Geometry-preserving vector field reconstruction of high-dimensional cell-state dynamics using ddHodge.

Area of Science:

• Computational Biology
• Developmental Biology
• Genomics

Background:

• Cell differentiation involves dynamic gene expression changes, crucial for development.
• Single-cell RNA sequencing (scRNA-seq) provides data to infer these dynamics.
• Existing velocity-based methods struggle with data sparsity and high dimensionality to capture acceleration.

Purpose of the Study:

• To develop a robust computational framework for precise vector-field reconstruction from scRNA-seq data.
• To extract second-order derivative information, including cell state acceleration.
• To analyze gene expression dynamics and quantify differentiation potency.

Main Methods:

• Developed ddHodge, a framework utilizing Hodge decomposition for vector-field reconstruction.
• Extended ddHodge to approximate high-dimensional gene expression dynamics on low-dimensional manifolds.
• Applied ddHodge to scRNA-seq data from mouse embryogenesis.

Main Results:

• ddHodge accurately recovers vector field components (gradient, curl, divergence) and cell state acceleration.
• Revealed gene expression dynamics during development follow a potential landscape gradient system.
• Quantified differentiation potency using divergence and identified key potency-driving genes.

Conclusions:

• ddHodge provides a general computational framework for analyzing complex biological systems.
• The study elucidates cell fate decisions in developmental processes using real data.
• Identified potential landscapes and key genes governing differentiation potency.