Figure 1.

Retroactivity effects lead to signal distortion, and attenuation of output signals when additional targets are added. Comparison of retroactivity effects on a signaling system with a direct coupling (DC) architecture (left) and one with an insulator, represented by a phosphorylation-dephosphorylation cycle (right). (A) Cartoon schematic of the signaling system. In the DC system (Eq. 1), the input binds directly to the target. With an insulator (Eq. 9), the input drives phosphorylation of an intermediate signaling molecule, whose phosphorylated form binds to the target. (B) Illustration of distortion. The ideal output signal (dashed, and see Eq. 3 in text) with retroactivity effects neglected, is plotted against the output for each system with nonlinear dynamics (solid), given by Eq. 2 for the DC system and Eq. 10 for the insulator. (C) Illustration of competition effect. The output signal in a system with a single target (solid) is compared with the output signal when multiple targets are present (dashed). Note the greatly reduced amplitude of variation of the output in the DC system. Plots of the output signals in each system are shown in the steady state, over a single period of k(t). This plot was made using the parameters k(t) = 0.01(1 + sin(0.005t)); δ = 0.01; α₁ = β₁ = 0.01; α₂ = β₂ = k₁ = k₂ = 10; k_on = k_off = 10; p_tot = 100; and X_tot = 800, Y_tot = 800 for the insulator. Parameters specifying the interaction with the new promoter p^′ in the perturbed system are k^′_on = k^′_off = 10, and p^′_tot = 60.