5D Bacterial quorum sensing

Quorum sensing is a form of system stimulus and response that is correlated to population density. Many species of bacteria use quorum sensing to coordinate various types of behavior including bioluminescence, biofilm formation, virulence, and antibiotic resistance, based on the local density of the bacterial population [10, 7, 9, 24, 40, 36, 42, 27]. In an analogous fashion, some social insects use quorum sensing to determine where to nest [6]. Quorum sensing also has several useful applications outside the biological realm, for example, in computing and robotics. Roughly speaking, quorum sensing can function as a decision-making process in any decentralized system, provided that individual components have (i) some mechanism for determining the number or density of other components they interact with and (ii) a stereotypical response once some threshold has been reached. In the case of bacteria, quorum sensing involves the production and extracellular secretion of certain signaling molecules called autoinducers. Each cell also has receptors that can specifically detect the signaling molecule (inducer) via ligandreceptor binding, which then activates transcription of certain genes, including those for inducer synthesis. However, since there is a low likelihood of an individual bacterium detecting its own secreted inducer, the cell must encounter signaling molecules secreted by other cells in its environment in order for gene transcription to be activated. When only a few other bacteria of the same kind are in the vicinity (low bacterial population density), diffusion reduces the concentration of the inducer in the surrounding medium to almost zero, resulting in small amounts of inducer being produced. On the other hand, as the population grows, the concentration of the inducer passes a threshold, causing more inducer to be synthesized. This generates a positive feedback loop that fully activates the receptor, and induces the up-regulation of other specific genes. Hence, all of the cells initiate transcription at approximately the same time, resulting in some form of coordinated behavior. The basic process at the single-cell level is shown in Fig. 5D.1. Most models of bacterial quorum sensing are based on deterministic ordinary differential equations (ODEs), in which both the individual cells and the extracellular medium are treated as well-mixed compartments (fast diffusion limit) [21, 38, 8, 28, 11, 2, 17, 5, 6]. (For a discussion of spatial models that take into account bulk diffusion of the autoinducer in the extracellular domain see Refs. [8, 29, 23, 30, 19] .) Suppose that there are N cells labeled i = 1, . . . ,N. Let U(t) denote the concentration of signaling molecules in the extracellular space and let ui be the corresponding intracellular concentration within the i-th cell. Suppose that there are K other chemical species within each cell, which together with the signaling molecule comprise a regulatory network. Let vi = (vi,1, . . . ,vi,K) with vi,k the concentration of species k within the i-th cell. A deterministic model of quorum sensing can then be written in the general form [28]