标题： 基因调控自催化反馈回路的韧性 显示英文标题

标题： Resilience of the autocatalytic feedback loop for gene regulation

摘要： 基因表达对刺激的响应由转录因子（TF）通过反馈回路基序来调控，目的是在不确定性和扰动的情况下维持所需的转录因子浓度。在这项工作中，我们考虑了基因调控的自催化反馈回路的随机模型，并以概率方式量化了其恢复力，即 \( \text\{\textit{即，也就是说}\} \)，它在存在噪声的情况下保持与指定转录因子浓度相关的平衡状态的能力以及相应的吸引域。我们表明，形成更大的寡聚体（对应于调节函数的更大Hill系数，从而更尖锐的非线性）可以改善系统的恢复力，即使在接近转录因子临界浓度时也是如此。我们的形式化结果基于依赖Fokker-Planck方程的随机公式，并辅以数值模拟。 显示英文摘要

摘要： Gene expression in response to stimuli is regulated by transcription factors (TFs) through feedback loop motifs, aimed at maintaining the desired TF concentration despite uncertainties and perturbations. In this work, we consider a stochastic model of the autocatalytic feedback loop for gene regulation and we probabilistically quantify its resilience, \textit{i.e.}, its ability to preserve the equilibrium associated with a prescribed concentration of TFs, and the corresponding basin of attraction, in the presence of noise. We show that the formation of larger oligomers, corresponding to larger Hill coefficients of the regulation function, and thus to sharper non-linearities, improves the system resilience, even close to critical concentrations of TFs. Our formal results within a stochastic formulation relying on the Fokker-Planck equation are accompanied by numerical simulations.