Abstract—MAPK and PI3K−Akt−mTOR signaling cascades regulate important cellular processes. There was developed the mathematical model that was used for the analysis of the interactions within these cascades. Stability analysis of the PI3K–Ak–mTOR signaling pathway model showed that the baseline state of the signaling pathway is metastable and signal transduction can be activated by overcritical exogenous stimulation. An explicit expression was obtained for the threshold level of external stimuli. It was shown that triggering events in the dynamics of the signaling pathway are described by the fold catastrophe of the elementary catastrophe theory. A discussion about whether the results obtained are significant for molecular hematology and hemostaseology is presented.

中文翻译：

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PI3K–Akt–mTOR 信号通路的稳定性分析

摘要—MAPK 和PI3K-Akt-mTOR 信号级联调节重要的细胞过程。开发了用于分析这些级联内相互作用的数学模型。PI3K-Ak-mTOR 信号通路模型的稳定性分析表明，信号通路的基线状态是亚稳态的，信号转导可以被过度临界的外源性刺激激活。获得了外部刺激阈值水平的明确表达。结果表明，信号通路动力学中的触发事件由基本突变理论的折叠突变描述。讨论了所获得的结果是否对分子血液学和止血学具有重要意义。