A Probabilistic Analysis of Shotgun Sequencing for Metagenomics

Abstract

Genome sequencing is the basis for many modern biological and medicinal studies. With recent technological advances, metagenomics has become a problem of interest. This problem entails the analysis and reconstruction of multiple DNA sequences from different sources. Shotgun genome sequencing works by breaking up long DNA sequences into shorter segments called reads. Given this collection of reads, one would like to reconstruct the original collection of DNA sequences. For experimental design in metagenomics, it is important to understand how the minimal read length necessary for reliable reconstruction depends on the number and characteristics of the genomes involved. Utilizing simple probabilistic models for each DNA sequence, we analyze the identifiability of collections of M genomes of length N in an asymptotic regime in which N tends to infinity and M may grow with N. Our first main result provides a threshold in terms of M and N so that if the read length exceeds the threshold, then a simple greedy algorithm successfully reconstructs the full collection of genomes with probability tending to one. Our second main result establishes a lower threshold in terms of M and N such that if the read length is shorter than the threshold, then reconstruction of the full collection of genomes is impossible with probability tending to one.