Design Principles of Regulatory Networks: Finding Network Topologies That Can Achieve Dual Function of Adaptation and Timeliness

In biochemical systems, finding design principle that links the desired function and network topologies is important to uncover the complex regulation logic. In this paper, a universal methodology is proposed to find the design principle for dual function of adaptation and timeliness in three-node enzyme regulatory networks. Firstly, in changing circumstances, many biochemical systems not only need to be adaptive but also rapid and timely. Besides adaptation, the timeliness function is introduced to quantify system’s response speed. Secondly, an effective searching method is used to acquire sufficient bi-functional networks. The constrained many-objective genetic algorithm with loose-K ranking is used to optimize four quantities of dual function, i.e., sensitivity, precision, peak time and settle down time. Based on 30 independent runs, we can obtain 179 bi-functional topologies and 4290 circuits. Thirdly, by means of topology clustering and statistical analysis, we find that one or two negative feedback loops (NFBLs) coupled with incoherent feedforward loop (IFFL) emerges as recurrent topology motif. The coupling of NFBLs with type-3 IFFL and the coupling of NFBL with type-1 IFFL is helpful to improve topology robustness and bi-functional performance, respectively. Owing to its universality, our methodology can be extended to other desired functions or regulatory networks.