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)

Motivation: PacBio single molecule real-time sequencing is a third-generation sequencing technique producing long reads, with com-paratively lower throughput and higher error rate. Errors include numerous indels and complicate downstream analysis like mapping or de novo assembly. A hybrid strategy that takes advantage of the high accuracy of second-generation short reads has been proposed for correcting long reads. Mapping of short reads on long reads pro-vides sufficient coverage to eliminate up to 99% of errors, however, at the expense of prohibitive running times and considerable amounts of disk and memory space. Results: We present LoRDEC, a hybrid error correction method that builds a succinct de Bruijn graph representing the short reads, and seeks a corrective sequence for each erroneous region in the long reads by traversing chosen paths in the graph. In comparison, LoRDEC is at least six times faster and requires at least 93% less memory or disk space than available tools, while achieving comparable accuracy.

https://hal-lirmm.ccsd.cnrs.fr/lirmm-01100451/document

LoRDEC: accurate and efficient long read error correction.

[서평]「Algorithms on Strings, Trees, and Sequences」

Expression.- Spectral Clustering Gene Ontology Terms to Group Genes by Function.- Dynamic De-Novo Prediction of microRNAs Associated with Cell Conditions: A Search Pruned by Expression.- Clustering Gene Expression Series with Prior Knowledge.- A Linear Time Biclustering Algorithm for Time Series Gene Expression Data.- Time-Window Analysis of Developmental Gene Expression Data with Multiple Genetic Backgrounds.- Phylogeny.- A Lookahead Branch-and-Bound Algorithm for the Maximum Quartet Consistency Problem.- Computing the Quartet Distance Between Trees of Arbitrary Degree.- Using Semi-definite Programming to Enhance Supertree Resolvability.- An Efficient Reduction from Constrained to Unconstrained Maximum Agreement Subtree.- Pattern Identification in Biogeography.- On the Complexity of Several Haplotyping Problems.- A Hidden Markov Technique for Haplotype Reconstruction.- Algorithms for Imperfect Phylogeny Haplotyping (IPPH) with a Single Homoplasy or Recombination Event.- Networks.- A Faster Algorithm for Detecting Network Motifs.- Reaction Motifs in Metabolic Networks.- Reconstructing Metabolic Networks Using Interval Analysis.- Genome Rearrangements.- A 1.375-Approximation Algorithm for Sorting by Transpositions.- A New Tight Upper Bound on the Transposition Distance.- Perfect Sorting by Reversals Is Not Always Difficult.- Minimum Recombination Histories by Branch and Bound.- Sequences.- A Unifying Framework for Seed Sensitivity and Its Application to Subset Seeds.- Generalized Planted (l,d)-Motif Problem with Negative Set.- Alignment of Tandem Repeats with Excision, Duplication, Substitution and Indels (EDSI).- The Peres-Shields Order Estimator for Fixed and Variable Length Markov Models with Applications to DNA Sequence Similarity.- Multiple Structural RNA Alignment with Lagrangian Relaxation.- Faster Algorithms for Optimal Multiple Sequence Alignment Based on Pairwise Comparisons.- Ortholog Clustering on a Multipartite Graph.- Linear Time Algorithm for Parsing RNA Secondary Structure.- A Compressed Format for Collections of Phylogenetic Trees and Improved Consensus Performance.- Structure.- Optimal Protein Threading by Cost-Splitting.- Efficient Parameterized Algorithm for Biopolymer Structure-Sequence Alignment.- Rotamer-Pair Energy Calculations Using a Trie Data Structure.- Improved Maintenance of Molecular Surfaces Using Dynamic Graph Connectivity.- The Main Structural Regularities of the Sandwich Proteins.- Discovery of Protein Substructures in EM Maps.

Algorithms in Bioinformatics: 5th International Workshop, WABI 2005, Mallorca, Spain, October 3-6, 2005, Proceedings (Lecture Notes in Computer Science / Lecture Notes in Bioinformatics)

The human reference genome is part of the foundation of modern human biology and a monumental scientific achievement. However, because it excludes a great deal of common human variation, it introduces a pervasive reference bias into the field of human genomics. To reduce this bias, it makes sense to draw on representative collections of human genomes, brought together into reference cohorts. There are a number of techniques to represent and organize data gleaned from these cohorts, many using ideas implicitly or explicitly borrowed from graph-based models. Here, we survey various projects underway to build and apply these graph-based structures-which we collectively refer to as genome graphs-and discuss the improvements in read mapping, variant calling, and haplotype determination that genome graphs are expected to produce.

/pdf/genome-graphs-and-the-evolution-of-genome-inference-22cyp53r36.pdf

Genome graphs and the evolution of genome inference

Background
Next Generation Sequencing (NGS) has dramatically enhanced our ability to sequence genomes, but not to assemble them. In practice, many published genome sequences remain in the state of a large set of contigs. Each contig describes the sequence found along some path of the assembly graph, however, the set of contigs does not record all the sequence information contained in that graph. Although many subsequent analyses can be performed with the set of contigs, one may ask whether mapping reads on the contigs is as informative as mapping them on the paths of the assembly graph. Currently, one lacks practical tools to perform mapping on such graphs.

Results
Here, we propose a formal definition of mapping on a de Bruijn graph, analyse the problem complexity which turns out to be NP-complete, and provide a practical solution. We propose a pipeline called GGMAP (Greedy Graph MAPping). Its novelty is a procedure to map reads on branching paths of the graph, for which we designed a heuristic algorithm called BGREAT (de Bruijn Graph REAd mapping Tool). For the sake of efficiency, BGREAT rewrites a read sequence as a succession of unitigs sequences. GGMAP can map millions of reads per CPU hour on a de Bruijn graph built from a large set of human genomic reads. Surprisingly, results show that up to 22 % more reads can be mapped on the graph but not on the contig set.

Conclusions
Although mapping reads on a de Bruijn graph is complex task, our proposal offers a practical solution combining efficiency with an improved mapping capacity compared to assembly-based mapping even for complex eukaryotic data.

/pdf/read-mapping-on-de-bruijn-graphs-40o7ob0a0b.pdf

Read mapping on de Bruijn graphs

Background Next Generation Sequencing (NGS) has dramatically enhanced our ability to sequence genomes, but not to assemble them. In practice, many published genome sequences remain in the state of a large set of contigs. Each contig describes the sequence found along some path of the assembly graph, however, the set of contigs does not record all the sequence information contained in that graph. Although many subsequent analyses can be performed with the set of contigs, one may ask whether mapping reads on the contigs is as informative as mapping them on the paths of the assembly graph. Currently, one lacks practical tools to perform mapping on such graphs. Results Here, we propose a formal definition of mapping on a de Bruijn graph, analyse the problem complexity which turns out to be NP-complete, and provide a practical solution.We propose a pipeline called GGMAP (Greedy Graph MAPping). Its novelty is a procedure to map reads on branching paths of the graph, for which we designed a heuristic algorithm called BGREAT (de Bruijn Graph REAd mapping Tool). For the sake of efficiency, BGREAT rewrites a read sequence as a succession of unitigs sequences. GGMAP can map millions of reads per CPU hour on a de Bruijn graph built from a large set of human genomic reads. Surprisingly, results show that up to 22% more reads can be mapped on the graph but not on the contig set. Conclusions Although mapping reads on a de Bruijn graph is complex task, our proposal offers a practical solution combining efficiency with an improved mapping capacity compared to assembly-based mapping even for complex eukaryotic data. Availability: this http URL Keywords: Read mapping; De bruijn graphs; NGS; NP-completeness

/pdf/read-mapping-on-de-bruijn-graph-39etnmgjf1.pdf

Read Mapping on de Bruijn graph

New technologies have tremendously increased sequencing throughput compared to traditional techniques, thereby complicating DNA assembly. Hence, assembly programs resort to de Bruijn graphs (dBG) of k-mers of short reads to compute a set of long contigs, each being a putative segment of the sequenced molecule. Other types of DNA sequence analysis, as well as preprocessing of the reads for assembly, use classical data structures to index all substrings of the reads. It is thus interesting to exhibit algorithms that directly build a dBG of order k from a pre-existing index, and especially a contracted version of the dBG, where non branching paths are condensed into single nodes. Here, we formalise the relationship between suffix trees/arrays and dBGs, and exhibit linear time algorithms for constructing the full or contracted dBGs. Finally, we provide hints explaining why this bridge between indexes and dBGs enables to dynamically update the order k of the graph.

/pdf/from-indexing-data-structures-to-de-bruijn-graphs-34paouivhp.pdf

From Indexing Data Structures to de Bruijn Graphs

Reverse engineering of compact suffix trees and links

Recent large-scale community sequencing efforts allow at an unprecedented level of detail the identification of genomic regions that show signatures of natural selection. Traditional methods for identifying such regions from individuals’ haplotype data, however, require excessive computing times and therefore are not applicable to current datasets. In 2019, Cunha et al. (Advances in bioinformatics and computational biology: 11th Brazilian symposium on bioinformatics, BSB 2018, Niteroi, Brazil, October 30 - November 1, 2018, Proceedings, 2018. https://doi.org/10.1007/978-3-030-01722-4_3) suggested the maximal perfect haplotype block as a very simple combinatorial pattern, forming the basis of a new method to perform rapid genome-wide selection scans. The algorithm they presented for identifying these blocks, however, had a worst-case running time quadratic in the genome length. It was posed as an open problem whether an optimal, linear-time algorithm exists. In this paper we give two algorithms that achieve this time bound, one conceptually very simple one using suffix trees and a second one using the positional Burrows–Wheeler Transform, that is very efficient also in practice.

/pdf/finding-all-maximal-perfect-haplotype-blocks-in-linear-time-1ozistiw4h.pdf

Bastien Cazaux

Papers

Read mapping on de Bruijn graphs

Read Mapping on de Bruijn graph

From Indexing Data Structures to de Bruijn Graphs

Reverse engineering of compact suffix trees and links

Finding all maximal perfect haplotype blocks in linear time.