Fast alignment of mass spectra in large proteomics datasets, capturing dissimilarities arising from multiple complex modifications of peptides.

BACKGROUND: In proteomics, the interpretation of mass spectra representing peptides carrying multiple complex modifications remains challenging, as it is difficult to strike a balance between reasonable execution time, a limited number of false positives, and a huge search space allowing any number of modifications without a priori. The scientific community needs new developments in this area to aid in the discovery of novel post-translational modifications that may play important roles in disease. RESULTS: To make progress on this issue, we implemented SpecGlobX (SpecGlob eXTended to eXperimental spectra), a standalone Java application that quickly determines the best spectral alignments of a (possibly very large) list of Peptide-to-Spectrum Matches (PSMs) provided by any open modification search method, or generated by the user. As input, SpecGlobX reads a file containing spectra in MGF or mzML format and a semicolon-delimited spreadsheet describing the PSMs. SpecGlobX returns the best alignment for each PSM as output, splitting the mass difference between the spectrum and the peptide into one or more shifts while considering the possibility of non-aligned masses (a phenomenon resulting from many situations including neutral losses). SpecGlobX is fast, able to align one million PSMs in about 1.5 min on a standard desktop. Firstly, we remind the foundations of the algorithm and detail how we adapted SpecGlob (the method we previously developed following the same aim, but limited to the interpretation of perfect simulated spectra) to the interpretation of imperfect experimental spectra. Then, we highlight the interest of SpecGlobX as a complementary tool downstream to three open modification search methods on a large simulated spectra dataset. Finally, we ran SpecGlobX on a proteome-wide dataset downloaded from PRIDE to demonstrate that SpecGlobX functions just as well on simulated and experimental spectra. We then carefully analyzed a limited set of interpretations. CONCLUSIONS: SpecGlobX is helpful as a decision support tool, providing keys to interpret peptides carrying complex modifications still poorly considered by current open modification search software. Better alignment of PSMs enhances confidence in the identification of spectra provided by open modification search methods and should improve the interpretation rate of spectra.

Reversal and Transposition Distance on Unbalanced Genomes Using Intergenic Information.

The most common way to calculate the rearrangement distance between two genomes is to use the size of a minimum length sequence of rearrangements that transforms one of the two given genomes into the other, where the genomes are represented as permutations using only their gene order, based on the assumption that genomes have the same gene content. With the advance of research in genome rearrangements, new works extended the classical models by either considering genomes with different gene content (unbalanced genomes) or including more genomic characteristics to the mathematical representation of the genomes, such as the distribution of intergenic regions sizes. In this study, we study the Reversal, Transposition, and Indel (Insertion and Deletion) Distance using intergenic information, which allows comparing unbalanced genomes, because indels are included in the rearrangement model (i.e., the set of possible rearrangements allowed when we compute the distance). For the particular case of transpositions and indels on unbalanced genomes, we present a 4-approximation algorithm, improving a previous 4.5 approximation. This algorithm is extended so as to deal with gene orientation and to maintain the 4-approximation factor for the Reversal, Transposition, and Indel Distance on unbalanced genomes. Furthermore, we evaluate the proposed algorithms using experiments on simulated data.

MAGNETO: An Automated Workflow for Genome-Resolved Metagenomics.

Metagenome-assembled genomes (MAGs) represent individual genomes recovered from metagenomic data. MAGs are extremely useful to analyze uncultured microbial genomic diversity, as well as to characterize associated functional and metabolic potential in natural environments. Recent computational developments have considerably improved MAG reconstruction but also emphasized several limitations, such as the nonbinning of sequence regions with repetitions or distinct nucleotidic composition. Different assembly and binning strategies are often used; however, it still remains unclear which assembly strategy, in combination with which binning approach, offers the best performance for MAG recovery. Several workflows have been proposed in order to reconstruct MAGs, but users are usually limited to single-metagenome assembly or need to manually define sets of metagenomes to coassemble prior to genome binning. Here, we present MAGNETO, an automated workflow dedicated to MAG reconstruction, which includes a fully-automated coassembly step informed by optimal clustering of metagenomic distances, and implements complementary genome binning strategies, for improving MAG recovery. MAGNETO is implemented as a Snakemake workflow and is available at: https://gitlab.univ-nantes.fr/bird_pipeline_registry/magneto. IMPORTANCE Genome-resolved metagenomics has led to the discovery of previously untapped biodiversity within the microbial world. As the development of computational methods for the recovery of genomes from metagenomes continues, existing strategies need to be evaluated and compared to eventually lead to standardized computational workflows. In this study, we compared commonly used assembly and binning strategies and assessed their performance using both simulated and real metagenomic data sets. We propose a novel approach to automate coassembly, avoiding the requirement for a priori knowledge to combine metagenomic information. The comparison against a previous coassembly approach demonstrates a strong impact of this step on genome binning results, but also the benefits of informing coassembly for improving the quality of recovered genomes. MAGNETO integrates complementary assembly-binning strategies to optimize genome reconstruction and provides a complete reads-to-genomes workflow for the growing microbiome research community.

Sorting Permutations by Intergenic Operations.

Genome Rearrangements are events that affect large stretches of genomes during evolution. Many mathematical models have been used to estimate the evolutionary distance between two genomes based on genome rearrangements. However, most of them focused on the (order of the) genes of a genome, disregarding other important elements in it. Recently, researchers have shown that considering regions between each pair of genes, called intergenic regions, can enhance distance estimation in realistic data. Two of the most studied genome rearrangements are the reversal, which inverts a sequence of genes, and the transposition, which occurs when two adjacent gene sequences swap their positions inside the genome. In this work, we study the transposition distance between two genomes, but we also consider intergenic regions, a problem we name Sorting by Intergenic Transpositions. We show that this problem is NP-hard and propose two approximation algorithms, with factors 3.5 and 2.5, considering two distinct definitions for the problem. We also investigate the signed reversal and transposition distance between two genomes considering their intergenic regions. This second problem is called Sorting by Signed Intergenic Reversals and Intergenic Transpositions. We show that this problem is NP-hard and develop two approximation algorithms, with factors 3 and 2.5. We check how these algorithms behave when assigning weights for genome rearrangements. Finally, we implemented all these algorithms and tested them on real and simulated data.

Evaluation of open search methods based on theoretical mass spectra comparison.

BACKGROUND: Mass spectrometry remains the privileged method to characterize proteins. Nevertheless, most of the spectra generated by an experiment remain unidentified after their analysis, mostly because of the modifications they carry. Open Modification Search (OMS) methods offer a promising answer to this problem. However, assessing the quality of OMS identifications remains a difficult task. METHODS: Aiming at better understanding the relationship between (1) similarity of pairs of spectra provided by OMS methods and (2) relevance of their corresponding peptide sequences, we used a dataset composed of theoretical spectra only, on which we applied two OMS strategies. We also introduced two appropriately defined measures for evaluating the above mentioned spectra/sequence relevance in this context: one is a color classification representing the level of difficulty to retrieve the proper sequence of the peptide that generated the identified spectrum ; the other, called LIPR, is the proportion of common masses, in a given Peptide Spectrum Match (PSM), that represent dissimilar sequences. These two measures were also considered in conjunction with the False Discovery Rate (FDR). RESULTS: According to our measures, the strategy that selects the best candidate by taking the mass difference between two spectra into account yields better quality results. Besides, although the FDR remains an interesting indicator in OMS methods (as shown by LIPR), it is questionable: indeed, our color classification shows that a non negligible proportion of relevant spectra/sequence interpretations corresponds to PSMs coming from the decoy database. CONCLUSIONS: The three above mentioned measures allowed us to clearly determine which of the two studied OMS strategies outperformed the other, both in terms of number of identifications and of accuracy of these identifications. Even though quality evaluation of PSMs in OMS methods remains challenging, the study of theoretical spectra is a favorable framework for going further in this direction.

Sorting Signed Permutations by Intergenic Reversals.

Genome rearrangements are mutations affecting large portions of a genome, and a reversal is one of the most studied genome rearrangements in the literature through the Sorting by Reversals (SbR) problem. SbR is solvable in polynomial time on signed permutations (i.e., the gene orientation is known), and it is NP-hard on unsigned permutations. This problem (and many others considering genome rearrangements) models genome as a list of its genes in the order they appear, ignoring all other information present in the genome. Recent works claimed that the incorporation of the size of intergenic regions, i.e., sequences of nucleotides between genes, may result in better estimators for the real distance between genomes. Here we introduce the Sorting Signed Permutations by Intergenic Reversals problem, that sorts a signed permutation using reversals both on gene order and intergenic sizes. We show that this problem is NP-hard by a reduction from the 3-partition problem. Then, we propose a 2-approximation algorithm for it. Finally, we also incorporate intergenic indels (i.e., insertions or deletions of intergenic regions) to overcome a limitation of sorting by conservative events (such as reversals) and propose two approximation algorithms.

Sorting by Genome Rearrangements on Both Gene Order and Intergenic Sizes.

During the evolutionary process, genomes are affected by various genome rearrangements, that is, events that modify large stretches of the genetic material. In the literature, a large number of models have been proposed to estimate the number of events that occurred during evolution; most of them represent a genome as an ordered sequence of genes, and, in particular, disregard the genetic material between consecutive genes. However, recent studies showed that taking into account the genetic material between consecutive genes can enhance evolutionary distance estimations. Reversal and transposition are genome rearrangements that have been widely studied in the literature. A reversal inverts a (contiguous) segment of the genome, while a transposition swaps the positions of two consecutive segments. Genomes also undergo nonconservative events (events that alter the amount of genetic material) such as insertions and deletions, in which genetic material from intergenic regions of the genome is inserted or deleted, respectively. In this article, we study a genome rearrangement model that considers both gene order and sizes of intergenic regions. We investigate the reversal distance, and also the reversal and transposition distance between two genomes in two scenarios: with and without nonconservative events. We show that these problems are NP-hard and we present constant ratio approximation algorithms for all of them. More precisely, we provide a 4-approximation algorithm for the reversal distance, both in the conservative and nonconservative versions. For the reversal and transposition distance, we provide a 4.5-approximation algorithm, both in the conservative and nonconservative versions. We also perform experimental tests to verify the behavior of our algorithms, as well as to compare the practical and theoretical results. We finally extend our study to scenarios in which events have different costs, and we present constant ratio approximation algorithms for each scenario.

Super short operations on both gene order and intergenic sizes.

BACKGROUND: The evolutionary distance between two genomes can be estimated by computing a minimum length sequence of operations, called genome rearrangements, that transform one genome into another. Usually, a genome is modeled as an ordered sequence of genes, and most of the studies in the genome rearrangement literature consist in shaping biological scenarios into mathematical models. For instance, allowing different genome rearrangements operations at the same time, adding constraints to these rearrangements (e.g., each rearrangement can affect at most a given number of genes), considering that a rearrangement implies a cost depending on its length rather than a unit cost, etc. Most of the works, however, have overlooked some important features inside genomes, such as the presence of sequences of nucleotides between genes, called intergenic regions. RESULTS AND CONCLUSIONS: In this work, we investigate the problem of computing the distance between two genomes, taking into account both gene order and intergenic sizes. The genome rearrangement operations we consider here are constrained types of reversals and transpositions, called super short reversals (SSRs) and super short transpositions (SSTs), which affect up to two (consecutive) genes. We denote by super short operations (SSOs) any SSR or SST. We show 3-approximation algorithms when the orientation of the genes is not considered when we allow SSRs, SSTs, or SSOs, and 5-approximation algorithms when considering the orientation for either SSRs or SSOs. We also show that these algorithms improve their approximation factors when the input permutation has a higher number of inversions, where the approximation factor decreases from 3 to either 2 or 1.5, and from 5 to either 3 or 2.

Sorting signed circular permutations by super short operations.

BACKGROUND: One way to estimate the evolutionary distance between two given genomes is to determine the minimum number of large-scale mutations, or genome rearrangements, that are necessary to transform one into the other. In this context, genomes can be represented as ordered sequences of genes, each gene being represented by a signed integer. If no gene is repeated, genomes are thus modeled as signed permutations of the form π=(π1π2…πn) , and in that case we can consider without loss of generality that one of them is the identity permutation ιn=(12…n) , and that we just need to sort the other (i.e., transform it into ιn ). The most studied genome rearrangement events are reversals, where a segment of the genome is reversed and reincorporated at the same location; and transpositions, where two consecutive segments are exchanged. Many variants, e.g., combining different types of (possibly constrained) rearrangements, have been proposed in the literature. One of them considers that the number of genes involved, in a reversal or a transposition, is never greater than two, which is known as the problem of sorting by super short operations (or SSOs). RESULTS AND CONCLUSIONS: All problems considering SSOs in permutations have been shown to be in P , except for one, namely sorting signed circular permutations by super short reversals and super short transpositions. Here we fill this gap by introducing a new graph structure called cyclic permutation graph and providing a series of intermediate results, which allows us to design a polynomial algorithm for sorting signed circular permutations by super short reversals and super short transpositions.

Matching algorithms for assigning orthologs after genome duplication events.

In this paper, we introduce and analyze two graph-based models for assigning orthologs in the presence of whole-genome duplications, using similarity information between pairs of genes. The common feature of our two models is that genes of the first genome may be assigned two orthologs from the second genome, which has undergone a whole-genome duplication. Additionally, our models incorporate the new notion of duplication bonus, a parameter that reflects how assigning two orthologs to a given gene should be rewarded or penalized. Our work is mainly focused on developing exact and reasonably time-consuming algorithms for these two models: we show that the first one is polynomial-time solvable, while the second is NP-hard. For the latter, we thus design two fixed-parameter algorithms, i.e. exact algorithms whose running times are exponential only with respect to a small and well-chosen input parameter. Finally, for both models, we evaluate our algorithms on pairs of plant genomes. Our experiments show that the NP-hard model yields a better cluster quality at the cost of lower coverage, due to the fact that our instances cannot be completely solved by our algorithms. However, our results are altogether encouraging and show that our methods yield biologically significant predictions of orthologs when the duplication bonus value is properly chosen.

Algorithms for computing the double cut and join distance on both gene order and intergenic sizes.

BACKGROUND: Combinatorial works on genome rearrangements have so far ignored the influence of intergene sizes, i.e. the number of nucleotides between consecutive genes, although it was recently shown decisive for the accuracy of inference methods (Biller et al. in Genome Biol Evol 8:1427-39, 2016; Biller et al. in Beckmann A, Bienvenu L, Jonoska N, editors. Proceedings of Pursuit of the Universal-12th conference on computability in Europe, CiE 2016, Lecture notes in computer science, vol 9709, Paris, France, June 27-July 1, 2016. Berlin: Springer, p. 35-44, 2016). In this line, we define a new genome rearrangement model called wDCJ, a generalization of the well-known double cut and join (or DCJ) operation that modifies both the gene order and the intergene size distribution of a genome. RESULTS: We first provide a generic formula for the wDCJ distance between two genomes, and show that computing this distance is strongly NP-complete. We then propose an approximation algorithm of ratio 4/3, and two exact ones: a fixed-parameter tractable (FPT) algorithm and an integer linear programming (ILP) formulation. CONCLUSIONS: We provide theoretical and empirical bounds on the expected growth of the parameter at the center of our FPT and ILP algorithms, assuming a probabilistic model of evolution under wDCJ, which shows that both these algorithms should run reasonably fast in practice.

SpecOMS: A Full Open Modification Search Method Performing All-to-All Spectra Comparisons within Minutes.

The analysis of discovery proteomics experiments relies on algorithms that identify peptides from their tandem mass spectra. The almost exhaustive interpretation of these spectra remains an unresolved issue. At present, an important number of missing interpretations is probably due to peptides displaying post-translational modifications and variants that yield spectra that are particularly difficult to interpret. However, the emergence of a new generation of mass spectrometers that provide high fragment ion accuracy has paved the way for more efficient algorithms. We present a new software, SpecOMS, that can handle the computational complexity of pairwise comparisons of spectra in the context of large volumes. SpecOMS can compare a whole set of experimental spectra generated by a discovery proteomics experiment to a whole set of theoretical spectra deduced from a protein database in a few minutes on a standard workstation. SpecOMS can ingeniously exploit those capabilities to improve the peptide identification process, allowing strong competition between all possible peptides for spectrum interpretation. Remarkably, this software resolves the drawbacks (i.e., efficiency problems and decreased sensitivity) that usually accompany open modification searches. We highlight this promising approach using results obtained from the analysis of a public human data set downloaded from the PRIDE (PRoteomics IDEntification) database.

Sorting permutations by prefix and suffix rearrangements.

Some interesting combinatorial problems have been motivated by genome rearrangements, which are mutations that affect large portions of a genome. When we represent genomes as permutations, the goal is to transform a given permutation into the identity permutation with the minimum number of rearrangements. When they affect segments from the beginning (respectively end) of the permutation, they are called prefix (respectively suffix) rearrangements. This paper presents results for rearrangement problems that involve prefix and suffix versions of reversals and transpositions considering unsigned and signed permutations. We give 2-approximation and ([Formula: see text])-approximation algorithms for these problems, where [Formula: see text] is a constant divided by the number of breakpoints (pairs of consecutive elements that should not be consecutive in the identity permutation) in the input permutation. We also give bounds for the diameters concerning these problems and provide ways of improving the practical results of our algorithms.

Genome rearrangements with indels in intergenes restrict the scenario space.

BACKGROUND: Given two genomes that have diverged by a series of rearrangements, we infer minimum Double Cut-and-Join (DCJ) scenarios to explain their organization differences, coupled with indel scenarios to explain their intergene size distribution, where DCJs themselves also alter the sizes of broken intergenes. RESULTS: We give a polynomial-time algorithm that, given two genomes with arbitrary intergene size distributions, outputs a DCJ scenario which optimizes on the number of DCJs, and given this optimal number of DCJs, optimizes on the total sum of the sizes of the indels. CONCLUSIONS: We show that there is a valuable information in the intergene sizes concerning the rearrangement scenario itself. On simulated data we show that statistical properties of the inferred scenarios are closer to the true ones than DCJ only scenarios, i.e. scenarios which do not handle intergene sizes.

Hybrid de novo tandem repeat detection using short and long reads.

BACKGROUND: As one of the most studied genome rearrangements, tandem repeats have a considerable impact on genetic backgrounds of inherited diseases. Many methods designed for tandem repeat detection on reference sequences obtain high quality results. However, in the case of a de novo context, where no reference sequence is available, tandem repeat detection remains a difficult problem. The short reads obtained with the second-generation sequencing methods are not long enough to span regions that contain long repeats. This length limitation was tackled by the long reads obtained with the third-generation sequencing platforms such as Pacific Biosciences technologies. Nevertheless, the gain on the read length came with a significant increase of the error rate. The main objective of nowadays studies on long reads is to handle the high error rate up to 16%. METHODS: In this paper we present MixTaR, the first de novo method for tandem repeat detection that combines the high-quality of short reads and the large length of long reads. Our hybrid algorithm uses the set of short reads for tandem repeat pattern detection based on a de Bruijn graph. These patterns are then validated using the long reads, and the tandem repeat sequences are constructed using local greedy assemblies. RESULTS: MixTaR is tested with both simulated and real reads from complex organisms. For a complete analysis of its robustness to errors, we use short and long reads with different error rates. The results are then analysed in terms of number of tandem repeats detected and the length of their patterns. CONCLUSIONS: Our method shows high precision and sensitivity. With low false positive rates even for highly erroneous reads, MixTaR is able to detect accurate tandem repeats with pattern lengths varying within a significant interval.

Efficient tools for computing the number of breakpoints and the number of adjacencies between two genomes with duplicate genes.

Comparing genomes of different species is a fundamental problem in comparative genomics. Recent research has resulted in the introduction of different measures between pairs of genomes: for example, reversal distance, number of breakpoints, and number of common or conserved intervals. However, classical methods used for computing such measures are seriously compromised when genomes have several copies of the same gene scattered across them. Most approaches to overcome this difficulty are based either on the exemplar model, which keeps exactly one copy in each genome of each duplicated gene, or on the maximum matching model, which keeps as many copies as possible of each duplicated gene. The goal is to find an exemplar matching, respectively a maximum matching, that optimizes the studied measure. Unfortunately, it turns out that, in presence of duplications, this problem for each above-mentioned measure is NP-hard. In this paper, we propose to compute the minimum number of breakpoints and the maximum number of adjacencies between two genomes in presence of duplications using two different approaches. The first one is an exact, generic 0-1 linear programming approach, while the second is a collection of three heuristics. Each of these approaches is applied on each problem and for each of the following models: exemplar, maximum matching and intermediate model, that we introduce here. All these programs are run on a well-known public benchmark dataset of gamma-Proteobacteria, and their performances are discussed.

Comparing genomes with duplications: a computational complexity point of view.

In this paper, we are interested in the computational complexity of computing (dis)similarity measures between two genomes when they contain duplicated genes or genomic markers, a problem that happens frequently when comparing whole nuclear genomes. Recently, several methods ( [1], [2]) have been proposed that are based on two steps to compute a given (dis)similarity measure M between two genomes G_1 and G_2: first, one establishes a oneto- one correspondence between genes of G_1 and genes of G_2 ; second, once this correspondence is established, it defines explicitly a permutation and it is then possible to quantify their similarity using classical measures defined for permutations, like the number of breakpoints. Hence these methods rely on two elements: a way to establish a one-to-one correspondence between genes of a pair of genomes, and a (dis)similarity measure for permutations. The problem is then, given a (dis)similarity measure for permutations, to compute a correspondence that defines an optimal permutation for this measure. We are interested here in two models to compute a one-to-one correspondence: the exemplar model, where all but one copy are deleted in both genomes for each gene family, and the matching model, that computes a maximal correspondence for each gene family. We show that for these two models, and for three (dis)similarity measures on permutations, namely the number of common intervals, the maximum adjacency disruption (MAD) number and the summed adjacency disruption (SAD) number, the problem of computing an optimal correspondence is NP-complete, and even APXhard for the MAD number and SAD number.

Exemplar longest common subsequence.

In this paper, we investigate the computational and approximation complexity of the Exemplar Longest Common Subsequence of a set of sequences (ELCS problem), a generalization of the Longest Common Subsequence problem, where the input sequences are over the union of two disjoint sets of symbols, a set of mandatory symbols and a set of optional symbols. We show that different versions of the problem are APX-hard even for instances with two sequences. Moreover, we show that the related problem of determining the existence of a feasible solution of the Exemplar Longest Common Subsequence of two sequences is NP-hard. On the positive side, we first present an efficient algorithm for the ELCS problem over instances of two sequences where each mandatory symbol can appear in total at most three times in the sequences. Furthermore, we present two fixed-parameter algorithms for the ELCS problem over instances of two sequences where the parameter is the number of mandatory symbols.

A pseudo-boolean framework for computing rearrangement distances between genomes with duplicates.

Computing genomic distances between whole genomes is a fundamental problem in comparative genomics. Recent researches have resulted in different genomic distance definitions, for example, number of breakpoints, number of common intervals, number of conserved intervals, and Maximum Adjacency Disruption number. Unfortunately, it turns out that, in presence of duplications, most problems are NP-hard, and hence several heuristics have been recently proposed. However, while it is relatively easy to compare heuristics between them, until now very little is known about the absolute accuracy of these heuristics. Therefore, there is a great need for algorithmic approaches that compute exact solutions for these genomic distances. In this paper, we present a novel generic pseudo-boolean approach for computing the exact genomic distance between two whole genomes in presence of duplications, and put strong emphasis on common intervals under the maximum matching model. Of particular importance, we show three heuristics which provide very good results on a well-known public dataset of gamma-Proteobacteria.

Recursive graphs with small-world scale-free properties.

We discuss a category of graphs, recursive clique trees, which have small-world and scale-free properties and allow a fine tuning of the clustering and the power-law exponent of their discrete degree distribution. We determine relevant characteristics of those graphs: the diameter, degree distribution, and clustering parameter. The graphs have also an interesting recursive property, and generalize recent constructions with fixed degree distributions.