Fig. 3.

Scaling of the optimal capacity with “ITR noise” parameters y_max and 1/F . The optimal capacity ${\text{log}}_2\tilde{Z}$ for different fixed values of the mRNA number M in the ITR model is plotted against “ITR noise” parameters properly rescaled by M, to observe the compensation between translational noise components and the input noise. (a) For the diffusion noise due to the intermediary protein y, the relevant parameter is M × y_max, where y_max is the maximal concentration of y. (b) For the shot noise due to the expression of intermediary mRNA and protein y, the relevant parameter is M × (1/F), where 1/F is the inverse Fano factor. In both cases, we set the remaining noise sources to be as small as possible: C = 1000 and F = 1 for (a), C = 1000 and y_max = 1000 for (b). A perfect collapse in (a), comparable to that in (b), could only be achieved for Fano factors F ≪ 1, which are biologically unrealistic.