HAT: Hypergraph analysis toolbox.

Recent advances in biological technologies, such as multi-way chromosome conformation capture (3C), require development of methods for analysis of multi-way interactions. Hypergraphs are mathematically tractable objects that can be utilized to precisely represent and analyze multi-way interactions. Here we present the Hypergraph Analysis Toolbox (HAT), a software package for visualization and analysis of multi-way interactions in complex systems.

Biomarker Selection for Adaptive Systems.

Biomarkers enable objective monitoring of a given cell or state in a biological system and are widely used in research, biomanufacturing, and clinical practice. However, identifying appropriate biomarkers that are both robustly measurable and capture a state accurately remains challenging. We present a framework for biomarker identification based upon observability guided sensor selection. Our methods, Dynamic Sensor Selection (DSS) and Structure-Guided Sensor Selection (SGSS), utilize temporal models and experimental data, offering a template for applying observability theory to unconventional data obtained from biological systems. Unlike conventional methods that assume well-known, fixed dynamics, DSS adaptively select biomarkers or sensors that maximize observability while accounting for the time-varying nature of biological systems. Additionally, SGSS incorporates structural information and diverse data to identify sensors which are resilient against inaccuracies in our model of the underlying system. We validate our approaches by performing estimation on high dimensional systems derived from temporal gene expression data from partial observations.

Deciphering multi-way interactions in the human genome.

Chromatin architecture, a key regulator of gene expression, can be inferred using chromatin contact data from chromosome conformation capture, or Hi-C. However, classical Hi-C does not preserve multi-way contacts. Here we use long sequencing reads to map genome-wide multi-way contacts and investigate higher order chromatin organization in the human genome. We use hypergraph theory for data representation and analysis, and quantify higher order structures in neonatal fibroblasts, biopsied adult fibroblasts, and B lymphocytes. By integrating multi-way contacts with chromatin accessibility, gene expression, and transcription factor binding, we introduce a data-driven method to identify cell type-specific transcription clusters. We provide transcription factor-mediated functional building blocks for cell identity that serve as a global signature for cell types.