Fig. 3
Behavior of the combined FF/FB system. a The addition of W to the network motif results in a negative feedback loop involving Z and W. b Illustration of the mechanism of negative feedback. Z activates W and is repressed by W. Illustration of Y not shown (see Fig. 1b). c Dynamics of the output, z(t), upon a step-increase in x from 1 to 10 at time t = 0 for the combined FF/FB system. Blue curve: perfect adaptation. Red and yellow curves: near-perfect adaptation, such that |f| = 0.05. d Normalized output of z(t). When the curves are normalized, it is clear that the red and yellow curves are tuned for near-perfect adaptation. The value of C needed to achieve NPA is more distant from CPA than for the FF only system. e Heatmap of the normalized range of C values under which NPA is achieved. Black curves delimiting Regions I and II are analogous to those described in Fig. 2. In the biologically realistic region (defined for the FF/FB system), the range of C values under which NPA can be achieved ranges from 25 to 100% of CPA. f Heatmap of the ratio of ranges of C values for which NPA is achieved for the FF/FB system vs the FF only system. The addition of a FB loop increases the range of values of C by 21--54%