An Efficient Algorithm For Chinese Postman Walk on Bi-directed de Bruijn Graphs

Sequence assembly from short reads is an important problem in biology. It is known that solving the sequence assembly problem exactly on a bi-directed de Bruijn graph or a string graph is intractable. However finding a Shortest Double stranded DNA string (SDDNA) containing all the k-long words in the reads seems to be a good heuristic to get close to the original genome. This problem is equivalent to finding a cyclic Chinese Postman (CP) walk on the underlying un-weighted bi-directed de Bruijn graph built from the reads. The Chinese Postman walk Problem (CPP) is solved by reducing it to a general bi-directed flow on this graph which runs in O(|E|2 log2(|V |)) time. In this paper we show that the cyclic CPP on bi-directed graphs can be solved without reducing it to bi-directed flow. We present a ?(p(|V | + |E|) log(|V |) + (dmaxp)3) time algorithm to solve the cyclic CPP on a weighted bi-directed de Bruijn graph, where p = max{|{v|din(v) - dout(v) > 0}|, |{v|din(v) - dout(v) < 0}|} and dmax = max{|din(v) - dout(v)}. Our algorithm performs asymptotically better than the bidirected flow algorithm when the number of imbalanced nodes p is much less than the nodes in the bi-directed graph. From our experimental results on various datasets, we have noticed that the value of p/|V | lies between 0.08% and 0.13% with 95% probability

Cerulean: A hybrid assembly using high throughput short and long reads

Genome assembly using high throughput data with short reads, arguably, remains an unresolvable task in repetitive genomes, since when the length of a repeat exceeds the read length, it becomes difficult to unambiguously connect the flanking regions. The emergence of third generation sequencing (Pacific Biosciences) with long reads enables the opportunity to resolve complicated repeats that could not be resolved by the short read data. However, these long reads have high error rate and it is an uphill task to assemble the genome without using additional high quality short reads. Recently, Koren et al. 2012 proposed an approach to use high quality short reads data to correct these long reads and, thus, make the assembly from long reads possible. However, due to the large size of both dataset (short and long reads), error-correction of these long reads requires excessively high computational resources, even on small bacterial genomes. In this work, instead of error correction of long reads, we first assemble the short reads and later map these long reads on the assembly graph to resolve repeats. Contribution: We present a hybrid assembly approach that is both computationally effective and produces high quality assemblies. Our algorithm first operates with a simplified version of the assembly graph consisting only of long contigs and gradually improves the assembly by adding smaller contigs in each iteration. In contrast to the state-of-the-art long reads error correction technique, which requires high computational resources and long running time on a supercomputer even for bacterial genome datasets, our software can produce comparable assembly using only a standard desktop in a short running time.Comment: Peer-reviewed and presented as part of the 13th Workshop on Algorithms in Bioinformatics (WABI2013

Orthology guided transcriptome assembly of Italian ryegrass and meadow fescue for single-nucleotide polymorphism discovery

Single-nucleotide polymorphisms (SNPs) represent natural DNA sequence variation. They can be used for various applications including the construction of high-density genetic maps, analysis of genetic variability, genome-wide association studies, and mapbased cloning. Here we report on transcriptome sequencing in the two forage grasses, meadow fescue (Festuca pratensis Huds.) and Italian ryegrass (Lolium multiflorum Lam.), and identification of various classes of SNPs. Using the Orthology Guided Assembly (OGA) strategy, we assembled and annotated a total of 18,952 and 19,036 transcripts for Italian ryegrass and meadow fescue, respectively. In addition, we used transcriptome sequence data of perennial ryegrass (L. perenne L.) from a previous study to identify 16,613 transcripts shared across all three species. Large numbers of intraspecific SNPs were identified in all three species: 248,000 in meadow fescue, 715,000 in Italian ryegrass, and 529,000 in perennial ryegrass. Moreover, we identified almost 25,000 interspecific SNPs located in 5343 genes that can distinguish meadow fescue from Italian ryegrass and 15,000 SNPs located in 3976 genes that discriminate meadow fescue from both Lolium species. All identified SNPs were positioned in silico on the seven linkage groups (LGs) of L. perenne using the GenomeZipper approach. With the identification and positioning of interspecific SNPs, our study provides a valuable resource for the grass research and breeding community and will enable detailed characterization of genomic composition and gene expression analysis in prospective Festuca Lolium hybrids

Mapping-free and assembly-free discovery of inversion breakpoints from raw NGS reads

International audienceWe propose a formal model and an algorithm for detecting inversion breakpoints without a reference genome, directly from raw NGS data. This model is characterized by a fixed size topological pattern in the de Bruijn Graph. We describe precisely the possible sources of false pos- itives and false negatives and we additionally propose a sequence-based filter giving a good trade-off between precision and recall of the method. We implemented these ideas in a prototype called TakeABreak. Ap- plied on simulated inversions in genomes of various complexity (from E. coli to a human chromosome dataset), TakeABreak provided promising results with a low memory footprint and a small computational time

PERGA

Since the read lengths of high throughput sequencing (HTS) technologies are short, de novo assembly which plays significant roles in many applications remains a great challenge. Most of the state-of-the-art approaches base on de Bruijn graph strategy and overlap-layout strategy. However, these approaches which depend on k-mers or read overlaps do not fully utilize information of single-end and paired-end reads when resolving branches, e.g. the number and positions of reads supporting each possible extension are not taken into account when resolving branches. We present PERGA (Paired-End Reads Guided Assembler), a novel sequence-reads-guided de novo assembly approach, which adopts greedy-like prediction strategy for assembling reads to contigs and scaffolds. Instead of using single-end reads to construct contig, PERGA uses paired-end reads and different read overlap size thresholds ranging from Omax to Omin to resolve the gaps and branches. Moreover, by constructing a decision model using machine learning approach based on branch features, PERGA can determine the correct extension in 99.7% of cases. When the correct extension cannot be determined, PERGA will try to extend the contigs by all feasible extensions and determine the correct extension by using look ahead technology. We evaluated PERGA on both simulated Illumina data sets and real data sets, and it constructed longer and more correct contigs and scaffolds than other state-of-the-art assemblers IDBA-UD, Velvet, ABySS, SGA and CABOG. Availability: https://github.com/hitbio/PERG

IDBA- A Practical Iterative de Bruijn Graph De Novo Assembler

Abstract. The de Bruijn graph assembly approach breaks reads into k-mers before assembling them into contigs. The string graph approach forms contigs by connecting two reads with k or more overlapping nucleotides. Both approaches face the problem of false-positive vertices from erroneous reads, missing vertices due to non-uniform coverage and branching due to erroneous reads and repeat regions. A proper choice of k is crucial but for any single k there is always a trade-off: a small k favors the situation of erroneous reads and non-uniform coverage, and a large k favors short repeat regions. We propose an iterative de Bruijn graph approach iterating from small to large k capturing merits of all values in between. With real and simulated data, our IDBA algorithm is superior to all existing algorithms by constructing longer contigs with similar accuracy and using less memory. The running time of IDBA is comparable with existing algorithms. Availability: IDBA is available a

Algorithms for Three Versions of the Shortest Common Superstring Problem

Abstract. The input to the Shortest Common Superstring (SCS) problem is a set S of k words of total length n. In the classical version the output is an explicit word SCS(S) in which each s ∈ S occurs at least once. In our paper we consider two versions with multiple occurrences, in which the input includes additional numbers (multiplicities), given in binary. Our output is the word SCS(S) given implicitly in a compact form, since its real size could be exponential. We also consider a case when all input words are of length two, where our main algorithmic tool is a compact representation of Eulerian cycles in multigraphs. Due to exponential multiplicities of edges such cycles can be exponential and the compact representation is needed. Other tools used in our paper are a polynomial case of integer linear programming and a min-plus product of matrices.