2023/08/11 by Bernadette J. Stolz, Stolz, Bernadette J., Jagdeep Dhesi +9 · 4 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Neuroscience · #55N31 #92C17 #Algebraic Topology (math.AT) #Cell Behavior (q-bio.CB) #FOS: Biological sciences #FOS: Mathematics #Neuroinflammation and Neurodegeneration Mechanisms #Quantitative Methods (q-bio.QM) #Single-cell and spatial transcriptomics #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2308.06205
openalex publication_date 2023/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Topological data analysis (TDA) is an active field of mathematics for quantifying shape in complex data. Standard methods in TDA such as persistent homology (PH) are typically focused on the analysis of data consisting of a single entity (e.g., cells or molecular species). However, state-of-the-art data collection techniques now generate exquisitely detailed multispecies data, prompting a need for methods that can examine and quantify the relations among them. Such heterogeneous data types arise in many contexts, ranging from biomedical imaging, geospatial analysis, to species ecology. Here, we propose two methods for encoding spatial relations among different data types that are based on Dowker complexes and Witness complexes. We apply the methods to synthetic multispecies data of a tumor microenvironment and analyze topological features that capture relations between different cell types, e.g., blood vessels, macrophages, tumor cells, and necrotic cells. We demonstrate that relational topological features can extract biological insight, including the dominant immune cell phenotype (an important predictor of patient prognosis) and the parameter regimes of a data-generating model. The methods provide a quantitative perspective on the relational analysis of multispecies spatial data, overcome the limits of traditional PH, and are readily computable.