Geometric Quantification of Cell Phenotype Transition Manifolds with Information Geometry

Abstract

Cell phenotype transition (CPT) plays a pivotal role in various biological processes like development. Recent advancements in single-cell sequencing techniques have uncovered that cell transition dynamics during development are confined on low-dimensional manifolds. However, existing methods are inadequate for directly quantifying the manifolds from experimental data. Here we present SCIM (single cell information manifolds), a novel geometry-guided method to quantify the CPT manifolds using information geometry. In particular, we convert single cells’ high-dimensional gene vectors into probability distributions via Gaussian embedding. The Fisher metric is naturally defined in this embedding space. With the transformed Gaussian distributions, we calculate the coarse Ricci curvature of each single cell. Our analyses reveal that the cells with low curvature are associated with critical transitions. To further examine the invariant characteristics of the manifolds of CPT, we compute the information velocity of each single cell based on RNA velocity. Remarkably, the regions with high information velocity correspond with the low curvature regions, indicating that the geometry can guide the dynamics of single cells on the manifolds. The proposed method not only unveils the invariant characteristics of the CPT manifolds, but also establishes a generic approach for quantifying the intricate dynamics on the CPT manifolds.