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.

A word x that is absent from a word y is called minimal if all its proper factors occur in y. Given a collection of k words y 1 , y 2 , . . . , y k over an alphabet Σ, we are asked to compute the set M y1#...#y k of minimal absent words of length at most of word y = y 1 #y 2 # . . . #y k , # / ∈ Σ. In data compression, this corresponds to computing the antidictionary of k documents. In bioinformatics, it corresponds to computing words that are absent from a genome of k chromosomes. This computation generally requires Ω(n) space for n = |y| using any of the plenty available O(n)-time algorithms. This is because an Ω(n)-sized text index is constructed over y which can be impractical for large n. We do the identical computation incrementally using output-sensitive space. This goal is reasonable when || M y1#...#y N || = o(n), for all N ∈ [1, k]. For instance, in the human genome, n ≈ 3 × 10 9 but || M 12 y1#...#y k || ≈ 10 6 . We consider a constantsized alphabet for stating our results. We show that all M y1 , . . . , M y1#...#y k can be computed in O(kn + k N =1 || M y1#...#y N ||) total time using O(MaxIn + MaxOut) space, where MaxIn is the length of the longest word in {y 1 , . . . , y k } and MaxOut = max{|| M y1#...#y N || : N ∈ [1, k]}. Proof-of-concept experimental results are also provided confirming our theoretical findings and justifying our contribution.

In this paper we introduce a new family of string processing problems. We are given two or more strings and we are asked to compute a factor common to all strings that preserves a specific property and has maximal length. Here we consider three fundamental string properties: square-free factors, periodic factors, and palindromic factors under three different settings, one per property. In the first setting, we are given a string x and we are asked to construct a data structure over x answering the following type of on-line queries: given string y, find a longest square-free factor common to x and y. In the second setting, we are given k strings and an integer 1 < k ≤ k and we are asked to find a longest periodic factor common to at least k strings. In the third setting, we are given two strings and we are asked to find a longest palindromic factor common to the two strings. We present linear-time solutions for all settings. We anticipate that our paradigm can be extended to other string properties or settings.

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Uncertain sequences are compact representations of sets of similar strings. They highlight common segments by collapsing them, and explicitly represent varying segments by listing all possible options. A generalized degenerate string (GD string) is a type of uncertain sequence. Formally, a GD string Ŝ is a sequence of n sets of strings of total size N, where the ith set contains strings of the same length ki but this length can vary between different sets. We denote by W the sum of these lengths k0, k1, . . . , kn-1. Our main result is an 𝒪(N + M)-time algorithm for deciding whether two GD strings of total sizes N and M, respectively, over an integer alphabet, have a non-empty intersection. This result is based on a combinatorial result of independent interest: although the intersection of two GD strings can be exponential in the total size of the two strings, it can be represented in linear space. We then apply our string comparison tool to devise a simple algorithm for computing all palindromes in Ŝ in 𝒪(min{W, n2}N)-time. We complement this upper bound by showing a similar conditional lower bound for computing maximal palindromes in Ŝ. We also show that a result, which is essentially the same as our string comparison linear-time algorithm, can be obtained by employing an automata-based approach.

Although real-world text datasets, such as DNA sequences, are far from being uniformly random, average-case string searching algorithms perform significantly better than worst-case ones in most applications of interest. In this paper, we study the problem of computing the longest prefix of each suffix of a given string of length n over a constantsized alphabet that occurs elsewhere in the string with k-errors. This problem has already been studied under the Hamming distance model. Our first result is an improvement upon the state-of-the-art average-case time complexity for non-constant k and using only linear space under the Hamming distance model. Notably, we show that our technique can be extended to the edit distance model with the same time and space complexities. Specifically, our algorithms run in O(n log k n log log n) time on average using O(n) space. We show that our technique is applicable to several algorithmic problems in computational biology and elsewhere.

MotivationConserved non-coding elements (CNEs) represent an enigmatic class of genomic elements which, despite being extremely conserved across evolution, do not encode for proteins. Their functions are still largely unknown. Thus, there exists a need to systematically investigate their roles in genomes. Towards this direction, identifying sets of CNEs in a wide range of organisms is an important first step. Currently, there are no tools published in the literature for systematically identifying CNEs in genomes.ResultsWe fill this gap by presenting CNEFinder; a tool for identifying CNEs between two given DNA sequences with user-defined criteria. The results presented here show the tool’s ability of identifying CNEs accurately and efficiently. CNEFinder is based on a k-mer technique for computing maximal exact matches. The tool thus does not require or compute whole-genome alignments or indexes, such as the suffix array or the Burrows Wheeler Transform (BWT), which makes it flexible to use on a wide scale.Availability and implementationFree software under the terms of the GNU GPL (https://github.com/lorrainea/CNEFinder).

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