Figure 3: Propagation of fluctuations.
From: Delay-induced anomalous fluctuations in intracellular regulation
The panel (a) illustrates the auto-regulation of X and X's regulation of Y. The auto-regulation is repressive and has the same properties as in Figure 2b, with feedback gain φ=0.75 and n=1,000 synthesis steps. The negative regulation of Y is modelled using a Hill function F(X)=k/(1+(X/K)2). In (b), we plot the mean number of X molecules (orange line) and its deviation (shaded area). The red circle shows the mean number of Y molecules, which is achieved using K=〈X〉/50, the maximal rate k=α (equal maximum rate of X). The decay rate constant of Y is 0.001. (c) Sensitivity amplification (ΔY/Y)/(ΔX/X) when perturbing the maximal rate of X molecules by 5%. From top to bottom, K=〈X〉/5, 〈X〉/25 and 〈X〉/50, with all other parameters as in (b). The dashed line is the large-molecule limit amplification, where 〈F(X)〉=F(〈X〉), calculated for a 5% perturbation, which is approaching −2 (the Hill coefficient) when the perturbation becomes infinitesimally small.
