Substrate concentration effect on gene expression in genetic circuits with additional positive feedback

In gene regulatory networks, gene regulation loops often occur with multiple positive feedback, multiple negative feedback and coupled positive and negative feedback forms. In above gene regulation loops, auto-activation loops are ubiquitous regulatory motifs. This paper aims to investigate a two-component dual-positive feedback genetic circuit, which consists of a double negative feedback circuit and an additional positive feedback loop(APFL). We study effect of substrate concentration on gene expression in the single and the networked systems with APFLs, respectively. We find that substrate concentration can tune stochastic switch behavior in the signal system and then we explore relationship of substrate concentration with positive feedback strength in aspect of stochastic switch behavior. Furthermore, we also discuss gene expression and stochastic switch behavior in the networked systems with APFLs. Based on analysis in the networked systems, we discover that genes express in some specific cells and do not express in the other cells when the expression achieves its steady state. These results can be used to well explain the character of regionalization in the expression of genes and the phenomenon of gene differentiation.