Safety in Multi-Assembly via Paths Appearing in All Path Covers of a DAG

Abstract

A multi-assembly problem asks to reconstruct multiple genomic sequences from mixed reads sequenced from all of them. Standard formulations of such problems model a solution as a path cover in a directed acyclic graph, namely a set of paths that together cover all vertices of the graph. Since multi-assembly problems admit multiple solutions in practice, we consider an approach commonly used in standard genome assembly: output only partial solutions (contigs, or safe paths), that appear in all path cover solutions. We study constrained path covers, a restriction on the path cover solution that incorporate practical constraints arising in multi-assembly problems. We give efficient algorithms finding all maximal safe paths for constrained path covers. We compute the safe paths of splicing graphs constructed from transcript annotations of different species. Our algorithms run in less than 15 seconds per species and report RNA contigs that are over 99% precise and are up to 8 times longer than unitigs. Moreover, RNA contigs cover over 70% of the transcripts and their coding sequences in most cases. With their increased length to unitigs, high precision, and fast construction time, maximal safe paths can provide a better base set of sequences for transcript assembly programs.

Safety and Completeness in Flow Decompositions for RNA Assembly

“…This approach starts with a candidate solution and uses the characterization on its subpaths in an efficient manner (a similar approach was previously used by [16,1,11]). The solution of the algorithm is reported using a compact representation (referred as P c ), whose size can be Ω(mn) is the worst case but merely O(m + n) in the best case.…”

“…Safe and complete algorithms were also studied by Acosta et al [1] under a different genome assembly formulation of multiple circular walks. Recently, Cáceres et al [11] studied safe and complete algorithms for path covers in an application on RNA Assembly.…”

“…In addition, T denotes a path in the set of ground truth transcripts provided in the dataset. For each graph, we compute the following metrics which were also used earlier by [11] for safety in constrained path covers:…”

Improving RNA Assembly via Safety and Completeness in Flow Decompositions

“…This approach was also used by transcript assemblers modeling the problem as a minimum path cover (Liu and Dickerson, 2017 ; Trapnell et al, 2010 ), which can be solved in polynomial time [see Cáceres et al (2021) for a comprehensive survey on the problem]. However, even when the solution is restricted to minimum cardinality, multiple solutions still arise (Caceres et al, 2021 ; Williams et al, 2021 ). Therefore, practical methods usually incorporate different variations of the minimum-cardinality criterion (Baaijens et al, 2020 ; Baaijens et al, 2019 ; Bernard et al, 2013).…”

“…Recently, Caceres et al ( 2021 ) studied safe and complete algorithms for path covers in an application on RNA assembly. They optimized an avoid-and-test approach for computing all maximal safe paths for constrained path covers , which were able to cover 70% of transcripts with a precision of more than 99% on splice graphs built from transcript annotation.…”