Geometric multidimensional representation of omic signatures

Area of Science:

• Systems Biology
• Computational Biology
• Bioinformatics

Background:

• Multi-omic signatures are crucial for biomarker discovery and precision oncology.
• Current methods often reduce complex biological data to simplistic one-dimensional summaries, losing valuable organizational information.

Purpose of the Study:

• To introduce a novel geometric framework for reconceptualizing and analyzing multi-omic signatures.
• To preserve and measure the intrinsic multidimensional structure and functional coherence of omic data.

Main Methods:

• Developed a geometric framework representing omic signatures as convex polytopes in a shared latent space.
• Integrated regulatory, phenotypic, microenvironmental, immune, and clinical data.
• Applied geometric measurements (e.g., volume, asymmetry) to analyze 24,796 metabolic regulatory circuitries across 32 TCGA cancer types.

Main Results:

• Geometric analysis revealed predominant discordance in metabolic regulatory circuitries, with most exhibiting high-dimensional and asymmetric geometries.
• Fully concordant circuitries were rare and structurally constrained.
• Identified reproducible stratification patterns of metabolic pathways based on geometric phenotypes, surpassing conventional methods.

Conclusions:

• The geometric framework transforms omic signatures into measurable geometric objects, enabling principled comparison and de-redundancy of multi-omic biomarkers.
• Provides a scalable method for analyzing complex biological systems in cancer and other fields.
• The SigPolytope Shiny application offers access to geometric representations and descriptors.