Regulatory dynamics of synthetic gene networks with positive feedback

Biological processes are governed by complex networks ranging from gene regulation to signal transduction. Positive feedback is a key element in such networks. The regulation enables cells to adopt multiple internal expression states in response to a single external input signal. However, past works lacked a dynamical aspect of this system. To address the dynamical property of the positive feedback system, we employ synthetic gene circuits in Escherichia coli to measure the rise-time of both the no-feedback system and the positive feedback system. We show that the kinetics of gene expression is slowed down if the gene regulatory system includes positive feedback. We also report that the transition of gene switching behaviors from the hysteretic one to the graded one occurs. A mathematical model based on the chemical reactions shows that the response delay is an inherited property of the positive feedback system. Furthermore, with the aid of the phase diagram, we demonstrate the decline of the feedback activation causes the transition of switching behaviors. Our findings provide a further understanding of a positive feedback system in a living cell from a dynamical point of view.