The Metagenomic Binning Problem: Clustering Markov Sequences

Abstract

The goal of metagenomics is to study the composition of microbial communities, typically using high-throughput shotgun sequencing. In the metagenomic binning problem, we observe random substrings (called contigs) from a mixture of genomes and want to cluster them according to their genome of origin. Based on the empirical observation that genomes of different bacterial species can be distinguished based on their tetranucleotide frequencies, we model this task as the problem of clustering N sequences generated by M distinct Markov processes, where M N . Utilizing the large-deviation principle for Markov processes, we establish the information-theoretic limit for perfect binning. Specifically, we show that the length of the contigs must scale with the inverse of the Chernoff Information between the two most similar species. Our result also implies that contigs should be binned using the conditional relative entropy as a measure of distance, as opposed to the Euclidean distance often used in practice.

Improving Bacterial Genome Assembly Using a Test of Strand Orientation

“…We first define two information-theoretic measures (Moulin and Veeravalli, 2018;Cover and Thomas, 2006;Greenberg and Shomorony, 2019) used in the properties following.…”

“…In order to develop a mathematically sound TNF-based orientation test, we utilize a probabilistic model for generating a genome with a given TNF. This model is based on a framework previously used to study the information-theoretic limits of metagenomic binning (Greenberg and Shomorony, 2019). Note that an i.i.d.…”