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Spatial Profiling of Protein and RNA Expression in Tissue: An Approach to Fine-Tune Virtual Microdissection
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Revealing tissue architecture through the hypercomplex Fourier analysis of spatial transcriptomics data.

Hildreth Robert Frost1

  • 1Biomedical Data Science, Dartmouth College, Hanover, NH 03755, United States.

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|November 6, 2025
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Summary
This summary is machine-generated.

We introduce a novel method using quaternion Fourier transforms for spatial transcriptomics (ST) data analysis. This approach represents transcriptomic features as rotations, enabling advanced visualization and analysis of ST data.

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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.