Co-Linear Chaining on Pangenome Graphs

Pangenome reference graphs are useful in genomics because they compactly represent the genetic diversity within a species, a capability that linear references lack. However, efficiently aligning sequences to these graphs with complex topology and cycles can be challenging. The seed-chain-extend based alignment algorithms use co-linear chaining as a standard technique to identify a good cluster of exact seed matches that can be combined to form an alignment. Recent works show how the co-linear chaining problem can be efficiently solved for acyclic pangenome graphs by exploiting their small width [Makinen et al., TALG\u2719] and how incorporating gap cost in the scoring function improves alignment accuracy [Chandra and Jain, RECOMB\u2723]. However, it remains open on how to effectively generalize these techniques for general pangenome graphs which contain cycles. Here we present the first practical formulation and an exact algorithm for co-linear chaining on cyclic pangenome graphs. We rigorously prove the correctness and computational complexity of the proposed algorithm. We evaluate the empirical performance of our algorithm by aligning simulated long reads from the human genome to a cyclic pangenome graph constructed from 95 publicly available haplotype-resolved human genome assemblies. While the existing heuristic-based algorithms are faster, the proposed algorithm provides a significant advantage in terms of accuracy

Long read mapping at scale: Algorithms and applications

Capability to sequence DNA has been around for four decades now, providing ample time to explore its myriad applications and the concomitant development of bioinformatics methods to support them. Nevertheless, disruptive technological changes in sequencing often upend prevailing protocols and characteristics of what can be sequenced, necessitating a new direction of development for bioinformatics algorithms and software. We are now at the cusp of the next revolution in sequencing due to the development of long and ultra-long read sequencing technologies by Pacific Biosciences (PacBio) and Oxford Nanopore Technologies (ONT). Long reads are attractive because they narrow the scale gap between sizes of genomes and sizes of sequenced reads, with the promise of avoiding assembly errors and repeat resolution challenges that plague short read assemblers. However, long reads themselves sport error rates in the vicinity of 10-15%, compared to the high accuracy of short reads (< 1%). There is an urgent need to develop bioinformatics methods to fully realize the potential of long-read sequencers. Mapping and alignment of reads to a reference is typically the first step in genomics applications. Though long read technologies are still evolving, research efforts in bioinformatics have already produced many alignment-based and alignment-free read mapping algorithms. Yet, much work lays ahead in designing provably efficient algorithms, formally characterizing the quality of results, and developing methods that scale to larger input datasets and growing reference databases. While the current model to represent the reference as a collection of linear genomes is still favored due to its simplicity, mapping to graph-based representations, where the graph encodes genetic variations in a human population also becomes imperative. This dissertation work is focused on provably good and scalable algorithms for mapping long reads to both linear and graph references. We make the following contributions: 1. We develop fast and approximate algorithms for end-to-end and split mapping of long reads to reference genomes. Our work is the first to demonstrate scaling to the entire NCBI database, the collection of all curated and non-redundant genomes. 2. We generalize the mapping algorithm to accelerate the related problems of computing pairwise whole-genome comparisons. We shed light on two fundamental biological questions concerning genomic duplications and delineating microbial species boundaries. 3. We provide new complexity results for aligning reads to graphs under Hamming and edit distance models to classify the problem variants for which existence of a polynomial time solution is unlikely. In contrast to prior results that assume alphabets as a function of the problem size, we prove that the problem variants that allow edits in graph remain NP-complete for even constant-sized alphabets, thereby resolving computational complexity of the problem for DNA and protein sequence to graph alignments. 4. Finally, we propose a new parallel algorithm to optimally align long reads to large variation graphs derived from human genomes. It demonstrates near linear scaling on multi-core CPUs, resulting in run-time reduction from multiple days to three hours when aligning a long read set to an MHC human variation graph.Ph.D