Fig 2. The core σ^B circuit is capable of generating both response behaviours.

(A,B) For various noise amplitudes (η), the CLE adaptation of the Narula model is exposed to a stress step (at t = 0, red dashed line). (A) Mean [σ^B] in response to the input (average over n = 150 simulations). The amplitude of the single response pulse increases with noise. (B) For each value of η, four different simulations are shown. There is little variation between the individual trajectories. (C,D) Illustration of our measures for the degree with which the system exhibits the single response pulse (C) and stochastic pulsing (D) behaviours. A simulation is divided into a transient phase (t ∈ [0.0, 5.0]) and an asymptotic phase (t ∈ [5.0, 200.0], but we note that in this figure the x-axis is cut to t = 50 to better display both phases). Next, we find the maximum activity in the transient phase, the maximum activity in the asymptotic phase, and the mean activity in the asymptotic phase. The single response pulse measure (C) is defined as the maximum transient activity (orange line) divided by the maximum asymptotic activity (magenta line). The stochastic pulsing measure (D) is defined as the maximum asymptotic activity (orange line) divided by the mean asymptotic activity (magenta line). In practice, a mean measure over several (n > 50) simulations is always used. (E,F) The parameters η (noise amplitude) and k_K2 (a proxy for the system’s proneness to oscillations) are varied. For each parameter combination, the maximum magnitude of the single response pulse (E) and stochastic pulsing (F) behaviours that can be achieved by varying the parameter p_stress (20.0 μM< p_stress < 200.0 μM) is found and plotted. (G) The single response pulse behaviour is maximised at (k_K2, η) = (15.0hr⁻¹, 0.04). For these values, four simulations are shown. (H) The stochastic pulsing behaviour is maximised at (k_K2, η) = (9.0hr⁻¹, 0.06). For these values, four simulations are shown. (G,H) These simulations demonstrate that the CRN of the Narula model can generate both behaviours while exposed to intrinsic noise only. (I,J) It is possible to recreate both response behaviours, single pulse response (I) and stochastic pulsing (J), using the Gillespie algorithm. This demonstrates that the responses are not dependent on the modelling approach used. Parameter values and other details on simulation conditions for this figure are described in S1–S3 Tables.