Figure 2

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 $\tilde{\alpha }$ and $\tilde{\beta }$ with respect to that of $\tilde{D}$. Given a set of values ($\tilde{\alpha }$, $\tilde{\beta }$) the dynamics of the autoinducer shows different behaviors depending on the value of the diffusion parameter since the transitions lines are located at $\tilde{\alpha }$, $\tilde{\beta }$ = 1 + $\tilde{D}$. 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 ($\tilde{\alpha }$, $\tilde{\beta }$) 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 $\tilde{\alpha }$ (blue region). The low constitutive expression assumption is prescribed by the constraint $\tilde{\alpha }>2\tilde{\beta }$(red colored region).