Choosing an order for constructing a de Bruijn graph (DBG) is a crucial step in de novo assembly, as no single value allows complete genome reconstruction. The variable-order de Bruijn graph (voDBG) addresses this limitation by combining DBGs of multiple orders in a single structure connected by contextual relationships. This representation enables new connections to be identified or ambiguities to be resolved during assembly. However, voDBGs currently lack a formal definition of contigs. In this paper, we give the first formal definition of contigs for voDBGs. We show that, for a frequency range [𝓁,h] with 𝓁 > h/2, nodes whose labels occur with frequency f ∈ [𝓁, h] in the reads spell sequences of the genome with high probability under uniform sampling assumptions. We call these sequences (𝓁,h)-tigs. We also present an efficient algorithm to enumerate (𝓁,h)-tigs from a voDBG that accounts for homopolymer errors. Experiments on PacBio HiFi data show that our method significantly improves contiguity compared to unitigs in fixed-order DBGs while remaining considerably lighter than full genome assemblers.

MOTIVATION: Aligning reads to a variation graph is a standard task in pangenomics, with downstream applications such as improving variant calling. While the vg toolkit [Garrison et al. (Variation graph toolkit improves read mapping by representing genetic variation in the reference. Nat Biotechnol 2018;36:875-9)] is a popular aligner of short reads, GraphAligner [Rautiainen and Marschall (GraphAligner: rapid and versatile sequence-to-graph alignment. Genome Biol 2020;21:253-28)] is the state-of-the-art aligner of erroneous long reads. GraphAligner works by finding candidate read occurrences based on individually extending the best seeds of the read in the variation graph. However, a more principled approach recognized in the community is to co-linearly chain multiple seeds. RESULTS: We present a new algorithm to co-linearly chain a set of seeds in a string labeled acyclic graph, together with the first efficient implementation of such a co-linear chaining algorithm into a new aligner of erroneous long reads to acyclic variation graphs, GraphChainer. We run experiments aligning real and simulated PacBio CLR reads with average error rates 15% and 5%. Compared to GraphAligner, GraphChainer aligns 12-17% more reads, and 21-28% more total read length, on real PacBio CLR reads from human chromosomes 1, 22, and the whole human pangenome. On both simulated and real data, GraphChainer aligns between 95% and 99% of all reads, and of total read length. We also show that minigraph [Li et al. (The design and construction of reference pangenome graphs with minigraph. Genome Biol 2020;21:265-19.)] and minichain [Chandra and Jain (Sequence to graph alignment using gap-sensitive co-linear chaining. In: Proceedings of the 27th Annual International Conference on Research in Computational Molecular Biology (RECOMB 2023). Springer, 2023, 58-73.)] obtain an accuracy of <60% on this setting. AVAILABILITY AND IMPLEMENTATION: GraphChainer is freely available at https://github.com/algbio/GraphChainer. The datasets and evaluation pipeline can be reached from the previous address.

During viral infection, intrahost mutation and recombination can lead to significant evolution, resulting in a population of viruses that harbor multiple haplotypes. The task of reconstructing these haplotypes from short-read sequencing data is called viral quasispecies assembly, and it can be categorized as a multiassembly problem. We consider the de novo version of the problem, where no reference is available. We present ViQUF, a de novo viral quasispecies assembler that addresses haplotype assembly and quantification. ViQUF obtains a first draft of the assembly graph from a de Bruijn graph. Then, solving a min-cost flow over a flow network built for each pair of adjacent vertices based on their paired-end information creates an approximate paired assembly graph with suggested frequency values as edge labels, which is the first frequency estimation. Then, original haplotypes are obtained through a greedy path reconstruction guided by a min-cost flow solution in the approximate paired assembly graph. ViQUF outputs the contigs with their frequency estimations. Results on real and simulated data show that ViQUF is at least four times faster using at most half of the memory than previous methods, while maintaining, and in some cases outperforming, the high quality of assembly and frequency estimation of overlap graph-based methodologies, which are known to be more accurate but slower than the de Bruijn graph-based approaches.

BACKGROUND: De novo genome assembly typically produces a set of contigs instead of the complete genome. Thus additional data such as genetic linkage maps, optical maps, or Hi-C data is needed to resolve the complete structure of the genome. Most of the previous work uses the additional data to order and orient contigs. RESULTS: Here we introduce a framework to guide genome assembly with additional data. Our approach is based on clustering the reads, such that each read in each cluster originates from nearby positions in the genome according to the additional data. These sets are then assembled independently and the resulting contigs are further assembled in a hierarchical manner. We implemented our approach for genetic linkage maps in a tool called HGGA. CONCLUSIONS: Our experiments on simulated and real Pacific Biosciences long reads and genetic linkage maps show that HGGA produces a more contiguous assembly with less contigs and from 1.2 to 9.8 times higher NGA50 or N50 than a plain assembly of the reads and 1.03 to 6.5 times higher NGA50 or N50 than a previous approach integrating genetic linkage maps with contig assembly. Furthermore, also the correctness of the assembly remains similar or improves as compared to an assembly using only the read data.

The extraction of k-mers from reads is an important task in many bioinformatics applications, such as all DNA sequence analysis methods based on de Bruijn graphs. These methods tend to be more accurate when the used k-mers are unique in the analyzed DNA, and thus the use of longer k-mers is preferred. When the read lengths of short read sequencing technologies increase, the error rate will become the determining factor for the largest possible value of k. Here we propose LoMeX which uses spaced seeds to extract long k-mers accurately even in the presence of sequencing errors. Our experiments show that LoMeX can extract long k-mers from current Illumina reads with a similar or higher recall than a standard k-mer counting tool. Furthermore, our experiments on simulated data show that when the read length further increases enabling even longer k-mers, the performance of standard k-mer counters declines, whereas LoMeX still extracts long k-mers successfully.

A key problem in processing raw optical mapping data (Rmaps) is finding Rmaps originating from the same genomic region. These sets of related Rmaps can be used to correct errors in Rmap data, and to find overlaps between Rmaps to assemble consensus optical maps. Previous Rmap overlap aligners are computationally very expensive and do not scale to large eukaryotic data sets. We present Selkie, an Rmap overlap aligner based on a spaced $(\ell,k)$(ℓ,k)-mer index which was pioneered in the Rmap error correction tool Elmeri. Here we present a space efficient version of the index which is twice as fast as prior art while using just a quarter of the memory on a human data set. Moreover, our index can be used for filtering candidates for Rmap overlap computation, whereas Elmeri used the index only for error correction of Rmaps. By combining our filtering of Rmaps with the exhaustive, but highly accurate, algorithm of Valouev et al. (2006), Selkie maintains or increases the accuracy of finding overlapping Rmaps on a bacterial dataset while being at least four times faster. Furthermore, for finding overlaps in a human dataset, Selkie is up to two orders of magnitude faster than previous methods.

MOTIVATION: The de Bruijn graph is one of the fundamental data structures for analysis of high throughput sequencing data. In order to be applicable to population-scale studies, it is essential to build and store the graph in a space- and time-efficient manner. In addition, due to the ever-changing nature of population studies, it has become essential to update the graph after construction, e.g. add and remove nodes and edges. Although there has been substantial effort on making the construction and storage of the graph efficient, there is a limited amount of work in building the graph in an efficient and mutable manner. Hence, most space efficient data structures require complete reconstruction of the graph in order to add or remove edges or nodes. RESULTS: In this article, we present DynamicBOSS, a succinct representation of the de Bruijn graph that allows for an unlimited number of additions and deletions of nodes and edges. We compare our method with other competing methods and demonstrate that DynamicBOSS is the only method that supports both addition and deletion and is applicable to very large samples (e.g. greater than 15 billion k-mers). Competing dynamic methods, e.g. FDBG cannot be constructed on large scale datasets, or cannot support both addition and deletion, e.g. BiFrost. AVAILABILITY AND IMPLEMENTATION: DynamicBOSS is publicly available at https://github.com/baharpan/dynboss. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: RNA viruses exhibit a high mutation rate and thus they exist in infected cells as a population of closely related strains called viral quasispecies. The viral quasispecies assembly problem asks to characterize the quasispecies present in a sample from high-throughput sequencing data. We study the de novo version of the problem, where reference sequences of the quasispecies are not available. Current methods for assembling viral quasispecies are either based on overlap graphs or on de Bruijn graphs. Overlap graph-based methods tend to be accurate but slow, whereas de Bruijn graph-based methods are fast but less accurate. RESULTS: We present viaDBG, which is a fast and accurate de Bruijn graph-based tool for de novo assembly of viral quasispecies. We first iteratively correct sequencing errors in the reads, which allows us to use large k-mers in the de Bruijn graph. To incorporate the paired-end information in the graph, we also adapt the paired de Bruijn graph for viral quasispecies assembly. These features enable the use of long-range information in contig construction without compromising the speed of de Bruijn graph-based approaches. Our experimental results show that viaDBG is both accurate and fast, whereas previous methods are either fast or accurate but not both. In particular, viaDBG has comparable or better accuracy than SAVAGE, while being at least nine times faster. Furthermore, the speed of viaDBG is comparable to PEHaplo but viaDBG is able to retrieve also low abundance quasispecies, which are often missed by PEHaplo. AVAILABILITY AND IMPLEMENTATION: viaDBG is implemented in C++ and it is publicly available at https://bitbucket.org/bfreirec1/viadbg. All datasets used in this article are publicly available at https://bitbucket.org/bfreirec1/data-viadbg/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Genome wide optical maps are high resolution restriction maps that give a unique numeric representation to a genome. They are produced by assembling hundreds of thousands of single molecule optical maps, which are called Rmaps. Unfortunately, there exists very few choices for assembling Rmap data. There exists only one publicly-available non-proprietary method for assembly and one proprietary method that is available via an executable. Furthermore, the publicly-available method, by Valouev et al. (2006), follows the overlap-layout-consensus (OLC) paradigm, and therefore, is unable to scale for relatively large genomes. The algorithm behind the proprietary method, Bionano Genomics' Solve, is largely unknown. In this paper, we extend the definition of bi-labels in the paired de Bruijn graph to the context of optical mapping data, and present the first de Bruijn graph based method for Rmap assembly. We implement our approach, which we refer to as rmapper, and compare its performance against the assembler of Valouev et al. (2006) and Solve by Bionano Genomics on data from three genomes - E. coli, human, and climbing perch fish (Anabas Testudineus). Our method was the only one able to successfully run on all three genomes. The method of Valouev et al. (2006) only successfully ran on E. coli and Bionano Solve successfully ran on E. coli and human but not on the fish genome. Moreover, on the human genome rmapper was at least 130 times faster than Bionano Solve, used five times less memory and produced the highest genome fraction with zero mis-assemblies.

MOTIVATION: Optical mapping data is used in many core genomics applications, including structural variation detection, scaffolding assembled contigs and mis-assembly detection. However, the pervasiveness of spurious and deleted cut sites in the raw data, which are called Rmaps, make assembly and alignment of them challenging. Although there exists another method to error correct Rmap data, named cOMet, it is unable to scale to even moderately large sized genomes. The challenge faced in error correction is in determining pairs of Rmaps that originate from the same region of the same genome. RESULTS: We create an efficient method for determining pairs of Rmaps that contain significant overlaps between them. Our method relies on the novel and nontrivial adaption and application of spaced seeds in the context of optical mapping, which allows for spurious and deleted cut sites to be accounted for. We apply our method to detecting and correcting these errors. The resulting error correction method, referred to as Elmeri, improves upon the results of state-of-the-art correction methods but in a fraction of the time. More specifically, cOMet required 9.9 CPU days to error correct Rmap data generated from the human genome, whereas Elmeri required less than 15 CPU hours and improved the quality of the Rmaps by more than four times compared to cOMet. AVAILABILITY AND IMPLEMENTATION: Elmeri is publicly available under GNU Affero General Public License at https://github.com/LeenaSalmela/Elmeri. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Bioinformatics (2019) doi:10.1093/bioinformatics/btz663 Incorrect supplementary material was published alongside the above manuscript. This has now been replaced with the correct material.

BACKGROUND: The long reads produced by third generation sequencing technologies have significantly boosted the results of genome assembly but still, genome-wide assemblies solely based on read data cannot be produced. Thus, for example, optical mapping data has been used to further improve genome assemblies but it has mostly been applied in a post-processing stage after contig assembly. RESULTS: We propose OPTICALKERMIT which directly integrates genome wide optical maps into contig assembly. We show how genome wide optical maps can be used to localize reads on the genome and then we adapt the Kermit method, which originally incorporated genetic linkage maps to the miniasm assembler, to use this information in contig assembly. Our experimental results show that incorporating genome wide optical maps to the contig assembly of miniasm increases NGA50 while the number of misassemblies decreases or stays the same. Furthermore, when compared to the Canu assembler, OPTICALKERMIT produces an assembly with almost three times higher NGA50 with a lower number of misassemblies on real A. thaliana reads. CONCLUSIONS: OPTICALKERMIT successfully incorporates optical mapping data directly to contig assembly of eukaryotic genomes. Our results show that this is a promising approach to improve the contiguity of genome assemblies.

Many bioinformatics problems admit a large number of solutions, with no way of distinguishing the correct one among them. One approach of coping with this issue is to look at the partial solutions common to all solutions. Such partial solutions have been called safe, and an algorithm outputting all safe solutions has been called safe and complete. In this paper we develop a general technique that automatically provides a safe and complete algorithm to problems solvable by dynamic programming. We illustrate it by applying it to the bioinformatics problem of RNA folding, assuming the simplistic folding model maximizing the number of paired bases. Our safe and complete algorithm has time complexity O(n^3M(n)) and space complexity O(n^3) where n is the length of the RNA sequence and M(n) in Omega(n) is the time complexity of arithmetic operations on O(n)-bit integers. We also implement this algorithm and show that, despite an exponential number of optimal solutions, our algorithm is efficient in practice.

MOTIVATION: Optical maps are high-resolution restriction maps (Rmaps) that give a unique numeric representation to a genome. Used in concert with sequence reads, they provide a useful tool for genome assembly and for discovering structural variations and rearrangements. Although they have been a regular feature of modern genome assembly projects, optical maps have been mainly used in post-processing step and not in the genome assembly process itself. Several methods have been proposed for pairwise alignment of single molecule optical maps-called Rmaps, or for aligning optical maps to assembled reads. However, the problem of aligning an Rmap to a graph representing the sequence data of the same genome has not been studied before. Such an alignment provides a mapping between two sets of data: optical maps and sequence data which will facilitate the usage of optical maps in the sequence assembly step itself. RESULTS: We define the problem of aligning an Rmap to a de Bruijn graph and present the first algorithm for solving this problem which is based on a seed-and-extend approach. We demonstrate that our method is capable of aligning 73% of Rmaps generated from the Escherichia coli genome to the de Bruijn graph constructed from short reads generated from the same genome. We validate the alignments and show that our method achieves an accuracy of 99.6%. We also show that our method scales to larger genomes. In particular, we show that 76% of Rmaps can be aligned to the de Bruijn graph in the case of human data. AVAILABILITY AND IMPLEMENTATION: The software for aligning optical maps to de Bruijn graph, omGraph is written in C++ and is publicly available under GNU General Public License at https://github.com/kingufl/omGraph. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Gap filling has emerged as a natural sub-problem of many de novo genome assembly projects. The gap filling problem generally asks for an $s$s-$t$t path in an assembly graph whose length matches the gap length estimate. Several methods have addressed it, but only few have focused on strategies for dealing with multiple gap filling solutions and for guaranteeing reliable results. Such strategies include reporting only unique solutions, or exhaustively enumerating all filling solutions and heuristically creating their consensus. Our main contribution is a new method for reliable gap filling: filling gaps with those sub-paths common to all gap filling solutions. We call these partial solutions safe, following the framework of (Tomescu and Medvedev, RECOMB 2016). We give an efficient safe algorithm running in $O(dm)$O(dm) time and space, where $d$d is the gap length estimate and $m$m is the number of edges of the assembly graph. To show the benefits of this method, we implemented this algorithm for the problem of filling gaps in scaffolds. Our experimental results on bacterial and on conservative human assemblies show that, on average, our method can retrieve over 73 percent more safe and correct bases as compared to previous methods, with a similar precision.

With long reads getting even longer and cheaper, large scale sequencing projects can be accomplished without short reads at an affordable cost. Due to the high error rates and less mature tools, de novo assembly of long reads is still challenging and often results in a large collection of contigs. Dense linkage maps are collections of markers whose location on the genome is approximately known. Therefore they provide long range information that has the potential to greatly aid in de novo assembly. Previously linkage maps have been used to detect misassemblies and to manually order contigs. However, no fully automated tools exist to incorporate linkage maps in assembly but instead large amounts of manual labour is needed to order the contigs into chromosomes. We formulate the genome assembly problem in the presence of linkage maps and present the first method for guided genome assembly using linkage maps. Our method is based on an additional cleaning step added to the assembly. We show that it can simplify the underlying assembly graph, resulting in more contiguous assemblies and reducing the amount of misassemblies when compared to de novo assembly.

While long reads produced by third-generation sequencing technology from, e.g, Pacific Biosciences have been shown to increase the quality of draft genomes in repetitive regions, fundamental computational challenges remain in overcoming their high error rate and assembling them efficiently. In this paper we show that the de Bruijn graph built on the long reads can be efficiently and substantially disentangled using optical mapping data as auxiliary information. Fundamental to our approach is the use of the positional de Bruijn graph and a succinct data structure for constructing and traversing this graph. Our experimental results show that over 97.7% of directed cycles have been removed from the resulting positional de Bruijn graph as compared to its non-positional counterpart. Our results thus indicate that disentangling the de Bruijn graph using positional information is a promising direction for developing a simple and efficient assembly algorithm for long reads.

Motivation: New long read sequencing technologies, like PacBio SMRT and Oxford NanoPore, can produce sequencing reads up to 50 000 bp long but with an error rate of at least 15%. Reducing the error rate is necessary for subsequent utilization of the reads in, e.g. de novo genome assembly. The error correction problem has been tackled either by aligning the long reads against each other or by a hybrid approach that uses the more accurate short reads produced by second generation sequencing technologies to correct the long reads. Results: We present an error correction method that uses long reads only. The method consists of two phases: first, we use an iterative alignment-free correction method based on de Bruijn graphs with increasing length of k -mers, and second, the corrected reads are further polished using long-distance dependencies that are found using multiple alignments. According to our experiments, the proposed method is the most accurate one relying on long reads only for read sets with high coverage. Furthermore, when the coverage of the read set is at least 75×, the throughput of the new method is at least 20% higher. Availability and Implementation: LoRMA is freely available at http://www.cs.helsinki.fi/u/lmsalmel/LoRMA/ . Contact: [email protected].

MOTIVATION: PacBio single molecule real-time sequencing is a third-generation sequencing technique producing long reads, with comparatively 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 provides 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. Availability and implementaion: LoRDEC is written in C++, tested on Linux platforms and freely available at http://atgc.lirmm.fr/lordec.

BACKGROUND: For the development of genome assembly tools, some comprehensive and efficiently computable validation measures are required to assess the quality of the assembly. The mostly used N50 measure summarizes the assembly results by the length of the scaffold (or contig) overlapping the midpoint of the length-order concatenation of scaffolds (contigs). Especially for scaffold assemblies it is non-trivial to combine a correctness measure to the N50 values, and the current methods for doing this are rather involved. RESULTS: We propose a simple but rigorous normalized N50 assembly metric that combines N50 with such a correctness measure; assembly is split into as many parts as necessary to align each part to the reference. For scalability, we first compute maximal local approximate matches between scaffolds and reference in distributed manner, and then proceed with co-linear chaining to find a global alignment. Best alignment is removed from the scaffold and the process is iterated with the remaining scaffold content in order to split the scaffold into correctly aligning parts. The proposed normalized N50 metric is then the N50 value computed for the final correctly aligning parts. As a side result of independent interest, we show how to modify co-linear chaining to restrict gaps to produce a more sensible global alignment. CONCLUSIONS: We propose and implement a comprehensive and efficient approach to compute a metric that summarizes scaffold assembly correctness and length. Our implementation can be downloaded from http://www.cs.helsinki.fi/group/scaffold/normalizedN50/.

MOTIVATION: Assembling genomes from short read data has become increasingly popular, but the problem remains computationally challenging especially for larger genomes. We study the scaffolding phase of sequence assembly where preassembled contigs are ordered based on mate pair data. RESULTS: We present MIP Scaffolder that divides the scaffolding problem into smaller subproblems and solves these with mixed integer programming. The scaffolding problem can be represented as a graph and the biconnected components of this graph can be solved independently. We present a technique for restricting the size of these subproblems so that they can be solved accurately with mixed integer programming. We compare MIP Scaffolder to two state of the art methods, SOPRA and SSPACE. MIP Scaffolder is fast and produces better or as good scaffolds as its competitors on large genomes. AVAILABILITY: The source code of MIP Scaffolder is freely available at http://www.cs.helsinki.fi/u/lmsalmel/mip-scaffolder/. CONTACT: [email protected].

MOTIVATION: Current sequencing technologies produce a large number of erroneous reads. The sequencing errors present a major challenge in utilizing the data in de novo sequencing projects as assemblers have difficulties in dealing with errors. RESULTS: We present Coral which corrects sequencing errors by forming multiple alignments. Unlike previous tools for error correction, Coral can utilize also bases distant from the error in the correction process because the whole read is present in the alignment. Coral is easily adjustable to reads produced by different sequencing technologies like Illumina Genome Analyzer and Roche/454 Life Sciences sequencing platforms because the sequencing error model can be defined by the user. We show that our method is able to reduce the error rate of reads more than previous methods. AVAILABILITY: The source code of Coral is freely available at http://www.cs.helsinki.fi/u/lmsalmel/coral/.

MOTIVATION: High-throughput sequencing technologies produce large sets of short reads that may contain errors. These sequencing errors make de novo assembly challenging. Error correction aims to reduce the error rate prior assembly. Many de novo sequencing projects use reads from several sequencing technologies to get the benefits of all used technologies and to alleviate their shortcomings. However, combining such a mixed set of reads is problematic as many tools are specific to one sequencing platform. The SOLiD sequencing platform is especially problematic in this regard because of the two base color coding of the reads. Therefore, new tools for working with mixed read sets are needed. RESULTS: We present an error correction tool for correcting substitutions, insertions and deletions in a mixed set of reads produced by various sequencing platforms. We first develop a method for correcting reads from any sequencing technology producing base space reads such as the SOLEXA/Illumina and Roche/454 Life Sciences sequencing platforms. We then further refine the algorithm to correct the color space reads from the Applied Biosystems SOLiD sequencing platform together with normal base space reads. Our new tool is based on the SHREC program that is aimed at correcting SOLEXA/Illumina reads. Our experiments show that we can detect errors with 99% sensitivity and >98% specificity if the combined sequencing coverage of the sets is at least 12. We also show that the error rate of the reads is greatly reduced. AVAILABILITY: The JAVA source code is freely available at http://www.cs.helsinki.fi/u/lmsalmel/hybrid-shrec/ CONTACT: [email protected]