IEEE Trans Nanobioscience. 2013 Dec;12(4):321-31. doi: 10.1109/TNB.2013.2271220.
Multistability of biological systems with complex nonlinear regulatory schemes is an important research topic in system biology. In many models of biological systems, the regulatory functions are of saturation type. The linear sectors, in which the saturation type functions reside, have been extensively adopted to deal with these saturation type functions. The stability analysis resulting from linear sectors is however often conservative as a wide linear section is required to include a large portion of a saturation type function. In this paper, we utilize piecewise linear sectors, recently adopted in nonlinear control theory, to investigate multistability of a class of biological systems with sum regulatory schemes. We will estimate the domain of attraction of each stable equilibrium and examine the robust stability of each equilibrium in the face of disturbances that are bounded in magnitude or energy. A genetic toggle switch in Escherichia coli is employed as an example to illustrate the applicability and effectiveness of our analysis method.
具有复杂非线性调节方案的生物系统的多稳定性是系统生物学中的一个重要研究课题。在许多生物系统模型中，调节功能具有饱和类型。线性部分，其中包含饱和类型的功能，已经被广泛采用来处理这些饱和类型的功能。然而，由于需要一个宽的线性部分来包含饱和类型函数的大部分，因此由线性部分得出的稳定性分析往往是保守的。在本文中，我们利用最近在非线性控制理论中采用的分段线性部分来研究一类具有和调节方案的生物系统的多稳定性。我们将估计每个稳定平衡点的吸引域，并在面对幅度或能量有限的干扰时检查每个平衡点的鲁棒稳定性。大肠杆菌中的遗传振子开关被用作示例来说明我们的分析方法的适用性和有效性。
