Fraction of bound proteins (Poisson initial state). A dose-response curve (the fraction of the bound proteins φ plotted as a function of a) for a Poisson-like ensemble: = ⟨L0⟩2 + ⟨L0⟩ and = ⟨P0⟩2 + ⟨P0⟩. Each curve is obtained by varying ⟨L0⟩ for a fixed value of ⟨P0⟩. The thickest full line is the reference Hill curve φ
(a), plotted with K = 1, depicting the mean field limit. The shape of the curve does not depend on the values of the ensemble parameters ⟨L0⟩ and ⟨P0⟩. The thin curves are fluctuation-corrected dose-response graphs obtained using the PARNES method. The full line was obtained with ⟨P0⟩ = 1, the dashed line with ⟨P0⟩ = 2, and the dotted line with ⟨P0⟩ = 4. The curves that account for noise (thinner curves) approach the reference mean field curve from below for large values of ⟨P0⟩ but are distinct otherwise.