Fig. 2

Deterministic and stochastic simulations of the MRN-NA model. a Deterministic simulation of the time evolution of the concentrations proteins y(1), y(2) and y(3) for different Hill coefficients. The input signal S is applied from simulation steps 250 to 500. The dissociation constants are set to K(2) = K(4) = 43; all other corresponding parameter values are set as the same as the previously published MRN [12] (Table 2). The simulated time evolution is shown for y(2) and y(3) at n = 7 (red and magenta lines), and at n = 8 (black and cyan lines). b The hysteresis curves of y(2) at different Hill coefficients n = 7 and n = 8 are consistent with the numerical integration of the rate equations. c The hysteresis curves of y(3) at different Hill coefficients n = 7 and n = 8 are consistent with the numerical integration of the rate equations. d Trajectories of the stochastic simulation of y(1), y(2) and y(3) at Hill coefficient n = 7. e Trajectories of the stochastic simulation of y(1), y(2) and y(3) at Hill coefficient n = 8. f, g Stochastic fluctuations in the MRN and MRN-NA models during the interval from simulation step 270 to 500, and F during the period from simulation steps 500 to 750. g The coefficients of variation (CVs) from the simulated stochastic trajectories during the signal period as a function of changing dissociation constants K(2) = K(4)at Hill coefficient n = 8. For more optimal comparability between the two models, the parameters associated to the negative autoregulation reactions were tuned to conserve the high steady state levels between both models. Shown are the CVs of y(2) (MRN: red line; MRN-NA: black line), and y(3) (MRN: magenta line; MRN-NA: cyan line)