GraphFP

GraphFP reconstructs potential energy landscapes of cell-state transitions from time-series single-cell RNA sequencing (scRNA-seq) data to quantify stochastic cellular dynamics and cell–cell interactions.

Key Features:

• Nonlinear Fokker-Planck Equation on Graphs: Implements a nonlinear Fokker-Planck equation on graphs to represent and analyze cell–cell interactions in evolving cellular populations.
• Dynamic Inference Framework: Infers cellular transition processes by reconstructing potential energy landscapes using a dynamic optimal transport framework solved with the adjoint method of optimal control.
• Reconstruction of Cell State Potential Energy: Reconstructs potential energy of cell states to infer differentiation potency and to chart probability flows between paired cell states during dynamic processes such as cell differentiation.
• Quantification of Stochastic Dynamics: Models cell-type frequencies on a probability simplex in continuous time to quantify stochastic dynamics of cellular transitions.
• Robustness and Flexibility: Maintains robustness across cluster labeling resolutions and parameter choices.
• Model-Based Delineation of Cell-Cell Interactions: Includes a nonlinear quadratic term to explicitly incorporate and delineate cell–cell interactions driving differentiation.

Scientific Applications:

• Embryonic murine cerebral cortex development: Applied to time-series scRNA-seq from embryonic murine cerebral cortex development to evaluate dynamic cell-state transitions.
• Developmental biology: Maps differentiation trajectories and energy landscapes in developmental systems.
• Cancer progression: Analyzes tumor cell-state transitions and stochastic dynamics relevant to cancer progression.
• Regenerative medicine: Characterizes dynamic cellular processes relevant to tissue regeneration and reprogramming.

Methodology:

Formulates a nonlinear Fokker-Planck equation on graphs and recasts model inference as a dynamic optimal transport problem solved via the adjoint method of optimal control, incorporating a nonlinear quadratic interaction term and modeling cell-type frequencies on a continuous-time probability simplex.