Optimality Conditions for Cell-Fate Heterogeneity That Maximize the Effects of Growth Factors in PC12 Cells

Recently, the heterogeneity that arises from stochastic fate decisions has been reported for several types of cancer-derived cell lines and several types of clonal cells grown under constant environmental conditions. However, the relation between this stochasticity and the responsiveness to extracellular stimuli remains largely unknown. Here we focused on the fate decisions of the PC12 cell line, which was derived from rat pheochromocytoma, and is a model system to study differentiation into sympathetic neurons. Whereas epidermal growth factor (EGF) stimulates the proliferation of populations of PC12 cells, nerve growth factor (NGF) promotes the differentiation of neurites to neuron-like cells. We found that phenotypic heterogeneity increased with time at several surrounding serum concentrations, suggesting stochastic cell-fate decisions in single cells. We made a simple mathematical model assuming Markovian transitions of the cell fates, and estimated the transition rates based on Bayes' theorem. The model suggests that depending on the serum concentration, EGF (NGF) even directs differentiation (proliferation) at the single-cell level. The maximum effects of the growth factors were ensured when the transition rates were appropriately controlled by the serum concentration to produce a nonextremal, moderate amount of cell-fate heterogeneity. Our model was validated by the experimental finding that the means and variances of the local cell densities obey a power-law relationship. These results suggest that even when efficient responses to growth factors are observed at the population level, the growth factors stochastically direct the cell-fate decisions in different directions at the single-cell level.

近年来，已有研究报道，在多种癌源细胞系以及于恒定环境条件下培养的多种克隆细胞中，均存在由随机细胞命运决定所产生的细胞异质性。然而，这类随机性与细胞对胞外刺激的响应性之间的关联，目前仍未得到充分阐明。本研究聚焦于PC12细胞系（PC12 cell line）的细胞命运决定：该细胞系源自大鼠嗜铬细胞瘤，是研究交感神经元分化的经典模型系统。表皮生长因子（epidermal growth factor, EGF）可促进PC12细胞群体的增殖，而神经生长因子（nerve growth factor, NGF）则诱导细胞长出神经突并分化为神经元样细胞。我们发现，在多种外周血清浓度条件下，细胞的表型异质性随培养时间延长而升高，这提示单细胞水平存在随机的细胞命运决定事件。我们构建了一个简化的数学模型，假设细胞命运遵循马尔可夫转变过程，并基于贝叶斯定理（Bayes' theorem）估算了转变速率。该模型表明，依据血清浓度的差异，表皮生长因子与神经生长因子在单细胞水平甚至可发挥与群体水平相反的调控作用：即表皮生长因子可诱导单细胞分化，神经生长因子可促进单细胞增殖。当血清浓度适度调控细胞命运转变速率，以产生非极端的中等水平细胞命运异质性时，生长因子可发挥最佳调控效应。实验结果显示，局部细胞密度的均值与方差服从幂律关系，这验证了我们的模型。上述结果表明，即便在群体水平可观测到细胞对生长因子的高效响应，生长因子仍可在单细胞水平通过随机方式引导细胞向不同方向完成命运决定。