Construction of minimal DFAs from biological motifs

Deterministic finite automata (DFAs) are constructed for various purposes in computational biology. Little attention, however, has been given to the efficient construction of minimal DFAs. In this article, we define simple non-deterministic finite automata (NFAs) and prove that the standard subset construction transforms NFAs of this type into minimal DFAs. Furthermore, we show how simple NFAs can be constructed from two types of patterns popular in bioinformatics, namely (sets of) generalized strings and (generalized) strings with a Hamming neighborhood

Sensitive Long-Indel-Aware Alignment of Sequencing Reads

The tremdendous advances in high-throughput sequencing technologies have made population-scale sequencing as performed in the 1000 Genomes project and the Genome of the Netherlands project possible. Next-generation sequencing has allowed genom-wide discovery of variations beyond single-nucleotide polymorphisms (SNPs), in particular of structural variations (SVs) like deletions, insertions, duplications, translocations, inversions, and even more complex rearrangements. Here, we design a read aligner with special emphasis on the following properties: (1) high sensitivity, i.e. find all (reasonable) alignments; (2) ability to find (long) indels; (3) statistically sound alignment scores; and (4) runtime fast enough to be applied to whole genome data. We compare performance to BWA, bowtie2, stampy and find that our methods is especially advantageous on reads containing larger indels

Next Generation Cluster Editing

This work aims at improving the quality of structural variant prediction from the mapped reads of a sequenced genome. We suggest a new model based on cluster editing in weighted graphs and introduce a new heuristic algorithm that allows to solve this problem quickly and with a good approximation on the huge graphs that arise from biological datasets

Constructing Founder Sets Under Allelic and Non-Allelic Homologous Recombination

Homologous recombination between the maternal and paternal copies of a chromosome is a key mechanism for human inheritance and shapes population genetic properties of our species. However, a similar mechanism can also act between different copies of the same sequence, then called non-allelic homologous recombination (NAHR). This process can result in genomic rearrangements - including deletion, duplication, and inversion - and is underlying many genomic disorders. Despite its importance for genome evolution and disease, there is a lack of computational models to study genomic loci prone to NAHR. In this work, we propose such a computational model, providing a unified framework for both (allelic) homologous recombination and NAHR. Our model represents a set of genomes as a graph, where human haplotypes correspond to walks through this graph. We formulate two founder set problems under our recombination model, provide flow-based algorithms for their solution, and demonstrate scalability to problem instances arising in practice

SNP and indel frequencies at transcription start sites and at canonical and alternative translation initiation sites in the human genome

Single-nucleotide polymorphisms (SNPs) are the most common form of genetic variation in humans and drive phenotypic variation. Due to evolutionary conservation, SNPs and indels (insertion and deletions) are depleted in functionally important sequence elements. Recently, population-scale sequencing efforts such as the 1000 Genomes Project and the Genome of the Netherlands Project have catalogued large numbers of sequence variants. Here, we present a systematic analysis of the polymorphisms reported by these two projects in different coding and non-coding genomic elements of the human genome (intergenic regions, CpG islands, promoters, 5' UTRs, coding exons, 3' UTRs, introns, and intragenic regions). Furthermore, we were especially interested in the distribution of SNPs and indels in direct vicinity to the transcription start site (TSS) and translation start site (CSS). Thereby, we discovered an enrichment of dinucleotides CpG and CpA and an accumulation of SNPs at base position -1 relative to the TSS that involved primarily CpG and CpA dinucleotides. Genes having a CpG dinucleotide at TSS position -1 were enriched in the functional GO terms "Phosphoprotein", "Alternative splicing", and "Protein binding". Focusing on the CSS, we compared SNP patterns in the flanking regions of canonical and alternative AUG and near-cognate start sites where we considered alternative starts previously identified by experimental ribosome profiling. We observed similar conservation patterns of canonical and alternative translation start sites, which underlines the importance of alternative translation mechanisms for cellular function

An Algorithm to Compute the Character Access Count Distribution for Pattern Matching Algorithms

We propose a framework for the exact probabilistic analysis of window-based pattern matching algorithms, such as Boyer--Moore, Horspool, Backward DAWG Matching, Backward Oracle Matching, and more. In particular, we develop an algorithm that efficiently computes the distribution of a pattern matching algorithm's running time cost (such as the number of text character accesses) for any given pattern in a random text model. Text models range from simple uniform models to higher-order Markov models or hidden Markov models (HMMs). Furthermore, we provide an algorithm to compute the exact distribution of \emph{differences} in running time cost of two pattern matching algorithms. Methodologically, we use extensions of finite automata which we call \emph{deterministic arithmetic automata} (DAAs) and \emph{probabilistic arithmetic automata} (PAAs)~\cite{Marschall2008}. Given an algorithm, a pattern, and a text model, a PAA is constructed from which the sought distributions can be derived using dynamic programming. To our knowledge, this is the first time that substring- or suffix-based pattern matching algorithms are analyzed exactly by computing the whole distribution of running time cost. Experimentally, we compare Horspool's algorithm, Backward DAWG Matching, and Backward Oracle Matching on prototypical patterns of short length and provide statistics on the size of minimal DAAs for these computations

CLEVER: Clique-Enumerating Variant Finder

Next-generation sequencing techniques have facilitated a large scale analysis of human genetic variation. Despite the advances in sequencing speeds, the computational discovery of structural variants is not yet standard. It is likely that many variants have remained undiscovered in most sequenced individuals. Here we present a novel internal segment size based approach, which organizes all, including also concordant reads into a read alignment graph where max-cliques represent maximal contradiction-free groups of alignments. A specifically engineered algorithm then enumerates all max-cliques and statistically evaluates them for their potential to reflect insertions or deletions (indels). For the first time in the literature, we compare a large range of state-of-the-art approaches using simulated Illumina reads from a fully annotated genome and present various relevant performance statistics. We achieve superior performance rates in particular on indels of sizes 20--100, which have been exposed as a current major challenge in the SV discovery literature and where prior insert size based approaches have limitations. In that size range, we outperform even split read aligners. We achieve good results also on real data where we make a substantial amount of correct predictions as the only tool, which complement the predictions of split-read aligners. CLEVER is open source (GPL) and available from http://clever-sv.googlecode.com.Comment: 30 pages, 8 figure

Mixed-order Ambisonics recording and playback for improving horizontal directionality

Planar (2D) and periphonic (3D) higher-order Ambisonics (HOA) systems are widely used to reproduce spatial properties of acoustic scenarios. Mixed-order Ambisonics (MOA) systems combine the benefit of higher order 2D systems, i.e. a high spatial resolution over a larger usable frequency bandwidth, with a lower order 3D system to reproduce elevated sound sources. In order to record MOA signals, the location of the microphones on a hard sphere were optimized to provide a robust MOA encoding. A detailed analysis of the encoding and decoding process showed that MOA can improve both the spatial resolution in the horizontal plane and the usable frequency bandwidth for playback as well as recording. Hence the described MOA scheme provides a promising method for improving the performance of current 3D sound reproduction systems.7 page(s