Population model of quorum sensing with multiple parallel pathways

Quorum sensing (QS) is a bacterial communication mechanism that uses signal-receptor binding to regulate gene expression based on cell density, resulting in group behaviors such as biofilm formation, bioluminescence and stress response. In certain bacterial species such as Vibrio harveyi, several parallel QS signaling pathways drive a single phosphorylation–dephosphorylation cycle, which in turn regulates QS target genes. In this paper, we investigate the possible role of parallel signaling pathways by developing a mathematical model of QS in V. harveyi at both the single-cell and population levels. First we explore how signal integration may be achieved at the single-cell level, and how different model parameters influence the process. We then consider two examples of signal integration at the population level: a one-population model responding to two environmental cues (cell density and mass transfer), and a two-population model with distinct cell densities. In each case, we use contraction analysis to reduce the population model to an effective single-cell model