Figure 5
Multi-dimensional dynamical analysis of the mixed-feedback, 3-layer MAPK cascade.
(a) Schematic diagram of the mixed feedback cascade. (b) Three types of dynamics can occur in the system: oscillations, bistable fixed-points, or bistability with mixed oscillatory and fixed-point steady state. Here, the system is initialised differently by random initialisation of the concentrations of pS1, pS2 and pS3 given that the total S1, S2 and S3 levels are fixed. Parameter values used for oscillation S1t = 100, S2t = 100, S3t = 100, k1 = 0.1, k2 = 0.01, k3 = 0.01, k4 = 0.01, k5 = 0.01, k6 = 0.01, n1 = 10, K1 = 1, n2 = 15, K2 = 8, α = 10; for bistable fixed point: S1t = 0.22, S2t = 10, S3t = 53, k1 = 0.0012, k2 = 0.006, k3 = 0.049, k4 = 0.084, k5 = 0.043, k6 = 0.066, n1 = 5, K1 = 9.5, n2 = 10, K2 = 15, α = 95 ; and for mixed bistability: S1t = 20, S2t = 50, S3t = 30, k1 = 0.001, k2 = 0.08, k3 = 0.001, k4 = 0.08, k5 = 0.001, k6 = 0.05, n1 = 10, K1 = 0.66, n2 = 5, K2 = 0.8, α = 96. (c–e) Multi-dimensional bifurcation analysis of the cascade for: (c) the species abundances and feedback strength (d) the species abundances, the rate constants and feedback strength and (e) all parameters. The yellow boxes are for highlighting purpose. Bistable (BS) and oscillation (OS) sets are indicated in red and green, respectively.
