Mean first passage time of cell activation for different burst size values. Mean first passage time of cell activation as a function of autoinducer concentration for different values of the burst size for LuxR (bR) and LuxI (bI) and for the deterministic solution: (A) low to high transition MFPT in the lux01 operon, (B) low to high transition MFPT in the lux02 operon. The lower (upper) limit of the shaded regions is the 10% (90%) quantile curve of the distribution of FPT for the cases bR=bI=20 (blue shaded region) and bR=bI=0.01 (green shaded region). The MFPT reveals a non-trivial behaviour: for low autoinducer concentration noise helps cells to jump quicker to the high state, while for high autoinducer concentration noise slows down the cells activation (see text). Intersections of the quantile 10% and quantile 90% curves with a horizontal line at t=10h indicate the autoinducer concentration for which 10% of cell trajectories have jumped to the high state (left arrow) and the concentration for which 90% of cell trajectories have been activated (right arrow). The precision after 10h of induction (inversely proportional to the width of the region delimited by the arrows), increases when decreasing the noise in LuxR (see text). Note that in the case of the lux01 operon, we only change the value of bRsince GFP does not contribute to the activation process.
Weber and Buceta BMC Systems Biology 2013 7:6 doi:10.1186/1752-0509-7-6