Relational Persistent Homology for Multispecies Data with Application to the Tumor Microenvironment

Area of Science:

• Mathematics
• Computational Biology
• Data Science

Background:

• Topological Data Analysis (TDA) and persistent homology (PH) traditionally analyze single-entity data.
• Modern data collection yields complex multispecies datasets requiring relational analysis.
• Applications span biomedical imaging, geospatial analysis, and species ecology.

Purpose of the Study:

• Develop novel TDA methods for quantifying spatial relations in multispecies data.
• Adapt Dowker complexes and Witness complexes for heterogeneous data analysis.
• Apply methods to tumor microenvironment data to extract biological insights.

Main Methods:

• Proposed two novel methods for encoding spatial relations among different data types.
• Utilized Dowker complexes and Witness complexes as foundational frameworks.
• Applied methods to synthetic multispecies tumor microenvironment data.

Main Results:

• Identified topological features capturing inter-species cell type relations (e.g., tumor cells, immune cells).
• Extracted significant biological insights, including dominant immune cell phenotype.
• Demonstrated ability to infer parameter regimes of data-generating models.

Conclusions:

• Developed quantitative methods for relational analysis of multispecies spatial data.
• Overcame limitations of traditional persistent homology for complex datasets.
• Methods are readily computable and offer new perspectives in TDA.