去分化稳定化干细胞谱系：从CTMC到扩散理论和阈值
Dedifferentiation stabilizes stem cell lineages: From CTMC to diffusion theory and thresholds
AI总结：
该研究通过CTMC模型和扩散理论分析了干细胞谱系在群体波动下的稳定性，揭示了去分化流对维持稳态的重要性，并提出了稳态约束定律。
摘要：
我们研究了小 niches 中的干细胞-终分化（TD）谱系，其中来自离散分裂和死亡事件的群体噪声不可忽略。从一个机制性的五通道、密度依赖的CTMC（对称自我更新、对称分化、不对称分裂、去分化、TD死亡）出发，我们推导了其均值场极限和一个函数 CLT，得到一个化学 Langevin 扩散，其显式状态依赖的协方差精确匹配 CTMC 的聚合通道级无限小协方差。在此扩散近似中我们移除去分化流，获得一个明确的二元对立：在亚临界 regime 中，干细胞坐标在渐近几乎必然地灭绝，而在超临界 regime 中，多项式矩指数发散。这在扩散层面识别了严格分层谱系在群体波动下的结构失效模式，并阐明了循环返回流如何挽救稳态。为了解释，我们还从损伤结构传输模型中推导出一个精确的总 ODE 框架，并获得两个稳态约束（比率和平衡定律），将 compartments 比例与周转和平衡去分化与命运偏倚联系起来。数值实验验证了 $Ω^{-1/2}$ 振荡标度，展示了病理学，并对比了定理假设内的全局收敛与定理外阈值（Allee 型）行为。
英文摘要：
We study stem-terminally differentiated (TD) lineages in small niches where demographic noise from discrete division and death events is non-negligible. Starting from a mechanistic five-channel, density-dependent CTMC (symmetric self-renewal, symmetric differentiation, asymmetric division, dedifferentiation, TD death), we derive its mean-field limit and a functional CLT, obtaining a chemical Langevin diffusion whose explicit state-dependent covariance exactly matches the CTMC's aggregated channel-wise infinitesimal covariances. Within this diffusion approximation we remove the dedifferentiation flux and obtain a sharp dichotomy: in subcritical regimes the stem coordinate becomes extinct asymptotically almost surely, whereas in supercritical regimes polynomial moments diverge exponentially. This identifies, at the diffusion level, a structural failure mode of strictly hierarchical lineages under demographic fluctuations and clarifies how a cyclic return flux can rescue homeostasis. For interpretation we also derive an exact totals ODE backbone from a damage-structured transport model and obtain two steady-state constraints (ratio and equalization laws) linking compartment ratios to turnover and balancing dedifferentiation against fate bias. Numerical experiments corroborate the $Ω^{-1/2}$ fluctuation scaling, illustrate the pathology, and contrast theorem-regime global convergence with threshold (Allee-type) behaviour outside the theorem hypotheses.
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