Exploring cores and skeletons in oscillatory gene regulatory networks by a functional weight approach

The topological structures of complex networks are often very complicated and there are huge amount of data in their dynamics. It is important to extract useful information from the available data and to explore some simple reduced structures (if they exist) which play key roles determining different functions of the networks. In this paper, models of gene regulatory networks (GRNs) are studied and a method of functional weight analysis is proposed to quantitatively measure the importance of all topological interactions from the data of oscillation. This method allows us to obtain some simple skeleton interactions and core structures. The latter play the role of oscillation sources while the former reveal the main signal propagation paths from the sources throughout the networks. Different control strategies and detailed statistical results demonstrate the validity, significance and efficiency of the analysis.