Local stability analysis for a class of quorum-sensing networks with cyclic gene regulatory networks

Quorum-sensing is one of cell-to-cell communication mechanisms for bacteria, and it essentially involves in biological dynamics such as gene expression. In this paper, we derive analytical expressions for local stability/instability conditions for a class of quorum-sensing networks with cyclic gene regulatory networks. The conditions lead to two biological facts on local stability of the quorum-sensing network. First, we clarify that there exists three parameters which play essential roles in local stability of the quorum-sensing network. Second, we show a relationship between gene networks and quorum-sensing network for achieving the local instability.