Mathematical modeling and quantitative analysis of phenotypic plasticity during tumor evolution based on single-cell data.

Tumor is a complex and aggressive type of disease that poses significant health challenges. Understanding the cellular mechanisms underlying its progression is crucial for developing effective treatments. In this study, we develop a novel mathematical framework to investigate the role of cellular plasticity and heterogeneity in tumor progression. By leveraging temporal single-cell data, we propose a reaction-convection-diffusion model that effectively captures the spatiotemporal dynamics of tumor cells and macrophages within the tumor microenvironment. Through theoretical analysis, we obtain the estimate of the pulse wave speed and analyze the stability of the homogeneous steady state solutions. Notably, we employe the AddModuleScore function to quantify cellular plasticity. One of the highlights of our approach is the introduction of pulse wave speed as a quantitative measure to precisely gauge the rate of cell phenotype transitions, as well as the novel implementation of the high-plasticity cell state/low-plasticity cell state ratio as an indicator of tumor malignancy. Furthermore, the bifurcation analysis reveals the complex dynamics of tumor cell populations. Our extensive analysis demonstrates that an increased rate of phenotype transition is associated with heightened malignancy, attributable to the tumor's ability to explore a wider phenotypic space. The study also investigates how the proliferation rate and the death rate of tumor cells, phenotypic convection velocity, and the midpoint of the phenotype transition stage affect the speed of tumor cell phenotype transitions and the progression to adenocarcinoma. These insights and quantitative measures can help guide the development of targeted therapeutic strategies to regulate cellular plasticity and control tumor progression effectively.