Probability densities of the signaling molecule and parameter space. Panel A: Schematic representation of the different probability densities of the autoinducer concentration depending on the value of and with respect to that of . Given a set of values (, ) the dynamics of the autoinducer shows different behaviors depending on the value of the diffusion parameter since the transitions lines are located at , = 1 + . The constraints of our modelling in terms of the parameters values make the region on the top-left corner non-accessible (see text). Panel B: Parameter space diagram (, ) indicating the sets of parameters used in the simulations (solid squares): γ1 = (8, 2), γ2 = (15, 5), γ3 = (8, 0.5), γ4 = (15, 0.5). The experimental values reported for the degradation rate of the mRNA leads to a biological meaningful range for (blue region). The low constitutive expression assumption is prescribed by the constraint (red colored region).