Hair follicles (HFs) are mini skin organs that undergo cyclic growth. Various signals regulate HF cell fate decisions jointly. Recent experimental results suggest that transforming growth factor beta (TGF-$\beta$) exhibits a dual role in HF cell fate regulation that can be either anti- or pro-apoptosis. To understand the underlying mechanisms of HF cell fate control, we develop a novel probabilistic Boolean network (pBN) model on the HF epithelial cell gene regulation dynamics. First, the model is derived from literature, then refined using single-cell RNA sequencing data. Using the model, we both explore the mechanisms underlying HF cell fate decisions and make predictions that could potentially guide future experiments: 1) we propose that a threshold-like switch in the TGF-$\beta$ strength may necessitate the dual roles of TGF-$\beta$ in either activating apoptosis or cell proliferation, in cooperation with bone morphogenetic protein (BMP) and tumor necrosis factor (TNF) and at different stages of a follicle growth cycle; 2) our model shows concordance with the high-activator-low-inhibitor theory of anagen initiation; 3) we predict that TNF may be more effective in catagen initiation than TGF-$\beta$, and they may cooperate in a two-step fashion; 4) finally, predictions of gene knockout and overexpression reveal the roles in HF cell fate regulations of each gene. Attractor and motif analysis from the associated Boolean networks reveal the relations between the topological structure of the gene regulation network and the cell fate regulation mechanism. A discrete spatial model equipped with the pBN illustrates how TGF-$\beta$ and TNF cooperate in initiating and driving the apoptosis wave during catagen.

毛囊 (HF) 是经历周期性生长的微型皮肤器官。各种信号共同调节 HF 细胞的命运决定。最近的实验结果表明，转化生长因子β（TGF-$\beta$）在 HF 细胞命运调节中表现出双重作用，可以是抗凋亡，也可以是促凋亡。为了了解心力衰竭细胞命运控制的潜在机制，我们开发了一种关于心力衰竭上皮细胞基因调控动力学的新型概率布尔网络（pBN）模型。首先，该模型源自文献，然后使用单细胞 RNA 测序数据进行改进。使用该模型，我们既探索了 HF 细胞命运决定的机制，又做出了可能指导未来实验的预测：1）我们提出 TGF-β 中的类似阈值的开关$\beta$强度可能需要 TGF-β 的双重作用$\beta$与骨形态发生蛋白 (BMP) 和肿瘤坏死因子 (TNF) 配合，在卵泡生长周期的不同阶段激活细胞凋亡或细胞增殖；2）我们的模型显示与生长期起始的高激活剂-低抑制剂理论一致；3) 我们预测 TNF 在退行期启动中可能比 TGF-更有效$\beta$，并且他们可以分两步进行合作；4）最后，基因敲除和过度表达的预测揭示了每个基因在HF细胞命运调控中的作用。来自相关布尔网络的吸引子和基序分析揭示了基因调控网络的拓扑结构与细胞命运调控机制之间的关系。配备 pBN 的离散空间模型说明了 TGF-$\beta$和TNF在退行期协同启动和驱动细胞凋亡波。