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Open Access Highly Accessed Research article

Dynamics of the quorum sensing switch: stochastic and non-stationary effects

Marc Weber and Javier Buceta*

Author Affiliations

Computer Simulation and Modelling (Co.S.Mo.) Lab, Parc Científic de Barcelona, C/ Baldiri Reixac 4, 08028 Barcelona, Spain

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BMC Systems Biology 2013, 7:6  doi:10.1186/1752-0509-7-6

Published: 16 January 2013

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Additional file 1:

Text S1. Chemical equations for the deterministic model.

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Additional file 2:

Video S1. Movie of the stochastic simulation. Movie of the stochastic simulation for the lux02 operon, 10 h of induction at <a onClick="popup('http://www.biomedcentral.com/1752-0509/7/6/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/7/6/mathml/M3">View MathML</a>, burst size bR=bI=4. Cells are modelled as individual compartments containing a copy of the LuxR/LuxI regulatory network. The Gillespie algorithm (see text for details) is used to integrate the stochastic dynamics of the whole system of cells. Cell growth and division is explicitly taken into account as well as a certain degree of stochasticity in the cell cycle duration. Cells movement is purely aesthetic since we do not include any spatial effects in our model and consider a well-mixed environment. The number of cells (N=100) is maintained constant by removing one cell at random each time a cell divides.

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Additional file 3:

Figure S1. Intra and extracellular autoinducer as a function of exogeneous autoinducer concentration. Response curves to autoinducer induction for lux01 (A, C and E) and lux02 (B, D and E) operons. Total autoinducer concentration <a onClick="popup('http://www.biomedcentral.com/1752-0509/7/6/mathml/M17','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/7/6/mathml/M17">View MathML</a> in the external volume and in the cells (A and B), intracellular concentration cA(C and D), and extracellular concentration <a onClick="popup('http://www.biomedcentral.com/1752-0509/7/6/mathml/M18','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/7/6/mathml/M18">View MathML</a> (E and F), as a function of the exogenous autoinducer concentration, <a onClick="popup('http://www.biomedcentral.com/1752-0509/7/6/mathml/M19','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/7/6/mathml/M19">View MathML</a>, in the deterministic model. All graphs represent the steady-state response for increasing (blue curve) and decreasing (red curve) autoinducer concentrations. The exogeneous autoinducer concentration <a onClick="popup('http://www.biomedcentral.com/1752-0509/7/6/mathml/M20','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/7/6/mathml/M20">View MathML</a> controls the autoinducer concentration in the medium by means of an influx and an efflux (see main text). Upon activation of the operon, LuxR is produced at high levels, thus sequestering autoinducer molecules inside the cells. The bound form of autoinducer cannot diffuse out of the cell and is therefore not subjected to the influx and efflux. This explains why the total concentration of autoinducer in the system, <a onClick="popup('http://www.biomedcentral.com/1752-0509/7/6/mathml/M21','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/7/6/mathml/M21">View MathML</a> is slightly larger than <a onClick="popup('http://www.biomedcentral.com/1752-0509/7/6/mathml/M22','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/7/6/mathml/M22">View MathML</a>, when the operon is activated. For the same reason, the free form of autoinducer, both in the cell and in the medium, is slightly smaller.

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Additional file 4:

Figure S2. Cell response distribution during decreasing-concentration trajectories. Cell response distribution for decreasing-concentration trajectories for lux01 (left) and lux02 (right) strains in the stochastic model. Cells are initially induced at <a onClick="popup('http://www.biomedcentral.com/1752-0509/7/6/mathml/M45','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/7/6/mathml/M45">View MathML</a> for 2 hours. The concentration of exogenous autoinducer <a onClick="popup('http://www.biomedcentral.com/1752-0509/7/6/mathml/M46','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/7/6/mathml/M46">View MathML</a> is then hourly decreased in order to simulate the experiments (see [10]). The cell distribution reveals the variety of cell trajectories in comparison to the deterministic population average solution (green line). The cells jump to the high state for a wide range of times and autoinducer concentrations. Note also that fluctuations leads to a stabilization of the low state with respect to the deterministic solution.

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Additional file 5:

Figure S3. Trajectory of chemical species in individual cells. Trajectory of chemical species LuxR mRNA (mR), LuxR, LuxI, intracellular autoinducer (AI), regulatory complex (LuxR·AI)2(AL2) and promoter bound to complex (P10), in an individual cell for the following control parameter and burst size values: (A) <a onClick="popup('http://www.biomedcentral.com/1752-0509/7/6/mathml/M56','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/7/6/mathml/M56">View MathML</a>, (B) <a onClick="popup('http://www.biomedcentral.com/1752-0509/7/6/mathml/M57','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/7/6/mathml/M57">View MathML</a>, (C) <a onClick="popup('http://www.biomedcentral.com/1752-0509/7/6/mathml/M58','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/7/6/mathml/M58">View MathML</a>, (D) <a onClick="popup('http://www.biomedcentral.com/1752-0509/7/6/mathml/M59','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/7/6/mathml/M59">View MathML</a>.

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