= Solution
A fluorescent reporter associated with one phase of the <repressilator> should show repeated rises and falls in a tracked cell, with the same underlying oscillatory period but generally delayed and smoothed relative to instantaneous <promoter> activity. If mature <GFP> is fused to a repressor and is sufficiently fast to mature, <fluorescence> approximately tracks that <protein>'s abundance. If <GFP> is a separately expressed reporter, its own production, maturation, degradation and dilution introduce an additional filter.
For example, $\dot G=\beta_Gg(t)-\delta_GG$ converts a periodic gate $g(t)$ into a periodic, phase-lagged <concentration>. Very stable <GFP> can accumulate a large baseline and obscure oscillations rather than reproducing the regulator trace exactly; maturation delay and <photobleaching>[bleaching] also matter. Biological noise and cell-to-cell phase differences can make individual cycles irregular and wash out oscillations in a population average. The appropriate sketch is therefore a delayed, rounded oscillatory <fluorescence> trace, with amplitude and baseline depending on reporter turnover, rather than an unqualified copy of a Boolean gate.
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