Optimal tuning of bacterial sensing potential
- Department of Biomedical Engineering, Duke University, Durham, NC, USA
- Institute for Genome Sciences and Policy, Duke University, Durham, NC, USA
Correspondence to: Lingchong You1,2 CIEMAS 2345, Duke University, 101 Science Drive, Box 3382, Durham, NC 27708, USA. Tel.: +1 919 660 8408; Fax: +1 919 668 0795; Email: you@duke.edu
Received 13 November 2008; Accepted 15 May 2009; Published online 7 July 2009
Article highlights
- Despite their tremendous diversity, all bacterial quorum sensing systems share a core signaling module comprising signal synthesis, transport, degradation, and detection.
- This core module allows us to define a generic metric, 'sensing potential', that quantifies the ability of QS bacteria to sense their surroundings. Despite its simplicity, the metric captures the activation properties of diverse QS systems and is readily extendable depending on the specific configuration of a QS module.
- The metric provides a concise way to study the benefits of QS regulation for the host such as in the case of QS controlled exoenzyme secretion for nutrient foraging.
Synopsis
Quorum sensing (QS) is a cell–cell communication mechanism that enables bacteria to sense and respond to changes in their cell density. It regulates a wide variety of biological functions, such as bioluminescence, virulence and nutrient foraging. There is tremendous physical and functional diversity in these QS systems, in terms of the genetic elements used, the biochemical and transport properties of signaling molecules, their target functions and the context in which QS-mediated functions are activated. Cutting across this diversity, however, is a simple and universally conserved signaling module that consists of signal synthesis, transport, degradation and detection as the fundamental biochemical parameters (Figure 1).
Figure 1
Sensing framework. (A) Type I: the extracellular signal concentration (Ae, red box) is sensed. (B) Type II: the intracellular concentration (Ai, red box) is sensed. Arrows represent reactions. Stippled arrows represent transport. (C) The steady-state signal concentration (A) decreases with Ve. The parameters of the lux system of V. fischeri are used to plot the curve (see Supplementary Text 2). At a sufficiently small Ve, A will exceed the threshold level K to elicit effector response. Inset: by definition, K is the signal concentration to induce an effector (brown line). Experimentally, a QS system often shows a graded response (blue curve) and K is determined as the half-activation signal concentration. (D) Sensing potential (
) as a function of basic physical and biochemical parameters of QS modules for Type I and Type II systems (see Materials and methods).
By exploiting its universality, we analyze the dynamics of the core QS module in terms of its fundamental parameters and develop a metric, sensing potential. The sensing potential quantifies the ability of a single bacterium to measure the volume of its microenvironment or, equivalently, that of an average bacterium in a population to measure the population density. Despite its simplicity, the metric faithfully accounts for the activation properties of diverse QS systems. In doing this analysis, we also present a comprehensive survey of the available quantitative information on the kinetics of QS systems studied. Importantly, although the metric is derived from the core module, it is generally applicable for any QS system, in which the dependence of sensing potential on basic biochemical parameters will be constrained by the specific configuration of the QS module.
We suggest that the sensing potential also provides a concise way to characterize the benefit of QS regulation. For instance, two QS systems can have the same sensing potential resulting from different parameters or regulatory mechanisms; but their phenotypic consequences would be the same for their respective host cells. To illustrate the application of sensing potential, we extend our analysis to study how and when QS regulation of a function benefits the host (Figure 4). Using the cost–benefit analysis of a typical QS-controlled function (exoenzyme production), we show that sensing potential uniquely determines the scenarios, in which QS regulation of bacterial functions becomes advantageous. We further define the general characteristics of functions that can be captured by the same analysis and follow the same conclusion.
Figure 4
Effector model and optimal sensor tuning. (A) A QS-mediated synthesis of a costly but beneficial exoenzyme for nutrient foraging. Subscripts i and e refer to concentrations inside the cell and in the enclosure, respectively. Enzyme synthesis under QS control is modeled as 
where Emax is maximal enzyme-synthesis rate. (B) Fitness increase (
f) due to effector activation controlled by QS sensors with distinct sensing potentials. Typical early (large ), intermediate and late (small ) inducing sensors are shown. (C) Collective fitness nT as a function . opt here marks the sensing potential for maximum nT. Colored circles mark nT values for corresponding fitness curves for the three sensors shown in B. Note that nT under QS regulation (finite positive ) is greater than with effector shut off (=0) and effector constitutively activated ( 
) showing QS regulation is advantageous. The following parameters were used for generating the figures: Cost–benefit: bn=1000, bnm=104 nM, cp=0.4, cpm=10-4 nM-1 hr. Effector: Dp=100 hr-1, dp=0.01 hr-1. Nutrient: Dn=100 hr-1, dn=0.01 hr-1. Reaction: kn=103 nM hr-1, Km=100 nM. Induction: Emax=103 nM hr-1. Growth: Constitutive rate g0=1 hr-1, fitness f (unitless) was scaled by m=0.01 hr-1 before adding to g0, n0=100, nm=109 cell per ml. T=15 h. See Materials and methods for modeling details. (D) Optimal QS characteristics (opt) for a general beneficial effector. nT calculated for one parameter set of the general benefit function is shown for the case, in which QS regulation is beneficial. Typical QS activation characteristics corresponding to cell density (early or late induction) are marked. nT from QS regulation is higher than with effector shutoff (nT at =0) or constitutive activation (nT at ) and is maximal at a unique finite opt. Inset: collective fitness curves for other parameter sets, in which QS proves advantageous. The opt for each curve is determined by the effector characteristics. Curves shown are from at least 100 combinations of the cost and benefit parameters bn (between 10–103) and cp (between 0.1–1). Similar results are generated when the other parameters, such as bnm, cpm, bnv, x, y are changed (data not shown). The following specific parameters were used to generate D: x, y=1, bn=200, bnm=1, bnv=10-3, cp=0.4 and cpm=10-4.
The analysis provides new insights into the functional design of QS systems. Further, the quantitative framework defined in this study serves as a foundation for analyzing dynamics and evolution of QS, as well as for engineering communication-based synthetic gene circuits.
Acknowledgements
This work was partially supported by the National Institutes of Health, a DuPont Young Investigator Award (to LY) and the David and Lucile Packard Foundation. We thank J Ozaki and D Tu for initial work on this project and G Truskey and M Kuehn for comments and discussions.
