The Distance and Median Problems in the Single-Cut-Or-Join Model with Single-Gene Duplications

Background. In the field of genome rearrangement algorithms, models accounting for gene duplication lead often to hard problems. For example, while computing the pairwise distance is tractable in most duplication-free models, the problem is NP-complete for most extensions of these models accounting for duplicated genes. Moreover, problems involving more than two genomes, such as the genome median and the Small Parsimony problem, are intractable for most duplication-free models, with some exceptions, for example the Single-Cut-or-Join (SCJ) model. Results. We introduce a variant of the SCJ distance that accounts for duplicated genes, in the context of directed evolution from an ancestral genome to a descendant genome where orthology relations between ancestral genes and their descendant are known. Our model includes two duplication mechanisms: single-gene tandem duplication and the creation of single-gene circular chromosomes. We prove that in this model, computing the directed distance and a parsimonious evolutionary scenario in terms of SCJ and single-gene duplication events can be done in linear time. We also show that the directed median problem is tractable for this distance, while the rooted median problem, where we assume that one of the given genomes is ancestral to the median, is NP-complete. We also describe an Integer Linear Program for solving this problem. We evaluate the directed distance and rooted median algorithms on simulated data. Conclusion. Our results provide a simple genome rearrangement model, extending the SCJ model to account for single-gene duplications, for which we prove a mix of tractability and hardness results. For the NP-complete rooted median problem, we design a simple Integer Linear Program. Our publicly available implementation of these algorithms for the directed distance and median problems allow to solve efficiently these problems on large instances

The Tandem Duplication Distance Is NP-Hard

In computational biology, tandem duplication is an important biological phenomenon which can occur either at the genome or at the DNA level. A tandem duplication takes a copy of a genome segment and inserts it right after the segment - this can be represented as the string operation AXB ? AXXB. Tandem exon duplications have been found in many species such as human, fly or worm, and have been largely studied in computational biology. The Tandem Duplication (TD) distance problem we investigate in this paper is defined as follows: given two strings S and T over the same alphabet, compute the smallest sequence of tandem duplications required to convert S to T. The natural question of whether the TD distance can be computed in polynomial time was posed in 2004 by Leupold et al. and had remained open, despite the fact that tandem duplications have received much attention ever since. In this paper, we prove that this problem is NP-hard, settling the 16-year old open problem. We further show that this hardness holds even if all characters of S are distinct. This is known as the exemplar TD distance, which is of special relevance in bioinformatics. One of the tools we develop for the reduction is a new problem called the Cost-Effective Subgraph, for which we obtain W[1]-hardness results that might be of independent interest. We finally show that computing the exemplar TD distance between S and T is fixed-parameter tractable. Our results open the door to many other questions, and we conclude with several open problems

Reconstruction Codes for DNA Sequences with Uniform Tandem-Duplication Errors

DNA as a data storage medium has several advantages, including far greater data density compared to electronic media. We propose that schemes for data storage in the DNA of living organisms may benefit from studying the reconstruction problem, which is applicable whenever multiple reads of noisy data are available. This strategy is uniquely suited to the medium, which inherently replicates stored data in multiple distinct ways, caused by mutations. We consider noise introduced solely by uniform tandem-duplication, and utilize the relation to constant-weight integer codes in the Manhattan metric. By bounding the intersection of the cross-polytope with hyperplanes, we prove the existence of reconstruction codes with greater capacity than known error-correcting codes, which we can determine analytically for any set of parameters.Comment: 11 pages, 2 figures, Latex; version accepted for publicatio

Clusters of microRNAs emerge by new hairpins in existing transcripts

Genetic linkage may result in the expression of multiple products from a polycistronic transcript, under the control of a single promoter. In animals, protein-coding polycistronic transcripts are rare. However, microRNAs are frequently clustered in the genomes of animals, and these clusters are often transcribed as a single unit. The evolution of microRNA clusters has been the subject of much speculation, and a selective advantage of clusters of functionally related microRNAs is often proposed. However, the origin of microRNA clusters has not been so far explored. Here, we study the evolution of microRNA clusters in Drosophila melanogaster. We observed that the majority of microRNA clusters arose by the de novo formation of new microRNA-like hairpins in existing microRNA transcripts. Some clusters also emerged by tandem duplication of a single microRNA. Comparative genomics show that these clusters are unlikely to split or undergo rearrangements. We did not find any instances of clusters appearing by rearrangement of pre-existing microRNA genes. We propose a model for microRNA cluster evolution in which selection over one of the microRNAs in the cluster interferes with the evolution of the other linked microRNAs. Our analysis suggests that the study of microRNAs and small RNAs must consider linkage associations

Formation of regulatory modules by local sequence duplication

Turnover of regulatory sequence and function is an important part of molecular evolution. But what are the modes of sequence evolution leading to rapid formation and loss of regulatory sites? Here, we show that a large fraction of neighboring transcription factor binding sites in the fly genome have formed from a common sequence origin by local duplications. This mode of evolution is found to produce regulatory information: duplications can seed new sites in the neighborhood of existing sites. Duplicate seeds evolve subsequently by point mutations, often towards binding a different factor than their ancestral neighbor sites. These results are based on a statistical analysis of 346 cis-regulatory modules in the Drosophila melanogaster genome, and a comparison set of intergenic regulatory sequence in Saccharomyces cerevisiae. In fly regulatory modules, pairs of binding sites show significantly enhanced sequence similarity up to distances of about 50 bp. We analyze these data in terms of an evolutionary model with two distinct modes of site formation: (i) evolution from independent sequence origin and (ii) divergent evolution following duplication of a common ancestor sequence. Our results suggest that pervasive formation of binding sites by local sequence duplications distinguishes the complex regulatory architecture of higher eukaryotes from the simpler architecture of unicellular organisms

Landscape of standing variation for tandem duplications in Drosophila yakuba and Drosophila simulans

We have used whole genome paired-end Illumina sequence data to identify tandem duplications in 20 isofemale lines of D. yakuba, and 20 isofemale lines of D. simulans and performed genome wide validation with PacBio long molecule sequencing. We identify 1,415 tandem duplications that are segregating in D. yakuba as well as 975 duplications in D. simulans, indicating greater variation in D. yakuba. Additionally, we observe high rates of secondary deletions at duplicated sites, with 8% of duplicated sites in D. simulans and 17% of sites in D. yakuba modified with deletions. These secondary deletions are consistent with the action of the large loop mismatch repair system acting to remove polymorphic tandem duplication, resulting in rapid dynamics of gain and loss in duplicated alleles and a richer substrate of genetic novelty than has been previously reported. Most duplications are present in only single strains, suggesting deleterious impacts are common. D. simulans shows larger numbers of whole gene duplications in comparison to larger proportions of gene fragments in D. yakuba. D. simulans displays an excess of high frequency variants on the X chromosome, consistent with adaptive evolution through duplications on the D. simulans X or demographic forces driving duplicates to high frequency. We identify 78 chimeric genes in D. yakuba and 38 chimeric genes in D. simulans, as well as 143 cases of recruited non-coding sequence in D. yakuba and 96 in D. simulans, in agreement with rates of chimeric gene origination in D. melanogaster. Together, these results suggest that tandem duplications often result in complex variation beyond whole gene duplications that offers a rich substrate of standing variation that is likely to contribute both to detrimental phenotypes and disease, as well as to adaptive evolutionary change.Comment: Revised Version- Accepted at Molecular Biology and Evolutio

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

The Capacity of Some P\'olya String Models

We study random string-duplication systems, which we call P\'olya string models. These are motivated by DNA storage in living organisms, and certain random mutation processes that affect their genome. Unlike previous works that study the combinatorial capacity of string-duplication systems, or various string statistics, this work provides exact capacity or bounds on it, for several probabilistic models. In particular, we study the capacity of noisy string-duplication systems, including the tandem-duplication, end-duplication, and interspersed-duplication systems. Interesting connections are drawn between some systems and the signature of random permutations, as well as to the beta distribution common in population genetics

Genomic analysis of NAC transcription factors in banana (Musa acuminata) and definition of NAC orthologous groups for monocots and dicots

Identifying the molecular mechanisms underlying tolerance to abiotic stresses is important in crop breeding. A comprehensive understanding of the gene families associated with drought tolerance is therefore highly relevant. NAC transcription factors form a large plant-specific gene family involved in the regulation of tissue development and responses to biotic and abiotic stresses. The main goal of this study was to set up a framework of orthologous groups determined by an expert sequence comparison of NAC genes from both monocots and dicots. In order to clarify the orthologous relationships among NAC genes of different species, we performed an in-depth comparative study of four divergent taxa, in dicots and monocots, whose genomes have already been completely sequenced: Arabidopsis thaliana, Vitis vinifera, Musa acuminata and Oryza sativa. Due to independent evolution, NAC copy number is highly variable in these plant genomes. Based on an expert NAC sequence comparison, we propose forty orthologous groups of NAC sequences that were probably derived from an ancestor gene present in the most recent common ancestor of dicots and monocots. These orthologous groups provide a curated resource for large-scale protein sequence annotation of NAC transcription factors. The established orthology relationships also provide a useful reference for NAC function studies in newly sequenced genomes such as M. acuminata and other plant species