Multiple Matching of Rectangular Patterns

AbstractWe describe the first worst-case efficient algorithm for simultaneously matching multiple rectangular patterns of varying sizes and aspect ratios in a rectangular text. Efficient means significantly more efficient asymptotically than applying known algorithms that handle one height (or width or aspect ratio) at a time for each height. Our algorithm features an interesting use of multidimensional range searching, as well as new adaptations of several known techniques for two-dimensional string matching. We also extend our algorithm to a dynamic setting where the set of patterns can change over time

Dynamic dictionary matching with failure functions

AbstractAmir and Farach (1991) and Amir et al. (to appear) recently initiated the study of the dynamic dictionary pattern matching problem. The dictionary D contains a set of patterns that can change over time by insertion and deletion of individual patterns. The user may also present a text string and ask to search for all occurrences of any patterns in the text. For the static dictionary problem, Aho and Corasick (1975) gave a strategy based on a failure function automaton that takes O(|D|log|Σ|) time to build a dictionary of size |D| and searches a text T in time O(|T|log|Σ|+tocc), where tocc, is the total number of pattern occurrences in the text.Amir et al. (to appear) used an automaton based on suffix trees to solve the dynamic problem. Their method can insert or delete a pattern P in time O(|P|log|D|) and can search a text in time O((|T|+tocc)log|D|).We show that the same bounds can be achieved using a framework based on failure functions. We then show that our approach also allows us to achieve faster search times at the expense of the update times; for constant k, we can achieve linear O(|T|(k+log|Σ|)+k tocc) search time with an update time of O(k|P∥D|1k). This is advantageous if the search texts are much larger than the dictionary or searches are more frequent than updates.Finally, we show how to build the initial dictionary in O(|D|log|Σ|) time, regardless of what combination of search and update times is used

Exploring single-sample SNP and INDEL calling with whole-genome de novo assembly

Motivation: Eugene Myers in his string graph paper (Myers, 2005) suggested that in a string graph or equivalently a unitig graph, any path spells a valid assembly. As a string/unitig graph also encodes every valid assembly of reads, such a graph, provided that it can be constructed correctly, is in fact a lossless representation of reads. In principle, every analysis based on whole-genome shotgun sequencing (WGS) data, such as SNP and insertion/deletion (INDEL) calling, can also be achieved with unitigs. Results: To explore the feasibility of using de novo assembly in the context of resequencing, we developed a de novo assembler, fermi, that assembles Illumina short reads into unitigs while preserving most of information of the input reads. SNPs and INDELs can be called by mapping the unitigs against a reference genome. By applying the method on 35-fold human resequencing data, we showed that in comparison to the standard pipeline, our approach yields similar accuracy for SNP calling and better results for INDEL calling. It has higher sensitivity than other de novo assembly based methods for variant calling. Our work suggests that variant calling with de novo assembly be a beneficial complement to the standard variant calling pipeline for whole-genome resequencing. In the methodological aspects, we proposed FMD-index for forward-backward extension of DNA sequences, a fast algorithm for finding all super-maximal exact matches and one-pass construction of unitigs from an FMD-index. Availability: http://github.com/lh3/fermi Contact: [email protected]: Rev2: submitted version with minor improvements; 7 page

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

SEQuel: improving the accuracy of genome assemblies

Motivation: Assemblies of next-generation sequencing (NGS) data, although accurate, still contain a substantial number of errors that need to be corrected after the assembly process. We develop SEQuel, a tool that corrects errors (i.e. insertions, deletions and substitution errors) in the assembled contigs. Fundamental to the algorithm behind SEQuel is the positional de Bruijn graph, a graph structure that models k-mers within reads while incorporating the approximate positions of reads into the model

Safe and complete contig assembly via omnitigs

Contig assembly is the first stage that most assemblers solve when reconstructing a genome from a set of reads. Its output consists of contigs -- a set of strings that are promised to appear in any genome that could have generated the reads. From the introduction of contigs 20 years ago, assemblers have tried to obtain longer and longer contigs, but the following question was never solved: given a genome graph $G$ (e.g. a de Bruijn, or a string graph), what are all the strings that can be safely reported from $G$ as contigs? In this paper we finally answer this question, and also give a polynomial time algorithm to find them. Our experiments show that these strings, which we call omnitigs, are 66% to 82% longer on average than the popular unitigs, and 29% of dbSNP locations have more neighbors in omnitigs than in unitigs.Comment: Full version of the paper in the proceedings of RECOMB 201

Efficient genome ancestry inference in complex pedigrees with inbreeding

Motivation: High-density SNP data of model animal resources provides opportunities for fine-resolution genetic variation studies. These genetic resources are generated through a variety of breeding schemes that involve multiple generations of matings derived from a set of founder animals. In this article, we investigate the problem of inferring the most probable ancestry of resulting genotypes, given a set of founder genotypes. Due to computational difficulty, existing methods either handle only small pedigree data or disregard the pedigree structure. However, large pedigrees of model animal resources often contain repetitive substructures that can be utilized in accelerating computation

The liver pharmacological and xenobiotic gene response repertoire

We have used a supervised classification approach to systematically mine a large microarray database derived from livers of compound-treated rats. Thirty-four distinct signatures (classifiers) for pharmacological and toxicological end points can be identified. Just 200 genes are sufficient to classify these end points. Signatures were enriched in xenobiotic and immune response genes and contain un-annotated genes, indicating that not all key genes in the liver xenobiotic responses have been characterized. Many signatures with equal classification capabilities but with no gene in common can be derived for the same phenotypic end point. The analysis of the union of all genes present in these signatures can reveal the underlying biology of that end point as illustrated here using liver fibrosis signatures. Our approach using the whole genome and a diverse set of compounds allows a comprehensive view of most pharmacological and toxicological questions and is applicable to other situations such as disease and development

Assembly complexity of prokaryotic genomes using short reads

<p>Abstract</p> <p>Background</p> <p>De Bruijn graphs are a theoretical framework underlying several modern genome assembly programs, especially those that deal with very short reads. We describe an application of de Bruijn graphs to analyze the global repeat structure of prokaryotic genomes.</p> <p>Results</p> <p>We provide the first survey of the repeat structure of a large number of genomes. The analysis gives an upper-bound on the performance of genome assemblers for <it>de novo </it>reconstruction of genomes across a wide range of read lengths. Further, we demonstrate that the majority of genes in prokaryotic genomes can be reconstructed uniquely using very short reads even if the genomes themselves cannot. The non-reconstructible genes are overwhelmingly related to mobile elements (transposons, IS elements, and prophages).</p> <p>Conclusions</p> <p>Our results improve upon previous studies on the feasibility of assembly with short reads and provide a comprehensive benchmark against which to compare the performance of the short-read assemblers currently being developed.</p