Paul Medvedev

Computational methods for discovering structural variation with next-generation sequencing

In the last several years, a number of studies have described large-scale structural variation in several genomes. Traditionally, such methods have used whole-genome array comparative genome hybridization or single-nucleotide polymorphism arrays to detect large regions subject to copy-number variation. Later techniques have been based on paired-end mapping of Sanger sequencing data, providing better resolution and accuracy. With the advent of next-generation sequencing, a new generation of methods is being developed to tackle the challenges of short reads, while taking advantage of the high coverage the new sequencing technologies provide. In this survey, we describe these methods, including their strengths and their limitations, and future research directions.

Informed and automated k-mer size selection for genome assembly

MOTIVATION Genome assembly tools based on the de Bruijn graph framework rely on a parameter k, which represents a trade-off between several competing effects that are difficult to quantify. There is currently a lack of tools that would automatically estimate the best k to use and/or quickly generate histograms of k-mer abundances that would allow the user to make an informed decision. RESULTS We develop a fast and accurate sampling method that constructs approximate abundance histograms with several orders of magnitude performance improvement over traditional methods. We then present a fast heuristic that uses the generated abundance histograms for putative k values to estimate the best possible value of k. We test the effectiveness of our tool using diverse sequencing datasets and find that its choice of k leads to some of the best assemblies. AVAILABILITY Our tool KmerGenie is freely available at: http://kmergenie.bx.psu.edu/.

Detecting copy number variation with mated short reads.

The development of high-throughput sequencing (HTS) technologies has opened the door to novel methods for detecting copy number variants (CNVs) in the human genome. While in the past CNVs have been detected based on array CGH data, recent studies have shown that depth-of-coverage information from HTS technologies can also be used for the reliable identification of large copy-variable regions. Such methods, however, are hindered by sequencing biases that lead certain regions of the genome to be over- or undersampled, lowering their resolution and ability to accurately identify the exact breakpoints of the variants. In this work, we develop a method for CNV detection that supplements the depth-of-coverage with paired-end mapping information, where mate pairs mapping discordantly to the reference serve to indicate the presence of variation. Our algorithm, called CNVer, combines this information within a unified computational framework called the donor graph, allowing us to better mitigate the sequencing biases that cause uneven local coverage and accurately predict CNVs. We use CNVer to detect 4879 CNVs in the recently described genome of a Yoruban individual. Most of the calls (77%) coincide with previously known variants within the Database of Genomic Variants, while 81% of deletion copy number variants previously known for this individual coincide with one of our loss calls. Furthermore, we demonstrate that CNVer can reconstruct the absolute copy counts of segments of the donor genome and evaluate the feasibility of using CNVer with low coverage datasets.

Computability of models for sequence assembly

Graph-theoretic models have come to the forefront as some of the most powerful and practical methods for sequence assembly. Simultaneously, the computational hardness of the underlying graph algorithms has remained open. Here we present two theoretical results about the complexity of these models for sequence assembly. In the first part, we show sequence assembly to be NP-hard under two different models: string graphs and de Bruijn graphs. Together with an earlier result on the NP-hardness of overlap graphs, this demonstrates that all of the popular graph-theoretic sequence assembly paradigms are NP-hard. In our second result, we give the first, to our knowledge, optimal polynomial time algorithm for genome assembly that explicitly models the double-strandedness of DNA. We solve the Chinese Postman Problem on bidirected graphs using bidirected flow techniques and show to how to use it to find the shortest doublestranded DNA sequence which contains a given set of k-long words. This algorithm has applications to sequencing by hybridization and short read assembly.

Error correction of high-throughput sequencing datasets with non-uniform coverage

Motivation: The continuing improvements to high-throughput sequencing (HTS) platforms have begun to unfold a myriad of new applications. As a result, error correction of sequencing reads remains an important problem. Though several tools do an excellent job of correcting datasets where the reads are sampled close to uniformly, the problem of correcting reads coming from drastically non-uniform datasets, such as those from single-cell sequencing, remains open. Results: In this article, we develop the method Hammer for error correction without any uniformity assumptions. Hammer is based on a combination of a Hamming graph and a simple probabilistic model for sequencing errors. It is a simple and adaptable algorithm that improves on other tools on non-uniform single-cell data, while achieving comparable results on normal multi-cell data. Availability: http://www.cs.toronto.edu/~pashadag. Contact: pmedvedev@cs.ucsd.edu

Maximum Likelihood Genome Assembly

Whole genome shotgun assembly is the process of taking many short sequenced segments (reads) and reconstructing the genome from which they originated. We demonstrate how the technique of bidirected network flow can be used to explicitly model the double-stranded nature of DNA for genome assembly. By combining an algorithm for the Chinese Postman Problem on bidirected graphs with the construction of a bidirected de Bruijn graph, we are able to find the shortest double-stranded DNA sequence that contains a given set of k-long DNA molecules. This is the first exact polynomial time algorithm for the assembly of a double-stranded genome. Furthermore, we propose a maximum likelihood framework for assembling the genome that is the most likely source of the reads, in lieu of the standard maximum parsimony approach (which finds the shortest genome subject to some constraints). In this setting, we give a bidirected network flow-based algorithm that, by taking advantage of high coverage, accurately estimates the copy counts of repeats in a genome. Our second algorithm combines these predicted copy counts with matepair data in order to assemble the reads into contigs. We run our algorithms on simulated read data from Escherichia coli and predict copy counts with extremely high accuracy, while assembling long contigs.

Shortest paths between shortest paths

a b s t r a c t We study the following problem on reconfiguring shortest paths in graphs: Given two shortest s-t paths, what is the minimum number of steps required to transform one into the other, where each intermediate path must also be a shortest s-t path and must differ from the previous one by only one vertex. We prove that the shortest reconfiguration sequence can be exponential in the size of the graph and that it is NP-hard to compute the shortest reconfiguration sequence even when we know that the sequence has polynomial length.

Paired de bruijn graphs: a novel approach for incorporating mate pair information into genome assemblers.

The recent proliferation of next generation sequencing with short reads has enabled many new experimental opportunities but, at the same time, has raised formidable computational challenges in genome assembly. One of the key advances that has led to an improvement in contig lengths has been mate pairs, which facilitate the assembly of repeating regions. Mate pairs have been algorithmically incorporated into most next generation assemblers as various heuristic post-processing steps to correct the assembly graph or to link contigs into scaffolds. Such methods have allowed the identification of longer contigs than would be possible with single reads; however, they can still fail to resolve complex repeats. Thus, improved methods for incorporating mate pairs will have a strong effect on contig length in the future. Here, we introduce the paired de Bruijn graph, a generalization of the de Bruijn graph that incorporates mate pair information into the graph structure itself instead of analyzing mate pairs at a post-processing step. This graph has the potential to be used in place of the de Bruijn graph in any de Bruijn graph based assembler, maintaining all other assembly steps such as error-correction and repeat resolution. Through assembly results on simulated perfect data, we argue that this can effectively improve the contig sizes in assembly.

On the representation of de Bruijn graphs.

The de Bruijn graph plays an important role in bioinformatics, especially in the context of de novo assembly. However, the representation of the de Bruijn graph in memory is a computational bottleneck for many assemblers. Recent papers proposed a navigational data structure approach in order to improve memory usage. We prove several theoretical space lower bounds to show the limitations of these types of approaches. We further design and implement a general data structure (dbgfm) and demonstrate its use on a human whole-genome dataset, achieving space usage of 1.5 GB and a 46% improvement over previous approaches. As part of dbgfm, we develop the notion of frequency-based minimizers and show how it can be used to enumerate all maximal simple paths of the de Bruijn graph using only 43 MB of memory. Finally, we demonstrate that our approach can be integrated into an existing assembler by modifying the ABySS software to use dbgfm.

The relative worst order ratio applied to seat reservation

The seat reservation problem is the problem of assigning passengers to seats on a train with n seats and k stations enroute in an online manner. The performance of algorithms for this problem is studied using the relative worst order ratio, a fairly new measure for the quality of online algorithms, which allows for direct comparisons between algorithms. This study has yielded new separations between algorithms. For example, for both variants of the problem considered, using the relative worst order ratio, First-Fit and Best-Fit are shown to be better than Worst-Fit.