Yuan Meichen, Qu Junlin, Hong Weirong, Li Pu
College of Energy Engineering, Zhejiang University, Hangzhou 310027, China.
Process Optimization Group, Institute of Automation and Systems Engineering, Technische Universität Ilmenau, Ilmenau 98684, Germany.
R Soc Open Sci. 2020 Jan 8;7(1):191698. doi: 10.1098/rsos.191698. eCollection 2020 Jan.
Periodic rhythms are ubiquitous phenomena that illuminate the underlying mechanism of cyclic activities in biological systems, which can be represented by cyclic attractors of the related biological network. Disorders of periodic rhythms are detrimental to the natural behaviours of living organisms. Previous studies have shown that the state transition from one to another attractor can be accomplished by regulating external signals. However, most of these studies until now have mainly focused on point attractors while ignoring cyclic ones. The aim of this study is to investigate an approach for reconciling abnormal periodic rhythms, such as diminished circadian amplitude and phase delay, to the regular rhythms of complex biological networks. For this purpose, we formulate and solve a mixed-integer nonlinear dynamic optimization problem simultaneously to identify regulation variables and to determine optimal control strategies for state transition and adjustment of periodic rhythms. Numerical experiments are implemented in three examples including a chaotic system, a mammalian circadian rhythm system and a gastric cancer gene regulatory network. The results show that regulating a small number of biochemical molecules in the network is sufficient to successfully drive the system to the target cyclic attractor by implementing an optimal control strategy.
周期性节律是普遍存在的现象，它揭示了生物系统中循环活动的潜在机制，这种机制可以由相关生物网络的循环吸引子来表示。周期性节律紊乱对生物体的自然行为有害。先前的研究表明，从一个吸引子到另一个吸引子的状态转变可以通过调节外部信号来实现。然而，到目前为止，这些研究大多主要集中在点吸引子上，而忽略了循环吸引子。本研究的目的是研究一种方法，使异常的周期性节律（如昼夜节律振幅减小和相位延迟）与复杂生物网络的正常节律相协调。为此，我们同时制定并求解一个混合整数非线性动态优化问题，以识别调节变量，并确定周期性节律状态转变和调整的最优控制策略。在包括混沌系统、哺乳动物昼夜节律系统和胃癌基因调控网络的三个例子中进行了数值实验。结果表明，通过实施最优控制策略，调节网络中少量的生化分子就足以成功地将系统驱动到目标循环吸引子。
