containing SVs because of the need to simultaneously span the SV (e.g. make a large gap) and perform precise local alignments at the flanking ends.

RESULTS

Here, we formulate the computations involved in this problem and describe a dynamic-programming algorithm for its solution. Specifically, our algorithm, called AGE for Alignment with Gap Excision, finds the optimal solution by simultaneously aligning the 5' and 3' ends of two given sequences and introducing a 'large-gap jump' between the local end alignments to maximize the total alignment score. We also describe extensions allowing the application of AGE to tandem duplications, inversions and complex events involving two large gaps. We develop a memory-efficient implementation of AGE (allowing application to long contigs) and make it available as a downloadable software package. Finally, we applied AGE for breakpoint determination and standardization in the 1000 Genomes Project by aligning locally assembled contigs to the human genome.

AVAILABILITY AND IMPLEMENTATION

AGE is freely available at http://sv.gersteinlab.org/age.

Retro-MoRFs: identifying protein binding sites by normal and reverse alignment and intrinsic disorder prediction

Many cell functions in all living organisms rely on protein-based molecular recognition involving disorder-to-order transitions upon binding by molecular recognition features (MoRFs). A well accepted computational tool for identifying likely protein-protein interactions is sequence alignment. In this paper, we propose the combination of sequence alignment and disorder prediction as a tool to improve the confidence of identifying MoRF-based protein-protein interactions. The method of reverse sequence alignment is also rationalized here as a novel approach for finding additional interaction regions, leading to the concept of a retro-MoRF, which has the reversed sequence of an identified MoRF. The set of retro-MoRF binding partners likely overlap the partner-sets of the originally identified MoRFs. The high abundance of MoRF-containing intrinsically disordered proteins in nature suggests the possibility that the number of retro-MoRFs could likewise be very high. This hypothesis provides new grounds for exploring the mysteries of protein-protein interaction networks at the genome level.

Walking tree heuristics for comparative genomic alignments

Genomic sequence data is available for an ever-increasing number of organisms, but the full meaning of this data remains an enigma. String alignment is one approach for deciphering the information contained in genetic strings. Sequences which are conserved across species will help identify genes and other important structures. Similarity between species can be scored by measuring how well their sequences align. The walking tree method is an approximate string alignment method that can handle insertions, deletions, substitutions, translocations, and more than one level of inversion. We will describe this method and recent improvements which allow fast alignment of megabase strings. We will show examples in which the method located or discovered genes. We show how the method can be used to construct phylogenetic trees. We also show that the method can be used to identify essential regions for protein function.

Multiple genome rearrangement and breakpoint phylogeny

Multiple alignment of macromolecular sequences generalizes from N = 2 to N > or = 3 the comparison of N sequences which have diverged through the local processes of insertion, deletion and substitution. Gene-order sequences diverge through non-local genome rearrangement processes such as inversion (or reversal) and transposition. In this paper we show which formulations of multiple alignment have counterparts in multiple rearrangement. Based on difficulties inherent in rearrangement edit-distance calculation and interpretation, we argue for the simpler "breakpoint analysis." Consensus-based multiple rearrangement of N > or = 3 orders can be solved exactly through reduction to instances of the Travelling Salesman Problem (TSP). We propose a branch-and-bound solution to TSP particularly suited to these instances. Simulations show how non-uniqueness of the solution is attenuated with increasing numbers of data genomes. Tree-based multiple alignment can be achieved to a great degree of accuracy by decomposing the tree into a number of overlapping 3-stars centered on the non-terminal nodes, and solving the consensus-based problem iteratively for these nodes until convergence. Accuracy improves with very careful initializations at the non-terminal nodes. The degree of non-uniqueness of solutions depends on the position of the node in the tree in terms of path length to the terminal vertices.

Sequence alignment with tandem duplication

Algorithm development for comparing and aligning biological sequences has, until recently, been based on the SI model of mutational events which assumes that modification of sequences proceeds through any of the operations of substitution, insertion or deletion (the latter two collectively termed indels). While this model has worked fairly well, it has long been apparent that other mutational events occur. In this paper, we introduce a new model, the DSI model which includes another common mutational event, tandem duplication. Tandem duplication produces tandem repeats which are common in DNA, making up perhaps 10% of the human genome. They are responsible for some human diseases and may serve a multitude of functions in DNA regulation and evolution. Using the DSI model, we develop new exact and heuristic algorithms for comparing and aligning DNA sequences when they contain tandem repeats.

On near-optimal alignments of biological sequences

A near-optimal alignment between a pair of sequences is an alignment whose score lies within the neighborhood of the optimal score. We present an efficient method for representing all alignments whose score is within any given delta from the optimal score. The representation is a compact graph that makes it easy to impose additional biological constraints and select one desirable alignment from the large set of alignments. We study the combinatorial nature of near-optimal alignments, and define a set of "canonical" near-optimal alignments. We then show how to enumerate near-optimal alignments efficiently in order of their score, and count their number. When applied to comparisons of two distantly related proteins, near-optimal alignments reveal that the most conserved regions among the near-optimal alignments are the highly structured regions in the proteins. We also show that by counting the number of near optimal alignments as a function of the distance from the optimal score, we can select a good set of parameters that best constraints the biologically relevant alignments.

Parametric sequence comparisons

Current algorithms can find optimal alignments of two nucleic acid or protein sequences, often by using dynamic programming. While the choice of algorithm penalty parameters greatly influences the quality of the resulting alignments, this choice has been done in an ad hoc manner. In this work, we present an algorithm to efficiently find the optimal alignments for all choices of the penalty parameters. It is then possible to systematically explore these alignments for those with the most biological or statistical interest. Several examples illustrate the method.