Figure 1.
Quorum-Sensing Network of an Octopine-Type Agrobacterium Ti Plasmid
Blue ellipses represent proteins, red rectangles indicate mRNA species, and green flattened circles denote metabolites. Open circle arrowheads represent enzymatic activation of a reaction or transport, and open triangle arrowheads denote translation. Essential bimolecular reactions are shown explicitly as open squares. S represents two substrates of the autoinducer synthetase TraI, and Ø denotes protein degradation.
Figure 2.
Nullclines of the Reduced Quorum-Sensing Model at Several Extracellular Concentrations of AAI
Nullclines represent lines on which the respective variable does not change with time (e.g., d[traRd]/dt = 0 on the TraRd nullcline), and their intersections correspond to the stationary states of the model. The TraRd nullcline is shown as a solid black line and the Ai nullcline at three values of Ae—(a) 35 nM, (b) 67 nM, and (c) 142 nM—is shown in color. Positions of stable stationary states are marked by filled circles for the off network state and by filled boxes for the on state. The open circle indicates the unstable steady state of a saddle type.
Figure 3.
Dependence of the Critical Extracellular Concentration of Autoinducer on the Autoinducer–Transporter Dissociation Coefficient
= k5/k4 Predicted by the Intracellular Model
The solid line is fitted to the computed data points indicated by the filled squares. The value of = 0.592 nM used throughout the simulations reported in this paper is shown as an empty square.
Figure 4.
Transition to Quorum Sensing in the Stochastic Model of Intracellular Dynamics
TraRd concentration averaged over 6 × 106 s (filled squares) is plotted against extracellular concentration of AAI. The prediction of the deterministic model is shown as a solid line for comparison.
Figure 5.
Transition of a Model Bacterial Population to Quorum Sensing in a Homogeneous Liquid Medium
Intracellular concentrations of TraRd (thick red line) and TraM (thin blue line, filled circles) are plotted against the population density that exponentially grows with time.
(A) Dynamics of an individual cell in the stochastic population model.
(B) Dynamics of the stochastic population model averaged over ten bacteria.
(C) Behavior of the deterministic population model.
Figure 6.
Critical Extracellular Concentration of Autoinducer Depends on the Growth Rate of a Bacterial Population
The difference between the actual critical concentration Aec computed using the deterministic population model and the value predicted by the intracellular model Aec,∞ is plotted against the duration of cell cycle Tc (filled circles). As shown by the linear fit (solid line), Aec approaches Aec,∞ according to the power law Aec − Aec,∞∝T − 0.61c.
Figure 7.
Transition to Quorum Sensing in a Model Bacterial Population Growing as an Attached Biofilm
(A) Spatial gradient of autoinducer created by the biofilm after 7 h of growth at two different values of AAI diffusion coefficient: (a) 10−5 cm2/s and (b) 10−6 cm2/s. The x-axis is perpendicular to the plane of the biofilm, which is positioned at x = 0.
(B) Intracellular copy numbers of TraRd and TraM averaged over 20 randomly selected bacteria versus the population density for the slower diffusion of AAI.
Table 1.
Model Variables and Equations
Figure 8.
Extracellular Concentration of AAI in the Culture of the TraM-Defective Mutant Strain K588 versus Time in the Exponential Growth Phase
The model (solid line) is fitted to the experimental data (filled squares). All parameters are as in Table S1, except k11, which is set to zero to model the inability of mutated TraM to sequester TraRd.