Geometric Quantification of Cell Phenotype Transition Manifolds with Information Geometry

Abstract

Cell phenotype transition (CPT) is crucial in development and other biological processes. Advances in single-cell sequencing reveal that CPT dynamics are confined to low-dimensional manifolds, yet current methods cannot directly quantify these manifolds. We present SCIM (single cell information manifolds), a geometry-guided approach using information geometry. SCIM embeds single-cell gene expression profiles as Gaussian distributions, defining the Fisher metric naturally in this space. We compute each cells coarse Ricci curvature, finding that low-curvature cells mark critical transitions. By further calculating each cells information velocity from RNA velocity, we find that regions with high information velocity coincide with low curvature, suggesting that geometry guides cellular dynamics on CPT manifolds. SCIM uncovers invariant features of CPT manifolds and provides a general framework for quantifying dynamics on these manifolds.