Fig. 5.

LMA for the toggle switch and for a feedback loop with nonlinear protein degradation. a (upper panel) Illustrates a toggle switch (with two active and two inactive promoters), whereby two proteins P and M are expressed and mutually repress each other. (lower panel) illustrates how the toggle switch system is decoupled by the LMA into two independent linear networks. b Shows the LMA predictions for time-evolution of the marginal distributions of the two proteins, P and M, in the toggle switch for three different time points. The parameters are: ρ₁ = 60, ρ₂ = 25, ρ₃ = 45, ρ₄ = 30, σ₁ = σ₃ = 0.004, σ₂ = σ₄ = 0.25 and k = 1. c Shows the feedback loop with nonlinear protein degradation via an effective Michaelis–Menten reaction. d Shows the LMA predictions for steady-state protein distributions of the system shown in c for three different values of the Michaelin–Menten constant K. The other parameters are: ρ_u = 3, ρ_b = 0, σ_b = 4 × 10⁻⁴, σ_u = 0.25 and k_d = 20