# Topological data analysis captures horizontal gene transfer in antimicrobial resistance gene families among clinically relevant bacteria

## TL;DR

This paper shows how topological data analysis can detect horizontal gene transfer in antibiotic resistance genes among bacteria, offering a new way to study resistance spread without genomic sequences.

## Contribution

The paper introduces the use of persistent homology to identify horizontal gene transfer patterns in resistomes using topological 1-holes.

## Key findings

- Simulations show two 1-holes form for every three genomes undergoing horizontal gene transfer.
- 1-holes were confirmed in a documented case of horizontal gene transfer between two bacterial genera.
- Klebsiella and Escherichia resistomes show 1-holes, while Enterobacter does not.

## Abstract

Antibiotic resistance, projected to cause 10 million deaths annually by 2050, remains a critical health threat. Hospitals drive multidrug resistance via horizontal gene transfer. The 2023 Critical Assessment of Massive Data Analysis challenge presents resistance markers from 146 Johns Hopkins bacterial isolates, aiming to analyze resistomes without metadata or genomic sequences. Persistent homology, a topological data analysis method, effectively captures processes beyond vertical inheritance. A 1-hole is a topological feature representing a loop or gap in the data, where relationships form a circular structure rather than a linear one. Unlike vertical inheritance, which lacks topological 1-holes, horizontal gene transfer generates distinct patterns. Since antimicrobial resistance genes often spread via horizontal gene transfer, we simulated vertical and horizontal inheritance in bacterial resistomes. The number of 1-holes from simulations and a documented horizontal gene transfer case was analyzed using persistence barcodes. In a simulated population of binary sequences, we observed that, on average, two 1-holes form for every three genomes undergoing horizontal gene transfer. Using a presence-absence gene table, we confirmed the existence of 1-holes in a documented case of horizontal gene transfer between two bacterial genera in a Pittsburgh hospital. Notably, the Critical Assessment of Massive Data Analysis resistomes of Klebsiella and Escherichia exhibit 1-holes, while Enterobacter shows none. Lastly, we provide a mathematical example of a non-tree-like space that contains no 1-holes. Persistent homology provides a framework for uncovering complex clinical patterns, offering an alternative to understanding resistance mobility using presence-absence data, which could be obtained through methods beyond genomic sequencing.