Figure 2.

Removing coupling with unsaturatable phosphatases. (A) The fold increase in S₁ phosphorylation as a function of the K_M,P of the shared phosphatase for both substrates in a 2-Kinase/1-Phosphatase loop. (B) The fraction S₁^∗ as a function of r₁ at r₂ = 0 (black) and r₂ = 2 (red) when K_M,P = 10x[S]₀. Note that there is very little difference between these curves. (C) The normalized fraction of phosphorylated substrate S₁^∗ as a function of time after the removal of input signal. In these simulations, the concentration of S₂ and K₂ are 0. The systems were allowed to run to steady state at high K₁ activity (r₁ = 2); at t = 0, the activity of the kinase was set to 0 (i.e., r₁ = 0). The y axes were normalized by y₁ = (y – min_y) / (max_y – min_y), where min_y is the fraction S₁^∗ at r₁ = 0 and max_y is the fraction S₁^∗ at r₁ = 2 at steady state. (D) The half-life of S₁ phosphorylation as a function of K_M,P with two total concentrations of P (10 nM, green, and 1 μM, purple). Note that the black, red, and blue dots are shown to illustrate the relationship between (D) and (C). The dashed orange line shows the linear approximation of t_1/2 for highly unsaturated phosphatases (t_1/2 = K_M,P/k_cat,P[P]₀). To see this figure in color, go online.