Effect of the substrate concentration on the additional positive feedback in genetic circuits

In the gene regulatory network, the gene regulation loop often occurs with multiple positive feedback, multiple negative feedback and coupled positive and negative feedback forms. In the above gene regulation loops, the auto-activation loop acts are ubiquitous regulatory motifs in complex bio-molecular networks. In this paper, we study the effect of the substrate concentration for gene expression considering an additional positive feedback loop (APFL). First, we find that the substrate concentration can tune the stochastic switch behavior in the additional positive feedback loop. Then, we study the relationship of the substrate concentration with the positive feedback strength in the aspect of the stochastic switch behavior. Furthermore, we also find the gene differentiation phenomenon in the different substrate concentration without colored noise and with colored noise, respectively, when the feedback strength in the additional positive feedback loop (APFL) is sufficiently large.