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.

翻译：越来越多的证据强调了癌症组织中普遍存在的层级结构。该层级结构的基础是癌症干细胞，这是一类具有通过细胞分化产生整个癌症组织关键作用的细胞亚群。近年来，癌细胞可塑性现象（即癌症干细胞与非干细胞癌细胞之间的动态相互转化）引起了广泛关注。由于从实验数据中检测癌细胞可塑性仍是一项严峻挑战，我们提出了一种贝叶斯统计框架，旨在利用癌症干细胞比例的时间数据推断癌细胞的表型可塑性。我们的方法基于一个能够捕捉细胞动态行为的随机模型。借助贝叶斯分析，我们探索了由该随机模型的柯尔莫哥洛夫向前方程推导出的癌症干细胞比例矩方程。通过引入常微分方程的改进欧拉法，我们开发了一种用于非线性常微分方程模型参数估计的新统计方法，这也为成分数据研究提供了新思路。大量模拟结果有力验证了所提出方法的有效性。为进一步佐证研究结论，我们将该方法应用于分析已发表的SW620结肠癌细胞系数据。我们的结果与原位实验一致，从而强化了该方法在识别和量化癌细胞表型可塑性方面的实用性。