Kinetics of the AHL regulatory system in a model biofilm system: how many bacteria constitute a "quorum"?

Acylated homoserine lactones (AHLs) regulate a wide variety of phenotypes in Gram-negative bacteria. Most research suggests that AHL-mediated phenotypes are not expressed in populations until late logarithmic phase or stationary phase. Here, we model how the concentration of AHLs inside bacterial cells and in a biofilm changes over time as a function of population growth rate, diffusion of AHLs and the rate of autoinduction. Our theoretical results show that the concentration of AHLs inside a single bacterium (and by implication induction of a phenotype) has a non-trivial behaviour over time, and often exhibits a rapid increase early in population growth. This rapid increase is followed by a plateau, followed by another rise in the concentration of AHLs, to a second plateau. High concentrations of AHLs inside the bacterial cell early in population growth are positively affected by slow diffusion rates out of the cell and the biofilm, slow bacterial growth rates and fast autoinduction. In contrast, fast growth rates, slow autoinduction rates and high diffusion rates result in a high concentration plateau in stationary phase. More generally, the density-dependent nature of AHL regulation can be viewed as a trade-off between factors that dilute intracellular concentrations of AHLs (diffusion out of the cell, cell division), and those that increase concentrations (a slowing or restriction of diffusion or growth, or autoinduction). These results suggest that expression of AHL-mediated phenotypes can occur at relatively low cell densities and low external/environmental AHL concentrations.