A safe and complete algorithm for metagenomic assembly

Veli Mäkinen,Nidia Obscura Acosta,Alexandru I. Tomescu

doi:10.1186/s13015-018-0122-7

Abstract

BackgroundReconstructing the genome of a species from short fragments is one of the oldest bioinformatics problems. Metagenomic assembly is a variant of the problem asking to reconstruct the circular genomes of all bacterial species present in a sequencing sample. This problem can be naturally formulated as finding a collection of circular walks of a directed graph G that together cover all nodes, or edges, of G.ApproachWe address this problem with the “safe and complete” framework of Tomescu and Medvedev (Research in computational Molecular biology—20th annual conference, RECOMB 9649:152–163, 2016). An algorithm is called safe if it returns only those walks (also called safe) that appear as subwalk in all metagenomic assembly solutions for G. A safe algorithm is called complete if it returns all safe walks of G.ResultsWe give graph-theoretic characterizations of the safe walks of G, and a safe and complete algorithm finding all safe walks of G. In the node-covering case, our algorithm runs in time O(m^2 + n^3), and in the edge-covering case it runs in time O(m^2n); n and m denote the number of nodes and edges, respectively, of G. This algorithm constitutes the first theoretical tight upper bound on what can be safely assembled from metagenomic reads using this problem formulation.

Highlights

Reconstructing the genome of a species from short fragments is one of the oldest bioinformatics problems
In the node-covering case, our algorithm runs in time O(m2 + n3), and in the edge-covering case it runs in time O(m2n); n and m denote the number of nodes and edges, respectively, of G. This algorithm constitutes the first theoretical tight upper bound on what can be safely assembled from metagenomic reads using this problem formulation
One of the oldest bioinformatics problems is to reconstruct the genome of an individual from short fragments sequenced from it, called reads

Summary

Introduction

Reconstructing the genome of a species from short fragments is one of the oldest bioinformatics problems. For any node-covering metagenomic reconstruction R and any C ∈ R containing w as sub-walk, we replace C with the circular walk C′ obtained as follows. Our characterization of the edge-safe walks considered in this paper is: Theorem 4 Let G be a strongly connected graph.

Results

Conclusion