周期性营养摄入下基因表达的核糖体种群最优控制
Optimal control of ribosome population for gene expression under periodic nutrient intake
AI总结：
该研究构建了含资源与核糖体种群调控的蛋白质生产动力学模型，通过解析与准静态近似求解最优控制问题，发现核糖体种群的进食-禁食期切换调控可最大化维持蛋白生产，并确定了对应调控参数范围。
摘要：
蛋白质翻译是基因表达的核心环节，由核糖体介导完成。由于核糖体在细胞质量构成和能量消耗中均占显著比例，实现核糖体种群的高效管理对细胞代谢与生长同样至关重要。受“核糖体的主动降解与生成均存在营养依赖调控机制”这一生物学证据启发，我们提出了一个蛋白质生产动力学模型，该模型纳入了资源动力学以及核糖体种群的调控机制。在“主动降解与生物合成是最大化并维持蛋白质生产的最优方式”这一假设下，我们旨在定性复现核糖体种群动力学的实验观测结果。在构建相应的优化问题后，我们首先通过解析方法研究了恒定资源输入下解的稳定性与全局行为，并刻画了振荡幅度以及向全局平衡的收敛速率。我们进一步利用这些结果，在准静态近似下简化并求解了该问题。通过采用生物物理参数值，我们发现最优控制解会使两种调控机制与核糖体种群在进食期和禁食期之间切换，这表明实验中观测到的核糖体种群的强调控作用可实现蛋白质生产的最大化与维持。最后，我们确定了可观测到该调控模式的控制值范围，该范围取决于禁食的强度。
英文摘要：
Translation of proteins is a fundamental part of gene expression that is mediated by ribosomes. As ribosomes significantly contribute to both cellular mass and energy consumption, achieving efficient management of the ribosome population is also crucial to metabolism and growth. Inspired by biological evidence for nutrient-dependent mechanisms that control both ribosome active degradation and genesis, we introduce a dynamical model of protein production, that includes the dynamics of resources and control over the ribosome population. Under the hypothesis that active degradation and biogenesis are optimal for maximizing and maintaining protein production, we aim to qualitatively reproduce empirical observations of the ribosome population dynamics. Upon formulating the associated optimization problem, we first analytically study the stability and global behaviour of solutions under constant resource input, and characterize the extent of oscillations and convergence rate to a global equilibrium. We further use these results to simplify and solve the problem under a quasi-static approximation. Using biophysical parameter values, we find that optimal control solutions lead to both control mechanisms and the ribosome population switching between periods of feeding and fasting, suggesting that the intense regulation of ribosome population observed in experiments allows to maximize and maintain protein production. Finally, we find some range for the control values over which such a regime can be observed, depending on the intensity of fasting.
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