Signal S drives synthesis of both a response element R and a second species X. X in turn accelerates degradation of R. Because the steady state of R depends only on the rate constants — not on S — the system's steady-state response is independent of signal strength, even though R responds transiently to every change in S. Adjust the signal and rate constants below and watch the concentration-vs-time curves update.
Reaction network: S → R (rate k1S), R → ∅ (rate k2RX), S → X (rate k3S), X → ∅ (rate k4X)
Drag across the plot to inspect values at a given time.
Notice that R returns to the same steady-state value after each step increase in S — R's transient peak height grows with each step, but its resting value does not. This is the defining signature of perfect adaptation.
This ModelBrick describes a simple linear response element supplemented with a second signaling pathway (through species X), creating a response mechanism that exhibits perfect adaptation to the signal. Although the pathway shows a transient response to changes in signal strength, its steady-state response is independent of the signal strength (S). Originally built and simulated in VCell and exported as SBML.