Bayesian Inference of Phenotypic Plasticity of Cancer Cells Based on Dynamic Model for Temporal Cell Proportion Data

Mounting evidence underscores the prevalent hierarchical organization of cancer tissues. At the foundation of this hierarchy reside cancer stem cells, a subset of cells endowed with the pivotal role of engendering the entire cancer tissue through cell differentiation. In recent times, substantial attention has been directed towards the phenomenon of cancer cell plasticity, where the dynamic interconversion between cancer stem cells and non-stem cancer cells has garnered significant interest. Since the task of detecting cancer cell plasticity from empirical data remains a formidable challenge, we propose a Bayesian statistical framework designed to infer phenotypic plasticity within cancer cells, utilizing temporal data on cancer stem cell proportions. Our approach is grounded in a stochastic model, adept at capturing the dynamic behaviors of cells. Leveraging Bayesian analysis, we explore the moment equation governing cancer stem cell proportions, derived from the Kolmogorov forward equation of our stochastic model. With improved Euler method for ordinary differential equations, a new statistical method for parameter estimation in nonlinear ordinary differential equations models is developed, which also provides novel ideas for the study of compositional data. Extensive simulations robustly validate the efficacy of our proposed method. To further corroborate our findings, we apply our approach to analyze published data from SW620 colon cancer cell lines. Our results harmonize with \emph{in situ} experiments, thereby reinforcing the utility of our method in discerning and quantifying phenotypic plasticity within cancer cells.