Figure 4

Adaptation and Weber’s law implementation via intronic miRNA-mediated self-regulation. (A) Schematic view of adaptative behaviour for a step-like input. S and P are the sensitivity and precision measures described in the main text. (B) Schematic view of Weber’s law implementation for a two-step input function. E is the error in fold-change detection, as defined in the main text. (C) A summarizing heat-map of the iMSL performances in implementing adaptation and Weber’s law, as a function of the effective activation q/h _r and the repression strength 1/h. The grey region is the adaptive region (P > 10 and S > 2C V _p ), while the region where the system implements also Weber’s law (E < 0.1) is depicted with a color code representing the E value as reported in the legend. In the red zone the system is not sensitive enough to input variations (S < 2C V _p ). On the right, the target protein-level response to a two-step input is reported for the parameters values identified by the corresponding lower-case letters in the heat-map. The shaded regions correspond to the 2C V _p sensitivity threshold, showing that for a too strong repression the circuit response cannot produce a signal beyond the noise level (plots in the red rectangle). The parameter setting is the following: mRNA and protein half-lifes as in Figure2, miRNA half-life is τ _s = 8 hours, k _r = 2.12819s⁻¹, k _p = 0.048s⁻¹, the input function starts from an initial value of q₀ = 40 and makes two consecutive steps with fold-change F = 4.