BACKGROUND Autophagy and apoptosis are two important physiological processes that determine cell survival or death in response to different stress signals. The regulatory mechanisms of these two processes share B-cell lymphoma-2 family proteins and AMBRA1, which are present in both the endoplasmic reticulum and mitochondria. B-cell lymphoma-2 family proteins sense different stresses and interact with AMBRA1 to regulate autophagy and apoptosis, which are respectively mediated by Beclin1 and Caspases. Therefore, we investigated how different levels of stress on B-cell lymphoma-2 family proteins that bind to AMBRA1 in the endoplasmic reticulum and mitochondria regulate the switch from autophagy to apoptosis. METHODS In this paper, we considered the responses of B-cell lymphoma-2 family proteins, which bind to AMBRA1 in both the endoplasmic reticulum and mitochondria, to two different levels of stress in a model originally proposed by Kapuy et al. We investigated how these two stress levels affect the transition from autophagy to apoptosis and their effects on apoptosis activation over time. Additionally, we analyzed how the feedback regulation in this model affects the bifurcation diagrams of two levels of stress and cell fate decisions between autophagy and apoptosis. RESULTS Autophagy is activated for minor stress in mitochondria regardless of endoplasmic reticulum stress, while apoptosis is activated for only significant stress in mitochondria. Apoptosis is only sensitive to mitochondria stress. The time duration before apoptosis activation is longer in the presence of high AMBRA1 levels with high endoplasmic reticulum and mitochondria stress. AMBRA1 can compete with B-cell lymphoma-2 family proteins to bind and activate Beclin1 and thus promote the autophagy process for a long time before apoptosis. Furthermore, apoptosis is prone to occur with increasing activation of Caspases, inactivation of Beclin1-A and the Michaelis constant of Caspases. CONCLUSION A novel mathematical model has been developed to understand the complex regulatory mechanisms of autophagy and apoptosis. Our model may be applied to further autophagy-apoptosis dynamic modeling experiments and simulations.

中文翻译：

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自噬和细胞凋亡受到内质网和线粒体中 AMBRA1 对 Bcl2 的应激的调节。

背景技术自噬和凋亡是决定细胞响应不同应激信号的存活或死亡的两个重要的生理过程。这两个过程的调节机制共享 B 细胞淋巴瘤 2 家族蛋白和 AMBRA1，它们均存在于内质网和线粒体中。B细胞淋巴瘤2家族蛋白感知不同的应激并与AMBRA1相互作用来调节自噬和细胞凋亡，这分别由Beclin1和Caspase介导。因此，我们研究了内质网和线粒体中与 AMBRA1 结合的 B 细胞淋巴瘤 2 家族蛋白的不同应激水平如何调节从自噬到凋亡的转换。方法在本文中，我们考虑了 B 细胞淋巴瘤 2 家族蛋白（其在内质网和线粒体中均与 AMBRA1 结合）对最初由 Kapuy 等人提出的模型中两种不同水平的应激的反应。我们研究了这两种应激水平如何影响从自噬到细胞凋亡的转变，以及它们随着时间的推移对细胞凋亡激活的影响。此外，我们分析了该模型中的反馈调节如何影响自噬和凋亡之间两个应激水平和细胞命运决定的分叉图。结果 无论内质网应激如何，线粒体中的轻微应激都会激活自噬，而只有线粒体中出现重大应激时，细胞凋亡才会激活。细胞凋亡仅对线粒体应激敏感。当 AMBRA1 水平较高且内质网和线粒体应激较高时，细胞凋亡激活前的持续时间会更长。AMBRA1可以与B细胞淋巴瘤2家族蛋白竞争结合并激活Beclin1，从而在细胞凋亡前长时间促进自噬过程。此外，随着Caspase的激活、Beclin1-A的失活和Caspase的米氏常数的增加，细胞凋亡容易发生。结论 开发了一种新的数学模型来理解自噬和细胞凋亡的复杂调节机制。我们的模型可应用于进一步的自噬-凋亡动态建模实验和模拟。