Abstract
Biological functions of bacteria can be regulated by monitoring their own population density induced by the quorum sensing system. However, quantitative insight into the system's dynamics and regulatory mechanism remain challenging. Here, we construct a comprehensive mathematical model of the synthetic quorum sensing circuit that controls population density in Escherichia coli. Simulations agree well with experimental results obtained under different ribosome-binding site (RBS) efficiencies. We present a quantitative description of the component dynamics and show how the components respond to isopropyl-β-D-1-thiogalactopyranoside (IPTG) induction. The optimal IPTG-induction range for efficiently controlling population density is quantified. The controllable area of population density by acyl-homoserine lactone (AHL) permeability is quantified as well, indicating that high AHL permeability should be treated with a high dose of IPTG, while low AHL permeability should be induced with low dose for efficiently controlling. Unexpectedly, an oscillatory behavior of the growth curve is observed with proper RBS-binding strengths and the oscillation is greatly restricted by the bacterial death induced by toxic metabolic by-products. Moreover, we identify that the mechanism underlying the emergence of oscillation is determined by the negative feedback loop structure within the signaling. Bifurcation analysis and landscape theory are further employed to study the stochastic dynamic and global stability of the system, revealing two faces of toxic metabolic by-products in controlling oscillatory behavior. Overall, our study presents a quantitative basis for understanding and new insights into the control mechanism of quorum sensing system, providing possible clues to guide the development of more rational control strategy.