Revealing tissue architecture through the hypercomplex Fourier analysis of spatial transcriptomics data

Area of Science:

• Computational Biology
• Bioinformatics
• Data Science

Background:

• Spatial transcriptomics (ST) generates high-resolution gene expression data.
• Analyzing complex ST data requires advanced computational methods.
• Quaternions, hypercomplex numbers, are traditionally used in computer graphics.

Purpose of the Study:

• To develop a novel approach for analyzing spatial transcriptomics data.
• To leverage quaternion mathematics for enhanced ST data representation and analysis.
• To enable new visualization techniques for transcriptomic data.

Main Methods:

• Utilizing a quaternion-domain discrete Fourier transform for ST data analysis.
• Representing ST data locations with quaternions, encoding sequencing depth and transcriptomic features.
• Applying Fourier-based image analysis techniques to multidimensional ST data.

Main Results:

• The proposed model represents transcriptomic states as 3D rotations using quaternions.
• This enables powerful Fourier-based analysis and visualization of ST data.
• Demonstrated effectiveness on Visium HD data, with potential for single-cell RNA-sequencing data.

Conclusions:

• Quaternion-based analysis offers a powerful new framework for spatial transcriptomics.
• The method facilitates novel visualizations capturing transcriptomic uncertainty.
• An R package (QSC) is available for implementing hypercomplex Fourier analysis of ST data.