From single cells to communities: Mathematical perspectives on bacterial quorum sensing.

The complex social lives of microbes, defined by sophisticated communication networks and cooperative behaviors, play a pivotal role in their survival and adaptation. Central to these interactions is Quorum Sensing (QS), a mechanism widely used by bacterial species for population-scale communication and subsequent gene regulation. QS involves coordinated synthesis, release, and detection of signaling molecules known as autoinducers (AIs). By sensing the concentration of AI as a proxy for the local density of the bacterial population, QS orchestrates the modulation of target gene expression. The molecular foundations of QS have been revealed, but fundamental quantitative challenges remain in the pursuit of a complete understanding of QS dynamics. Mathematical modeling has become an essential tool for investigating QS dynamics at both single-cell and population levels. A variety of modeling approaches, including deterministic, stochastic, non-spatial, and spatial frameworks have been employed to explore the complexities of QS systems. We provide an overview of mathematical models developed to describe and analyze QS mechanisms and dynamics, highlighting their contributions and limitations. Looking ahead, QS modeling is poised to support synthetic biology, antimicrobial therapy, environmental management, and more, offering new strategies to manipulate bacterial behavior for improving biotechnological applications, combating infections, and optimizing industrial processes.