Figure 6.

Shifting in a gene expression model. (A.i) Diagram for transcription factor-mediated gene expression. X is the transcription factor; a filled rectangle represents gene y; the arrow pointing at the rectangle is the promoter region; α and β are the binding and unbinding rates of X to the promoter, θ and ω are the activation and deactivation rates of the promoter, γ and δ are the production and degradation + dilution rates for protein Y. (A.ii) Reaction scheme of the model. (A.iii) Output Y vs time for different inputs. (A.iv) Output Y vs input X (concentration of the transcription factor) for different times. For A.iii and A.iv Y has been normalized to its maximum (γ P_T/δ). Filled circles over the curves mark the EC₅₀. Here all kinetic rates are equal to 1 and the activation time of X has a τ_n = 10. (A.v) EC₅₀ vs. time for the curves in (A.iv). Maximal EC₅₀ (ME) is indicated with a horizontal dotted line in (A.iv), the Time window (TW) with a horizontal line in (A.v) The color scale indicates the time. (A.vi) Time window (TW) vs. Maximal EC₅₀ (ME) for 200 randomly selected parameter sets out of the 10⁴ total scanned (ρ = 0.8562, using all parameter sets) (see Supplementary Information for a description of the scanning procedure). (B–K) Each plot shows ME for 150 × 150 values of the indicated parameters (see TW in Fig. S2). In each panel, the rest of the parameters were equal to 1.