GAMS code of state transition from POA6 to CYA in gastric cancer network from Reconciling periodic rhythms of large-scale biological networks by optimal control

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.

周期节律是一类普遍存在的现象，可揭示生物系统中循环活动的内在机制，其可通过相关生物网络的循环吸引子（cyclic attractors）加以表征。周期节律紊乱会损害生物体的正常生命行为。已有研究证实，通过调控外部信号，可实现不同吸引子间的状态转移。但截至目前，绝大多数相关研究均聚焦于点吸引子（point attractors），却忽略了循环吸引子。本研究旨在探索一种方法，将异常周期节律（如衰减的昼夜节律振幅与相位延迟）校正为复杂生物网络的正常节律。为此，我们构建并求解了混合整数非线性动态优化问题，以同步识别调控变量，并确定用于状态转移与周期节律调整的最优控制策略。我们通过三个示例开展数值实验，分别为混沌系统、哺乳动物昼夜节律系统与胃癌基因调控网络。实验结果表明，仅需调控网络中的少量生物分子，结合最优控制策略即可成功将系统驱动至目标循环吸引子。