Differential Equation Modeling of Cell Population Dynamics in Skeletal Muscle Regeneration from Single-Cell Transcriptomic Data

Abstract

Research in muscle stem cells (MuSCs) has consistently aimed to enhance our understanding of the complex dynamics within muscle tissues. However, traditional computational models for muscle regeneration often rely on aggregated data, potentially missing the subtle complexities of MuSCs and their cellular niches. The emergence of single-cell RNA sequencing (scRNA-seq) data offers a significant opportunity to refine these models and enhance our understanding of cellular interactions in muscle regeneration. In this study, we introduce a non-linear ordinary differential equation model, consisting of 10 variables and 22 parameters, to precisely capture the dynamics of key cell types involved in skeletal muscle repair. Focusing on myogenic lineage cells and immune cells, the model delineates critical cell fate decisions such as quiescence, activation, proliferation, differentiation, infiltration, apoptosis, and exfiltration in response to muscle damage and intercellular communication. We adapted this model to scRNA-seq data, from which we generated and refined population dynamic datasets. These datasets were further refined with supplementary experimental data, allowing for the determination of precise cell counts per tissue volume (cells/mm³). The robustness of our model is validated by its ability to mirror the observed population dynamics. Additionally, a thorough sensitivity analysis was performed, involving several perturbations of parameters within a range of ±10% of their baseline values to highlight their influence and validate the reliability of our model.