A physics-informed neural SDE network for learning cellular dynamics from time-series scRNA-seq data.

Area of Science:

• Computational Biology
• Systems Biology
• Single-cell Genomics

Background:

• Reconstructing cellular potential energy landscapes (Waddington landscapes) from time-series single-cell RNA sequencing (scRNA-seq) data is crucial for understanding cell dynamics.
• Current data-driven methods often lack physical principles, limiting prediction accuracy and interpretability.

Purpose of the Study:

• To develop a physics-informed framework, PI-SDE, for accurate and interpretable reconstruction of cellular dynamics.
• To integrate physical principles, specifically the Hamilton-Jacobi equation, into neural stochastic differential equations for learning from scRNA-seq data.

Main Methods:

• Proposed PI-SDE, a physics-informed neural stochastic differential equation (SDE) framework.
• Combined Hamilton-Jacobi (HJ) equation with neural SDE, enforcing the HJ equation to reconstruct the cellular potential energy function based on potential energy theory.
• Integrated the principle of least action into the learning process.

Main Results:

• PI-SDE demonstrated improved prediction accuracy for gene expression at held-out time points on real scRNA-seq datasets.
• The reconstructed potential energy landscape provided biologically interpretable insights into cell differentiation.
• The framework showed enhanced model performance, robustness, and stability.

Conclusions:

• Incorporating the HJ regularization term is vital for accurate dynamic inference and prediction in scRNA-seq data analysis.
• PI-SDE offers a robust and interpretable approach to modeling cell differentiation dynamics.
• The PI-SDE software is publicly available for broader research application.