Skip to main content
Fig. 2 | Journal of Biological Engineering

Fig. 2

From: The engineering principles of combining a transcriptional incoherent feedforward loop with negative feedback

Fig. 2

Tuning the I1-FFL for near perfect adaptation. a Dynamics of the output, z(t), upon a step-increase in x from 1 to 10 at time t = 0. Blue curve: perfect adaptation. Red and yellow curves: near-perfect adaptation, such that |f| = 0.05. b Normalized output of z(t). When the curves are normalized, it is clear that the red and yellow curves achieve near-perfect adaptation. c Heatmap of the value of C required for perfect adaptation given K1, K2, for a step increase in x from 1 to 10. Red curves (here and elsewhere) represent contours whose values are indicated directly on plot. Note that axis limits for K1 range from strong (10− 2) to very weak (106) affinity, while those for K2 range from very strong (10− 6) to weak (102). d Heatmap of peak metric, P. As K1 becomes too low, this metric drops to unacceptably low values. e Absolute levels of the peak in output. Orange curves: P = 0.1 and CPA = 0.01. These curves, together with the zpeak = 0.01 contour, delimit a biologically realistic region of the parameter space. f Heatmap of the normalized range of C values under which NPA is achieved. Black curves delimit two regions in which NPA is achievable with any value of C. In Region I, Y and Z are decoupled, and change only slightly upon increase in X. Region II is described in [12] as a FCD region, which requires NPA. In the biologically realistic region of the parameter space, the values of C under which NPA can be achieved ranges from 13 to 65% of CPA

Back to article page