Figure 3: Conditions for bistability and the emergence of relaxation oscillations.
From: Relaxation oscillations and hierarchy of feedbacks in MAPK signaling
With all negative feedbacks removed, the system exhibits either bistable switching or graded responses to EGF stimulation depending on parameter values. (A) Range of parameters governing positive feedback for which the system exhibits bistability (for some EGF concentrations higher than 0.1 pg/ml). The parameters are ratios of rate constants, which characterize the relative nucleotide exchange activity of SOS when the REM domain in SOS is not bound to RAS or bound to RAS-GDP compared to the activity when the REM domain is bound to RAS-GTP (k2C/k2A and k2B/k2A). We vary these ratios with k2A fixed at the value given in Supplementary Table S1. (B) Range of parameters governing saturation of RasGAP for which the system exhibits bistability (for some EGF concentrations higher than 0.1 pg/ml). The parameters considered in this diagram characterize RasGAP activity: the ratio of enzyme (RasGAPtot) to substrate (RAStot) and the rate constant for dissociation of the enzyme-product complex (u3). We vary the ratio RasGAPtot/RAStot by varying RasGAPtot while keeping the value of the product b3 × RasGAPtot constant. This product governs the rate of formation of the enzyme-substrate complex. For more information about parameters, see Supplementary Table S1. In both panels, a solid dot marks the location in parameter space that corresponds to the values of parameters given in Supplementary Table S1. In panel B, an open dot marks the location in parameter space that corresponds to the values of parameters in the model of Stites et al. (Ref. 34). (C) Bifurcation diagram showing the active ERK fraction vs. the level of EGFRa–SOSu complexes in the system without all three negative feedbacks. Solid lines show two stable steady states; dashed line shows unstable steady state. (D) Analysis of the system with the negative feedback from ERK to SOS present and other two negative feedbacks absent. Parametric plot shows a projection of the limit cycle on the (active ERK fraction)—(EGFRa–SOSu complexes) plane.
