Many tissues undergo a steady turnover, where cell divisions are on average balanced with cell deaths. Cell fate decisions such as stem cell (SC) differentiations, proliferations, or differentiated cell (DC) deaths, may be controlled by cell populations through cell-to-cell signaling. Here, we examine a class of mathematical models of turnover in SC lineages to understand engineering design principles of control (feedback) loops, that may operate in such systems. By using ordinary differential equations that describe the co-dynamics of SCs and DCs, we study the effect of different types of mutations that interfere with feedback present within cellular networks. For instance, we find that mutants that do not participate in feedback are less dangerous in the sense that they will not rise from low numbers, whereas mutants that do not respond to feedback signals could rise and replace the wild-type population. Additionally, we asked if different feedback networks can have different degrees of resilience against such mutations. We found that all minimal networks, that is networks consisting of exactly one feedback loop that is sufficient for homeostatic stability of the wild-type population, are equally vulnerable. Mutants with a weakened/eliminated feedback parameter might expand from lower numbers and either enter unlimited growth or reach an equilibrium with an increased number of SCs and DCs. Therefore, from an evolutionary viewpoint, it appears advantageous to combine feedback loops, creating redundant feedback networks. Interestingly, from an engineering prospective, not all such redundant systems are equally resilient. For some of them, any mutation that weakens/eliminates one of the loops will lead to a population growth of SCs. For others, the population of SCs can actually shrink as a result of “cutting” one of the loops, thus slowing down further unwanted transformations.

中文翻译：

---

细胞反馈网络及其抵御突变的能力

许多组织经历稳定的周转，其中细胞分裂平均与细胞死亡平衡。细胞命运决定，例如干细胞 (SC) 分化、增殖或分化细胞 (DC) 死亡，可能由细胞群通过细胞间信号传导来控制。在这里，我们检查了 SC 谱系中的一类转换数学模型，以了解可能在此类系统中运行的控制（反馈）回路的工程设计原则。通过使用描述 SCs 和 DCs 的协同动力学的常微分方程，我们研究了干扰细胞网络中存在的反馈的不同类型突变的影响。例如，我们发现不参与反馈的突变体的危险性较小，因为它们不会从低数量中崛起，而对反馈信号不响应的突变体可能会上升并取代野生型种群。此外，我们询问不同的反馈网络是否可以对此类突变具有不同程度的弹性。我们发现所有最小网络，即仅由一个反馈回路组成的网络，足以满足野生型种群的稳态稳定性，同样容易受到攻击。具有弱化/消除反馈参数的突变体可能会从较低的数量扩展，并进入无限增长或在 SC 和 DC 数量增加的情况下达到平衡。因此，从进化的角度来看，结合反馈回路，创建冗余反馈网络似乎是有利的。有趣的是，从工程的角度来看，并非所有此类冗余系统都具有同样的弹性。对于其中一些人来说，任何削弱/消除循环之一的突变都将导致 SC 的种群增长。对于其他人来说，由于“切断”其中一个循环，SC 的数量实际上会减少，从而减慢进一步不需要的转换。