Genomics data analysis via spectral shape and topology.

Area of Science:

• Computational Biology
• Genomics
• Data Visualization

Background:

• High-dimensional genomic data analysis often loses crucial information with standard methods.
• Topological data analysis, specifically Mapper, offers a graphical approach to understand complex data structures.
• Statistical analysis tools for Mapper outputs are currently limited.

Purpose of the Study:

• To develop and validate a novel workflow for RNA-sequencing data analysis integrating Mapper, differential gene expression, and spectral shape analysis.
• To identify distinct subgroups within tumor samples and understand their underlying gene regulation patterns.
• To establish a statistical framework for analyzing Mapper graphical structures.

Main Methods:

• Integration of Mapper algorithm with Gaussian mixture approximation for data clustering.
• Differential gene expression analysis using DESeq2.
• Development of a scoring method based on heat kernel signatures for statistical inference on Mapper graphs.

Main Results:

• The proposed workflow successfully separates tumor and healthy subjects based on RNA-seq data.
• Two distinct subgroups of tumor subjects were identified, each exhibiting unique gene expression profiles.
• These subgroups suggest two discrete pathways in lung cancer formation, surpassing the resolution of methods like t-SNE.
• A novel statistical scoring method for Mapper graphical structures was developed.

Conclusions:

• The integrated Mapper-based workflow provides a powerful approach for uncovering hidden structures in high-dimensional genomic data.
• This method can identify distinct subtypes of cancer, offering insights into disease heterogeneity and potential therapeutic targets.
• The developed statistical framework enhances the utility of Mapper for rigorous scientific investigation and hypothesis testing.