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

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 Cech complex. The Barycentric subcomplex allows a natural mapping of the reads along with their coverage of organisms while the Cech 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 Cech model that uses less information is equally effective, suggesting that even partial information when augmented with the appropriate structure is quite powerful.

AI-enabled evaluation of genome-wide association relevance and polygenic risk score prediction in Alzheimer's disease.

GWAS focuses on significance loosing false positives; machine learning probes sub-significant features relying on predictivity. Yet, these are far from orthogonal. We sought to explore how these inform each other in sub-genome-wide significant situations to define relevance for predictive features. We introduce the SVM-based RubricOE that selects heavily cross-validated feature sets, and LDpred2 PRS as a strong contrast to SVM, to explore significance and predictivity. Our Alzheimer's test case notoriously lacks strong genetic signals except for few very strong phenotype-SNP associations, which suits the problem we are exploring. We found that the most significant SNPs among ML and PRS-selected SNPs captured most of the predictivity, while weaker associations tend also to contribute weakly to predictivity. SNPs with weak associations tend not to contribute to predictivity, but deletion of these features does not injure it. Significance provides a ranking that helps identify weakly predictive features.

Simplicial complex entropy for time series analysis.

The complex behavior of many systems in nature requires the application of robust methodologies capable of identifying changes in their dynamics. In the case of time series (which are sensed values of a system during a time interval), several methods have been proposed to evaluate their irregularity. However, for some types of dynamics such as stochastic and chaotic, new approaches are required that can provide a better characterization of them. In this paper we present the simplicial complex approximate entropy, which is based on the conditional probability of the occurrence of elements of a simplicial complex. Our results show that this entropy measure provides a wide range of values with details not easily identifiable with standard methods. In particular, we show that our method is able to quantify the irregularity in simulated random sequences and those from low-dimensional chaotic dynamics. Furthermore, it is possible to consistently differentiate cardiac interbeat sequences from healthy subjects and from patients with heart failure, as well as to identify changes between dynamical states of coupled chaotic maps. Our results highlight the importance of the structures revealed by the simplicial complexes, which holds promise for applications of this approach in various contexts.