Analysis of the Effect of Branch Position on the Trajectory Stability of Gene Regulatory Networks

Revealing the relationship between the dynamics and structure of gene regulatory networks is a challenging issue in system biology. This study focuses on the trajectory stability which is a typical dynamic characteristic of regulatory networks. Based on the ITC network model which forms the main structure in a regulatory network, we analyzed how the positions of branches affect the trajectory stability of the network. In theoretical analysis, it has been proven that the branch’s position will affect the trajectory stability in two ways. On one side, if inserting an independent branch or a branch at the first node of the ITC model, the trajectory stability of the network will decrease slightly; on the other side, if inserting a branch at the end node of the ITC model, the trajectory stability will considerably increase. In simulation, it has also been shown that if inserting a branch at middle position, the trajectory stability will be affected by a combination of these two effects. These findings can not only help to reveal the topological origin of trajectory stability in regulatory networks, but to provide guidance in designing robust artificial network in synthetic biology.