These two pictures are drawn with the same parameters coming from related literature. Both figures point out that the output signal (GFP, yellow line) will form a pulse immediately after the input signal alters.
Figure 1: This figure shows the concentration variation of chemical molecules when the input signal is at positive edge when t=0.
Figure 2: This figure shows the concentration variation of chemical molecules when the input signal is at negative edge when t=0.
Figure 3: This graph shows the variation of AHL, cI, LuxR and GFP responding to the addition of input
signal(IPTG). It is easy to find that the level of AHL and cI shares the same changing tendency
with that of IPTG, whereas the contents of LuxR protein changes inversely with that of IPTG.
Therefore, the output signal (GFP) only exists at the edge of IPTG curves where the input signal
switches from 1 to 0 or from 0 to 1.