随机基因表达振荡的最小混合模型中的精确功率谱
Exact power spectrum in a minimal hybrid model of stochastic gene expression oscillations
AI总结：
本研究通过解析方法求解最小混合基因表达模型，揭示噪声诱导的振荡机制，并发现负反馈强度增加导致三相随机分岔，翻译爆发增强振荡鲁棒性，为Thomas猜想提供新见解。
摘要：
单细胞中的随机振荡通常以非单调功率谱和振荡自相关函数为特征。在此，我们发展了一种解析方法，用于研究一个最小混合模型中的随机振荡，该模型包括启动子状态切换、蛋白质合成与降解以及基因反馈回路。由于确定性理论预测稳定的不动点，我们模型中观察到的振荡是噪声诱导的。蛋白质浓度波动的自相关函数、功率谱和稳态分布均以闭式形式计算，无需任何近似。利用这一精确可解模型，我们展示了持续振荡作为沿基因状态切换诱导的随机滞回环的圆周运动。随着负反馈强度的增加，观察到三相随机分岔，揭示了随机爆发如何演变为随机振荡。在我们的模型中，当蛋白质相对稳定且基因切换相对缓慢时，振荡倾向于发生。翻译爆发被发现能增强随机振荡的鲁棒性并扩大其区域。这些结果为R. Thomas关于单细胞基因表达动力学的两个猜想提供了更深入的见解。
英文摘要：
Stochastic oscillations in individual cells are usually characterized by a non-monotonic power spectrum with an oscillatory autocorrelation function. Here we develop an analytical approach of stochastic oscillations in a minimal hybrid model of stochastic gene expression including promoter state switching, protein synthesis and degradation, as well as a genetic feedback loop. The oscillations observed in our model are noise-induced since the deterministic theory predicts stable fixed points. The autocorrelated function, power spectrum, and steady-state distribution of protein concentration fluctuations are computed in closed form without making any approximations. Using the exactly solvable model, we illustrate sustained oscillations as a circular motion along a stochastic hysteresis loop induced by gene state switching. A triphasic stochastic bifurcation upon the increasing strength of negative feedback is observed, which reveals how stochastic bursts evolve into stochastic oscillations. In our model, oscillations tend to occur when the protein is relatively stable and when gene switching is relatively slow. Translational bursting is found to enhance the robustness and broaden the region of stochastic oscillations. These results provide deeper insights into R. Thomas' two conjectures for single-cell gene expression kinetics.
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