Meyer-Baese Anke, Koshkouei Ali J, Emmett Mark R, Goodall David P
Department of Scientific Computing, Florida State University, Tallahassee, FL 32310-6046, United States.
Neural Netw. 2009 Jul-Aug;22(5-6):658-63. doi: 10.1016/j.neunet.2009.06.051. Epub 2009 Jul 14.
Biological networks are prone to internal parametric fluctuations and external noises. Robustness represents a crucial property of these networks, which militates the effects of internal fluctuations and external noises. In this paper biological networks are formulated as coupled nonlinear differential systems operating at different time-scales under vanishing perturbations. In contrast to previous work viewing biological parametric uncertain systems as perturbations to a known nominal linear system, the perturbed biological system is modeled as nonlinear perturbations to a known nonlinear idealized system and is represented by two time-scales (subsystems). In addition, conditions for the existence of a global uniform attractor of the perturbed biological system are presented. By using an appropriate Lyapunov function for the coupled system, a maximal upper bound for the fast time-scale associated with the fast state is derived. The proposed robust system design principles are potentially applicable to robust biosynthetic network design. Finally, two examples of two important biological networks, a neural network and a gene regulatory network, are presented to illustrate the applicability of the developed theoretical framework.
生物网络容易受到内部参数波动和外部噪声的影响。鲁棒性是这些网络的一个关键特性，它能减轻内部波动和外部噪声的影响。在本文中，生物网络被表述为在消失扰动下于不同时间尺度运行的耦合非线性微分系统。与之前将生物参数不确定系统视为对已知标称线性系统的扰动的工作不同，受扰生物系统被建模为对已知非线性理想化系统的非线性扰动，并由两个时间尺度（子系统）表示。此外，还给出了受扰生物系统全局一致吸引子存在的条件。通过为耦合系统使用适当的李雅普诺夫函数，推导出了与快速状态相关的快速时间尺度的最大上界。所提出的鲁棒系统设计原则可能适用于鲁棒生物合成网络设计。最后，给出了两个重要生物网络的例子，即神经网络和基因调控网络，以说明所发展理论框架的适用性。
