Signal enrichment with strain-level resolution in metagenomes using topological data analysis

Abstract

Background A metagenome is a collection of genomes, usually in a micro-environment, and sequencing a metagenomic sample en masse is a powerful means for investigating the community of the constituent microorganisms. One of the challenges is in distinguishing between similar organisms due to rampant multiple possible assignments of sequencing reads, resulting in false positive identifications. We map the problem to a topological data analysis (TDA) framework that extracts information from the geometric structure of data. Here the structure is defined by multi-way relationships between the sequencing reads using a reference database. Results Based primarily on the patterns of co-mapping of the reads to multiple organisms in the reference database, we use two models: one a subcomplex of a Barycentric subdivision complex and the other a Čech complex. The Barycentric subcomplex allows a natural mapping of the reads along with their coverage of organisms while the Čech complex takes simply the number of reads into account to map the problem to homology computation. Using simulated genome mixtures we show not just enrichment of signal but also microbe identification with strain-level resolution. Conclusions In particular, in the most refractory of cases where alternative algorithms that exploit unique reads (i.e., mapped to unique organisms) fail, we show that the TDA approach continues to show consistent performance. The Čech model that uses less information is equally effective, suggesting that even partial information when augmented with the appropriate structure is quite powerful.

Navigating the COVID-19 Data Landscape: Automated Hypothesis Generation using Topological Data Analysis

“…TDA and Applications TDA has several key advantages over traditional data analysis and dimensionality reduction techniques such as PCA, multi-dimensional scaling, and cluster analysis, owing to its robustness, visualization capabilities, and coordinate-free properties [15]. Since initial work on the Mapper framework by Singh et al [19], TDA has gained wider use with a demonstrated ability to glean insightful structural information in the context of many applications such as cancer [14], microbial ecology [8], wildfires [2], agricultural phenomics [12], and more. To the best of our knowledge, our effort represents one of the first to adopt TDA for epidemics.…”

Harmonic Persistent Homology

“…The first important contribution of the current paper is that we prove concrete stability results for harmonic persistence homology in the context of general filtrations of simplicial complexes (without any underlying assumption that the simplicial complex is approximating some Riemannian manifold). This is very important in applications (such as in genomics) where persistent homology methods are applied to "relationship" data as opposed to point-cloud data from some R n (see [27] and also [25,21,22,28] for recent representative examples of such applications). The stability results proved in this paper allow us to infer that harmonic persistence theory is applicable when topological data analysis is used outside the context of manifold learning (such as in genomics).…”