Department of Applied Mathematics, National Yang Ming Chiao Tung University, National Chiao Tung University, Hsinchu, Taiwan, 300.
Bull Math Biol. 2021 Apr 23;83(6):62. doi: 10.1007/s11538-021-00883-7.
We investigate oscillations in coupled systems. The methodology is based on the Hopf bifurcation theorem and a condition extended from the Routh-Hurwitz criterion. Such a condition leads to locating the bifurcation values of the parameters. With such an approach, we analyze a single-cell system modeling the minimal genetic negative feedback loop and the coupled-cell system composed by these single-cell systems. We study the oscillatory properties for these systems and compare these properties between the model with Hill-type repression and the one with protein-sequestration-based repression. As the parameters move from the Hopf bifurcation value for single cells to the one for coupled cells, we compute the eigenvalues of the linearized systems to obtain the magnitude of the collective frequency when the periodic solution of the coupled-cell system is generated. Extending from this information on the parameter values, we further compute and compare the collective frequency for the coupled-cell system and the average frequency of the decoupled individual cells. To compare these scenarios with other biological oscillators, we perform parallel analysis and computations on a segmentation clock model.
我们研究了耦合系统中的振荡。该方法基于 Hopf 分岔定理和从 Routh-Hurwitz 准则扩展而来的条件。这样的条件导致了分叉参数值的定位。通过这种方法，我们分析了一个单细胞系统模型，该模型模拟了最小遗传负反馈回路，以及由这些单细胞系统组成的耦合细胞系统。我们研究了这些系统的振荡特性，并比较了基于 Hill 型抑制和基于蛋白隔离的抑制的模型之间的这些特性。当参数从单细胞的 Hopf 分岔值移动到耦合细胞的分岔值时，我们计算线性化系统的特征值，以获得耦合细胞系统的周期解产生时的集体频率的幅度。从这些关于参数值的信息扩展，我们进一步计算和比较了耦合细胞系统的集体频率和去耦单个细胞的平均频率。为了将这些情况与其他生物振荡器进行比较，我们对分段时钟模型进行了并行分析和计算。
