There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The lion's share of bacteria in various environments cannot be cloned in the laboratory and thus cannot be sequenced using existing technologies. A major goal of single-cell genomics is to complement gene-centric metagenomic data with whole-genome assemblies of uncultivated organisms. Assembly of single-cell data is challenging because of highly non-uniform read coverage as well as elevated levels of sequencing errors and chimeric reads. We describe SPAdes, a new assembler for both single-cell and standard (multicell) assembly, and demonstrate that it improves on the recently released E+V-SC assembler (specialized for single-cell data) and on popular assemblers Velvet and SoapDeNovo (for multicell data). SPAdes generates single-cell assemblies, providing information about genomes of uncultivatable bacteria that vastly exceeds what may be obtained via traditional metagenomics studies. SPAdes is available online ( http://bioinf.spbau.ru/spades ). It is distributed as open source software.

SPAdes, a new genome assembly algorithm and its applications to single-cell sequencing ( 7th Annual SFAF Meeting, 2012)

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

KEGG(Kyoto Encyclopedia of Genes and Genomes)〔和文〕 (特集 ゲノム医学の現在と未来--基礎と臨床) -- (データベース)

Background
Multiple genome alignment remains a challenging problem. Effects of recombination including rearrangement, segmental duplication, gain, and loss can create a mosaic pattern of homology even among closely related organisms.

https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0011147&type=printable

progressiveMauve: Multiple Genome Alignment with Gene Gain, Loss and Rearrangement

While the genomes of many organisms have been sequenced over the last few years, transforming such raw sequence data into knowledge remains a hard task. A great number of prediction programs have been developed that try to address one part of this problem, which consists of locating the genes along a genome. This paper reviews the existing approaches to predicting genes in eukaryotic genomes and underlines their intrinsic advantages and limitations. The main mathematical models and computational algorithms adopted are also briefly described and the resulting software classified according to both the method and the type of evidence used. Finally, the several difficulties and pitfalls encountered by the programs are detailed, showing that improvements are needed and that new directions must be considered.

https://biblio.ugent.be/publication/153964/file/4146378.pdf

Current methods of gene prediction, their strengths and weaknesses

Completing the genome sequence of an organism is an important task in comparative, functional and structural genomics. However, this remains a challenging issue from both a computational and an experimental viewpoint. Genome scaffolding (i.e. the process of ordering and orientating contigs) of de novo assemblies usually represents the first step in most genome finishing pipelines. In this paper, we present MeDuSa (Multi-Draft based Scaffolder), an algorithm for genome scaffolding. MeDuSa exploits information obtained from a set of (draft or closed) genomes from related organisms to determine the correct order and orientation of the contigs. MeDuSa formalises the scaffolding problem by means of a combinatorial optimisation formulation on graphs and implements an efficient constant factor approximation algorithm to solve it. In contrast to currently used scaffolders, it does not require either prior knowledge on the microrganisms dataset under analysis (e.g. their phylogenetic relationships) or the availability of paired end read libraries. This makes usability and running time two additional important features of our method. Moreover, benchmarks and tests on real bacterial datasets showed that MeDuSa is highly accurate and, in most cases, outperforms traditional scaffolders. The possibility to use MeDuSa on eukaryotic datasets has also been evaluated, leading to interesting results. MeDuSa web server: http://combo.dbe.unifi.it/medusa A stand-alone version of the software can be downloaded from https://github.com/combogenomics/medusa/releases. All results presented in this work have been obtained with MeDuSa v. 1.3. marco.fondi@unifi.it.

MeDuSa: a multi-draft based scaffolder

This paper introduces two exact algorithms for extracting conserved structured motifs from a set of DNA sequences. Structured motifs may be described as an ordered collection of p ≥ 1 "boxes" (each box corresponding to one part of the structured motif), p substitution rates (one for each box) and p - 1 intervals of distance (one for each pair of successive boxes in the collection). The contents of the boxes - that is, the motifs themselves - are unknown at the start of the algorithm. This is precisely what the algorithms are meant to find. A suffix tree is used for finding such motifs. The algorithms are efficient enough to be able to infer site consensi, such as, for instance, promoter sequences or regulatory sites, from a set of unaligned sequences corresponding to the noncoding regions upstream from all genes of a genome. In particular, both algorithms time complexity scales linearly with N2n where n is the average length of the sequences and N their number. An application to the identification of prom...

Algorithms for extracting structured motifs using a suffix tree with an application to promoter and regulatory site consensus identification.

We present in this paper two algorithms. The first one extracts repeated motifs from a sequence defined over an alphabet Σ. For instance, Σ may be equal to (A, C, G, T} and the sequence represents an encoding of a DNA macromolecule. The motifs searched correspond to words over the same alphabet which occur a minimum number q of times in the sequence with at most e mismatches each time (q is called the quorum constraint). The second algorithm extracts common motifs from a set of N ≥ 2 sequences. In this case, the motifs must occur, again with at most e mismatches, in 1 ≤ q ≤ N distinct sequences of the set. In both cases, the words representing the motifs may never be present exactly in the sequences. We therefore speak of the motifs, repeated in a sequence or common to a set of them, as being external objects and denote them by the expression valid models if they verify the quorum constraint q. The approach we introduce here for finding all valid models corresponding to either repeated or common motifs starts by building a suffix tree of the sequence(s) and then, after some further preprocessing, uses this tree to simply spell the models. Assuming an alphabet of fixed size, the total time needed is O(nN 2 V(e, κ)) using O(nN 2 /ω) space, where n is the (average) length of the sequence(s), k is the length of the models sought or is the length of the longest possible valid models, ω is the size of a word machine and V(e,κ) is the number of words of length κ at a Hamming distance at most e from another κ-length word. V(e,κ) may be majored by k e |Σ| e . This improves on an algorithm by Waterman [23]. It is also a better time bound than our previous approach [15] for the common motifs problem whenever N < k|Σ|, and a better space bound when N/ω < k. It is a better time and space bound in absolute for the repeated motifs problem. The complexities obtained in this second case are O(nV(e,k)) and O(n) respectively. Finally, we suggest how to extend these algorithms to deal with gaps.

Spelling Approximate Repeated or Common Motifs Using a Suffix Tree

The discovery of microRNAs (miRNAs), almost 10 years ago, changed dramatically our perspective on eukaryotic gene expression regulation. However, the broad and important functions of these regulators are only now becoming apparent. The expansion of our catalogue of miRNA genes and the identification of the genes they regulate owe much to the development of sophisticated computational tools that have helped either to focus or interpret experimental assays. In this article, we review the methods for miRNA gene finding and target identification that have been proposed in the last few years. We identify some problems that current approaches have not yet been able to overcome and we offer some perspectives on the next generation of computational methods.

/pdf/current-tools-for-the-identification-of-mirna-genes-and-46ochk4sxs.pdf

Marie-France Sagot

Papers

Current methods of gene prediction, their strengths and weaknesses

MeDuSa: a multi-draft based scaffolder

Algorithms for extracting structured motifs using a suffix tree with an application to promoter and regulatory site consensus identification.

Spelling Approximate Repeated or Common Motifs Using a Suffix Tree

Current tools for the identification of miRNA genes and their targets