Interpretable spherical geometry of single-cell state transitions from dominant principal components
- 1Johns Hopkins University
Abstract
Single-cell RNA-seq atlases are commonly explored with nonlinear embeddings that preserve neighborhoods but provide limited coordinate-level interpretation. We asked whether projecting the dominant principal components (PCs) of single-cell gene expression onto a unit sphere would yield an interpretable coordinate system. SPHERE-PCA L2-normalizes the first three PC coordinates, aligns a biologically defined root to the north pole, and represents each cell by three coordinates: root-aligned geodesic distance ({theta}), angular position ({phi}), and pre-projection radial magnitude (r). Across developmental and disease-associated datasets, this representation reveals structured spherical geometry, ranging from near-great-circle trajectories to multi-arc manifolds. In developmental atlases, root-aligned geodesic distance increases as CytoTRACE-inferred stemness decreases, while gene-coordinate analyses separate programs associated with angular position from those associated with radial magnitude. Fixed-loading perturbations decompose each gene's effect on cell position into progression, branch- or state-position, and radial activity components. SPHERE-PCA therefore provides a deterministic, loading-preserving coordinate framework for interpreting dominant transcriptomic variance and establishing a transparent geometric coordinate framework for perturbation analysis and virtual-cell models.
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BibTeX
@misc{yuan2026interpretable,
title = {{Interpretable spherical geometry of single-cell state transitions from dominant principal components}},
author = {L. Yuan and X. Li and M. Le and S. C. Hicks and A. Deshpande and J. M. Taube and A. S. Szalay},
howpublished = {bioRxiv},
year = {2026},
month = sep,
doi = {10.64898/2026.09.11.751061},
url = {https://www.biorxiv.org/content/10.64898/2026.09.11.751061v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Interpretable spherical geometry of single-cell state transitions from dominant principal components
AU - L. Yuan
AU - X. Li
AU - M. Le
AU - S. C. Hicks
AU - A. Deshpande
AU - J. M. Taube
AU - A. S. Szalay
PY - 2026
DA - 2026/09/11
PB - bioRxiv
DO - 10.64898/2026.09.11.751061
UR - https://www.biorxiv.org/content/10.64898/2026.09.11.751061v1
AB - Single-cell RNA-seq atlases are commonly explored with nonlinear embeddings that preserve neighborhoods but provide limited coordinate-level interpretation. We asked whether projecting the dominant principal components (PCs) of single-cell gene expression onto a unit sphere would yield an interpretable coordinate system. SPHERE-PCA L2-normalizes the first three PC coordinates, aligns a biologically defined root to the north pole, and represents each cell by three coordinates: root-aligned geodesic distance ({theta}), angular position ({phi}), and pre-projection radial magnitude (r). Across developmental and disease-associated datasets, this representation reveals structured spherical geometry, ranging from near-great-circle trajectories to multi-arc manifolds. In developmental atlases, root-aligned geodesic distance increases as CytoTRACE-inferred stemness decreases, while gene-coordinate analyses separate programs associated with angular position from those associated with radial magnitude. Fixed-loading perturbations decompose each gene's effect on cell position into progression, branch- or state-position, and radial activity components. SPHERE-PCA therefore provides a deterministic, loading-preserving coordinate framework for interpreting dominant transcriptomic variance and establishing a transparent geometric coordinate framework for perturbation analysis and virtual-cell models.
ER -