Dynamic inference of cell developmental complex energy landscape from time series single-cell transcriptomic data.

Area of Science:

• Computational Biology
• Developmental Biology
• Systems Biology

Background:

• Time series single-cell RNA sequencing (scRNA-seq) data enable studying cellular dynamics.
• Inferring cell population evolution from scRNA-seq is complex due to biological stochasticity and nonlinearity.
• Advanced mathematical models are needed to reconstruct dynamic cell transitions and interactions.

Purpose of the Study:

• To develop GraphFP, a novel framework for dynamic inference from time series scRNA-seq data.
• To reconstruct cell state-transition potential energy landscapes and uncover nonlinear cell-cell interactions.
• To provide a robust method for analyzing cellular differentiation processes.

Main Methods:

• GraphFP utilizes a nonlinear Fokker-Planck equation on a graph.
• The model incorporates cell-cell interactions via a nonlinear quadratic term in free energy.
• Inference is framed as a dynamic optimal transport problem, solved using optimal control adjoint methods.

Main Results:

• GraphFP successfully reconstructs cell state potential energy, indicating cellular differentiation potency.
• The framework accurately maps probability flows between cell states during differentiation.
• It quantifies stochastic cell type frequency dynamics on a probability simplex in continuous time.
• GraphFP demonstrates robustness to variations in clustering resolution and parameter choices.

Conclusions:

• GraphFP offers a powerful, model-based approach to analyze cell differentiation dynamics from scRNA-seq data.
• The framework effectively delineates cell-cell interactions driving developmental processes.
• GraphFP provides insights into the complex potential energy landscape governing cell state transitions.