An expectation–maximization algorithm for estimating proportions of deletions among bacterial populations with application to study antibiotic resistance gene transfer in Enterococcus faecalis

The emergence of antibiotic resistance in bacteria limits the availability of antibiotic choices for treatment and infection control, thereby representing a major threat to human health. The de novo mutation of bacterial genomes is an essential mechanism by which bacteria acquire antibiotic resistance. Previously, deletion mutations within bacterial immune systems, ranging from dozens to thousands of base pairs (bps) in length, have been associated with the spread of antibiotic resistance. Most current methods for evaluating genomic structural variations (SVs) have concentrated on detecting them, rather than estimating the proportions of populations that carry distinct SVs. A better understanding of the distribution of mutations and subpopulations dynamics in bacterial populations is needed to appreciate antibiotic resistance evolution and movement of resistance genes through populations. Here, we propose a statistical model to estimate the proportions of genomic deletions in a mixed population based on Expectation–Maximization (EM) algorithms and next-generation sequencing (NGS) data. The method integrates both insert size and split-read mapping information to iteratively update estimated distributions. The proposed method was evaluated with three simulations that demonstrated the production of accurate estimations. The proposed method was then applied to investigate the horizontal transfers of antibiotic resistance genes in concert with changes in the CRISPR-Cas system of E. faecalis.