Bacteria that regulate gene expression in response to changes in cell density are said to engage in quorum sensing. To synchronize their programs of gene expression during the growth of a colony, and perform collective tasks such as resisting antibiotics or inducing virulence factors during infection of a host, quorum-sensing bacteria need to glean as much information as possible about their cell density.
Despite many experimental studies, the biophysical limits on quorum-sensing information transfer remain unclear. Biochemically, a hallmark of quorum-sensing systems is feedback, be it within the intracellular biochemical pathways or mediated via diffusible molecules at the level of the colony. We employ a biologically relevant model for quorum sensing with feedbacks to quantify the information available to a bacterium during the growth of a colony. Specifically, we consider the quorum-sensing system as an information channel and optimize the mutual information between cell density and the expression of a monitor gene by varying the functional form of feedback, i.e. by varying the encoding scheme of the channel.
Our rigorous approach yields a physically interpretable expression for the optimal quorum-sensing information transfer, bypassing the need to infer unknown biological parameters. Moreover, our theoretical analysis characterizes the dual role of feedbacks in promoting information transfer: (1) At the population level, feedbacks allow the detection channels of individual cells to operate at their information capacity. (2) Intracellularly, feedbacks increase the capacity of detection channels by reducing the effective timescale of the quorum-sensing response. Finally, we contrast the information capabilities of distinct feedback mechanisms observed in quorum sensing—regulation by transcription factor or by small RNAs—and suggest complementary roles when both mechanisms are present in the same circuit. This work extends the information theoretical concept of histogram equalization—originally developed in the context of neuroscience—to include the benefit of feedbacks to information transfer in biological systems, a general result that is applicable well beyond quorum sensing.