Fig. 4.

Schematic illustrating the limited DR of AI concentrations. (A) A single bacterial cell, consuming oxygen and secreting AI. The AI concentration in the vicinity of the cell is proportional to the difference between the ${\text{O}}_2$ concentration at infinity, ${\left[{\text{O}}_2\right]}_{\infty }$, and the ${\text{O}}_2$ concentration in the vicinity of the cell, ${\left[{\text{O}}_2\right]}_0$. (B) A bacterial colony, consuming ${\text{O}}_2$ and secreting AI. If the ${\text{O}}_2$ concentration inside the colony is close to zero, the AI concentration approaches a maximum value $\propto {\left[{\text{O}}_2\right]}_{\infty }$. This relation between the AI concentration and ${\text{O}}_2$ concentration leads to the upper limit on the DR of AI described in Eqs. 2–4.