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First, we use AHL for input and regard injection of AHL as clicking.                     LuxR is generated constitutive.                     Injecting AHL to Double Click Bacteria brings dimer of AHL and luxR.                     We take lux promoter repressed by the dimer.                     As the dimer represses Plux,                     transcription of proteins under the Plux is stopped.                     So in our project,                     CLICK controls transcription of overall DNA sequence.

Second,there is a cI promoter above gfp DNA sequence.                     cI works as repressor.                     You can see cI DNA sequence is under lux promoter.                     As AHL come into Double Click Bacteria, generation of cI is stopped.                     Therefore, repressor of cI promoter disappears.                     (Because the cause of repress(cI) which is kind of protein will be decomposed.)                     If there isn't cI, bacteria shine with gfp.                     We can say cI recognizes the existence of input in this DNA sequence.

                        Third, there is AND Gate with T7ptag and supD.
                        As you know, T7ptag becomes T7 polymerase in case of existing supD.
                        T7 polymerase is translated to T7 protein and T7 works as activator of T7 promoter.
                        There is a T7 promoter above gfp DNA sequence.
                        If T7 have been generated once,
                        the T7 promoter starts translating and we can see bacteria shine with gfp.
                        On initial state(there isn't any click), bacteria don't have supD.
                        So there isn't any T7 polymerase and gfp cannot be genernated, in spite of being T7ptag in bacteria.
                        T7ptag which is a kind of mRNA is decomposed so fast.
                        However supD under lacI promoter is generated late.
                        Because, transcription of supD starts working after most of lacI are decomposed.
                        After 1st click, supD exist.(supD is a kind of tRNA which is stable.)
                        There isn't input anymore, promoter above T7ptag DNA sequence starts activating.
                        As a result of reacting T7ptag and supD, the AND Gate is going to be available.
                        In this case, the AND Gate remembers that there was a click.
                        Moreover,

                        Actually, there is a hybrid promoter(cI/T7) above gfp DNA sequence.
                        T7 works as activator and cI works as repressor to the promoter.