Phase plane visualization (A) and time series (B) of a toxin excitation.

A: Phase plane visualization of the simplified 2D system (3) (red) and the 4D ODE system (2) (blue, dashed). The vectors represent the direction of the flow in each point. NC(x) and NC(y) correspond to the nullclines of the system (2), whereby the excitability threshold is marked by the dashed line. The equilibrium is determined by the cross-section of the nullclines. For toxin levels higher than x = κ the mRNA cleavage is switched on. B: The same trajectories are shown as a time course, together with the analytic estimate (6) of the excitation. We define the excitation time as the time that the toxin level is higher than the threshold for the mRNA cleavage, κ. (δa = 1.5, ε = 0.074.).