Linking molecular and population processes in mathematical models of quorum sensing

Many bacteria alter their behaviors as a function of population density, via a process known as quorum sensing (QS). QS is achieved by the synthesis and detection of diffusible signal molecules, often involving complex signal transduction pathways and regulatory networks. Mathematical models have been developed to investigate a number of aspects of QS, resulting in a wide range of model structures; many have focused on either the molecular or the population scale. In this paper, I show that many published models fail to satisfy physical constraints (such as conservation of matter) or rely on a priori assumptions that may not be valid. I present new, simple models of canonical Gram-negative and Gram-positive QS systems, in both well-mixed and biofilm populations, focusing on the interaction between molecular and population processes. I show that this interaction may be crucial for several important features of QS, including bistability and the localization of QS in space. The results highlight the need to link molecular and population processes carefully in QS models, provide a general framework for understanding the behavior of complex system-specific models, and suggest new directions for both theoretical and experimental work.