What is Special of “five” in Biological Regulatory Networks?

Understanding the potential mechanism to achieve dual biological properties is a fundamental challenge in systems biology, which is related to small network modules constructed by nonlinear dynamics. The previous work of adaptation mainly focused on biological regulatory networks whose number of nodes n≤ 4 , without consideration in the oscillatory process. In this paper, we extend the study to multi-node ( n≤ 9 ) networks, propose the adaptation concept under oscillation cases and compare a class of regulatory networks on oscillation and adaptation performance based on enzymatic dynamics. Through computational studies, a specific strongly symmetric and coupled five-node network topology is found, which is proved to be the minimal structure with excellent performance on both oscillation and adaptation. It indicates regulatory networks with this topological structure are promising candidates to achieve these dual dynamic properties. We present a thorough analysis on this topology which shows significant advantages, including essentiality, parameter variation, frequency adjustment and perfect adaptation. Notably, this specific topology is exactly the same as the yin–yang five-element network in traditional Chinese medicine, and our approach might reveal its characteristics in systems science.