Synthetic gene circuits wire natural regulatory parts into new logic. Both circuits here use Hill-function repression:
dm_i/dt = -m_i + α/(1 + p_j^n) + α0
dp_i/dt = -β·(p_i - m_i)
The repressilator (Elowitz & Leibler, 2000) wires three repressors in a ring — A represses B, B represses C, C represses A — producing sustained oscillation with no external clock. The toggle switch (Gardner, Cantor & Collins, 2000) has two genes mutually repressing each other, giving two stable states: a "pulse" of one gene flips the whole circuit and it stays flipped, a synthetic biological memory bit.
- Circuit toggle — switches the wiring between the 3-gene oscillator and the 2-gene bistable switch.
- Repression strength (Hill n) — steeper repressor response makes oscillations/switching sharper and more digital-like.
- Protein degradation — faster degradation shortens the repressilator's oscillation period.
- Leaky expression — baseline transcription even when repressed; too much leakiness prevents genes from fully turning off.
- Pulse buttons (toggle mode) — inject a transient burst of one gene's protein to flip the switch, like a real synthetic-biology "set/reset" signal.
These two circuits are foundational building blocks of synthetic biology — used as engineered timers, biosensors that report a stable "yes/no" once triggered, and components of programmable cell therapies.