Traveling waves in response to a diffusing quorum sensing signal in spatially-extended bacterial colonies.

In the behavior known as quorum sensing (QS), bacteria release diffusible signal molecules known as autoinducers, which by accumulating in the environment induce population-wide changes in gene expression. Although QS has been extensively studied in well-mixed systems, the ability of diffusing QS signals to synchronize gene expression in spatially extended colonies is not well understood. Here we investigate the one-dimensional spatial propagation of QS-circuit activation in a simple, analytically tractable reaction-diffusion model for the LuxR-LuxI circuit, which regulates bioluminescence of the marine bacterium Aliivibrio fischeri. The quorum activation loop is modeled by a Hill function with a cooperativity exponent (m=2.2). The model is parameterized from laboratory data and captures the major empirical properties of the LuxR-LuxI system and its QS regulation of A. fischeri bioluminescence. Our simulations of the model show propagating waves of activation or deactivation of the QS circuit in a spatially extended colony. We further prove analytically that the model equations possess a traveling wave solution. This mathematical proof yields the rate of autoinducer degradation that is compatible with a traveling wave of gene expression as well as the critical degradation rate at which the nature of the wave switches from activation to deactivation. Our results can be used to predict the direction and activating or deactivating nature of a wave of gene expression in experimentally controlled bacterial populations subject to a diffusing autoinducer signal.

Entropy-driven motility of Sinorhizobium meliloti on a semi-solid surface.

Sinorhizobium meliloti growing on soft agar can exhibit an unusual surface spreading behaviour that differs from other bacterial surface motilities. Bacteria in the colony secrete an exopolysaccharide-rich mucoid fluid that expands outward on the surface, carrying within it a suspension of actively dividing cells. The moving slime disperses the cells in complex and dynamic patterns indicative of simultaneous bacterial growth, swimming and aggregation. We find that while flagellar swimming is required to maintain the cells in suspension, the spreading and the associated pattern formation are primarily driven by the secreted exopolysaccharide EPS II, which creates two entropy-increasing effects: an osmotic flow of water from the agar to the mucoid fluid and a crowding or depletion attraction between the cells. Activation of these physical/chemical phenomena may be a useful function for the high molecular weight EPS II, a galactoglucan whose biosynthesis is tightly regulated by the ExpR/SinI/SinR quorum-sensing system: unlike bacterial colonies that spread via bacterium-generated, physical propulsive forces, S. meliloti under quorum conditions may use EPS II to activate purely entropic forces within its environment, so that it can disperse by passively 'surfing' on those forces.

Quorum activation at a distance: spatiotemporal patterns of gene regulation from diffusion of an autoinducer signal.

Quorum sensing (QS) bacteria regulate gene expression collectively by exchanging diffusible signal molecules known as autoinducers. Although QS is often studied in well-stirred laboratory cultures, QS bacteria colonize many physically and chemically heterogeneous environments where signal molecules are transported primarily by diffusion. This raises questions of the effective distance range of QS and the degree to which colony behavior can be synchronized over such distances. We have combined experiments and modeling to investigate the spatiotemporal patterns of gene expression that develop in response to a diffusing autoinducer signal. We embedded a QS strain in a narrow agar lane and introduced exogenous autoinducer at one terminus of the lane. We then measured the expression of a QS reporter as a function of space and time as the autoinducer diffused along the lane. The diffusing signal readily activates the reporter over distances of ~1 cm on time scales of ~10 h. However, the patterns of activation are qualitatively unlike the familiar spreading patterns of simple diffusion, as the kinetics of response are surprisingly insensitive to the distance the signal has traveled. We were able to reproduce these patterns with a mathematical model that combines simple diffusion of the signal with logistic growth of the bacteria and cooperative activation of the reporter. In a wild-type QS strain, we also observed the propagation of a unique spatiotemporal excitation. Our results show that a chemical signal transported only by diffusion can be remarkably effective in synchronizing gene expression over macroscopic distances.