Amborella trichopoda is strongly supported as the single living species of the sister lineage to all other extant flowering plants, providing a unique reference for inferring the genome content and structure of the most recent common ancestor (MRCA) of living angiosperms. Sequencing the Amborella genome, we identified an ancient genome duplication predating angiosperm diversification, without evidence of subsequent, lineage-specific genome duplications. Comparisons between Amborella and other angiosperms facilitated reconstruction of the ancestral angiosperm gene content and gene order in the MRCA of core eudicots. We identify new gene families, gene duplications, and floral protein-protein interactions that first appeared in the ancestral angiosperm. Transposable elements in Amborella are ancient and highly divergent, with no recent transposon radiations. Population genomic analysis across Amborella's native range in New Caledonia reveals a recent genetic bottleneck and geographic structure with conservation implications.

BackgroundAn absent word of a word y of length n is a word that does not occur in y. It is a minimal absent word if all its proper factors occur in y. Minimal absent words have been computed in genomes of organisms from all domains of life; their computation also provides a fast alternative for measuring approximation in sequence comparison. There exists an -time and -space algorithm for computing all minimal absent words on a fixed-sized alphabet based on the construction of suffix automata (Crochemore et al., 1998). No implementation of this algorithm is publicly available. There also exists an -time and -space algorithm for the same problem based on the construction of suffix arrays (Pinho et al., 2009). An implementation of this algorithm was also provided by the authors and is currently the fastest available.ResultsOur contribution in this article is twofold: first, we bridge this unpleasant gap by presenting an -time and -space algorithm for computing all minimal absent words based on the construction of suffix arrays; and second, we provide the respective implementation of this algorithm. Experimental results, using real and synthetic data, show that this implementation outperforms the one by Pinho et al. The open-source code of our implementation is freely available at http://github.com/solonas13/maw.ConclusionsClassical notions for sequence comparison are increasingly being replaced by other similarity measures that refer to the composition of sequences in terms of their constituent patterns. One such measure is the minimal absent words. In this article, we present a new linear-time and linear-space algorithm for the computation of minimal absent words based on the suffix array.

BackgroundA fundamental assumption of all widely-used multiple sequence alignment techniques is that the left- and right-most positions of the input sequences are relevant to the alignment. However, the position where a sequence starts or ends can be totally arbitrary due to a number of reasons: arbitrariness in the linearisation (sequencing) of a circular molecular structure; or inconsistencies introduced into sequence databases due to different linearisation standards. These scenarios are relevant, for instance, in the process of multiple sequence alignment of mitochondrial DNA, viroid, viral or other genomes, which have a circular molecular structure. A solution for these inconsistencies would be to identify a suitable rotation (cyclic shift) for each sequence; these refined sequences may in turn lead to improved multiple sequence alignments using the preferred multiple sequence alignment program.ResultsWe present MARS, a new heuristic method for improving Multiple circular sequence Alignment using Refined Sequences. MARS was implemented in the C++ programming language as a program to compute the rotations (cyclic shifts) required to best align a set of input sequences. Experimental results, using real and synthetic data, show that MARS improves the alignments, with respect to standard genetic measures and the inferred maximum-likelihood-based phylogenies, and outperforms state-of-the-art methods both in terms of accuracy and efficiency. Our results show, among others, that the average pairwise distance in the multiple sequence alignment of a dataset of widely-studied mitochondrial DNA sequences is reduced by around 5% when MARS is applied before a multiple sequence alignment is performed.ConclusionsAnalysing multiple sequences simultaneously is fundamental in biological research and multiple sequence alignment has been found to be a popular method for this task. Conventional alignment techniques cannot be used effectively when the position where sequences start is arbitrary. We present here a method, which can be used in conjunction with any multiple sequence alignment program, to address this problem effectively and efficiently.

String data are often disseminated to support applications such as location-based service provision or DNA sequence analysis. This dissemination, however, may expose sensitive patterns that model confidential knowledge (e.g., trips to mental health clinics from a string representing a user's location history). In this paper, we consider the problem of sanitizing a string by concealing the occurrences of sensitive patterns, while maintaining data utility. First, we propose a time-optimal algorithm, TFS-ALGO, to construct the shortest string preserving the order of appearance and the frequency of all non-sensitive patterns. Such a string allows accurately performing tasks based on the sequential nature and pattern frequencies of the string. Second, we propose a time-optimal algorithm, PFS-ALGO, which preserves a partial order of appearance of non-sensitive patterns but produces a much shorter string that can be analyzed more efficiently. The strings produced by either of these algorithms may reveal the location of sensitive patterns. In response, we propose a heuristic, MCSR-ALGO, which replaces letters in these strings with carefully selected letters, so that sensitive patterns are not reinstated and occurrences of spurious patterns are prevented. We implemented our sanitization approach that applies TFS-ALGO, PFS-ALGO and then MCSR-ALGO and experimentally show that it is effective and efficient.

Background The deviation of the observed frequency of a word w from its expected frequency in a given sequence x is used to determine whether or not the word is avoided. This concept is particularly useful in DNA linguistic analysis. The value of the deviation of w, denoted by , effectively characterises the extent of a word by its edge contrast in the context in which it occurs. A word w of length is a -avoided word in x if , for a given threshold . Notice that such a word may be completely absent from x. Hence, computing all such words naïvely can be a very time-consuming procedure, in particular for large k.Results In this article, we propose an -time and -space algorithm to compute all -avoided words of length k in a given sequence of length n over a fixed-sized alphabet. We also present a time-optimal -time algorithm to compute all -avoided words (of any length) in a sequence of length n over an integer alphabet of size . In addition, we provide a tight asymptotic upper bound for the number of -avoided words over an integer alphabet and the expected length of the longest one. We make available an implementation of our algorithm. Experimental results, using both real and synthetic data, show the efficiency and applicability of our implementation in biological sequence analysis.ConclusionsThe systematic search for avoided words is particularly useful for biological sequence analysis. We present a linear-time and linear-space algorithm for the computation of avoided words of length k in a given sequence x. We suggest a modification to this algorithm so that it computes all avoided words of x, irrespective of their length, within the same time complexity. We also present combinatorial results with regards to avoided words and absent words.

DNA sequencing is the process of determining the exact order of the nucleotide bases of an individual's genome in order to catalogue sequence variation and understand its biological implications. Whole-genome sequencing techniques produce masses of data in the form of short sequences known as reads. Assembling these reads into a whole genome constitutes a major algorithmic challenge. Most assembly algorithms utilise de Bruijn graphs constructed from reads for this purpose. A critical step of these algorithms is to detect typical motif structures in the graph caused by sequencing errors and genome repeats, and filter them out; one such complex subgraph class is a so-called superbubble. In this paper, we propose an O(n + m)-time algorithm to detect all superbubbles in a directed acyclic graph with n vertices and m (directed) edges, improving the best-known O(m log m)-time algorithm by Sung et al.

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