Dey Abhishek, Sen Shaunak
Department of Electrical Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110 016, India.
IET Syst Biol. 2018 Jun;12(3):93-100. doi: 10.1049/iet-syb.2017.0026.
Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of analytical and computational approaches, the authors adapt and develop the method of describing functions to represent the input-output responses of biomolecular signalling systems. They approximate representative systems exhibiting various saturating and hysteretic dynamics in a way that is better than the standard linearisation. Furthermore, they develop analytical upper bounds for the computational error estimates. Finally, they use these error estimates to augment the limit cycle analysis with a simple and quick way to bound the predicted oscillation amplitude. These results provide system approximations that can add more insight into the local behaviour of these systems than standard linearisation, compute responses to other periodic inputs and to analyse limit cycles.
数学方法为复杂系统的分析和设计提供了有用的框架。然而，在诸如生物学等新的领域中，既需要对现有方法进行调整，也需要开发新的方法。作者结合分析方法和计算方法，对描述函数的方法进行了调整和开发，以表示生物分子信号系统的输入-输出响应。他们以比标准线性化更好的方式对表现出各种饱和和滞后动力学的代表性系统进行近似。此外，他们还为计算误差估计建立了分析上界。最后，他们利用这些误差估计，通过一种简单快速的方法来界定预测的振荡幅度，从而增强极限环分析。这些结果提供的系统近似比标准线性化能更深入地洞察这些系统的局部行为，能计算对其他周期性输入的响应并分析极限环。
