Part a: Δ-vs-Σ trajectories upon decreasing contribution of the non-specific background. The width of the curve, β, defines the logarithm of the binding strength of non-specific hybridization in the absence of specific transcripts (Eq. (12)). Part b shows two trajectories of different height. The PM/MM-gain parameter s defines the height in the absence of saturation. The narrowing of the trajectories decreases the maximum (see Eq. (13)).