酵母细胞代谢振荡的非线性延迟模型
A Nonlinear Delay Model for Metabolic Oscillations in Yeast Cells
AI总结：
本文构建含资源约束的单蛋白与三蛋白时间延迟模型，通过谱元法、参数空间仿真和边值问题分析揭示酵母代谢振荡机制。
摘要：
我们提出了两个关于酵母细胞代谢振荡的时间延迟模型。我们的模型检验了一个假说，即振荡的产生是由于多条通路共享一种有限资源，我们将该资源等同于可用核糖体的数量。我们首先探索了一个单蛋白模型，其中包含一个控制细胞可用总资源的约束方程。随后，该模型被扩展为包含三种共享同一资源池的蛋白质。在恒定延迟下，我们采用三种方法从数值上检测振荡。首先，我们使用谱元法将系统近似为一个离散映射，并通过考察其特征值来评估平衡点处线性化系统的稳定性。第二种方法是在参数空间的二维投影中绘制仿真轨迹的振幅。我们使用与已发表实验结果一致的历史函数来获得代谢振荡。最后，利用谱元法将系统转化为一个边值问题，其解对应于系统的近似周期解。结果表明，可用总资源与时间延迟的某些组合会导致振荡。我们观察到，参数空间中的振荡区域位于容许稳态的区域之间，这些稳态分别对应零产出和恒定产出。在所有蛋白质都需要相同生产时间的三蛋白模型中也发现了类似行为。然而，在低可用资源条件下，蛋白质生产率的峰值出现偏移，这表明我们的模型捕捉到了共享资源池的动力学。
英文摘要：
We introduce two time-delay models of metabolic oscillations in yeast cells. Our model tests a hypothesis that the oscillations occur as multiple pathways share a limited resource which we equate to the number of available ribosomes. We initially explore a single-protein model with a constraint equation governing the total resource available to the cell. The model is then extended to include three proteins that share a resource pool. Three approaches are considered at constant delay to numerically detect oscillations. First, we use a spectral element method to approximate the system as a discrete map and evaluate the stability of the linearized system about its equilibria by examining its eigenvalues. For the second method, we plot amplitudes of the simulation trajectories in 2D projections of the parameter space. We use a history function that is consistent with published experimental results to obtain metabolic oscillations. Finally, the spectral element method is used to convert the system to a boundary value problem whose solutions correspond to approximate periodic solutions of the system. Our results show that certain combinations of total resource available and the time delay, lead to oscillations. We observe that an oscillation region in the parameter space is between regions admitting steady states that correspond to zero and constant production. Similar behavior is found with the three-protein model where all proteins require the same production time. However, a shift in the protein production rates peaks occurs for low available resource suggesting that our model captures the shared resource pool dynamics.
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